HELLO KITTY <3 ILYYY Emojis & Text

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⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣰⡿⠛⠛⠿⢶⣦⣀⠀⢀⣀⣀⣀⣀⣠⡾⠋⠀⠀⠹⣷⣄⣤⣶⡶⠿⠿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠉⢹⡟⠁⠀⠀⣀⣀⠘⣿⠉⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣾⡋⣽⠿⠛⠿⢶⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⢈⣻⡏⠀⠀⠀⠀⣿⣀⠀⠈⠙⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠙⢷⣄⣀⣀⣼⣏⣿⠀⠀⢀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡉⠉⠁⢀⣠⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠗⠾⠟⠋⢹⣷⠀⠀⠀⠀ ⢀⣤⣤⣤⣿⣤⣄⠀⠀⠀⠴⠚⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⠀⢀⣈⣿⣀⣀⡀⠀ ⠀⠀⠀⠈⣿⣠⣾⠟⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⡤⠶⢦⡀⠀⠀⠀⠀⠹⠯⠃⠀⠀⠀⠈⠉⢩⡿⠉⠉⠉⠁ ⠀⠀⣤⡶⠿⣿⣇⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠓⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣯⣀⣀⠀⠀ ⠀⢰⣯⠀⠀⠈⠻⠀⠀⠀⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠉⠉⠁⠀ ⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⢀⣀⣀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⢷⣄⡀⠀⠀⠀ ⠀⠀⠀⠈⠙⣷⠀⠀⠀⣴⠟⠉⠉⠀⠀⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⠟⠉⠀⠀⠈⠉⠀⠀⠀ ⠀⠀⠀⠀⠰⣿⠀⠀⠀⠙⢧⣤⡶⠟⢀⣿⠛⢟⡟⡯⠽⢶⡶⠾⢿⣻⣏⣹⡏⣁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠙⠛⠛⠋⠀⠀⢀⣽⠟⠛⠖⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠿⠟⠋⠹⣷⣤⣀⡀⠄⣡⣀⣠⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⣉⣻⣏⣉⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⢀⣀⣠⣀⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⠛⠛⠶⣤⣤⡴⠶⢶⣿⣟⣿⣻⣿⡋⠉⠁⠹⣇⠀⠀⠀ ⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣾⣿⣿⡿⣿⣷⣶⣶⣿⡄⠀⠀ ⠀⠀⠀⣿⡖⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠿⢿⣽⣷⣿⣿⣯⢿⡟⠀⠀ ⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣽⣾⢿⡅⠀⠀ ⠀⠀⣾⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣨⣧⣀⡀ ⠘⠛⢻⡛⠃⣰⡏⠙⠉⠛⣦⠀⠀⠀⠀⢠⡞⠋⠙⠉⣷⢈⣡⣇⡀⠀ ⠀⠰⠾⣿⣳⠋⠀⠀⠀⠀⡿⠀⣞⣿⠆⢸⡄⠀⠀⠀⠈⢷⣽⠋⠉⠀ ⠀⠀⢠⡼⣇⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠻⣤⣀⠀⠀⢘⡏⠳⠀⠀ ⠀⠀⠀⠀⠙⠳⠶⠛⠛⠶⠶⠶⣤⣤⣤⠶⠶⠾⠛⠲⠖⠋⠀⠀⠀⠀

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

ฅ^•ﻌ•^ฅ

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠶⢦⣄⠀⠀⠀⠀⠀⣴⠟⠛⢧⣠⣶⣿⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠁⡟⠦⠌⠛⠉⠉⠉⢹⠇⢠⣶⣼⣷⣞⢙⣧⣿⡀⠀⠀⢠⠤⣄⠀⡏⠀⡏⠀⠀⠀ ⠀⠀⡖⢲⡎⠘⡆⠀⠀⠀⠀⠀⢸⣤⠃⠀⠀⠀⠀⠀⠀⣿⠀⠈⢻⡃⠀⢸⡿⡄⠈⣿⠀⠀⠀⡇⠀⠈⠿⠀⠀⡇⠀⠀ ⠀⠸⡄⠈⠀⠀⡏⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠘⠷⠖⠛⠛⠛⢿⡗⢋⣴⠏⠀⠀⠀⠹⡄⠀⠀⠀⠀⠇⠀⠀ ⠀⠀⠉⠣⢄⡼⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⡀⢀⣀⠀⠀⠀⠑⠦⡄⠀⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠾⣷⠆⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠐⢺⡟⠉⠉⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢿⡦⠀⠀⠛⠃⠀⠀⢠⢶⣄⠀⠀⠈⠛⠀⠀⠀⣺⠓⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣖⡀⣀⣀⡀⠀⠈⠉⠉⠀⠀⣀⣀⣀⠀⣲⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡆ ⢻⡈⠻⣦⣀⣀⣀⣀⣀⠀⠀⠀⠁⣴⠟⠉⠁⠀⠉⠛⢦⡀⢀⡴⠛⠉⠁⠈⠙⠻⣄⠀⠁⣀⣠⣤⣤⣤⣤⡤⠖⠋⣸⠇ ⡿⠳⣤⣀⡀⠀⠀⠉⠉⠉⠳⢦⣼⠃⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣦⡞⠉⠀⠀⠀⠀⠀⢀⣠⠶⢻⡆ ⠻⣦⣀⠀⠀⠀⡴⠶⢦⡀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡴⠚⠳⡄⠈⢉⣀⣠⡾⠁ ⠀⠸⣍⣉⣁⡀⣇⠀⠀⠑⠀⢠⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣰⢷⡀⠀⠓⠀⢀⡇⢤⣈⣭⠿⠁⠀ ⠀⠀⠀⠙⠷⠤⠿⠶⠦⠶⠞⠋⠘⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡼⠃⠈⠻⠦⠴⠖⠻⠶⠶⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀⢀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣁⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⢀⣀⣀⡀ ⠀⠀⠀⠀⣼⠝⠉⠉⠛⠷⣦⣤⣶⣶⣶⣶⡾⠃⠀⠈⢻⡾⠛⠉⠉⢻ ⠀⠀⠀⠀⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣼⠁⠀⣾⢻⡶⠛⠲⣄⣤⠼⢧⣄ ⠀⠀⠀⠀⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⢙⣿⡀⠀⠀⣹⢶⡄⠀⣹⡀ ⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠒⢺⡛⠛⠁⣰⠏ ⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⢹⡇ ⢠⡶⢼⣷⢤⠄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠾⣿⠖⠶⠆ ⠀⠀⢈⣿⣀⡀⠀⠀⢿⡿⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠸⣿⠇⠀⠀⠠⣴⣿⣄⣀ ⠀⠘⠋⠹⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠯⣦⠽⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⠃ ⠀⠀⣠⡴⠟⠻⣧⡶⠳⣦⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⠋⠛⠶⠄⠀ ⠀⠀⠁⠀⢀⡾⠛⠂⣀⡈⠀⢹⣧⣤⣄⣀⣀⣠⣤⣤⣴⣶⣾⠛⠁ ⠀⠀⠀⠀⠈⣷⣤⠄⠛⠃⠈⢿⢹⣄⠀⠀⠀⢠⡿⠀⠈⢷⡉⣻⣦⣤⣀ ⠀⠀⠀⠀⣼⠏⢿⣤⣴⡷⣶⡟⠀⠙⠳⠶⠶⠛⠁⠀⠀⠈⣿⡋⠀⠈⣿⠆ ⠀⠀⠀⠀⢻⣆⠀⠀⢸⣿⣜⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⣽ ⠀⠀⠀⠀⠀⠙⠻⣶⠞⠃⠙⠶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠾⠋ ⠀⠀⠀⠀⠀⠀⢸⡿⠶⢶⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⡶⢾⡇ ⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⡇ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣀⣀⣀⣀⣠⣿⣀⣀⣀⣀⣀⣠⣴⠟ ⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠋⠉

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠷⡞⠛⢳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⣷⠾⣻⢷⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣷⠑⡆⢳⡆⠀⣿⠀⠀⠀⠀⠀⢭⢓⠿⠇⠀⠀⠀⠀⠀⣿⠀⢰⡟⠐⢃⡞⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅⡹⡈⠿⡀⢹⡇⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⢹⠉⣀⠏⡽⢁⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠐⡜⠣⠬⠙⠦⢄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠛⠶⡟⠐⠃⣞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⠛⠛⠛⠛⣤⣍⡏⠁⠀⠀⣀⣀⠈⢻⡄⠀⠀⠀⠀⢠⠟⠁⣀⣄⠀⠀⠈⣿⣩⣤⠛⠛⠛⠻⣤⣀⠀⠀⠀ ⠀⣠⡔⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠛⠀⢨⣿⠀⠀⠀⠀⣞⡇⠀⠛⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠹⢧⣀⠀ ⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡟⠀⠀⠀⠀⢣⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⣀⠀⣼⠇ ⠀⠻⢆⣴⣤⣤⣤⣯⣭⣵⣦⣤⣤⣼⣄⡸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣾⣧⣤⣴⣾⣿⣿⣿⣤⣤⣼⣤⡼⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀

⠀⠀⠀⠀⠀⣀⣴⣶⠀⢰⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⢡⡿⠛⠀⠘⠻⣿⡟⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⡷⠋⠀⠀⠀⠀⠀⠈⢿⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⠀⠀⠀⠀⠀⣠⣾⠿⢿⣦⡸⣷⣾⣷⣦⣤⡀⣀⣀⣠⠤⢤⣄⣀⠀⠀⠀ ⢸⣿⡏⠆⠀⠀⠀⠀⣿⡇⢀⣼⡿⠁⠀⠀⠀⠙⢿⡟⢻⡿⠋⠀⠸⢿⣿⡟⢆⠀ ⠸⣿⣿⡀⠀⠀⠀⠀⠙⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠹⣷⣬⡆ ⠀⠻⣿⣷⣄⠀⠀⠀⣀⣠⢿⣇⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⡆⠀⠀⠀⠀⣹⣿⡇ ⠀⠀⠙⠿⣿⣿⣶⣿⣷⣶⣿⣿⣿⣦⣀⠀⠀⣀⣴⣿⣁⣼⡟⠀⠀⠀⢀⣿⣿⠇ ⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠁⠈⠛⠿⣿⣿⣿⣿⠋⠙⠛⠋⠀⠀⠀⠀⠈⠉⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢻⣿⣷⣄⠀⠀⠀⢀⣤⣤⣤⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣭⣛⣿⠿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀

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

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

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

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

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

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

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

⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣼⠀⠀⠀⣀⡴⠖⠚⠛⠓⠶⣄⡀⢼⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⢿⡄⠀⠀⠀⠀⢹⠀⢠⡞⢁⣴⡶⠦⣄⣠⡤⣄⠙⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢠⣀⣠⣀⣀⡟⠁⠀⠀⠀⠀⠹⣦⣤⡤⣤⠾⠀⡞⠀⡞⠉⠀⠀⠈⠉⠀⠉⣧⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠀⢀⣴⠋⠁⠀⠈⠛⠧⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⣇⠀⠻⣄⠀⠀⠀⠀⠀⣰⠟⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣧⢸⠃⠀⠀⠀⠀⢠⡶⠋⠙⠳⣄⠀⠾⢧⡀⠀⠀⠀⠀⠹⣇⠀⠘⠶⣄⠀⣀⡴⠋⢠⣯⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡿⣆⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡆⠀⠀⣹⡴⠀⠀⠀⠀⠘⠷⣄⣀⡈⠙⣁⣠⡴⠋⠁⠹⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣮⣷⣶⠗⠀⠻⣄⠀⠀⣀⠞⠁⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢹⡏⠀⠀⠀⠈⠉⠉⢡⣀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠸⣇⠀⠀⠀⠀⠀⠀⣸⠫⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠙⢦⣀⣀⣀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀ ⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⡀⠀⠀⠀⠀⣧⠀ ⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡄⠀⠀⢸⡆ ⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⢼⡇ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢸⡇ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢿⣿⠿⠒⠀⣿⣸⠃ ⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢀⣴⡾⠟⠛⠛⡿⠇⠀⠀⠀⠀⠀⠀⣤⣴⡦⠀⠈⠉⠀⠀⠀⠀⠀⣿⡏⠀ ⠀⠀⠀⠰⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠐⠿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡁⠀ ⠀⠀⠀⠀⢨⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⠤⠚⠉⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡷⠦⣄⣀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠈⠉⠙⠓⠒⠶⠬⣷⣶⣤⣤⣤⠤⠶⣶⣶⣦⣤⣤⣤⣴⠶⠛⠋⠉⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢛⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠋⠀⠉⠓⠦⣤⣀⣀⣀⣀⣀⡤⠶⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀ ⢀⣀⣠⢏⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢄⢀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠠⣀⣀⣀⡀⠀⠀⠀⣀⣼⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡦⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⣾⣿⣿⣿⣷⠄⠀⠰⠤⣀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⢺⣿⣿⣿⣿⡄⠀⠀⣿⣿⢿⣿⣿⣦⣦⣦⣶⣼⣭⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⡆⠂⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⡿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⡀⢀⣿⣿⣿⣿⠀⢸⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⡟⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠛⠋⠁⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀ ⠀⠜⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⠄⣠⠀ ⠠⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠛⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⢳⣾⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⢨⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⡿⠿⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠉⠻⠿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

please dont post gross stuff on here!! kids who are young like probably 9 year olds are just trying to find cute combos. spread the word (≧ヮ≦) also people who are spreading the word, please do not put curse words. its the same example for kids with the gross things but with curse words. thanks love<3 bye!! /ᐠ - ˕ -マ

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠤⣦⢴⠟⠋⠁⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⢴⣾⡙⣻⡷⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠘⢿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠆⠀⠀⢰⣿⣦⠤⠔⠀⢹⣧⣀⣀⠀⠀⠀⠈⠀⡀⠀⠀⠀ ⠀⠀⣸⣆⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣀⡀⠀⠀⠀⠀⠾⠂⠀⠀⠀⢻⡏⠀⠀⢾⡛⠻⣯⣉⠁⠀⠀⠀⢀⡿⣤⣀⡀ ⠠⣴⣟⣻⡷⢶⠀⠀⠀⣾⠀⠀⠀⢰⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⠀⠈⠛⠛⠛⣿⠛⠂⠀⠐⠻⣷⣼⠟⠉ ⠀⠀⠹⡿⠀⠀⠀⠀⠀⣿⣠⣀⣒⠀⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠔⠀⠀⠀⠀⠈⠋⠀⠀ ⠀⣠⠀⠀⠀⠀⠀⢀⣤⣿⠟⣿⡉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⡿⢶⣤⡀⠀⠘⠟⢁⣿⡞⠛⠉⠀⠀⠀⠀⠀⠀⠀⣰⣤⣤⡶⠤⣤⣄⠀⠀⠀⠀⠺⣧⡀⠀⠀⣴⠟⢿⡆⠀⠀⠀ ⠛⢷⣾⠋⠀⠀⠀⠀⣾⠛⢷⣤⣀⡀⠀⠀⠀⠀⠀⣼⠋⡁⢻⡀⢀⠀⠉⠀⠀⠀⠀⠀⠈⢻⣤⠀⣿⠐⢸⡇⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣷⠄⠀⠀⠀⠁⠀⢀⣸⡷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡏⠀⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣼⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠈⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠿⠛⠋⠉⠁⠈⠀⠀⠀⠀⢑⣴⡾⠿⠿⠿⣿⣿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠛⠛⠛⠻⠶⣤⡀⠀⠀⠘⣠⡾⠋⠁⠀⠀⠀⠀⠀⠙⠳⣌⢹⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠈⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⡿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⣼⡟⢱⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⢁⣾⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⢸⡄⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣡⠀⠘⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠁⣾⣿⠁⠀⠜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠃⢸⢳⡀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡈⠀⠈⠈⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠁⣸⣿⡇⠀⠀⣷⣼⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠈⢻⣇⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠇⢀⣿⣿⣧⠀⠀⣿⡟⠀⠙⢦⣀⡀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠈⠙⠒⠦⠤⠤⠖⠛⠉⠀⠀⠀⠈⢿⡄⢠⠀⠘⢻⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⣸⣿⣿⣿⠀⠀⣿⠁⠀⠀⠀⠀⠉⠙⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⣄⠀⢸⣧⢠⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⡆⠠⡏⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡆⢈⣿⡷⠀⠀⠂⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣧⡔⣿⠀⠀⠀⠀⠀⠈⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⣸⣿⠻⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣧⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣄⣀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠊⠉⣰⡿⠟⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⢿⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠅⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⢿⣿⡿⢗⢈⠀⠹⠟⠻⣷⣄⠀⠀⣀⣀⣀⡀⠀⠀⣠⡤⠶⠒⠒⣒⣒⣚⣛⣛⣒⣒⡶⠛⠉⠉⠙⠛⢶⣤⣤⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠚⣇⠀⢸⣿⠀⣴⡸⠀⠀⠀⣶⣿⡿⠟⠋⠉⠁⠈⠉⣻⣿⡿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⣩⡿⠆⠀⠀⠀⠀⠀⠙⣷⣾⠀⠀⠃⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡀⠈⣿⣇⠈⠁⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠻⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣇⠀⢿⡍⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⢠⣿⢿⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡄⠸⣷⣄⡁⠀⠀⠀⠛⢿⣤⡀⠀⠀⠀⠀⠀⣻⣿⡟⣛⣷⣤⣤⣤⣤⣤⣤⣤⣤⣼⡷⣤⣀⣀⣀⣤⣾⣿⣥⣤⣤⣿⣏⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣌⣿⠤⠿⠗⠛⠛⠛⠛⠛⠉⠉⠙⠓⠦⠤⠴⠞⠋⠁⠀⠉⠉⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⠚⠛⢋⣩⣭⠿⠿⣿⣿⣿⣿⣏⣩⣭⣿⣿⡿⠶⠶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠻⢶⣦⣤⣿⣽⣶⣛⠛⠉⠉⠉⠉⠁⠉⢿⣍⣀⣀⣠⣴⡾⠿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⡻⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠟⠋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠤⠤⠤⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠒⠒⠲⠤⠄⣀⠀⠀⠀⣠⠞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠖⠒⠒⠒⠈⠉⠉⠉⠉⠑⠒⠒⠲⠤⠤⣴⣤⣀⣀⡀⠀⠀⠀⠀⠀⠙⣯⡉⠉⠉ ⠀⠀⠀⠀⠀⠀⢠⡿⠉⠀⠀⣀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠘⠃⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣰⡶ ⠀⠀⠀⠀⠀⢸⣡⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄ ⠀⠀⠀⠀⠀⠀⠻⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠛⠿⣿⣿⣿ ⠀⠀⠀⠀⣀⣠⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠀⠀⠀⠀⢀⣀⣀⠤⢄⣀⠀⠀⠀⠀⠀⡥⠀⠀⠀⠀⠀⠉ ⢀⣤⣶⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡤⠖⠊⠉⠀⠀⠀⠀⠀⠉⠲⣄⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠉⠉⠉⠉⠉⠙⠒⠒ ⣿⣿⣿⣿⣿⣿⣿⠿⠋⠱⡀⠀⠀⠀⢀⡴⠀⣠⣶⣶⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⢳⡀⠀⢠⠟⠀⠘⣿⠟⠁⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⠛⠁⠀⠀⠀⠀⢀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⢉⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⡠⠚⠁⡠⠊⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠓⠤⠄⠀⣀⠠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⡦⣄⠈⠀⢀⡞⠁⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⡒⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⢸⡄⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡷⠒⠐⠒⢲⠞⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡄⣠⠞⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠳⣄⡀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⣀⡴⠋⠁⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

