Rilakkuma Pancake <3 Emojis & Text

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⣿⣷⣶⣶⣶⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣀⣀⣀⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀ ⠈⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠠⣧⡀⢠⣿⣿⣿⣿⣿⠿⢿⣿⣆⡒⠀⠈⣨⡾⠛⠁⠀⠉⠻⢿⣿⣿⡄⠀⠀⠀ ⠀⢸⣿⣾⣿⣿⣿⠋⠀⠀⠀⠈⠉⠛⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀ ⠀⢸⣽⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣴⠄⠀⢻⡇⠀⠀⠀ ⠀⣼⡏⡌⢿⣏⠀⠀⣀⠀⠀⢀⡠⠀⠀⢀⣀⠀⠈⠓⠒⠋⠁⠀⠀⣸⠁⠀⠀⠀ ⠀⠙⡟⢄⢸⢼⣦⠀⠈⠉⠛⠉⠀⠀⢀⣈⣀⡄⠀⠀⠔⠂⠁⢂⡰⠁⠀⠀⠀⠀ ⠀⠀⠘⠣⢼⣺⡿⠷⢶⣶⣄⠀⠀⠀⠈⠳⠴⠇⠐⠀⠀⠀⣠⣮⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⠀⠀⠀⠹⣿⣷⡤⠄⠠⠤⢶⣶⡚⡀⠀⠀⠈⡄⠁⠀⠀⠀⣀⣤ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠘⠚⠑⢄⣀⠠⠃⠀⠰⢶⣿⣿⣿ ⠀⠀⠀⠀⠀⠘⢤⠠⠐⣸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣶⣶⣶⣤⣾⣿⠟⠿ ⠒⠒⠒⠤⠤⢄⣤⣊⠁⠀⠀⠀⠀⠔⠁⠀⠀⠁⠀⠀⠀⢸⠁⠀⠀⠈⠁⠀⠀⠀

░░░░░░░░░░░░░░░░░░░░░░ ░░░░░▄▄░░░░░░▄▄▄▄░░░░░ ░░░▐▀▀▄█▀▀▀▀▀▒▄▒▀▌░░░░ ░░░▐▒█▀▒▒▒▒▒▒▒▒▀█░░░░░ ░░░░█▒▒▒▒▒▒▒▒▒▒▒▀▌░░░░ ░░░░▌▒██▒▒▒▒██▒▒▒▐░░░░ ░░░░▌▒▒▄▒██▒▄▄▒▒▒▐░░░░ ░░░▐▒▒▒▀▄█▀█▄▀▒▒▒▒█▄░░ ░░░▀█▄▒▒▐▐▄▌▌▒▒▄▐▄▐░░░ ░░▄▀▒▒▄▒▒▀▀▀▒▒▒▒▀▒▀▄░░ ░░█▒▀█▀▌▒▒▒▒▒▄▄▄▐▒▒▐░░ ░░░▀▄▄▌▌▒▒▒▒▐▒▒▒▀▒▒▐░░ ░░░░░░░▐▌▒▒▒▒▀▄▄▄▄▄▀░░ ░░░░░░░░▐▄▒▒▒▒▒▒▒▒▐░░░ ░░░░░░░░▌▒▒▒▒▄▄▒▒▒▐░░░

⠀⢸⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠸⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⡆⠀⠀⠀⠀⠀⠀⠇⠀⠀⡺⠀⠀⠀⠀⠀⢰⠃⠀⠀ ⠀⠀⢡⠀⠀⠀⠀⠀⣀⣼⠀⠀⠀⢀⢔⣒⠒⡢⣸⠀⠀⠀ ⠀⠀⠈⡄⢠⠄⠠⠎⠀⠀⠱⠒⠂⡆⢏⠀⠉⢨⠀⠀⠀⠀ ⠀⠀⠀⠰⣇⠀⢠⠊⠉⡂⠑⡄⠀⠘⢌⣑⢐⡡⠓⢄⠀⠀ ⠀⠀⠀⢀⠟⡟⠀⠑⠒⣁⡠⠃⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀ ⠀⠀⢀⠊⠀⠑⠄⠠⠜⠀⠀⠀⢀⡀⠤⠤⠤⢄⡀⠀⠀⢇ ⠀⠀⡎⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠈⠑⢄⢸ ⠀⠀⡁⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠈⣾ ⠀⠀⢇⠀⠀⠀⠀⡎⠀⠰⠋⠉⠉⠀⠀⠀⠒⡀⠀⠀⠀⡏ ⠀⠀⠈⢆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⠞⠀ ⠀⠀⠀⠀⡱⠢⠄⣘⣤⣀⠀⠀⣀⡀⠀⣀⣀⢄⠊⠁⠀⠀ ⠀⠀⠀⡸⠦⣀⠀⠀⢀⣉⠩⠔⠋⠉⠉⠁⠀⠀⢇⠀⠀⠀ ⢀⣠⡞⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢀⠀⠀⢀⠆⠀⠀

⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠋⠀⠀⠀⠙⠷⠞⠛⠲⠾⠋⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠹⣦⡄⠀⠀⢿⠗⢀⣀⡀⢿⡿⠀⠀⣠⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⡰⠋⢩⣶⡉⢳⡀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⠀⠀⡇⢀⠈⣍⠀⡀⡇⠀⢠⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣀⠙⣷⣀⠹⣌⡉⠈⣉⡴⢁⣠⡟⢁⣀⣤⣀⡀⠀ ⠀⣰⡟⠋⠉⠉⠻⡏⠈⠑⠲⠭⠭⠴⠒⠉⠈⣻⠛⠉⠀⠉⠻⣦ ⠠⣿⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿ ⠀⢻⣆⡀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⢀⣴⠟ ⠀⠀⠉⠛⣿⡭⠥⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣤⣩⡟⠋⠁⠀ ⠀⠀⠀⣼⠋⠀⠀⠀⠉⠳⡀⠀⠀⢀⡴⠋⠀⠀⠀⠘⣷⠀⠀⠀ ⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢹⠀⠀⡼⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀ ⠀⠀⠀⠈⢿⣄⡀⠀⠀⠀⣼⡦⠤⣷⡀⠀⠀⠀⣠⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠳⠶⠛⠉⠀⠀⠈⠛⠶⠶⠛⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

˚₊•𓂅𓏲ʚ🥞ɞ𓂅𓏲•₊˚

⠀⠀⠀⢀⡀⠀⠀⠀⢀⡴⣖⣆⡠⠤⡄⠀⠀ ⠀⠀⠀⡏⠈⠉⠒⠒⢾⣱⢯⣟⢳⣖⡷⡄⠀ ⠀⠀⢀⡗⠀⠀⠀⠀⠈⠉⠉⠛⢿⣻⣼⠁⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⣀ ⠀⠒⢺⡒⠀⠰⠆⠀⠀⣀⠀⠀⠶⠀⠀⡬⠄ ⡤⠚⡳⠷⣆⠀⠀⠀⠀⣉⠁⠀⢀⣀⠝⠑⠂ ⠣⢄⠀⠀⢀⣟⡿⠋⠁⠀⠉⠙⣧⡀⢹⠀⠀ ⠀⠰⣛⢯⡻⣜⣳⢤⣄⣠⣀⢀⡼⠓⠁⠀⠀ ⠀⠀⠟⢾⣱⢎⣜⡣⢞⡥⣻⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠾⡈⠉⠚⢓⠯⠶⠝⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⠢⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠐⠒⠒⠒⠒⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀ ⠤⠄⠀⣀⠀⢀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀ ⠀⠀⠀⠀⣰⠇⠀⢀⡀⠤⠐⠒⠂⠈⠉⠉⠉⠉⠁⠐⠒⢲⣤⣤⣄⡀⠀⠙⡍⠉ ⠀⠀⠀⣰⢁⡄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣦⣄⡶ ⠀⠀⠀⠱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠻⣿⣿⣿ ⠀⢀⣀⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠀⠀⡀⠀⠤⠀⡀⠀⠀⠄⠀⠈⠉ ⣶⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⢢⠘⠒⠂⠠⠤ ⣿⣿⣿⡿⠋⠙⡄⠀⢠⠂⣴⡿⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀ ⠿⠛⠁⠀⢀⡀⢸⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀ ⡀⠀⢀⠔⢡⠂⠸⡀⠀⠀⠀⠀⠀⢀⠜⠆⣀⣀⡀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀ ⠙⢢⠁⠔⠁⠀⠀⠑⠠⢄⡀⣀⣀⠎⠀⠀⠀⡠⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⠀⠀⠀⠀⠀⠎⠀⡠⠃⠀⠀⠀⡰⠁⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣀⠁⠀⠀⢀⠠⠄⢒⡰⠊⠀⠀⢀⡠⠊⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠈⠶⠀⢰⡇⠀⠀⠀⢀⡼⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠚⠻⠄⠠⠤⠤⠤⠴⠂⠠⠴⠿⠛⠂⠀⢠ ⠀⠀⣀⡴⣤⣀⠀⠊⠀⢸⡇⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⣄⠀⠀⢀⡠⠤⠤⢀⣀⠀⠀⠀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣾ ⠀⠘⢻⣴⢻⠋⡆⠀⠀⢸⣿⣀⢀⠀⢻⡄⠀⠀⠀⣀⡴⠞⠛⠉⠉⠉⠉⠓⠲⢏⠀⠀⠀⠀⠒⠂⠀⠀⠀⠒⠀⠀⠀⣠⡄⠀⠀⠀⠀⢸ ⣐⡣⡿⠿⠇⢰⡇⠀⠀⢸⣿⢠⢸⠂⣿⢿⣦⣴⢞⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡶⠒⢭⡉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠤⠖⠒⠉ ⠖⣼⣿⣿⣧⠏⡇⠀⠀⢸⣿⢹⣿⣷⡿⠛⢩⣯⣾⣋⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡿⢼⠟⡟⠀⡇⠀⠀⠸⣿⣎⣿⡏⠀⠀⠀⠉⠛⠛⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⢸⠈⡇⠀⠇⠀⠀⢠⣿⣿⠟⠋⠉⠽⠓⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠔⠿⠥⠴⠶⠶⠶⠆⠀⠠⠦⠄⠀⠀⠀ ⢹⠀⠘⠀⠇⠀⠀⠀⠀⢨⠏⠀⠀⠀⠀⠀⠉⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⡇⠀⡇⠀⢀⡏⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⢸⠀⡄⠀⡇⢣⠀⠀⠀⠀⠀⠀ ⣿⠀⢸⠀⣧⣴⣿⣶⣾⣧⡀⠀⠀⢀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠴⠶⠶⣾⠀⡄⠀⣧⣼⠀⠀⢠⡖⠒⠲ ⣿⣀⣸⣿⣿⣿⠟⣿⣿⣿⣿⣦⣄⣨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣯⡀⠀⠀⠈⠻⠷⠶⠿⠙⠋⠉⠙⠁⠀⠀ ⣿⣿⣿⣿⣭⣍⣴⣿⣿⡟⠛⢛⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡟⠛⠻⣿⣿⠿⠿⠚⠉⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣶⣶⣶⣿⣧⣤⣤⣤⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⣸⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣻⣿⣿⣟⡛⡛⠻⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⠀⣀⣴⡏⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣛⣛⣻⣿⣿⣿⣿⣿⣿⣛⡛⡻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⠧⠿⠋⠀⠀⠀⢠⣿⣶⡶⡶⠶⠶⢷⢶⣶⣶⣶⣶⠶⠶⠶ ⠉⢉⣙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣻⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣟⣻⣛⣻ ⠉⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠻⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠾⠿⠿⠏⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠉⠙⢺⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣄⡔⠀⠀⢈⣇⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠿⠦⠧⠤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣌⠙⣿⣿⣿⣤⣀⣀⣀⣴⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣶⣿⣿⣿⣿⣿⣿⣮⣻⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣷⣶⣤⣴⣿⣿⣿⣿⣋⣽⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⠻⣿⣿⣿⣿⣿⣿⣿⣟⣋⣭⣿⣿⣿⣷⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠶⣤⣀⡀ ⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⣤⣶⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣦⣴⣾⣿⡇ ⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⠿⣿⡿⢿⣿⣿⣧⣿⣿⣿⣿⣿⡿⠁ ⠜⠿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠊⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⡁⠀⠘⠀⢹⠁⠀⢹⣿⢿⣿⣿⡟⢻⡿⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣋⠁⠀⠀⠉⠉⣸⡤⠤⣀⣸⠀⠀⢸⠁⠀⠉⠈⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⡇⠀⠙⠉⠲⡄⢰⡿⠀⠀⠀⠈⡇⠀⡞⠒⠒⢲⠀⠀⡜⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠹⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣷⡀⠀⠀⠀⢸⣽⣧⡀⠀⠀⠀⢸⡼⠁⠀⠀⢸⢀⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⣿⣿⣍⠉⠒⢄⠀⠘⣧⣤⡈⠒⡶⣆⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣷⣦⣘⠉⠁⠻⢿⣿⣷⠃⢸⠒⢤⠀⠀⡞⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣼⠃⠀⢠⣷⣦⣧⡜⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⣿⣠⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠈⠋⠙⠛⠉⠛⠉⠿⠿⠛⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠁⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⠟⠻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣰⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⣶⣄⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣦⠤⠶⠶⠶⣿⠿⠛⠛⠓⠒⠲⠤⠴⠃⠀⣼⣿⣿⠄⠀⠀ ⠀⠀⠀⢿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⠀⠀ ⠀⠀⢀⣼⠟⠁⠀⠀⡀⠀⠀⠀⢀⣲⣦⣀⣤⠖⣂⣀⣀⠀⠀⢙⣿⣿⣷⡄⠀⠀ ⠀⠀⣾⠏⠀⠀⠀⠀⠉⠛⢿⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣴⣿⡿⢿⣿⡄⠀ ⠀⣼⡇⠀⠀⠀⠀⠀⣀⣨⣽⣿⣿⠛⠉⠉⠉⣿⣿⣿⣿⣿⠛⠉⠀⠀⠻⣿⣿⡄ ⢰⣿⠀⠀⠀⠀⠀⠛⣻⣿⣿⡟⠙⠇⠀⠀⠀⠟⠛⢧⣝⣿⣷⣤⡑⢦⣀⠹⣿⣧ ⣼⣿⠃⣷⠀⠀⠀⣰⣿⣿⣿⠀⠀⣤⣶⣶⣦⡄⠀⠀⣿⣿⣿⣿⡛⢷⣽⣿⣿⡟ ⣿⣿⢠⡸⣷⡀⠀⣿⣿⣿⣿⠀⠀⠰⠿⠿⠆⠁⠀⢀⣿⣿⣿⡝⣿⣌⢿⣿⡟⠀ ⢻⣿⠀⢳⣿⡻⣄⠸⡿⣿⢻⣷⣶⠀⣀⣀⡀⣶⣶⣿⣯⣿⣾⣿⣞⣿⣾⠏⠀⠀ ⠘⣿⠀⠈⢿⣷⣌⡁⠀⠹⠈⠋⣿⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠹⣧⠰⡄⢪⡙⠿⣿⣿⣶⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠘⢧⠹⣦⡙⢶⣤⣽⣿⣿⠟⡟⣿⣿⠻⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠳⢦⣿⣦⣌⢻⣿⣿⣦⡀⠀⠀⠀⣠⣿⣿⣿⣿⠿⠿⠿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠿⠦⠤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⡠⠤⠤⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⡀⠀ ⠀⢠⠄⡜⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⡆ ⠀⢸⠀⣃⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⡇ ⠀⠘⠀⠸⡄⠀⠀⠀⠀⠀⢫⠁⠐⠒⠒⠲⡞⠀⠀⠀⠀⠀⠀⢠⠁ ⠀⠀⠀⠀⠱⡀⠀⠀⣀⡠⢜⡇⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⢀⡟⠀ ⡠⠂⠀⠀⠀⠑⡴⠢⠧⠲⠆⡜⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⡟⠁⠀ ⢡⠀⠀⠀⠀⠰⣁⠘⠅⢈⠟⠃⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢇⠀⠀ ⠈⠀⠀⠀⠀⠀⠛⠒⠒⢃⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢸⠄⠀ ⠘⠀⠀⠀⠀⠀⡆⡠⠊⠁⠀⠀⠀⠀⠀⠀⠉⠐⠤⡀⠀⠀⡼⠀⠀ ⠁⠀⠀⠀⠀⠀⠘⡅⣾⣷⠀⠀⠀⠀⠀⢸⣿⣇⠀⠈⡀⡴⠅⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢚⢍⡀⠐⢦⣀⣤⡈⠛⢋⡠⠔⡏⠀⢀⡸⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡁⠈⣲⠛⠯⢍⣿⢩⣁⣘⠆⠉⢦⢤⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠄⠢⠄⠤⡋⢁⠄⢄⠠⠊⢸⠜⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢈⠀⠀⠀⡈⢁⠀⢸⠀⣠⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠈⠙⠂⠚⠈⠀⠀⠀⠀⠀⠀

⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀ ⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢸⠀⠀⢀⣠⠤⠴⠦⢤⣀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⢧⡀⠀⠀⢸⠀⣰⢋⣴⠶⢦⣤⠤⣌⢻⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⡇⠀⢀⡴⠖⠲⢴⡃⠀⠀⠀⠀⢳⠖⠒⠚⠀⡇⢸⡀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣀⡟⠀⠀⠀⢀⡤⠖⠤⡀⢠⣏⡀⠀⠀⠀⢧⡀⠹⣄⡀⠀⣠⠏⣸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⣟⠀⠀⠀⣹⠀⠀⢳⡄⠀⠀⠀⠓⠤⣀⣉⣉⡤⠞⠋⠙⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢿⡟⠁⠘⠦⠤⠴⠃⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀ ⠀⠀⠀⠀⢀⡼⠁⢸⡀⠀⠀⠀⠀⢸⠖⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡄⠀ ⠀⠀⠀⢀⠞⠀⠀⠀⠳⢄⣀⣀⡤⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⣷⠀ ⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠘⡇ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⣇ ⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠘⡄⡽ ⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠏⠋⠀⣷⡇ ⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢠⡾⠋⠁⠀⠈⠁⠀⠀⠀⠀⠀⠟⠃⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠠⣷⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⠔⠋⠀⠀⠀⠀⠀⡼⠉⠀ ⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⠈⠙⠒⠲⠤⠽⢦⣤⣀⡤⠤⢤⣤⣤⣀⣠⡤⠶⠚⠛⠓⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⠎⠀⠀⠈⠙⠒⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀ ⣀⣰⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⠀⢀⣸⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡇⠀⠀⠀⢹⠖⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢡⠀⣡⠞⠉⠉⠳⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⣠⠔⠒⠢⣄⢸⣦⠾⣗⣧⠀⠀⠀⢀⡇⠤⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⣸⡆ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠸⠋⠀⠀⠀⢹⠓⠦⠖⠋⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉ ⠀⠀⠀⢀⣀⠼⠆⢠⠒⠉⠙⢢⠀⠀⢀⡼⠀⠄⢸⢦⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⠀⠀⠀⣇⠀⠀⠀⢀⡇⠀⠉⢳⡶⠖⠋⠀⠀⠀⢠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀ ⠀⠀⠘⣆⠀⠀⢀⠈⠢⠤⠤⠊⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣸⠉⠑⠲⠤⢤⣀⣠⠤⠖⠁⠀⠉⠒⠤⠤⣤⣤⠀⠀⠀⠀⢱⣦⣀⠀⠀ ⠀⠀⡰⠋⠉⠉⡟⠀⠀⠀⠀⢸⡗⠒⠖⠋⢀⣀⠀⠀⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡶⠀⠀⠀⠀⠙⢦⠉⣳ ⡠⠊⠀⠀⠀⠀⠙⠦⢤⡤⠔⠛⠁⠀⠀⠀⢀⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠸⠀⠀⠀⠀⠀⠀⣴⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⣀⠀⠀⣀⠴⠋⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⡀⠀⢳⡀⠀⠀⣠⡾⠋⠀ ⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠉⡏⠀⠀⠀⢀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠈⡏⠁⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⢀⡴⢻⠃⠀⠀⠀⠀⢀⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠀⢀⡼⠁⠀⢰⣿⠇⠀⠀ ⠀⠀⣀⠴⠋⢠⠏⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠀⠀⠀⠀⠀⡘⠀⣻⢥⣀⣴⡿⡧⠀⠀⠀ ⣞⠉⠀⠀⠰⠁⠀⠀⠀⠀⠈⠁⢣⠀⠀⠀⠀⠀⠙⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⢀⣜⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⣾⡇⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠒⠁⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⢿⠱⣿⡇⢼⡇⠀⠀⠀⠀ ⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠀⣀⠴⡞⡿⠃⠀⠀⠀⣿⣧⠞⡀⠀⠀⠀⠀ ⠀⠀⠀⠉⠓⠒⠦⠤⢤⡦⢄⡀⠈⠀⢉⣲⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠲⠋⢁⠀⠈⢇⠀⠀⠀⠀⠈⠏⢠⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⢧⠀⢸⣆⠀⠀⠀⠀⣿⠞⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⢀⣀⡀⣀⣠⣤⣤⠶⠶⠒⠒⠛⠛⠻⠷⠶⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢖⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣫⣁⠀⠉⠛⣷⣦⣶⠾⠋⠉⠡⠤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢷⣶⠶⠶⠚⠉⠀⠀⣽⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣿⡿⠟⠛⠷⢶⣤⣄⣀⣀⠴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠘⢷⣄⠀⣠⣶⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⢤⣤⣶⣶⣶⠿⠋⠁⠀⠁⠛⠿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣈⠻⣷⣿⣿⣿⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢿⣿⡿⠂⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠿⠛⠻⣿⣿⣿⡿⣿⣿⣿⣇⠈⠉⠛⠋⣁⣀⠈⠻⢿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⠁⠀⠀⢠⠈⠙⢿⠇⡏⠘⣇⠙⠲⢶⣶⣿⣛⣛⣧⠄⠀⠙⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣰⡟⠻⠃⡆⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠐⣶⠚⠋⠉⣳⣦⣬⣴⣇⡀⠉⠳⢦⣴⠟⠛⠉⣿⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⣡⣼⣾⡄⠀⠀⠀⠀⠀⠀⠀⢨⣿⣷⣆⣈⡛⠩⠉⠁⣨⡿⠟⢁⣀⠀⢠⠞⢿⣷⣶⡾⠛⢺⢤⢀⢀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡾⠀⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣾⠏⠀⠐⠋⠉⠂⠀⠀⠈⠻⡿⠁⠀⠀⠘⠛⠹⢼⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⣤⣽⣿⣿⠟⢀⠄⠀⠀⠀⠀⠀⠀⠀⠚⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣠⣴⣿⠇⣼⣿⡿⢋⣴⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⣩⣸⣿⠀⠀⠀⢀⣠⣤⣴⣶⣶⣦⣄⠹⣷⡀⠀⠀⠀⣽⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠟⢁⣾⣿⣿⣷⡿⢁⣰⡟⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣿⣿⣿⡋⠀⠀⢠⣿⠛⣿⡿⠻⣿⣿⣿⣷⠹⣷⠀⠀⢀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠃⠀⣾⣿⣿⣿⣫⣴⣿⠏⢀⣴⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⢂⠀⠀⢿⣿⡟⢳⣶⣿⣿⢻⣿⠀⢹⡶⣠⣸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⡟⠃⠀⢰⣿⣿⣿⣿⣿⡟⢁⣴⣿⠏⢀⣼⡆⠀⠀⠹⠇⠁⠻⠙⠟⠇⣿⣿⣿⢠⣄⠈⢿⣿⡄⣿⣿⣿⢸⠇⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⣿⠟⠁⣠⣿⡿⠃⠀⢀⣠⣤⣤⣤⣄⣀⠀⢻⣿⣿⣿⣿⣦⣈⠛⢃⣿⡿⠿⠂⠀⣠⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢫⣿⣿⣿⣿⣿⡟⢁⣠⣾⣿⠟⠁⠀⣰⡿⠛⣿⣿⣿⣿⣿⣯⡬⠛⠿⠿⠿⠿⠿⠿⠿⠛⠷⠶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⢸⣿⣿⣿⡿⠋⠀⠀⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⠖⠂⠀⠼⠋⢀⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣶⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀ ⢸⣿⣿⣿⠟⠀⣰⡞⢠⠂⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⣋⣠⣤⡄⠈⠰⢻⡿⣿⢿⣿⠿⣻⡿⢛⣽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⢸⣿⣿⡟⢀⣾⣿⣱⣿⡞⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⠇⠀⡀⠀⠀⠁⠚⠁⠘⠋⢠⡾⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡀ ⠼⣻⣿⢡⣿⣿⣿⣿⣿⣷⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣾⣿⣀⡿⠀⣠⠄⠀⠀⠀⠀⠀⣤⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠣ ⠀⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣠⡄⣿⣿⣿⡇⢠⣿⡀⣾⢣⣾⣰⣆⢿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⠃⠀ ⠀⠺⠟⠋⣿⠟⠛⣽⣿⣿⣿⣿⣿⣿⢿⡿⠋⠘⣿⣿⣿⣿⣿⣇⣾⣿⣷⣿⣿⣿⣷⣄⢿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠉⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠟⠛⣿⠟⠋⠀⠀⠀⠀⠀⠀⠈⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠹⢿⣿⡝⠿⣇⠙⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠻⣿⣿⠿⣿⣿⡿⢻⣿⣿⠋⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⠀⠘⠋⠀⠈⢿⠇⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

⠀⠀⠀⠀⢠⠖⠲⣄⡀⠀⠀⠀⠀⡴⠒⠢⣀⣠⠤⠖⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠙⠒⠒⠒⢺⠃⢠⢤⡿⠤⣀⢀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠗⠀⠀⠀⠀⠀⠀⠀⠸⣄⣨⢿⡀⢀⡿⡄⢉⠆⠀⠀⠀⠀⠀ ⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢫⡈⣠⠞⢦⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢘⡆⠀⠀⠀⠀ ⢀⡀⡧⠤⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠉⢩⠏⠉⠁⠀⠀ ⠀⠀⣳⡠⠄⠀⠀⠀⠀⠀⠀⢆⡰⠀⠀⠀⠀⠈⠀⢀⣀⡜⢯⠉⠐⢤⠀ ⠀⠈⠀⣱⢴⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⡾⣄⠸⣋⣷⠀⡇ ⠀⠀⠀⠀⠀⣠⢽⡛⠙⣟⠛⢟⣻⡿⡻⠛⡯⡽⠒⣤⡿⣮⣇⠘⢋⠔⠁ ⠀⠀⠀⠀⡎⠀⠀⢘⠄⢸⠉⠉⠉⠉⠉⠉⢱⢰⠓⢩⠀⠀⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠙⡖⠂⢊⠀⣸⠤⠤⠤⠤⠤⠤⢼⠸⠒⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣅⠇⠃⢁⣿⠉⡉⠉⢩⠒⡞⢻⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢹⠯⠯⠭⠴⠧⠀⠀⣉⠤⣼⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠦⠄⣀⣀⣀⡠⠤⠮⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⡴⢲⣀⡀⢀⣀⣀⣤⣤⣤⣄⣀⠠⣞⢿⣀⣟⣿⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠼⠧⡷⢼⠥⠿⡉⠉⠀⠀⠀⠀⠀⠉⢹⣉⡹⡭⡯⢤⡜⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⢷⣊⡟⢺⠳⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⠽⣇⣹⠒⠛⠦⣄⠀⠀ ⠀⣠⠔⠋⠀⠈⢩⠧⠞⢉⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠘⡘⡆⠀⠀⠀⠙⠢ ⠞⠁⠀⠀⠀⠀⢸⠀⠀⢿⣿⠆⠀⠀⠀⠀⠀⣀⠀⠀⠻⠟⠀⠇⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⠁⠀⠀⠀⠹⣍⣹⠃⠀⠀⠀⠀⣔⣼⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡼⠉⠛⠦⢤⣀⣀⣰⠒⢦⠴⢶⡋⠙⡴⠚⠉⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⣼⣽⠞⠻⠞⠉⢻⡍⠙⢦⡀⠀⠀⠀⠙⠲⢤⣤ ⠶⠖⠚⠋⠀⠀⠀⠀⠀⠀⠀⣰⡟⡛⣄⠀⠀⢀⠼⠡⣠⠬⢿⠶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢯⣀⣀⠀⠭⠱⠵⠀⠀⢇⡀⠀⠀⢈⢷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⠀⠀⠁⠈⡷⡿⠒⠲⡶⠒⢆⣭⣒⠖⠏⠁⢹⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣬⠳⠤⡔⠊⢒⣻⣄⠀⠀⢀⣜⠂⠀⠀⣀⣶⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠤⠤⣴⠾⠷⠶⠿⡷⠖⠛⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢠⠋⠉⠉⠒⠲⢤⣀⣠⡀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⡠⠖⠋⠉⠀⠀⠀⠀⠉⠉⠢⣄⠀⠀⠀⢀⠼⠤⠇⠀ ⠀⠀⠀⣀⠔⠊⠁⠀⢨⠏⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⠀⠀⠱⣄⡴⠃⠀⠀⠀⠀ ⢸⣉⠿⣁⠀⠀⠀⢀⡇⠀⠀⠀⠀⢿⣽⣿⣼⡠⠤⢄⣀⠀⠀⢱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⢦⡀⢸⠀⠀⠀⡠⠒⠒⠚⠛⠉⠀⢠⣀⡌⠳⡀⡌⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⣆⠀⢰⠁⣀⣀⠀⠀⣀⠀⠈⡽⣧⢀⡷⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡤⢄⠀⠈⠢⣸⣄⢽⣞⡂⠀⠈⠁⣀⡜⠁⣩⡷⠿⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢯⣁⡸⠀⠀⠀⡬⣽⣿⡀⠙⣆⡸⠛⠠⢧⠀⡿⠯⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡀⠀⠀⡤⠤⣵⠁⢸⣻⡤⠏⠀⠀⠀⠀⢹⠀⠀⠀⡊⠱⣀⠀⠀⠀ ⠀⠀⢀⠜⠀⢘⠀⠀⠱⠲⢜⣢⣤⣧⠀⠀⠀⠀⠀⢴⠇⠀⠀⠀⠧⠠⠜⠀⠀⠀ ⠀⠀⠘⠤⠤⠚⠀⠀⠀⠀⠀⠀⢸⠁⠁⠀⣀⠎⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⡴⠤⠄⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣏⣈⢈⡬⠋⠉⠁⠉⠉⠊⠉⠉⠉⠛⢦⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁ ⠀⠀⣠⠎⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀ ⠞⢁⡠⣞⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠊⠁⠀⠀⠀⠀ ⠓⢼⠧⣏⠉⡡⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀ ⠔⢀⠀⣜⡩⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀ ⠂⠈⣀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠈⠙⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠒⠀⠐⠂⠁⠁⠂⠤⠄⠀⠀⠀⠀⠀⠃⢄⠀⠀⢀⡜ ⠀⠀⠀⠀⠀⡲⣠⣁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡌⠢⡀⠀⠀⠀⣸⠏⠉⠁⠀ ⠀⠀⠀⣠⠔⣽⣿⣿⡆⠀⠀⠀⠀⡀⠀⠀⠸⣿⣿⡇⠀⢣⠀⠀⣴⠁⠀⠀⠀⠀ ⠀⠀⠀⡸⠀⠙⢿⠿⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⢀⠔⣠⠎⠁⠀⠀⠀⠀⠀ ⡟⠦⡀⠒⠄⡒⠭⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠚⠐⠺⣀⠤⡄⠀⠀⠀⠀⠀ ⡄⠀⢈⠕⠈⠁⠁⠐⠒⠀⠀⠀⠀⠒⠂⠈⢁⡀⠤⠐⠊⠁⠀⠀⡇⠀⠀⠀⠀⠀ ⠁⠀⡌⠀⠀⠊⠉⠑⠐⠒⠤⣀⣀⠤⡂⠉⠀⠀⠀⠀⠀⠀⢀⠔⡂⠀⠀⠀⠀⠀ ⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢉⣢⠵⠀⠀⠀⠀⢀⠠⢲⠁⠀⠈⡆⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⢊⠠⠤⢄⢹⠁⠀⠀⠀⠉⠰⣂⣉⠉⣁⢢⠀⠀⠀⠀ ⠀⠀⠀⠰⢠⠁⠐⠆⠘⠁⠀⠀⠀⠀⠀⠀⠑⠂⢀⠀⢡⠇⠀⠀⠀ ⠀⠀⠀⠰⠘⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡊⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⣠⡄⠀⠀⠀⠇⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠋⢁⢤⡄⠈⢃⠀⠀⠀⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢇⠀⠤⣉⡡⠀⡜⠀⠀⣠⠁⠀⠀⠀⠀ ⠀⠀⠀⢀⠊⠁⠂⠤⡴⡽⠋⠉⠉⠙⢿⡯⠤⠐⠈⠀⠑⢄⠀⠀⠀ ⠀⠀⢀⠆⠀⠀⠀⠀⠷⠁⠀⡦⣤⣆⠀⢳⠲⣄⠆⠀⠀⠈⡄⠀⠀ ⠀⠀⡘⠀⠀⠀⠀⠄⠘⣄⠀⢣⡿⠓⠉⠁⠈⠁⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⣇⠀⠀⠀⠀⠈⠒⠒⠛⢧⠆⡀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀ ⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢅⣀⢀⣀⢴⡒⡒⠯⠤⠤⢄⠀ ⠀⠀⠀⢸⠢⢀⣀⠀⣄⠀⠀⠀⢰⣨⡾⡈⢰⣹⠇⠀⢀⠤⢄⠀⢡ ⡠⠊⠁⠀⠉⠂⠀⠀⠀⠈⢋⠉⢙⢍⡁⠈⠐⠁⠀⡔⠁⠀⠀⡇⠸ ⠃⠰⠂⠀⠂⢄⠀⠀⠀⠀⠈⢄⣑⠾⢅⠀⠀⠀⢸⠀⠀⢀⠜⡠⠃ ⢆⠐⢄⠀⠀⠀⢣⠀⠀⠀⢠⠎⠀⠀⠈⠑⠤⡀⠀⠉⢉⡠⠊⠀⠀ ⠀⠑⠄⡁⠒⠐⠊⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢀⠖⠁⠀⠀⠀⠀⠈⠢⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠊⠀⢠⠗⠒⠠⠤⠐⠀⠉⠐⡨⠄⠠⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠊⢀⠀⠰⠘⡜⠑⡲⠊⠀⠀⠀⠀⠈⠒⠠⡘⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠃⠀⠂⠠⠃⠀⢸⠊⠁⠀⠀⢀⡄⠀⠀⠀⠀⠀⠈⡞⠄⠀⠀⠀⠀ ⠀⠀⠀⡘⠀⢸⠀⠀⠀⠀⠸⣀⠀⠀⣀⠈⠁⢀⣀⠀⠀⠀⠠⠃⠘⡄⠀⠀⠀ ⠀⠀⢀⠇⠀⠸⡀⠠⠀⠀⠀⠈⢆⠀⢩⠁⠀⠀⡄⠀⠠⠞⠁⠀⠀⠇⠀⠀⠀ ⠀⠀⡸⠀⠀⠀⢣⠀⠆⠀⠀⠀⠀⠑⢶⣀⠠⢀⢰⡐⠁⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠇⠀⠀⠀⠀⠱⣰⠀⠀⠀⠀⠀⠀⠳⢥⠦⠊⡀⠀⠀⠀⠀⠀⠈⢆⠀⠀ ⠀⢰⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢀⠐⠊⠰⠀⠀⠀⠀⠀⠀⠈⢇⠀ ⠀⠘⠀⠀⠀⠀⠀⠀⢀⠜⡄⠀⠀⠀⠀⠀⢘⠀⠀⠁⠣⡀⢀⠀⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠀⠀⡠⠊⠀⢣⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⢈⠞⠀⠀⠀⠀⡸⠀ ⠀⡇⠀⠀⠀⢀⡔⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⢂⠀⠆⢰⣧⠀⠀⠀⢀⠔⠁⠀ ⢸⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⢂⢰⠀⠀⠑⠑⠒⠊⠁⠀⠀⠀ ⠉⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠓⠀⠀⠤⠤⠼⠾⠀⠀⠀⠀⡤⠠⢤⣶⠀⠠

⠀⠀⠀⠀⢀⠄⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⢱⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀ ⠀⠀⠀⠀⢀⣀⠀⡊⣅⡕⠉⠑⡀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇ ⠀⠀⠀⠘⠀⢀⡑⠉⠉⠓⠠⡐⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑ ⠀⢠⠂⠈⠌⠀⠈⡆⠐⢧⠤⠋⠒⢁⡀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠐⢄⠀⠀⠀ ⠀⢘⠤⢀⠈⠒⠊⣄⣀⠜⠀⠀⠀⡠⠃⠁⠒⠂⠐⠊⠀⠉⠒⠒⢆⡀⠀⠱⡢⢄ ⠔⠁⠀⠈⠂⡤⠒⠁⠀⢀⠍⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠈⡄⠀⠀⢈⠮ ⠀⠀⠀⠀⡔⠀⠐⠒⠂⠁⢀⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠆⢸⠂⢀⡇⠀ ⠀⢀⡠⠪⠁⠀⠀⡰⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⣀⡀⠀⠈⠩⠠⣌⢀⣾⠃⠀ ⣎⠁⢀⠁⠀⠀⠈⢡⠀⠀⠈⡙⡉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣡⡾⣿⢿⠉⠀⠀ ⠙⠢⡀⠈⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡀⠤⡾⠉⠁⢿⡜⡀⠀⠀ ⠀⠀⠀⠉⢉⠋⠐⠂⠐⠊⠁⠒⠀⠀⠀⠀⠐⠒⠈⠉⠐⡄⢡⡀⠀⢀⡴⠃⠀⠀

⠀⠉⠑⢦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠂⠛⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠳⢦⡀⠀⢀⣴⠛⠁⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⢰⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢉⢳⡾⠁⠀⠀⠀⠀⠀⠀⣨⠷⠚⠉⠉⠑⠦⡀⠀⠀⢀⡾⠿⠋⠩⠍⠉⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠙⣆⠒⠛⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⣦⢰⣤⢿⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠏⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠃⠀⠀⠀⠀⢿⡀⠀⢸⠉⢳⡦⠖⠀⠀⠳⡀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠿⣷⡀⢰⡏⠀⠀⠀⠀⠀⠈⠓⠶⠶⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡈⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⡙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣆⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠙⠛⠒⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠙⠦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠈⠳⠤⠤⢤⡤⠴⠚⠋⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠤⠤⠤⠤⠤⠤⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠈⠙⠲⣤ ⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠐⠋ ⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀ ⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀ ⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⣠⣶⡿⠿⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣄⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀ ⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣠⡟⠁⠀⢠⣾⣿⡟⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠁⠉⠙⣿⣿⣦⡀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸⠏⠀⠀⣴⣿⣿⣿⣇⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⣼⣿⣿⣷⣄⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⠀⠀⠀⢸⠇⠀⠀⢸⣿⣿⡿⠘⣿⣷⣄⡀⣠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣠⣾⣿⣿⠉⣿⣿⡆⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⡿⠀⠀⠀⣿⣟⣋⠁⠀⠉⣛⣿⡿⠟⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠾⣿⣟⡉⠀⠀⠙⢻⣿⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡆⠀⠀⠸⡇⠀⠀⠀⢻⣿⣿⣿⢰⣿⣿⣯⣀⢀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡅⠀⢹⣿⣿⣯⢰⣿⣿⡿⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣧⡄⠀⠀⣧⠀⠀⠀⠀⠛⠿⠿⢿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣿⣿⣿⡿⣿⠿⠛⠁⠀⠀⠀⠀⢸⠁⠀⠀⠀⣠⠂⠀⠀ ⠀⠀⠀⠀⠀⠹⣇⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢰⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣰⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⡾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠼⠻⣦⣀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⡴⣯⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣝⢦⣀⠀⠀⣠⠔⠚⠉⠉⠉⠑⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠊⠉⠉⠓⠢⣄⠀⠀⠀⠀⠀⣠⣞⣥⠖⠋⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠀⠀⠀⠀⠀⡴⠛⣇⣀⠠⣌⣙⣾⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⣀⣴⠿⠛⣿⡏⠀⠀⠀⡏⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠂⠀⠀⠚⠁⣼⠏⠀⠀⠀⢀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⠀⠀⡇⣿⡇⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⢩⡿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⡆⠀⠀⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣦⣤⠀⠀⣸⠁⠀⠀⠀⠀⢰⠀⣞⣠⠞⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⢦⣵⠀⡆⠟⡅⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⡼⠋⠁⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠉⢧⡇⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠉⠀⠀⠀⠑⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⣛⠃⣀⣀⣀⣀⣠⣄⣰⣟⣀⣄⠀⣿⣷⣀⣀⣄⢀⣤⣼⣧⣴⡀⣀⣀⠀ ⠘⠀⠀⢀⣀⡀⠀⠀⠀⠀⠈⠛⡿⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣭⡬⢛⣇⣇⣿⣻⢸⣇⢹⡏⣿⡽⠀⡙⣿⠋⣿⡿⣻⣿⠟⡇⣽⠈⣏⣿⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⢿⣟⣿⣻⣟⣯⣟⣿⣻⣟⢿⣻⣟⡿⣽⣻⣽⣻⢯⣟⣯⠿⣝⢯⡳⣙⣎⢳⡙⢮⡱⢫⡜⣥⢫⡜⣥⢫⡜⣱⣽⡚⠓⠫⢾⠥⠯⣜⡱ ⠿⢛⣩⣵⣶⣶⣶⣯⡍⣟⢿⣾⣯⣿⣿⣻⣿⣾⢷⣟⣾⣳⣟⣾⣳⣯⣿⣳⣯⣟⣷⣻⢾⣽⣻⢾⡽⣻⡝⣎⡳⣍⢎⢧⡙⢧⣍⢳⡘⢆⡳⡘⢆⡳⢜⣵⣿⣿⣷⣦⣤⣘⣥⣤⡭ ⣾⣿⣿⢿⣿⣻⢿⣿⣿⣿⣽⢻⣿⣿⣽⣿⣷⡿⣿⣯⣿⣽⣾⢿⣽⣷⢿⡯⠓⢉⠉⠩⡉⠑⢿⣯⣷⣻⡼⣣⡝⡜⣎⠶⣙⠦⢎⢦⡙⢦⠱⣩⢖⡱⣻⡷⢿⣿⣟⣿⣿⣿⣿⣿⣦ ⣿⡟⣿⣟⣼⣻⢿⣼⣻⢿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣧⣿⢧⣟⣿⠿⢛⡟⢀⢤⡀⠀⠀⠘⠤⠀⢇⡄⣛⠻⢧⣟⡧⡜⢧⡛⣼⢛⡤⢻⡘⢧⢣⡜⣣⣻⡇⣿⣟⢻⣿⣿⡿⣟⣧⣿ ⣷⣻⠷⣞⣳⢯⣟⣾⡽⢟⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡫⢦⡙⣲⡡⠂⢸⠁⠀⠀⠀⠀⡁⡸⠚⢴⣋⠶⣬⣙⡻⢶⣹⢒⠯⣜⢣⠝⣪⠑⣎⡿⣣⣛⠿⣿⢹⣿⣟⣿⣿⢿⡏ ⣶⣯⣭⣭⣭⣭⣽⣶⢿⣻⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣬⢓⢧⢳⣽⣗⠀⡋⠀⠀⠀⠀⠀⠈⠀⢀⡼⣍⠿⡶⣥⣋⢿⢦⣋⠞⡌⢎⡜⠤⢋⣾⣱⡿⣽⡾⣵⣏⣛⡛⡟⣞⢫⡽ ⣟⣾⣽⣯⣿⣽⣷⣿⣿⣻⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⡵⣣⡿⢞⡽⣛⡾⣟⠷⣤⣤⣤⣤⡤⡶⣏⣛⡴⡩⢞⡱⣊⠳⡾⢸⣦⠹⣜⠲⣌⢣⢻⣿⣿⣹⢷⣻⣽⢻⣯⢿⡽⣞⣯⣽ ⢸⢋⣥⣶⣿⣶⣶⣮⣽⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣿⣵⢊⠷⡸⢥⡓⢮⡽⣺⠱⢎⡲⣑⢣⢍⡳⣝⡹⢳⢧⣭⢞⡕⣼⢺⡽⣎⠷⡭⢏⡻⣿⣳⢯⣯⠷⡞⠿⢮⣟⡽⡽⣞⣽ ⡆⢿⣿⣿⣿⣿⣿⡿⡿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣔⠀⣹⣯⢶⣙⢦⣹⣎⠷⣡⠛⡤⠓⣌⠲⣌⢲⠥⠟⢋⠅⢂⣿⣿⢎⣼⢳⡜⣫⠵⡫⠵⣙⣿⢭⢲⡹⣜⡹⢲⡜⡲⢭⡙⣿ ⣿⣷⣈⠉⠹⠿⠉⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢉⣷⣸⡏⣉⠿⣷⢏⣶⣎⣰⣉⡰⢉⡀⠇⠀⠀⠀⣀⡸⠎⢹⣱⡾⢿⢇⡷⣸⢁⢷⡉⣷⣿⣿⣷⣇⢷⡈⢷⢇⡾⢱⢇⡹⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢠⠣⣿⠿⢷⣯⣗⣯⠿⣜⣥⣒⣤⣣⣴⣴⣦⣧⢷⣲⠻⠿⢫⣽⡴⡈⠀⠑⢇⢏⠶⣽⣻⢿⡿⣿⣿⣷⣿⣮⣾⣜⣧⣮⣵⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠠⡇⣧⡙⢿⣶⣮⢿⣼⣻⢧⣦⣶⣤⣦⣤⣤⣤⣦⣴⣶⣷⠿⠟⣏⡇⣇⠀⠀⠀⢪⣛⠶⣹⠮⣝⡳⣟⢾⣻⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢠⣱⣷⣌⡻⢶⣽⡽⢮⡶⣭⣛⣾⣹⡟⡟⢛⣋⣍⣩⣴⡤⢶⡷⣋⣸⡟⡹⢇⠀⠀⠀⣏⠞⣥⠛⣬⢓⡭⢞⡭⣟⣾⣻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡄⠀⢀⢎⢫⠿⣻⣿⣶⣮⣍⣣⢟⣳⣟⡶⠳⢟⡛⣛⣋⣍⣭⣴⣼⠷⠞⠌⠓⠷⣽⣾⠄⠀⠀⢹⣚⢶⡹⢆⡯⣜⣏⢾⡱⣏⣷⢻⡾⣝⠶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠇⠀⠁⢸⣸⠀⠀⣉⠛⡛⢛⠻⠟⡟⣎⢳⢛⡛⡛⢛⠋⣍⣩⣡⣤⣶⠧⢄⠀⠀⠈⠙⠲⣠⢀⣾⡹⢮⡝⣝⡲⢵⣪⢳⣝⡳⢮⠷⣹⢎⡟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⣿⢠⠈⠑⣮⣴⣥⠓⠚⢱⢫⡟⢻⣿⣿⣿⠛⠛⠋⡅⢢⣤⣴⣼⢢⠀⠀⠀⠀⠐⠉⢪⡝⢳⡎⣧⢹⢲⣥⢳⡎⣵⢫⡝⣶⡝⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠷⣍⠲⠬⣌⣙⢛⠻⣛⠞⡶⠥⠦⠤⠦⠼⠶⠳⠾⢛⢛⡯⠇⢸⡽⠂⠄⣀⠀⠀⢀⡈⡄⢈⠙⠪⢗⠚⠓⠚⠓⠉⠉⠀⠁⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠈⠻⠶⣬⣌⣫⡑⣎⡛⠶⣙⠒⡓⢚⠒⡚⠓⢈⠪⠅⠐⠂⠁⠀⢀⣰⣼⡿⣟⡳⣏⢷⣼⡤⠂⢔⠋⢖⠶⣠⣦⣄⣀⣀⠄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⡦⣀⠀⠀⠈⠚⠵⠽⠧⠿⠽⠧⠿⠼⠧⠛⠛⠙⠁⠀⠀⠀⠀⣠⣴⣿⣿⣿⢿⣽⣻⡽⣞⢧⣟⣷⣤⡃⠀⠈⠀⡙⠛⠪⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠃⠀⢱⡱⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠊⠉⠁⠀⠈⠉⠉⠓⠵⢄⡑⡢⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠖⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠻⣤⣹⡶⢄⡀⠀ ⠀⠀⠀⡔⠁⠀⠀⠀⠞⠠⢄⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠘⠌⠛⢦⣌⠐ ⠀⢀⠎⠀⠀⠀⠀⡸⡃⣤⠊⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⡄⠀⠈⠓ ⠀⡌⠀⠀⠀⠀⠀⣏⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠸⠀⠀⠀ ⢰⠀⠀⠀⠀⠀⢀⡧⠒⠂⠈⠉⠉⠉⠀⠐⠒⠤⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⡈⠀⠀⠀⠀⠀⢸⡀⠀⢀⡄⠀⠀⠀⠀⢀⣀⢀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢸⠽⠿⢯⠀⠀⠀⠀⠀⠀⠹⠟⢿⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⢰⡀⠀⠀⠀⠀⢸⠑⢢⣄⣀⡀⣉⣁⡀⢀⣀⡠⡴⢣⡀⠀⠀⠀⣠⠃⠀⠀ ⠀⠑⢄⣀⣀⡠⠃⠀⠈⠈⠢⢍⠟⠟⠛⢏⣡⠊⠀⠀⢻⠒⠐⠒⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡜⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⢎⠀⠈⠠⢒⡄⠈⠐⠊⠠⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠶⢶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡿⠁⠀⠀⢸⣏⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠈⠀⠀⠀⠀⠘⣿⣆⠹⣿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠿⠖⠒⠒⠒⠒⠶⠶⠤⣤⣿⣿⡆⠹⣧⠉⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣿⣦⣆⡐⠀⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣔⡢⣀⡉⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣥⣀⠀⢹⣿⢶⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠁⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡻⢷⣾⣧⡟⠀⠙⠳⣦⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠉⠛⢿⣷⣤⡀⠀⠙⠳⣤ ⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠈⠻⢿⣷⣤⡀⠀ ⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢦⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣆⠀⠀⠀⠀⠉⠻⣿⣆ ⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣸⠐⢾⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠖⠃⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⢁⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀ ⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣥⠶⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠲⠦⣄⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀ ⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣄⠀⢀⣠⣴⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣀⢰⣤⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢙⣿⣿⣿⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⠛⠉⠙⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠉⠈⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠿⠟⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀ ⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠉⡷⣦⣤⣄⣀⡀⠀⢀⣤⣤⣤⣤⡄⠀⠀⣀⣀⣠⣤⡴⢾⡿⠋⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢰⠇⠈⠳⣬⡉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⠛⢩⡼⠋⠀⠀⠀⠙⣷⣦⣀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠷⣤⣀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⢸⠀⠀⠀⠈⠻⢦⣀⣴⠏⠛⠟⠋⠁⠉⢷⣄⣠⣾⠋⠀⠀⠀⠀⠀⠀⢻⢹⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠙⠋⠘⡆⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⣼⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⢠⠏⠀⠲⣄⡀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢀⡴⠃⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⣴⠛⠀⠀⠀⠈⠉⢍⡑⠒⢶⣄⠀⠀⠀⠉⠙⠒⠉⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠈⠒⢾⡙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣿⣿⣿⣦⣾⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⣋⣽⡟⢉⣷⠞⠉⠀⠺⠛⠛⣻⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣒⣯⣵⠖⠛⢉⡠⠤⣾⡟⢀⠀⠀⠀⠙⣧⡻⢟⣿⡿⣶⣦⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢒⡿⠛⠉⠉⠋⠁⠀⢰⣿⠁⢀⣿⠁⣿⡄⠀⠺⣿⣤⠉⣁⣀⠀⠀⣹⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣳⣾⡟⠀⠀⠀⠀⠀⣸⡇⢸⣿⡀⠈⠿⣧⣌⠙⠳⠀⠈⠁⣼⡟⣿⠟⠿⠛⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢑⣿⡿⠁⠀⠀⠀⠀⠀⢻⣇⠈⠹⣷⣄⠀⠈⠛⠣⣀⣀⢀⣄⣋⣑⡛⠛⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⠏⢉⣁⣠⡤⠤⢤⣀⡠⣿⡿⠀⠀⣦⣍⣷⣦⣶⣾⡿⠿⠟⠀⠀⠁⠈⠙⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣷⡀⢾⣤⡀⠉⠀⠀⠀⠀⢍⡛⢧⡀⠀⠈⢡⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⠻⣷⣄⣉⣛⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠒⠻⢿⣿⡟⠃⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢿⣏⣿⣦⣍⡛⢻⣛⠛⡛⠛⠉⠀⠀⠀⠀⠀⢀⣴⠾⢚⡿⠷⠤⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⢸⣏⢹⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⠲⠷⣄⠀⣡⠾⠋⢡⡘⣦⣧⡙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠗⠁⠀⠈⢿⣆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣨⡷⢦⣴⣽⣶⣿⠟⠋⠻⣦⡝⠢⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣫⠄⠀⠀⠀⠈⠻⣦⠸⡿⢿⣿⣿⣿⣿⣿⠙⠻⠿⣿⠟⢳⣾⣿⣿⣿⣶⣒⡀⠀⠀⠛⢧⡀⠙⢆⠀⠀⠀⠀ ⠀⠀⠀⣽⣡⠂⠀⠀⠀⠀⠀⢻⣄⠘⣄⠉⠛⠻⣿⡟⠀⠀⠀⡀⠀⣸⡅⠀⠙⠿⣿⣿⣿⣧⣤⠀⠈⢻⣆⢸⣄⠀⠀⠀ ⠀⠀⠀⢹⢇⠀⠀⠀⠀⠀⠛⢿⣿⠳⢼⣶⣤⡶⠀⠀⠀⠀⣰⡿⠐⢿⡇⠀⠀⠀⠈⠉⠻⢿⣿⣿⣧⣄⠉⠀⠉⠳⡄⠀ ⠀⠀⠀⢸⠸⣷⡀⠀⠀⠀⠀⠀⠙⣦⡈⣿⡋⠀⠀⠀⢀⣠⡿⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣷⣦⣄⡀⢧⠀ ⠀⠀⠀⢸⡄⠙⢿⣄⠀⠀⠀⠀⠀⠈⢻⣽⣷⣤⡀⠀⠞⠋⢀⢀⣀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⡇⣸⠀ ⠀⠀⠀⢠⣧⡀⠀⢙⠛⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⣄⣼⣿⡟⠋⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠛⠁⠀ ⠀⠀⠀⠈⣿⠇⠀⢾⣤⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣿⡤⠀⢸⡟⠀⠀⠀⠀⢠⣾⢻⣿⣿⣿⣿⡿⠟⠠⠤⣤⣀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣽⠁⣠⠏⠀⢾⣧⣤⣾⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣥⣄⣠⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡾⢁⣼⡏⠀⠀⠀⠀⠀⣼⡿⠋⠛⢿⣿⢿⡯⠤⠤⠖⠚⠉⠉⠙⠛⠃⣠⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠟⠁⠸⠿⢟⣠⣄⣠⣴⣿⢧⡀⠀⠀⠀⢀⡞⠀⠐⠀⢀⣴⡤⠤⠤⢴⣾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⠀⠀⠀⠀⠈⠹⠽⠻⣉⢻⡓⣾⣦⠀⠀⠘⠧⣄⣀⣀⣈⠀⣀⣀⠀⠀⠉⢹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠦⠤⠖⠒⠒⠲⠦⠤⣾⣾⣽⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠱⠊⡱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠤⢄⣑⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣢⠐⡄⠀⠉⠑⠒⠒⠒⣄ ⠀⠀⠀⣀⠴⠋⠀⠀⠀⡎⠀⠘⠿⠀⠀⢠⣀⢄⡢⠉⣔⣲⢸⠀⠀⠀⠀⠀⠀⢘ ⡠⠒⠉⠀⠀⠀⠀⠀⡰⢅⠫⠭⠝⠀⠀⠀⠀⠀⠀⢀⣀⣤⡋⠙⠢⢄⣀⣀⡠⠊ ⢇⠀⠀⠀⠀⠀⢀⠜⠁⠀⠉⡕⠒⠒⠒⠒⠒⠛⠉⠹⡄⣀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠑⠂⠤⠔⠒⠁⠀⠀⡎⠱⡃⠀⠀⡄⠀⠄⠀⠀⠠⠟⠉⡷⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠴⣄⡸⠤⣄⠴⠤⠴⠄⠼⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢶⡶⢴⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣔⡾⠕⡛⣼⠏⠀⠈⢅⡯⢷⢤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⢀⣒⡼⠉⠉⠉⡄⣾⠀⣾⠸⢄⠘⠷⣩⣤⣀⡽⠁ ⠀⠀⠀⠀⠀⠀⢠⢪⡿⠀⠀⠀⢐⡇⠙⢦⡈⠛⢆⣀⣀⣛⣛⢢⠀⠀ ⠀⠀⠀⠀⠀⢠⡖⣥⡒⠒⠀⠒⡸⣇⠀⠓⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢷⡻⣮⣭⣀⣀⠀⠈⠉⠁⢈⣻⣟⠉⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠔⢹⡛⣿⣶⣶⣶⣶⣶⡦⠦⡀⡫⠖⠕⣼⡡⡀⠀⠀⠀⠀⠀ ⠀⢐⡋⠀⠀⢳⡘⣿⣿⣿⣿⡿⣧⣤⢾⣵⣿⣟⠉⠙⠲⡕⠠⠀⠀⠀ ⠀⢸⠄⠀⠀⢀⣣⡐⡌⠛⠿⠃⠀⡄⢨⡄⠙⠻⢿⣧⣄⡙⠆⠧⡀⠀ ⠀⢸⢦⡀⠀⠀⠙⣌⣛⠋⠀⢀⣰⠇⢸⡇⠀⠀⠀⠉⠛⠻⣦⣀⡸⠀ ⠀⢸⠈⠳⠄⠀⠀⠈⢻⣷⣦⡈⣡⡤⠞⢤⠀⠀⠀⠀⠀⠀⠙⢿⠵⠀ ⠀⠨⡇⠐⡦⠀⠀⠀⣠⣿⣿⣿⡟⠁⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢈⡏⡠⠣⣄⣠⣞⣿⣿⣿⣯⣥⣽⢓⣀⡀⢸⡄⠀⠀⠀⠀⠀⠀⠀ ⢠⠞⣼⡅⠀⢀⣴⠛⠉⠛⡻⠒⠒⢉⠀⢉⣡⠚⠁⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠉⠿⢫⢳⣵⡄⠀⠣⠄⠠⠭⠄⣀⣉⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠑⠤⡀⢀⠔⠒⠲⡃⠀⠀⠀⠀⢡⠀⢠⣼⠁⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⡰⠈⠀⠈⢢⠐⠭⡀⠀⠈⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀ ⠂⠀⠈⣌⠙⡢⠀⠡⢀⠀⡀⠌⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠛⢌⢢⠀⠀⠀⠀ ⠀⠀⠀⠈⢳⡀⠀⠀⠀⡰⠄⣀⣀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢗⢄⠀⠀ ⠀⠀⠀⡰⠁⠀⠒⠒⠊⠀⡀⠤⠀⠒⠒⠒⠒⠀⠤⠄⡀⠀⠀⠀⠀⠀⠈⠳⡈⠲ ⠀⠀⢰⠃⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠸⡀ ⠀⠀⡇⠀⠀⡰⠁⣰⡟⠉⠻⡆⠀⠀⠀⠀⠀⠀⢠⠞⠛⢶⣄⠈⠢⡀⠀⠀⠀⠁ ⠀⠀⡇⠀⡸⠀⣼⡟⢳⣄⣰⣧⠀⠀⠀⠀⠀⠀⢸⣀⣠⡾⠻⣧⠀⠰⡀⠀⠀⠀ ⠀⠀⡇⠀⡇⠀⠻⣧⣶⣯⣼⡟⠀⠀⠀⠀⠀⠀⠹⣧⣹⣷⣴⡾⠀⠀⡇⠀⠀⠀ ⠀⠀⠘⡄⢡⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠃⢠⠃⠀ ⠀⠀⠀⠘⢦⡑⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⢴⠁⠀⠀ ⠀⠀⠀⠀⡀⡌⠚⠷⡔⠁⠀⠀⠁⠢⡀⠀⠠⠊⠀⠀⠈⢂⡠⠔⣷⠁⡟⠀⠀⠀ ⠀⠀⠀⢠⠊⠀⠀⡞⡄⠀⠀⠀⠀⠀⢱⠎⠀⠀⠀⠀⠀⢸⣳⠀⡿⠀⡇⠀⠀⠀ ⠀⠙⠁⠀⠀⢀⡗⠉⠈⠀⠀⠀⠀⢀⠌⠡⠀⠀⠀⠀⠀⠁⠈⢂⠀⠀⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⢤⣇⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣟⣤⣤⣴⢴⣴⠸⡧⣤⣴⣖⢠⡄

⠀⠀⠀⠀⠈⢿⡟⠁⠀⠀⣾⣿⣃⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⣿⠿⠿⣿⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠺⡛⠷⣾⡟⠀⠀⡰⢱⠋⠒⠊⡹⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠈⠉⡟⡇⠀⡰⢳⠃⠀⠀⡰⢁⡆⠀⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⡇⡇⡰⣡⠃⠀⢀⣴⠃⡜⠇⠀⢳⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⣟⡿⣽⠃⠀⡠⣞⣾⠤⠗⠒⠒⠚⠓⠚⠿⢿⣿⡏⠉⠻⣿⣿⠃⠀⠀ ⠀⠀⠀⢀⠏⢰⠃⣠⢚⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡀⠀⢙⣏⣈⠁⠀ ⠀⠀⢀⠎⢲⠷⠊⣨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⢷⠀⠁⠘⠀⠀ ⠀⢀⣫⠞⠉⡼⠾⠁⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⢇⠀⠀⠀⠀ ⢀⠞⠁⡠⠊⢠⠃⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⡆⠀⠀⠀ ⠎⢯⠊⠀⠀⡌⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⢀⠏⠀⠀⢰⠁⠀⠀⠀⠀⢀⡇⠤⠀⠒⠒⠒⠒⠒⠂⢧⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠋⠀⠀⠀⣸⠀⠀⠀⠀⠀⢸⠤⣀⣤⠀⠀⠀⠀⠰⠖⢻⡆⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⡜⡟⠳⣒⠒⡖⠒⠒⣖⣉⠥⠛⢢⣀⣀⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠚⢄⣀⣀⠜⠁⡇⠀⠀⠀⠃⠀⠀⢸⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡤⢄⣠⠼⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⠤⠔⠁⢀⣧⠀⠀⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠹⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠊⠀⠉⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠙⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠁⠈⠛⢷⣄⠀⢀⣠⣴⡶⠿⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠙⢿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⠏⠀⠀⠀⠀⠀⢻⣿⠿⠋⠁⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⢻⡿⠀⠀⠀⣤⣤⣤⣾⣿⣦⣤⣀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣿⣠⣿⠋⠀⠀⠈⢻⣶⠶⠶⢶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⢀⣽⡇⠀⠀⠀⠀⢨⣿⣄⠀⠀⠀⢹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠛⠛⠛⢿⣤⣀⣀⣴⣿⣧⣽⠂⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣏⠀⠉⠁⠀⢠⣾⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⣀⣴⠟⠁⠀⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠠⠶⠖⠛⢻⣿⠛⠛⠓⠲⠤⣤⠀⠀⠀ ⠀⠀⢀⣀⣼⣧⣤⣤⣤⡄⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠉⠉⠁⠸⣿⠀⠀⠀⠀⠀⠀⠀⠸⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⠀⠀⠀⠀⠓⠒⠲⣿⣷⣤⣤⣤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠄⣹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣼⠿⢻⣧⠀⠀⠀⠉⠳⣦⡀⠀ ⠀⠀⠀⢠⠴⠞⢿⣧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⡿⠃⠀⠘⣿⢀⣀⣀⡀⠀⠈⢿⡄ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣧⡀⠀⠀⢽⠻⠉⢻⣿⠀⠀⠁⣿ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠛⠷⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⡾⠟⠋⠁⣿⢸⠿⣦⡀⠘⢷⣤⣼⢿⡆⠀⢀⡿ ⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠈⣩⣽⠿⠟⠻⣿⡿⠿⠿⢿⣿⠿⣿⡿⠿⢿⣿⠿⣿⡿⢿⣿⣭⣉⣡⣴⣶⣤⣀⢠⣿⣿⣞⣩⣷⡀⠀⠻⠷⠋⠁⣠⡾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠿⣷⣄⠀⠀⠈⢿⣄⠀⠀⠉⠳⢦⣙⣷⠟⢁⡼⠋⠀⠀⣿⡌⢻⡏⠀⢀⣬⣿⣿⣿⠿⢿⣳⠾⣇⠀⠀⢀⣠⡾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠹⣧⡀⠀⠘⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⡇⠀⣧⣾⣫⡿⠟⢻⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠉⠁⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣀⣀⡀⠀⣰⠟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⣦⣄⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠏⠉⠛⠛⠋⠀⠀⠀⢸⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡇⠀⢸⣏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣠⠄⢠⡞⠓⢶⠀⣼⢿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢾⣀⣸⠳⠴⠂⠀⡟⣾⠁⠀⠀⠀⠀⠀⠀⢀⡭⠿⢯⡉⠉⠙⡇⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⣀⣁⣀⣰⣀⣿⣇⣿⡆⠐⢲⡄⠀⠀⠀⠸⢧⣤⣬⡛⠂⠀⣿⣤⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣭⣭⣭⣍⣍⣉⣐⣒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠑⢈⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢻⡟⠋⠉⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡃⣀⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠛⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠟⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢄⠙⣠⠇⠀⠀⣠⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⠁⠀⠀⢰⠁⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣆⢀⣀⠤⠖⠒⢢⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡮⠁⠉⠁⠒⠤⢀⡼⠖⠀⠐⣗⠢⡀⢸⣏⡁⠀⠀⢀⡠⠥⠒⠲⠤⢄ ⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣀⣈⣍⣈⡿⡘⠁⣹⡚⠁⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⣇⣠⡶⣍⣀⣠⠴⠛⠻⢇⣜⡁⠺⠽⠀⠀⠀⢠⡞⠁ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢷⡀⠀⠀⢀⡏⠀⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡉⢳⡄⣸⠁⠀⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠿⢻⡖⠒⠂ ⠈⠉⠸⡍⠈⠀⠀⠘⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣶⡄⠀⠀⠠⢸⠅⣀⠀ ⠀⠀⠔⢷⠈⠀⠀⠀⠘⠛⠁⠀⠀⠀⣤⢤⠀⠀⠀⠀⠸⠿⠁⠀⢀⣠⠟⠀⠀⠀ ⠀⠀⠀⣀⠷⢎⠁⠀⢀⡀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠈⠒⠀⠀ ⠀⠀⠀⠁⠀⠀⠉⡖⠀⠈⠑⡦⠤⠄⠄⠀⠤⠤⠤⡖⠉⠉⠹⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠞⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠋⠉⠉⠉⠉⠁⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠉⠓⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠈⢙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣸⠀⠀⠀⠀⠀⣸⠞⠉⠉⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢉⠀⠉⣠⠖⠋⠉⠓⢦⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⣧⠀⣸⣦⡀⡇⠀⠀⠀⠀⠈⣇⠀⠀⣸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⣄⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠈⢳⣤⡽⠛⠉⠓⢶⣧⡀⠀⠀⠀⣰⠇⠈⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢼⣄ ⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⢹⠉⠛⠞⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣼⡆⢀⡴⠋⠉⠉⠳⡄⠀⠀⠀⢠⡟⠀⢤⠈⣻⣄⡀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⠉⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⡄⠐⠚⠻⣤⣀⣀⡴⡃⠀⠉⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢀⡾⠁⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠘⢙⡶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠱⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣷⣄⠀⠀⣠⠄⠈⠙⠓⠚⠉⣄⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠉⠙⠒⠶⠶⠶⠒⠋⠁⠀⠀⠀⠀⠈⠉⠓⠒⠶⣶⡒⠀⠀⠀⠀⠀⠺⣝⠶⣄⣀⠀ ⠀⠀⢀⡴⠋⠈⠉⠉⡏⠀⠀⠀⠀⠀⠀⣿⠉⠓⠶⠊⠁⢀⡀⠀⠀⠀⢀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠓⠀⠀⠀⠀⠀⠘⢧⡀⠈⣿ ⢀⡴⠋⠀⠀⠀⠀⠀⠹⣤⣀⣀⣀⡤⠞⠛⠀⠀⠀⠀⠀⠀⣹⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢸⣸⡃ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⠀⠀⢹⡄⠀⠀⠀⠀⠀⢀⣾⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠤⠤⣤⡤⠤⠞⠋⠀⠀⠀⣠⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢹⣦⡀⠀⠀⣶⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⢈⡇⠀⠀⠀⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⢫⠇⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠀⠀⠀⡾⠁⠀⠀⣶⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⣀⡴⠋⢀⡞⠀⠀⠀⠀⠀⠀⣀⡾⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠤⠀⢴⣟⠁⠀⢀⣴⣿⣏⠀⠀⠀⠀ ⣀⣠⠴⠚⠁⠀⢠⠟⠀⠀⠀⠀⠀⣠⡴⢻⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠃⠀⠀⠀⠀⢀⠼⠋⢀⡼⣯⣹⣷⣿⣿⠣⠟⠀⠀⠀⠀ ⢻⢀⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢀⠍⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢟⣵⢿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀ ⣿⣯⠀⠀⠀⠀⠃⠠⣀⠀⠀⠀⠀⠀⠀⠀⠞⡆⠀⠀⠀⠀⠀⠐⠋⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢿⠃⣾⣿⣧⢠⣿⠀⠀⠀⠀⠀⠀ ⠀⠿⢷⣰⠀⠀⠀⠀⠈⠁⠀⠀⠀⠤⡀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠀⠀⠀⢀⣠⠴⣻⡿⠁⠀⠈⠀⢸⣿⣯⣼⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠲⢤⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠻⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⠋⠉⠳⡝⠀⠀⠀⠀⠀⠈⠿⠿⠁⢰⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⡽⠋⠳⠦⢤⣀⣀⡠⠤⠟⠛⠒⠲⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠖⠒⠋⠉⠘⠀⠠⣄⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣣⢠⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⣷⡀⠀⠀⠀⠀⠀⣿⠛⠁⠀⠀⠀⠀⠀⠀

