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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿ ⣿⡇⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⢸⣿ ⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿ ⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿ ⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿ ⣿⡇⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⠆⢸⣿ ⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿ ⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿ ⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿ ⣿⡇⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⢸⣿ ⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀ ⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⡇⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀ ⠀⢸⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣹⡇⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀ ⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⡇⠀ ⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠛⠛⠛⠶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠋⢁⣠⣴⣶⣶⣶⣬⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠉⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠁⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀ ⠀⠀⠀⠀⢀⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀ ⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀ ⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⢿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠛⢉⣠⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⡄⠐⢦⣤⣤⣴⣾⠿⠛⣁⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⢦⣄⣀⠉⣉⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡴⠛⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠬⣷⠄⠀⠀⠀⠀⢰⣆⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠐⢿⣬⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⢠⣤⡀⠀⠙⣆⠀⠀⠀⠀⠙⠀⠀⠀⠀ ⠀⠀⣸⡄⠀⠀⠀⢀⡏⠀⠀⣀⡀⠀⠀⠀⠛⠀⠀⠈⣯⠀⠀⢞⣛⣯⡉⠀⠀⠀⣸⢦⣄⡀ ⠀⠺⢿⡿⠛⠀⠀⢸⡇⠀⡀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⢉⡏⠁⠀⠈⠛⡾⠋⠀ ⠀⢀⠈⠁⠀⠀⢀⣹⡷⣶⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⢦⡄⠀⠰⠋⣹⡷⠛⠁⠀⠀⠀⠀⠀⣠⣤⡤⠤⣄⠀⠀⠀⠸⣧⡀⠀⣴⠛⣦⠀⠀⠀ ⠈⠻⠟⠁⠀⠀⠘⠋⠻⢶⣤⣀⠀⠀⠀⠾⠡⠸⣇⠀⠀⠀⠀⠀⠀⠈⠳⣆⡿⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠐⠏⠃⠀⠀⠀⠀⠀⠀⠀⠙⣇⣸⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
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👩‍⚕️🩺💉🩹🧑🏾‍⚕️🩸💊👨‍⚕️
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠉⢻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⠴⠛⣁⡤⠔⠀⠈⠛⠉⠀⢰⣶⣶⣤⠄⠀⠀⠈⣿⣿⣦⣴⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⣡⣴⣾⣿⣿⢿⣋⡥⠴⠚⠉⠀⠀⠀⠀⢀⣀⣀⣀⣙⣋⡁⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣼⣿⣿⡿⠟⠋⠁⠀⠀⠀⢀⣀⡤⠴⠞⠛⠉⠉⠁⠀⠀⢈⡉⠛⠒⠦⢤⣀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⡿⠋⠀⣀⣀⣠⡤⠖⠛⠉⢀⣤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠙⠷⣄⠀⠉⠉⠉⠉⠉⠀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⢳⣿⣿⣿⣿⠋⠀⠀⠀⣠⠋⠀⣠⠇⠀⠀⠀⠀⢰⠀⠀⢰⡀⢣⡀⠀⠀⠀⠘⢮⠳⣄⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⡾⣿⣿⣿⠋⠀⠀⠀⡴⠁⠀⡰⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⢣⠀⢳⠀⠀⢀⣀⣀⡆⠘⢧⠀⠀⠀⢠⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣧⢿⣿⠃⠀⠀⠀⡼⠁⠀⢠⠃⠀⡆⠀⠀⠀⠀⠸⠀⡇⠀⠈⡆⠈⢇⠀⢹⣿⣿⣷⣶⣮⣷⡀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣞⣿⣿⣿⣿⣾⠇⠀⠀⠀⢸⠁⠀⢀⡎⠀⢰⠁⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⠈⢧⠀⣸⣿⣿⣿⣿⣿⣷⣤⠎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣯⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⡇⠀⠀⢸⠁⠀⡿⠀⠀⠀⠀⠀⡇⢀⡇⠀⠀⢰⡀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⢳⣿⣿⣿⣿⣿⣿⣿⡞⣦⠈⠁⠀⠀⠀⠀⠀ ⠀⣠⣿⣿⣿⣿⣿⣿⠃⡜⠀⡆⠀⠀⡇⠀⢀⡇⠀⢀⡇⠀⠀⠀⠀⢸⠀⢸⣇⠉⠉⠲⡧⣄⠙⢿⣿⣿⣿⠟⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⡄⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⠃⠘⡇⢰⢧⠀⠀⡇⠀⠈⡇⠀⢸⠀⠀⠀⠀⢀⠇⠀⡿⢸⠀⠀⠀⣇⠈⠳⡄⠀⠀⠀⠀⢹⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⡿⡇⠀⠀⠀⠀⠀ ⢹⣿⣿⣿⣿⡿⠁⠀⠀⡇⢸⢸⠀⢠⡇⠀⢸⡇⠀⢸⡇⢰⠀⢰⠈⠀⢠⠃⠈⡆⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠇⠀⠀⠀⠀⠀ ⠈⢻⣿⣿⡿⢁⠀⠀⠀⡇⠘⡇⠀⠘⡇⠀⢸⣇⠀⠘⣷⢸⠀⢸⠀⠀⢸⣸⣖⣛⣢⣀⠁⠇⠀⡕⡀⠀⠀⠀⠘⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡟⡠⠋⠀⠀⠀⣇⠃⡇⠀⠈⣷⠀⠸⣹⡆⠀⠙⣼⡆⠈⣇⠀⠸⠛⠛⢻⣿⣿⣿⣶⣤⣧⠃⠀⠀⠀⢸⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡟⡴⠁⠀⠀⡠⢸⣿⠀⡇⠀⠀⣿⡀⠠⠧⠽⠄⠀⠀⢿⠀⠹⠧⠀⠀⠀⣤⣴⡿⣿⣿⠘⡿⠀⠀⢀⠀⠸⠀⠀⠀⠀⢻⣿⡿⣯⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰ ⢀⡏⣼⠁⢀⠀⡼⠁⢸⢸⠀⣷⠀⡀⣯⢷⠟⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣛⣿⠏⢰⡇⠀⠀⢸⠀⢠⡆⠀⠀⠀⠈⠻⡿⠋⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣼⣾⡏⠀⡾⡼⠁⠀⣿⢸⡇⢻⡄⢰⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⡄⠀⠈⠀⢸⡆⠀⠀⠀⡄⢀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣷⢻⡇⠀⣷⠃⢀⡜⢹⡄⣷⣨⠟⠛⠉⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⠀⠃⠀⠀⠀⢸⢿⠀⠀⠀⢀⣸⡧⢰⠇⠀⠀⣀⡀⠀⠀⠀⠀⠀⠿ ⣿⠀⢧⠸⣿⢀⡞⠀⠀⣳⠟⠁⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢀⣾⠁⠀⠀⡇⠀⣾⣿⣆⠀⠀⣿⣿⠁⣾⠐⣻⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠈⠃⠈⠧⣿⣾⠁⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠋⠘⠀⠀⠀⡇⢀⠇⡼⠹⡄⢠⣿⢁⠀⣿⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠟⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⠉⢙⣶⣤⣀⣀⣠⣴⣶⠿⠋⢸⠀⠀⠀⠀⠀⢸⠁⣸⡰⠃⡴⠻⣼⠘⡟⠀⡏⢸⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡿⠾⣿⣼⡏⠉⠻⡁⠀⠀⠘⢦⡀⢀⡆⢀⡎⢰⠏⢠⠞⠁⠀⠘⡿⢁⣸⣅⢸⠀⠀⠀⠀⠚⠓⢆⠀⠀⠀ ⠀⠀⠀⢀⣧⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠛⢦⣿⢿⣇⠀⠀⠀⠀⠀⠀⣠⠞⠋⢃⡞⢡⢧⡔⠁⡠⠀⢀⢼⡷⠋⠁⣝⣎⣄⠀⠀⠀⠀⠀⠀⠱⡄⠀ ⠀⠀⠀⠚⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠠⢻⠇⣰⠋⠹⣾⡛⠲⢦⣤⡤⠒⠋⠁⢀⣴⠚⠤⠚⠈⣳⠞⠀⢀⡴⠋⠀⠀⠀⠙⣽⢻⣆⠀⠀⠀⠀⠀⠀⠹⠀ ⠀⠀⠀⣰⠟⡜⠳⣦⣤⣤⣤⡤⠔⠒⠋⠉⠁⠀⠀⢾⣟⠁⠀⠀⠈⠙⢶⡤⣤⣤⣤⠖⠚⠉⠁⠀⢀⣄⡾⠋⢁⡴⢻⠀⠀⠀⠀⠀⠀⢸⡀⠱⠱⣄⠀⠀⠀⠀⠈⡄ ⠀⠀⠀⣏⠀⡟⢦⣽⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⢠⠞⠛⢺⡀⠀⠀⠀⠀⠀⢠⣿⠋⠀⡰⠋⢀⡞⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠇⠱⡀⠀⠀⠀⠰ ⠀⠀⣠⢿⡀⣸⠀⠙⠳⢦⣤⣄⣀⣀⣀⣤⣴⠞⠋⠀⠀⠀⠀⠀⠀⠘⣦⣤⠞⡀⠀⠀⠀⠀⠀⣼⠟⢀⡞⠁⠀⠸⣇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡯⠤⠗⠛⠀⠀⠀⠀⠀⠠⠀⠀⣇⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠜⠁⠀⠀⠀⠀⢠⢯⣠⠏⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⢀⣿⡴⡏⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⢟⣭⣴⣾⣿⣿⠉⠭⠩⣤⡉⠻⠷⣦⣌⡙⠻⣶⣮⠙⠿⣿⣿⣳⣜⢦⡀⠀⠀⠀⠀⣀⡴⠋⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⢤⣄⡀⠀⠑⠢⢤⣀⠀⠀⠀⣠⣾⢟⣵⣿⣿⣿⡿⠋⢿⣆⣠⢓⡘⢿⡆⠀⠈⢹⣿⣶⡝⢿⣧⡀⠘⢷⣝⢮⢷⡕⣄⣀⡴⢚⣩⣶⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠑⠒⠢⣤⣌⣉⠒⣾⠋⢀⣾⣿⣿⡿⠃⠀⠀⠸⡏⠀⢸⣷⠘⣿⡄⠀⢲⡝⢿⣿⣦⣻⣿⣦⡈⢿⣦⠀⠹⣮⢳⣾⠋⠉⠉⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⠋⢉⡿⠁⢀⣾⣿⣿⡿⠃⠀⢀⣼⢠⣿⣠⢸⣿⡇⢸⣿⣆⣘⢧⠈⠻⣿⣿⣿⣿⣷⡀⠙⣧⠘⣏⢧⡙⣦⡀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡇⠀⣼⠁⠀⣾⣿⣿⠿⢁⠀⢀⡼⠁⣼⣿⣿⡈⣿⣷⡀⣹⣿⣾⣷⡀⠀⣘⠿⢿⣿⣿⣷⡄⠙⣧⠈⠈⢻⡜⢷⡀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣏⡶⣼⠇⣠⣸⢏⣿⡿⢠⡏⡼⣿⠃⢰⣿⣿⢿⡇⢿⡟⢷⣷⣿⣿⣷⣿⣆⠀⠐⣿⣻⣿⣿⣿⣄⠸⣧⡀⠀⢻⣎⢷⣤⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⡏⣰⢣⡟⣼⣿⢃⡏⣼⣷⡏⢠⣿⣿⡇⠈⣧⠸⣿⡀⢻⣯⢿⣿⣿⣿⣧⠀⠈⢿⣿⣿⣿⣿⣆⠙⣷⡄⠀⠹⣧⡻⣷⡜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⢸⡿⣼⣹⣿⡏⡾⢱⡟⢸⡇⣾⣿⡟⠀⠀⠹⡆⣿⣇⠀⠙⢷⡝⢿⣿⣿⣷⣤⡀⠻⣿⣿⣿⣿⣧⡙⣿⣄⠀⠹⣷⣻⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣧⣿⢇⣿⣿⣿⢱⠃⣾⠁⣸⣿⣿⡟⠀⠀⢀⣠⢿⡸⣿⡄⠀⠈⠻⣦⠉⠻⢿⣿⣿⣧⣽⣿⣿⣿⣿⣷⡘⣿⣧⡀⠘⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⡏⣼⣿⣿⡿⢸⠀⣿⢀⣿⣿⡏⣠⡤⠚⠉⠀⠀⢳⣽⣷⡀⠀⠀⠈⠳⢄⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⡄⠈⢻⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡟⣸⣿⣿⣿⢇⡇⣰⡇⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠈⢻⣿⣧⠀⠀⠀⠀⠀⡵⢒⣦⣖⡊⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⢳⣿⣿⣿⣿⢸⣃⣿⠇⣿⡟⠀⢀⣠⢴⣂⣐⠦⠄⠀⠀⠹⣿⣧⠀⠀⠀⠀⢰⣿⠛⢻⣿⣿⣷⣮⡿⢿⣯⣿⣿⣿⣿⣿⣷⣄⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⢧⣿⣿⣿⣿⡿⣼⣿⣿⢀⣿⠀⣀⣼⣾⠿⣿⣿⣶⡄⠀⠀⠀⠈⢿⣧⠀⠀⠀⠚⣷⣤⣾⣿⣿⣷⠹⣿⣦⣿⣯⢹⣿⣿⣿⣿⣿⣧⣀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⢉⣿⢿⣅⣠⣿⣿⣿⡅⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⣿⠿⣿⣿⣿⣿⠀⣸⡿⢿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⡯⣿⣿⢸⣿⣿⡏⢸⣿⣿⣯⣿⠟⠷⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⢦⣐⣀⡢⢆⠀⠉⠀⢸⣿⡇⣿⣿⣿⣿⣿⡛⣿⢿⣿⣿⣿⣿⣷⣄⡀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⢿⣿⣿⣿⡇⠀⣿⢿⢿⡿⠿⠷⣄⠻⣄⣉⣉⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⠛⠛⠁⠀⠀⠀⢞⣿⡆⣿⣿⣿⣿⣿⣧⡹⡆⠈⠉⠛⠛⠿⠿⠿⣦⣄ ⠀⠀⢠⣾⣿⣿⠏⢸⣿⣿⣿⡷⢸⣿⠘⢸⣿⠀⠀⠀⠀⠚⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣿⣿⣿⣿⣿⣿⣷⣻⡄⠀⠀⠀⠀⠀⠀⠀⠈ ⢀⣴⢟⣿⣿⠋⠀⢸⣿⣿⣿⡇⣸⣿⡆⠩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣿⢾⣿⣿⣿⡌⠻⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠋⢁⣾⡿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣿⢸⣿⣿⣿⣿⣦⣤⣴⠟⠋⠉⠙⠲⣄⠀⠀⠀⠀ ⢀⣾⠋⠀⠀⠀⠀⢸⣿⣿⡿⠟⣿⣿⣿⠀⢸⡏⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⣧⣿⣿⣿⡿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀ ⠋⠁⠀⠀⠀⠀⠀⢸⠟⠋⠀⠀⣿⣿⣿⣇⠀⣷⡀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⢹⣿⣿⣿⡄⣸⣷⡀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⣿⡈⢿⣿⣏⢸⣷⡄⠀⠀⠀⠀⠈⠻⣖⠤⢄⣀⠀⠀⠀⠀⣠⠖⢫⡏⠀⢀⡔⠀⠀⣸⣿⠟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠙⢿⣿⣿⣝⠶⣄⡀⠀⠀⠀⠈⠳⣄⡈⠉⠒⠒⠋⠁⢠⠏⢀⡴⠋⠀⠀⣰⡿⠋⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡄⠀⠀⢠⠀⠀⠀⠀⠘⢆⠀⠀⠉⠛⠿⢆⡈⠉⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⣰⣋⡴⠚⠀⠀⠀⡴⠛⠁⣸⢹⣿⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣇⠀⠀⠘⣆⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⢷⠓⠢⣄⠀⠀⠀⠀⠀⠀⢰⠇⣾⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠘⠆⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢠⠟⠀⠈⢧⠀⠈⠳⣄⠀⠀⠀⢠⠇⠀⣿⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⢹⡆⠀⠀⠀⢦⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⡎⠀⡔⠲⡌⢳⡀⠀⠈⠳⣄⣰⠏⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⡄⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⡟⢸⣿⣦⠀⠀⠀⠳⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠟⠀⠀⢧⣀⡼⠀⡇⠀⠀⠀⠀⠁⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠘⣿⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⡇⠘⣿⣿⣷⡀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⠃⠀⣿⣿⣿⣿⣦⡀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⢿⣿⣿⣿⣿⡟⣦⡀⢠⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢀⡰⠃⣠⠆⠀⠀⠀⣸⢻⡇⠀⠀
🧑🏿‍⚕️🧑🏾‍⚕️🧑🏽‍⚕️🧑🏼‍⚕️🧑🏻‍⚕️🧑‍⚕️
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⡴⠋⠀⠀⠀⣀⣠⡤⠔⠒⠋⠁⠀⠀⠀⠐⠒⠚⠛⠻⢭⣗⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⣀⡴⠒⠉⠁⠀⠀⠀⠀⠀⠀⣰⠖⠒⠦⣄⡀⠀⠀⠀⠀⠉⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠳⣄⠀⠀⠀⠹⣎⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠳⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠀⠀⠀⠀⠀⠀⠀⠸⡇⠈⢢⡀⠀⢦⠀⠈⠳⣄⡀⠀⠈⠳⢄⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠐⢲⠗⢤⣄⡀⠀⠀⠀⠀⣀⣠⠤⣤⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⡇⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠳⡄⠈⢣⠀⠀⠀⠙⠢⣄⡀⠀⠙⠛⢷⡤⣄⣀⡀⠀⠀⣠⡷⠀⠀⠀ ⠀⢀⣼⠐⢻⣿⠟⢷⡀⠀⠚⠋⠉⠉⠳⡟⢷⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢹⡄⠈⢳⡀⠀⠀⠀⠀⢯⣓⠲⣤⣬⣷⡀⠈⠉⣩⡽⠋⠁⠀⠀⠀ ⣰⠊⡿⣠⢿⡿⣆⢀⢷⡀⠀⠀⠀⠀⣰⠇⠀⣧⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠈⣇⠀⢀⠀⠀⠀⠀⢸⠀⠀⢀⣀⣻⡀⠀⢳⡄⠀⠀⠀⠀⢿⡆⣷⠀⠘⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠁⢼⡿⠁⠀⠙⢿⢷⣹⡟⠲⠶⠖⠛⠁⠀⣰⠇⠀⠀⠀⠀⡶⠀⣸⠁⠀⠀⢀⣸⠀⠈⣇⠀⠀⠀⢸⠀⠀⠀⠀⠈⢧⠀⠀⠹⣄⠘⣄⠀⠈⣧⠸⡀⠀⢹⡄⠀⠀⠀⢀⡀⠀⠀⠀ ⠀⢸⡇⢷⠀⣴⢻⠂⡇⠙⠦⠤⣀⡤⠤⢾⡁⠀⠀⠀⠀⣼⠁⣰⣃⠤⠖⠛⠋⢸⡀⠀⢹⡀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣆⠀⢸⣌⠢⡘⢆⠀⠸⣆⡇⠀⢸⡇⠀⣠⠔⠋⠀⠀⠀⠀ ⠀⢸⡇⠈⣷⠁⢸⡇⢻⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⠋⣰⠛⠁⠀⠀⠀⠀⠘⡇⠀⢸⡇⠀⠀⡾⠀⠀⠀⠀⠀⠀⢻⡀⢸⣽⡆⠘⣯⣧⠀⢻⡇⠀⢨⣧⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⢸⢠⡞⠙⣆⢸⠃⠈⢷⠀⠀⠀⠀⠀⠀⣧⠀⠀⢠⣏⡼⠃⠀⠀⠀⠀⠀⠀⠀⣷⠀⡟⣧⠀⣸⠃⠀⠀⣀⣀⡀⠀⠀⣇⡸⣿⣿⠀⡏⠻⣇⠀⡇⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⢸⡀⠀⣨⣿⠂⠀⠈⢧⠀⠀⠀⠀⠀⢹⡀⣠⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⠀⢿⣠⠃⢀⣾⣿⣷⡶⢷⡶⠀⣸⣧⡏⡏⡆⢸⠀⢸⡄⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠈⠳⡼⠁⢸⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢟⠃⠁⠀⠀⠀⢀⡠⣤⣖⣺⣤⠄⠋⠀⠀⡟⠁⠀⠈⠙⠉⠉⠁⠀⠀⠀⠟⣿⠀⣇⡇⡸⠀⢾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⣴⠊⠳⣄⣸⠀⠀⠀⠀⠈⢳⡀⠀⢀⠀⠘⡇⠀⠀⣠⣶⣿⡿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⣿⡴⠃⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄ ⡞⢀⡇⠀⠀⣨⢿⠀⠀⠀⠀⣠⡴⠋⠀⠈⠳⣄⠈⠢⣌⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⣯⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠊⠀⠈ ⠀⢸⡇⣤⠊⠀⣾⠀⠀⠀⠘⢻⣿⠑⠲⣆⠀⠘⠳⣄⠈⠓⢦⣄⠠⠄⢦⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⠼⠿⠗⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀ ⠀⢸⡟⠀⠳⠄⡇⠀⠀⠀⠀⠈⢾⡆⢀⡸⣦⠀⠀⠈⠻⡗⠒⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠀⠀⠀⣰⠋⠀⠀⠀ ⢠⢾⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠙⠲⠭⣍⡷⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⣠⠞⠁⠀⠀⠀⠀ ⠁⠸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀⣀⡀⠀⠀⠹⣆⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠆⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣿⠀⠀⢠⠶⠭⠥⠭⣧⠀⠀⢻⣆⠀⠉⠛⠛⠲⣶⣒⠒⡾⠁⠀⠀⢸⣓⡶⠀⠀⢰⡿⠳⣶⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⡏⠀⠀⡏⠀⠀⠀⠀⠈⢧⡀⠀⢿⣦⣄⡀⠀⠀⠙⣿⡠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢸⠁⠀⢠⠇⠀⠀⠀⠀⠀⠀⢳⡀⢸⣿⠳⢟⡦⣄⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣴⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⣰⠃⠀⠀⠀⠀⠀⢀⣿⠀⢀⡾⠀⢄⣀⠀⠀⠀⠀⠀⢷⡀⡏⡇⠀⠻⣆⡙⡿⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣤⡄⠀⠀⠀⣾⣯⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⡾⢹⢀⡞⠀⠀⠀⠈⠉⠓⢤⣀⠀⠀⣿⣿⡇⠀⠀⠈⠛⢦⡜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡏⠀⠀⠀⠀⠀⢀⡼⠁⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣿⣿⠇⠀⠀⠀⠀⢨⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀ ⠠⠫⠁⠀⠀⠀⠀⢀⡞⠁⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⠿⢤⡀⠀⠀⠀⢸⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠁⠀⠀ ⢁⠆⠀⠀⠀⠀⣠⠎⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⠶⠋⠉⠀⠀⠙⠦⡄⣀⡼⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⢀⠂⠀⠀⠀ ⡞⠀⠀⠀⣀⠜⠁⢀⡴⢉⡇⠀⠀⠀⠀⠀⠀⠀⠘⢇⡘⣧⣄⣀⣀⣀⡤⠴⠚⠛⠁⣀⠘⢦⡙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⢀⡤⠖⠒⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠲⢤⡀⠀ ⢀⡟⢠⡖⠋⠙⢳⣤⠽⠖⠛⠉⠉⠉⠉⠉⠉⠙⠓⠾⣤⡖⠋⠙⠲⡄⠹⡄ ⢸⡀⣿⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⣹⠀⡇ ⠈⢧⣘⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣏⡴⠃ ⠀⠀⡽⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢹⡀⠀ ⠀⠀⡇⠀⠀⠀⠠⣯⣽⡇⠀⣠⠴⠚⠓⠲⣄⠀⢰⣯⣽⡇⠀⠀⠀⠀⡇⠀ ⠀⠀⡇⠀⠀⣀⣀⣉⠋⢁⡞⠁⠀⣤⣤⠀⠈⠳⡄⠉⣋⣁⣀⠀⠀⠀⡇⠀ ⠀⠀⣇⠀⠘⠻⠿⠟⠃⢸⠀⠦⣄⡼⢯⣄⡤⠆⣷⠘⠻⠿⠟⠃⠀⢰⠇⠀ ⠀⠀⠹⣄⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⣠⠟⠀⠀ ⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠤⠤⠤⣤⣤⡤⠤⠤⠶⠒⠋⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠋⠉⠉⠀⠀⠀⠉⠉⠉⠛⠻⠶⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡐⣴⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣷⡄⠀⠀⠀⠀⠀⠀ ⣬⣿⠃⠀⠀⢠⣤⡄⠀⠀⠀⠀⠉⠲⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣄⣀⣀⡀⠀ ⣿⣿⣄⠀⠀⣸⣿⡁⠀⠀⠀⠀⠀⣴⠀⠀⠈⠛⠻⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡽⠇⠀ ⣿⣿⡛⠛⠛⠋⠈⠻⢦⣤⣠⣤⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⡄ ⠈⠛⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⢾⠛⠇ ⠀⠀⠀⠀⢭⡛⣷⢶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢿⣄⣀⣤⣤⣴⣶⠟⠛⠋⢉⣤⣶⣮⠀⠀ ⠀⠀⠀⠀⠀⣶⣇⠀⢀⣽⠟⠛⠛⠛⠛⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠾⢷⣤⣀⠀⢀⣠⣾⠟⠉⠁⠀⠈⢿⡟⠶⣶⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⢷⣾⠇⠀⢀⣤⣤⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⣷⠀⠸⣏⠹⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⢺⣿⣿⡇⠀⠀⣟⠀⢰⣆⠀⠘⣷⠀⠀⠀⢰⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⣦⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡇⢰⢤⡌⠉⠁⠀⠀⠀⠻⠶⠟⠙⠷⠾⠋⠀⠀⠀⠘⠿⠿⠿⠁⣀⢠⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣷⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠚⠋⠀⠀⠀⠀⢠⡟⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⠀⢿⣟⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⢀⣆⣤⣀⣿⠀⢸⡏⠙⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣛⣿⡿⣿⡿⢛⡁⠸⢷⣀⠀⠀⠀⠈⠙⡛⠷⢶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⡶⠾⣿⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠛⠉⠉⠉⠁⠀⠀⠈⠉⠉⠙⠛⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠹⣧⡀⠀⠀⠀⡏⠉⠙⠋⢹⡆ ⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠉⠛⠿⣦⡀⠀⠸⣷⡀⠀⠀⠹⣄⠀⠠⡹⠃ ⠀⢀⣿⠃⠀⠀⠀⠀⣠⣶⠾⠟⠛⠉⠉⠛⠿⣶⣄⠀⠀⠀⠀⣰⠃⢀⣠⣤⣄⠀⠈⢻⣦⠀⢻⣧⠀⠀⠀⠈⠓⠋⠀⠀ ⠀⢸⣿⠀⠀⠀⣠⣾⠋⠁⠀⠀⢀⣠⣤⣤⣤⣈⠙⣷⣄⠀⢠⣏⣶⣿⣿⣿⣿⣿⣦⠀⢻⣧⠘⣿⢀⢸⡛⠛⢲⠀⠀⠀ ⠀⣾⡇⠀⠀⢠⡿⠁⠀⠀⣠⣾⡿⢿⣿⣿⣿⣿⣷⣌⢿⣆⢸⣿⡋⠉⢉⣿⣿⣿⣿⣧⠈⣿⠀⣿⣿⠀⠹⠶⠋⠀⠀⠀ ⠈⡟⣿⠀⠀⢸⠇⠀⢀⣼⣄⠈⠀⣸⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣶⣿⣻⣿⣿⣿⣿⣤⣿⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⢷⢹⡆⠀⢸⡄⠀⣾⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣇⣿⢹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠏⣸⢧⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣇⢳⡀⠈⢧⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢎⠃⠀⠈⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠟⠁⠀⠀⠈⠻⣿⣿⣿⣿⡿⠟⠁⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⠀⠀⠈⠙⡻⠿⢿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⣀⡀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡤⠬⣷⣄⡲⣤⣈⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢛⡵⠚⠁⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣇⠀⠀⠀⢻⣿⠒⠭⣟⣷⢶⣤⣤⣤⣤⣤⣤⣤⣤⣶⢾⣟⠯⠗⠊⠁⠀⠀⠀⣾⠟⠁⠀⢘⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣧⠀⠀⠈⣿⡄⠀⠀⠈⠉⠛⠛⠛⠛⠛⠒⠋⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⠇⠀⠀⠙⠛⠛⠒⠒⠛⠛⠛⠻⠿⢷⡢⣤⣔⡶⠿⠟⠛⠛⠛⠻⠿⠽⠟⠁⠀⠀⢺⡿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⠒⠲⠛⠙⠲⠦⢼⣿⡿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⢸⣇⡇⠀⠀⠀⠀⠀ ⠀⠀⠹⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡻⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⢀⡾⡿⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⢀⣠⣴⢯⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⣖⡿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠘⠮⣷⣶⡤⡤⠴⠾⠟⠋⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣴⡾⠗⠛⢮⡑⢦⠄⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⡞⠉⠁⠉⡇⠸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢲⡏⠀⠀⠀⠀⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⣰⣟⡀⠀⠀⠀⢹⠀⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣠⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⣠⠂⠀⢀⢿⠏⠁⠀⠻⡶⡿⣅⣸⡖⢨⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡽⢧⠤⠤⣄⡀⢆⠀⠀⢀⡴⣫⡀⠀⠀⠀⠀⢳⣤⣤⠤⡤⠞⠁⠀⠚⠁⡌⠀⠀⠀⠀⢹⡉⠉⠛⠦⣸⠸⡆⠀⠀⠀ ⠙⢶⣤⡀⠀⢠⡇⠀⠀⢧⠀⠀⠉⠠⠕⣦⡾⠋⠁⠈⠓⠒⠒⠒⠉⠀⠈⠉⢣⡀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⣇⠀⠀⠲⢾⣷⣷⠀⠀⠀ ⠉⠉⠉⠁⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠦⣄⣀⡞⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡼⢹⡀⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣇⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⠉⠉⢻⡁⠀⠀⠀⢸⠀⠀⠀⠋⠁⠈⡇⠀⠀ ⠀⠀⠀⠀⠀⠞⢳⡀⠀⢠⡞⠁⠀⡔⠁⠀⠀⣴⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢷⡦⠤⠤⢞⡄⠀⠀⢤⠀⠀⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⠃⣼⡴⢀⡞⠀⠀⠀⣰⢣⠃⠀⠀⠀⠀⠀⠘⣶⡀⠀⠀⡀⣆⢧⠀⠀⠀⢀⠘⣧⠀⠀⠀⠉⠛⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡽⠁⡜⠀⠀⠀⣰⡏⡸⡸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⠘⣼⠀⠀⠀⡼⡀⣎⠳⢄⡠⠖⠋⠹⣏⢹⡀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⢫⢿⣿⢁⢶⠁⠀⠀⢠⢿⠀⠁⠁⠀⠀⠀⠀⢠⠀⠈⣧⠀⠀⠈⠀⠛⡇⠀⡔⠀⢧⠹⣇⠀⠸⡄⠀⠀⢹⡆⠃⠀⢧⠀ ⠀⠀⠀⠀⠀⠀⣿⣼⡇⣎⠊⠀⠀⠀⡎⡇⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⠀⠀⠀⠀⠀⣧⠀⠀⠁⠘⠀⠿⠀⢠⠇⠀⠀⢸⣿⡀⣦⠘⡆ ⠀⠀⠀⠀⠀⠀⣸⣿⢰⡹⠀⠀⠀⣰⠃⣇⡇⠀⠀⠀⢀⡀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠈⣠⡿⣦⡤⣤⣼⣿⡛⠿⣦⢓ ⠀⠀⠀⠀⠀⣰⡟⡇⢸⡇⠀⠀⠸⣿⠀⣟⡆⠀⠀⠀⢸⡇⠀⠀⣿⣧⢻⠀⠀⠀⣠⣤⡇⠀⠀⠀⠀⠀⠀⢿⣾⠨⡇⣸⢻⡿⣿⡲⢈⡶ ⠀⠀⠀⠀⣠⣿⠃⣧⢸⣇⠀⠀⢀⡇⠙⠫⣇⣀⣀⣠⠬⠧⠶⠼⢹⡿⠾⢔⣒⣭⣁⣼⡇⠀⠀⠀⠀⠀⠀⣺⡟⢠⣇⢧⠸⣾⣿⡇⡫⢇ ⠀⠀⢀⣼⡿⠉⠀⣿⢞⡎⠋⠉⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣿⣇⡾⢿⠘⢳⡬⢿⣗⢂⣄ ⠀⢠⡾⣽⠁⠀⠀⠈⠈⣷⣤⣼⣶⣷⣷⣶⡖⠃⠀⠀⠀⠀⠀⠀⠐⢾⣿⣶⣾⣦⣖⣾⣤⠄⠀⠀⠀⠀⠀⢻⡜⢷⡘⢮⠙⢷⠤⣽⣿⠋ ⢠⡿⢡⡏⠀⠀⢀⠀⠀⣾⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠻⣿⠭⠋⠀⠀⠀⠀⠀⠀⣧⠀⡷⡞⢿⢽⣖⠉⠀⠀ ⡞⠀⣾⠁⠀⠀⣸⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠁⠀⠀⠀⢨⠀⠀⢸⣿⡼⢹⠁⠀⠈⣿⡄⠀⠀ ⡇⠀⣿⢠⠀⠀⣿⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⡼⠀⠀⢠⣧⠇⡾⠀⠀⠀⢻⡇⠀⠀ ⠁⠰⢿⣼⣄⠀⢻⠀⡟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢠⢏⡇⠀⠀⢸⣿⠠⠇⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠙⣧⣰⡿⣆⣴⡎⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⡞⣸⠀⠀⣰⢇⣿⠀⠀⠀⠀⠀⠀⠃⠀⠀ ⠀⠀⠀⠀⠘⢿⡶⢿⡧⣿⣻⣯⡷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠐⠐⠛⢠⠃⠀⡰⠃⣸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠶⠤⣤⣍⡻⣿⠁⠀⠉⠓⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⡷⣀⡤⠶⣤⠏⠀⢛⣁⡴⣣⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠁⠀⠀⠀⣸⢀⡇⠀⠀⠀⠀⡼⠀⠈⠙⢲⣶⣶⠲⣿⣭⡤⠊⠀⡗⠛⢦⠤⣟⡋⣿⣽⠿⡏⠁⠘⡌⠹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⢠⣧⣼⡄⣀⡀⠀⣸⢃⣀⣀⣀⣸⢼⣏⣀⠼⠋⠀⠀⣸⠋⠉⠙⠒⠥⣟⠟⡁⠀⡆⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⣀⡀⣾⣿⡟⠉⣩⣹⠞⠉⠉⠉⠁⡝⣣⢾⠋⢀⣀⠤⣖⣪⠇⠀⠀⠀⠀⢰⡃⠀⢧⠀⢇⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀ ⠀⠀⠾⢷⢠⡤⣤⣹⣿⠉⡇⠀⠏⠀⠀⠀⠀⠀⡸⣷⣿⣿⣭⣵⡶⠿⢛⡏⠀⠀⠀⠀⢠⠃⠙⠦⣘⡄⠸⡄⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀ ⢀⠄⠀⠈⠁⠈⣹⢻⣯⠀⢣⠀⣷⠃⡀⠀⠀⠰⠥⠿⣻⠟⠉⠀⢀⣠⡾⠶⣒⡤⣀⢠⠏⠀⠀⠀⠈⠛⠦⡷⠤⠤⠤⢤⠈⢇⠀⠀⠀⠀ ⠀⠀⠠⠔⠒⢋⡏⠀⡟⠀⢸⠀⡿⢤⡈⣂⠀⠀⠀⠈⠀⠀⠀⠀⢻⣿⣽⡒⢲⢬⣙⣯⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡧⢸⡟⢻⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⢀⡸⢷⠀⢸⠀⣷⠀⠙⠚⠲⡐⠤⠀⠀⠀⠀⣴⣏⠀⠀⠛⠛⠷⣧⡿⠀⠀⠀⠀⠀⠀⠀⣸⠄⢀⣠⠿⠁⢸⠁⠀⠀⠀ ⠀⠀⠀⠀⢰⢁⡞⠀⣼⡄⢸⡄⣿⠀⠀⠀⠀⠈⠒⣋⣧⣡⣶⠛⡌⢣⣀⣀⣠⢴⠧⠤⠴⠶⠒⠒⠒⣋⡭⠖⠚⠉⠀⠀⠀⣼⠀⠀⠀⠀ ⠀⠀⠀⢀⣣⠎⠀⠀⠈⡗⠀⡇⢸⠢⠠⠴⠒⠋⠉⢁⣀⣠⡇⠔⢚⠉⠀⠐⠂⣯⡤⠴⠖⠒⠚⠛⠉⢁⣀⣀⣀⢤⡄⡀⠲⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢻⠊⠁⢾⠀⠀⠀⠀⠀⠀⠗⡆⢠⡄⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠸⠀⡘⢸⠀⠀⠀⢠⠆⠸⠀⡇⡌⠃⠀⠀⠂⢸⠀⠀⢰⠀ ⠀⠀⠀⣠⠀⠃⢰⢀⠇⠸⠀⠀⢠⢻⢠⠃⠀⣧⢁⣰⠀⣸⣀⡀⠄⠀⠘⠀ ⠀⠀⠀⢃⣷⡾⠿⣾⣝⠂⠆⢠⠃⣨⠂⠀⢀⠗⣡⡼⢿⣛⠒⠯⣕⣆⣀⠀ ⠀⠀⢠⣿⠏⢀⣴⣿⣿⣦⠘⠃⠀⠁⠀⠀⠈⠼⣩⣾⣿⣯⡿⣦⠀⢫⢷⠀ ⠀⠀⣼⣿⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⡹⣿⢷⣸⠀⢸⣸⠇ ⠀⠀⢹⠛⢦⠹⡻⢋⣭⠿⠃⠀⠀⠀⠀⠀⠀⠀⠻⢿⣈⠕⢀⠜⠀⢩⠃⠀ ⠀⠀⠀⡆⠀⠀⠈⠀⠀⠀⠀⡠⠤⠤⠢⢴⠶⣦⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⡇⢀⠠⠤⠐⠩⠭⣇⠀⠠⠔⠢⠭⡄⠂⠀⠀ ⢀⡈⢆⣇⠀⠀⠀⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⠤⠊⠀⠀⠀⠀ ⠀⠈⠑⢭⡉⠒⠤⢂⣀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⢀⡙⣧⠤⠄⣀⡀⠀⠀ ⠀⠀⠠⢉⠆⡰⠑⠤⣀⣟⣍⠁⣒⡒⣒⡂⠀⠀⠉⢀⣀⢇⢌⡅⠀⡀⠀⠀ ⠀⠀⠠⠁⠈⠀⠀⡐⣪⠗⠊⠋⠁⡟⠗⠤⣍⠭⠔⠊⠉⠉⠑⢜⣄⡛⠀⠀ ⠀⠀⠀⠀⠀⠀⡌⣰⠃⢀⣀⡤⠖⠳⠺⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡿⠿⠻⢶⣍⠳⣤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣠⠟⠉⠉⠈⢹⡇⢸⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠋⠀⠀⠀⠀⠙⢳⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢀⣼⠏⠀⠀⠀⠀⠘⡇⠀⢿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣶⠞⠛⢶⣀⢀⣀⡀⠀⣷⡀⠸⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠨⣧⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣠⠟⡿⠁⠀⠀⠀⢻⡏⣿⣳⣤⡿⠟⢰⡾⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⠿⣶⠶⠤⣄⣀⠘⣦⡀⠀⠀⢀⡴⢚⣦⡀⠀⠀⠀⠀⠀⢘⣆⣴⣶⠶⢶⠶⠋⠀⠀⠐⠋⠁⣰⠁⠀⠀⠀⠀⠀⢻⡈⠉⠘⠛⠦⢈⡇⢻⡆⠀⠀⠀⠀ ⠳⢶⣄⣀⠀⠀⠀⢸⡏⠀⠀⠘⣇⠀⠀⠉⠉⢈⡳⣤⣠⣾⠗⠋⠉⠙⠶⠦⠤⠤⠴⠞⠉⠉⠉⠉⢿⣀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢴⣼⣿⣮⣷⠀⠀⠀⠀ ⠶⠶⠿⠿⠇⠀⠀⢸⠁⠀⠀⠀⢸⡄⠀⠀⠀⠈⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠈⠙⣻⢿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣠⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡉⠓⠶⠶⠧⢤⣀⣀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⣾⠋⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢣⣀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠀⠀⠀⢷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⠏⢷⡀⠀⠀⢠⡾⠋⠀⢀⡴⠁⠀⠀⠀⣠⢆⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠀⠀⠀⠀⠀⢿⣦⢤⣀⣠⡞⡇⠀⠀⠀⢠⡀⠀⠀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡶⠀⣼⢁⡆⢀⡞⠀⠀⠀⠀⢀⡟⡾⠀⠀⠀⠀⠀⠀⠀⠀⢷⢠⠀⠀⠀⠀⠀⣜⢻⡀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠛⠒⢦⡀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⣼⢯⡟⠀⡼⠁⠀⠀⠀⢠⡿⢀⠇⡴⠀⠀⠀⠀⠀⠀⠀⠘⣾⠀⠀⠀⠀⣦⠹⡌⣧⠀⠀⠀⠀⢷⠀⡹⢦⡀⠀⠀⢀⣠⠴⢿⣶⠶⡆⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣯⡏⠀⣸⠃⠀⠀⠀⢠⣿⠁⡼⢰⠃⠀⠀⠀⠀⠀⠀⢀⠀⣷⡆⠀⠀⠀⢹⡀⢷⣿⠀⠀⠀⠀⡞⡆⢻⡄⠙⠶⢶⡉⠁⠀⠈⢿⡆⢹⡄⠈⢆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢫⡿⣿⡞⢀⣇⡇⠀⠀⠀⢀⡟⡏⠀⠀⠈⠀⠀⠀⡆⠀⠀⠰⡀⠀⠈⣷⠀⠀⠀⠈⠁⠘⢹⠀⠀⢠⢳⠀⢷⠘⣿⡀⠀⠘⡇⠀⠀⠀⢸⣿⡌⠃⠀⠸⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⣿⢃⣞⡜⠀⠀⠀⠀⣼⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠈⠀⠘⠀⢹⡇⠀⢀⡇⠀⠀⠀⠀⣿⣧⠀⢠⡀⢹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⢸⢿⠀⠀⠀⠀⣠⡏⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣿⠀⠀⠀⠀⠀⠀⠄⡟⠀⠀⠀⠀⠀⠀⠀⠁⢀⣾⣁⣀⠀⠀⢠⣿⣿⣷⣾⣧⡈⢇ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⡎⡏⠀⠀⠀⢠⣾⠀⣿⣾⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⣼⣧⢠⣼⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⣾⢯⠏⣿⠉⢛⣿⣿⣹⣆⣉⡙⢷⠐ ⠀⠀⠀⠀⠀⠀⢀⣾⡏⣿⠀⡇⡇⠀⠀⠀⠙⣿⣄⢻⣼⡀⠀⠀⠀⠀⢠⣟⠀⠀⠀⡿⣿⣾⣿⠀⠀⢀⣀⣤⢶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⢺⢆⣼⢻⡿⠻⢿⡍⢃⣸⡟ ⠀⠀⠀⠀⠀⢀⣾⡿⠁⡇⡆⡇⣇⠀⠀⠀⢀⡇⠈⠛⠦⣇⣀⣀⣀⣠⠾⠿⠶⠷⠶⠇⣿⡧⠿⠶⣚⣩⣧⣀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⣾⡀⢧⠘⢿⣿⣿⣏⢉⡴⢆ ⠀⠀⠀⢀⣴⣿⡗⠃⠀⢳⣧⣹⡜⠖⠒⠋⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢠⣿⣿⠘⢷⣄⣸⣿⣷⠮⠀⠉ ⠀⠀⢀⣾⢿⡏⠀⠀⠀⠸⠏⠻⣇⠀⠠⣤⣠⣤⣤⣄⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣠⣤⡠⣄⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠹⣿⡀⢿⡰⢦⣿⡍⠙⠳⣶⣽⠗ ⠀⢰⣿⢇⣿⠁⠀⠀⠀⠀⠀⢀⢿⣻⣿⣿⣿⡿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⣿⣿⣿⣾⣿⣟⣁⠀⠀⠀⠀⠀⠀⠀⣸⡇⠘⢷⣀⡻⣦⣬⣛⣉⣻⠿⠇⠀ ⢰⣿⠇⣸⡇⠀⠀⠀⢠⠀⠀⢈⣿⡄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡟⠶⠁⠀⠀⠀⠀⡀⠀⠀⣿⣿⠀⣸⢿⡏⠹⠿⢿⣯⡁⠀⠀⠀ ⡾⠁⠰⡿⠁⠀⠀⠀⣸⠀⠀⠘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠞⠀⠀⠀⠀⠀⢀⠇⠀⠀⢹⣿⣴⡟⣼⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⡇⠀⢸⡇⢀⠀⠀⠀⣿⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⣯⡾⢀⡇⠀⠀⠀⠈⣷⢿⠀⠀⠀ ⡷⢀⣸⣇⢸⡀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢀⡆⡟⠀⠀⠀⢸⣿⡇⢸⠇⠀⠀⠀⠀⠈⢸⠀⠀⠀ ⠀⠈⠙⠿⣾⡷⠄⠀⣹⡄⠸⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⡾⢸⠃⠀⠀⢀⣾⣿⠁⠚⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣄⣸⡿⣷⣠⣾⡏⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣠⡾⠁⡿⠀⠀⢠⡿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⡶⣿⣿⣸⣷⢻⣿⣹⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠆⠾⠿⠁⣼⠁⠀⢠⡞⠁⣼⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣹⣅⣈⣉⡘⠿⣿⡿⣿⠀⠈⠙⠶⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⠀⠀⣀⣀⠀⣸⠃⠠⠶⠟⠀⣸⢇⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠁⠉⠉⠙⠻⢷⡞⢹⡇⠀⠀⠀⠀⠀⣩⠙⠲⠦⣄⣀⣀⣀⣀⣀⣀⡤⠴⠶⣲⠿⢹⣝⣶⡞⠉⠙⣿⣃⣤⣤⠴⣶⣚⣵⠟⢹⡿⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⡾⠀⡼⠀⠀⠀⠀⠠⢠⡟⠀⠀⠀⠀⠉⡿⣽⣿⠙⠷⣿⣶⠶⠉⠀⢸⣍⣉⣙⡖⠻⡯⣅⣰⣿⣺⠟⡏⠀⠀⠀⠇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣸⣧⣶⣇⢀⣀⠀⠀⢀⡿⢀⡀⢀⣀⣀⣠⡵⣿⣏⣀⡤⠞⠉⠀⠀⢀⡿⠁⠉⠉⠉⠛⠦⣼⡽⢻⡁⠀⡇⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢰⣿⣯⣿⠛⠋⣉⢻⡴⠟⠋⠉⠉⠉⠉⡽⢧⣴⣿⠋⠉⠀⣀⣀⡤⠶⣿⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣧⠀⢹⡀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣰⣏⠀⠀⠀⠛⠶⣾⣿⠻⡇⠀⢀⡿⠋⠀⠀⠀⠀⠀⠀⣴⣀⣾⣷⡧⠴⣖⣚⡭⣷⣾⣿⠃⠀⠀⠀⠀⠀⢀⡞⠳⣄⠀⠹⡄⠘⣇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠁⢘⠤⠟⣛⣿⣾⣿⡏⠀⢹⠀⢸⡀⡠⠀⠀⠀⠀⠀⣰⠉⣿⣟⣿⣶⠿⠿⠚⠍⠉⣰⣏⠀⠀⠀⠀⠀⢀⡾⠀⠀⠈⠙⢦⣿⡀⢹⡆⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⢏⣿⡇⠀⢸⡄⢸⡏⠁⣀⠀⠀⠀⠀⠳⠒⠟⣿⠿⠹⠀⠀⠀⣀⣶⣛⠻⠿⢝⣶⣤⣀⡾⠁⠀⠀⠀⠀⠀⠈⠙⢶⡟⠶⠶⠶⠶⢶⣀⠸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠴⠖⠛⢻⡏⠀⢸⡇⠀⢸⡇⢸⣟⣤⣀⢓⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⣻⣏⣹⡒⠲⣦⣉⣉⣻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸⡆⢨⡟⠛⢿⡆⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⢀⡟⠀⢀⣾⡅⠀⠈⡇⠸⡇⠀⠛⠮⠿⢤⠀⣄⡀⠀⠀⠀⠀⠀⣀⣾⠉⠉⠉⠷⠶⢿⣤⣿⣹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⠀⠀⣠⣾⠇⠀⢸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡸⠁⣼⠃⠀⣧⠀⠀⡇⠀⡇⠀⠀⠀⠀⠈⠳⣌⣡⡴⣆⠰⢀⣀⣿⡙⢦⡀⠀⠀⠀⠈⢁⡟⠋⠁⢀⣀⣀⣀⣀⣀⣤⠴⠶⣛⣣⠶⠞⠋⠀⠀⠂⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠇⣼⠃⠀⠰⣿⡆⠀⣧⠀⣧⠀⠀⠀⠀⠀⣀⣀⣀⡤⠽⠶⠾⡿⠁⠻⣀⣷⠤⠶⠶⠖⣿⠃⠉⠉⠉⠉⠉⣉⣉⣀⡤⠶⠋⠉⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣈⡼⠃⠀⠀⠀⢸⡟⠀⢸⡄⣿⠠⠠⠶⠖⠛⠉⠉⠀⢀⣀⣀⣾⢁⠖⢋⡉⠀⢀⠂⠀⢀⣷⡴⠶⠶⠚⠛⠋⠉⠉⠁⢀⣀⣠⣠⣀⣆⣖⠆⡀⠘⠆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠴⠚⠛⠉⠉⠉⠉⠉⠙⠲⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣄⠈⢳⡀⠀⢇⠈⠉⡆ ⢰⠃⠀⠀⣠⠶⠚⠋⠙⠲⣄⠀⠀⡰⢁⣤⣄⡈⢳⡀⣧⠀⣀⡑⠊⠀ ⣼⠀⠀⡞⠁⢀⣤⢾⣿⣶⣬⣳⡄⣷⠛⢻⣿⣿⡄⣷⢸⡆⠣⠜⠀⠀ ⡿⡀⢸⠁⢠⣧⣀⡼⢿⣿⣿⡏⡿⣿⣷⣯⣿⣿⣷⡟⣼⡇⠀⠀⠀⠀ ⠰⢡⠈⢆⣿⣿⣿⣿⣿⣿⢿⡿⠃⢻⣿⣿⣿⣿⡟⠀⡙⠀⠀⠀⠀⠀ ⠀⠑⢄⠀⠛⠿⠿⣿⠿⠿⠛⠁⠀⠀⠙⠛⠛⡁⡠⠊⠀⠀⠀⠀⠀⠀ ⠀⡄⠒⠳⣴⡢⣄⣁⠀⠀⠀⠀⢀⣀⡤⣔⠏⠊⢁⡤⠒⢠⠀⠀⠀⠀ ⠀⠱⡄⠀⢿⣀⠉⣘⣛⣛⡛⠉⠋⢈⣁⣀⣀⣀⣸⠀⢀⡞⠀⠀⠀⠀ ⠀⣾⠁⠀⠀⠀⠀⠀⠀⠈⠙⣽⠛⠉⠀⠀⠈⠉⠁⠀⠈⢿⠀⠀⠀⠀ ⠸⣿⠀⠀⠀⠀⠀⠉⠛⣧⠈⠉⠐⢺⡟⠉⠁⠀⠀⠀⠀⣸⡄⠀⠀⠀ ⠀⠀⠑⢄⣀⠀⠀⠀⣸⠇⠀⠀⠀⠘⣇⡀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⡿⠛⢿⣿⡆⠀⠀⢰⣿⡿⠛⢿⣷⡄⠀⠀⠀ ⠀⠀⠀⢸⣿⡇⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⢸⣿⡇⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣀⣤⣿⣷⣶⣶⣾⣿⣤⣀⣿⡿⠀⠀⠀⠀ ⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀ ⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀ ⢠⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⡄ ⢸⣿⣿⣿⣿⣿⣤⣤⣤⣿⣿⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⡇ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠙⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⠋⠀ ⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠒⠚⠛⠓⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠓⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠒⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢀⣀⣤⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣆⠀⠀⠀⠀⠀⠀⣙⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⢠⠞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠀⠀⠀⠀⣿⠉⠀⠀⠀⣰⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠹⣆⠀⢀⣼⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠘⣏⠑⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢻⡄⠀⠈⠓⢟⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠙⢧⡀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣠⣶⣴⡿⠀⠀⠀⠀⠹⣆⠀⠀⣼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠙⡷⢤⣤⣸⣆⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⡄⢠⣏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠸⣷⡄⠀⢧⠀⠀⠀⠀⠀⢠⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⣧⡟⠹⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠹⣆⠀⢻⡎⠲⢼⣧⠀⠀⣀⡠⠾⣦⣤⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠷⣤⡹⣄⠀⠚⣆⠀⠉⢹⡢⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠉⠙⠳⣄⢻⡇⠀⠈⠁⠈⢡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠲⠀⠀⠀⠀⠀⠈⠳⣿⠀⠀⠀⠀⠀⠘⢿⠦⣤⣀⣀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠾⣟⡶⠂⡀⠀⠀⠀⠈⠘⠆⠀⢀⣄⠀⠀⠀⢳⡄⠈⠉⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡴⠖⢛⣿⠫⠢⠶⣏⠉⠹⢥⢶⣻⠜⠛⡗⠤⣠⢚⡇⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠟⠁⠀⢀⣿⠁⠀⠀⠀⠈⢧⠀⡞⠀⠀⠀⢀⡼⢆⠀⠉⠑⣢⣤⠀⠀⣘⣧⠤⠤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠻⣁⠀⠀⠀⠛⠛⠛⡆⡞⠉⠀⣠⠶⠛⠛⠛⠛⢶⣄⠀⠈⢹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣇⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡄⠀⠀⠀⣹⣧⡀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠻⣇⠀⠀⠀⠀⣿⠤⣴⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣷⠀⠀⢀⣿⢈⡇⠀⠀⣀⣀⣤⡴⠟⢉⣹⡟⠉⠉⠉⠉⠁⠀⠀⠀⠀⠙⣷⡢⠴⠒⣹⡶⠟⠀⠀⠀⠀⠀⠀⠀ ⠠⣤⣤⣤⠾⠃⢀⣠⠟⠁⣾⢥⣀⠀⣻⡄⠀⢰⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠛⠒⠛⠋⠁⠀⠀⠙⠶⣬⣭⣽⣋⣒⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⠉⠶⠤⠄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢧⠀⠀⠀⠈⡢⢀⣀⠀⠀⠀⠀⢀⡠⠗⠂⡝ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⡀⠀⠀⠀⠀⠀⠙⠢⣀⠀⢇⠀⢠⠎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡀⠀⢩⡀⠀⠀⠀⣀⣰⠀⠈⢦⠀⠑⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⡦⠤⠥⠀⠀⢸⣿⡏⠀⠀⠀⢣⢰⡅⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⡄⠹⡢⢰⡀⠀⣀⢆⡘⠟⠁⠀⠀⠀⠘⠇⢱⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠈⠒⠵⣄⢱⡀⠹⠚⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣂⡀⠀⠀⠑⠇⠀⠀⠈⢳⠠⢄⣀⣀⣀⠤⠋⠀⠀ ⠀⠀⠀⣀⠤⢤⠔⠩⢟⠳⡤⡤⠴⡤⠠⡶⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡜⠁⠀⡟⠀⠀⠀⢢⠃⠀⠠⠦⡄⠌⠑⣠⠤⠷⣖⠒⠢⡄⠀⠀⠀ ⠀⠀⣇⠀⠀⢧⠀⠀⠀⠀⢱⡀⠀⠀⠸⠀⠈⣀⡀⠀⠈⢧⠀⡷⠀⠀⠀ ⠀⠀⢸⠄⠀⡼⡧⠀⣀⣠⠴⢓⡶⠒⠒⠊⠉⠁⠘⣦⠤⢺⠽⠃⠀⠀⠀ ⠐⠶⠯⠴⠊⠀⢗⣂⣸⢤⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠢⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣶⣶⣏⡁⣄⣀⣀⠀⣀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠤⠴⠻⢗⠋⠁⠀⠀⠈⠉⠛⠦⢿⣾⡳⠾⣤⣄⡀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡠⠤⠤⠬⣿⡶⢤⣠⠖⠉⠀⢀⠀⠀⠀⢁⣀⡠⠤⠄⠀⠀⠀⠤⠬⣻⠿⢦⣙⡋⢼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠶⠋⠀⠀⠀⠀⠀⢸⡅⠀⣧⠀⠀⢀⡤⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠉⠒⠮⣷⣶⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠏⠀⠀⠀⠀⠀⠀⢠⡄⠇⢠⠟⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢹⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠀⣰⣿⠇⣠⢿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⣤⣀⢀⣤⣼⣏⡟⠀⣇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⣿⣶⠿⣿⣿⣿⣄⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⢙⡿⣄⣀⣰⠇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⣼⢧⡀⢠⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡀⠀⠀⠰⡄⠀⠀⠀⠀⣰⠀⢇⠀⣴⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⠘⠀⣸⡏⠀⢃⡸⠀⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣸⠤⠄⠱⣄⠀⠀⢳⡄⠀⢀⡼⠃⠀⣸⣴⣿⡆⠀⠀⠀⠀⣇⠀⠀⠀⠀ ⠀⠀⠀⢸⢀⣿⠀⠀⠘⡇⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⡿⠛⣛⡓⠊⠙⠒⠚⠉⠓⠋⠀⣠⡾⠿⠿⣿⠃⢀⡄⠀⡀⠸⡄⠀⠀⠀ ⠀⠀⠀⢸⣾⠃⠀⠀⠀⣿⣿⢰⠃⢀⡆⠀⠀⠀⠀⣀⣴⣿⠏⡐⠉⣠⣹⡆⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢀⣿⣖⢩⠇⠀⢹⣆⢣⠀⠀⠀ ⠀⠀⠀⢸⡟⠀⠀⠀⠀⢸⡏⢿⠀⣼⠁⠀⠀⠀⠀⠉⢹⣯⠀⣏⣿⣿⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣭⣿⣿⣤⣄⡄⠘⣾⠀⠀⠀ ⠀⠀⠀⣼⠇⠀⠀⠀⢀⣿⣷⣎⡜⢹⠀⠀⠀⠀⠀⢀⠀⠹⣇⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⡉⠀⠀⠀⠀⠀⠀⠉⠳⣿⣀⠀⢀ ⠀⠀⠀⢹⠀⠀⠀⠀⡼⡽⠋⣿⠀⠘⡀⠀⠀⠀⠀⠈⢿⣶⡼⠗⠀⠀⠀⠀⠀⠀⠐⠒⣡⢴⡟⠋⣉⣽⡆⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠈ ⠀⠀⠀⡏⠀⠀⠀⡼⢡⢧⢰⠋⢧⡀⡇⠀⠀⠀⠀⠀⠀⠻⣽⡯⠶⠶⠦⢤⡤⢤⣶⠛⠀⠼⠤⠯⠿⠛⠁⠀⣠⡤⢤⡀⠀⠀⠀⠻⠇⡀ ⠀⠀⢸⠁⠀⠀⡜⢠⠇⡸⠈⡇⠀⠉⠱⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⡄⠙⢯⣿⣏⡀⠀⠀⠀⢀⡿⠃⠀⢠⡿⠀⠀⠙⢧⠀⠀⠀⠀⠉ ⠀⠀⡌⠀⢠⠎⣠⠃⢠⠇⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠒⠚⢽⣆⣰⠟⠉⠉⠻⣦⠀⠀⠿⠇⠀⠀⢸⡆⠀⠀⠀⣸⡇⠀⠀⠐⣶ ⠀⡰⢁⠔⢁⡴⠁⠀⡜⠀⠀⠀⠀⠈⠙⡄⠀⠀⠀⠀⠀⠀⠀⠑⢢⡄⠙⣷⡄⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠻⢦⡤⠴⠟⠁⠀⠀⠀⠉ ⡴⡥⠦⠔⠁⠀⠀⣰⠁⠀⠀⠀⢀⣠⣤⠬⢷⣄⡀⠀⠀⠙⠻⣍⠁⠀⠀⠈⠷⣶⣄⣀⣽⢷⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⣠⢟⣿⣋⣡⣿⣻⠛⠓⢾⣏⠉⠁⠀⠀⠀⠀⠀⠙⢿⠛⠛⣛⣷⣬⡝⣲⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀ ⠀⠀⠀⠀⣀⡞⠀⡔⡶⠛⠉⠉⠉⣹⣧⣼⣿⠛⠀⣤⡴⢿⠷⣤⣀⠀⠀⠀⠀⠀⠀⢱⡾⠏⠁⠉⠉⠋⠉⠉⠉⠛⠻⣷⣶⣞⠁⠙⠢⢄
⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀ ⠀⠀⢀⣴⠟⠋⠉⠉⠉⠉⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠉⠉⠉⠉⠙⠻⢷⣄⠀⠀ ⠀⣴⡟⠁⢀⣤⡶⠞⠛⠷⢶⣄⠀⣻⣧⣴⠶⠞⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠛⠷⢶⣴⣿⡁⣠⣴⠾⠛⠛⠶⣦⣄⠀⠹⣧⠀ ⢰⡟⠀⢠⡿⠁⠀⠀⠀⢀⣠⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣄⠀⠀⠀⠈⢻⣆⠀⢹⣇ ⢸⡇⠀⢸⡇⠀⠀⣠⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀⠀⠀⣿⠀⢸⣿ ⠘⣿⡀⠘⣧⣀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣸⡏⠀⣼⡇ ⠀⠘⢷⣄⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣀⣼⠏⠀ ⠀⠀⠀⢹⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀ ⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠠⣿⣇⣨⣿⣷⠀⠀⢀⣠⡶⠟⠛⠛⠛⠷⣦⣄⠀⠀⢰⣿⣅⣸⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡿⠏⠀⣴⡟⠋⠀⠀⠀⠀⠀⠀⠈⠹⣷⡀⠈⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⢀⣀⣤⣤⣤⣄⡀⠀⠀⣾⠋⠀⠀⠀⢰⣶⣶⣶⠀⠀⠀⠈⢿⡄⠀⢀⣠⣤⣤⣤⣀⡀⠀⠀⠀⢀⣿⠀⠀ ⠀⠀⠘⣿⠀⠀⠀⠿⣿⣿⣿⣿⣿⠿⠀⣸⡇⢠⣦⣀⠀⠀⣹⣿⡃⠀⠀⣀⣤⠘⣿⠀⠿⣿⣿⣿⣿⣿⠿⠀⠀⠀⢸⡟⠀⠀ ⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠉⠛⠛⠛⠋⠉⠛⠻⠛⠋⠁⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀ ⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠶⠶⠶⠶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⢶⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⡶⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣉⣤⣤⣤⣉⠛⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣠⣴⡾⠟⠋⠉⠉⠉⠓⠀⠹⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢁⣠⣶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣠⣴⣾⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⣿⣿⡿⠋⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿ ⣿⣿⡿⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿ ⣿⡿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⣀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⢁⣤⡶⠟⠋⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡀⢻⣯⡙⠛⠛⠋⠁⣀⣤⠾⠛⢁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣄⡙⠻⠿⣶⠶⠿⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠸⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⢻⡄⠀⠀ ⢀⠀⠀⠀⠀⡞⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠈⢧⠀⠀ ⠀⠀⠀⠀⢰⢁⠀⣇⠀⠀⠀⠀⠀⠈⠀⠐⣄⡀⠀⠀⠤⢤⠊⢮⠢⡄⠀⠘⡇⠀ ⡀⠀⠀⠀⡎⡜⣄⣌⣆⠤⡂⡄⠀⠀⠆⢄⠙⡛⠲⡔⢳⢊⠁⢛⣾⠁⠀⠀⠁⠀ ⠁⠀⠀⠀⣧⣁⣈⡳⡀⠑⠜⠾⢔⡤⣘⡀⠉⠻⢍⡉⠉⠀⠺⡑⢼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠿⣽⣿⡀⠀⠒⠒⠂⠀⠉⠢⢴⣵⣶⣻⣷⣦⣬⢺⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⢃⠀⡿⡯⣻⠀⠀⠀⠀⠀⠀⠰⣿⣽⣻⣽⡍⠛⣿⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡆⠐⠪⠽⠉⠀⠀⠀⠀⠀⠀⠀⠀⣻⡥⠚⣀⡀⠁⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠉⢀⢜⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠰⡲⣟⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠏⠀⠀⠀⠀⠀⠀ ⢠⡀⡀⠱⣄⠹⢇⡑⠠⡀⠘⠏⠙⠽⠀⠀⠀⠀⠀⠀⡀⡴⠋⠀⠀⢀⠄⣀⠀⡆ ⠀⢳⣿⡦⣄⣁⣦⠤⡝⣫⣑⠤⣀⣀⡀⠠⠤⠐⠈⢡⡮⠀⠀⢀⣴⡫⠔⠉⠢⣱ ⠀⠀⠈⠉⠉⣁⠤⡰⠒⡩⡽⠋⢩⣿⠄⠠⠄⠄⢊⠩⠒⠒⢻⣍⣴⣤⡀⢀⣀⠀ ⠀⠀⠀⢠⠎⠀⢠⠁⡴⡱⠀⠀⠈⠅⠀⢀⠠⠂⠁⠀⠀⠀⡘⠘⠀⢀⠀⠁⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⢀⣀⣀⣤⣀⣀⣾⣿⣟⣉⣛⣛⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠤⠤⡀⠀⠀⠀⠀⠀⠻⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠋⠀⠀⠀⠘⡀⣄⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⡇⢳⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⣀⣀⣀⣀⡀⡾⢛⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠉⢛⣋⡛⠁⢳⣾⣿⣿⣿⣿⣿⣿⡟⠀⠹⣿⣿⣿⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣄⣀⠀ ⠇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠁⠴⠒⠉⠀⠘⣿⣿⣿⣿⡎⢷⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⠃⠀ ⠘⡄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⠈⢧⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀ ⠀⠳⢄⣀⣀⣾⣿⣿⣿⣿⣿⣿⠀⠀⢀⣠⣤⣀⠀⠀⠀⠻⣿⣿⠀⣴⣢⡤⠀⠘⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⢻⣿⣿⣿⣿⡎⢀⣼⡿⠟⠋⠁⠀⠀⠀⠀⠈⠱⠀⠀⠉⠙⠛⢶⣼⣿⣹⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡇⢸⣿⣿⣿⣿⠓⢻⡽⠀⠀⠀⠀⠀⢀⡠⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠸⠸⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠀⠳⣿⣷⣿⡇⠀⠀⠀⢀⡀⠀⡇⢀⡀⠀⠀⠀⢈⠀⠀⠀⠀⢀⣠⣾⡇⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⡄⠀⠸⣏⠹⣷⡀⠀⢠⠋⡈⢠⠋⡱⠁⣀⡀⠀⡼⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠘⡆⢠⠟⣷⢦⣿⠢⣬⠀⣧⠃⢸⡡⢊⡴⠃⠈⠀⠀⢀⣠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣡⠎⠀⢩⣸⣿⡄⠹⠐⠀⠀⠀⡀⠺⠚⣡⣾⠶⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠐⠁⣻⣿⣄⠀⠀⠀⠀⠀⢠⡏⠉⠁⢰⢻⣿⣟⣻⣿⣿⣿⣿⣿⡄⠀⢰⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠓⡏⢹⠀⠀⠀⠀⠀⢸⠁⠀⠀⠘⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣦⡏⢇⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣆⣸⡃⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⠀⠀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣴⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠤⡀⠀⠀⠘⢶⣶⣾⣿⣿⣿⣿⣿⣿⣾⣷⣄⠀⠀⠀⠀⠀ ⡎⠀⠀⢰⢔⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⢠⣤⣤⣼⢻⣿⣿⣿⣿⠻⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣆⠀⠀ ⠀⠐⠀⢀⣿⣿⣿⣿⠇⠀⢹⣿⣿⣿⡇⡘⣿⣿⣿⣿⣿⣿⢄⡀ ⠆⠀⠀⢰⣿⣿⣿⡟⠐⠁⠀⠹⣿⣿⠸⡀⠙⣿⣿⣿⣿⣿⠔⠀ ⠘⠄⢀⣾⣿⣿⡿⠃⣀⣤⡄⠀⠘⢿⠇⢤⣄⡘⣿⢿⣿⠏⠀⠀ ⠀⠀⠘⡏⣿⣿⡿⢴⡏⠁⠀⠀⣀⣀⠁⠀⠀⠙⠛⣾⡏⠀⠀⠀ ⠀⠀⠀⡀⠿⡿⣇⠀⠀⠀⢠⠀⠀⠀⠰⠀⠀⠀⢀⡷⠀⠀⠀⠀ ⠀⠀⠀⠁⠈⢟⢻⡄⢀⢂⠨⠢⢀⡀⡰⠀⠀⢰⣿⡇⠀⠀⠀⠐ ⠀⠀⠀⠀⢃⠎⡏⣮⢲⠘⠃⠓⡔⢅⣄⣤⣶⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠢⢈⣸⣦⠀⠀⠀⠰⠉⢡⣻⣿⣿⣿⣿⣧⢀⡆⠀ ⠀⠀⠀⢀⣤⣾⣿⣏⡔⠀⠀⢀⠂⠀⠀⣿⡏⣿⣿⣿⣿⣿⣤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⣵⣶⣿⣿⠉⢍⢠⡈⠻⠶⣬⡙⢷⣮⠙⠿⣿⣷⣶⣄⠀⠀⢀⣠⢖⡡⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠒⠤⠄⣈⡑⠢⠤⢀⡴⠛⣵⣿⣿⠟⠉⢹⡶⠈⣌⢻⡄⠀⠘⣿⣷⣹⣷⣄⠹⣿⠛⢻⣷⣶⡯⠶⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⠟⢲⡞⠁⣼⣿⣿⠏⠀⢠⢸⣇⡀⣿⡎⢿⣆⠸⡌⠻⣿⣿⣿⣧⠈⢷⡀⡿⣝⣧⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⢀⡞⠀⣼⣿⡿⢃⠀⣠⠏⣼⣿⡇⢿⣧⢘⣿⣿⣧⠀⠙⠿⣿⣿⣷⡈⢷⡀⠘⣞⢧⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣷⡾⢡⢤⣯⣿⢣⢎⣾⡟⢠⣿⡿⣿⢸⡏⢿⣿⣿⣿⣷⡀⠘⣿⣿⣿⣷⡈⢷⡀⠘⣯⣳⣦⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣧⡟⣟⣾⣯⡟⣼⢻⢃⣿⡿⠁⠸⡌⣿⡀⠻⣟⣿⣿⣿⣄⠈⢿⣿⣿⣿⣌⢿⣄⠘⢷⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⢹⣿⣿⢿⢱⡇⢸⣿⡿⠁⠀⣀⣷⣿⣧⠀⠙⢦⡙⠻⣿⣷⣦⣻⣿⣿⣿⣎⣿⣦⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⢧⣿⣿⡿⠈⢸⢇⣿⣿⣡⠔⠊⠁⠀⢳⣿⡆⠀⠀⠙⢦⡈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣧⡀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣼⣿⣿⣯⢇⣿⣸⣿⠁⠀⢀⠀⣀⠀⠀⠻⣿⡄⠀⠀⠀⢛⣽⢧⣤⣌⡿⣿⣿⣿⣿⣿⣿⣆⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⢿⣿⡇⣸⠃⢀⣾⣿⣿⣦⡀⠀⠀⠙⢿⡄⠀⠀⢼⣅⣼⣿⣿⡿⣯⣽⣿⢻⣿⣿⣿⣷⡀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⡇⣿⢙⣿⣏⣠⣿⣿⡇⠀⠀⠀⠈⠻⣆⠀⠸⡿⢿⣿⣿⠇⢹⠿⣿⡈⣿⣿⣿⣿⣿⣷⣾⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⠸⣿⣷⣿⣿⡇⢿⠿⢿⡟⡋⠀⠀⠀⠀⠀⠈⠣⡀⠑⢤⣤⣶⠀⠀⠀⣿⡇⣿⣿⣿⣿⢹⡟⠿⣿⣿⣷⣤⡀⠀ ⠀⠀⢠⣿⣿⠏⣿⣿⣿⢀⣿⡏⣿⠉⠛⠊⠳⣤⣶⠇⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⣷⣷⡀⠀⠈⠉⠉⠙⠓ ⢀⣴⣿⣿⠃⠀⣿⣿⣿⢸⣿⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⡏⠿⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⠋⣸⡿⠁⠀⠀⣿⣿⣿⣿⣿⡄⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⣿⣿⣿⣿⣦⣤⠟⠋⠉⠒⢦⡀⠀⠀ ⡴⠏⠀⠀⠀⠀⣿⡿⠋⢹⣿⣇⠘⣇⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⣿⣿⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠁⠀⠀⢸⣿⣿⡄⢹⡄⠀⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠀⠀⠀⠀⠈⣿⠻⣿⣟⣿⣄⠀⠀⠀⠉⢲⡤⢄⡀⠀⠀⠀⡠⠞⡟⠀⣠⠀⠀⣾⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡄⠈⠻⣿⣿⠓⠤⠀⠀⠀⠙⠦⣈⠉⠒⠉⢀⡞⢀⠜⠁⠀⣸⠟⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⢂⠀⠀⠀⠘⠆⠀⠀⠉⠓⣄⠀⠀⠀⠀⠀⠀⠉⢲⣤⣞⡊⠁⠀⠀⠚⠁⢰⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣇⠀⠈⢆⢀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⢠⠋⠘⡄⠈⠢⡀⠀⠀⢀⠇⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⡟⣆⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⢠⠃⠰⠲⡜⡆⠀⠈⠢⣠⠎⠀⣿⡟⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡄⠀⠀ ⠀⠀⠀⣿⣿⠁⣿⣦⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠃⠀⠘⠂⠃⠸⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⣿⣿⠀⣿⣿⣷⡄⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢠⣿⠀⠀ ⠀⠀⠀⣿⣿⠀⢻⣿⣿⣿⣦⣄⠀⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⢀⡜⢁⠄⠀⠀⢸⣿⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢘⡆⠀⠀⠀⣀⣤⣤⣤⣂⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣆⠀⢀⢔⣾⣯⣶⣿⣿⣿⣿⣿⠛⠉⢉⠞⢀⣾⠀⠀⠀ ⠀⠀⠀⠉⠉⢹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⡟⠀⠀⠀ ⢀⣄⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⡀⠀ ⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄ ⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⠕⠀⠀ ⠘⠁⢸⣿⣿⣿⣿⣿⣿⡟⠏⠀⢰⣿⣿⣿⣿⣿⠈⢿⣿⣿⣷⡈⠂⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⡏⣀⣈⣥⣄⢻⣿⣿⣿⣿⣐⠈⣿⣿⣿⡧⠔⠀⠀ ⠀⠀⠈⠙⢿⡿⢿⣿⢧⠀⠁⢀⠠⠀⠟⠁⠈⠉⠛⠋⢿⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⠐⡶⠝⢀⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠢⣸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⠤⠍⠡⢄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⠀⠀⡖⠒⠋⠁⠀⠀⠀⠰⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠎⠐⠠⢇⡀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠈⠑⠂⠽⠮⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⣠⡦⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣴⠋⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠎⡀⠀⠀⠀⡼⠁⠀⢠⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠃⡔⠀⠀⢀⣼⠃⠀⠀⡼⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⢇⠞⠀⠀⢀⣾⠇⠀⠀⢠⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⠑⠀⠀⠀⣼⣿⠀⠀⠀⣼⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠰⠣⢤⡴⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀ ⠀⠀⠀⢠⠏⡗⠀⡀⠀⢰⡟⣿⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⡄⠀⢣⠀⠀⠀⠀⠀⢧⣠⠀⠀⠀⠀⢠⠀⠀⢿⡆⠀⠀ ⠀⠀⠀⡞⢸⠁⢠⠁⠀⣿⢁⣻⠀⠀⠀⢸⠀⠀⠀⡄⢸⠀⠀⠀⠘⡀⣸⡀⠀⢧⠀⠈⢣⢄⣀⠠⢴⠊⠙⡇⠀⠀⠀⠀⣇⠀⢸⣧⠀⠀ ⠀⠀⠀⡇⣸⠀⠐⠀⢸⡟⠉⣛⡇⠀⠀⠈⡄⠀⠀⢿⠈⡄⠀⠀⠀⢃⠈⠁⠁⠘⡆⠀⠈⡎⡇⠀⠘⡄⠀⢱⡀⠀⠀⠀⢸⠀⢸⣿⠀⠀ ⠀⠀⢸⡇⡟⡆⠀⠀⢸⠁⠀⢿⢸⠀⣦⠀⣇⠀⠀⠘⣇⠘⡀⡄⠀⠘⡆⡇⠀⠀⢹⠀⠀⠇⡇⠀⠀⡇⠀⠀⠑⢄⠀⠀⠀⡇⢸⢹⠀⠀ ⠀⠀⠈⣧⡗⡀⢰⠀⢈⢀⣤⣾⣿⢦⡽⠶⠼⣆⡘⣄⠘⢧⣀⠘⣤⢔⣺⣿⣶⣤⣄⣷⠀⠀⢇⠀⠀⡷⣄⠀⠢⡀⠑⠤⠄⣁⣇⣾⠀⠀ ⠀⢀⣤⣾⣷⡷⣸⣀⣾⣿⣿⣿⠿⢻⣿⡄⠀⠈⠉⠉⠁⠀⠉⠛⣿⣿⡿⠟⢿⣿⣿⣿⡄⠀⢸⠀⠀⡷⣌⠑⠢⣬⠶⣴⣾⣿⣿⣇⣀⣀ ⣰⡿⢻⠟⢻⡇⣿⣿⣿⣿⡿⠀⠀⠀⠰⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁⠀⠈⠬⢿⣿⣿⣧⣸⠀⠀⡇⠈⠑⠲⠤⢀⣷⣿⡿⣿⣶⣋⠉ ⠱⠁⣎⣀⡜⢇⠙⠛⣿⡃⠀⠀⠀⠋⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠂⠀⠀⣿⣿⠛⠻⠀⢸⣷⣏⠳⡄⠀⠘⣿⣇⣧⡏⠹⡉⠀ ⣳⣀⣽⠛⢁⣼⡆⠀⢸⣧⠀⠳⠤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⣤⣀⡖⠚⢹⣿⠀⡄⠀⣼⢯⣄⣁⣷⣀⣸⣿⣿⠃⢱⡀⠙⠦ ⠳⠭⢤⡒⢁⣼⣿⡀⡀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠃⢠⣏⣤⡀⢀⠟⠋⡱⠻⣯⠀⠈⢿⣠⣠ ⠀⠀⣄⣀⡠⡞⠏⢷⣧⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⢀⣼⠋⠤⠔⠊⣠⠞⠀⠀⢿⣆⠀⠀⠉⠉ ⠀⠀⠈⠛⠋⠁⠰⡘⣿⡏⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢀⣾⡏⠀⣀⡠⠚⠁⠀⠀⠀⠈⠛⠒⠶⠶⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⠘⣷⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢋⣿⠇⣠⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⡀⠀⠉⠓⠤⣀⠀⠀⠀⣀⣀⣀⠤⡴⠖⠋⡱⢃⣾⣏⡔⠁⠀⠀⣀⣀⣀⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠑⠲⢄⡀⠀⠀⠀⠀⠙⠛⠓⠀⠀⠀⣀⣈⣉⣉⣿⣅⣔⣁⣀⠒⠛⠓⠛⠉⠁⢉⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠢⠄⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠤⠬⢣⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡴⠋⡉⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣶⣶⠶⠾⠿⠿⢿⣦⣦⡙⢶⣶⢦⣄⠀⣦⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠛⠛⢿⡁⠀⠀⠀⠀⠀⠠⢀⡈⠛⠲⠿⢿⣟⠛⠻⣶⡦⢄⡀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣈⣟⣳⣤⣄⣀⡤⠞⠁⠀⠀⠀⣀⠀⠀⠈⠂⠀⢀⣠⠤⠤⠤⠠⠤⠤⢄⣈⣻⠿⢿⣆⣙⠛⠃⣬⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠙⡿⠀⠈⣏⠀⠀⠀⠒⠈⣉⡭⠶⠒⡒⠋⠉⠉⠀⠀⠀⠀⠀⠐⠤⡀⠈⠉⠓⠲⢬⣉⠻⣤⣩⣙⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣻⡤⠀⠀⡠⠛⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠙⠀⣾⠏⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⠀⠈⣷⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡾⠀⢠⣿⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⣴⡟⣿⠁⣰⠋⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⣿⢷⡤⢄⣠⡶⣾⣿⣴⠏⠀⣿⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠘⠿⣷⣶⡶⣿⣺⣿⣿⣧⣀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠿⣿⡇⠈⠉⠀⡿⠉⠁⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡏⠙⠒⢒⣾⠃⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⣇⠀⠀⡀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⢠⢿⠿⣤⠀⢸⠁⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢹⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣰⡞⠀⢹⡀⢠⣿⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡇⢀⡾⡏⠀⢸⡆⡿⠀⣴⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣰⠇⠤⠀⠹⣄⠀⠀⠀⢻⣆⠀⠀⢀⣸⡿⠁⠀⢸⣧⢿⡿⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⡸⣻⠀⠀⠀⢳⠃⢠⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣰⣿⣶⡶⠿⠦⡌⠛⠶⠤⠼⠏⠓⠤⠾⠃⠀⣀⣴⣿⣿⣿⣇⡇⠀⢀⡄⠀⡀⠀⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⣷⠇⠀⠀⠀⢸⡇⡞⡟⢹⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠋⡠⠖⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠉⠉⠉⢸⣿⢀⣠⢾⠀⠀⢱⣄⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⡟⣷⡇⡏⠀⢀⡏⠀⠀⠀⠀⠀⣤⣤⣾⣿⡟⠀⡞⢁⣠⣶⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⣼⣿⣯⣄⡼⠀⠀⢸⡟⣆⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⣻⡇⠻⡇⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⣏⢹⣿⡟⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⣙⣬⣿⣿⣷⣤⣄⣸⠁⠹⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢠⣿⣷⣤⢃⡞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠻⢿⣿⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠉⠉⠁⠉⠉⠀⠀⠉⠙⠳⣤⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠟⡇⠀⠀⠀⠀⠀⡼⣼⡿⣾⡜⠁⢸⡄⠀⠀⠀⠀⠀⠀⠹⣦⣄⡈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠆⢀⣴⣿⡿⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠃⠀⠶ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⢃⢏⠁⣿⣇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣭⣍⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣠⠞⣹⡏⢁⣀⣤⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⣰⠃⡼⢸⠀⡟⠘⢦⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣽⡭⠭⠽⣶⠶⢤⣤⠴⢶⣶⠟⠁⠀⠿⣦⣽⣵⠟⠛⠁⠀⠀⢠⣤⠶⣤⡀⠀⠀⠀⠀⠙⡿⢂⡀ ⠀⠀⠀⢼⠃⠀⠀⠀⡰⠃⡸⠃⡿⠀⣷⠀⠀⠉⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣀⡈⠓⢮⡙⣿⣿⠀⠀⠀⠀⠀⠀⢈⣾⡧⠀⠀⢠⡿⡃⠀⠈⠙⣧⡀⠀⠀⠀⢡⣀⠋ ⠀⠀⠀⡼⠀⠀⢀⡜⠁⣰⠃⢰⠇⠀⠙⣆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠲⣤⢀⣀⣀⡴⢾⠁⠀⣠⡿⠿⠿⡷⣦⠀⠀⠀⢰⢻⡇⠀⠀⠀⣾⣋⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⣄⣀ ⠀⠀⢰⠃⠀⣠⠏⢀⡜⠁⠀⡼⠀⠀⠀⠈⠓⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠙⠾⣆⣾⠋⠀⠀⠀⠀⢹⣧⠀⠀⠈⠛⠃⠀⠀⠀⢻⣯⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠈⣿ ⠀⢠⠏⢠⠞⠁⣠⠟⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠓⣢⠄⠙⢷⣶⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⠶⠛⠋⠀⠀⠀⠀⠀⠉ ⣠⢏⣴⣁⡤⠞⠁⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢀⣠⣄⣙⣦⡀⠀⠀⠀⠀⠙⠳⣶⠒⠉⠁⠀⠀⠈⠻⣦⣤⢀⠀⢀⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠁⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⢠⣾⢿⣪⠿⠀⣿⡿⡷⢤⣄⣤⡤⠴⠴⠋⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⢾⡿⣿⣆⣉⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣀⣀⣰⣛⣱⣿⠶⠶⢾⣯⣼⡇⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⠀⣠⣤⡼⢿⣿⣧⣨⣿⣶⣄⣀⣀⣀⣀⡀⠀⠀⣀⡀⣴⡙⠻⠶ ⠀⠀⠀⠀⢀⣀⣴⠇⠀⡴⣻⠟⠋⠉⠀⠀⢁⣰⣯⣖⢾⣶⠛⠁⢠⣴⡶⠿⣿⠿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡻⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⢹⢿⡟⣿⣏⠀⠈⠙⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠶⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀ ⠀⠀⣠⣾⡿⠀⠀⠀⠀⣴⣿⣏⣹⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣹⡆⠀⠀⠀⠀⢻⣷⣤⡀⠀ ⢀⡾⢡⣾⠃⠀⠀⠀⠀⠹⣿⣿⠿⠀⠀⣦⠀⠀⢠⡆⠘⢿⣿⡿⠃⠀⠀⠀⠀⠀⢻⣿⢿⡄ ⢸⣇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣧ ⣼⠿⣷⣟⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣿⣿⠟⣿ ⢿⡀⠈⠙⠻⢶⣭⣟⣿⠶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡶⢾⣛⣯⡷⠿⠋⠁⠀⣿ ⢸⡇⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠶⠶⠿⠶⠤⠴⠴⠾⠿⠟⠒⠛⠛⠋⠉⠁⠀⠀⠀⠀⢀⣿ ⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇ ⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀ ⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀ ⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⡷⠶⣤⣤⣀⣀⣀⣀⣠⣤⠴⠶⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⠶⠶⠶⠶⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⡿⠿⣿⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⠿⣿⣶ ⢸⣿⠃⠀⠀⠀⠈⠉⠙⠛⠿⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠟⠛⠋⠉⠁⠀⠀⠀⠸⣿ ⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⣴⣶⣾⠿⠿⠿⠟⠛⠛⠛⠿⠿⠿⢿⣶⣶⣤⣴⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢻⣿⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⣿ ⠸⣿⡆⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢸⣿ ⠀⢿⣷⡀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⢀⣿⡟ ⠀⠈⣿⣧⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣾⡿⠀ ⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀ ⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀ ⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀ ⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⠀⢻⣿⡀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠁⠀⠈⠙⣷⣤⢾⠂⠀⠀⠀⠀⣿⡟⠀ ⠀⠀⠈⣿⣧⠀⠀⠀⠸⢯⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠀⠀⠀⠀⠀⠸⠷⠞⠃⠀⠀⠀⣸⣿⠃⠀ ⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⢤⣀⣀⣦⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢯⣏⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠿⢿⣶⡀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠈⢿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⡇⠀⢰⡆⠀⠀⠀⢰⡄⠀⠀⠀⢠⡆⠀⠀⠀⢰⡆⠀⢸⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠙⣿⡀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⢀⣿⠉⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣶⣾⣿⣾⣷⡀⠀⢀⡿⠁⠀⠀⠀⠈⢿⡀⠀⠀⣾⣷⣿⣷⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠿⣿⣶⣶⣶⣶⣶⣿⣿⣶⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢤⣦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀ ⠀⢿⣿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⢿⡿⠁ ⠀⢸⠀⠁⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⡿⠃⠀⢸⡀⠀ ⠀⢸⠀⠀⠀⠈⣎⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣟⡀⡇⠀⠀⠀⡇⠀ ⠀⢸⠀⠀⠀⠀⢸⣄⠹⣿⣿⣿⣦⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢠⣾⣿⣿⣿⣿⣫⣾⡇⠀⠀⠀⣷⠀ ⠀⣾⠀⠀⠀⠀⠘⡜⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⢽⠁⠀⠀⠀⣿⠀ ⠀⢸⠀⠀⠀⠀⠰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⣄⡀⠀⠀⣿⠀ ⠀⢸⡆⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⠀⠀⢰⣿⠀ ⢳⡸⣿⣤⣄⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⢴⣿⣳⠀ ⠠⣽⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣡⠏ ⠤⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠄ ⠀⠰⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠄ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠊⢻⠈⢿⣿⣿⣿⣿⣿⣿⡏⠙⢻⡇⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡏⠘⡇⠀⠀⠸⡄⠈⣿⣿⣿⣿⣿⡏⠀⠀⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣶⣶⣤⣀⠡⠀⠈⢻⣿⣿⣿⠀⢀⣤⣶⣶⣦⣄⣿⣿⣿⡟⠛⢻⣿⣿⣧⠀ ⠴⠛⠁⠈⣿⡀⠉⢻⣿⣿⣿⣿⢹⣾⣿⣿⣿⡆⠀⠀⠙⢿⡄⠀⢿⣽⣿⣿⡏⣿⣿⣿⡟⠀⢀⣾⠇⠀⠉⠛ ⠀⠀⠀⠀⠈⣷⡀⠈⢿⣿⣇⠘⠘⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡽⠛⣣⣿⣿⠃⢀⣾⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠟⠙⢦⣌⡻⣿⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣥⡶⠋⠛⠧⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⣿⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢟⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣬⣁⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⢓⢤⣀⠀⠀⠀⠶⠿⠷⠀⠀⠀⣀⣤⣾⣿⢿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢃⡞⣰⠈⠓⢦⢄⣀⠀⣀⣠⣴⠞⠁⢸⠇⣿⡀⣿⠿⣿⣿⣿⣿⣿⣷⡄⠀ ⠀⠀⠀⣿⣿⣿⠟⠋⠉⠉⠉⠣⣼⠃⣟⠂⣄⠈⠳⡍⠉⢉⡾⠁⠀⠀⡿⣸⡟⠋⠀⠀⠈⠉⠹⣿⣿⣿⡇⠀ ⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⢻⣦⠙⢇⠀⠉⣶⢿⠀⡿⣆⠈⠁⣰⣇⣿⣧⡀⠀⠀⠀⠀⠀⠈⣿⣿⠇⠀ ⠀⠀⠀⣿⣧⠀⠀⠀⠀⢠⠴⠶⢾⣿⠆⡌⠆⣰⣧⡄⣤⣠⣿⡀⣰⢻⣷⣮⣉⡀⠀⠀⠒⠲⠆⣰⣿⣿⠀⠀ ⠀⠀⠀⢻⣿⡈⠙⠛⠛⠛⣀⣐⣤⣶⣿⣯⠈⠀⠘⣿⣷⣿⠏⡟⠁⣸⣿⣿⣿⡟⠻⠥⠴⠶⠾⢻⣿⣿⣆⠀ ⠀⠀⠀⣸⣿⣟⠒⠠⠄⠂⣠⣿⣿⣿⣿⣿⡄⠀⠀⢻⣷⣿⠀⠀⠀⣿⣿⣿⣿⣿⣄⠀⠀⢀⣴⣿⣿⣿⡏⠀ ⠀⠀⢠⣿⣿⢿⣷⣦⣤⣾⣿⣿⠙⢿⣿⣿⣷⡀⠀⣸⣿⡿⡄⠀⢰⣿⣿⡿⢋⣿⣿⣷⣶⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠘⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣷⠀⣟⣽⣾⣿⢠⣿⡿⠋⣰⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⡆⠀ ⠀⠀⢠⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⡿⣿⣿⣿⣿⣿⡿⢋⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⣿⣿⠇⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀⣠⡾⢛⣦⣄⣰⠶⣆⣾⡙⣶⡤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⢤⣀⣿⡄⡟⠁⡇⢸⡅⠈⡿⠀⣿⡏⠹⡿⠀⢿⡏⠙⣆⠀⠀ ⠀⠀⢠⡖⢲⡸⡅⠈⣿⠇⢷⡇⢸⡇⠀⣇⠀⡇⠀⢻⣷⠀⢷⠀⣼⠀⢰⠇⠀⠀ ⠀⠀⠘⣧⠀⣇⢧⠀⢸⡄⠸⡇⢸⣷⠀⢿⠀⣷⠀⡿⢹⠀⢸⣤⡇⠀⣾⠓⢦⠀ ⢠⡞⠳⡿⣄⡸⣼⡆⢸⡇⠀⡇⠀⣿⡄⢸⠀⢹⢰⡇⢸⡆⠘⣿⠁⢀⡏⠀⣼⠀ ⠘⣧⠀⣟⠉⣧⢹⡇⠸⡇⠀⣷⠀⣿⡇⢸⡇⠸⣿⠀⣼⡇⢠⡏⠀⢸⠃⢰⠇⠀ ⠀⠘⡆⢹⡀⠸⡆⢷⠀⡇⠀⢻⠀⢸⣿⢸⡇⢀⡏⢰⣿⡇⣸⠁⠀⣾⠀⣿⣄⠀ ⢀⣴⢿⡄⢧⠀⢹⣼⡀⣻⣀⣘⣧⣀⣿⣼⣇⣼⣅⣾⣸⣧⡏⠀⠀⡏⢸⣧⠈⢳ ⣾⠁⣿⣷⡘⣦⡴⠿⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣤⣰⡇⣿⡟⠀⢸ ⢹⡄⠙⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠟⠁⠀⣼ ⠀⢻⡄⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢀⡏ ⠀⠀⢻⡄⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢸⠇ ⠀⠀⠀⢻⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠈⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⡏⠀ ⠀⠀⠀⠀⢻⡄⢰⣿⡏⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⣱⡄⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢸⡇⠘⠿⡿⠿⠁⠀⠀⣶⡀⢐⣶⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⣼⠁⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀ ⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⣿⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡾⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠄⡀⠠⢀⠀⢀⣴⣿⣾⠿⣙⠴⠌⠓⣮⡳⣍⢻⡷⣦⣀⢄⣪⠂⠁⠀⠀⠀⠀⠀ ⠀⠀⠈⡶⢲⠃⣾⡿⠁⡀⣇⢸⡼⣆⡎⢻⣿⣧⠱⡌⢟⢅⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣥⢇⣘⡿⣵⡶⢱⡿⡾⡧⣽⣿⣄⠩⣿⣷⡘⡄⢫⣦⡸⡀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣮⣽⠻⡜⣧⡿⠁⢣⣧⠙⣝⢿⣦⡙⣿⣷⡝⣄⠻⣷⡇⠀⠀⠀⠀⠀ ⠀⠀⢸⡿⣽⡿⣆⢧⣿⠥⠒⠉⢻⡆⠈⠃⢉⡛⠿⣿⣿⣿⣧⡙⣧⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣷⣼⢸⠁⣤⣦⡂⠀⠻⡄⠀⢰⣛⣷⣾⣻⡿⣿⣷⣌⠣⡀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⡝⣧⣿⠧⠀⠀⠘⢆⠘⡛⢛⠃⠛⣧⣿⣿⡿⣷⣿⣦⡀⠀ ⠀⣠⣿⢻⣿⡇⡿⣿⠓⠑⠮⠞⠀⠀⠀⠀⠁⠈⠉⠀⠀⣿⣿⣿⣷⣧⠈⠉⠙⠒ ⢘⡿⠁⢸⣿⣷⣇⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣼⣿⣷⣙⡿⠃⠤⡀⠀ ⠚⠀⠀⡸⠛⢹⣿⡘⡌⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣿⣿⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⢰⠀⠀⠈⡟⢷⣻⣄⠀⠁⢢⠄⣀⢀⠠⡚⢀⠀⣸⢿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⢀⠀⠘⠄⠙⠳⡅⠀⠀⠁⠂⢄⣴⠐⠁⠀⢃⢻⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⢆⠈⢐⡀⠀⠀⠀⠈⠢⡀⠀⠠⢁⢃⠑⢄⢀⠌⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⢸⣦⠀⠳⡀⠀⠀⠀⠀⠈⠐⠁⠀⠂⠆⠀⠀⢰⡿⠀⠀⠀⠰⠁⠀⡇⠀ ⠀⠸⣿⠸⣿⣷⣄⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⢊⠀⠀⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠈⣧⠀⠀⠀ ⣠⢪⠏⠀⠀⢸⣿⡆⢀⡀⠀⡄⢿⣷⠇⠀⠀⠘⣿⣆⠀ ⣿⡻⣄⠀⠀⠀⠀⠀⠈⠛⠚⠁⠀⠀⠀⠀⠀⣀⣿⣼⠀ ⡇⠙⠻⠿⣷⣶⣤⠤⢤⠤⠤⢤⣤⢤⣶⣶⠿⠟⠋⢸⠂ ⢷⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣸⠀ ⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀ ⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠙⢲⣤⣄⣀⣀⣀⣀⣀⣤⡖⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠦⣄⣀⠀⠀⠀⠀⣀⣠⠴⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⢦⠀⠀⠀⠀⠙⠢⡀⠀⢀⠈⠱⡀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⡸⠁⠀⠀⢀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠘⢆⠀⠉⠂⡘⣦⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⢠⠄⠀⢠⠇⠀⠀⠀⢸⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢣⠀⠀⢙⣿⣇⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⡏⠀⠀⢸⠀⠀⠀⠀⠘⡄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢣⠀⢄⠈⢿⡇⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⡘⠀⠀⢰⠃⠀⠀⡞⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠈⡆⠀⠑⣾⣿⠀⠀⢀⣼⠟⣧⠀⠀⠀⠀⠀ ⠼⠀⠀⠀⠀⠀⢰⠃⡇⠀⠀⡾⡄⠀⠀⣷⠀⠀⠀⠀⠀⢸⢧⠀⠀⠀⣹⢿⠀⠀⠀⠀⠀⠀⢹⠈⠢⣼⣾⣇⣴⠛⠁⠀⢹⠀⠀⠀⠀⠀ ⠀⠀⢢⠀⠀⠀⢸⢸⠁⠀⠀⠃⡧⢄⣰⡿⡄⠀⠀⠀⠀⢨⣀⠷⣖⠉⢹⠀⣧⠀⠀⠀⠀⠀⠸⡆⠢⣀⣿⡟⢿⣤⣀⣀⣸⡆⠀⠀⠀⠀ ⠉⠒⢤⣧⠀⠀⢺⢸⠀⠀⢈⡆⢳⠀⢘⡟⢻⡂⠀⠀⠀⢹⠀⢀⣼⡷⣟⡛⠻⣶⣤⡀⠀⠀⠀⡿⣀⣸⠟⠷⡀⠙⠻⠿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠉⠓⠀⢸⢸⡄⠀⠘⡇⢸⣷⣾⢟⣲⠷⣤⡀⠀⢸⡆⠉⢸⠃⠀⢻⡄⢯⡿⠀⠀⢠⣴⠃⢹⠁⢠⡄⠘⣆⠀⠀⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡀⢸⣿⡇⠀⠀⢱⠈⣿⣁⡏⣈⣧⠈⠙⢤⡐⢇⠀⠸⣎⠛⣹⡇⢺⠁⠀⠀⣼⣿⢠⠃⢠⠟⡋⢠⠟⡅⠀⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠁⠀⣿⣿⣄⠀⠀⢧⢹⡈⢧⣉⡿⠀⠀⠀⠉⠺⠄⠀⠈⠛⠉⠀⠈⡇⠀⢀⣿⠏⢀⣀⣸⡞⢀⠇⠀⢡⠀⡇⠀⠀⠀⠀⠀ ⣤⠶⢻⡿⠿⠆⠀⠸⡇⢻⣧⠀⠈⣷⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡾⠇⠀⠉⠀⢀⣠⠜⠀⠀⠸⡄⡇⠀⠀⠀⠀⠀ ⠀⢀⣸⠃⠀⠀⠀⠀⠘⠀⠻⣧⡀⢹⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢹⠏⠀⠀⣨⢛⣿⣿⣿⠀⠀⠀⠸⣇⡀⠀⠀⠀⠀⠀ ⠾⢋⣥⣶⠟⠀⠀⠀⠀⠀⠀⠈⠋⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⢀⡴⠁⢸⣿⣿⣿⡄⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠉⠡⡿⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢸⣿⣿⢹⣇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⣦⣶⠿⠛⠋⠉⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠘⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡤⠤⢤⣀⣔⣶⠤⠔⣚⠭⢻⠘⡏⢱⣦⣄⣀⣀⣠⣴⣾⣿⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠗⢀⣉⣉⠹⠿⣾⡍⠀⠀⠈⡖⣷⠈⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠉⠙⢦⡀⠀⠈⢇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⢋⡠⠋⡁⠀⠀⡠⠟⠁⠀⠀⢀⣱⣿⣧⣸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⢠⠀⠀⠀⠱⡄⠀⠸⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠈⢀⠔⡏⠀⠀⡤⠊⠉⠀⠀⢸⠋⠉⢉⠹⡿⠋⢇⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠹⡀⠀⢣⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⢰⠃⠀⡜⠀⠀⠀⢠⠀⠙⣤⠞⢡⠞⠀⢀⡼⠀⠀⣀⡠⢾⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⢣⠀⠘⡆⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⢸⠁⠑⢄⠀⢸⢀⠔⠁⣰⠁⠀⠀⠘⠃⠜⠁⠀⢀⡆⠀⠀⢀⡠⠒⠉⠁⠉⠑⢄⠀⠀⠈⡆⠀⢹⠀⠀ ⠀⠀⠀⠀⠀⣠⡆⠀⠀⠼⣿⣧⡇⠀⠀⠀⠑⡷⠋⢀⡜⠉⠦⣀⡀⠀⣀⡠⠔⠊⠉⡇⡠⠖⠁⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⢱⠀⠀⣇⠀ ⠀⠀⠀⠀⣼⣷⡇⠀⢀⠜⣡⣿⠃⠀⠀⢀⡜⠁⢠⠎⠀⠀⠀⠈⢉⡉⠁⠀⠀⠀⢸⡇⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢸⠀⢇⠸⡀ ⠀⠀⠀⠘⣧⡉⠓⠒⢁⠜⠩⣇⢀⠀⣠⠎⠀⣠⠃⠀⠀⠰⢀⠔⠁⠀⠀⠀⠀⠀⡟⡇⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⢸⠀⡇ ⠀⠀⠀⡴⣇⠈⠁⠀⠉⢀⠀⡼⠠⡶⠉⠉⠈⠉⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠁⡇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⡄⠀⡇⢸ ⠀⠀⠀⢦⡈⣉⡡⠖⠊⠁⠀⣑⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⢛⣷⠀⡇⠘
⠀⠀⠀⠀⢀⡠⠴⠒⠒⠢⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀ ⠀⣼⡧⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠀⠀ ⡞⠉⢠⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⡀ ⣟⠒⠛⠢⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣣ ⠀⠉⣲⠤⣄⣀⣀⣀⣀⠀⠀⠀⡀⠀⠀⣦⠤⢴⣖⢊⣽⡄ ⠀⠀⠙⡾⠁⣴⡄⢀⢀⠀⠀⠀⢈⣅⠈⠁⠀⠀⣇⢹⣻⠀ ⠀⠀⠀⡇⠶⠉⠀⠈⠊⠓⠊⠀⠘⠛⢠⠤⠀⠀⡏⠀⠁⠀ ⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀ ⢦⣶⡶⠸⡈⠙⠢⠤⣀⣀⡀⠀⢀⣀⡠⡴⠊⠁⠀⠀⠀⠀
⣤⠀⣰⣿⠋⠀⡇⠀⠀⠀⠀⢸⠁⠀⠀⠈⠛⣗⠢⠤⠊⠉⠣⡀⡈⡇⠀⠀⠉⠣ ⢰⣾⣿⠟⠀⠀⠇⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢅⠘⢄⠀⢀⡀ ⠀⠉⡍⡇⠀⠀⣴⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⢸⡀⢄⣒⡠⠤⠤⠀⣣⡀⡩⢝⢕ ⠀⠀⣿⠁⠀⠀⢿⡀⠀⠀⠀⡇⠀⢀⡠⢄⣒⠌⠟⠉⠀⠉⠉⠉⢹⣿⣵⣾⢿⣥ ⠀⠀⢸⡶⢄⣸⡽⠁⠀⠀⠀⡧⣲⢵⣮⠗⠁⠀⠀⠀⠀⠀⠀⠀⢸⢁⣢⣜⡼⠟ ⠀⠀⠈⡿⠵⠶⢭⣄⣒⣒⣚⣿⣿⣿⠁⡞⠁⠀⢀⠎⡅⠀⠀⢠⠋⠉⠀⠀⠀⠀ ⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⡧⠃⠈⠀⠊⠀⠧⣀⠀⡌⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠀⠀⡤⡀⠀⢠⢤⠀⠀⢇⠀⠙⠁⠄⠘⠓⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⠄⠃⣇⠀⢸⠉⠤⢜⢸⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠀⢠⠆⠀⠠⠶⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠌⡨⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⡇⠇⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡆⣧⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣋⠹⠤⢤⣄⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⠗⠛⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡼⠀⠀⡄⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⣴⠞⣫⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠀⠀⠀⠀⣀⡾⠁⠀⣸⣇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⡤⠶⠶⠾⠿⢿⣿⣿⣷⣶⣶⣾⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⢤⣀⣤⣾⠟⠀⢀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⡀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⢶⣽⣿⣿⣿⣿⣿⣟⡿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠒⠀⠀ ⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠗ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⢁⡤⠀⠀⠀ ⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠴⠞⠋⠀⠀⠀⠀ ⣴⡿⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡿⣿⠟⠀⠀⠘⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠳⣄⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡟⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⡄⠀⠈⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⠁⠈⣀⣤⡤⠄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣇⣷⠀⠀⠀⣤⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠉⢀⣀⣀⣤⣤⣀⡈⢿⣿⣿⢻⣿⣿⣿⣿⣿⣿⠀⠉⠓⠆⢻⣿⣿⣿⣿⣿⣿⣷⣶⣦⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠘⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠾⣿⣿⠿⠿⠟⠛⠛⠁⠈⢿⡿⣼⣿⠿⢿⣿⣿⣿⣿⣷⣦⣤⣾⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢈⣿⠟⠁⠀⠀⠀⠉⠙⠛⠛⠛⠉⣹⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠉⠻⣿⣿⠈⠛⠷⠀⠀⠀⠀⢀⡴⠚⠉⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣹⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢠⠶⠶⣤⡈⢿⡇⠀⢀⠀⢀⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢹⡇⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⢸⣍⠉⠁⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠤⠤⠤⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣶⡤⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⣾⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢤⡀⠀⠀⠀⣸⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠈⠓⠦⣴⣏⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠉⠓⠲⣤⣀⠀⠀⠙⢷⣄⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⣤⣈⠛⢦⡈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠈⠻⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣀⡶⠄⠐⠂⢳⣤⠖⠋⠉⠙⠉⢦⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡸⢷⠒⠤⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣾⣁⡤⠀⠀⣨⠚⢻⣖⣲⣶⣦⡄⢲⡷⠴⠒⡞⠛⣻⠛⠟⠳⡛⢿⠿⣷⣴⣀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣩⡏⠀⢀⣸⡷⢤⣼⣿⣿⢿⣿⣇⠀⠁⠀⠀⠘⡄⠀⠀⠀⠀⢱⠘⡄⠀⠈⢫⡚⢵⡤⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠟⠋⠀⠀⢸⣏⠛⠓⠻⢿⣿⠖⠋⣿⣿⣻⣾⣿⠅⠀⣤⣶⣾⣟⣁⣠⡿⠿⠿⢿⣅⣙⣶⣶⣔⠛⣄⣈⢻⣷⡀⠀⠀⠀⠀ ⠛⠛⢿⣿⠟⢦⣀⠀⢀⣿⠸⣆⠀⢀⠏⠀⢢⣰⣿⣿⣾⡿⢿⣶⠖⠋⠁⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⠉⢻⡛⠛⠿⣦⣹⡳⣤⣄⠀⠀ ⣶⣶⠋⠁⢠⡿⠛⣿⣿⣿⡀⠙⣦⣾⠖⢒⣶⢿⡿⠯⢭⣍⣿⣿⣀⣒⣢⣤⣤⣼⣧⡄⠀⠀⣀⣀⣀⠀⢀⣸⣇⠀⠀⢈⣏⡷⢻⣿⡇⠀ ⡟⠉⠠⣠⡿⠁⠀⣿⣿⣹⣇⠀⢸⡇⠀⢸⣿⣸⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢉⣿⣿⡇⠀⠀⠐⠒⠒⠒⠀⣿⣿⠫⡤⢤⣧⣀⣀⣻⠇⠀ ⠓⠤⣀⡟⠣⣄⢠⣿⣿⡇⣿⣄⡾⠀⠀⣸⠀⠀⠀⠀⠀⣼⣿⣇⣀⣇⠀⠀⣸⣿⣿⡇⠀⠀⡄⠀⠀⠀⡄⣿⣿⠀⣧⠀⣿⠁⠈⣿⡆⠀ ⠀⢀⡞⠋⠑⠺⣿⣿⣿⣷⢸⣿⡇⠀⠀⣿⠀⠀⠀⠀⠘⣿⣿⠋⠉⣯⡙⠛⣿⣿⣿⣧⠀⠀⡇⠀⠀⢠⣇⣿⣿⣤⣿⣀⣿⠀⠀⢸⣷⠀ ⠆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⣿⣧⢀⠀⣧⠀⠀⠀⠀⠀⣿⣿⡄⠀⣿⡇⠀⣿⡇⡟⣿⠀⢸⡇⠀⠀⣾⣿⣿⣿⢰⣿⣿⣿⠀⠀⢸⣿⣴ ⡶⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⢸⠀⣼⠀⠀⠀⡀⢰⠛⠛⠛⠒⠓⠷⠤⣿⡇⠇⣿⡄⢸⡇⠀⢠⣿⣿⢿⣇⣾⣿⣷⡏⠀⠀⣼⣿⣿ ⠀⠠⠂⠀⣔⣼⣿⣿⣿⣿⣿⣿⡇⢸⣇⣿⠀⠀⠀⣧⢨⡇⡀⢀⠀⠀⠀⣀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡟⠁⠀⠀⣿⣿⣿ ⠀⠀⠂⠚⢀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡄⠀⠉⣿⣿⡿⠿⠛⠛⠻⠷⢶⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⢶⣶⣖⣾⠇⠀⠀⢰⣿⣿⣿ ⠀⠀⠀⠀⣸⠟⣿⣿⣿⡿⡇⠘⣧⣼⣿⣿⡇⠀⠀⢸⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡿⣼⠀⢀⣸⣿⣿⣿ ⠀⠀⠀⢀⡿⢾⣿⣿⣿⡇⡇⠀⣿⣿⣿⣿⣷⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠚⠉⠉⠉⠉⠉ ⠀⠀⠀⣾⠃⣾⣿⣿⣿⠉⡇⠀⣿⣿⣿⣿⣿⡀⢰⢤⣿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⢀⣿⣿⣿⣿⣼⡇⠀⡇⣿⣿⣿⣿⣧⣸⡿⣿⡇⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢚⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⠀⢸⣿⣿⣿⣿⣿⡇⠀⡇⢸⣿⣿⣿⣿⣿⣇⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠉⠀⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⢿⣿⣿⣿⣿⣿⣾⣿⡀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠃⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⠈⢿⣿⣿⣿⣿⣏⣿⣷⣤⣄⣈⣑⢲⣤⣀⣀⣀⣤⢶⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣀⡤⢴⣶⡿ ⡏⠀⣀⣿⣿⣿⣿⣿⠛⢻⠗⠐⠉⠉⠑⠚⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠼⠟⠋⠋⠉⠉⣿⣿⡟⠀⠀⠀⠀⠀⡟⠀⠀⠀⣏⢷ ⠁⠀⣼⣿⣿⣿⣿⡇⢀⠇⠀⠀⠀⠀⠀⠀⠈⢺⡟⢿⣿⣿⣿⣿⣿⠿⢿⠿⢛⢻⡟⠲⣶⡲⠤⣤⠞⢻⠃⠀⠀⠀⠀⢰⡇⠀⠀⠀⢻⠨ ⠀⢰⣿⣿⣿⣿⣿⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠉⢻⣿⠛⠿⢷⣦⣲⡿⠿⡧⠤⠛⣷⠀⢻⣆⡎⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠸⠀ ⢀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠈⣿⠁⠀⠀⠈⡿⠋⠉⢻⡆⠀⠸⣧⠀⡟⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⣧ ⣾⣿⣿⣿⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣸⣆⠀⠀⠀⢙⣿⠿⢿⣄⡀⠀⢻⡶⠁⠀⠀⠀⠀⠀⠀⢸⠻⣧⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠿⠿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⡀⠀⢀⣠⣤⣶⣶⣶⣷⣶⣶⣿⣿⣷⣶⣶⣶⣶⣮⣝⡻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡤⠔⠒⢤⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡜⠉⠀⠀⠀⠀⢳⠀⢀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠀⠀⠀⠀⠀⠀⠈⡇⣼⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⣇⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⡇⢀⣀⣀⣀⣀⣀⠀⡿⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⡆⠀⠀⠀⠀⠀ ⡇⠘⠙⠻⠛⠛⠛⠃⢧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡽⡄⠀⠀⠀⠠ ⡇⠀⠀⠛⠛⠙⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠠⠁ ⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣠⠄⠻⣿⣿⣿⣿⣿⣿⠹⣷⠠⠤⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡉⠓⢤⠆⠀ ⢣⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⢀⠴⠋⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇⠻⡇⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⠞⠀⠀ ⠈⡆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡼⣧⠀⠻⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⢱⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⢿⠀⠀⢙⣀⠀⠀⠀⢿⣿⣿⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠙⠒⠦⠤⣼⣿⣿⣿⣿⣿⣿⣿⢻⡏⠀⢀⣤⣖⣲⣭⡶⠀⠀⠀⠀⠀⠙⢿⣞⠀⠼⠶⣾⣭⣤⣀⠈⢿⣿⡞⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡿⣻⣿⣿⣿⣿⣿⢸⠀⣠⣾⡿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠈⠉⠛⣿⣦⣿⡇⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠃⢿⣿⣿⣿⣿⣿⠸⠴⢫⣱⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣧⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠀⢸⠙⣿⣿⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡰⠊⠉⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣂⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠘⡇⣿⣿⠟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡆⠀⠘⢾⣿⣸⢻⣷⡄⠀⠀⠀⠀⣀⣀⠀⣿⠀⣀⡀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠀⢀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢿⡟⢙⢿⣆⠀⠀⠀⣴⠁⡸⠀⡼⠋⣱⠃⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢸⣷⣤⣘⡛⣦⣀⠠⠃⠀⡇⡼⠀⣼⢁⡴⠊⣹⠀⠴⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⡾⠀⣿⠙⣿⣯⠈⢿⣇⠀⡿⠃⠀⠷⠟⢠⠞⢁⡠⢤⡄⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⡈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⢠⡿⣿⡆⠀⠛⠈⠀⠀⠀⠀⡄⠛⠚⣡⣴⣾⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡀⠠⠊⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠋⠁⠀⡿⢿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢠⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣠⣤⣯⠽⠛⣇⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⡿⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣇⠈⢧⢠⠏⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠈⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢸⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣆⣨⢋⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠘⣿⣿⡗⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣇⠤⠂⠠⣱⣆⣁⡙⣑⡀⣠⡤⣤⣤⣤⣄⣄⡐⠇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⠿⣏⣏⣀⡼⣤⣿⡿⣿⠌⠁⢀⡂⢁⣀⡰⢡⠉⠩⡒⢄⡀⠀⠀⠀ ⠿⢿⡿⣅⠀⢸⢣⠁⡙⠩⣰⣿⣾⢷⡤⠛⠛⠒⡞⠉⠉⠒⠛⢳⠹⢶⣻⣆⣀⠀ ⡿⠅⣰⠋⢹⣿⡀⢳⠃⢱⢻⠛⠚⡯⡇⠀⠲⢶⣶⠀⠀⣀⣀⢰⣧⠄⢹⠋⢽⠁ ⠣⢬⣣⢄⣾⣇⣧⡜⠀⡏⠁⠀⢠⣿⣀⣆⡀⣿⣿⠀⢀⠀⠀⢸⡇⠃⢹⠉⢻⠀ ⠀⠃⠀⢹⣿⣿⣸⣇⠀⡇⠀⠀⢸⣿⠀⣷⠈⡟⣿⠀⡌⠀⣸⣾⡇⣿⣾⠀⢸⣇ ⠂⡀⠀⣸⣿⣿⣿⡏⡇⡇⠀⢠⢨⠉⠁⠙⠚⠃⠻⠦⠿⠠⠿⠯⠷⢿⡏⠀⣾⣿ ⠀⠂⢊⣿⣿⣿⡿⡇⣿⣧⠀⢸⣾⠗⠓⠒⠯⠀⠀⠀⠀⠀⠤⠴⣶⡼⡀⠀⣿⣿ ⠀⠀⣸⣼⣿⡏⡇⣿⣿⣿⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠥⠐⠛⠛ ⠀⢠⡇⣿⣿⣇⡇⣿⣿⣿⡆⣧⣟⢧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⠁⠀⠀⠀⠀ ⠀⣞⢱⣿⣿⣿⡇⡇⢿⣿⣿⣧⣿⢄⠁⠀⠀⠀⠀⠀⠀⠉⢀⣵⠀⠀⠀⠀⠀⠀ ⡼⢁⣾⣿⣿⣿⡇⡇⠘⣿⣿⣿⣿⣦⣈⡂⠄⣀⢀⣠⣴⣾⣿⡏⠀⠀⢀⣀⢠⡤ ⠃⢸⣿⣿⡟⠩⠁⠉⠉⠈⣻⣿⣿⣿⣿⣿⣿⢷⠞⣉⣉⣙⣿⠁⠀⠀⣸⠀⠈⡝ ⢀⣿⣿⣿⠇⠃⠀⠀⠀⠀⠈⢦⠙⣿⠻⠦⣳⣿⡤⠙⡄⢳⡄⠀⠀⠀⣿⠀⠀⠃ ⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⢳⣹⠀⠀⢫⡤⣜⠀⢹⡜⠀⠀⠀⠀⡿⡆⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠾⢳⣦⡀⠀⢀⣠⣶⣦⡄⢠⣾⠟⢷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠙⣿⣷⡾⢿⣿⠀⣼⡟⠛⢿⣦⣿⠇⢹⣧⣼⣿⣦⣄⣿⡟⠙⣷⠀⣤⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⣿⣦⡀⣿⡏⠀⢸⡿⠀⢿⡇⠀⠈⣿⡿⠀⢸⣿⣿⡀⠈⣿⣿⠃⠀⢿⣿⡟⠉⠻⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣀⠀⣿⡏⠀⠈⣿⣿⡿⠹⣇⣿⠁⠀⣼⡇⠀⢸⣿⠀⠀⣿⡇⠀⠀⣿⣿⡇⠀⢸⣿⠀⠀⢸⣿⠁⠀⢰⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠉⢻⣧⠸⣇⠀⠀⠸⣿⡇⠀⢻⣿⠀⠀⣿⡇⠀⠀⣿⡄⠀⣿⡇⠀⠀⣿⡿⣷⠀⠈⣿⡆⠀⣼⡟⠀⠀⣼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⣿⡄⢿⡀⠀⠀⣿⡇⠀⠸⣿⠀⠀⣿⣿⠀⠀⢸⡇⠀⢸⣇⠀⢀⣿⠁⣿⠀⠀⢻⣇⢠⣿⠀⠀⢠⣿⣷⣤⣄⡀⠀ ⠀⠀⢀⣀⡀⢿⣇⠀⠹⣧⢸⣇⠀⠀⣿⡇⠀⠀⣿⡀⠀⢿⣿⡆⠀⢸⣇⠀⢸⣿⠀⢸⡟⠀⣿⡆⠀⠈⣿⣼⡇⠀⠀⢸⡏⠀⠀⢻⡇⠀ ⠀⣰⡿⠛⢻⡞⣿⡀⠀⢻⣆⣿⠀⠀⣿⡇⠀⠀⢻⡇⠀⢸⣿⣇⠀⠸⣿⠀⠈⣿⡄⣿⠇⠀⢹⡇⠀⠀⣿⣿⠀⠀⠀⣿⠃⠀⠀⣿⠇⠀ ⠀⣿⡇⠀⠀⣿⣾⠿⣿⡌⢿⣿⡆⠀⢸⡇⠀⠀⢸⡇⠀⢸⣿⣿⠀⠀⣿⠀⠀⢹⣷⣿⠀⠀⣸⡇⠀⠀⣿⡏⠀⠀⢀⣿⠀⠀⢸⡟⠀⠀ ⠀⠸⣷⡀⠀⣿⡁⠀⠹⣧⠈⢿⣧⠀⢸⣇⠀⠀⢸⣇⠀⠀⣿⣿⡇⠀⣿⠀⠀⢸⣿⡇⠀⣠⣿⡇⠀⠀⣿⠁⠀⠀⢸⡏⠀⢠⣿⠃⠀⠀ ⠀⠀⠹⣧⠀⢸⣧⠀⠀⢿⡆⠘⣿⠀⠸⣿⠀⠀⠸⣿⠀⠀⢸⣿⣇⠀⣿⠀⠀⠀⣿⠁⢠⣿⢹⡟⠀⣸⡟⠀⠀⠀⣼⡇⠀⣾⡏⠀⠀⠀ ⠀⠀⠀⣿⣧⠀⢿⡄⠀⠈⣿⡀⣿⡇⠀⣿⡀⠀⠀⣿⡄⠀⠀⣿⣿⢠⣿⠀⠀⢸⡟⠀⣼⡿⢸⡇⢀⣿⠇⠀⠀⠀⣿⠀⢰⣿⠻⢷⣤⠀ ⠀⢀⣠⣿⣿⡄⠘⣷⠀⠀⠘⣷⣿⣇⠀⢹⣧⠀⠀⢸⣷⣀⣀⣸⣿⣼⣿⣆⣠⣾⣇⣠⣿⡁⣸⡇⣼⡿⠀⠀⠀⢰⣿⠀⣾⢿⣦⠀⠹⣷ ⢰⣿⠋⣠⣼⣿⡀⢹⣧⠀⠀⣹⣿⣿⣶⠿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠿⢷⣿⣇⡀⠀⠀⣸⡇⢰⣿⣾⡟⠀⠀⢿ ⣿⡇⠀⣿⣿⣿⣧⠀⣿⣷⡾⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄⣿⡇⣸⣿⡿⠁⠀⠀⣿ ⢹⣷⠀⠘⢿⣿⣿⣷⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⣿⣿⠃⠀⠀⢀⣿ ⠀⢿⣧⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠁⠀⠀⠀⢸⡿ ⠀⠈⢿⣧⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⣿⡇ ⠀⠀⠈⢿⣧⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⣿⠀ ⠀⠀⠀⠈⢻⣧⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⡟⠀ ⠀⠀⠀⠀⠀⢿⣆⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠘⣿⡄⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⢹⣷⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⣠⣶⣶⡶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⡿⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢰⣿⣿⣿⡀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣀⣸⣷⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠈⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣤⡄⠀⠀⢴⣶⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⠒⠒⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢠⡴⠚⠛⠛⢦⡀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢀⣿⣤⠤⠤⣤⣼⣇⡀⢀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠼⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀ ⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀ ⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀ ⠀⠀⡇⠀⠀⠀⠀⢠⣖⠀⠀⣿⢸⠀⠀⢸⠈⡇⠀⣤⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⢀⡇⠀⡶⠶⠶⣼⣹⣦⠤⠗⠸⣤⣤⣼⠀⣧⣠⡿⣧⣤⣤⡀⠀⢠⡇⠀ ⢀⡾⠁⠀⣽⠀⣼⠋⠙⢻⣷⡀⠀⠀⠀⠀⠀⢠⣾⢿⣷⣦⠸⡇⠀⠈⢧⠀ ⢸⠁⠀⣼⠁⠀⣧⠀⣀⡾⢻⡇⠀⠀⠀⠀⠀⣿⠀⠀⡿⣿⠀⠳⡄⠀⠈⣇ ⠘⣇⠀⣿⢦⡤⠼⣿⠿⠿⠋⠀⢀⠀⠀⡀⠀⠙⠿⢿⠿⣯⠤⣤⢿⡇⢠⡏ ⠀⠈⢧⢸⡆⠳⣤⣸⠂⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⢼⣁⡴⠋⡼⢰⠏⠀ ⠀⠀⠺⠞⠀⠀⠀⠙⠶⢤⣀⡀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠉⠀⠀⠹⠿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⡀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢠⣾⠕⠁⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢠⡿⠃⠀⢀⡞⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢰⡟⠀⠀⠀⡜⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢰⠃⠀⠀⠀⢠⡏⠀⠀⠀⢰⠃⠀⠀⡀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⠃⠀⠀⠀⣰⡿⠀⠀⠀⠀⡟⠀⠀⠀⡇⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⡴⠃⠀⠀⠀⣰⣻⠃⠀⠀⠀⢴⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡟⢜⡀⠀⠀⠀⢰⣫⡏⠀⠀⠀⠀⣾⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢊⠁⢀⡄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⢿⡃⠈⠀⠀⠀⢀⣯⢏⡇⠀⠀⠀⢸⢻⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢰⠁⠈⠛⠛⠂⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⣼⠃⠀⡰⠀⠀⣾⡜⣼⡇⠀⠀⠀⡞⢸⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⢹⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠻⣦⣾⠀⠀⠀⠀⠀⠸⡆⠀⠀⢿⣧⠀⠀⠀ ⠀⠀⠀⠀⡿⠀⡏⠀⢠⡇⠀⢰⣳⠁⡿⡇⠀⠀⢀⠃⢸⠀⠀⠀⢸⡄⢸⡄⠀⠀⠀⠀⣧⠀⢸⡀⠀⠘⣇⠀⠀⠙⢦⣀⣀⣀⣀⣴⠚⠁⢻⠀⠀⠀⠀⠀⠀⢱⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⡇⢀⣧⠀⢸⠀⠀⣸⡿⠖⡿⣿⠂⠀⢸⠀⢸⠀⠀⠀⠈⣷⠈⣇⠀⠀⠀⠀⢸⡈⠙⡏⠓⠀⢹⡄⠀⠀⢸⠈⡇⠀⠀⠸⡀⠀⠈⣇⠀⠀⠀⠀⠀⠸⡇⠀⢸⣼⠀⠀⠀ ⠀⠀⠀⢰⡇⣸⢹⠀⠘⠀⠀⣿⠀⠀⣷⡟⡆⠀⣸⠀⢸⡀⠀⠀⠀⢿⡆⠸⡀⠐⠀⠀⠀⢇⠀⡇⠀⠀⠀⣿⠀⠀⠈⡆⣇⠀⠀⠀⣇⠀⠀⠘⢦⠀⠀⠀⠀⠀⢳⠀⢸⢹⡀⠀⠀ ⠀⠀⠀⢸⡇⡟⣸⠀⣧⠀⢠⡏⠀⠀⠸⣧⢻⠀⢿⡄⠀⣧⠀⠸⡀⠈⣷⡄⢳⠀⣧⠀⠀⠘⣆⢣⠀⠀⠀⠘⡆⠀⠀⡇⢸⠀⠀⠀⣿⠀⠀⢀⠈⠳⣄⠀⠀⠀⢸⠀⡼⢸⡇⠀⠀ ⠀⠀⠀⠘⣇⡇⢇⠀⣿⠀⢸⡇⢀⡤⣶⣿⣿⢦⡜⠿⢶⣽⣇⣀⢳⡀⠈⠻⣄⡇⠘⣦⡴⣖⣿⣾⣷⣶⣦⣄⢹⣦⠀⠃⢸⡀⠀⠀⣿⢦⡀⠈⠳⡀⠈⠳⠦⠤⢸⢀⢇⣾⡇⠀⠀ ⠀⠀⠀⣀⣼⣯⣼⡄⢸⡆⢸⣷⣿⣿⣿⣿⣿⠿⢿⣆⠀⠀⠈⠛⠓⠛⠛⠀⠈⠛⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡇⠀⠀⣿⡀⠑⠶⣄⣈⠳⢤⣀⣴⣾⣿⣿⡟⠀⠀⠀ ⠀⣠⣞⣻⣿⣿⣿⠃⡏⣧⣾⣿⣿⣿⡟⠋⠀⢸⠛⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠃⠀⠀⠿⠿⣿⣿⣿⣦⣀⢸⡇⠀⠀⣿⠙⢦⣀⡀⠒⠉⢉⡽⣹⣿⣹⣿⠛⣲⡶⠶ ⡼⡽⠋⣰⠋⠀⣿⡀⡇⣿⣿⣷⡿⠟⠀⠀⢀⣀⠁⢹⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⠀⠀⠒⠒⠛⣻⣿⣿⣿⢸⡇⠀⠀⡏⢀⣀⠈⠉⠑⠂⢸⢣⡿⢹⠟⣿⣿⣯⣄⠀ ⢱⠁⢰⠃⢀⣴⢻⡇⠃⠋⢹⣯⠓⠀⠀⠀⠈⠉⠀⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠛⠀⠀⠀⣿⣿⡟⠚⢻⠃⠀⢸⣿⣯⡛⠱⡄⠀⠀⠸⣮⡇⢸⣤⡇⠘⣆⠈⠀ ⢸⠀⠉⣩⠿⠋⢀⣧⡇⠀⠘⡿⣆⠀⠳⣄⣀⣤⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⡀⠀⢀⡤⠴⠋⣿⣿⠀⠘⠀⠀⣸⡿⡁⠙⠃⣿⠀⠀⣾⣿⢻⢿⠁⢧⠀⠈⠣⣀ ⣮⠽⠟⠋⣀⡴⠋⣿⢳⠀⠀⠛⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁⠀⠀⣿⣿⡆⡇⠀⠈⣿⢉⠋⢙⠓⣿⣶⠾⢻⡟⡇⡇⠀⠸⡧⡄⠀⠀ ⠉⠓⠒⠾⣍⡠⠞⣿⡸⣇⢠⠐⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⣧⠃⠀⣼⣧⡼⠴⠁⣰⠏⠁⣠⠎⠀⡇⡇⠀⠀⠙⢭⣲⣾ ⠀⠀⢠⣀⡀⣠⢼⡏⡇⢹⢾⢲⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣹⡟⠀⣰⣽⢡⡤⠤⠚⠁⢀⡴⠃⠀⠀⢻⣾⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠿⠖⠋⠀⢹⡌⣾⣿⠏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡟⣷⠁⡰⣣⠇⠀⠀⠀⣠⠶⠉⠀⠀⠀⠀⠀⠳⠽⢦⣴⣶⣶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠘⣟⡇⠈⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⢹⣽⠇⠔⣱⠿⠶⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣿⡀⠀⠀⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⡟⢀⣯⡿⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⡀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⣀⣀⣠⣤⡤⢶⠖⠛⠉⣠⠎⢠⣾⣟⣤⠚⠀⠀⠀⢀⣀⣠⣤⣤⠤⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠓⠂⠀⠀⠀⠀⠉⠉⠋⠙⠻⣯⡀⠴⠒⠀⠐⠒⠺⠷⠶⠛⠛⠋⠉⠓⡶⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠖⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠒⠶⠦⢤⣀⡀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠈⠉⠁⠛⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠞⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀
⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⡇⠀⢰⢰⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢏⠉⠁⠀⠀⠀⠀ ⠀⠀⢰⠀⡇⢀⠀⠡⣧⡀⠀⣧⠀⠀⡀⠇⠀⠀⠀⡆⠀⢀⠀⠀⠀ ⠀⠀⠘⠐⣷⢸⡀⠀⠀⡉⠀⣇⡱⠁⡀⢻⠀⠀⠀⢱⠈⠁⠀⠀⠀ ⠀⠀⡌⡰⠊⢋⣧⡀⠀⢧⠀⡇⢀⠈⠢⣸⠀⠀⠀⢸⠀⠀⣀⠄⠀ ⠀⠀⡗⣡⣶⣼⡟⠕⢄⣘⣂⡽⣿⣿⣿⣮⣤⡀⢠⢸⠀⠉⢸⠀⠀ ⠀⠸⡿⠍⠷⠿⡵⠀⠀⠀⠀⠀⢸⡙⣭⣛⠋⠀⡀⢸⢣⠀⢸⠀⠀ ⠀⠀⡏⡆⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠶⢼⠀⢠⠃⢸⡸⠀⠂⠀⠀ ⠀⠀⡇⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠀⡟⠁⢠⠀⡄⠀ ⠀⠀⢃⠀⡅⠂⠄⡀⠀⠀⠀⢀⠀⠀⢐⠇⠈⠀⢀⠃⢠⠀⣴⣇⠂ ⠀⠀⢸⠀⣇⠀⠀⠀⡩⢙⡏⠀⠀⣀⣌⠀⠀⡰⣘⣰⠏⠷⠿⡁⠀ ⠘⠄⠀⢇⠏⠴⢊⢋⡔⠁⡀⠀⠀⣠⡂⠄⠊⢘⠡⢊⠂⢄⠐⠀⠑ ⠀⠈⡲⢤⠵⠥⠁⡮⠐⠠⢈⢢⡍⡲⡀⠀⡀⠀⠴⠁⠀⠀⠡⠀⠀ ⠀⠈⠀⠈⡢⠀⢠⠀⠀⠀⠀⠙⠃⠀⠈⠪⠠⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⣀⣀⢔⡊⠙⠟⢠⣄⠀⠀⣿⣉⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣮⣾⠿⠛⠀⣁⠠⠄⠒⠒⢒⠀⠄⣘⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣧⣶⠞⠁⡐⢁⠀⠀⠀⠀⡑⡀⠀⠳⢄⠀⠀⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⠏⠀⡐⢀⠃⠀⠀⠀⠀⠀⢠⣰⣷⣶⢆⠀⣿⣿⣄⠀⠀⠀⠀ ⠀⣰⣿⣿⠿⠀⠀⠀⡈⢰⠀⠀⠀⡇⢀⡈⢿⣿⣿⠀⢻⣿⣿⣿⣣⡀⠀⠀ ⢰⣿⣿⠏⠀⠂⢰⠀⡇⣀⡀⠀⠠⢣⠀⡏⢂⠉⠀⠃⣼⣿⣿⣿⣷⡇⠀⠀ ⠈⢻⠣⠀⢠⠀⢸⠀⣇⠹⡇⠇⠸⠶⣦⣵⣸⠀⠀⠀⠸⣿⣿⣿⠃⠀⠀⠀ ⢀⡳⠀⡔⣼⢠⢈⡧⠿⠆⠘⠈⠀⠀⣾⡿⡙⠀⠀⡀⠀⠹⡿⠇⠀⠀⠀⢰ ⣼⡇⡞⠠⠏⡼⠜⠣⡀⠀⠀⠀⠀⠀⠀⠠⡇⠂⠀⡇⠀⣠⢧⠀⡀⠀⠀⠸ ⠘⠐⠧⣡⡎⠀⠀⠀⢰⣄⡀⠀⠀⢀⣠⠗⠃⢀⢰⡙⡄⣟⢸⡘⠀⠀⠀⠀ ⠀⠀⡜⡜⠀⠀⠀⠀⠈⢣⡾⣷⠘⠋⠀⢄⡀⡘⢆⠜⠈⣎⢤⡇⠀⠐⢄⠀ ⠀⠀⣿⣀⠀⠀⣀⠤⠀⣊⠌⠻⣒⠄⢒⡡⠔⠈⡱⢁⠜⠁⠘⡿⣄⠀⠀⠃ ⠀⢸⡸⠺⣉⠀⠀⢀⡠⠘⠀⠀⣞⡺⠀⠀⢠⢏⠔⢱⠀⠀⠀⡇⠘⠡⠀⠘ ⠀⠃⠋⠀⠀⠀⠈⡞⠀⠀⠀⠀⢸⠊⠀⠀⣜⠎⠀⠀⢂⠀⢀⠇⠀⠀⠀⠀
⠀⠀⠀⠀⣠⡶⢦⣄⠀⠀⠀⠀⠀⠀⠀⣠⡶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡟⢀⡀⠙⣷⡀⠀⠀⠀⢀⡾⢋⡤⡙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⠇⠙⣄⠘⠧⠤⠤⠤⣾⢡⠏⠀⢱⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡟⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡏⠀⢀⡖⠲⣄⠀⠀⠀⣀⠤⠊⠁⠀⢣⡀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣠⠤⠞⠀⠀⠈⠑⠦⠊⠁⠀⠀⠀⠀⠀⠙⠒⡂⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⢀⡇⢱⠀⢱⣶⡄⠀⢠⣤⣤⡄⠀⠀⣴⣶⡆⠀⠰⠥⡀⠘⣧⠀⠀⠀⢀⣀⣀⡀ ⢸⡇⡞⠀⠈⠋⠁⠀⢈⣩⣭⣁⠀⠀⠉⠉⠀⠀⠀⢠⢇⣤⡿⠀⣠⡶⠛⠉⢸⠃ ⠘⠷⠿⣤⣄⣀⡀⠀⠹⣏⣠⠟⠁⠀⠀⣀⣀⣤⡶⠟⠋⠁⢀⡾⠋⠀⠀⠀⢸⡄ ⠀⠀⠀⠀⠀⠉⠉⡟⠛⠒⠒⠒⠚⠛⠋⠉⠁⠈⠻⣦⠀⠀⢸⢇⡠⡄⠀⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⡄⠀⠀⠀⣤⠀⠀⠀⠘⣧⠀⢸⠉⠀⠧⠴⠲⣸⡇ ⠀⠀⠀⠀⣾⠛⢷⣧⡀⢀⣸⡇⠀⣀⢤⣿⠞⠛⢻⡄⢹⣆⣿⠀⠀⠀⠀⣠⡟⠀ ⠀⠀⠀⠀⢹⡆⠀⢿⡈⠉⠸⡟⠊⠁⢸⡇⠀⠀⣸⡇⢈⡟⠁⠀⢀⣠⡾⠋⠀⠀ ⠀⠀⠀⠀⠀⠻⠶⠾⠷⠶⠶⠷⠶⠶⠾⠧⠤⠾⠿⠴⠾⠷⠶⠛⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠎⠀⠀⠀⢁⠀⠀⠈⠢⠀⠈⢢⡀⠀⠑⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠎⠀⠐⠀⠘⠀⠀⠀⠀⠀⢃⠀⠀⠀⠡⢀⠙⣶⠀⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⡌⠂⠀⡇⠀⡆⠀⠀⠘⡄⠀⢸⣄⠀⠀⠀⢃⠑⢴⡆⢀⡴⢳⠀⠀⠀ ⠀⢄⠀⠀⢻⠀⠸⣇⡀⢇⠀⠀⠀⡑⡤⠐⡙⡀⠀⠀⠸⡠⡙⡷⣏⣀⢀⠀⠀⠀ ⠉⠚⢆⠀⢸⠀⢰⢰⣈⣏⣇⠀⠈⡄⢼⠟⢍⢳⡦⠀⢀⠣⠜⠙⢌⠙⢻⠀⠀⠀ ⠀⠀⣀⠀⣾⡀⠘⡸⡏⣎⣇⠑⢄⢃⠘⣖⡺⠘⠁⠀⣿⠐⢰⡛⡘⠀⢸⠀⠀⠀ ⣠⢤⡿⠀⢹⢱⡄⠑⣧⡑⠃⠀⠀⠈⠀⠀⠀⠀⡆⡸⠃⠐⠚⡡⠁⢸⢸⠀⠀⠀ ⡠⢜⣠⠀⠀⠁⠙⠦⣷⠁⠀⠀⠀⠀⠀⠀⠀⠤⠜⠀⡐⣹⣿⡇⠀⠸⡄⠀⠀⠀ ⠀⠩⢧⣶⠆⠀⠀⠀⠀⠢⡀⠀⣀⣀⡀⠀⠀⠀⣠⠎⠀⣿⣿⣇⠀⠀⣧⠀⠀⠀ ⠀⠀⠀⠉⡀⢀⣀⣀⠠⡔⢾⢟⢭⣀⣀⣀⣤⡾⠁⠀⠀⢻⣿⣿⡆⠀⢸⠀⠀⠀ ⠀⠀⠀⣠⢋⠬⠉⢻⠇⠀⠈⣸⡘⣿⣿⡟⠋⠀⠀⢀⠔⠁⠀⠀⠙⢀⠀⠃⠀⠀ ⠀⠀⠀⡅⠁⢈⢰⠁⡠⠂⠈⢹⠋⡩⡻⠻⠀⠀⠀⠆⠀⠀⠀⢡⠀⠀⢂⠘⡀⠀ ⠀⠀⠀⠅⠀⢸⡆⠰⠢⡀⠸⠠⢋⠌⠀⠲⠠⠒⢨⠀⠀⡠⠄⠒⢄⠀⠀⡄⢡⠀ ⠀⠀⢀⣾⠀⢘⢿⠇⠀⠈⠗⢠⠂⠑⠤⠤⠐⠈⢹⠔⠡⠀⠀⠀⠀⠱⡀⠃⠀⡄ ⠀⠀⢪⣙⠐⡑⠹⠠⢀⡊⣠⡁⠀⠠⠂⠀⠀⢀⢿⢠⠁⠀⠀⠀⠀⠀⠐⡄⢰⢀ ⠀⠀⡙⣀⠠⠐⠘⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⢎⢷⢸⠸
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⡿⠟⠛⠛⠛⠛⠛⢿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠛⠛⠛⠛⠛⠿⣷⣦⡀⠀⠀⠀ ⠀⠀⣰⣿⠟⠁⠀⠀⣀⣀⣀⣀⣀⠀⠈⠙⢿⣦⡀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⣀⡀⠀⠀⣰⣾⠟⠁⠀⢀⣀⣀⣀⣀⡀⠀⠀⠙⢿⣦⡀⠀ ⠀⣼⡿⠁⠀⣠⣶⡿⠟⠋⠉⠙⠻⢿⣦⡀⣀⣿⣷⣾⠿⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠿⠿⣾⣿⣅⣀⣴⣾⠿⠛⠉⠉⠛⠿⣷⣄⠀⠀⠹⣷⡀ ⢸⣿⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⢀⣠⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣧⣄⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⢻⣷ ⣿⡇⠀⠀⣿⠇⠀⠀⠀⠀⣠⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡀⠀⠀⠀⠈⣿⡇⠀⢸⣿ ⢻⣧⠀⠀⣿⡆⠀⠀⣠⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⡀⠀⠀⣿⡇⠀⢸⣿ ⠈⣿⣆⠀⠸⣷⣄⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣼⡟⠀⢀⣿⠏ ⠀⠘⣿⣦⡀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⣠⣿⠏⠀ ⠀⠀⠈⠻⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠁⠀⠀ ⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀ ⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣀⣼⣿⣿⠀⠀⠀⠀⣀⣴⡾⠿⠛⠋⠙⠻⠿⣷⣦⡀⠀⠀⠀⢸⣿⣇⣀⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⢀⣼⡿⠋⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠻⣿⡄⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣤⣄⠀⠀⣾⡟⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠂⠀⠀⠀⠀⠸⣿⡄⠀⣠⣤⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⣾⡇⠀⠀ ⠀⠀⠀⢻⣧⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⣿⠀⢠⣧⡀⠀⠀⠀⢘⣿⣟⠁⠀⠀⠀⣠⣶⡄⢻⣷⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀⣿⠇⠀⠀ ⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢸⣿⡀⠀⠙⠻⠿⣶⡾⠿⠋⠻⠿⣷⡶⠿⠟⠉⠀⣼⡿⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀ ⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣦⣄⣀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠷⠶⠶⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣶⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣶⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⢀⣙⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠘⣽⡆⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀ ⢁⡀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢿⣦⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠖⢢⣸⣆⣀⠀⠀⠀⠈⣿⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠁⣰⠀⢸⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣷⣦⣀⠀⠀⠀⣞⠉⢉⣦⣤⢬⣇⣀⣭⡿⠀⠀⠀⠸⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⢀⡟⢠⠟⡆⢸⡀⢱⣄⣠⣶⠀⢣⠀⠀⠀⠀⢸⡰⣄⠀⠘⣏⠛⠻⢶⡞⠙⢲⠏⡁⠀⠐⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢸⡇⠸⠀⠘⢿⣿⠛⠛⣄⠀⠳⣌⣧⠀⠀⠀⠀⣇⠢⠙⢶⣾⢧⡤⢾⡤⠶⠿⣤⣁⣤⠴⡎⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣷⣇⢠⣦⣬⣙⠢⡀⠈⠑⠢⠿⠛⠳⢼⡗⠤⣸⣄⠀⠀⠈⠛⢳⣄⠄⠀⠀⠀⠀⠙⢦⡈⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣻⣷⣌⠂⠀⠀⠠⠤⣤⠴⠆⠀⠈⠉⠹⡄⢀⡴⣋⣤⣶⣶⣶⣶⣶⣄⡀⠙⠲⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡟⣿⠟⠛⢻⠟⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣾⣿⣿⣿⣷⣧⣽⣿⣿⣿⣷⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡟⣆⠀⢸⣿⣿⣝⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣛⣿⣤⡾⢷⣤⣸⡇⠉⠛⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣇⠈⠀⣀⡁⠾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣽⡿⠋⠈⣿⠃⠀⠀⣸⠋⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣽⡀⠀⠉⠙⠳⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣓⣒⣋⠁⣀⣠⡎⠁⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠤⠼⠋⠉⠁⣆⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠀⠸⡗⣶⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢛⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⡀⠀⠹⣦⢨⠙⢦⡀⠀⠀⠀⢸⣿⠗⠲⣖⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⣶⠀⣀⠀⠀⠳⣄⠀⠙⠿⢄⣀⠉⢲⣄⠀⠀⠙⠋⠉⠙⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣾⠏⠀⠀⠀⠀⠀⢀⡖⠀⣠⡄⠀⢸⠀ ⠀⠘⣧⣹⣷⣤⣀⠀⠉⠲⢤⡀⠈⢉⣹⢿⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⡒⠋⢁⡤⣞⠁⠀⠀⠀⠀⢀⣴⡟⣁⡔⠃⠳⡄⠈⣶ ⠀⠀⠈⠿⣿⣮⣽⣿⣦⠶⠿⠛⠛⠻⠬⣮⡳⣤⣌⣙⣶⡶⣶⡖⠒⠛⠉⠁⠀⠀⠀⣀⣬⠞⠉⠀⢀⣀⣀⣴⡿⠷⠚⠉⠀⠀⠀⠈⠓⠾ ⠀⠀⠀⠀⠀⠉⠉⠉⠀⣀⣤⠶⢶⠒⠒⢲⣯⣽⠟⠉⠀⡾⣯⣧⠀⠠⢤⣀⣠⠔⠋⠁⡠⠋⠉⠉⠉⠙⣷⠶⢶⡎⠤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⢰⠃⠀⣠⡏⡼⠁⠀⠀⠈⢿⠟⠁⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⢠⠏⠙⠛⠉⠉⠉⠀⠴⠛⠛⠲⣄ ⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢠⠏⠀⢰⡏⠰⠃⠀⠀⠀⠀⠈⣦⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⢀⡎⡠⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠒⠒⣲⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠁⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⣠⣶⣿⠿⠛⠉⠁⠀⠀⠻⠿⠿⠋⠉⠁⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⡿⢿⣦⣄⡀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡴⠋⠀⠀⠀⢀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⢰⡄⠀⢳⡌⠉⠃⠀⠈⠛⠿⣷⣤⡀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡴⠋⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⢿⠀⠀⠈⠳⣄⣸⠃⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⠙⢿⣦⡃⠀⠀⠀⠀⠀⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣥⡀⠀⠀⣠⠟⠁⠀⠀⢠⠖⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠈⠹⣄⠀⠀⢸⣇⠀⠀⠀⠀⠀⢠⡀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢶⣴⠃⠀⠀⠀⠀⡞⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⢷⣀⠀⠀⠀⠈⢧⠀⢸⡿⣆⠀⠀⠀⠀⠀⠻⡄⠀⠈⢮⢧⡀⠀⠀⠀⠀⠰⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⢳⣄⣀⠀⢘⡶⠋⢳⢻⡄⠀⠀⠀⠀⠀⠹⣄⠀⠈⢧⡻⡄⠀⠀⠀⠀⠱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠘⣦⠈⠙⠻⣅⠀⢸⡆⢳⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⢧⠻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠤⠶⠒⠉⠉⠉⠙⠒⡏⠀⠀⠀⠈⠳⣤⣀⠙⣶⠿⢤⣸⣧⡀⠀⠀⠀⠀⠀⢻⡄⠀⠈⣷⢻⡄⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣿⠈⠙⢿⡄⠈⡇⢻⡝⠲⣦⢠⠀⠀⠈⢷⠀⠀⠈⡎⢷⠀⠀⠀ ⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠀⠀⠀⠀⠀⣶⠄⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⢹⣼⠃⠈⢧⠀⠈⠙⡆⠀⠀⢸⡄⡆⠀⢹⠘⡇⠀⠀ ⠀⠈⢳⣀⠀⠀⠀⠀⠀⠰⡾⠷⣿⠀⠀⠀⠀⠀⠀⡏⠀⠀⡞⠀⢀⡄⠀⠀⠀⢸⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠿⢿⠳⡄⢸⡄⠀⠀⢧⠀⠀⠀⡇⢹⠀⠸⡆⢻⣀⠀ ⣀⠠⣴⠟⠳⠦⣤⣀⣀⣀⣀⣠⣽⠀⠀⠀⠀⠀⢀⡇⠀⣠⡇⠀⢸⡆⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠀⢻⡀⣧⠀⠀⢸⡄⠀⠀⢳⢸⠀⠀⣧⢸⡇⢧ ⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⠉⠀⢸⡇⠀⣴⠀⠀⣸⠀⢠⣿⠀⠀⣼⠃⠀⠀⣰⡏⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣀⣴⠞⠃⢿⢀⠀⠸⡇⠀⠀⢸⣼⠀⠀⠛⠘⡇⢸ ⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⡇⠀⢠⣟⣠⢯⠏⠀⣰⣿⣀⣀⣴⣿⠒⢒⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢸⣸⠀⢸⣧⠀⠀⢸⣿⠀⠀⠀⠀⠁⣿ ⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠀⠀⠈⠉⠁⢸⣷⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣓⣒⣲⠶⠦⢸⣿⡇⠀⣿⠀⠀⢸⣿⠀⠀⠀⠀⢀⣿ ⣶⡴⠟⠋⠀⠀⠀⠀⠀⢀⠀⢀⣴⠟⢿⠀⠀⠀⠀⠀⠀⠸⡇⢻⣷⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⢿⣿⣿⣿⣿⣿⣿⣧⣸⣿⠀⠀⢸⣿⠀⡀⡄⠀⢸⣿ ⣧⡀⠀⠀⠀⠀⠀⢠⣴⠟⠛⡿⢵⡶⣾⠀⠀⠀⠀⠀⠀⠰⡇⠈⣿⡟⠻⢿⣿⠟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⢳⣦⡞⣽⣀⣿⠁⠀⠀⠙ ⠙⣻⣦⣤⣤⣤⣤⣤⡤⠴⠺⡇⠀⣷⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⢿⡀⠀⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⣿⣿⡇⢸⠃⠀⣾⡟⣧⠈⠉⠉⠀⠀⢸⣶ ⠀⠉⢻⣾⡟⠁⠀⠀⠀⠀⠀⢧⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠻⠿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠀⠀⣶⣿⠟⠀⠀⠀⣸⠃⢻⣿⠀⠀⠀⠀⠀⢸⣿ ⠀⢠⣿⡟⠀⠀⢀⡄⠀⠀⠀⡘⢧⡀⢹⠆⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠯⠍⠀⠀⠀⠀⢰⡏⠀⢸⣾⠀⠀⠀⠀⠀⢸⣿ ⢶⣿⡟⠀⠀⠀⡿⠁⠀⠀⢸⡇⠀⠙⣾⠆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣿⠀⠀⠀⠀⠀⢸⣿ ⣾⣿⠁⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿ ⣿⢿⣇⠀⠀⠀⣧⠀⠀⠀⢸⡇⠀⠀⣾⣰⠀⠀⠀⠀⠐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⣿ ⠀⠀⠹⣄⠀⠀⠘⣇⠀⠀⢸⣧⠀⠀⣿⡇⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠏⠀⠀⡇⠀⠀⠀⠀⢠⣿⣿ ⠀⠀⠀⠙⢦⡀⠀⠘⣦⡀⠘⣿⡆⢠⡟⢀⡾⠀⠀⢈⣾⠋⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠏⠀⠀⣼⠀⢸⡇⠀⠀⢸⠀⡾⢸⣿ ⠀⠀⠀⠀⠈⠳⣄⠀⠈⠻⣄⡸⣿⡾⠁⣼⠁⠀⠀⣸⡟⠀⠀⠀⠙⠓⠦⣄⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠛⣡⡿⠀⠀⣰⡇⠀⣼⠀⠀⢀⡟⣰⠃⢸⣿ ⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⡀⢙⡿⠃⣸⡇⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⢲⣶⢤⣤⣤⣤⣤⠤⠤⠴⠖⠒⢻⣿⠏⢰⣏⣼⡟⠀⠀⣰⠟⢀⣼⡏⠀⠀⣾⣷⠟⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⢱⣾⡟⠀⠀⣤⡿⠟⢧⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢀⣿⣿⠏⠀⢀⡾⢁⡴⢛⡟⠀⢀⣼⣿⡏⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⢋⣴⣿⡟⠀⢠⣾⡟⠁⠀⠈⢷⠈⠧⣄⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣠⠶⢛⣷⣼⠟⠁⠠⢴⣫⠶⠛⠲⣾⠡⢄⣼⣿⣏⣀⣀⡀⢸⣿ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⢏⣀⣠⣿⠟⠀⠀⠀⠀⠈⠳⠤⣄⠙⠛⠓⠲⠤⠤⠤⠤⠧⠤⢀⣀⡤⠴⠛⠛⠁⣠⡏⠙⢿⣦⣤⣴⣿⣆⠀⢀⣼⢃⣠⡾⠟⠁⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⠟⠛⠛⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢳⢤⡴⠶⠤⠤⠶⠤⢶⣄⣤⠤⠴⠛⠋⡉⠀⠀⠀⠹⣿⣿⣿⣿⣖⠛⠛⠛⠉⠀⠀⠀⡀⣀⣀⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠹⣿⣿⠆⠀⠀⠀⠀⠀⠸⣿⡏⠉⣻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠔⣒⣶⣶⣶⠖⢋⡤⠖⠉⠀⠀⠀⠀⠻⠿⠗⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣡⣾⣿⡿⠛⠋⠉⠁⢀⣀⡠⠤⠒⠚⠛⠛⠓⡒⠂⠤⢀⡀⠻⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡿⢃⣀⣠⣤⠔⠊⠉⡠⠄⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠈⠑⣦⡈⠉⠉⠉⠉⢩⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⢀⠎⠀⡰⠁⠀⠀⠀⠀⠀⠐⡈⢣⠀⠀⠀⠙⠙⢦⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠀⠀⢀⠎⠀⡼⠀⠀⠀⠀⠀⠀⢠⠀⢱⠀⢇⠀⣾⣷⣦⣤⣧⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⡿⠀⠀⠀⠏⠀⢰⠁⢠⠀⠀⠀⠀⠀⡌⠀⠀⠀⢸⣿⣿⣿⣿⣿⡍⢣⠀⣿⣿⣿⣿⣷⣤⠂⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⡿⡇⠀⠀⠸⠀⠀⡆⠀⡘⠀⠀⠀⠐⠀⣧⠠⢀⣀⠈⢿⣿⣿⣿⣿⠃⠀⢻⣿⣿⣿⣿⣿⣏⢆⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⡟⢠⠀⡄⠀⢀⠀⠐⠇⠀⡇⠀⠀⠀⠀⢀⡿⠀⠀⢹⠑⠈⠙⠛⠋⠙⡆⠀⣼⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⠏⠀⠠⠀⢃⠀⣸⠀⢰⡀⢠⡇⠀⠀⡀⠀⣸⠀⡇⠀⢸⡄⠈⡄⠀⠀⠀⡇⠀⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠘⢿⣿⢏⠄⠀⠀⡀⠀⠀⢸⠀⢸⣇⠀⢳⣴⠀⡇⠀⣇⣷⣾⣦⣀⡁⠀⣧⠀⠀⠀⡁⠀⠸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⣸⢃⠈⠀⢀⢠⡇⠀⠀⢸⡇⠈⠿⡄⠈⠻⡆⢹⡄⠃⠁⢘⣻⣿⣿⢿⡎⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀ ⠀⢠⣳⠇⠀⢠⠋⢸⡇⢰⠀⢸⣷⠼⠛⠻⠄⠀⠁⠀⠀⠀⠀⢸⣟⣿⡟⢸⠁⠀⠀⠀⡄⠀⠀⠀⠻⡷⢻⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⣿⣿⠀⣶⠃⢀⣦⢿⠸⣆⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢠⠀⠀⠀⣧⠀⠀⠀⢀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢿ ⢸⡟⢧⢀⡿⢠⠎⠸⣸⠖⠋⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣸⠀⠀⡀⢀⣿⡀⠀⢠⣾⠇⡏⣀⣠⠔⠀⠀⠀⠀⠈ ⠀⠛⠈⢦⣷⡎⢀⣴⠁⠀⠀⠀⠀⠀⢱⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠞⠛⠀⠀⡁⢸⢻⢷⠀⣸⢟⠀⡇⠺⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠟⣽⠋⠀⠀⠀⠀⠀⠀⠘⢿⠉⣳⣦⣄⣀⣤⣶⠞⠉⡇⠀⠀⠀⢠⠁⣞⠎⡴⢣⡟⡟⢰⠃⠇⠀⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⠀⡏⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣟⢻⣿⡇⠈⠃⠀⠀⠘⢀⣴⢀⡌⡜⢡⠞⠀⠀⣹⣡⠞⣤⠀⠀⠀⠀⠉⠢⡀⠀ ⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡞⣨⠿⣯⣷⣄⣀⣀⡤⠖⠁⣀⠞⡸⠙⣅⠞⠀⡨⠋⠀⠈⢾⣷⡄⠀⠀⠀⠀⠹⡀ ⠀⠀⠀⢠⢿⡓⢦⣄⣀⠤⠤⠒⠛⠉⠀⠰⣿⠁⠀⠈⠓⣦⢤⣤⡤⠖⠚⠁⠀⣀⡔⠁⡠⢺⠁⠀⠀⠀⠈⡇⠻⢢⡀⠀⠀⠀⡅ ⠀⠀⠀⣯⠈⡻⢾⡉⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⢰⠋⢙⡇⠀⠀⠀⠀⣼⠋⢠⠞⠁⡎⠀⠀⠀⠀⠀⡇⠀⠈⠈⠄⠀⠀⠘ ⠀⠀⣰⠛⡦⠇⠀⠉⠁⠐⠒⢲⢒⡟⠁⠀⠀⠀⠀⠀⠈⣿⢫⠆⠀⠀⠀⢰⡏⡰⠃⠀⠀⠳⡀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢀⣏⣽⠁⠀⠀⠀⠀⢣⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⢉⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡔⣹⣿⣤⣿⣿⣧⣤⡿⣹⣿⡇⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣯⢹⣷⣼⣿⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡸⢠⣿⣿⣿⣿⢙⣿⣿⣧⡟⣿⣇⣿⣿⣿⣿⣿⡟⣿⠀⠈⣻⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣿⣏⣻⣿⣿⣭⣿⣿⣿⡀⠀⠀⢻⣿⣿⣾⣿⡟⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⢀⡀⠹⣿⣿⣿⣤⣾⣿⠁⢸⣿⠛⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠖⠊⢹⣿⣿⠿⣿⣿⡇⠈⢿⣿⡇⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣷⣿⣿⡆⠁⣿⢧⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⣿⠻⣿⣿⣿⣿⣿⡟⠀⣀⠤⢾⡇⣧⠀⣿⣿⡁⠀⣼⣿⣡⣶⣾⣭⣅⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢉⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡏⠀⣿⣿⣿⣿⡿⢡⣼⣿⣿⣿⣷⡿⢠⣿⠁⡇⣰⠃⠟⣹⣿⣿⣿⡿⠋⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⡿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠸⣧⣸⣿⣿⣿⣿⣿⢯⣩⣿⣟⣭⠟⣷⠞⠁⠠⠟⠁⠀⠀⠀⠉⠓⠋⠁⠀⣸⣿⣿⣿⢙⣼⣿⣿⣿⣿⣿⣮⣳⠯⢶⡤⠀ ⠀⠀⣀⣠⢿⣿⣿⣿⣿⣿⢩⠞⢯⠏⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣇⡾⠘⣿⣿⣿⣿⣏⠛⠛⠓⠉⠀⠀ ⠀⠀⠉⠉⣉⣽⣿⣿⣿⣿⡇⢰⠉⣀⡠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⡈⠛⢯⣿⠀⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣧⡘⠁⡠⠜⠁⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣶⠈⢿⠀⢹⣿⣿⣿⢹⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡟⢿⣿⣿⡿⣶⣷⣤⣾⣄⡀⠀⠈⠉⠁⠀⠀⠁⠀⠀⣼⣿⣿⣿⡟⠋⠁⢀⡼⠃⣸⣿⣿⣿⠈⣿⡆⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣌⠻⣿⣧⠀⠀⠉⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣸⣿⠃⣿⢻⡇⠀⡠⠋⢀⡜⢹⠃⣿⣿⣀⣿⡇⠀⠀⠀⠀ ⠀⠀⢸⡟⢿⣿⣿⢿⣿⣷⣝⢿⣷⡀⠀⠀⠀⠈⢻⣿⣆⠀⠀⢀⣀⣴⣿⡇⠀⣿⢸⣧⠀⠀⠰⠋⣠⢼⣿⠟⢻⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⣿⡇⣸⣿⣿⣮⠻⣿⣿⣷⣮⣍⡉⠀⠀⣠⣴⣿⣿⡟⠋⢉⣿⠛⣿⠉⡆⢸⣸⣯⠣⣤⣴⣾⣿⣿⣃⣤⣾⣿⣿⠇⢹⡀⠀⠀ ⠀⠀⣿⠀⢷⣿⣿⣿⣧⣬⠛⢉⣿⣿⠉⢲⣾⣿⣿⣿⣿⡇⠀⣾⠃⠀⡿⡆⣧⢀⣿⣿⣿⠁⠹⣿⣿⣿⣿⣿⣿⢿⡟⠀⠀⡇⠀⠀ ⠀⠀⣿⡇⠈⢿⠛⢿⣟⠉⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⠀⣇⢹⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠿⣵⣿⣷⠀⢠⡇⠀⠀ ⠀⠀⣿⡻⣄⠸⢧⢴⣿⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡀⠴⠾⠀⢻⣿⣿⣿⣿⣿⣯⡉⠉⠻⣿⣾⣿⡟⢨⣷⡿⠁⠀⠀ ⠀⠀⠹⡝⢿⣿⣦⣤⣶⣿⣿⠟⠙⢡⣿⣿⣿⣿⣿⣿⠋⠀⠸⣿⣷⡄⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⣆⣸⡛⣛⣦⣀⣸⣿⡅⠀⠀⠀ ⠀⠀⠀⢙⣾⣿⡿⠿⣿⣿⢡⣐⣀⣾⣿⣿⣿⣿⣿⣿⠐⡶⣤⣿⣿⣿⣿⡂⠀⠀⠙⣿⣿⣿⣿⣿⣿⣯⠉⠹⢧⡞⢣⢻⣷⡀⠀⠀ ⠀⠀⣰⡿⢡⣿⠿⣟⣻⡟⠚⠛⣿⣿⣿⣿⠛⣿⣿⣿⣷⣖⠚⠃⠛⣿⣿⣿⣦⡀⠀⠪⢿⣿⣿⣿⣿⣿⣧⠀⠈⡗⠻⡄⣿⣧⡀⠀ ⠀⣰⡟⢀⣏⠟⢫⡁⠀⢙⠶⠦⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣦⡀⠀⠈⠛⣿⢿⣿⣆⠀⠀⠹⣿⣿⣿⣿⣿⡴⢀⡇⠀⢹⣿⡏⣷⠀ ⢀⣿⡇⣸⡁⠀⣾⡄⠼⡏⠀⢸⣿⣿⣿⢿⠀⠸⣿⣿⣿⠽⣿⡻⣖⠚⠓⢙⣏⠙⠙⢷⣀⠀⠘⣿⣿⣿⣿⡏⢹⣿⣿⣿⣟⠁⢻⡇
⢠⣣⣰⣣⠀⠘⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⣟⡗ ⠧⡞⢳⠊⡇⠰⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠉⠁ ⠀⠁⠘⠐⠂⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣟⢷⡀⠀⠀⠀ ⠀⠀⠀⠀⢸⡿⢻⢿⣿⣿⢹⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣎⢧⣿⡄⠀⠀ ⠀⠀⠀⠀⢸⣥⡇⣾⣿⣿⣮⣿⣿⡇⡿⣰⣡⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡏⡇⣿⣿⣿⣇⡿⢁⡀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⠝⠓⢬⠉⠉⠀⠃⠀⠾⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆ ⠀⠀⣀⣤⣼⣿⣟⡅⠀⠀⢦⠀⠀⠀⠀⠀⠀⠤⠐⠊⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣸⣿⣿⣿⣿⣿⣷⠄⠀⢀⠀⠀⠀⠀⠀⠔⠂⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⢳⡿⠿⠿⠿⣿⣎⠁⠁⠀⠀⠤⣊⠤⠐⠂⠩⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⡹⣅⣇⠀⠀⠀⠘⢸⣿⡄⢠⠐⠂⠓⠈⠀⠀⠀⢀⣾⢏⣿⣿⣿⣿⣿⣿⠟⠁⠀ ⠊⠀⠑⢄⠀⠂⢀⠀⣿⢿⣄⡀⠣⣀⠀⠀⠀⡀⠞⣁⣾⢟⣿⠟⢋⠕⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠁⠒⠻⡏⢿⣿⡷⣶⣤⣍⢠⡴⠊⠈⡠⠀⠁⢠⠊⡸⣠⣶⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢔⡟⠋⠉⢙⠄⠀⣔⠋⠇⡠⠊⣀⣀⡠⠥⢴⣿⣿⣿⣿⢠ ⠀⠀⠀⠀⠀⠀⠊⠂⠀⣿⣿⠿⢾⣾⣿⣧⣇⠈⣠⣷⣶⣶⣶⢸⣿⣿⣿⣿⣿⣺
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣾⣾⣷⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⡋⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣖⠷⠖⠒⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣮⡳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡀⢻⣿⣿⠙⣿⣿⣌⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠄⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣷⡘⣿⣿⣷⡜⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠘⡀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠠⠜⠃⢡⠂⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⣿⣿⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⢠⢄⢠⠀⠀⠀⠀ ⡠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣼⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠇⠈⣿⠘⢦⠈⣿⣿⣿⣿⣿⣿⣿⠀⡷⢻⡟⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠄⠄⠉⠀⠀⠀⠀ ⠀⢀⡴⠉⠀⠀⣤⣤⣤⣤⣴⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⡿⠖⠛⠛⠳⢾⣷⣇⣹⡿⠿⠟⠛⢃⣼⠷⠶⢿⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡴⠋⠀⠀⠀⣠⣿⣿⠿⢫⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡏⠀⠀⠀⠀⠀⣄⠹⣿⢷⣦⠀⠀⠀⢻⣏⡄⠀⠀⢸⢿⣿⣿⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢ ⠞⣠⢞⣵⠞⣡⣿⡟⡀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠘⣿⠀⠸⠇⠀⠀⠀⠀⠘⢽⡇⠀⠀⢸⢸⣿⣿⣿⡞⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡷⣋⡴⢟⡵⣿⡷⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⣿⣿⣿⣿⢿⣿⡄⠀⠀⠀⠀⢀⠀⠀⣀⠷ ⣿⢟⣥⠞⠃⠀⣿⣃⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢳⡀⠀⢀⣀⣠⡴⠟⠀⠀⠀⠀⠀⠀⠀⠠⣤⡾⠃⣾⣿⣿⣿⣿⢸⣿⣇⠀⠀⠀⠀⠈⠑⢦⣿⡻ ⢿⣫⠄⣀⠄⠒⣿⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣻⠋⢍⣏⣁⡄⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠰⠘⣿⣿⣿⣿⣿⣸⣿⣿⡄⢀⣀⠀⠀⣀⠀⢫⡿ ⣫⠔⣊⡥⠂⠀⣿⣼⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠁⠈⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⢿⡇⢸⣟⠿⣶⣆⡀⠈⠁ ⢶⣫⠵⢂⣠⠴⣿⡟⣭⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡇⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠸⠁⢸⣯⣻⣿⣬⣿⢷⣦ ⣯⠵⣛⣭⠤⠂⠛⠉⠛⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⠛⠋⠉⠉⠉⠛⠷ ⣚⣯⠥⢂⡀⠀⠀⠀⠀⠀⠸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐ ⠷⣒⣋⠉⠁⠀⠀⣀⣤⠄⠀⠘⣧⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⢿⡦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣽⡆⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⡭⠿⣶⣶⣿⣯⠥⠤⠀⠀⠀⠀⠈⠂⠀⢘⣫⠟⠋⠀⠀⠀⠀⠉⠙⠻⠿⠯⣿⠷⠤⢷⣄⡉⠉⠒⠶⣤⣤⣤⣤⣶⣿⣿⢿⡿⣋⣉⠑⠃⠀⠉⠳⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲ ⣉⣭⠽⠿⠷⠖⠂⠀⠀⠀⠀⠀⠀⠀⣴⠏⠉⠑⠲⡀⠀⣠⠞⠙⠒⠦⢄⣀⠈⠙⠦⣄⠀⠈⠉⠑⠲⢬⣛⠮⣽⠛⠿⣾⠿⠭⣁⠈⠙⠳⣄⡀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠂⠤⢤⣉ ⣒⣛⣛⡻⠋⠠⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢹⡈⠁⠀⠀⠀⠀⠀⠀⠉⠓⠦⢄⡙⢦⣤⠤⠤⠤⠬⣿⣻⠷⠞⢿⣿⢶⣭⡟⢦⣄⠀⠙⢦⠀⠀⢳⡄⠀⢀⣀⠀⠀⠒⠂⠠ ⣒⣒⣒⡒⠒⠒⠒⠒⠒⠒⠒⠀⢠⠇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣸⣿⣿⣿⣶⣯⣓⣦⣼⣿⣿⣿⣷⡄⠉⠓⢦⡈⢳⡀⠀⢳⠸⢵⢬⣭⣦⣤⢀⣀ ⠭⠭⠭⠥⢤⠤⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⡄⠀⠀⠙⢦⣹⣣⠈⣷⢄⠲⣶⡾⠶⠀⠠ ⢿⣍⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣾⣿⡿⠀⠀⠹⡟⠿⣿⣧⠀⠀⠀⠐⠋⠻⣄⢻⣟⣛⣛⣛⣋⣉⣉ ⣿⣓⡒⠢⠄⠀⠉⠉⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠰⡀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠉⠀⠀⠀⠀⠈⠳⣄⡈⠳⡄⠀⠀⠀⠦⡈⠻⣧⣬⣬⡤⠦⠤⠶ ⣿⡶⠬⣭⣀⡀⣀⣀⣀⢀⣀⠀⢻⣤⠀⠀⠀⠀⠀⢳⡀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡈⢦⡀⠀⠀⠘⢄⠈⢳⣶⠖⠒⣚⣉ ⡿⢭⣓⡲⠬⣭⣿⣟⠿⢿⣿⡄⠀⣏⣆⠀⠀⠀⠀⠀⢳⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢳⡀⠀⠀⠀⠳⡀⠙⣦⣬⣽⣽ ⣭⣒⠮⢍⠓⠲⣿⣟⢿⣶⣿⠇⢀⡟⣟⡄⠀⠀⠀⠀⠀⠹⣼⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢳⠀⠀⠀⠀⠹⡄⠈⣿⡻⣛ ⣷⢯⣝⠲⠄⠀⣿⢏⡀⡴⣿⣆⡟⠉⠙⠾⣄⠀⠀⠀⠀⠀⠹⣷⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢺⡇⠈⡆⠀⠀⠀⠀⠀⠀⢈⣉⠽ ⢯⡓⢦⣙⡀⠀⣿⠄⢳⠛⣿⠻⢾⣛⠲⢄⡈⠳⢄⠀⠀⠀⠀⡿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡜⡾⢰⠀⡇⠀⠀⠀⠀⠀⠀⢸⡦⠒ ⠳⣌⠻⢬⡙⠲⣿⣄⠀⠙⣿⠆⠀⠈⠳⣄⣙⡦⣄⠙⠒⠤⣄⣷⣤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡸⢱⠁⠁⢸⠆⡇⠀⠀⠀⠀⠀⠀⠀⣗⣉
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⡿⠉⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡿⠁⣀⡀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⢠⣤⡄⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠃⢰⠏⠻⣄⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⣼⡿⠁⣴⠏⠀⢻⣆⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡟⠀⡟⠀⠀⠹⣦⠀⠘⠿⠿⠿⠿⠟⠻⠿⠿⠅⢸⠃⠀⠀⠀⢹⡄⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡟⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠈⢻⣄⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⠁⠀⠀⢀⣾⠁⠈⠻⣦⡀⠀⠀⠀⠀⢀⣤⠶⠋⠁⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠇⠀⠀⢀⡾⠁⠀⠀⠀⠈⠙⢷⣄⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⢤⣄⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⢰⡟⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡏⠈⣷⠀⠀⣿⣿⣷⡄⠀⠀⠀⢠⣤⣤⣤⣤⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠰⢿⣤⣄⡀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀ ⣿⡇⠀⣸⡆⠀⠹⣿⣿⠇⠀⠀⠀⠸⠿⠿⠿⠿⠀⠀⠀⠀⠸⠿⠿⠋⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⡆⠀⠀⠀⣠⣴⣾⠿⠛⢻⣿⠃ ⣿⠁⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣠⣴⣿⠿⠃⠀⣴⣾⡿⠋⠁⠀⠀⢸⡇⠀ ⣿⣷⣬⣿⣄⣀⠀⠀⠀⠀⠀⠀⠘⢿⣏⠙⢀⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⠉⠀⠀⣠⣾⡟⠋⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠈⠉⠛⠛⠻⠿⢷⣶⣦⣤⣀⣀⣘⠛⠿⠟⠋⠀⢀⣀⣀⣀⣤⣴⣶⣶⠿⢿⣿⣅⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡟⠛⠛⠿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠙⣿⣧⡀⠀⠀⠀⢸⡿⠀⣠⣤⡆⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⢸⣷⠞⠋⢰⡇⠀⢀⣀⡀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⢸⡇⠀⠀⠀⠷⠴⠟⠁⢷⣼⣿⠀ ⠀⠀⠀⠀⠀⠀⣾⡿⠿⣿⣾⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⣿⣥⣶⡿⠿⢿⣦⠀⠈⣿⡇⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⢿⣿⡶⣄⣀⡴⠿⣿⣄⠀⣠⠶⠛⢹⣿⠟⠁⠀⠀⠈⣿⡇⠀⢹⣷⣾⡿⠁⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠈⢿⣇⠈⠉⠀⠀⣿⠛⠛⠁⠀⠀⢸⡇⠀⠀⠀⠀⢀⣿⠇⠀⢸⣿⠉⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⡀⣸⣿⡀⠀⠀⢀⣿⡄⠀⠀⠀⠀⣸⡇⠀⠀⢀⣠⣾⡟⠀⢀⣾⣟⠀⣀⣠⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⠀⠀⠐⣢⡤⠄⠒⠂⢹⡄⣠⡴⠛⠉⠉⢫⠉⢳⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⡶⠦⣄⠀⠢⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠛⢻⣠⡴⠛⠁⠀⠀⠀⠒⣠⣿⣧⣀⣀⣤⣄⡈⡄⣀⣳⡄⠤⣔⣒⣲⣾⣍⣵⣯⣵⣖⣒⣒⢦⡴⣆⡀⡰⠁⠜⠀⠀⠀⠑⠀⠆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢶⣶⠟⠀⠀⢠⡞⠁⠀⣿⣿⣤⣟⣮⣻⢯⠐⢾⠏⠙⠁⠘⡄⠀⠼⠀⠈⠃⠈⢦⠈⣏⠉⠶⠻⣷⢖⡄⣀⠀⠀⡀⠈⠀⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠿⠿⢵⣿⢃⣾⠇⢀⣀⣠⡿⠽⠳⢤⣿⣿⣿⠟⣿⣿⣼⠀⠉⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠈⣇⠸⡄⠀⠀⠈⢧⢍⠳⠿⡂⢀⠀⠀⠀⠄⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢸⣏⠙⠿⠞⣻⡿⢟⣻⠴⠛⢻⣿⣿⡻⣦⣿⢞⣁⠀⢠⣤⣶⣾⣏⠛⢀⣀⣻⣿⣿⣿⣿⣜⣀⠹⣤⣤⣤⠬⠯⢦⡀⠘⢿⣷⡒⠂⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢠⣾⠹⣆⠀⠀⠀⣴⠉⠙⡄⢀⣾⣿⣽⢩⣿⣿⣯⣢⣤⡴⠟⠛⠉⠉⠙⢉⣿⠋⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⣿⠶⣾⣿⣷⡀⢻⡽⣆⠀⠀⠀⠀⠀ ⣀⠀⣀⣿⠿⠑⢨⣿⣶⣤⣄⣼⣧⠀⠻⣆⠀⢰⠇⣀⣀⠙⢺⣾⣏⡿⠿⣯⣄⣽⣿⡇⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠉⠻⣶⣿⡸⣻⣿⣂⡀⠀ ⣿⣿⡏⠀⠀⢀⣿⡟⠈⢻⣿⣾⣿⡀⠀⠹⣷⡿⠞⠉⢨⣿⠇⡿⠚⠓⢶⠦⢴⣧⣽⣅⣉⣉⣛⣒⣲⣶⣾⡇⣷⠀⠀⠀⢠⣀⣀⣀⡀⣀⣠⡜⣿⣀⣀⣀⣀⣷⠨⠏⢳⡝⣷⠀⠀ ⣿⠁⠙⢤⣀⣿⠏⠀⠀⢸⣿⣿⢻⣇⠀⠀⢸⡇⠀⠀⣼⣿⢸⠃⠀⠀⠀⠀⣼⡇⣿⠀⠀⠀⠀⠀⠈⣉⣿⡟⣿⠀⠀⠀⠐⠒⠒⠒⠲⡤⢸⡇⣿⠭⢥⣤⣀⣸⣄⣀⣀⣻⡽⠀⠀ ⣧⣀⠀⠀⣻⣯⡀⠀⠀⣾⣿⣿⠘⣿⣆⠀⣿⠁⠀⠀⡟⠙⠉⠀⠀⠀⠀⢠⣿⣷⡇⠀⢰⡀⠀⠀⠀⣿⣿⡄⡏⡄⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇⣿⠀⠘⡇⠀⢻⣿⠉⠙⣿⣧⠀⠀ ⠀⠉⠛⣶⣧⣌⡙⠶⣴⣿⣿⣿⡇⢹⣿⣾⡏⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⣼⣿⣿⡷⠶⣾⣧⣤⣤⣰⣏⣇⣿⣧⡁⠀⠀⣿⠀⠀⠀⠀⢸⢸⡇⣿⠀⠀⡇⠀⢸⣿⠀⠀⢸⣿⡀⠀ ⠀⠀⣼⠋⠁⠀⠉⠙⣿⣿⣿⣿⣿⠈⣿⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡀⢿⣿⣿⠁⠀⢸⣤⡄⠈⢹⣿⡷⣿⢸⡇⠀⠀⣿⠀⠀⠀⢀⣿⣼⣷⣿⠶⢶⡷⣤⣸⡟⠀⠀⠀⣿⡇⠀ ⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⢙⣿⣆⢀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⡟⣿⡄⠀⣾⢧⡇⠀⢸⣿⡇⣿⢸⣇⠀⠀⣯⠀⠀⠀⣼⣿⡟⡿⣿⠀⣼⣿⡧⣿⡇⠀⠀⠀⣿⣷⣼ ⣦⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣼⣿⣿⢸⡀⠈⡇⠀⠀⠀⠀⠈⢀⡾⠷⢸⠿⠤⣼⣼⣧⣀⣾⣿⡇⣿⢸⣧⠀⢠⣿⠀⠀⢀⣿⣿⣻⣧⣟⢰⣿⣼⣆⣿⠃⠀⠀⣄⣿⣿⣿ ⠏⠀⠀⠂⢀⠀⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢸⡇⠀⠀⠀⢀⡆⠈⡇⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠃⠛⠸⠹⢧⣬⣿⣤⣤⣼⢻⣯⣿⣸⠥⠿⠿⢿⣿⡟⠀⠀⠀⣿⣿⣾⣿ ⠀⠀⠫⠃⢈⡖⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⡎⣷⠀⠀⠀⠀⣷⢀⣷⢤⣀⣠⣀⡀⠀⠠⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣸⡏⠐⠀⠀⠀⣿⣿⣷⣿ ⠀⠀⠐⠊⠚⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣇⣿⠀⠀⠉⠉⣿⣿⣿⡿⠿⠛⠓⠻⠿⠿⣶⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣲⣷⣖⣢⣿⠃⠀⠀⠀⢸⣿⣿⣿⣼ ⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⡟⠈⢿⡇⣸⣿⣿⣽⡆⠀⠀⠀⣿⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠙⢋⣿⡏⣰⠇⠀⠀⢸⣟⣿⣿⣿ ⠀⠀⠀⠀⠀⣼⣏⣸⣿⣿⣿⣿⠁⣿⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣱⡟⣠⣤⠴⠿⠿⠯⠿⠿ ⠀⠀⠀⠀⢠⣿⠋⣽⣿⣿⣿⣿⢠⣿⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡿⠛⠉⠁⠀⠠⠀⠐⠂⠀ ⠀⠀⠀⠀⣾⠏⣨⣿⣿⣿⣿⣿⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⣿⢴⣿⡟⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⠁⢹⣿⣿⣿⣿⡟⣸⣿⠀⢸⡇⣿⣿⣿⣿⣿⣷⠀⣿⠾⣿⣧⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢾⡿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⠋⠀⣿⣿⣿⣿⣿⡟⣿⣿⠀⢸⠂⢻⣿⣿⣿⣿⣿⣧⣿⡀⣿⣿⡄⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠁⠰⢋⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⣼⢋⡄⢠⣿⣿⣿⣿⣿⣧⣿⣿⠀⢸⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⡟⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣇⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡟⠁⢠⢰⣿⣿⣿⣿⣿⣿⣿⣽⣿⠀⢸⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⢿⣿⣦⣄⡀⠀⠉⠳⢦⣄⡀⠀⠀⠀⢀⣠⣴⢾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿ ⡿⠁⠀⠘⣾⣿⣿⣿⣿⣿⣿⣯⣭⣿⣀⡨⠧⠤⣄⣈⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⠋⠓⣾⣿⣯⡾⠿⠿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢰⡟⠋⠁⠀⣿⢿⣄ ⡇⠀⢠⢢⣿⣿⣿⣿⣿⣿⠁⠀⡼⠃⠀⠀⠀⠀⠀⠀⠁⢽⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣾⣛⡒⠂⠀⠀⠀⠒⠐⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡆⢻ ⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⡙⢿⣿⣿⣿⡿⣿⣽⡛⠛⣿⠿⠟⣋⢿⡍⠉⢿⣷⡒⠒⡒⣖⠛⠛⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⡇⠤ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣵⡀⠙⢿⣿⣷⠿⣿⣿⣶⣌⠲⣶⣿⣾⣇⣠⡤⢿⣷⠀⠘⣞⡆⣸⠁⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⢷⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⣿⣿⠆⠈⠀⠉⠻⣿⣷⠶⠦⣽⡆⠀⠀⢷⢧⠀⠸⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠸⡄ ⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣂⠘⡿⡀⠀⠀⠀⠀⣿⣁⠀⠀⣠⡇⠀⠀⠈⡟⡆⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⡀⠀⠀⠀⠀⡟ ⣾⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣦⣱⣷⠀⠀⠀⠀⠈⣻⣿⠛⢿⡢⣀⡀⠀⢸⣾⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢿⣇⠀⠀⠀⠀⢻