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

⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢀⣾⡿⠋⠉⠁⢠⣿⠏⢁⣿⣿⣿⠏⠉⢸⣿⡏⠉⢻⣿⣿⡇⠈⠙⢿⣿⣿⣿⣷⡆⠀⠀⢇⠢⣈⡒⡤ ⣿⣿⣿⣿⣿⣏⣴⡇⠀⠀⠀⢠⡿⠋⠀⠀⠀⣰⣿⠋⠀⣼⣿⣿⠏⠀⠀⡾⣿⠁⠀⠀⣿⣿⣷⠀⠀⠀⠹⣿⣿⣿⣿⣄⢀⣿⣷⣿⣶⣶ ⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⡟⠁⠀⠀⠀⢰⣿⠇⠀⢰⣿⣿⡷⠀⣀⣜⣁⣻⣀⣀⣀⣸⢻⣿⡇⠀⠀⠀⠘⣿⣿⣷⠹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠃⠀⠀⣠⣿⠀⠀⠀⠀⢠⣿⡏⠀⢀⣿⣿⡿⠛⣩⣿⠿⠛⢻⡏⠉⠉⢹⠉⢿⣿⡀⠀⠀⠀⠹⣿⣿⡆⠙⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡏⠀⠀⣰⣿⡟⠀⠀⠀⢀⣾⣿⠀⠀⣸⣿⡿⢥⣶⠝⠁⠀⠀⠀⡇⠀⠀⡜⠰⡀⢻⡇⠀⠀⠀⠀⢿⣿⣿⠀⠸⣿⣿⣿⡿ ⣿⣿⢿⣿⣿⡃⠀⣼⣿⣿⡇⣀⣀⣤⣾⣿⡇⠀⠰⣼⡟⣠⠎⠁⠀⢀⣠⠔⠁⢹⣀⣠⣧⣶⣦⣤⣷⣤⣤⣠⣤⠼⣿⣿⡆⠀⢹⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣏⣁⣼⣿⣿⣿⠀⢠⣾⣟⡔⠁⠀⠀⠀⢸⠁⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣿⣿⣇⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣟⣹⣿⣿⣿⡿⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⢰⣾⢟⣻⡿⠛⢻⢋⣻⣏⣱⠞⠙⣄⡀⠀⣿⡽⣿⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢘⡅⠚⠋⠉⠁⠀⠀⠀⠀⣔⣾⢏⢦⢄⣿⣧⣿⡆⠀⠈⣿⣿ ⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⡿⢻⣿⣿⡿⠋⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠀⢂⢻⣿⣿⣿⡇⠀⠀⢽⣿ ⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣷⣿⣿⣿⣿⡷⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⢀⣠⣾⣟⡖⢻⣿⣿⠃⠀⠀⣿⣿ ⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⠟⣻⠿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠿⠛⠉⠁⢰⢸⣿⡿⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠋⠰⢟⣿⠌⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⢠⡇⣿ ⣿⣿⣿⣿⣿⣿⣏⠓⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⢾⣿⡟⠀⠀⠀⣼⠃⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⣰⠏⢰⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⣡⣴⣾⣿⣿⣿⣿⡿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⣰⠏⣠⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⣃⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣼⣿⣃⠤⠚⠚⠉⠉⠉⠙⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⢀⡄⠀⠀⠀⠀⠀⠀⠙⢽⣿⠿⠋⠉⠁⠀⢠⡆⢰⠃⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢯⠀⠀⠀⠀⢀⡞⢠⠋⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣸⢠⠃⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡆⢠⠉⢿⣿⣿⡟⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⡇⠇⠀⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣼⠀⠈⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⡗⠤⣀⠀⠀⠀⠀⠀⠑⢄⣀⡞⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⠀⠀⠹⢇⠀⢻⣿⣿⣿⣿⣿⣿⣧⠀⠈⠻⣷⣦⣤⣀⡀⠀⠉⠀⠀⠀⣀⡴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠟⠀⠀⠀⠈⠳⣄⢻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠻⢿⣿⣿⣿⣷⣶⣴⣾⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣄⠀⠀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠉⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢱⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠫⣦⡤⣄⣩⠤⠬⣁⠀⠈⠉⠑⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣶⡆⠀⣤⠑⠦⠤⠼⠁⠀⢠⠖⠒⠢⢄⢈⣽⡦⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣛⣿⣏⠉⠑⢄⠀⠀⠀⠀⣘⠢⠤⣠⠼⠃⠉⣁⠀⠍⠢⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢲⡟⠲⢤⣄⣀⡙⠓⠲⠶⠀⠀⠘⠧⣬⣞⠒⣻⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢉⢿⣿⣿⣭⡟⠛⢁⠤⡀⠀⠀⢨⠟⢿⠒⠶⢶⣾⣾⢿⣾⢛⣾⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣻⣦⣻⣿⣿⣁⠀⢻⣤⣇⣸⡄⠘⠶⠞⠁⢸⣁⣸⣿⣿⡿⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢧⡸⣮⠛⠛⠻⠿⢿⣿⣿⣙⣿⠋⠉⠓⣾⣦⣿⠚⠙⣿⣿⣿⣷⠏⠀⠀⠀ ⠀⠀⢀⣤⡶⢶⣾⠟⢉⣿⡿⢩⣇⠀⡼⣿⢾⡶⢄⠀⠀⠀⠈⠙⣛⣭⣷⣤⡴⣿⣿⣿⣶⣶⣿⣿⡿⠋⢳⡀⠀⠀ ⠀⢠⠟⣅⣠⣿⣃⡴⣯⣾⡿⣿⠻⢿⣅⣠⡾⠽⠒⠤⣀⠀⠀⠘⢧⣀⠈⠉⠛⢭⠉⢉⠟⠛⠛⢍⠀⣠⠜⡇⠀⠀ ⠀⢸⣀⣼⠞⢉⡥⣾⣿⢸⣵⣿⣴⣿⠿⠻⢤⣠⡴⣏⠭⣉⡳⠶⣤⣄⣭⣍⣚⡉⠀⠈⠑⠒⣶⣭⣶⣽⡾⠁⠀⠀ ⠀⠀⠉⢀⠴⡏⠀⣻⣿⣾⡿⠟⠉⠀⠀⠀⠀⠉⠒⠦⢶⣉⡴⠚⠁⣠⣾⠋⣩⡿⠶⢶⡟⢛⣿⠟⠛⣿⠀⠀⠀⠀ ⠀⠀⢰⠋⠳⣧⣴⣿⡿⠋⣀⠤⠠⡴⠒⣔⣲⣤⣤⣤⣤⣌⣉⣛⠛⠤⠥⢼⣋⣴⣶⣛⣄⣶⣷⠶⠞⢻⣆⠀⠀⠀ ⠀⠀⣼⣄⡠⢋⣿⣿⠒⢧⣼⣶⣶⣿⣟⠉⠉⣻⣿⣧⣽⣿⣿⣿⣿⣿⣶⣶⣲⡤⣤⣍⣁⠉⢯⣦⠀⠀⠹⣆⠀⠀ ⠀⣼⠃⠀⢠⣿⣿⣀⣟⣶⠟⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣤⣼⣇⣼⣿⣿⣿⣧⠀⠣⢹⡆⠀ ⢰⡟⠀⠀⣎⣿⣿⠟⠻⣿⣤⣤⣿⣿⣿⣿⣿⠟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣩⣿⣿⣿⣿⣻⣿⡆⢱⡇⣿⡀ ⣼⠃⠀⢸⣽⣿⣷⣀⣀⣼⠿⣤⣿⣿⣯⣬⡇⡀⠀⠀⢘⡿⠿⣿⣿⡟⠛⢿⣿⠿⠟⠉⢹⣿⣞⣿⣿⣼⣼⣿⢸⡇ ⣿⠀⠀⡏⣿⡟⣿⣿⣿⣿⣾⣿⣿⡿⢿⣿⡟⠙⢲⠖⢻⡧⣤⣿⣿⣧⣀⡜⢻⣿⣷⣶⣿⣿⢿⣿⣿⡏⡏⠹⣜⣷ ⣿⠀⠀⡇⣿⣿⣿⡿⣿⠋⠉⣙⠻⡷⣾⠋⠉⢲⣾⢷⣾⠿⠛⠒⠒⠻⣭⣟⣿⣿⣿⡟⠉⠙⣾⡿⣿⡇⡇⠀⢛⡿ ⢿⡀⠀⢷⣿⣇⡿⢷⡬⣽⠧⡀⢳⣸⢸⣦⣴⣿⠟⠉⠀⠀⣠⣴⡞⢛⠛⡛⠿⣯⡻⣿⣦⣾⣿⣿⣿⢷⠃⠀⢸⡇ ⢸⣷⡄⠘⣿⣿⡿⣦⡘⠾⣶⣷⠞⡼⢸⣻⣿⠋⡠⠊⠀⢲⡯⠀⣸⡟⣿⣧⡄⠈⢻⣿⣧⣿⣿⠛⡿⡼⠀⠀⣾⠃ ⠀⢿⣿⣄⢳⣿⣧⢻⣿⣤⡄⣿⠠⡇⡆⢿⡇⢰⣅⣀⣤⣼⣗⠒⠻⣿⣿⣿⠃⢀⣿⢧⢻⡏⠈⣹⣿⠃⠀⢰⡏⠀ ⠀⠈⣿⣧⣃⢻⣿⣷⡙⣿⣷⡘⡄⠻⠯⢼⣷⠀⢙⡏⠀⠀⠹⣗⢤⡀⠑⠘⢠⡾⠃⢸⢸⣿⣾⣿⠃⠀⢠⡿⠀⠀ ⠀⠀⠘⢿⣿⡣⡹⣿⣿⣮⣿⣷⡘⣄⠀⠀⢏⠓⡻⠁⠀⠀⠀⠀⠙⠛⠛⠛⠋⠀⣠⡎⣸⡿⡵⠁⠀⣠⡟⠁⠀⠀ ⠀⠀⠀⠈⠻⣿⣿⣮⠻⣿⣿⠉⢹⣌⠻⢷⣜⣦⡘⠦⠴⡺⣵⡤⠀⠀⠀⠀⠀⢀⣽⣵⡿⠋⠀⣀⣼⠋⠀⠀⠀⠀

⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⣿⣇⠀⠀⠀⠀ ⣿⢏⣹⣳⣯⣗⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠃⠒⣜⣮⢧⡀⠀⠀ ⣿⡞⠁⡉⠙⠻⣷⣿⢦⣤⣤⣶⣶⣶⣶⣶⣶⣾⣿⡿⠋⠀⠌⡐⠈⢿⣿⣣⠀⠀ ⣿⠀⢂⠐⡁⢂⣬⣿⣿⢫⠉⠀⠀⠀⠀⠀⠀⠜⡹⢿⣿⣿⣶⣶⣤⣈⣿⣷⣗⠀ ⡇⢀⣦⣼⣾⣿⣿⣿⡭⡃⠌⠀⠀⠀⠀⠀⠀⠀⠑⡹⣚⢿⣿⣿⣿⣿⣿⣿⣼⠀ ⣿⣿⣿⣿⣿⣿⣟⢧⢃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢎⠳⢯⡟⣿⣻⢿⣯⡷ ⣿⣿⡿⣟⡿⡓⢎⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⣬⣧⡝⢊⠙⣷ ⠟⢧⠛⠥⠃⢉⠀⣴⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⢸ ⠈⠄⡈⠤⣁⠢⡀⢿⣿⣿⣿⠃⠀⠀⠀⠀⢠⡄⠀⣴⠀⠀⡀⢙⢛⡛⠭⢠⠃⢆ ⠐⡠⢑⡒⡄⠓⡌⣌⢩⣩⠷⠶⣤⠀⠀⠀⠀⠳⠾⠃⢀⢸⡼⠋⠋⠛⢦⡃⠞⡠ ⢀⠱⡈⢖⡈⢣⠜⣠⠟⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠐⣾⠁⠀⠀⠀⠈⢧⢣⢸ ⣆⠠⢑⠢⣉⠆⢼⡟⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⣷⢯ ⡏⠀⠀⢁⠂⢌⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣗⠀⠀⠀⠀⠀⠀⠈⢯ ⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠃⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡏⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⠠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡄⣠⣿⠤⠶⠒⠒⠋⠉⠉⠙⠓⠲⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣋⣠⠤⠤⠤⣤⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡛⢻⠶⣤⣀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⡄⠈⠙⣧⠀⠀⠀ ⡇⠀⠀⠀⣆⠀⠀⠀⠀⣠⣾⠏⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠇⠀⠀⠘⣧⠀⠀ ⢻⡄⠀⠀⢻⣆⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⣇⠀ ⠘⣧⡀⠀⠈⣿⣦⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣿⢀⠀⠀⠀⠀⢿⡀ ⠀⠘⣧⡀⠀⠘⢟⢷⣼⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⡞⠉⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⣸⣷⣴⣿⢸⠀⠀⠀⠀⠸⡇ ⠀⠀⠘⢷⡀⠀⠀⠢⣹⣇⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠈⣷⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢹⣿⠈⣇⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠙⢦⣀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⣿⠻⡄⠀⠈⠛⠋⠁⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠁⠀⠈⣿⣧⣘⣦⠀⠀⢠⠇ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠻⣆⠀⠀⠀⠀⢰⣿⣧⡘⢦⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠤⢶⡀⠀⠀⠀⢀⡾⠀⠉⠛⠻⠛⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠶⠻⣇⠀⠙⢶⣿⣦⣤⡀⠀⡴⠻⡇⠀⠀⠀⠀⠀⠙⠶⣤⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣙⣛⣻⣿⣿⠃⠀⠀⡄⠀⠀⠀⠘⣄⠀⠈⣿⠁⠀⠀⣠⠞⢿⠟⣶⡄ ⠀⠀⠀⠀⠀⠀⣠⣿⣤⣶⡖⠠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠉⣟⣩⣥⣿⢤⣤⣼⠀⠀⠀⠰⣄⣼⠳⢼⡿⠀⠀⠀⣿⠖⢾⡷⢻⣿ ⠀⠀⠀⠀⠀⠀⠻⠏⣩⣿⣯⣀⣿⠿⠤⠇⠀⠀⠀⠀⠀⢰⠋⠉⠀⣶⣤⣀⣙⣷⡀⠐⠿⣟⠁⠀⠀⠀⠀⠀⠀⠙⠦⢾⣿⠾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⡀⠀⠀⠢⡁⢈⣿⡾⢧⣀⠀⢈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⢿⠟⠒⠲⠶⠟⠚⠉⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

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

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

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠛⠛⠉⠉⠉⠉⠉⠛⠻⠶⣤⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣯⠉⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠟⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠈⠙⠷⣦⣤⣄⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠻⣦⡀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢠⡾⠂⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀ ⠀⠀⠀⢀⣴⠟⠁⠀⣀⣤⠶⠞⠛⠻⠶⣤⡀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢤⣶⢻⡟⣶⢠⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃ ⠀⠀⢠⡟⠁⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠈⢿⣌⣛⡋⠀⠀⠀⠸⢧⡴⠛⠓⠞⠁⠀⠀⠀⠈⠛⠛⢈⣥⠟⠁⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠏⠀ ⠀⠀⣾⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡽⠟⠀⠀⠀⠀⠀⢀⣤⣤⣴⣤⣄⣀⣤⣤⠶⠞⠛⠁⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣤⣤⣤⣤⡶⠾⠋⠁⠀⠀ ⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣀⣀⣀⣀⣤⣤⣴⡟⠁⠘⣧⠀⠙⠻⠋⠛⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⢋⣩⣽⠿⣯⣽⡇⠸⠋⠀⠀⣸⡟⠷⣤⡀⠀⠀⠈⠻⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⠶⠶⠶⠚⠛⠋⠉⠀⣰⡟⠉⢀⡀⠀⣿⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣿⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠘⠷⣤⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣧⣀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⢈⣻⢦⣄⣀⣀⠀⢠⣴⣶⠞⠛⠉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠁⠀⠈⠛⢷⣤⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡠⠒⣈⠉⠹⣖⠂⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣪⠶⠛⠛⠉⠛⠛⠓⠤⡡⠀⠀⠀⠀ ⠀⠀⣴⣍⣆⣀⡴⢲⢲⣶⣤⣴⣤⣎⡣⡀⠀⠀ ⢀⢊⢘⣽⣿⡟⠀⠈⠄⢻⣘⢽⣿⣯⡁⠱⡀⠀ ⢌⣮⣯⣾⡟⠀⣉⡀⠀⠈⡡⢄⣃⣿⣷⣤⠃⠀ ⢹⠡⣿⣟⠣⣌⡀⠁⠇⠀⣓⡪⢏⣿⣾⣟⠆⠀ ⠀⠀⠿⢛⡲⢀⣀⠁⢀⣇⡀⢧⢊⡿⡣⠋⠀⠀ ⠀⠀⠀⠈⠻⢤⣸⣀⣀⣡⡀⣼⣾⡥⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠝⠉⢹⣿⣿⣿⣍⡦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⣸⣿⣿⣿⣷⡙⢌⢂