⠀⠀⣀⠀⡑⠀⡇⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠐⠒⠒⠁⠒⠋⠁⢠ ⢀⢻⣾⢳⠀⢀⡧⢀⢸⡄⠀⣀⠔⠚⠉⠘⠒⠺⡁⢀⣙⣂⣀⣙⣉⣁⠍⠉⠉⢹ ⢖⣯⣥⢾⠀⠀⡇⣼⡼⠝⣟⣗⠀⢀⡀⠀⠀⠀⠘⢉⠇⠀⠀⠀⠀⠀⠀⠈⠁⠀ ⡾⢺⠍⢸⠀⠀⣷⣿⠡⣄⡈⠉⠀⠈⠀⠀⠀⠀⠀⠀⢣⢀⣀⣀⣀⡀⠀⣀⠀⠀ ⠃⠀⠀⢀⠀⢠⠋⠀⠀⠐⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⣄⠀⠀⠀⠀ ⡆⢀⢸⣸⣤⣦⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⢤⡇⡀⣇⡆⠀⡤⠤ ⣧⣼⡿⠟⣽⡿⢷⣦⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠄⠀⠉⠓⠚⠉⠉⠁⠀ ⣿⡿⠛⢻⡿⠷⠒⡙⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡷⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⣿⣿⣿⡷⠶⢶⡇⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⣰⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠭⢽⡿⣿⠿⠯⢭⣧⠀⠀⠀⠀⠀⠀⠀⠈⠚⠚⠁⠀⢠⣿⣷⣾⣿⣿⣿⣷⣾⣶ ⠀⠛⠛⠛⠛⠛⠛⠻⢷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠗⠋⠉⠙⠋⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠐⠂⢤⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠴⠤⢼⣄⣄⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠿⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠑⠒⠂⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⠶⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠶⠖⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠲⠶⠶⣿⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡋⠁⠀⠀⠀⣀⣤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠘⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣀⠀⠠⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⣼⠇⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⢿⣤⡾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣥⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠉⠛⠿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⠋⠁⠀⠀⠀⠀⠀⠙⠓⢤⡀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⠤⠼⠧⠤⠤⠤⠤⢤⣄⣀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢻⡀⠀⠀⠀⠀⠀⣠⡶⠀⣠⣶⣿⣿⠂⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⢷⡀⠀⠀⢀⣼⠋⠀⢰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠘⠁⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣠⠠⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⢀⡰⠟⠁⠀⡴⠋⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠙⢦⣀⡀⠀⠀⠀⢀⣀⣠⡴⠶⠚⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⣄⠀⠀⢠⠟⠀⠀⣠⠞⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠉⠉⠉⠉⣉⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣶⠂⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣀⣀⡀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠻⡦⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡿⠉⠒⠒⠒⢺⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣧⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠾⣦⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠣⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠚⠉⠀⣀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⣀⣰⠞⠃⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⡇⠀⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⠁⣤⣤⠀⠉⠉⠛⠷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠋⢀⣴⣶⣾⣿⣿⣿⣿⣿⣶⣦⡀⠈⢻⣆⠀⠀⠀⠀ ⠀⠀⠀⣾⢃⣠⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⣄⡀⢻⡆⠀⠀⠀ ⠀⠀⣸⡿⢋⡁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢈⡙⢾⣇⠀⠀⠀ ⢀⣾⠋⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠙⢷⡄⠀ ⣾⡇⠀⣼⠀⠀⠀⠛⠀⠀⡀⢲⡶⢀⡀⠀⠛⠀⠀⠀⢿⠀⢸⣷⠀ ⠸⣧⡀⢹⡄⢀⣀⠀⠀⠈⠧⠞⠑⠖⠃⠀⠀⢀⣀⢀⡿⢀⣼⠇⠀ ⠀⠈⠙⢻⡿⠉⠉⢳⣄⣀⡀⠀⠀⢀⣀⣀⡞⠉⠉⢻⡟⠛⠁⠀⠀ ⠀⠀⠀⠀⠻⠶⠶⠾⠉⠛⠛⠛⠛⠛⠛⠉⠻⠶⠶⠟⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⡟⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⣼⡟⣿⣿⡶⢶⣶⣦⡄⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⢰⡿⣿⣿⣿⠿⣿⣩⡿⠁⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⣤⣤⣤⣤⣀⢀⣿⡏⠀⠀⠀⠀⢠⡟⣺⡿⣅⣀⣠⡴⠛⣧⡶⠶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠻⣄⠙⠻⠿⣿⣿⡇⠀⠀⠀⢀⡿⢠⡟⠀⠀⠈⠀⠀⡼⠋⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀ ⠀⠀⠀⠈⠛⠒⢲⣿⣿⠀⠀⠀⢀⣾⣥⡾⠀⠀⠀⠀⠀⡼⠁⣰⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡏⣿⠀⠀⢀⡾⢡⡾⠁⠀⠀⠀⠀⣸⠃⢀⣿⠀⠀⠈⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣹⠀⢀⡟⢁⡞⠁⠀⠀⠀⢀⣼⡏⠀⣼⢹⠀⠀⠀⢿⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡧⣿⢠⣿⣤⡟⠀⠀⠀⠀⣠⡟⢹⠃⢠⡏⠈⠆⠀⢀⣸⣧⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣹⠿⣦⡟⠀⠀⠀⣠⢾⣥⣻⣿⣠⠾⠓⠛⠉⠉⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⡿⡋⠀⠀⠙⢿⣿⣿⣿⡇⠐⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠋⢀⡟⠀⠀⣠⣾⡁⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⡄⡀⠀⠸⠿⢿⠛⠃⠿⠷⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠃⢀⡾⠀⣠⣞⡋⣨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⡀⠆⠀⣼⠶⢶⣄⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠁⣄⣾⣵⠞⠁⢈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⡆⠀⠉⠀⠈⠿⠀⠀⠀ ⠀⠀⠀⢀⡾⢁⣠⡼⠏⣁⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡞⣠⡞⠋⠀⢠⣼⢯⡟⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡟⠁⠀⠀⣠⠞⠁⡞⠀⠀⠀⠀⠀⠀⢠⣿⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀ ⠀⣼⠋⠀⠀⣠⠞⠁⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣿⣴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀ ⣼⢡⡓⣦⠞⠁⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠃⠀⣹⠃⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⢰⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣀⠤⠴⠖⠒⠛⠛⠛⠓⠒⠒⠒⠲⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⣴⠏⠀⠀⠀⠀⠀⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⣀⣤⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⠶⣤⣤⡴⠃⠀⠀⠀⠀⠀⠀⢠⠿⠋⠙⢛⣇⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢏⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⣷⠤⣭⣍⣀⣀⣀⣠⣤⠤⣤⠤⠖⠚⢉⡹⢦⡀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢻⡀⠀⠀⠀⠀⠀⠀⢰⠇⢸⠃⠈⠳⠦⣄⣐⣿⠀⠀⠀⠀⢻⣤⠴⠚⠁⠀⠀⢹⡶⢦⣶⠾⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⡹⣄⠀⠀⠀⠀⣰⠟⠀⣾⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠛⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢸⠤⣄⣀⡤⠴⠻⡄⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⣠⠋⠀⠀⡇⡇⠀⠀⠈⠲⠤⠤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡗⠒⠊⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡇⢷⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⣸⠀⠈⢧⡀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠤⠤⠶⠃⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⠶⠯⠭⣀⠀⢀⠔⠊⠉⠛⢗⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡾⡟⠁⠀⠀⠀⠈⢷⠃⠀⠀⠀⠀⠀⢣⢼⣆⠀⠀⠀⠀⠀ ⠀⠀⡸⡾⠹⡁⠀⠀⠀⢠⣶⢸⢠⣶⡄⠀⠀⠀⢸⡇⠘⣆⠀⠀⠀⠀ ⠀⡰⢹⠃⢠⡧⡀⠀⠀⠀⠉⠌⠡⢄⠀⠀⢀⡠⠛⡆⠀⢸⡀⠀⠀⠀ ⢀⠇⣿⡇⢸⠀⠈⠐⠒⠒⠈⠀⠀⠀⠀⠉⠀⠤⠄⢸⡀⢀⡇⠀⠀⠀ ⢸⠀⣿⣧⢹⠀⠀⠘⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⡰⣼⠇⠀⡇⠀⠀⠀ ⢸⠀⣿⡟⢻⣧⡀⠀⠀⠀⠀⢈⣀⣁⣀⣀⣀⠤⢴⣇⠀⠀⡇⠀⠀⠀ ⠘⡄⢯⠜⠀⢰⡟⠊⠉⢹⣟⠋⠉⠉⠉⢩⠗⠀⠀⠙⡇⠀⡇⠀⠀⠀ ⠀⢡⢸⠀⠀⢺⡄⠀⠀⠠⡿⣄⣀⣀⣀⣀⣇⠀⢀⣴⣃⣸⠁⠀⠀⠀ ⠀⠐⠚⠛⠉⠉⠉⠑⠒⠊⠉⣉⡠⠤⣤⡤⢤⡭⣭⣭⣍⣉⡉⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠺⢮⣭⣭⣥⣽⡦⠖⠚⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣿⡏⠀⢹⣶⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣸⡿⠋⠹⣇⣀⣤⣀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠸⣿⡉⡙⢿⣧⠀⢸⣿⠈⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠩⣿⣧⠀⢰⣿⠛⠿⣿⣦⣶⣿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠛⠛⠛⠻⠿⣷⣦⣽⣿⣷⣶⣿⠷⠿⣷⠾⠛⠋⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⣿⣶⣌⣿⣴⣿⣧⣬⣾⣿⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁⠀⠀⣨⣿⣄⣠⣿⣶⣤⣤⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⣀⣹⣏⠀⣸⣏⡁⠀⠀⢙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣿⡛⣹⡿⠉⣿⣥⡈⡝⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣽⣿⡿⠋⣹⡿⠻⣿⡝⠿⣷⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣱⣿⡇⠀⠘⡿⠿⣷⠿⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⢹⣿⣠⣴⣿⠃⠀⢹⣧⣀⣘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⢷⣤⢾⣧⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠉⠉⢉⣿⣄⣠⣾⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⠀⠈⢧⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣀ ⠀⠀⢠⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠉⠁⠀⢠⣾⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠘⡄⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛ ⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⣷⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀⠻⠿⠟⠁⠀⢀⠇⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠻⣿⡶⠿⠿⠿⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣾⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠛⠓⠛⠁⠀⢀⣤⣶⣶⣤⠀⠀⠀⢀⣬⣿⡿⠋⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠈⠻⠿⣷⣦⣄⣀⡀⠀⠀⠀⠀⣴⣟⠋⠻⣷⣶⣶⣶⣶⣿⠏⠀⠀⠹⣷⣶⡿⠟⠋⠁⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⢿⣿⣿⠈⡄⣀⣾⡟⠀⣀⣫⣿⣷⣤⣤⣤⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢋⣿⣷⠿⠿⢯⣤⣴⠟⠉⠉⠻⣿⣩⡍⠉⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣤⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣳⣿⣿⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⢸⣿⠀⠀⠶⣈⠛⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿ ⣤⣤⣤⣤⣶⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠻⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡍⢀⢀⡆⠃⠀⠙⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⡟⢉⡶⡄⠙⣷⣄⡀⠀⠀⠀⢀⣴⠟⢉⠚⡛⣀⣶⠟⠛⠛⠿⣾⠋⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡋⢰⠄⠆⠃⠧⠤⠉⠛⠻⠶⠶⠟⢁⢀⠀⠀⡆⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠻⣧⣤⣠⣄⣤⠀⠀⢙⢙⠰⠰⡆⠆⠊⠐⠀⠠⡇⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠹⠟⠉⠉⠙⢷⣄⢺⡟⠒⣀⣠⣀⠀⢙⢀⣄⣀⣤⠊⣽⠷⣦⣄⡀⠀⣠⣶⡋⠵⠁⠙⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠸⣾⠟⠉⠉⠙⠻⣿⠿⠋⠉⠻⣦⡀⢶⣤⢉⡹⣻⠫⠷⡁⠈⠄⠀⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⣿⡇⠘⣷⣄⠀⠀⠀⠀⠀⢀⣠⡿⡳⠠⣿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⣏⠈⠘⢙⠙⠐⡃⠀⠂⠀⠀⣠⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣦⠀⠙⣷⣤⣤⠴⠾⠛⢁⡽⠻⠘⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⣤⠰⠠⠄⠀⠄⠀⣃⣨⣶⣿⠟⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣷⣄⡀⠈⡉⠚⠋⠀⠋⠁⠁⠛⠘⠈⢻⣶⣄⠀⠀⠀⣠⣶⢿⠟⠃⠀⣀⣀⣀⣤⣴⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣶⣬⣶⣧⣭⣿⣶⣿⣿⣿⣶⣶⣾⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⣿⠏⠉⠉⠉⠉⠉⠉⠉⠉⢹⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣿⣿⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠟⠉⠁⠀⠀⠈⠙⠿⣿⣷⣄⣤⣴⣶⣶⣦⣤⣀⣠⣾⣿⠿⠋⠉⠉⠉⠉⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⠿⠛⠛⠛⠛⠻⠿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡿⠀⠀⠀⠀⠀⠛⠻⠛⣁⣤⣤⣶⣴⣤⣤⣀⠛⠿⠿⠋⠀⠀⠀⠀⢰⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⢉⣤⣤⣌⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⣿⣿⣿⣿⡆⠀⠈⢻⣧⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠘⠿⠿⠋⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠘⣿⡀⢠⣄⠀⠀⣰⣆⠀⠀⢀⣀⠀⣿⡇⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠀⠀⢿⣧⠀⠛⠿⠾⠛⠙⠿⠶⠟⠁⣰⡿⠀⠀⠀⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠈⠻⣿⣷⣄⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⢀⣼⣿⡟⠁⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡿⠛⢷⣦⣄⠈⠙⠻⠷⢶⡶⠾⠟⠋⠁⣀⣤⣾⠟⢿⣿⣷⣴⣾⣿⡿⠟⠛⠛⠿⣿⣿⣦⣄⠀⠀ ⠀⢠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠉⠻⣿⡍⠀⠀⠀⠈⠙⠻⠿⢶⣶⣶⣶⣶⣶⠾⠿⠛⠉⠀⠀⠀⠉⢻⣿⠛⠁⠀⠀⠀⠀⠀⠀⠉⢿⣿⣦⡀ ⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧ ⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿ ⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿ ⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃ ⠀⠈⢿⣿⣶⣄⡀⠀⠀⠀⢀⣠⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⣀⣀⣀⣀⣤⣾⣿⡿⠁⠀ ⠀⠀⠀⠙⠿⢿⣿⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⠿⠿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣤⣶⠶⠶⢶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⢶⣶⣦⣄⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⠈⠉⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠉⠀⠀⠀⠀⠉⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣤⣤⣤⣤⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣶⣄⡀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠛⠛⠛⠛⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣷⣶⣾⣿⣿⠟⠃⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣶⣶⣶⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⣉⡉⠉⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⠿⠷⠶⠶⠶⢦⣤⣤⣤⣀⣀⡀⣴⡿⠁⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠉⠉⠛⠻⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠏⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⣤⡀⠀⠀⢀⣤⣤⣤⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⡋⠀⠀⠀⠀⠀⠀⠐⢶⣤⣀⣀⡀⠀⠀⠀⠙⢶⣶⣿⣿⣿⣶⣾⣿⣟⣉⣤⣤⣤⣶⣶⣤⣤⣤⣀⠀⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣷⣶⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡿⠟⠛⠉⣡⣾⣿⣿⣿⣆⠀⠀ ⠀⠀⢰⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣙⣻⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣄⠀ ⠀⢀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠿⣿⣿⣿⣷⣄⠀⠀⠀⣄⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⡀ ⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⠛⣻⣿⣿⣿⣿⣿⡟⠁⢻⡿⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠛⢿⣦⣈⠛⢿⣿⣿⣷⣦⣀⠉⠻⣦⣄⠀⠀⠀⣿⣿⣿⣿⡇ ⢠⣿⣿⡇⣀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣿⣿⣿⣿⣿⣷⣦⣀⠙⢿⣶⣶⣬⣿⣿⣿⡇ ⣸⣿⣿⣿⡟⠀⢾⣷⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⠃⠀⢸⣿⣧⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠟⢛⣿⣿⣿⣿⡟⠻⠟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣎⢻⣿⣷⣄⠈⢿⣿⣿⣿⣿⣿⣿⡟⠀ ⣿⣿⣿⣿⠀⢆⠀⢿⣿⣷⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⣿⣿⣧⠹⣿⣿⣧⡀⢻⣿⣿⣿⣿⠟⠀⠀ ⢿⣿⣿⣿⠀⠸⣷⡜⣿⣿⣿⣄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣷⡘⣿⣿⣧⡘⣿⣿⣇⢨⣿⣿⡿⠋⠀⠀⠀ ⢸⣿⣿⣿⠀⠀⢹⣿⣿⣿⡹⣿⣧⡀⠀⠻⡏⢻⣿⣿⠛⣿⣿⣿⣿⣿⠃⠀⠀⣀⣄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣷⢹⣿⣿⣾⣿⡟⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣎⠛⠿⡆⠀⠁⠀⢿⡇⠀⢹⣿⢿⣿⣿⡀⣾⣿⣿⣿⣿⣿⡄⣸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⡀⠀⠀⠀⠻⣿⣿⣿⣷⣄⣀⠀⠀⠀⠈⠗⠀⠘⠏⠈⢿⣿⣷⣹⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⣷⠀⠀⡀⠀⠈⣛⠿⣿⣿⣿⣿⣷⣶⣦⣤⣀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣇⠀⠹⣦⡀⠘⣦⡀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣆⠀⢻⣷⣄⠈⠻⣷⣤⣀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣦⡀⠛⢿⣷⣄⠈⠻⢿⣿⣷⣶⣽⣿⣿⣿⣿⡟⠸⣿⠙⣿⣿⣿⣿⠏⠻⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⠙⢿⣷⣦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣄⠀⠋⠀⠈⠉⠉⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⣾⣿⣿⣿⣷⣄⠙⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢀⣠⣾⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⠈⠉⠻⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠉⠉⠲⢦⠀ ⠀⠀⢤⣀⠇⢸⠁⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠈⣧ ⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⣸⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⣿⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠓⠀⠒⠶⠶⢤⣤⣤⣤⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⣿⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⣀⣀⣀⣀⣀⣠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠄ ⠀⠀⣿⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⢠⠶⣄⣿⠉⠉⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀ ⠀⠀⡟⠀⠀⠀⠀⠀⠹⣆⠀⣀⠀⢹⡉⠁⢀⡈⠛⢲⠄⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀ ⡴⠚⠁⠀⠀⠀⠀⠀⠀⠈⣷⠋⠑⠚⠓⢹⠛⠃⢰⡁⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀ ⠱⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢸⣉⠇⠈⠛⣿⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠙⡆⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⣰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⢹⡀⠀⠀ ⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡇⠓⠊⠉⠓⠃⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀ ⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡤⠒⠋⠉⠀⠀⠀⠀⠀⠈⠉⠑⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠙⠦⡀⠀⠀⠀⢀⡞⠁⠀⠀ ⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠀⢠⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠘⡆⠀⢀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⣱⡠⠚⠉⠉⠙⢢⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢺⣭⣀⠀⠀⠲⢶⣀⣀⣀⣀⠀⠈⠙⠛⠁⢀⣠⠴⢻⡇⠀⠀⠀⢀⡼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠸⢍⣉⣒⣢⡼⠿⠿⢿⣿⠷⠴⠒⠒⢯⣡⠤⠖⢯⠀⠀⠀⡞⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣄⣀⣀⣠⠼⡀⠘⠓⠒⢞⣻⡿⠙⣶⠤⠀⢨⠇⠀⠀⡾⢖⠲⣞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠟⠙⢣⡀⠱⡀⠀⠀⠀⡸⠒⠋⢁⣀⣀⠀⠀⣠⠞⠀⢸⢀⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠱⡀⠈⠉⠉⠉⠱⢄⣠⠎⠀⠈⢶⠊⠁⠀⠀⡾⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡇⠀⠀⠀⠀⣄⠀⢸⡀⠀⠀⢸⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠖⠓⠒⠶⠖⠒⠋⠳⢤⣇⠀⠀⣼⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠉⠲⣄⡀⠀⠀⠀⢀⡠⠤⠤⢤⡾⠁⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠲⢤⡴⠋⠀⠀⠀⠀⠳⣀⠤⠤⢄⡀⠀⠀⢀⣼⠤⠤⠤⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠙⡄⠤⠾⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⢰⡄⠦⣷⣀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣄⠓⣨⠟⠉⠀⠈⠦⣀⣀⣀⡠⠞⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠹⣦⡇⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣼⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠳⡀⠀⠀⠀⠀⢀⡜⠉⠙⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡍⠲⢄⡀⠀ ⠀⠀⠀⠀⠀⢀⠞⠀⠀⠉⠓⠒⠒⠊⠉⠀⠀⢀⣠⠤⠴⠒⠒⠒⠂⠒⠒⠒⠒⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆⠀⠉⡷ ⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀ ⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⣠⠞⠉⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀ ⠀⠀⠀⢸⠃⠀⠀⠀⠀⣠⠞⠁⢀⣴⡿⠋⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠷⣶⣄⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠉⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⡴⠃⠀⣴⣿⣿⡀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⢸⣿⣷⣄⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠀⠀⠀⣸⠁⠀⣸⣿⡿⠘⣿⣄⣀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⣴⣿⡿⠹⣿⣆⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⢠⡇⠀⠀⣿⣯⣄⢀⣬⣿⠟⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⣿⣥⡄⢀⣭⣿⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⡀⠀⠈⡇⠀⠀⠙⢿⣿⣾⣿⣿⣶⣶⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣿⣿⣿⣾⡿⠏⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡀⠀⢧⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⠀⠀⢳⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣦⡈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣠⣞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣌⣳⣄⠀⢀⠤⠒⠈⠉⠐⠢⢄⡀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⠒⠤⡀⠀⠀⠀⣠⣞⡥⠚⢡⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⢠⠞⣱⠤⠀⠬⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢠⠚⠁⠀⠀⠀⠀⠀⠀⠘⣤⡴⠞⠋⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠃⠀⠀⠀⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢧⠀⠀⣿⡇⠀⢸⠃⠀⠀⠀⠀⠀ ⠀⠀⣤⣀⠀⢠⠋⠀⠀⠀⠀⢰⣣⠾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣼⡆⠀⠟⠀⠀⢸⠂⠀⠀⠀⠀⠀ ⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⣶⠟⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠀⠀⠀⠀⢰⢦⣤⠄⠀⠀⠀⠀⠀⣄⠀⠀⢰⣄⠀⠀⠀⡀⣤⣀⠀⠀⠀ ⠀⠀⠀⣀⠀⠀⠀⠀⠘⢷⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣩⢺⣿⣿⣻⢹⡛⣟⣿⠇⢘⣟⢻⣿⣾⣿⣿⢽⢰⣿⡀

⠀⠀⠀⠀⠀⠀⣿⡟⠓⠒⠀⠁⢈⡽⠟⠋⠉⠉⠉⠉⠙⠛⠶⠛⠛⠉⠉⠛⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⣿⠿⠖⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⠖⠋⠉⢠⡖⠋⠓⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣗⣤⠴⠖⠀⠀⠀⠀⠀⠀⠀ ⠟⠁⢀⣤⠶⢾⡀⣀⠀⠘⠓⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠧⢤⣼⣿⣀⣾⠋⠉⠙⡆⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠉⠉⢻⣦⣀⡴⠃⢠⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡗⠀⠀⠀⠀⠀⠀ ⠴⠲⢄⠀⠀⣰⠋⣬⡁⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⡀⠀⢨⠆⠀⠙⣏⠁⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡟⠀⠀⠀⠀⠀⠀ ⠉⠉⠁⣄⣀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠙⢧⣄⡀⠀⠀⠀ ⣄⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠈⠙⠻⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠈⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠉⠒⠒⠀⠐⠒⠋⠁⠀⠀⠉⠒⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢠⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⡀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡶⠦⠶⠖⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣤⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡄⠀⠱⡆⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⢣⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡿⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠰⠴⠂⠀⠀⠀⠀⠀⠙⠿⠿⠟⠁⠀⠀⠈⢣⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠇⠀⠀⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⢀⡠⠄⠀⠀⠀⠀⠀⠠⢤⣀⡠⠤⢀⠴⠁⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⣤⡀⠀⠀⣏⠀⠀⢀⣠⠤⠁⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣁⣠⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⠛⣄⡀⠀⠙⠢⢌⡀⠐⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉⠀⠀⠀⠈⢳⡤⠴⠒⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠈⠙⢲⠶⠒⠉⠈⠙⠒⠦⠤⣄⣀⣀⣀⣀⣀⣀⡠⠤⠤⠐⠒⠋⠉⠀⠀⠀⣀⡠⠴⠒⠉⠁⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⠀⠀⣴⠋⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠈⠀⢰⠃⠀⠀⠀⠊⠁⠀⠀⠉⠒⠒⠒⠒⢤⡀⠀⣀⣠⣤⣖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠙⠻⣇⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣈⣿⠟⠻⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⣧⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠟⠛⠛⠿⣿⣦⡀⠀⣀⣀⣀⠀⠀⣠⣶⣿⠿⠿⠿⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠈⠻⣿⠿⠿⠿⠿⠿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠈⠛⠛⣃⣤⡴⠶⢦⣤⣘⠛⠛⠁⠀⠀⠀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⡾⠋⠀⣴⣶⣦⠈⠙⢷⡀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⢀⣿⠀⠀⠀⠿⠿⠟⠀⠀⠈⣿⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠘⣿⠀⣤⡀⢀⣶⡀⠀⣠⠀⣿⠁⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀⠀⠻⣦⡈⠙⠋⠀⠙⠛⢁⣼⠏⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣴⣶⣶⣶⣶⣤⣨⣿⡿⣦⣀⠉⠻⢶⣤⣤⣤⠶⠛⠁⣠⣴⢿⣿⣅⣤⣶⣾⠿⠿⣷⣶⣤⡀⠀⠀ ⠀⣰⣿⠟⠋⠁⠀⠀⠉⠻⣿⡉⠀⠀⠉⠛⠷⠶⠦⠤⠴⠶⠾⠛⠉⠀⠀⠉⣿⠟⠁⠀⠀⠀⠀⠉⠻⣿⣆⠀ ⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄ ⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀ ⠀⠘⢿⣷⣦⣄⣀⣀⣤⡶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣤⣴⣾⡿⠋⠀⠀ ⠀⠀⠀⠈⠙⢻⣿⣉⣡⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⣿⡟⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⡿⠋⠁⠀⠀⠉⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠁⠉⠙⢻⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣶⣶⣿⡄⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⣤⣀⣠⣴⣾⡿⠉⠀⠀⠈⠻⣿⣦⣄⣀⣀⣤⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣷⣹⣿⣶⣤⣾⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣷⣦⣤⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣷⣾⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀ ⠀⣨⣿⣿⣿⣿⡟⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢟⣛⣿⣿⣿⣿⣿⣟⣶⡦ ⠴⠿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠙⢹⠛⣿⣾⡿⣿⠃ ⠀⠀⠘⣿⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠋⠤⠀⢸⠂⠚⡀⠅⠀⠀⠇⠀ ⠀⠀⠀⢻⣿⣿⣿⣄⠉⢿⣿⣿⣿⣿⣿⣿⡼⣿⡣⠀⠀⣟⠠⣄⠐⠀⠀⠐⠀⠀ ⠀⠀⠀⠸⠻⣿⣿⣿⣷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⣙⡿⠈⣔⣄⢡⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣮⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠉⠛⠻⠿⠿⢻⠿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀ ⠀⣀⡤⢀⡠⠔⠂⠉⠉⠁⠒⢡⡄⠘⠄⠀ ⠰⡁⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⠀⠀ ⠀⠑⠰⠀⠀⠀⠠⡄⠠⠖⣴⠖⠀⢠⡀⠀ ⠀⠀⣀⠀⠉⠟⠃⢀⠳⠃⠰⠄⠀⠀⡟⠀ ⠀⠀⢯⡀⠀⠠⠒⡅⠂⡔⠀⠀⣀⡦⠄⡄ ⠀⠀⠀⠀⠂⢀⣐⠂⠀⠒⠈⠇⣉⠀⠉⠀ ⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢈⠁⠀⠀⠀ ⠀⠀⠀⠚⠂⠀⡇⠀⠀⠀⠀⠀⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠁⠀⢠⣤⠠⠤⡀⢢⠀⠀ ⠀⠀⠀⠀⠀⡘⢀⠃⠀⠀⠀⠀⠑⠤⠇⠀ ⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⣠⠶⠶⠦⣄⠀⠀⠀ ⠀⣀⣤⣄⡀⠀⣠⠴⠛⠉⠀⠀⠀⠀⠈⠉⠺⠁⣤⣀⠀⠈⡇⠀⠀ ⡼⠉⠀⡀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⢀⣰⠇⠀⠀ ⡇⠀⢸⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠀⠀ ⠙⠦⣤⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⡶⢀⣠⣴⡄⠀⠀⢧⠀⠀⠀ ⠀⠀⣼⠀⠀⠠⢤⣤⣄⣈⠉⢁⡤⢦⡄⠛⠛⠤⠄⠀⠀⠘⣿⡄⠀ ⠀⠀⢹⠀⠀⠐⢈⡭⠛⠁⠀⢀⡹⠞⠓⠃⢶⠖⡄⠀⠀⠠⣾⠃⠀ ⠀⠸⣟⡃⠀⠀⠈⠀⠀⣠⠒⢉⣠⠤⢤⠀⠀⠀⢧⠀⢀⡞⠁⠀⠀ ⠀⠀⠻⢥⠄⠀⠀⢠⠎⠙⢠⠋⠰⢾⡁⠀⢀⠀⡸⢀⣾⠴⠒⣲⠄ ⠀⠀⠀⠈⠉⠲⣄⠘⠦⢴⣽⣀⣀⣀⡱⠤⠞⣫⠕⠋⢀⡠⠞⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⢙⡶⠤⠄⠀⠀⠀⠀⠀⠈⠁⣠⠴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠴⠋⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠃⣠⠔⠋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⡤⠤⠿⠛⠚⠋⠉⠙⣆⠀⠹⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠤⠿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠥⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠒⠤⣄⣀⡤⠤⠤⠤⠤⠤⢤⣀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⢁⡠⠤⠤⢤⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⠋⢁⣀⣀⣀⣉⠙⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠁⡰⠋⠀⢀⣀⣀⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⣁⣀⣀⣀⠈⠑⣌⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⢰⠃⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡄⠘⣆⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡚⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣤⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢀⣀⣀⣀⣠⣶⡆⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠉⠁⠀⠀⠀⠉⠻⡅⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢾⣹⣿⡆⠀⠀⢹⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠶⣄⣉⣉⡴⠀⠀⡼⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣨⠷⢤⣀⠀⠀⠀⡤⢶⣲⡿⠒⠚⠓⠲⣽⣿⣶⣴⠎⠁⠀⣀⠤⠚⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠉⠉⢻⢳⡿⠋⠀⠀⠀⠀⠀⠈⠉⢻⣿⠓⠊⠉⠁⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠘⡾⠁⠀⠀⣤⣄⣀⣴⣷⠀⠀⢻⡶⠲⣆⠀⡤⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⣼⠀⣿⢿⣞⣧⠤⠼⠓⠬⠽⠟⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣦⠀⠙⢆⠀⠀⠙⢤⡽⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠦⣴⣉⣉⣑⣲⡏⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⢀⣠⣾⡓⠒⢊⣹⠧⠤⠦⠤⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⣏⣿⠚⠟⢉⡵⣾⣷⠈⠁⠀⠀⠀⠀⠀⠀⠙⢦⠀ ⠀⠀⠀⠀⢀⣀⣠⡎⠙⠢⠤⣄⣀⣀⣰⣦⣀⠀⠀⠀⠀⠀⣷⣠⣿⠟⢆⠀⠸⣥⣿⠃⠀⠀⠀⡠⠔⠒⠲⣄⠀⠈⡇ ⠀⠀⣠⠞⠉⠀⠀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠈⠉⡟⠒⠒⠋⢛⡉⠙⡆⠀⠙⠒⠛⠁⠀⠀⣠⠊⠀⠀⠀⠀⢸⠀⢀⡇ ⠀⡼⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢰⠋⣹⣴⠇⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⡜⠀⡼⠁ ⢀⡇⠀⡴⠉⠁⠀⠉⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⣘⣺⠿⢧⡀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣠⠞⢀⡴⠁⠀ ⠀⣇⠀⢣⡀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠉⠒⠖⠒⠋⢀⡠⠊⠀⠀⠀ ⠀⠘⢆⠀⠙⢤⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⣀⣀⡤⠤⠒⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⠤⣀⠈⠙⠒⠦⠔⠊⠁⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠤⠤⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⡲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⣠⢊⣀⡀⠀⠀⠀⢀⣀⠤⠤⠤⠤⣀⠤⠚⠉⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⡟⠉⠀⠉⠙⠒⠲⠁⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⡜⠀⡇⢏⠓⠦⠤⡴⠃⠀⠀⠀⡆⠀⠀⠀⠙⠲⠤⣀⠀⠘⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡴⠀⠀⡸⠁⠀⠸⡌⠁⣠⠞⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢰⠁⠀⠠⠇⠀⠀⠀⣧⠈⠁⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠱⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠘⠤⡀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠘⠀⡜⠁⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠇⠀⠀⠘⣇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠙⠛⠁⠀⠀⠀⢩⠁⠀⠀⠀⢠⣮⠎⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢻⡄⠀⠸⡇⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢿⠀⠀⠀⠀⠘⡄⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢳⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠈⠑⢾⡞⠀⣀⣄⣀⡀⢹⢃⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠳⡄⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣠⣤⣤⢃⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠟⠋⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀ ⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠐⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀ ⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢠⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡎⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢳⠀⠀⠈⠳⣄⡰⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠈⡆⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀ ⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢰⠃⠀⣤⣏⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀ ⠀⠀⡿⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡇⠀⠀⢻⡿⣦⡀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀ ⠀⢰⡇⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠁⠀⠀⠀⠉⠉⠙⠓⠚⠋⠁⠀⠀⠀⠀⠀⠀ ⠠⠼⠥⠤⠤⠤⠤⠤⠤⠧⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠒⠒⠒⠒⠛⠛⠃⠀⠀⠀⠀⠀⠀⣿⠿⠸⠿⣿⣿⠇⠀⢀⠒

