ShowTheHentai
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢠⣾⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⣠⣴⠶⠾⠿⠿⠿⢷⣄⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣋⢀⡤⠞⢓⣒⡬⣕⢄⢰⠀⠀⢀⢀⡤⠚⣩⣭⡙⣦⡤⠆⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠉⠯⠢⢿⣿⠿⢻⠘⡎⠀⠰⠈⢟⠠⠼⠛⠛⠋⣡⢌⡀⠀⣿⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢐⠂⠐⠦⠤⠴⠚⣹⠠⠁⠀⡌⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠆⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠁⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⡆⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢊⢺⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠄⢰⡁⢠⠃⠀⠀⠀⠀⠀⢠⠇⠈⠐⠤⣀⠀⠀⡌⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⢠⠊⠀⠀⠀⠉⢹⠀⠀⠀⠀⡰⠉⠁⠀⠀⠀⣀⣀⢱⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡀⠉⢻⣷⢢⢤⣑⠒⠒⠒⢁⣀⣤⢶⢺⢻⡟⠁⠸⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡄⠀⢻⣸⢸⠈⡏⠉⡏⠁⡇⠸⢸⣸⡟⠀⢀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠰⡀⠈⣿⣿⣤⣇⣀⣇⣀⣧⣶⣾⡿⠁⠀⡌⣔⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣣⠀⠘⠿⣧⣽⣹⣻⣟⣏⠿⠋⠀⠀⡸⢰⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢠⠎⠹⡄⠀⠀⠐⠪⠭⠭⠍⠀⠀⠀⠀⠀⢠⠏⠀⠙⣌⣑⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⠀⠀⠀⡏⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⠀⠀⠀⢷⠀⠉⠐⠠⠌⡓⢄⡀⠀⠀⠀⠀ ⠀⢀⡠⠔⠒⠈⡩⠭⠉⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠁⠪⢓⠤⣀⠀ ⠋⠁⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠭