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⣀⣀⠀⠀ ⠀⣾⠛⠛⠻⢶⣤⣤⣤⣤⣤⣴⠏⠀⠈⠻⣶⠞⠛⠉⠙⣷⠀ ⠀⣿⠀⠀⠀⠀⠈⠉⠀⠀⢠⡟⠀⢠⡖⣶⠿⢶⣄⣀⣤⣿⡄ ⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣈⣻⡇⠀⠀⢹⣯⠀⠈⣿ ⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠳⢤⣴⡿⠾⠀⢀⢿ ⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠿⣷ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⠉⠀⠀⠀⠈⠙⠻⠿⣿⣿⠿⠋⠁⣰⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿ ⣿⣿⣿⠃⠀⣾⣿⣿⣶⣦⣄⣀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⠟⠀⠀⠈⠛⣿⣿⣿ ⣿⣿⣿⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠶⠘⣿⣿ ⣿⣿⣿⣷⡀⠀⠉⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠉⢿⣄⠀⠀⠀⢻⣷⣶⣶⣶⣶⣶⠚⠛⢷⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⡏⠀⠀⣹⣧⡀⠀⠀⣿⣿⣿⣿⣿⠏⠀⢀⣾⣿⣦⡀⠀⠈⣿⣿⣿⣿⣿ ⣿⣿⡟⠀⢀⣾⣿⣿⣿⣄⠀⢸⣿⣿⣿⠏⠀⣠⣿⣿⣿⣿⣷⣄⠀⠸⣿⣿⣿⣿ ⣿⡟⣀⣴⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⠏⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣶⣿⣿⣿⣷⣦⣄⣀⠀⠀⣀⣴⣾⠏⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⠁⠀⠀⠉⠙⠻⠿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⣠⣿⣿⣷⣤⠀⠀⠀ ⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣉⣧⠀⠀ ⠀⠀⠀⠈⢿⣿⣶⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣶⡀⠻⣿⣿⣿⡄⠈⠉⠉⠉⠉⠉⣥⣤⡈⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⠆⠘⢿⣿⣿⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠙⢿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⡿⠁⠀⠀⠀⠻⣿⡇⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠈⠻⣿⣇⠀⠀⠀⠀ ⠀⢠⠿⠋⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣦⣤⣄⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠒⠚⠋⠉⠉⠀⠀⠀⠀⡉⠛⢾⡄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⢲⣾⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣴⡿⠛⠿⢿⣿⣿⣽⣆⠀⠀⠀ ⠀⠀⣴⣿⠁⠀⣰⣿⣿⣿⣷⠀⠀⠀⣠⣾⡏⠀⠀⢀⣼⣿⣿⣿⣿⣦⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢰⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡏⢣⠀ ⢸⣿⣿⣿⣿⣿⡿⢿⣿⡿⠃⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⠇⠘⡇ ⢀⣿⣿⣿⣿⣯⣠⠾⠛⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⣴⠿⠟⠁⠀⠀⡇ ⠘⡇⠈⠉⠉⠉⠀⠀⠀⢀⡀⠀⠀⢀⣀⡀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡇ ⠀⢿⡀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀ ⠀⠈⣳⡀⠀⠀⠀⢀⡴⠒⠲⢄⣀⠤⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀ ⠀⠀⠐⢝⣦⣀⣠⣼⣧⡀⠀⠀⠀⠀⣰⣾⣧⣤⡀⠀⠀⠀⣠⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢽⡟⠀⣿⣷⡄⠀⠀⣨⣿⡏⠻⠎⣷⡤⠖⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠃⠀⠈⢿⣷⡀⠀⢿⡅⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠦⢤⣤⠞⠉⠉⠉⠉⠙⠦⢤⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠒⠉⠉⠉⠉⠉⠓⠂⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀ ⠀⠀⡰⠁⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠢⠀⠀ ⠀⡐⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣦⠀⠀⣰⣾⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠱⠀ ⡰⠀⠀⢀⣴⣿⠟⠉⢈⠟⠁⢹⣿⣿⡇⢀⣿⠟⠁⠀⡬⠛⣿⣿⣿⣷⣄⠀⠀⢡ ⡇⠀⣠⣿⡿⠁⠀⠀⢎⠀⢀⣼⣿⣿⡇⢸⠏⠀⠀⠘⠀⣰⣿⣿⣿⣿⣿⣦⠀⢸ ⡇⢠⠃⡿⠁⠀⠀⠀⠀⣷⣿⣿⣿⣿⡿⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⢧⢸ ⡇⡞⠀⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⢸⣆⡀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⢸⢸ ⡇⢧⠀⢷⣄⣀⣀⣴⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⢸ ⢰⠸⡄⠘⣿⡟⠻⣿⣿⣿⣿⣿⣿⡿⠁⠀⢻⣿⡉⠙⣿⣿⣿⣿⣿⣿⡏⠀⡞⡸ ⠀⢂⠹⣄⠘⣧⣠⣾⣿⡿⢿⣣⡿⠁⠀⠀⠀⠻⣿⣿⢿⡿⢟⣾⣿⠏⢀⠜⠠⠁ ⠀⠀⠢⡈⠑⠚⠿⠷⠶⠿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠛⠿⠾⠿⠿⠕⠛⠁⡰⠁⠀ ⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠠⠞⠙⠦⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⢀⣀⣀⣀⣀⣀⣀⣀⡠⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠾⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠻⠶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠙⢿⣄⠀⠀⠀⠉⠙⠻⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠳⣄⠀⠀⠀⠀⢸⠁⠈⢣⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠹⣧ ⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠸⡆⠀⠀⠀⠸⣇⠀⠈⣧⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⣠⣿⠀⠀⠀⠀⢻⣷⣾⣿⡆⠀⠀⠀⠀⠹⣆⠀⠀⢰⡿ ⠀⠀⠀⠀⢠⡿⢀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠘⡿⠿⠟⣇⠀⠀⠀⠀⠀⢹⡆⢀⣿⠃ ⠀⠀⠀⢠⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠉⠀⡇⠀⠀⠀⠀⠹⡀⠀⡏⢀⣴⣿⣿⣿⠀⢿⡿⠁⠀ ⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⡄⠀⠳⣤⡼⠁⠀⠀⠀⠀⠀⠙⠚⠁⡈⣛⠟⠛⠉⠀⢸⣧⠀⠀ ⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠃⠀⠀⢀⢲⡦⡀⠀⠀⠀⣀⣠⣤⣾⡿⠏⠀⠀⠀⠀⠀⣿⠀⠀ ⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡯⠭⣭⣿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢶⣿⣿⡛⠛⠛⠛⠾⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀ ⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠐⠛⠛⠋⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀ ⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀ ⠀⠀⠉⠛⠷⢶⣶⠶⠶⠶⠖⠛⠋⠁⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⣀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢀⣤⣿⠏⠀⠀⠀⠀⠀⠲⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣠⡴⠋⣹⡏⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣠⡴⠶⠛⠁⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠉⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣄⣀⣀⣀⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⢀⣤⣶⠆⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠙⣛⣡⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢠⠀⠐⢴⣄⠀⠀⢀⣤⣴⣶⣶⣦⣤⣀⡀⠀⢢⠄⠈⠏⠀⠄⠀⠀⠀ ⠀⢠⣠⡨⣆⠀⠈⠀⢢⣿⣿⣿⣿⡟⢻⡙⡿⣿⣿⣦⣘⠃⠀⣶⠆⠆⠀⠀⠀ ⠀⠜⣿⣯⠘⡆⠀⢴⡿⣯⡿⣭⣧⣤⢳⣿⡼⣾⣼⣿⣷⢁⠈⣻⠃⠀⠀⠀⠀ ⣤⠤⢻⣿⡇⠀⢀⣿⢹⣻⣷⣿⣿⣷⡿⢿⣷⣿⣿⣿⣿⣷⢧⡅⠈⠁⠀⠀⠀ ⠀⠀⢸⡏⠙⠄⣞⡟⣾⣿⠏⠉⢏⠿⠅⠘⠛⢘⣛⠸⣿⡿⠈⠧⠶⠂⠁⠀⠀ ⠀⠀⢸⣯⠀⢘⡻⣷⣧⡇⠀⠫⠭⠽⠁⠀⠴⡖⢒⡦⣿⡇⢀⡏⠐⠀⠀⠀⠀ ⠀⡇⠀⡿⠀⣜⢫⢿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢘⡧⠀⠀⠀⠀⠀ ⠀⡇⢀⡿⣱⡏⣾⣾⣷⣵⡀⠀⠀⠀⢀⣀⠀⠀⠀⢰⣿⣧⠈⢰⠀⠀⠀⠀⠀ ⠀⡇⠀⣼⡿⣼⣿⣳⣿⣿⣷⣄⠀⠀⠐⠂⠁⠀⣠⣿⣿⡟⡀⡄⡄⠀⠀⠀⠀ ⠀⢀⣾⣿⣽⣿⢣⣿⡿⣿⣿⠀⠑⠤⣀⣀⡤⣾⣿⣿⣿⣇⠀⢃⡇⠀⠀⠀⠀ ⣮⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣄⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡇⢸⠐⠀⠀⠀⠀ ⣿⣟⣿⣿⡿⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠢⡀⠀ ⣟⣾⣯⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠩⠀ ⣿⣿⡏⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢃ ⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠀⢀⣀⣀⣀⣀⣀⠀⠀⣿⣤⣤⣤⣤⣼⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣄⣀ ⠿⠿⠻⠿⠿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠙⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣿⣦⣄⣀⣀⣀⣤⣤⣤⣤⣴⣶⣾⣿⣿⢿⣿⣶⣶⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢫⣞⣽⣻⣿⠿⠛⠋⠉⠉⠉⠉⠙⠋⠛⠻⠿⢶⣿⣼⣏⠸⣿⡿⢿⣶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣯⣿⣟⣿⡿⠶⢶⠶⠶⠶⡶⢶⣶⣦⣤⣄⣀⠀⠀⢻⣯⢳⣭⣿⣷⣍⠿⣿⣦⡀⠀ ⠀⠀⠀⠀⣠⣶⣶⣶⣦⣄⡀⠀⢀⠠⢀⣴⣿⣿⣯⣩⣷⠟⠁⣀⠃⡄⢂⡑⢂⠐⡠⢀⠠⢀⠉⡙⣿⡀⠀⢿⣿⣟⣣⠜⣿⣖⡈⢻⣿⣆ ⢀⣤⣶⢟⣻⠟⡹⢏⣷⣿⣿⠀⠀⣠⣿⡿⠁⠀⢹⣿⠃⠠⢘⡀⠆⡈⢶⣍⠠⢈⠔⡀⢆⠈⢲⣔⠘⣷⣤⣶⠿⠛⠿⢿⣖⣿⣇⠀⠹⣿ ⢫⡷⢏⠿⣉⠎⡥⣛⣾⣲⡟⠀⣰⣿⠟⠀⠀⣀⣿⠇⠀⠀⠀⠀⠀⢈⣿⠇⠀⠁⠂⠐⠈⠂⠍⣿⣦⠈⠙⡀⡐⢈⠠⠈⠹⣿⣿⡆⢁⢹ ⣿⣧⣈⢦⡑⣎⡴⣯⡷⣿⠇⢠⣿⡟⢠⡖⢸⣹⣿⠀⡐⢂⠒⠀⢶⣾⣻⠃⠀⠤⡀⠄⡄⠀⠤⣿⣿⡄⢀⠰⣽⠀⡐⢈⠀⠌⠛⠃⡄⢈ ⣿⣽⣿⣷⣿⣻⣟⣧⠿⠋⠀⣼⣿⣣⣿⠀⢆⣿⣿⣤⣅⡂⠌⢈⢧⡟⢹⡁⠌⡐⠠⠈⠄⡁⢊⣿⠞⣿⡄⠘⣿⡄⠰⢡⢈⡒⠈⡔⢈⠄ ⠀⠀⠉⠉⠙⠉⠉⠁⠀⠀⠀⣻⣿⣿⣿⣈⣶⡝⠋⠟⠛⠿⠿⠞⠿⠃⠸⠶⠶⢶⣶⠧⣔⡠⢂⣿⠁⢺⣿⡀⢿⡃⢄⢃⠢⡱⢈⡐⠌⢂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡿⡟⢿⡅⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻⠧⠀⢸⡟⣷⣻⡇⠀⢎⠰⣁⠢⡐⢌⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢷⣙⣼⣶⣿⣄⣀⠀⠀⠈⠄⠀⠁⠂⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⡧⢈⠢⠑⡄⢢⠁⢆⡉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢏⣾⣿⠿⣿⣿⣿⣿⣷⡀⠀⠀⠀⡀⠀⠂⠀⠀⠠⠀⣴⡄⢀⠀⠀⣹⡷⣿⡷⠀⢂⠱⢈⡐⠌⢢⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢣⢾⣿⠃⡒⢄⠠⠈⠛⠿⠁⠀⠈⠀⠀⠐⠀⢀⣼⣿⣿⣿⣿⣶⣬⡄⢘⠧⣿⡏⠐⡀⣚⠠⠐⠌⡂⠌ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⣵⣿⣇⡘⠤⡉⠢⢁⠠⠀⠀⠀⠈⠀⠀⠀⠠⠘⠛⢛⠻⠿⠿⣿⣿⣿⣮⣞⣿⠅⠠⢐⡇⠄⢃⠘⡄⢃ ⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⡛⡍⣩⢙⡛⠿⣿⣦⡁⠀⠀⠘⣿⣄⣠⣴⣶⣿⣷⣿⣶⣦⣖⣠⠃⠤⣉⠉⡽⣾⡟⠀⢂⣿⢎⡁⠢⢈⠔⡡ ⠀⠀⠀⠀⠀⣴⣿⠟⡜⠁⠈⠑⡆⢣⠜⡳⣸⡽⣿⣦⡀⣴⣾⠿⠛⠉⣀⣤⡠⠤⣌⠩⡛⠿⣿⣦⠄⡽⣹⣿⠇⡈⣼⣟⡮⢀⠑⠠⢃⠖ ⠀⠀⠀⠀⣼⣿⠃⣼⠃⠀⠀⢠⡙⢢⢍⡱⢌⣿⣾⣽⣿⠟⢁⣤⡶⢟⠩⢤⡑⢎⡔⢣⢍⠲⣉⠻⣿⣔⢣⣿⠡⢰⣿⢎⡗⠠⠉⠄⢫⠜ ⠀⠀⠀⢀⣿⡿⠀⣿⡇⡔⢢⡁⢄⢣⢎⢲⠡⢎⡛⢭⢡⠛⣏⠱⣘⢢⡙⢦⡘⢦⡘⢥⡊⠵⡨⣇⠹⣿⣾⣏⢲⣿⣏⢾⡇⠐⡉⠄⢣⠚ ⠀⠀⠀⠀⣿⣷⠈⣿⡔⢬⠣⣜⠪⡜⣌⠲⡍⡖⣩⢆⢣⡙⡤⢓⡬⢢⡙⡤⣉⠦⡙⣤⠙⢦⡑⣿⡀⣿⣿⠧⣿⣏⢮⡳⡇⠱⢠⠈⢰⢋ ⠀⠀⠀⠀⢹⣿⡄⢹⣗⢌⠳⣌⠳⣘⢤⠳⣘⡜⣰⢊⡵⢬⣑⢣⡜⢥⡚⠴⣑⠮⣑⠦⡙⢦⣿⣿⠀⣿⣿⢻⣿⣜⢧⣻⡥⢙⡄⠈⠄⣫ ⠀⠀⠀⠀⠈⢿⣷⡀⢿⣎⡱⢌⡣⢍⠶⡙⢦⡜⠦⣍⠲⡥⢚⡆⡞⣥⢎⣣⠓⡼⣡⢞⣽⣿⣿⡏⣰⣿⣯⣿⣿⠿⣿⣼⡇⢺⠄⡁⢂⠱ ⠀⠀⠀⠀⠀⠈⢻⣿⣴⣮⣵⣾⣿⡌⡖⣹⠲⣘⠳⣌⠳⡜⣣⢞⡰⣭⣿⡿⣿⣴⣿⢿⣿⡽⡫⣴⣿⣿⡷⣿⢫⡝⡞⣿⣷⢹⡆⠐⠠⠘ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⠛⢣⣿⡿⢿⣿⠡⣇⠻⣌⠳⣜⢢⢿⣿⡿⠿⠃⠈⠛⠁⢸⣿⣓⣷⣿⣿⣿⣿⣏⢧⠯⣝⡜⣿⡧⣟⠠⢁⠂ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⢸⣿⣧⡳⣌⠳⣌⠳⡜⣬⣷⣾⠟⠂⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⣽⣿⣎⢯⡝⣾⡜⣿⡿⣱⠂⣂⠡ ⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⣆⡀⢂⣶⣾⡟⢏⡴⢫⠜⣣⢓⡬⣛⢿⣷⣦⣔⣢⢶⣴⣾⢿⡙⣿⣿⣿⣟⣿⣯⢞⡽⣳⣹⣿⠷⣍⠖⡠⢂ ⠀⠀⠀⠀⠀⢠⣿⣿⡜⡽⣻⣿⣿⣿⣷⣾⣮⠔⣋⢎⡱⣊⠴⣯⣾⣍⣿⣿⣿⣟⣯⣓⢮⡝⣦⢻⣿⣿⣻⣿⣾⡱⣧⣿⣏⠿⣐⠯⣐⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⡏⠁⣀⠄⢀⣀⣤⡤⢀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠷⠊⡼⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣡⢔⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑ ⠀⠀⠀⠀⠀⠀⢀⣠⡚⠍⡂⡽⠫⡕⣰⣄⠅⢸⣷⣶⣶⠶⡆⠀⠀⡠⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⢂⠜⣱⢊⠔⡳⢱⣿⡿⠃⠀⠘⢿⠟⠛⠈⠉⠙⢃⢳⡀⠃⠀⠀ ⠀⠀⠀⢀⠎⡰⢑⢎⡁⠕⠊⢀⠞⣞⣿⣦⣀⡶⠂⠀⠀⠀⣀⡀⣤⡜⠁⠀⠀⠀ ⢀⠆⠒⢅⡿⡻⠡⠘⠀⠀⠀⢸⠀⠈⠛⠟⠉⠀⠀⠀⣰⣿⣿⠁⢟⣿⣿⣆⠀⠀ ⡪⢁⠔⡿⡀⠁⠀⠀⠀⠀⠀⠀⠹⣿⡀⣄⣶⣴⣰⣀⣿⡟⠀⠀⣼⣿⠁⠀⠀⢀ ⡵⢋⣌⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠁⠂⠒⠁⠙⠋⠀⠔⢁⣿⡏⢳⠛⠋⠁ ⣰⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠀⠀⠀⠀⢀⣀⣠⡼⠶⠛⢻⠦⠥⠀⣀⠀ ⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠚⠉⠉⢙⢯⣀⠔⠂⣯⣁⠒⠈⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢀⡀⠀⣴⡤⣾⣷⠎⠁⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣔⣖⡒⠒⠤⢂⠯⠢⡈⠑⣼⠗⠛⡫⠭⠓⢖⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠙⠣⢹⢢⣀⠙⣖⠠⠬⣛⢱⠒⢁⢘⣛⠴⠶⠦⢉

⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢀⣾⡿⠋⠉⠁⢠⣿⠏⢁⣿⣿⣿⠏⠉⢸⣿⡏⠉⢻⣿⣿⡇⠈⠙⢿⣿⣿⣿⣷⡆⠀⠀⢇⠢⣈⡒⡤ ⣿⣿⣿⣿⣿⣏⣴⡇⠀⠀⠀⢠⡿⠋⠀⠀⠀⣰⣿⠋⠀⣼⣿⣿⠏⠀⠀⡾⣿⠁⠀⠀⣿⣿⣷⠀⠀⠀⠹⣿⣿⣿⣿⣄⢀⣿⣷⣿⣶⣶ ⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⡟⠁⠀⠀⠀⢰⣿⠇⠀⢰⣿⣿⡷⠀⣀⣜⣁⣻⣀⣀⣀⣸⢻⣿⡇⠀⠀⠀⠘⣿⣿⣷⠹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠃⠀⠀⣠⣿⠀⠀⠀⠀⢠⣿⡏⠀⢀⣿⣿⡿⠛⣩⣿⠿⠛⢻⡏⠉⠉⢹⠉⢿⣿⡀⠀⠀⠀⠹⣿⣿⡆⠙⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡏⠀⠀⣰⣿⡟⠀⠀⠀⢀⣾⣿⠀⠀⣸⣿⡿⢥⣶⠝⠁⠀⠀⠀⡇⠀⠀⡜⠰⡀⢻⡇⠀⠀⠀⠀⢿⣿⣿⠀⠸⣿⣿⣿⡿ ⣿⣿⢿⣿⣿⡃⠀⣼⣿⣿⡇⣀⣀⣤⣾⣿⡇⠀⠰⣼⡟⣠⠎⠁⠀⢀⣠⠔⠁⢹⣀⣠⣧⣶⣦⣤⣷⣤⣤⣠⣤⠼⣿⣿⡆⠀⢹⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣏⣁⣼⣿⣿⣿⠀⢠⣾⣟⡔⠁⠀⠀⠀⢸⠁⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣿⣿⣇⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣟⣹⣿⣿⣿⡿⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⢰⣾⢟⣻⡿⠛⢻⢋⣻⣏⣱⠞⠙⣄⡀⠀⣿⡽⣿⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢘⡅⠚⠋⠉⠁⠀⠀⠀⠀⣔⣾⢏⢦⢄⣿⣧⣿⡆⠀⠈⣿⣿ ⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⡿⢻⣿⣿⡿⠋⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠀⢂⢻⣿⣿⣿⡇⠀⠀⢽⣿ ⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣷⣿⣿⣿⣿⡷⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⢀⣠⣾⣟⡖⢻⣿⣿⠃⠀⠀⣿⣿ ⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⠟⣻⠿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠿⠛⠉⠁⢰⢸⣿⡿⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠋⠰⢟⣿⠌⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⢠⡇⣿ ⣿⣿⣿⣿⣿⣿⣏⠓⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⢾⣿⡟⠀⠀⠀⣼⠃⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⣰⠏⢰⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⣡⣴⣾⣿⣿⣿⣿⡿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⣰⠏⣠⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⣃⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣼⣿⣃⠤⠚⠚⠉⠉⠉⠙⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠀⢀⡄⠀⠀⠀⠀⠀⠀⠙⢽⣿⠿⠋⠉⠁⠀⢠⡆⢰⠃⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢯⠀⠀⠀⠀⢀⡞⢠⠋⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣸⢠⠃⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡆⢠⠉⢿⣿⣿⡟⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⡇⠇⠀⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣼⠀⠈⢿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⡗⠤⣀⠀⠀⠀⠀⠀⠑⢄⣀⡞⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⠀⠀⠹⢇⠀⢻⣿⣿⣿⣿⣿⣿⣧⠀⠈⠻⣷⣦⣤⣀⡀⠀⠉⠀⠀⠀⣀⡴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠟⠀⠀⠀⠈⠳⣄⢻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠻⢿⣿⣿⣿⣷⣶⣴⣾⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣄⠀⠀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠉⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢱⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

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

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

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

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

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

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⠶⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀ ⠀⣠⣾⠛⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀ ⣰⡿⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠹⣇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣆⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠤⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣧⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡟ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢻⠀⠻⣿⣿⣿⣯⣝⢢⣌⣙⣿⣛⠛⠛⣿⣯⠀⠀⠀⠈⢿⠀ ⠀⠀⠙⣿⣿⣿⣿⣿⣿⠋⢀⣀⠼⢧⣤⡙⢿⣿⣻⠿⢿⣟⣁⠀⠈⡇⠀⣾⢻⠂⡄⠀⠀⢸⠀ ⠀⠀⠀⠈⠀⢸⠈⢻⣿⣯⢁⣠⠤⣴⣬⠇⠸⠉⠙⠓⠻⠟⠚⠛⠋⠀⠼⠃⠀⠼⠦⠀⠀⡎⠀ ⠀⠀⠀⠀⠀⠘⣄⠀⡏⠑⠚⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠶⣾⡷⠒⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣠⠴⠒⠊⠉⠉⣙⡳⡄⢀⣤⣶⡭⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⢿⠀⠀⠀⠀⠀⢹⠁⡇⠀⠿⢄⡠⠀⠙⠢⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠻⡀⠀⠀⠿⠇⠘⠃⢧⠀⢠⠊⠀⣠⠶⠖⠙⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡥⠴⢧⣄⠀⠀⠀⠀⢀⣸⠤⣇⡀⠚⠀⡼⡅⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠘⠉⢣⠀⠀⡴⠛⠃⠀⠀⠹⡀⢠⡿⠁⠀⠀⠙⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⡇⠀⠀⠀⠀⠀⡼⠀⠀⡇⠀⠀⠀⠀⢠⡷⣾⡑⢤⡀⠀⡾⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢛⠟⢳⠀⠀⢀⡠⠾⢷⠒⢺⠛⢤⣀⡀⣄⡸⠀⠃⠑⠄⠁⢀⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⢸⠀⠈⡇⢻⡁⠀⠀⣿⠀⢸⡄⠀⠀⢰⣻⠁⠀⠀⠀⢀⠤⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⣀⣓⡠⠼⠞⠃⠀⠀⢽⠄⢸⡇⠀⠀⠀⠀⠉⠲⠤⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀ ⠀ (\__/) (•ㅅ•) Don’t talk to ＿ノヽ ノ＼＿ me or my son `/　`/ ⌒Ｙ⌒ Ｙ ヽ ever again. ( 　(三ヽ人　 /　 | |　ﾉ⌒＼ ￣￣ヽ ノ ヽ＿＿＿＞､＿_／ ｜( 王 ﾉ〈 (\__/) /ﾐ`ー―彡\ (•ㅅ•) / ╰ ╯ \ / \>

∧,,,∧ (• ⩊ •) |￣U U￣￣￣￣￣￣￣￣￣| | no inappropriate stuff pls + thanks ˚. ✦.˳·˖✶ ⋆.✧̣̇˚. | ￣￣￣￣￣￣￣￣￣￣￣￣✮ ⋆ ˚｡𖦹 ⋆｡°✩˚. ✦.˳·˖✶ ⋆.✧̣̇˚.˚. ✦.˳·˖✶ ⋆.✧̣̇˚.˚. ✦.˳·˖✶ ⋆.✧̣̇˚.