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠻⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢸⡿⣿⠇⠰⠟⠀⠀ ⠀⠀⠀⠀⣀⡤⣤⠶⠛⠉⠉⠀⠀⠉⠉⠛⠲⣤⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢧⠀⠀⠀⠀ ⠀⠀⡼⢁⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⡈⢧⠀⠀⠀ ⢀⡞⠁⣸⠁⠀⢠⠬⠓⠀⣀⠀⠀⢀⠀⠛⠥⣄⠀⠀⡇⠈⢳⡀⠀ ⡞⠀⠀⠹⣆⠀⠀⠆⠀⠀⠓⠊⠙⠚⠁⠀⠀⠀⠀⣰⠇⠀⠀⢻⠀ ⣇⠀⠀⠀⠈⣹⠶⠦⠤⠤⣤⣤⣤⡤⠤⠤⠴⠶⣏⠁⠀⠀⠀⣸⠁ ⠈⠓⠲⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠚⠁⠀

𖦹 ׂ 𓈒 🥞 ／ ⋆ ۪

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⡘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣰⡶⠶⠶⠎⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⠉⠰⣶⢶⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠀⢠⣤⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⢀⣶⡞⠉⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⢀⣀⣀⣄⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡶⢶⣆⠀⠀⠀⠀⠀⠀⠀ ⠇⢀⢠⣤⣿⣥⣤⣤⣤⣤⣤⣤⣤⣴⡿⣛⣭⣭⣭⣽⠛⠻⣿⣇⣧⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣤⠀⠀⠀⠀⠀ ⠀⣾⡾⣿⣏⣭⣭⣽⣭⣥⣶⣶⣿⣾⡏⠉⠉⠉⠉⠉⠽⣷⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣧⣀⠸⢶⣶⣶⣶⣴⣄⢀⡀⡀⡀⡀⠀⠀⠀⠀⡈⠛⣷⠀⠀⠀⠀ ⠀⣿⣿⣿⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣼⣿⣷⣅⣀⣀⣀⣀⣀⣀⣀⠼⣷⣼⣿⣿⡿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣷⣤⣿⠀⠀⠀⠀ ⠀⣿⣿⣿⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣀⣀⣿⣾⣏⣿⡟⢻⣿⢿⡿⡷⣿⣿⣿⡿⢿⣿⣿⣿⡇⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⡿⠿⢿⣾⣇⣛⣿⠀⠀⠀⠀ ⠮⢽⣿⣿⣿⣦⡇⠀⠀⠀⢠⣤⣤⣤⣤⣼⣿⠟⢯⣽⣿⣿⡿⡿⠛⠛⠿⢶⣶⣆⠀⠀⢸⣷⡄⠁⠀⢸⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⡆⠀⠀⠀ ⠀⣾⣟⠙⣿⣿⣿⣾⠀⣰⠾⣷⣿⡿⠛⢻⣿⣶⣾⣿⠭⠭⠥⠁⠀⠀⠈⠉⠉⠙⣷⣶⣤⣿⣷⣶⣠⣾⠉⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣾⣿⣍⡁⠀⠀⠀ ⠀⣿⣷⣼⠀⢻⢿⣿⣿⣿⡆⠰⣶⡞⠛⠚⠛⠛⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⡆⡛⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⣿⣿⣿⠿⣿⡇⠀⠀⠀ ⠀⠛⢻⣿⣶⣈⠈⠉⣿⣿⣷⣶⣿⣷⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⣇⢁⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⣿⣿⡟⠁⣠⣿⡇⠀⠀⠀ ⡀⠄⢠⣴⣿⣿⣧⣤⠀⢹⠝⢿⢿⠿⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⢸⣤⠄⣀⣤⣀⣀⣠⣥⣽⣿⣿⣿⣿⠛⠁⢀⣸⣿⣿⠃⠀⠀⠀ ⠀⠀⢸⣿⠙⣿⣿⣿⣶⣟⡀⠸⣿⡀⠈⠹⣿⣿⣷⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡇⢀⣻⣛⣿⣿⣿⣶⣿⣿⣿⣿⠏⢉⣉⣀⣶⣾⣿⣿⣿⡇⠀⠀⠀ ⠃⠀⢸⣿⣴⠙⠹⣗⡛⢿⣧⣴⣿⣧⡀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⣛⢛⢛⢛⡛⡛⡛⣛⢛⢛⢛⢛⣿⣿⠟⠛⠛⢛⠻⡿⠒⠐⠚⠃⠁⠀⠀⣠⣼⣿⢿⣿⡿⠛⣶⣿⡇⠀⠀⠀ ⡇⠀⠈⢹⣿⣿⣆⠀⣇⠈⠉⠻⣿⣿⣷⣖⣒⣶⡆⢀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣷⠀⠀⢸⡀⠃⠀⠀⠀⣰⣖⣖⣺⣿⣿⡿⠈⠉⢡⣾⣿⡍⠁⠀⠀⠀ ⠀⠀⠀⢀⣤⣿⣿⣿⣿⡆⠀⣆⠀⠛⠛⢻⣟⠻⣷⣴⣿⣿⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣿⣤⣤⡼⠀⢰⣴⣴⣦⣿⢻⣿⠛⠛⠃⠀⠀⣼⡿⣻⣿⣿⣧⡄⠀⠀ ⠃⠀⠀⠸⣿⡋⣿⣿⣿⣇⣀⣏⡀⠀⠀⠀⠉⠉⠉⠹⠿⠽⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⢿⡏⢙⣿⢶⣿⡿⠿⠿⠋⠀⠁⠀⠐⣀⣰⡿⠯⣃⣼⣿⣿⣿⡿⢶⣀ ⡇⠀⠀⠀⠛⣿⣿⣥⡿⣿⣿⣭⣿⣤⣤⣤⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣧⠀⠀⢳⠀⡇⠀⠀⠀⢠⣤⣤⡤⣤⡿⠛⠀⢠⣿⣿⣿⠛⠇⡇⠀⣬ ⡇⠀⠀⠀⠀⣉⣹⣿⡄⠈⡏⠹⠿⣿⣿⣿⣗⣶⣖⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠁⣱⣔⣀⣐⣿⣿⣿⣿⠋⢁⣀⡶⠈⢹⣿⣿⣿⡿⣿⠾⠉ ⡇⠀⠀⠀⣶⣿⣿⣿⣧⡄⢷⣤⢀⠀⠘⠛⠛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣴⡿⠛⠛⢛⠇⠀⠀⣶⣤⡞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⢸⣾⠏⣿⣿⣿⣿⣿⣿⣿⣀⣀⡰⠶⠀⠈⠀⠀⢀⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠉⣿⠉⠉⢻⠉⢿⣀⣀⣀⡴⠾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠘⢿⣾⡟⢳⣬⣿⣧⣿⣿⣿⣿⡟⠒⠒⠒⠒⠒⠻⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣽⣤⡜⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠛⠿⠶⠶⠿⠿⡿⢿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⠷⠾⣿⣿⣿⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢟⣓⣀⣆⣶⣶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⢀⣤⣶⣾⡿⠿⣷⣶⣄⠀⠻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣿⠟⠋⠀⠀⠀⠀⠙⢿⣆⠀⠸⣿⡆⠙⠿⣿⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⢀⡄⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠘⢿⣷⡄⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⡿⢁⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⣠⣴⣾⣿⡿⠿⢿⣿⣦⣄⠀⠀⠈⣿⣿⠀⠀⠀⣿⠀⠀⠀⣸⡟⠀⢠⣿⡇⠀⠀⠀⠈⢿⣿⡄⠀⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠿⣿⣿⣷⣤⣾⣿⡿⠋⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀⠸⣿⣷⡀⠀⠙⠳⠶⠾⠋⠀⢠⣾⡿⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀ ⠀⣸⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠋⠀⠀⠀⢀⣠⡀⠀⠀⠸⣿⡆⠀⢰⣿⣿⣿⣦⣀⣀⣀⣀⣠⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀ ⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀⢸⡏⠁⠀⠀⠀⢠⡿⠀⠀⣼⣿⡟⠙⠛⠻⠿⠿⠿⠛⠋⢁⣀⣤⣤⣤⣤⣤⣤⣄⣸⣿⣿⡄ ⢸⣿⣿⠇⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣦⣄⠀⠀⠀⠀⠘⣿⣷⠀⠀⠸⣧⣀⡀⣀⣠⡾⠁⠀⢠⣿⡿⠁⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣇ ⣿⣿⡿⠀⠀⠀⠀⣠⣾⣿⠿⠛⠋⠉⠙⠛⢿⣷⡄⠀⠀⠀⣿⣿⡇⠀⠀⠈⠙⠛⠛⠉⠀⢀⣴⣿⡿⠁⠀⣀⣴⣾⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿ ⣿⣿⡇⠀⠀⠀⢰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⣿⣿⣿⣦⣤⣀⣀⣀⣠⣤⣶⣿⡿⠋⢀⣴⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⣿⣿⠃⠀⠀⠀⣴⠀⠀⠀⠀⣼⡟⠀⠀⢠⣿⣿⠛⠿⠿⠿⠿⠿⠿⠛⠋⠁⣠⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣦⣤⣼⣿⣿ ⣿⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⢿⣄⣀⣀⣴⠟⠁⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿ ⣿⣿⡇⠀⠀⠀⢻⣿⣆⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⢻⣿⣇⠀⠀⠀⠀⠻⣿⣷⣤⣀⣀⠀⣀⣀⣀⣤⣾⣿⠟⠃⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇ ⢸⣿⣿⣷⣄⡀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⣀⣴⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇ ⠘⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⢻⣿⣿⠉⠻⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠟⠛⠋⠉⠉⣿⣿⣿⠃⠀ ⠀⠘⣿⣿⡆⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀ ⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣾⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣯⡉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣴⣤⣴⣶⣾⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣁⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⡄⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⣰⠃⢸⡿⠀⠀⠀⠀⢀⣴⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⢀⡾⠃⠀⣾⠃⠀⠀⢀⡴⠋⢠⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⣰⡿⠁⠀⣸⡏⠀⠀⣰⠟⠀⠄⢸⡇⠀⠀⠀⠀ ⠀⢶⣤⣀⡀⠀⠀⢰⡟⠀⠀⢰⣿⠁⠀⠀⣿⠀⠀⣴⡏⠀⣼⠀⢸⣧⠀⠀⠀⠀ ⠀⠈⣧⠉⠛⢶⣄⢸⡇⠀⠀⢸⣿⠀⠀⠀⢿⡄⢀⣿⠀⠀⢻⠀⠈⢿⣆⠀⠀⠀ ⠀⠀⣿⠀⠀⡀⢻⣦⢇⠀⠀⠸⣿⣀⠀⠀⠈⠻⣾⣿⠀⠀⠸⡄⠀⠘⣿⣆⠀⠀ ⠀⠀⣿⠀⠀⢧⠀⣿⡌⢀⣴⠾⠟⠛⠛⠷⣶⣄⠈⠻⣧⠀⠀⢧⠀⠀⠈⢻⣦⠀ ⠀⣼⡇⠀⠀⢸⠀⢸⣷⡟⠁⠀⣀⣤⣄⡀⠀⢻⡆⠀⢹⣧⠀⠸⡆⠀⠀⠀⢻⣇ ⢠⡿⠀⠀⠀⣿⠀⢸⣿⠀⠀⣼⠏⠉⠉⢻⠀⠀⣿⠀⢀⣿⠀⠀⢿⠀⠀⠀⠘⣿ ⣾⠃⠀⠀⢰⡇⠀⢸⣿⠀⠀⣿⠀⠐⠴⠊⠀⣰⡟⠀⣸⡿⠀⠀⢸⠆⠀⠀⠀⣿ ⣿⡀⠀⠀⢸⡇⠀⠘⣿⣄⠀⠙⢷⣤⣤⣤⡾⠏⠀⣰⣿⠃⠀⢀⣿⠀⠀⠀⣸⠏ ⠘⢷⡀⠀⠸⣷⡀⠀⠈⠻⣷⣤⣀⠀⠉⢀⣀⣤⣾⡿⠁⠀⢀⣾⠏⠀⢀⡴⠋⠀ ⠀⠀⠉⠑⠂⠙⠳⣤⡀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠁⠀⢀⣠⡿⠃⠐⠊⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠦⣤⣤⣤⣤⣤⣤⠶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡿⢸⣿⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⠿⠛⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⠿⣶⣤⣄⡀⠀⠀⠀⠀⠀⢸⡟⢹⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠃⣼⡏⠀⠀⢀⣠⣶⠿⠛⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠛⠿⣷⣤⡀⠀⠀⢸⣿⠀⢿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠃⠀⣿⠇⢀⣴⡿⠋⠁⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠘⣿⡄⠈⢿⣆⠀⠀⠀⠀ ⠀⠀⢠⣿⠃⠀⢸⣿⣠⣿⠋⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠄⠀⠀⠀⠀⠀⠙⣿⣄⢿⡇⠀⠈⣿⣆⠀⠀⠀ ⠀⠀⣾⡇⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠀⠀⠘⣿⡀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⢀⣿⠃⠀⠀ ⠀⠀⠘⠿⣶⣤⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣤⣶⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⣀⣴⣾⠟⢻⣿⠀⢠⡄⠀⣿⣦⡀⠀⠀⢸⡿⣦⣀⣶⣤⡀⣿⣷⡀⣤⠀⣠⣿⡇⠀⠀⠀⠀⠀⣴⡆⢀⡀⠀⠀⠀⢸⡏⠻⢿⣦⣄⡀⠀ ⣾⡟⠋⠀⠀⢈⣿⢠⣿⣷⣸⣯⡈⠛⢷⣤⣸⡇⠈⠉⠁⠈⠻⠟⠈⠻⠿⠷⠟⠀⢿⣀⣴⣿⣠⡾⢻⣧⣿⡇⢠⣿⣆⢸⣇⠀⠀⠈⠻⣷⡄ ⠛⢿⣶⣿⣍⣉⣙⣛⣿⡈⣩⠟⠁⠀⠀⠈⠁⢀⣤⣴⣦⣤⣤⣤⣤⣤⣤⣶⣶⣦⣌⠉⠁⠙⠋⠐⠛⢯⡈⢷⡿⣿⣿⣾⣋⣉⣽⣷⡾⠟⠁ ⠀⠀⢨⣿⢉⡿⠉⠉⠹⣿⠃⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠹⡆⣰⡟⠉⠉⢹⡏⢿⡇⠀⠀⠀ ⠀⠀⣼⡟⢸⡇⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⡿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠸⣧⠸⣿⠀⠀⠀ ⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠙⠶⣤⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠞⠁⠀⠀⠀⠀⠀⣿⠀⣿⡄⠀⠀ ⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠉⠉⠉⠛⣿⠉⠉⠉⡏⠉⠉⠉⢙⡿⠛⠛⠛⢻⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀ ⠀⠸⣿⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠒⠢⠤⣽⣦⠀⠀⠃⠀⢀⣤⣟⣁⣠⡤⠤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣿⡇⠀⠀ ⠀⠀⣿⡇⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣄⡀⠀⠀⠈⠛⠶⠶⠞⠛⠉⠀⠀⠀⢀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣿⠁⠀⠀ ⠀⠀⢹⣷⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡉⠛⠒⠦⠤⠤⠤⠤⠤⠤⠶⠒⢊⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣸⡟⠀⠀⠀ ⠀⠀⠈⢿⣇⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣀⣀⡀⠀⠀⣀⣀⣤⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢰⣿⠃⠀⠀⠀ ⠀⠀⠀⠈⢿⣆⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠛⠛⠛⠛⠛⠛⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣠⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣧⡈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢋⣴⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣾⠻⢷⣄⣠⣄⡀⢀⣤⣄⣠⣶⣦⣤⣽⣿⣄⢀⣾⣿⣤⣤⣶⣆⣀⣤⣄⢀⣠⣤⣀⣴⠟⢻⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣝⣏⠈⠙⠛⠉⢻⠉⠀⠈⢧⠀⢈⣿⣿⡇⠀⢰⠋⠀⠉⢹⠉⠛⠛⠉⣨⣏⣡⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢶⣶⣶⣾⣶⣤⣶⡿⠿⠟⠋⠘⠻⠿⠿⣦⣤⣴⣾⣶⣦⣶⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⡿⠿⠿⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠿⢿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠻⣿⣷⣤⡀⠀⠀⢀⣠⣴⣶⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣷⣾⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣶⡄ ⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠛⠛⠿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⠁⠀ ⠀⠀⢀⣴⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣿⠿⠟⠋⠁⠀⠀⠀⠀ ⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠙⣿⣿⣧⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⠀⠀⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢰⠀⠀⣆⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠁⠉⠉⠁⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣸⣧⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠾⣤⣤⢿⠛⠙⠏⣿⣿⣴⠀⠀⣦⣿⣿⠹⠋⠛⡾⣠⣤⠳⠈⠀ ⡆⣿⣿⢿⠋⣴⣀⣄⣿⣿⣠⠀⠀⠀⠀⣄⣿⣿⣀⣀⢷⠛⡿⣿⣿⠀ ⡇⣿⣿⣶⢠⠀⠀⠃⣿⢠⠀⠀⠀⠀⠀⠀⡄⣿⠘⠀⠀⡄⣶⣿⣿⠸ ⡆⣿⣿⠻⠙⠋⠟⣿⢻⠟⠿⣿⣿⣿⣿⠿⠻⡟⣿⠻⠉⠋⠟⣿⣿⢰ ⠀⣄⣶⣿⣿⣿⣿⣶⣤⣶⣶⣶⣿⣿⣶⣶⣴⣦⣶⣿⣿⣿⣿⣴⣠⠀