⠀⠀⠀⠀⢀⣴⣧⣽⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⡐⣿⣽⣿⣥⣟⣿⢹⣿⣿⣿⡟⢿⣿⣿⣿⣟⣧⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⢰⣸⣿⣿⣶⣿⠞⣸⣺⣿⣻⣿⣇⠀⢻⣿⣼⡿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣏⠠⣿⣿⣿⡟⢿⣿⠒⠠⢹⣿⣷⣾⣄⣿⠹⣧⡀⠀⠀ ⠀⠀⡟⣿⣿⣿⡟⣁⣴⣏⡅⣿⡇⠸⣯⣦⣤⣦⣿⣿⣿⣿⣿⣧⣰⡉⠁⠀ ⠀⠐⣇⣾⣿⣿⣜⣻⣟⡛⡵⠃⠷⠃⠁⠻⠽⠃⢻⣿⡟⣹⣿⣿⣿⡻⣢⡄ ⠠⠴⢿⣿⣿⣯⢚⠏⠀⠊⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⢷⠘⣿⣿⣯⠉⠉⠀ ⠀⢀⣽⣿⣿⣿⣜⠨⠙⡀⠀⢀⡀⠀⡀⠀⣠⣵⣿⡶⠙⡀⣿⣿⣹⡇⠀⠀ ⠀⣾⣿⣿⣞⢿⣏⠛⠻⢷⣤⡀⠀⠀⠀⢰⡟⡿⡏⢀⠌⡠⡟⣿⣿⡇⠀⠀ ⠀⣟⣿⣿⢿⣷⣟⠦⠀⠀⢙⣷⣄⠠⣴⣿⠄⡇⡷⡀⢊⣔⡿⢉⣿⣿⡄⠀ ⢰⡇⢾⣿⣧⢝⣻⣿⢑⣶⣿⣿⡇⣸⠃⡿⣲⣸⣷⣎⢻⣿⣿⣿⢿⠃⢸⠀ ⠈⡷⡈⣏⣽⣼⣿⣿⣾⣿⣿⣿⡇⣿⣀⠤⢹⣿⣿⣿⡟⠛⢿⣽⡟⣣⡞⠀ ⠀⠫⣻⣶⣶⡿⠋⢡⣿⣿⣿⡏⣀⢻⣷⡄⠀⠻⣿⣿⣿⣦⠯⢵⣢⢿⡄⠀ ⢀⡼⣽⣷⠺⡗⠛⣿⣿⠛⣿⣷⣕⠋⠻⣿⣦⡀⠸⢿⣿⣿⣧⠀⡓⢃⣿⡄ ⣼⢱⡊⢰⠠⠌⢹⣿⣿⠀⢿⣿⣻⡧⡤⠬⣯⠛⢆⡀⢻⣿⣿⡇⣧⣼⡟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡿⠿⠛⠉⠉⠉⠛⠻⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⣠⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣄⠀⠀⠀⠀⠀⠈⣿⣧⡀⠀⠀⠀⠀ ⠀⠀⢀⣴⠿⣻⡟⠀⠀⠀⠀⠀⢸⣿⣿⣦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣶⣄⠀⠀ ⠀⢰⣿⢃⣴⡟⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠃⠀⢠⣦⠀⠀⠀⢰⣆⠀⢻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠹⣿⣎⢿⣆⠀ ⠀⣿⡇⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⣤⣿⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⣿⡆ ⢰⣿⣷⡜⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⣼⣿⡇ ⢸⣿⠙⢿⣶⣝⡻⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⢛⣩⡿⠋⢹⡇ ⢸⣿⠀⠀⠉⠻⢿⣶⣾⣭⣛⡿⠿⣶⣶⣶⣦⣤⣤⣤⣄⣀⣤⣄⣤⣤⣤⣤⣤⣤⣶⣶⡾⠿⢿⣋⣭⣷⠿⠟⠉⠀⠀⢸⡿ ⢸⣿⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⢶⣦⣤⣤⣭⣭⣭⣍⣉⣉⣩⣭⣭⣭⣭⣤⠶⠶⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇ ⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀ ⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀ ⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣷⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣶⣟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠈⠙⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠖⠁⡴⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠊⠀⠀⠜⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀ ⠀⠀⠀⢠⢃⠁⢀⡞⠀⢰⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠘⣆⠀⠀ ⠀⠀⢠⡇⠁⠀⣾⠁⠀⣦⠀⠀⠀⠀⠀⠀⠀⡄⢀⠪⠵⠑⡄⠀⠀⠀⠀⢹⡄⠀ ⠀⠀⢆⠁⡄⢸⠹⡀⢀⠀⠀⢀⠀⠀⠀⠀⡀⢁⠈⢆⣀⣀⠕⠆⠀⠀⢃⠈⡇⠀ ⠀⢸⢸⠀⠀⡏⢩⢇⢈⢰⠀⠸⡰⠀⠀⢃⡇⠈⡆⠈⠀⠀⡆⠘⠄⠀⠈⠀⢇⠀ ⠀⠘⡔⡀⡀⣁⣴⣿⣼⠪⢦⣂⡱⣅⣢⣼⣶⣤⣴⡄⢸⠀⡧⣀⠂⡐⢄⣷⡼⠀ ⣠⢾⢿⣳⣷⣿⡟⠉⠛⡄⠀⠀⠀⠀⠘⠟⠉⢛⣿⣧⣸⠀⡏⠢⠝⢨⣿⣿⣷⠒ ⡅⢦⡌⣏⠉⣏⢀⣈⣡⠇⠀⠀⠀⠀⠀⣄⠈⢀⡸⣿⠙⠀⡿⠍⡄⢸⣧⠿⠘⢀ ⠫⠭⠊⣿⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⡄⣸⠩⢉⠟⡙⢏⠀⠓⣤ ⠀⠐⠖⠋⡼⡞⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣠⠇⢈⠠⠊⠀⠘⠧⠤⠄ ⠀⠀⠀⠀⠀⠹⡀⠑⠠⣀⠀⠀⠀⠀⠀⣀⠠⡰⣹⢃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠂⢄⠀⠀⠙⠓⠂⣀⠉⠤⠼⠯⠇⢑⣚⠚⠋⢑⠒⠈⠉⠁⠀⠈⠐⢄⠀⠀ ⠀⠀⠀⠀⠈⢢⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠃⠤⠀⠀⢀⠀⠉⠉⠁⢂⠀
⠀⣰⢦⠀⣠⢶⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠭⠳⠭ ⣼⠷⢺⣴⡿⠾⣇⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⢾⢐ ⠧⠴⡶⠚⢸⠇⢸⡏⠀⡸⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⡇⠀⣿⠀⣘⡀⢀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢻⣧⣹⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⢰⠏⣸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⢿⣿⡏⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢣⣧⣾⢠⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⡏⣾⣿⢀⣎⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣾⣿⣿⡟⣿⢻⣿⣿⣿⣿⣿⡇⢹⣷⠟⠋⠉⠀⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⣿⠸⣿⣿⣿⣿⡟⣄⢼⡏⠀⣠⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣟⣹⡿⣄⣉⠛⠛⠙⠃⠀⠸⠇⠀⠸⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠋⠁⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣧⢹⡀⠀⠀⠀⠐⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠒⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣷⣧⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⠀⠀⢀⡤⠀⠀⠄⠀⠀⠀⢀⠔⠉⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⠀⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠒⠐⠁⠀⠀⠀⠀⢀⡠⠐⠁⣀⣠⠤⠖⠊⣹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⣰⣿⣿⢁⡾⠛⠉⠁⠀⠀⠀⡉⢻⣿⣇⠀⠀⠀⠀⢠⠊⠉⡠⠔⣺⠉⠀⠀⠀⠀⠐⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀ ⣸⢏⡝⢸⡀⠀⠀⠀⠀⠀⠀⠃⢸⣿⣿⣆⠀⢠⠀⢸⠳⠾⠒⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠡⠊⠉⠛⢏⠀⠀⠀⢀⡀⠀⠀⠀⣿⣿⣿⣆⠀⠁⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⣾⣿⣿⣿⣿⣿⣿⡿⢟⡿⠋⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠑⢄⡀⠈⠀⠀⡀⠀⢿⣿⣿⣿⣧⣄⡀⠈⠣⢄⣀⠀⠀⠀⢀⣀⠤⠛⢁⣠⣾⡿⠟⠽⣿⡿⠋⠁⣠⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠂⠤⣼⣿⡇⢻⣿⣿⣿⣷⣶⣤⣄⡉⠉⠉⠁⣀⣤⡶⠁⠊⠁⢀⡠⠒⠁⠀⢀⡜⠁⢠⠃⢠⣤⣴⣶⠀⠀ ⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⣙⣿⣿⣿⡝⠻⠿⠿⠿⠖⣻⢿⠋⠀⠀⢀⠔⠉⠀⠀⠀⢠⠎⠀⠀⣾⣰⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⡏⠉⠁⠀⠀⠈⣩⠅⠀⠀⣴⡚⠁⢸⠀⠀⡰⠃⠀⠀⠀⠀⢀⣏⣤⣴⣾⣿⣿⣿⣿⣿⣿⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣉⠀⢸⣿⣶⣴⣶⣤⠚⣥⣠⣶⣾⡿⢱⡄⢇⡴⠊⢠⣴⣪⣉⣉⣉⣅⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠁⠀⠀⠀⠑⣿⣿⣿⠟⠛⠃⣿⣿⣿⣿⣿⣿⣧⡄⢄⣴⣿⣿⣿⣿⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⣼⣿⡤⠤⢤⣤⣤⣤⣶⣾⣿⣿⣿⣷⣾⣿⣴⣂⠀⡖⠀⠠⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⣠⠴⣿⣿⣯⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⢉⡿⠀⢰⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⢀⠤⠴⠒⠚⠛⣿⡿⣶⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣶⠋⢀⣴⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⣄⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀ ⠰⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠂⠀ ⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤ ⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣉⠉⠁ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⡧⣤⠔⠊⠁⠀⠀ ⠼⠛⠉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣧⠈⠳⡄⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⣀⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠈⡀⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⢉⣀⣠⣤⣄⡘⣿⣿⣿⣿⣿⣿⣿⣏⠉⠒⠘⣿⣿⣿⣿⣿⣷⣦⡴⠃⠀⠀ ⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠛⠟⠛⠛⠉⠉⠀⠘⢿⣿⠟⠛⠻⠿⣿⣿⣷⢶⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⢿⣿⡟⠻⣆⠀⠀⠀⠀⡠⠔⠀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠰⢻⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⢡⠶⣤⣈⡿⠀⠀⢀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⢸⡇⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠧⣅⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⠄⠀⠀⠀⢀⣀⣠⣤⠴⠖⠛⠉⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⠢⣄⣀⡞⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠉⠓⠢⢤⣀⠀⠙⢷⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⠬⣷⡎⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠶⠶⠶⠶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⣠⣤⡶⠶⠶⣶⣤⡀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠙⣿⡆⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⣿⣇⣠⣤⣤⣶⣤⣤⣀⣼⡏⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣴⡶⠟⠛⠉⠉⠀⠀⠀⠈⠉⠉⠙⠛⠿⣶⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀ ⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡁⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀ ⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⣸⡏⣿⡇⠀⠀⠀⢠⡟⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀ ⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⣿⠇⣿⡇⠀⠀⠀⢸⡇⢸⡇⠀⠀⣸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⢸⣇⠀⠀⣠⣤⣤⣤⣤⣤⣿⠻⣷⣤⣄⣠⣿⠆⢸⣇⣀⣀⣀⣸⡇⢸⣇⡀⢀⣿⣿⣇⣀⣀⣀⣀⡀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⣼⠏⠀⠀⢹⣇⠀⠀⢀⣼⣿⣾⣷⣾⣬⡉⠁⠀⠀⠉⠙⠛⠛⠋⠁⠈⠉⠉⣹⣟⣬⣟⡋⠉⠉⢻⡟⠀⠀⠀⢸⣧⠀⠀ ⠀⣼⠏⠀⠀⠀⢰⡿⠀⢀⣾⠋⠁⠀⠈⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⣿⣿⣿⣷⡀⢸⣇⠀⠀⠀⠀⢻⣧⠀ ⢰⡟⠀⠀⠀⣰⡿⠁⠀⢸⡏⠀⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⣿⣿⣿⡇⠀⢿⣄⠀⠀⠀⠀⢻⡆ ⠘⣧⠀⠀⢼⣿⣄⠀⠀⠘⣿⣦⣤⣴⣾⣏⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⣀⣠⣿⣉⣿⠇⠀⠀⠻⣦⣄⠀⠀⢘⣿ ⠀⢿⣄⠀⠸⣿⣿⣦⣤⡶⢾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣯⣤⣶⣤⣾⢟⣿⠀⠀⣼⡟ ⠀⠈⠻⣦⠀⠹⣧⠙⢿⣄⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠸⢷⣶⣶⡾⠗⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⣠⡿⠃⣼⠇⢀⣾⠟⠀ ⠀⠀⠀⢹⡇⢠⣿⠀⠀⠙⢿⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⡾⠋⠀⠀⣿⢀⣾⠏⠀⠀ ⠀⠀⠀⢸⣧⡾⠃⠀⠀⠀⠀⠉⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠉⠀⠀⠀⠀⢻⣼⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⠶⣦⣤⣤⣤⣤⣤⣴⡶⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀
⠀⠀⠀⡆⠀⠳⣦⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣦⣤⣀⠀⠀⠠⡡⠂⠀⠀ ⠀⠀⠀⠳⣄⠀⠙⠅⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⡀⠀ ⠀⠀⠀⠀⠈⠣⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⠀⠀⠇⠂⣾⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠂⠀ ⠀⠀⠀⠈⣾⡟⣿⣿⠇⣿⣿⣿⡿⡇⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⢒⠀⠀⢰⣿⣷⣿⣿⢕⣿⣿⣿⣇⣷⡠⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀ ⣁⢀⠀⢸⣻⣿⣿⣿⠀⢈⠍⠛⠻⠋⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀ ⠠⠘⠀⡏⣿⣿⣿⣿⡦⡀⠀⠀⠀⠀⢁⣀⡀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀ ⠀⠀⠀⡇⢿⣿⣿⣿⣷⠀⡶⣀⣒⣂⣁⠴⢄⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀ ⠀⠀⠀⢇⠈⠣⠻⣿⣿⣦⣰⣀⠒⠁⠀⢀⢼⣿⣿⣿⣿⣿⡿⠟⡹⠀⠀⠀ ⠀⠀⢠⠃⠀⠀⠀⠈⠙⠙⠛⡻⠛⢡⠟⡩⠫⣍⠜⡠⠊⠀⢀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡏⣾⣴⣷⣳⣎⣴⡀⠔⠁⡠⠁⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠘⡀⣼⢀⡎⢹⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⢸⠄ ⠀⠀⠀⠀⠀⢀⠊⠀⡐⠀⠀⢃⢩⠊⠀⠀⠸⢘⠂⠙⠁⠀⠀⠀⠀⡆⠺⠐ ⠀⠀⠀⠀⡡⠁⠀⠐⠀⠀⠀⢢⠆⠀⠀⠀⢂⠃⠀⠀⠀⠀⠀⠀⠀⠰⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠉⠀⠀⠀⠈⠙⢻⣷⡄⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⢀⣀⣿⣷⣤⣶⡾⠿⠿⠿⢿⣶⣶⣴⣿⣇⣀⡀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣾⡿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⢿⣷⣶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀ ⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣿⠃⣿⡇⠀⠀⠀⠀⠀⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀ ⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⡇⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⣿⡀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣤⣿⠇⢻⣿⣦⣤⣤⣤⣿⡇⠀⣿⣧⣀⣀⣀⣀⣸⣿⠁⢸⣇⣀⡀⢠⣿⠁⣿⣇⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⢰⣿⠃⠀⠀⠈⣿⡆⠀⠀⠀⠀⣨⣿⣷⣶⣶⣿⣭⡉⠉⠉⠀⠀⠈⠙⠛⠻⠿⠿⠟⠋⠀⠈⠙⠛⠛⢛⣛⣀⣛⡿⠛⠛⠛⠛⣿⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⢠⣿⠏⠀⠀⠀⠀⣹⣿⠀⠀⢀⣾⡟⠛⠉⠙⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣦⡀⠀⢸⣿⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀ ⢠⣿⠇⠀⠀⠀⠀⢠⣿⠇⠀⠀⣼⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⠛⠛⢿⣿⣿⣿⣧⠀⠸⣿⡀⠀⠀⠀⠀⠀⢹⣿⡀⠀ ⢸⣿⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣾⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⢿⣷⠀ ⢸⣿⠀⠀⠀⣼⣿⣧⠀⠀⠀⠀⢻⣿⣦⣄⣠⣴⣿⣿⡀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⡀⠀⢀⣼⣿⢁⣿⡿⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠘⣿⡇ ⠘⣿⡄⠀⠀⢹⣿⢿⣧⡀⢀⣠⣤⣽⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣠⣄⡀⢠⣾⡿⣿⠀⠀⠀⣰⣿⠃ ⠀⠙⣿⣆⠀⠈⢻⣧⠻⣿⣿⡟⠉⠙⠻⣿⣏⠉⠉⠉⠁⠀⠀⠀⠀⠀⣤⣀⡀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⣩⣾⠟⠋⠹⣿⣿⠏⣸⡿⠀⠀⣰⣿⠏⠀ ⠀⠀⠈⢻⣧⠀⠀⣿⡇⠈⠻⣷⣄⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⣠⣾⠟⠁⢀⣿⠃⢀⣾⡿⠋⠀⠀ ⠀⠀⠀⠈⣿⡇⠀⣿⡇⠀⠀⠈⠻⣿⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣾⠟⠁⠀⠀⢸⡏⠀⣾⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⣿⣇⣼⡿⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠛⠁⠀⠀⠀⠀⠘⣿⡄⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⢀⣼⣿⣿⠏⠏⠀⠀⢸⡇⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⣾⡇⠀⠀⠀⠀⠉⠁⠙⢿⣯⡽⣆⢤⣤⡀⠀⠀⢀⡩⠭⠍⡙⣦⠀⠀⠁⠀⠹⣿⡇⠀⠉⠉⠉⠉⠛⠾⣽⡂ ⣼⣿⠀⠀⢀⣾⣿⣿⡿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⡆⠉⠙⠒⠖⠋⠀⠀⠀⠀⠘⢷⡄⠐⡄⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠈⠻ ⠛⣉⣀⣼⣿⠛⣿⣿⡇⢠⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠻⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣻⣿⡟⢻⠀⠘⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣟⣷⡯⢿⠇⡾⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠠⢄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠹⣦⠀⠀⠙⠳⠦⢴⣿⣿⡷⠂ ⠀⠀⠀⠀⠀⡟⢀⡇⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⣠⠴⠒⠊⢉⣉⣤⣤⣤⣤⣤⣀⣈⠘⣷⡄⠀⠀⠀⣠⠞⢉⣤⠞ ⠀⠀⠀⠀⢸⠀⣼⡇⠀⠀⠀⠀⠀⣿⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⢉⣠⣴⡾⠿⢓⣉⣁⣀⣀⣀⣠⣄⣌⣙⠻⣯⣦⠶⠋⣁⡴⣋⣭⡾ ⠀⠀⠀⠀⢸⣿⣿⠀⠀⠸⠀⠀⠀⡿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠶⠊⢉⣁⣻⡿⠋⠁⠀⠀⠀⠈⠁⠀⠈⠉⠈⠀⣼⣿⣿⣏⣤⡶⣿⣽⣿⣟⢉⡀ ⠀⠀⠀⠀⡾⣿⣿⠀⠀⠀⠀⠀⢰⢇⣼⣧⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣀⣤⠴⠛⣉⣤⠴⣚⡯⠅⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡴⠾⠿⠛⣿⠛⣿⣘⣿ ⠀⠀⠀⠀⠓⣿⣿⣰⡆⠀⠀⠀⣿⠘⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡤⠞⢉⣤⣶⢟⣋⣵⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠁⠰⠀⢀⣴⡟⠀⣿⣿⡏ ⠀⠀⠀⠀⠀⠙⣿⣯⡙⠒⢦⣼⣿⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠉⣤⣾⢛⣽⣿⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣉⢠⣶⣶⣿⠿⠶⠖⠛⠋⠁ ⠀⠀⠀⠀⠀⠐⣿⣯⡛⠷⣦⣼⣍⠙⠲⠦⠤⣀⣀⣀⣀⣀⣀⣹⣷⠟⣿⣿⣿⣿⣿⠋⠀⣴⡿⢳⠀⠀⠀⠀⠀⣴⡯⠹⡆⠀⠀⠀⠀⠀⠀⢀⡾⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⡟⠲⠮⢹⠻⠿⣷⣶⣤⣤⣀⣀⣀⣀⣀⣉⣷⣿⣿⡿⣽⣿⣿⠀⠀⡟⠉⢹⡇⠀⠀⠀⢠⠿⠦⢭⡇⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠛⠉⠀⠁⣿⡟⣿⠀⢸⡇⠀⠸⠧⠤⢄⣀⡸⠀⠀⢰⠃⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⡴⠛⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠻⠦⣄⡀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡇⡿⠀⠠⣴⣶⡆⠀⠀⠀⠀⣴⣖⣂⠀⠀⠈⠙⠲⣤⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⡾⠀⡇⠀⠀⠉⠛⠀⠀⢤⣀⠀⠛⡟⠛⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡼⠉⣽⠀⠀⠀⠀⠀⣿⣀⣷⠀⠀⠀⢨⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣤⣀⠀⡟⠛⢻⡆⠀⠀⠀⠀⡏⠀⠹⡄⢀⣠⠾⡅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠉⠛⠃⠀⠸⢧⣤⣄⣠⣤⠧⠀⠀⠓⠋⠁⢰⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀⣠⣤⣠⠀⠀⠀⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢿⠟⠋⠀⣀⣀⠀⠟⠟⠉⠀⠀⠀⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⢀⡟⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐⢞⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⡀⠀⠀⠀⣀⠠⠐⣒⣤⢼⣿⣿⣿⠶⢶⣶⣦⡀⠀⠀⠀⠀⡔⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠈⢀⠴⠋⠁⠀⠀⠉⠁⠀⢀⠠⠈⠝⠋⠓⠦⣄⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢅⣀⠔⠁⠠⠀⠀⡌⠀⠀⠀⢆⠀⠙⠄⢸⡀⠀⠀⡈⠳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡌⠀⠀⠇⠀⢰⠀⠀⠀⠀⠀⠑⡤⢨⠊⣧⠀⠀⠘⡄⠩⢆⠀⠘ ⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠂⠉⠁⡇⠀⠑⡤⢷⢳⢧⢄⠀⠰⡀⢩⡆⠀ ⠑⣄⠀⠀⢠⢼⠀⠀⠀⠂⡄⠀⠀⢰⠀⢠⠀⠀⠀⠑⢠⠮⡘⡀⢠⠀⠇⡀⡼⠀ ⠀⡇⠉⠐⠒⠚⡀⠄⠸⢠⠁⡖⠀⡜⢀⠆⠀⠀⠀⠀⢸⡄⠔⢇⠈⠀⢸⡇⠁⢰ ⢀⡇⠀⠀⠀⠀⣷⠀⠁⠹⣾⣷⣾⣷⣿⠄⠀⠀⠀⠀⣐⣒⣤⣸⡀⡇⢸⠇⠀⣸ ⢏⡀⠀⠠⣒⡎⣺⠀⠀⠀⡇⢿⠛⢻⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⡻⢳⡾⠴⠃⢈ ⠈⡿⠁⠀⠀⣃⢻⠀⠀⠀⡇⠀⠛⠉⠀⠀⠀⠀⠀⠀⠘⠤⠞⠃⢀⠋⣿⠀⠀⢸ ⣼⠁⢰⠁⠀⡇⢹⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⢸ ⠉⢆⠈⢆⠀⡇⢸⢂⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡂⡏⠀⡀⣿ ⠀⠀⠣⢈⠢⢹⢆⠎⢀⡏⠈⠒⠠⠀⣀⠀⠀⠀⢀⣀⣀⢤⢲⠇⢠⢁⠇⢰⡙⢸ ⠀⠀⠀⣴⣷⢪⡞⢠⠞⠣⢄⠀⠀⠀⠈⡏⠉⠁⠀⢀⣝⡾⢋⢔⢕⡟⢠⡿⠁⢸ ⠀⠀⢸⣿⣿⠿⠴⠋⠀⠀⠑⠪⢤⣒⠒⠓⢂⣒⠩⠔⠉⢲⣶⣧⠼⠔⠋⠀⡀⢹