⠀⠀⠀⠀⠀⠀⣀⡠⠄⠒⠠⢄⠀⣀⠤⠒⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠐⠒⠤⡀⢀⡠⠔⠂⠠⢄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠂⢀⣀⣀⠀⠀⠉⠁⠀⣀⣀⣀⠀⠑⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⣀⣀⣀⠀⠈⠉⠀⢀⣀⣀⠀⠈⠲⡀⠀⠀⠀⠀ ⠀⠀⠀⣸⡏⠀⣴⢋⠤⢌⠙⠆⠀⢠⠎⢁⠤⠍⢧⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⢠⡞⡡⠤⡉⠳⠀⠀⡴⠉⡠⠬⡹⡄⠀⢸⡄⠀⠀⠀ ⠀⠀⢀⣽⡁⠀⣿⡀⢀⡘⡄⡇⠀⢸⢢⠇⢀⢢⣺⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣇⠀⢸⣏⠀⡐⢣⢸⠀⠀⡗⡜⢀⠐⣄⣧⠀⢸⣇⠀⠀⠀ ⠀⣰⠉⠙⠷⠀⢛⣟⣦⣄⣣⡇⠀⠘⣎⣰⣤⣾⡿⠁⠴⠋⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠉⠻⠆⠈⣿⣳⣤⣙⣼⠂⠀⢻⣁⣦⣼⣿⠇⠠⠞⠁⠙⣆⠀ ⣺⠁⠀⣠⠒⠶⣄⠉⠓⢚⣣⡠⠤⢤⣈⡓⠛⠋⢠⠖⠲⢤⡀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢐⡟⠀⢀⠔⠲⢦⡈⠑⠛⣋⣡⠤⠤⣄⣙⠚⠛⢁⡴⠒⠦⣄⠀⠨⡆ ⣽⠀⢸⠄⠣⡐⢹⠀⡤⠏⢁⢀⢀⠠⢀⠉⢦⡀⢹⡁⠔⡁⣗⠀⢸⡅⠀⠀⠀⠀⠀⠀⢸⡇⠀⡗⠘⢄⢈⡇⢠⠖⠉⡀⣀⠠⠄⡈⠳⣄⠈⣟⠠⢈⢸⠀⠀⣿ ⠹⣄⠸⣷⣤⣧⠞⣾⢁⠐⢀⠀⠠⠄⣀⠑⠄⢱⡸⣧⣴⣶⡟⢠⡟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡀⢿⣦⣾⡼⢳⡏⡠⠁⡀⠠⠠⢄⠈⠢⠈⣆⢿⣤⢶⣾⠃⣼⠃ ⠀⡸⢷⠈⠉⠉⢸⡟⣆⠀⢂⠌⣁⠒⡈⠢⢈⣾⣧⠈⠉⠉⢴⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⡆⠉⠉⠁⣾⣳⠀⡀⠆⡑⠄⢂⠙⠄⣱⣿⠀⠉⠉⠡⡾⡅⠀ ⠐⡇⠀⠀⠀⠀⠘⣿⡞⣦⣅⣂⣄⣂⣰⣵⣻⣽⠏⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⢻⣷⢳⣴⣈⣐⣈⣄⣮⣞⣯⡿⠂⠀⠀⠀⠀⣸⠀ ⠀⠘⢄⠀⠀⠀⠀⠈⠻⠶⣝⣮⣳⣭⣳⣧⠟⠋⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠙⠷⢮⣽⣭⣻⣜⣷⠾⠛⠁⠀⠀⠀⠀⡼⠃⠀ ⠀⠀⠈⡗⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡠⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠴⣟⠁⠀⠀ ⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠇⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀ ⠀⠀⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡶⣿⣿⣿⣥⣤⣀⡳⣶⣣⣶⣿⡿⠛⠻⠿⣷⡈⠛⣶⣶⣦⣉⣉⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠿⠋⢉⣤⣾⢋⣿⣿⠿⠟⢛⣿⣿⣿⣿⣿⣉⡁⠀⠀⠈⠛⠿⣤⣀⠹⣧⠀⠙⠛⢶⣭⣻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⢁⣤⣶⣲⣾⣿⣟⠘⣿⣷⣲⣾⣿⣿⣿⣿⣿⣿⣿⣭⣁⡀⠘⠲⢶⡀⠙⢷⣮⣷⢳⣄⠀⠈⠻⣽⣾⡙⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡗⣴⣿⣿⡿⣹⡟⣹⣿⣠⣿⣿⣿⣿⣿⡟⣿⢿⣿⣿⡹⣿⣿⡟⢷⣄⠀⠙⠳⣦⣜⢿⣷⠙⢷⡄⠀⠀⣿⣷⡘⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⡏⡉⣼⣿⣿⣿⡿⣿⠀⣿⣿⣟⣿⣿⣿⣿⣟⢀⡏⣟⢹⣯⢷⡘⣿⣿⣦⡙⢷⣄⠲⣌⠻⣶⡈⣷⠈⢻⣆⠀⣾⣿⣷⡌⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣱⣿⣶⣿⣿⣿⢣⣿⠄⣿⡆⣿⣿⣿⣿⢧⣿⡿⣿⢻⣿⣿⠈⣿⠀⣷⡈⢿⣿⣿⡀⢻⣧⣻⣷⣝⣿⣿⣷⣼⣿⡀⢹⣿⣿⣇⠈⢻⣯⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡏⣿⣿⡟⢸⣧⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⡇⢸⡏⣿⡆⢸⡆⠘⣧⠘⢿⣿⣷⡀⣿⣿⣿⣿⣾⣿⣿⣷⣿⣷⣦⣿⣿⣿⣧⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⢻⣿⡇⠘⣿⣿⢺⣿⣿⣿⣷⣣⡽⣿⣿⣇⠀⢻⣾⡇⠈⣿⠀⢿⢀⡘⢿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣆⡟⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⡇⣿⣿⣿⡸⣿⣇⠀⣿⣿⣾⣿⢿⣿⣿⣿⣇⢼⣿⡟⠀⠈⢿⣧⠀⣻⣧⢸⡏⢿⡈⢿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⠁⣿⣿⣿⣷⣿⣿⢸⣿⣿⣿⣿⣾⡿⣿⡇⢻⣿⣿⣿⡄⠀⠸⣿⣧⠘⢿⣯⣷⡸⣷⠀⢻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣸⡏⠻⣿⣿⣶⢀⣿⠻⣧⡈⢿⣽⢷⣿⣧⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣀⠻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⢹⣧⢸⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⣿⣿⣷⣶⣥⣽⣿⣿⣿⠦⠈⠳⣦⣽⣿⢿⣿⡿⢻⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣭⡳⢿⣶⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣷⠈⢿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠈⠁⠉⠉⠛⠓⠈⠁⠀⠀⠉⠳⣿⡇⢸⡿⣿⣿⣿⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⠻⣿⣄⠀⠀ ⠀⠀⠀⠀⠀⠸⣇⡈⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⢿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡟⠉⢻⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦⠄⢹⡽⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⢡⣾⣿⣇⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⣤⣿⣦⣬⣿⣿⣿⣟⣿⣀⡤⠀⢠⣧⣀⣿⣿⣿⣿⣿⢿⣿⡿⡇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡿⡇⠂⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⡿⠿⣄⠹⣿⠿⠿⠟⠭⣿⡿⠉⠀⠀⠸⢿⣟⠿⠿⠿⠫⣭⡿⠻⠗⡇⢠⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣷⠀⠀ ⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⣳⣿⣤⠀⣤⡴⠛⠀⠀⠀⣒⣠⡀⠙⢿⣤⣀⠀⣈⣀⣀⣼⡷⣿⠇⣾⣿⡂⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣄⡰⠀⠀⠀⠈⠁⠀⠐⠛⠁⠀⠀⠀⠚⠀⢀⣽⣷⡀⠀⠀⠈⠉⠀⠉⠀⠀⣰⠏⢰⡿⣻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡏⠀⠀ ⠀⠀⣼⣵⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡝⣿⣿⣿⡻⢷⣦⣄⣀⣀⠀⠀⠀⠀⠀⢠⣴⣞⣿⣿⣿⣿⢣⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⡾⠀⠀⠀ ⠀⠀⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⡟⠿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣟⣿⣿⣿⡿⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⢸⣿⡿⢋⣿⣿⢟⣱⢿⣿⣿⣻⠿⣯⣀⠀⠀⠀ ⠀⠀⠙⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⡃⣴⣼⡄⠉⠉⠉⠓⠊⠁⠀⠀⠀⠀⠈⢻⣭⡋⣙⠛⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⣾⠃⣠⣿⣻⡅⠈⣱⣿⡟⢹⣿⣆⠀⠉⠉⠉⠁ ⠀⠀⠀⠹⣆⢸⣏⢿⣿⣿⣿⣿⣿⣿⣄⣿⡇⠈⠛⣿⠀⠀⢀⡴⠆⠀⠀⠀⠀⣀⡴⣛⣉⣋⣙⣻⣷⢄⣀⠀⠀⠀⠙⢿⣷⣦⣾⡿⠛⣛⣉⣡⣴⣿⠟⠸⡅⠈⢯⡻⢷⣀⠀⠀⠀ ⠀⠀⠀⠀⠙⠆⢿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⠿⣀⣴⠞⠁⠀⠀⠀⠰⡾⠿⠞⠛⠉⠉⠉⠉⠉⢙⣿⠇⠀⠙⠶⢶⣭⣍⣿⣿⣿⠿⠛⣽⡿⠋⠀⠀⢷⡀⠀⠁⠀⠉⠑⠲⠄ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣹⣿⣿⢿⣿⣟⠻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣴⣶⡶⠟⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⢀⣠⣾⣟⣁⠸⣌⠛⢶⣿⣦⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠙⠿⢷⣤⣿⡟⠋⣿⣿⣦⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣾⣟⠁⠀⠀⠉⠁⡦⣷⣿⢷⣝⣷⣄⣈⡉⠉⠉⠳⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠟⢹⠁⠛⢿⣧⠤⢀⣹⡟⠀⢰⣿⣿⣿⡟⠻⣿⡦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢻⣿⣿⣦⡀⠀⠀⠀⣿⠸⣿⡇⠈⠛⠻⠶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣼⣿⣇⣰⣿⣿⡿⣿⣇⠀⠈⠙⠷⣯⣀⠀⠀⠀⠀⠀⠀⣀⢠⣽⡿⣫⠀⣸⣿⣿⣿⣿⡛⠳⢦⣸⣆⢻⣷⡀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⢀⣴⣿⠏⣿⣿⠟⠋⣴⣿⣿⣿⣆⠀⠀⠀⠈⠙⠳⠦⠤⢤⣤⣴⣶⣿⣿⣷⡟⠁⢹⣿⣿⣿⣿⣧⠀⠀⠙⣿⣿⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⢿⣟⣻⣿⡿⠟⠋⠉⣿⠃⢠⡾⢿⣿⣿⡯⠙⢿⣆⡀⠀⠀⠀⠀⠠⢨⣾⢿⣽⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠛⣧⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣴⠏⢠⡞⠀⠀⣿⣿⡇⠀⠀⠉⣿⡷⣶⡶⢾⣶⣿⣿⣿⣿⡿⠋⢀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣧⡀⠀⢹⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣧⢻⣿⣿⠀⠀⠀⢻⡇⠈⢷⣄⠀⠉⢛⣿⡿⠁⠀⣾⠃⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢹⣦⠹⣿⣇⠀⠀⠀⠻⠀⠀⠙⠲⠞⠛⠋⠀⠀⢀⡇⠐⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠈⣿⣧⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠃⠀⠀⣤⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠰⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⣻⡟⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠋⠀⣰⡟⠀⣸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠈⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡤⠚⠋⠉⠀⠀⠀⢀⣼⡟⠀⠀⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⢠⡾⣿⣇⠀⢸⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈ ⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡅⣿⣿⣶⣸⣿⣷⡀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⡄⠀⠀⠀⣤⣶⣤⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣧⠀⠸⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀ ⠀⠀⠀⡄⢀⡴⠟⢁⣾⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣦⢢⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠚⠉⠉⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣄⠀⢀ ⣠⡍⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣦⣤⣀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶ ⣿⠃⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠃⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠉⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⠀⠀⠀⣄⢸⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠁⠀⠀⡠⠎⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣇⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠂⠀⠀⠀⠀⠄⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠘⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠈⠛⢿⣿⣶⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⠉⠀⣀⣠⡶⠾⠛⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙⠳⠶⣤⣀⠀⠀⠀⢠⣿⠿⠋⠁⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢦⡀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠛⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡖⠲⢦⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⠄⠀⠀⠀⠀⠀⢠⡴⠀⣀⣠⣴⣦⡄⣿⠀⠀⢀⣠⣶⡄⠀⠀⠀⠀⠀ ⠀⣠⡴⠚⠛⠒⠦⢿⣄⠀⠈⡇⠀⣶⣶⣤⣀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠐⠛⢷⡄⠀⢸⣿⣿⣿⡿⠛⠉⠀⣿⠀⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⠈⢁⡀⣷⠀⠉⠛⠻⠿⣷⠀⠀⠘⢿⣿⣿⣼⣟⢋⣿⣿⣿⣿⡿⠋⠀⠀⠀⣴⣷⡄⠀⠀⠀⠀⠀⠀⠀⣠⠴⢿⡀⠹⣧⣤⣤⣀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⠖⠀⢰⠦⣼⠉⢿⡇⢀⣤⣶⣶⣾⡄⠀⠀⠀⢉⣟⣻⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠸⠟⠛⠛⠀⠀⠀⣀⣠⣤⣘⡅⠐⠈⢧⡀⣯⣍⡛⠛⠀⠀⠀⠀⠀ ⢿⠛⠦⠀⠀⠀⠀⠈⠷⢸⡀⠈⢿⡜⠛⠉⢡⣾⡇⠀⠀⠀⢸⡀⠀⠀⠲⠒⢀⣠⠤⠤⠤⣤⣤⣀⣀⣀⣠⡤⠖⠉⠁⠈⣆⠀⠙⣆⠀⠘⣇⠈⢻⣿⡄⠀⠀⠀⠀⠀ ⠘⢦⣀⡀⠀⣠⠴⠀⠀⠀⠀⠀⠀⠹⣦⡀⣼⡟⠀⠀⠀⠀⠀⠉⠁⠀⢨⠟⠉⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠘⡇⠀⢸⠀⠀⣹⠞⢉⣾⣃⡀⠀⠀⠀⠀ ⠀⠀⣟⠀⠀⠹⡒⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣤⡀⠀⠀⠀⠀⢠⡀⠀⣟⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸⠀⡸⠀⢠⡟⠀⠀⠀⢸⠇⠀⠀⠀⠀ ⠀⠀⠻⣇⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⢠⡏⢧⠀⠻⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸⡴⠃⢀⡞⠁⠀⠀⢠⣏⠀⠀⠀⠀⠀ ⠀⠀⠀⣹⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣼⠀⢸⡇⠀⠙⢆⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡏⠀⠀⣀⡴⠊⢀⣴⠟⠀⠀⠀⠀⠉⠈⣷⠀⠀⠀⠀ ⠀⠀⠀⣿⡀⠈⠉⢻⣿⡿⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⣷⠀⠀⠀⠙⠶⢤⣀⡎⠀⠀⠀⠀⢀⣰⡧⠴⠚⢁⣠⡶⠋⠁⠀⠀⠀⠠⣄⠀⠀⣾⠀⠀⠀⠀ ⠀⠀⠀⠹⣷⡀⠀⠀⢼⣷⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣿⣀⣀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣁⣀⣤⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀⡺⠃⢀⡼⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣷⠀⠀⠀⠙⠋⠙⠛⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⠄⠈⠉⠛⠛⠒⠓⠛⠛⢻⣿⡿⠿⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣤⡉⠀⠀⠀⠀⠀⠀⢀⡿⠓⠦⣄⣐⠒⠒⠒⢈⣱⠟⠁⠀⠀⡼⠁⠀⠀⠀⢀⡀⢠⣤⡞⠋⢃⣤⡾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣯⣥⣤⣴⣦⣤⣤⡶⠟⣷⠀⢤⡀⠉⠉⠓⠒⠋⠁⠀⠀⠀⠀⢷⣄⣀⣀⣀⣊⠀⠈⠻⣷⠻⣟⣿⣶⣦⣀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡏⠁⠀⠉⠉⠁⠐⠀⠀⠀⠀⠀⠛⠿⠒⢶⡾⠋⠁⠀⠀⣿⡀⠀⡈⠉⠲⠦⣄⣀⡀⠀⣀⠀⠀⢸⡏⠉⠙⠛⠛⠛⠛⡛⠿⠆⠉⠹⢶⡃⢹⣧⡀⠀⠀ ⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢿⡇⠀⠀⠙⠠⠤⣀⡀⠀⠀⢻⡀⠀⠘⣷⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠻⣯⡻⣿⡄⠀ ⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠓⠂⠀⠳⠀⠀⠹⣇⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠈⠳⠬⢻⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⡟⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡃⠀⡇⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠙⣇⠀⡇⢰⡏⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣽⣶⣿⠶⠷⣾⣶⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⣽⡟⢉⣠⣤⣤⣤⡈⠻⣯⡙⠻⢶⣤⣀⠀⠀⠀⠀⠀ ⠀⣀⣠⣴⠾⠛⠉⠀⠀⣸⡏⢠⣿⢋⣤⣦⡌⢻⡆⠸⣷⠀⠀⠈⠙⠿⣶⣤⣀⠀ ⠻⠿⣯⣄⡀⠀⠀⠀⠀⢿⡇⢸⣇⢸⣿⣿⡿⢸⡟⠀⣿⠀⠀⠀⠀⢀⣠⣭⡿⠟ ⠀⠀⠀⠉⢻⣷⣦⣄⡀⠘⣷⡀⠻⣦⣭⣩⣴⠿⠁⣼⠏⠀⣀⣶⣿⣟⠋⠁⠀⠀ ⠀⠀⠀⣠⡿⠁⣠⡽⠛⢷⣾⣿⣦⣄⣉⣉⣁⣴⣾⣿⡶⠟⠿⣅⡀⢻⣆⠀⠀⠀ ⠀⠀⣰⣿⠷⠋⠁⢀⣴⠟⢁⡼⠉⡿⠙⡏⢹⡉⢻⡄⠙⢦⡀⠀⠙⠳⢿⣧⠀⠀ ⠀⣴⡟⠀⠀⢀⣴⠟⠁⢀⡾⠁⢰⠇⠀⡇⠈⣧⠀⠻⡄⠀⠙⢦⡀⠀⠀⠹⣧⡀ ⣼⣿⣤⣤⣴⣿⣥⣤⣤⣾⣤⣤⣾⣤⣴⣧⣤⣿⣤⣤⣿⣦⣤⣤⣿⣦⣤⣤⣼⣷