⣿⣿⣶⣶⣦⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠛⠻⠿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⠀⣠⠀⠐⠤⠴⢂⣿⣿⡿⠋⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣄⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⣿⣿⣷⣌⣉⠁⠀⠀⢀⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⣶⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⢹⣯⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠄⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⠟⠛⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣤⣤⣴⡾⠋⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⡌⣷⠈⣿⣿⡇⠀⠀⠀⢠⣤⡀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣷⡈⠀⢸⣅⣹⣄⠀⠀⠀⠙⠛⠻⠾⠛⠋⠁⠀⠀⠀⠀⠀⠉⠁⢀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠠⡀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣧⣀⠂⢰⡛⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠶⠾⣿⡆⠀⢀⠖⠁⠀⠀⠀⠀⠀⣧⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠿⢄⣼⣟⣿⣿⣿⠿⣷⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⡿⠁⢠⠃⠀⠀⠀⠀⠀⣄⣼⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠏⠀⠀⠀⠉⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣬⣆⠀⠀⠀⠀⠀⠹⡝⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠟⠛⠉⠙⠛⠻⠿⢿⣿⣇⣸⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣬⠟⢧⡀⠀⠀⠀⠀⡼⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⡄⠒⠊⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣀⣠⠴⠚⠉⣽⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⠟⠻⢿ ⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠴⠒⠋⠃⠀⠀⠀⠀⠀⢀⡠⠒⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⣿⠟⠋⠉⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀ ⠀⠀⠈⠉⠉⠙⠛⠒⠶⠤⣶⣞⣁⣀⠀⠀⠀⠀⡠⠤⠀⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠒⢤⣠⡤⠀⢒⣲⣬⣭⣭⣭⣶⣤⣤⡤⠤⠒⣼⡅⠀ ⠀⠀⠀⠀⠀⠀⠀⠲⡟⣉⣙⣲⠔⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣌⡳⣴⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⣘⠟⠀⠀⠀⢠⡾⠛⢉⠛⡿⡟⡳⢬⣭⣴⡌⠻⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⢞⣭⠀⠀⠀⠀⢸⣇⠫⠉⢓⡶⠃⢉⢶⣭⡽⢀⠀⢱⠀⠀ ⠀⠀⠀⠀⠀⠀⢘⣇⣾⡿⠀⠀⠀⠀⠹⢿⣿⣿⡏⠀⠁⠀⠀⠹⡀⠈⠉⡟⠀⠀ ⠀⠀⠀⠀⣠⣶⠞⣽⣿⡕⣡⠀⠀⠀⢀⣠⣭⣿⠇⠀⡴⣶⢾⣶⡽⡄⠀⡇⠀⠀ ⠀⠀⣴⣿⣿⠇⣸⣿⣿⠞⣡⠞⡄⠀⠞⠻⠿⢿⣧⣀⢻⡏⣾⡿⠇⣷⣾⡇⠀⠀ ⢠⣾⣿⡟⠁⠀⢼⣿⣿⡟⣡⡾⠃⣠⢶⣶⣦⣜⠿⣿⡦⠥⠿⢋⣰⣿⣿⣿⡄⠀ ⢸⣿⠏⣠⡀⠀⣿⣿⣿⣿⣿⡤⣐⡁⢻⣿⣿⣿⡿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⢹⣟⣼⣷⣿⡀⣻⣿⣿⣿⣿⣿⡿⢠⣄⡄⡁⠈⠘⢁⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠨⠿⡿⢿⣿⣷⣿⣿⠿⣿⣿⣟⣴⣼⣿⣇⣷⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⡟⠇⠀ ⠀⠀⠀⠈⠹⠉⠀⠀⠀⠘⠙⢻⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⠿⡿⠇⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠻⠟⢻⠟⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣠⣤⡾⢿⣿⣿⠿⠟⠉⠉⠀⠀⣠⣴⣶⣖⠒⡤⠀⠠⢾⣿⣭⣭⣾⣛⣻⣿⣿⣿⣿⣯⣍⣛⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⠛⠉⢁⣀⠀⢤⡀⠹⣇⠀⠢⠂⠀⠤⣾⠹⣿⣷⣟⡴⠃⠀⣀⣼⣭⣟⠛⠯⠭⠼⠿⢿⣿⣿⣿⣿⣿⣯⣽⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡟⠁⢀⠎⠁⠀⠀⠈⠉⠆⠻⣿⣶⣀⣀⠀⠈⠓⠶⠶⠋⢁⣰⣾⣿⣭⡷⢖⣚⣿⠂⠌⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⠀⠐⠲⠶⢄⠈⢿⣿⣿⣿⣿⣿⣷⡾⠿⠿⢿⣿⣞⠳⠾⣷⣻⢿⣯⠽⠛⠛⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣝⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⢀⡠⠖⠛⠛⠛⠲⣄⡀⠑⠈⢿⣿⣿⣿⣿⣿⣿⣋⣩⠭⣒⣛⠭⡗⣶⠽⠛⠋⠉⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢧⡀⠀⠀⠀⠀⠀⠀ ⠸⡀⡠⠊⠉⠐⠲⢤⡂⢀⠀⠙⢦⡀⣀⠙⣿⣿⣿⣿⣿⣷⣶⠁⣲⣮⣝⣺⠷⠆⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣵⡀⠀⠀⠀⠀⠀ ⠀⠑⠁⠀⠀⠀⠀⠀⠈⠓⠷⣤⣠⣙⠻⠀⢸⣿⣿⣿⣿⣿⣿⣦⣶⡞⠉⠀⠀⠀⠀⠀⠸⠿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⠤⠝⠲⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠴⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠁⠄⠀⠘⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠀⠀⠀⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⢹⣿⣿⣿⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠘⣿⣿⡿⢟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⣀⠤⠤⠤⠀⠒⠒⢤⡤⠴⠞⠛⠻⠿⠛⠛⠛⠛⠛⠛⠋⠙⣿⠏⢻⣻⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠿⠻⢿⠿⠿⠿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜ ⬛🟥🟥🟥🟥🟥🟥🟥🟥⬛ ⬛⬛🟥🟥🟥🟥🟥🟥⬛⬛ ⬛⬜⬛🟥🟥🟥🟥⬛⬜⬛ ⬛⬜⬜⬛🟥🟥⬛⬜⬜⬛ ⬛⬛⬛⬛🟥🟥⬛⬛⬛⬛ ⬛🟥🟥🟥🟥🟥🟥🟥🟥⬛ ⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜ ⬛🟥🟥🟥🟥🟥🟥🟥🟥⬛ ⬛🟦⬛⬛🟥🟥⬛⬛🟦⬛ ⬛🟥⬛🟥⬛⬛🟥⬛🟥⬛ ⬜⬛⬛⬛🟥🟥⬛⬛⬛⬜ ⬜⬜⬛🟥🟥🟥🟥⬛⬜⬜ ⬜⬜⬛🟦⬛⬛🟦⬛⬜⬜ ⬜⬜⬛⬛⬜⬜⬛⬛⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠞⠛⠛⠛⠛⡟⣛⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠓⠦⣤⡀⠀⠀⢀⡴⠚⠉⠁⠈⠉⠛⢿⣛⡶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠙⢷⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡶⣿⠟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠸⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠏⣼⠏⢸⡇⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄⣇⠀⣶⣷⡆⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠇⣼⡿⠀⠈⣧⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⡞⢆⠙⠛⠁⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⢠⡏⢰⣿⡀⠀⢸⡿⠣⡀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠈⠓⢤⣀⡀⠀⢀⣠⠴⠋⠀⠹⣆⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀ ⠀⡾⠀⣿⣿⣇⠀⣹⠃⠀⠈⠑⠲⠤⠤⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⣀⣀⠀⢻⡀⡀⠀⢿⡀⠀⠀⠀⠀⠀ ⢰⡇⢸⣿⣿⣿⠀⣿⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⡆⢸⣷⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⢸⡇⢸⣿⣿⣿⡆⣿⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡴⢃⣾⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⢸⡇⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠔⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⢸⡇⠸⣿⡿⠀⡐⠹⠟⢷⣄⡀⢀⣀⣀⣀⣀⣀⣤⣴⣒⣒⣒⣒⣒⣒⣶⠚⠋⠉⠛⢧⣤⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠘⣇⠀⣿⡄⠦⠃⠀⠀⣾⡿⠋⠁⠀⠀⢈⣿⣟⠉⠉⠉⠁⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠙⣿⠀⠀⢸⠁⠀⠀⠀⠀⠀ ⠀⢻⡀⢹⡗⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢠⣿⠀⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠈⢇⠈⣷⣀⠀⠀⠈⠿⣦⡀⠀⠀⠀⢘⣿⣟⣳⣦⣤⣀⣀⣀⣀⣤⣷⣄⣀⣀⣠⣴⣿⣀⣠⣾⣃⣀⠀⡀⠀⠀⠀ ⠀⠀⠸⠗⠛⠛⠛⠉⠉⠉⠉⠉⠓⠒⠒⠋⠁⠀⠈⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠈⠉⠉⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣯⣉⣀⣴⣿⡿⠭⠿⠛⠛⠰⢿⡖⠛⠉⣉⣿⣷⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠷⢶⣶⣶⣶⣶⣾⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⣀⡤⣤⠶⠛⠉⠉⠀⠀⠉⠉⠛⠲⣤⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢧⠀⠀⠀⠀ ⠀⠀⡼⢁⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⡈⢧⠀⠀⠀ ⢀⡞⠁⣸⠁⠀⢠⠬⠓⠀⣀⠀⠀⢀⠀⠛⠥⣄⠀⠀⡇⠈⢳⡀⠀ ⡞⠀⠀⠹⣆⢰⣒⠆⠀⠀⠓⠊⠙⠚⠁⠀⠸⠭⠇⣰⠇⠀⠀⢻⠀ ⣇⠀⠀⠀⠈⣹⠶⠦⠤⠤⣤⣤⣤⡤⠤⠤⠴⠶⣏⠁⠀⠀⠀⣸⠁ ⠈⠓⠲⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠚⠁⠀

.　 +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠹⢦⡤⢤⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⠞⠋⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣄⡀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⢀⣀⣀⣀⣱⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣤⠶⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠃⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠀⠀⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡞⢻⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠉⠀⠈⠳⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⣤⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠶⢤⣀⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⣢⠔⠒⠂⠁⠒⠒⠒⠤⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⢢⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⠤⠂⠁⢠⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀ ⢰⠉⠀⠀⠀⠀⡇⢀⡘⠛⠀⢀⢀⠀⡀⠀⠀⢺⣿⠀⠰⡀⠀⠀⠀⠑⢄⡀⠀⠀ ⠸⡀⠀⠀⠀⠀⠘⣮⡚⠀⠀⠀⠀⠈⠁⠀⠀⠀⣒⣤⢦⢣⡀⠀⠀⠀⠀⠈⠑⡄ ⠀⠈⠑⠒⠒⠒⠉⠀⠀⠉⢁⠶⠒⠒⠀⠤⠤⠤⢤⡄⠓⠃⠳⣄⠀⠀⠀⠀⠀⡘ ⠀⠀⠀⠀⠀⠀⠘⠚⠀⢀⣧⡤⠖⠀⠀⠀⢀⠖⠉⠉⠓⢄⠀⠈⠑⠢⠤⠄⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠇⠀⠀⠀⠀⣇⠀⢠⡊⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠐⠠⠤⢀⣀⣘⠦⠤⠠⠜⠊⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⣦⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣾⠛⢷⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⠛⢿⣇⠀⣿⠟⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠹⣷⠀⣼⠟⢛⣿⣶⠾⠟⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠻⣶⡿⠿⠶⣿⠛⢿⡟⠋⠉⢻⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠛⠷⣾⠛⢿⠿⠟⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣠⣴⢿⡶⢾⡟⠳⣾⡋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣻⣶⡶⢻⣿⠶⣿⠷⣦⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣁⣾⡇⠈⣿⢶⣼⠿⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡴⠛⠉⣿⣦⣾⡇⠀⣿⣤⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢷⠶⣷⠀⠀⠀⠀⠙⠻⢶⣄⠀⠀ ⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⣼⠷⠶⠋⠈⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡄⠈⡆⠸⣇⠀⠀⠀⠀⠀⠀⠈⠛⢦ ⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡧⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣤⠄⠀⠀⠈⠛⠛⠁⠀⡸⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠙⢿⡛⠛⢋⡿⠁⠀⠀⠀⠀⠀⠀⠀⣠⢃⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⠞⠁⠀⣀⣤⣀⠀⠀⠀⣰⣷⡾⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠉⠻⢷⣦⣄⣀⣀⠀⠀⣰⡟⠛⢷⣶⣶⢶⣾⡋⠀⠙⣷⡶⠟⠋⠁⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠉⠉⠙⢛⣿⣿⣄⣤⣾⠏⣠⡤⠿⣿⣶⡶⢿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⣿⠟⠉⠉⠻⠏⠀⠀⠈⣿⠃⠀⡍⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣶ ⣤⣤⣤⣴⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠿⣄⠀⠀⠀⠀⠀⠀⣠⡟⢁⠀⠈⢀⣘⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⢸⢢⠹⠷⣤⣀⡀⣠⡼⠋⠈⡍⣰⠟⠉⠉⠻⠏⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣇⣘⢀⢀⠉⠃⠤⠌⣉⣉⠰⠀⠀⡇⠹⣄⠀⠀⠀⠀⠀⠀⢨⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠹⠟⠉⠙⢦⣀⡞⢂⣀⣀⡈⢐⣀⣀⣀⢛⡷⣤⣀⠀⣀⣴⠻⠈⢹⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣄⠀⠀⠀⠀⠀⠀⣸⡇⣿⠏⠁⠈⠙⡿⠋⠉⠙⢦⡸⢦⣬⡛⡛⠻⠀⠀⢀⣿⡧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠛⢦⣀⣀⣀⡤⠞⢻⡤⢽⣆⠀⠀⠀⠀⠀⠀⠀⣼⣆⠀⢀⠀⠀⠠⠀⣤⣾⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠉⠋⠛⠂⠐⠁⠒⠆⠋⢷⣄⡀⠀⢀⣤⢾⠗⠈⢀⣀⣠⣤⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣶⣶⣶⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣾⡿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠙⢲⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠘⠁⠀⠀⢸⣧⠹⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⠛⠒⠒⠒⠒⠒⠲⠼⢿⣧⠹⣆⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⣤⣀⣈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣄⡈⠹⣶⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠘⢯⡻⢾⣿⣏⠉⠳⢦⡀⠀ ⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⢠⡟⠒⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠉⠛⢷⣦⣀⠈⠓ ⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⡼⡄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠉⠻⣷⣄ ⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢰⠃⡇⠲⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠉ ⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀ ⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠐⠚⠁⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀ ⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠴⠒⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠢⢤⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⣿⣶⣿⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝⠉⠀⠉⠛⠁⠀⠀⢀⣀⣄⠀⠀⠀⠀⠈⠙⠁⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀ ⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠈⠑⢢⣄⣀⠀⠀⠀⢈⣉⣁⣀⡀⠀⠀⠀⢀⣀⣤⡶⢷⣄⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀ ⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢸⠉⠻⣍⠛⠶⣾⣿⣿⣿⣷⣶⠟⠟⢋⡵⠋⠀⠀⠙⣦⣄⡀⠀⢀⣀⠼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠦⣄⣀⣀⣀⡴⠋⠀⠀⠀⢸⠀⠀⠈⠓⠦⡾⠉⠛⠉⠀⠙⢦⡴⢟⠀⠀⠀⠀⠀⢻⡇⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢀⠇⠀⢄⡀⠀⠀⠀⠀⠀⢧⡀⠀⢀⡴⠃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠴⡎⠀⠀⠀⠈⠩⡉⢱⣄⠀⠀⠈⠉⠉⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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