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July 29, 2022, 9:40 p.m.
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March 19, 2023, 6:22 p.m.
LoveSquirtle

Found a lot of squirtles out here today! <3

Sept. 29, 2023, 1:46 p.m.
Anny

123213

May 25, 2022, 4:30 a.m.
beans

the reason this site has no users is that its quarantining for covid

March 19, 2023, 6:17 p.m.
FEET

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June 26, 2022, 7:27 p.m.
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⣠⣤⣤⣤⣤⣤⣄⡠⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠳⠤⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⠀⠀⢀⢖⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⢸⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⣴⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀ ⠀⠀⣾⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠿⠿⠿⠿⠿⣧⣄⡈⠛⠛⠛⣛⣛⣳⣶⣶⣦⣄⡀⠀⠀⠀⠀⡎⠀⠀ ⠀⠘⡿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣠⠤⠤⣤⣖⡺⢟⣩⠥⢒⡊⠭⠭⠝⢑⣒⠲⠤⢭⢖⣪⠭⠜⠓⢒⣒⠒⠒⢒⣛⢷⣄⠀⢀⡇⠀⠀ ⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣠⠞⠉⢀⣤⣿⡭⠷⡺⠚⠉⢩⣾⣩⡿⠻⣦⡀⠀⠀⠀⠁⠲⡠⠒⠁⠀⣴⣈⡿⠷⣦⠀⠈⠈⠙⠻⣄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡭⠟⠉⠁⠀⠀⠘⠓⠒⠲⡉⠀⠀⠀⢸⣿⣬⣷⣶⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣧⣿⣶⣿⠇⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠈⠓⣿⠶⠟⠁⠀⠀⠀⠀⠀⠘⠛⠂⠀⠈⠑⠠⢀⠈⢛⣿⣿⠛⠋⣀⡀⣀⠠⠐⠂⠀⢀⣀⠀⠙⠻⠿⢿⣍⡀⠤⠤⠒⢊⡍⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣤⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⣀⡤⡎⠀⠀⠀ ⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠶⠦⢤⣤⣀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⣇⣀⣀⣤⢶⠛⠁⢀⡏⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠐⠦⣤⣤⣀⣈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⢀⣀⣠⣤⠴⢻⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣄⣉⠉⠛⠛⠛⠻⠻⣿⣿⣿⠿⠿⠿⠛⠛⠋⠉⠁⣀⣴⠏⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉⡘⠀⠀⠀⠀⠀ ⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀ ⢸⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⠒⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀⣀⣀⠴⠚⠉⠀⢸⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠀⠈⠑⡤⠒⠒⢢⠖⣉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠩⠇⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠜⠒⠤⠀⠐⠒⠤⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄

May 9, 2022, 4:08 p.m.
AmberlynnWEED

I have lost everything, and I'm not sure how to continue. This summer I invested $17,500 (six months salary and my entire life savings) into ornamental gourd futures, hoping to capitalize on this lucrative emerging industry. After watching a video about Vincent Kosuga and his monopoly on onions, I decided I'd try to do something similar with another vegetable. I did some research and found out many agricultural forecasters expected this year's gourd yield would be far smaller than the past, due to deteriorating soil conditions in central Mexico and a warmer-than-average spring. At first, demand soared around Halloween and prices skyrocketed, but the gourd bubble burst on November 12th. Unfortunately, the coronavirus caused a massive drop-off in demand due to fewer families decorating their tables for thanksgiving, and prices plummeted. I had invested early enough that I thought I would still be fine, but then on the morning of December 2nd, a new email in my inbox caused my stomach to turn into a pretzel. The massive gourd shipment from Argentina, scheduled for early March, had arrived. I was planning on selling off my futures right before this, in February, but this ruined everything. To top it off, the gourds in this shipment were absolutely gargantuan, some topping 4 pounds each, causing the price-per-pound to drop like an anchor into the range of 6 cents per pound. I am ruined.

Dec. 24, 2024, 8:03 a.m.
FrishayUk

Stylish and practical, our Women's Leather Crossbody Shoulder Bags combine timeless elegance with everyday functionality. Crafted from premium leather, these bags offer comfort and durability while keeping your essentials organized and easily accessible. Perfect for any occasion, they add a touch of sophistication to your look. Visit: https://frishay.uk E-mail: [email protected]

Aug. 12, 2016, 2:23 a.m.
higaisha

Broke my never-leave-the-house streak of a couple good months trying to find an Eevee that was in the sighted section. It disappeared. Paras appeared under sightings as I was walking back home. What is the truth.

Aug. 15, 2016, 7:05 a.m.
OnlyNi17

Just finished updating my profile :)

Dec. 17, 2016, 7:30 p.m.
Pasteluma

I redownloaded the game just so I could use this. I also made a new account because wynaut :P I'd love to walk around and catch mons but it kinda just snowed s o

May 9, 2022, 4:07 p.m.
AmberlynnWEED

stroll into my local GameStop looking to pick up a copy of Binding of Isaac grab the game and take it to the charming maiden at the register "Pardon me, milady...but could you ring me up? A shame I don't have your number or I'd ring you up instead..." she giggles and takes the game, blushing as her fingers brush mine due to my fingerless gloves her eyes widen as she reads the game's title "Wow, I've never seen anyone buy this before! You must have special taste!" I smile and ready a witty response when suddenly a voice rings out from behind "Hahaha look at what this ♥♥♥♥♥♥ is buying! That's not Call of Duty Advanced Memefare! What a piece of ♥♥♥♥!" I quickly turn around, my cloak billowing behind me, to discern the source of the rude outburst generic dudebro caricature with a sports team cap and "the guy that beat you up that one time behind the school in early October" shirt is standing there guffawing "Excuse me sir...you may disparage my person if you wish, but it is untoward to swear in front of a lady." "♥♥♥♥ you ♥♥♥♥♥♥!" I smile quietly and tip my fedora low across my eyes, concealing them "As you wish..." I quickly swing my cane into his kneecap before he can react he bellows and charges forward I expertly sidestep him and the cashier screams as he crashes into the counter I draw my sword-cane and mutter a quiet oath as I drive it deep into his back "...requiescat in pace..." As I clean my blade the girl walks out from behind the counter, twirling her hair with her fingers "So...maybe you'd like to come over to my place to play that game sometime...? "No thanks, milady, it's only single player. Besides..." I sheath my sword "You're not my type." skate away on my Heelys