⠐⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡆ ⠀⡆⠀⢙⢦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⡍⠀⡆ ⠀⡇⠀⢸⣾⣿⣷⣶⣶⣶⣶⣶⣴⣿⣿⣿⠃⠀⡇ ⢀⢧⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣊⣠⡇ ⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⣿⣿⣿⡿⡏⢹⢹⣿⣿⡿⢻⠉⣿⣿⣿⣿⠀ ⠀⡼⢿⢿⣿⣧⣥⣤⡄⠻⣿⢁⣬⣤⣼⡿⠛⡿⢆ ⠀⠀⢨⢆⡻⡏⠘⠿⠁⠀⠈⠈⠿⠛⣿⣃⢾⠀⠀ ⠀⠀⠀⠀⠛⣿⠀⠀⠀⠀⠀⠀⠀⢀⣟⡇⠀⠀⠀ ⠀⠀⣴⣾⣿⣿⢫⡂⢄⣈⣁⡠⢲⢻⡻⢿⣷⣦⡀ ⠀⠀⡿⠉⠀⠈⣧⢣⠂⠇⢸⠀⣘⣯⠀⠀⠈⣿⠇ ⠀⠀⣿⡐⠒⢥⣽⣿⠈⢿⡿⠖⣼⣷⡒⠤⢐⣿⡆ ⠀⢠⣿⣷⣴⣿⡛⢿⣆⣸⣿⢠⡿⣻⣿⣶⣿⣿⡁ ⠀⢰⣿⣿⣿⣿⣿⣷⣽⣿⣿⣫⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⢔⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡜⠁⠀⠀⠀⡀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠁⡎⠀⠀⢸⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠈⠙⡒⠒⠢⠤⠤⢤⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⡇⠀⠀⠀⢧⠘⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠁⠀⡇⠀⠀⠀⠈⢦⣳⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⣧⠀⣆⠀⠀⠀⠙⢿⣄⡀⠀⢸⠹⡄⠀⡠⠔⠂⢸⡀⠀⠀⠀⠀⠀⣇⠀⣀⡠⠔⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⡎⠘⢦⣿⡀⣿⡄⠀⠀⠀⠀⡀⠈⠀⢸⠀⠘⠎⠀⠀⡀⠛⡇⠀⠀⠀⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡧⣀⣀⣭⣧⢸⣧⠀⠀⠀⠀⣧⠀⠀⢻⠈⠉⠒⠶⣎⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⣸⠋⠀⠈⢆⣿⢧⡀⠀⠀⢻⣆⠀⢸⡀⢀⡀⣀⡈⠳⣄⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⡔⠋⠀⠀ ⠀⠀⠀⢸⡿⠃⢀⣤⣖⣞⣿⣦⠳⡄⠀⠈⣿⡄⣈⣿⣿⣿⣿⣶⣿⣬⣳⠀⠀⠀⠀⡀⢸⠀⠀⠉⠁⠀⡇⠀⠀⠀ ⠀⠀⢀⢸⣧⣾⣿⡿⢿⣿⣷⠀⠁⠘⠒⠒⠾⡟⠿⠉⢿⣿⣿⣿⣿⣿⣿⣿⡦⠀⢀⠇⢸⣄⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⣿⣿⣇⢸⣾⢿⣿⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⠙⠫⣡⣏⣻⠉⠀⠀⢸⠀⢸⠉⣆⠀⠀⢰⠇⠀⠀⠀ ⠀⠀⠀⢸⢷⡀⠠⠅⠤⠴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⢘⡉⠁⣿⠀⠀⢀⡎⠀⢸⠀⢸⠄⠀⡼⠀⠀⠀⠀ ⠸⠀⠀⢸⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⡿⠀⠀⢺⠃⠀⣸⢄⡿⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⢀⡟⠀⢘⣿⡛⠀⠀⡀⠀⢀⡄⠀⠀ ⠀⠀⠀⢸⡇⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⡞⠀⠀⠀⡇⠀⠀⠀⢳⠀⣸⠇⠀⠀ ⠀⠀⠀⠈⡇⠀⢰⡈⠓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⠀⠋⠀⠀⠀⣸⠁⠀⣰⠀⢸⣠⣿⢀⠆⠀ ⠀⠀⠀⠀⣧⠀⠀⡇⠀⠀⠀⠈⠙⠒⠦⠤⣤⡶⠒⠉⠁⠀⠀⠀⡼⠁⠀⠀⠀⢀⢀⡇⢀⣤⢿⡆⣸⣿⠿⠋⠀⠀ ⠀⠀⠀⠀⢸⡀⠀⣧⠀⠀⠀⠀⢀⣠⡴⢋⣵⠏⠀⠀⠀⠀⣠⣼⣥⠀⠀⠀⣠⢾⣼⠤⣸⡛⠂⠛⠛⠛⢀⣀⠀⠀ ⠀⢦⠀⠀⠀⣇⢸⡇⠁⣤⡴⢋⡽⢋⡔⠉⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⡠⠞⠃⠸⠃⣠⠞⢳⣄⠀⢀⡠⠄⠀⠙⢆ ⠀⠈⢢⠀⠀⠈⢦⡁⣨⠋⣠⠊⢠⠿⠒⠉⠒⠤⡀⠀⣠⣤⠾⡷⠚⠉⠀⠀⠀⡰⠊⢀⡴⠁⠈⠙⠫⡀⠀⠀⠀⠀ ⠀⠀⠀⢉⡵⠦⠤⢉⣧⣴⠁⢀⣯⠴⠒⠒⢤⣀⠈⠢⡄⠉⠻⣄⠀⠀⠀⡴⠋⠀⣰⠟⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀ ⠀⠀⢠⠊⠀⠀⢷⡄⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠲⣾⠓⠚⠃⠈⠣⣀⠜⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠄⡙⠊⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠓⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣴⣆⠀⠀⣴⣶⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣐⡀⠀⠀⠀⠈⠁⠀⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣩⠝⢸⡭ ⢀⣿⣡⣿⠀⣾⣣⣼⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢠⣆⢦ ⣾⠋⠉⠹⢿⠟⣩⡙⢷⣤⠀⠀⢸⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠟⠹⢸ ⠇⠞⢻⠛⠛⢀⡟⠀⢸⡟⠀⠀⡿⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⣸⡃⢀⣚⠁⠀⢸⣥⢞⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠀⠀⠛⠃⠈⠛⠁⢀⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⣿⣆⠙⢮⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣳⢯⡟⣿⡟⣿⡿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢿⣧⣸⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⢀⣿⠁⣿⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⠃⠀⣸⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢡⡀⣼⠃⢰⣿⣿⣿⣿⣿⣿⢸⢸⣿⣿⣿⣿⣿⡏⣼⣿⡟⢀⡼⢱⠸⣿⣿⣿⡽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡾⣣⡟⠁⣿⣿⣿⣿⢻⣿⣿⢸⣾⣿⣿⣿⣿⣿⠇⣿⣿⢀⣮⣴⡾⡟⢻⣿⣿⢿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣷⣼⣿⣿⣿⡿⢸⣿⢹⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡟⠋⠀⠀⠀⠀⠉⠙⠋⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢹⣿⣿⣿⣿⡇⢸⣟⠸⣿⣿⣿⣿⣿⣿⢧⢀⣴⣿⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠓⢌⣿⠀⠻⠻⠿⠿⠿⠿⠈⠉⠀⣧⠀⠀⢿⣹⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠞⠛⠉⠓⢶⡆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠳⠇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⣭⡿⠋⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣷⡈⣇⠀⠀⠀⠀⠀⠘⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠖⠋⠁⠀⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣠⣴⣾⣿⣏⣼⣿⣿⣿⣿⣿⣷⡼⣆⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣰⣇⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⣼⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⠀⢀⣴⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢧⡀⠀⠀⣠⡴⠋⠀⠀⠑⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣀⣤⣾⡿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⢺⣿⣿⡿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⢀⣠⣤⠶⠒⠋⢉⡿⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀ ⢀⣿⣿⣿⠃⣼⡿⠿⠛⠉⠉⠉⠉⠉⠉⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⠖⠒⠋⢉⣠⠴⡶⠏⠉⠀⠀⠀⠀⢠⠏⠀⢸⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠚⣿⠟⣿⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⣿⣿⣿⣇⠀⠀⠀⡀⠀⣼⣆⡠⢞⣡⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⣤⠋⣴⣁⢸⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⣇⡀⢸⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⢡⠎⠁⠈⠙⢿⡀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠈⠁⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⡴⠛⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠉⠁⠀⠀⠀⠀⣿⣿⡿⣿⣿⣧⣀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⣀⣼⣿⣿⠟⣡⣿⡿⡿⠛⠉⠀⣰⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠤⣄⣀⣛⠀⠀⢸⣿⣷⠸⣿⣿⣿⣿⣶⣤⣀⡈⠉⠓⠲⠶⠶⠶⠶⠚⠉⠁⣀⡴⢋⡽⠛⠉⠀⠈⢀⠽⠊⠀⠀⢀⡾⠁⢠⡆⠀⠀⠀⢀⡄⡈⠀⠀ ⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠉⠀⠀⠀⠉⠛⠺⠿⣿⡇⠙⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⣀⣠⣴⡿⠋⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⣠⠟⠀⠀⣼⠁⣀⣝⣷⣽⣿⡇⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣈⣻⢿⣿⣿⣯⠙⣛⡛⠻⠿⠿⠯⢩⡿⡟⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣴⠋⠀⠀⢠⡇⣺⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⡏⠛⠂⠉⠈⠉⠉⠙⣋⠉⠁⠀⢀⣤⠖⠋⠀⡇⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⣸⠁⢀⡠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠰⣿⣧⣄⡀⣀⡀⠀⣠⠞⠁⢀⣀⣀⣾⡝⢦⠀⢰⠃⢀⡴⠊⠀⣀⠤⠴⠶⠶⠶⠖⠋⠉⢹⣙⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣮ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠋⡡⠖⢀⣀⢻⣿⣿⣿⣿⣿⣷⡄⡛⣷⣦⣴⣶⣮⣅⡸⢇⠘⠒⠛⡀⢘⣭⣶⣾⣶⣶⣶⣤⣿⣖⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⣿ ⠉⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠜⢉⡀⠀⠀⠀⠀⠐⢺⣿⣿⣿⡿⠋⠛⠃⢣⣿⣿⣿⣿⣿⣿⣿⣷⣤⢤⢤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣿⢷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣿
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⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠙⢞⢎⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⡠⠂⠀⠀⠀⠀⠀⠂⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈⢣⡣⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀⠊⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡷⡄⠀⠀⠀⠀⠹⣕⠵⠄⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠙⢌⠢⡀⠀⠀⠀⠈⢮⡀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡚⠀⠀⠀⢀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⠑⢝⠢⡀⠀⠀⠀⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠑⠅⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡇⠑⠦⢀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣼⣟⣾⣯⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠣⣤⣿⣝⡿⣾⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣹⣿⠱⣷⣿⣿⣿⣟⠀⢸⣿⣿⣿⣿⣿⣿⣿⠸⣿⡇⠀⢀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⡀⠀⠀⠀⠀⠀⣾⣿⣯⣏⣼⣿⣿⣿⣿⠏⢧⢸⣿⣿⣿⣿⣿⣿⣿⡆⢿⣧⣠⠞⠀⢻⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡇⠀⠀⠀⠀⠀⣿⣿⡿⣰⣿⣿⣿⣿⣿⠶⢦⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⢿⣤⠶⠞⠛⠛⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡌⡆⠀⠀⠀⠀⠀⠀⠀ ⠶⠋⠀⠀⠀⠀⠀⢸⣿⣿⣧⣿⣿⣿⣿⣿⣿⠀⠀⠈⠻⣟⢿⣿⣿⣿⣿⣟⣵⠟⠁⠀⠀⠀⠀⠀⠙⣿⣯⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⡇⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⢸⡟⣸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣤⡘⠆⠀⠉⠉⠁⢸⡏⠀⣤⡀⠀⠀⠀⠀⠀⢿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀ ⠞⠛⠀⢸⠃⠀⠀⣾⠁⣿⣽⣿⣿⣿⣿⣿⣷⡁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⠀⣋⠀⠀⢠⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡸⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠁⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠉⠛⠀⠀⠲⠤⠀⠀⠀⠀⠀⣠⠐⠖⠒⠚⠛⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡀⠀⠛⣷⠤⠤⠤⠤⠖⠒⠛⠛⠋⠉⣛⣦⣄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⣿⣇⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢫⠙⢶⣶⠢⢤⣤⣴⡶⠖⠛⠉⠀⠈⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠻⣿⠈⢿⣿⣿⣿⣿⣿⣿⣆⠀⠘⣄⠀⠐⠢⠖⠋⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣻⠂⠀⠀⠈⠳⠈⠻⢿⣿⣿⣿⣿⣿⣿⣶⣝⣦⣼⠁⠀⠀⠀⠀⠀⠀⣀⡴⣫⣿⣿⣿⣿⡿⣟⡿⣫⡾⣿⣿⡿⠟⠋⠁⠀⣠⠟⠓⠒⠶⠖⠒⠒⠂⠀⠢⢀⠀ ⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡝⠻⢿⣿⣿⠿⣶⣭⣟⣓⠒⣚⣛⡯⠵⢿⣟⠛⠿⠛⠁⡼⠁⠀⣠⠞⠁⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠉⣹⡿⠃⢀⡴⠋⠈⠳⣶⣠⠞⠁⣠⠞⠁⠀⠀⠀⠀⠀⡰⠫⠤⠤⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢰⣿⠁⣠⣏⣈⣡⢶⡄⢽⢁⣤⠞⣡⣤⠀⠀⠀⠀⣠⠞⠁⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠆⠀⣿⠇⢻⣿⣶⣶⣶⣝⣿⠉⢹⣵⣡⣴⣾⣆⠀⢀⠞⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣿⠀⠘⡄⢸⡏⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡴⠋⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠛⡄⠀⡇⢸⠁⠀⣰⣃⠀⢹⣿⣿⣿⣿⡟⢿⣿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⡾⠀⣰⠟⠁⠀⠀⠛⢿⣿⠋⢠⠊⠛⢷⣭⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣇⡎⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⢠⠇⠀⠀⠀⠀⢹⠀⢸⣇⡴⠋⠀⠀⠀⠀⠀⠈⣇⠀⢸⡤⠂⠀⠻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣿⠁⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⢀⠞⠁⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠘⡆⢸⡿⠁⠀⠀⠀⠀⠀⠀⢰⠃⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⣠⠎⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⣸⣁⣼⠃⠀⠀⠀⠀⠀⠀⢀⠇⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡇⡄⢀⠇⠀⠀⠀⠀ ⣀⠀⠀⠀⣀⣀⡀⠀⢀⡴⠁⠀⠀⡀⠀⠠⠃⠠⠀⠀⠀⠀⠀⠀⠁⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣶⣶⣦⣤⣨⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣬⣿⣼⣷⣄⠀⠀⠀⠠⠀⡠⠀ ⠀⠀⠀⠀⠀⡺⣿⣿⣿⣿⣿⣿⣿⣿⢸⢇⢹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⡠⠊⢀⣶⢶⣷⣿⣿⣿⣿⣿⣿⣿⠟⠈⢑⢯⣛⠛⢡⠓⠛⣿⣿⣇⠀⠀⠀⠀⠀ ⣵⡷⣹⣧⢼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠀⠁⠀⠈⠃⢀⢿⣿⣿⡆⠀⠀⠀⣠ ⡿⡉⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡶⣒⡌⠀⠀⠀⠌⠉⣿⣿⣿⣷⢀⣀⠈⠻ ⣷⣁⠴⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣇⠂⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⢸⡿⠷⣦ ⣇⠫⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠻⠁⠀⠀⠀⠠ ⣿⣷⠏⠀⠀⠀⢀⠽⢉⠀⠨⠉⡛⠳⡓⠨⠔⣲⣶⠾⣿⡍⠍⡈⠣⡀⠀⠀⠀⣀ ⣿⡿⠤⠀⠀⢀⠂⠀⠀⠆⠀⠀⠀⠉⠐⠱⣢⣤⣿⣍⣯⣿⡕⢌⡢⠘⡤⢶⣄⢀ ⡍⠁⠀⠀⠀⢸⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠙⢿⢷⡀⠈⠳⣹⣚⢿⠀ ⣇⣤⢄⣤⣠⠘⡄⠀⠈⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⢄⠈⠪⠫⡛⣳ ⣿⢋⠚⡿⢿⢠⠿⡀⠀⠈⢧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⠀⠑⠹⢿ ⢧⢇⢤⡂⢹⠑⠠⣪⡢⠄⣸⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢳⠀⠀⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⢤⣀⠀⠀⠀⠀⢠⠞⠉⢧⢀⡴⠚⠁⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠙⠦⣄⣰⠏⠀⠀⠈⠋⠀⠀⠀⠸⡇⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣀⣀⣸⡄⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢳⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⢉⡿⠂⠀⠀⠀ ⠀⠀⠀⠈⠛⢶⡴⠶⢶⣶⣶⣾⣿⣾⣶⣶⣶⣶⣶⣶⣶⣴⣦⡁⠀⠐⡆⣠⣴⣿⣵⣶⣶⣶⡶ ⠀⠀⠀⠀⠀⣼⣀⠄⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⠟⠃⠀ ⠀⠀⠀⠀⠀⣿⡳⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣥⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⢲⣩⡔⢯⡀⠀⠀⡇⠀⠀⠀⠀⢀⣠⢤⣀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⡀ ⠀⠀⠀⠀⠀⢀⡾⠃⣿⣇⡠⠃⠀⠀⡇⠀⠀⢀⢰⠉⠀⡠⠜⢧⢰⠀⠈⢿⡙⠛⠿⠿⠿⢿⣿ ⠀⠀⠀⠀⠀⣾⠁⠀⠘⠉⠀⡐⠉⠀⢱⣶⠀⡞⠯⠴⠛⡲⢀⡞⠀⢸⡶⢼⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡄⠀⠀⡰⠀⡈⠉⠁⠈⠸⡜⠀⣄⠀⠊⣠⠞⢱⣤⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠶⣜⡁⠀⠈⠁⠀⠀⠀⠀⢀⡈⢻⡉⣽⢤⣀⣷⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣶⡶⢶⠋⠉⠉⠉⠉⠉⠉⢹⡆⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢼⡅⣯⢰⢀⠀⠀⠀⢀⣀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡟⣿⣾⣾⣿⣿⣿⣿⢿⣿⣷⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢸⣿⣿⣿⣿⠿⣛⢿⣿⣓⣼⣻⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡶⢿⣥⣿⢇⡿⡉⠭⡑⢄⠣⣙⣦⣍⡛⠧⠹⣏⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣯⣐⣉⣿⣿⢰⡇⡱⢂⠍⢢⡑⢄⠺⣽⣳⣬⣑⣤⠷⣋⢙⣳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠶⠏⠀⣩⣾⣿⣿⣼⣧⣦⣵⣮⣥⣼⣌⣱⣧⣯⣽⣏⡰⢡⣶⠟⠛⠖⠲⣄⠀⠀⠀ ⠀⠀⠸⡇⠀⠀⣸⠋⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢿⠛⠉⢻⠀⠀⢀⡿⠀⠀⠀ ⠀⠀⠀⠙⢲⡖⠋⠀⠀⠀⢸⡏⢹⠋⢩⣼⠉⡌⢩⠉⡍⣽⡅⢰⣾⠀⠀⠘⣧⣴⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡰⢉⣛⡾⢡⡉⢜⡠⢃⣾⡯⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡱⢐⣣⠞⡡⠒⣌⢢⣴⣿⣿⣿⣿⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⢡⠌⣻⣶⣋⠔⣡⢓⣼⢿⣵⣿⡿⢿⣱⡾⢋⠽⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣦⡾⡽⢃⠝⣷⣴⠟⠁⠀⠙⣿⠵⣋⠳⣝⢮⣲⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣻⣿⣿⣦⣾⣿⣧⣝⢷⣌⣒⣤⠟⠀⠀⠀⠀⠈⠳⣦⣱⣾⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀ ⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢙⣿⣿⣿⣿⣾⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⢿⣿⣿⡿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄ ⠀⢻⠻⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡞⠋⡟⠁ ⠀⠘⠀⠀⠀⡿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡟⢹⠀⠀⢱⠀ ⠀⡀⠀⠀⠀⢳⣌⣿⣿⣷⣄⢀⣀⣠⣤⣤⣤⣀⣀⡀⣠⣾⣿⣿⣿⣵⡇⠀⠀⢸⠀ ⠀⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⢸⠀ ⠀⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠍⠀⠀⣼⠀ ⠰⣼⣧⣄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠦⣴⣿⡄ ⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠈⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣋⣹⡟⢿⣿⣿⣿⣿⣿⡯⣿⡏⢻⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⡏⢿⠀⠀⢧⠘⣿⣿⣿⣿⡟⠀⢸⠁⠈⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⣰⡿⣿⣿⣿⣿⣿⣇⣤⣤⣤⣈⠀⠘⢿⣿⡿⢀⣤⣴⣦⣤⣽⣿⣿⠛⢻⡿⣷⡀ ⠘⠉⠀⠹⡄⠈⣿⣿⡿⠏⣿⣿⣿⠃⠀⠀⠙⠃⠘⣿⣿⣿⣽⣿⣿⠇⢀⡾⠁⠀⠈ ⠀⠀⠀⢠⡿⢦⡘⢿⣧⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⣿⣋⡴⠿⣇⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⣽⠟⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣠⣤⣿⣧⣀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⣼⣿⣶⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⣿⡟⡈⡗⠢⣄⡀⠉⠉⢀⣠⠔⢺⡟⡏⢿⣿⣿⣿⣿⣦⡄⠀ ⠀⠀⢸⣿⣿⠟⠉⠉⠙⢥⡇⣗⠀⡈⢫⡁⠈⡽⠁⠀⣼⣹⠟⠉⠀⠉⠙⣿⣿⣿⠀ ⠀⠀⢸⣿⠁⠀⠀⠀⠀⢘⣧⠙⢆⠀⡾⠃⠸⣇⠁⢠⣧⠿⠦⠀⠀⡀⠀⢈⣿⡟⠀ ⠀⠀⢸⣿⠀⠤⠤⠴⠈⣙⣻⣥⡎⠚⢻⣾⣷⡿⡶⠁⣿⣿⣶⢤⣀⣀⣠⢾⣿⣧⠀ ⠀⠀⢀⣿⣗⠀⠀⠀⣹⣿⣿⣿⣧⠀⠈⣿⣿⡁⠀⢸⣿⣿⣿⣄⠀⠀⣠⣾⣿⣿⠀ ⠀⠀⣼⣿⣿⣷⣶⣾⣿⣏⠻⣿⣿⣆⢀⣿⢿⣇⢀⣿⣿⢟⣽⣿⣷⣾⣿⣿⣿⡇⠀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣬⡻⣿⣼⣿⣿⣿⣾⢟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠄⠒⣒⣲⣿⣿⣿⣿⣿⣶⣶⣤⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣀⡤⠒⠉⠁⣠⣴⡾⠿⠛⠛⢿⣿⡿⠿⠛⠋⠉⠙⠻⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡤⠚⠁⠀⢀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄⠀⢯⠙⠛⠉⠛⠷⣦⣄⠀⣸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡴⠊⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⠀⢸⠀⠀⠙⢦⡎⠀⠀⢳⠀⠀⠀⠀⠈⠙⢷⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⣀⡰⠋⠀⠀⢠⠃⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠙⣄⠀⢸⡄⠀⠀⠀⠐⣄⠀⠙⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡎⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡏⠙⢢⣀⠀⢘⡦⠻⣿⡀⠀⠀⠀⠘⢆⠀⠙⡿⣄⠀⠀⠀⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢠⡇⠀⠀⠀⠏⠀⠀⠀⢀⣀⣀⠀⡇⠀⠈⢆⠉⠻⣅⠀⡇⢳⠀⠀⠀⠀⠈⢇⠀⠘⡜⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠉⠇⠀⠀⠈⢱⠦⢬⡟⠓⡾⣷⢄⡀⠀⠀⠘⡆⠀⠸⡜⡄⠀⠀ ⢣⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⢆⡀⠙⣤⠇⠸⡀⠙⢳⠀⠀⢹⢀⠀⢳⢹⠀⠀ ⠀⠑⣄⡀⠀⠀⠀⠴⠾⢾⠀⠀⠀⠀⠘⠁⠀⡎⠀⡄⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠉⡿⢻⠳⡄⢧⠀⠈⡇⠀⠘⡞⡆⠘⡄⡇⠀ ⠐⢲⡏⠉⠓⠲⠤⠤⠴⢾⡀⠀⡀⠀⠸⠀⣸⠁⢠⡇⠀⠀⣰⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⣧⡈⢀⣥⢸⠀⠀⢃⠀⠀⡇⡇⠀⠇⡇⢰ ⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⡇⢸⠁⢀⣇⣴⡏⠀⣼⡃⢀⣴⡧⢤⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠋⠁⠈⣧⠀⢸⠀⠀⢹⡇⠀⠀⠀⢸ ⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⠈⠉⢸⣷⣾⣿⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣐⣒⣒⣤⢄⣿⡇⢸⡄⠀⢸⡇⠀⠀⢀⣾ ⡶⠛⠁⠀⠀⠀⢀⣤⢀⡜⣉⡇⠀⠀⠀⠀⢸⡇⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣅⡀⣾⡇⣠⠄⠘⢿ ⠳⣤⣀⣀⣀⣀⣋⣠⣾⠘⣯⡇⠀⠀⠀⠀⢸⡇⠘⣷⠈⠙⣭⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⢹⠛⢸⣿⡟⠓⠛⠀⠀⣤ ⠈⢙⣿⡟⠉⠁⠀⠀⠸⡀⢹⡇⠀⠀⠀⠀⢸⡇⠀⠈⠻⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣍⣉⣼⠿⠁⠀⢀⡏⢻⡇⠀⠀⠀⠀⣿ ⠀⣼⡟⠀⢀⡄⠀⠀⢠⠱⣄⡗⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⡞⠀⢸⡇⠀⠀⠀⠀⣿ ⣽⡟⠀⠀⢸⠁⠀⠀⣿⠀⠈⡏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⣿ ⠿⢷⠀⠀⠸⡄⠀⠀⣿⠀⠀⣧⡀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡀⢸⡇⠀⠀⠀⢰⣿ ⠀⠈⢧⡀⠀⠻⡀⠀⣿⡄⢀⡟⢀⠀⠀⢠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢘⡁⢸⠇⠀⢀⠀⣼⣿ ⠀⠀⠀⠱⣄⠀⠙⣄⠘⣷⡼⢁⡞⠀⠀⣾⠃⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⣺⠃⠀⣸⠁⢸⠀⠀⣼⢰⠁⣿ ⠀⠀⠀⠀⠈⠑⢦⣈⠙⣿⠃⡾⠀⠀⣰⣿⠀⠀⠀⠀⠈⠉⠓⠲⢤⣤⣤⣄⣀⠤⠤⠤⠴⢶⡾⢉⣏⣼⠏⠀⣴⠇⣠⡇⠀⣰⣿⠏⠀⣿ ⠀⠀⠀⠀⠀⣴⣿⣿⡟⢱⣿⠃⢀⣴⠟⠻⡔⢄⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⣠⡇⣼⡿⠁⣀⢞⡡⠊⣿⠀⢰⣿⠏⠀⠀⣿ ⠀⠀⠀⠀⣸⣿⣿⣯⣴⡿⠃⢠⣿⠃⠀⠀⠸⣄⡑⠢⡤⣀⣀⣀⡀⣼⠀⠀⠀⣀⡤⠔⠋⡼⢿⣏⠀⣈⣷⠉⠉⣽⠁⣴⡿⠛⠒⠀⠐⢿ ⠀⠀⠀⠀⣿⣿⣿⣿⠟⠳⠿⠟⠁⠀⠀⠀⠀⠀⠈⠒⠒⣦⡠⠤⠤⠤⠤⢤⣉⡤⠤⠒⠊⠁⠀⠙⣿⣿⣿⡶⠾⠓⠋⠁⠀⠀⢀⡀⠀⢸
⠀⠀⠀⠀⢨⢊⠠⠐⠂⠈⢀⠤⢈⠉⠙⠛⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠂⠁⠀⠀⢀⠔⠈⠀⠀⠈⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡔⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢀⠀⠀⠀⢁⢄⠀⡑⢄⠀⠈⡢⠀⠀⠀⠀⠀ ⠀⡆⣦⢄⠀⠤⠦⢅⠀⠀⠀⠀⠎⡄⠀⠀⢸⠀⢢⠑⡀⠁⠢⠌⣑⡂⠤⡤⠃ ⢪⡗⠻⢬⡦⠤⠔⢠⠂⠀⡀⡘⠀⣠⠠⠀⠀⠀⠐⢃⠐⡄⡀⢱⠇⢡⠀⠀⠀ ⢀⢘⡊⡜⡌⠀⠀⠇⠀⠰⡐⠂⠁⠘⠀⡇⢸⠀⠀⠀⡄⣯⢺⡆⠇⢸⠔⠀⠀ ⢸⣇⡰⠂⠰⡀⠀⠸⡠⠋⠀⠀⣀⠀⠜⣡⠂⡶⠶⠆⢰⣿⡌⢈⡴⠊⠀⠀⠀ ⡄⠎⢢⠀⠀⢑⠄⢄⠃⡠⠶⠛⠋⠁⠀⠁⠀⠀⠀⠀⣼⢸⢟⠜⠀⠀⠀⠀⡀ ⢀⠴⡁⠀⠀⢻⠐⣄⠑⢬⠢⠤⠖⠀⠀⠀⠀⡠⠐⠒⠛⠈⠀⠀⠀⡀⠐⠀⠄ ⠚⠀⢰⠀⠀⢠⠁⠚⣁⠀⢢⢀⡀⠀⠀⢀⠜⠀⠀⠀⠀⢀⡀⠀⠀⠈⠂⠊⠀ ⠀⠀⡈⠀⠀⠸⠀⠊⠉⠱⡈⢧⣀⠉⢧⡏⠀⠘⠁⠘⠭⠟⠁⠀⠀⠀⠀⠀⠀ ⠁⡰⠀⠀⠀⠆⡘⠠⢀⠀⠐⣸⡌⠣⡊⡇⠀⠀⠀⠀⠰⢤⡀⠰⠿⠃⠀⠀⠀ ⠠⠁⠀⢀⠌⡗⠀⠀⠀⠈⠐⣿⡁⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⡠⢂⢼⠀⠀⠀⠠⢠⡊⣁⡈⠦⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡀⡠⠔⠒⠐⠉⠙⣆⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠐⠿⠃⠀ ⠀⣄⠀⠀⢸⠀⢀⡀⠀⠸⠀⠘⡃⠠⣳⣖⠀⢀⣦⣀ ⠈⠻⠉⠀⣿⣤⢘⠉⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠙⠀ ⢼⡦⠀⢊⢿⡋⠀⠀⠀⡴⢴⠒⠄⠀⠘⢄⢠⠛⡄⠀ ⠀⠁⠀⠀⠀⠉⢱⠂⠀⠀⠺⠂⠀⠀⠀⠀⢻⣰⠁⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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