⣾⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⣿⡇⠀⠀⠀⠀⣤⣤⣤⣄⠀⠀⠀⢠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢸⣿ ⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢠⣾⣶⡄⢸⣿⣿⣿⡇⢀⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿ ⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⡏⠈⠹⣿⣿⣿⡀⠀⠀⠸⣿⣿⣿⠈⠻⠿⠟⠁⣿⣿⣿⡄⠀⣿⣿⣿⡏⠉⠉⣿⣿⣿⣷⠉⠉⢹⣿⣿⣿⠉⠉⠁⢸⣿ ⣿⡇⠀⠀⢰⣿⣿⠀⣿⣿⣷⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⡇⢠⣶⣦⡙⠛⢃⣤⣶⣶⣤⡀⢿⣿⣿⠇⠀⣿⣿⣿⣧⣤⣴⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⣾⣿⣧⣤⣿⣿⣿⡆⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⡇⠘⣿⣿⣷⢠⣾⣿⣿⣿⣿⣿⣄⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢸⡇ ⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣇⣀⣴⣿⣿⡿⠀⠀⠈⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢸⡇ ⣿⡇⠀⣿⣿⡏⠀⠀⠀⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢸⡇ ⣿⡇⠈⠉⠉⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⣼⡇ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠰⠀⠀⠀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣤⠶⠉⣒⣚⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢁⠍⢁⢃⡴⢋⡭⡐⢺⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡎⠀⠀⠿⠶⠼⠛⠛⠋⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠐⡭⣂⠌⠓⠆⣴⣅⠖⠊⡸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⢃⠀⢃⠂⠄⢀⡀⠀⠀⠐⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⢀⠜⠀⠀⡆⠀⠀⠢⡉⠐⠂⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⠧⡄⠖⢂⠜⠀⠀⠀⠀⠈⠂⠀⢸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠑⠠⠠⠁⠀⠀⠀⠀⠀⠀⠈⡀⢸⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢸⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⡗⠀⠀⡠⠐⠂⠉⠉⠉⠐⠂⠀⠀⠀⠢⠳⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣇⡀⠖⠀⣠⣴⠢⠍⠉⠃⠀⠀⠀⠀⠀⢇⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡏⠀⠘⣧⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢸⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣗⠴⣀⠸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡰⣣⢻⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡟⢷⣌⡊⠅⣐⣢⣤⢀⡀⠤⠄⠐⠂⢁⡠⢊⣾⠃⠸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠑⠪⣖⡢⠤⠼⠵⠾⠿⠛⠓⠈⣉⡴⡟⠁⠀⠀⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠒⠒⠒⠒⠲⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠀⣋⣀⡀⠀⠀⠀⠶⠄⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠏⠁⢀⣠⡄⠀⠙⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠤⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⢀⣠⠀⢹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣧⣆⠀⢀⣾⣤⣀⡀⠀⠀⣤⣾⣰⡀⡀⠛⢰⣤⣤⣴⣿⡀⢻⣿⣧⣾⣿⣀⣤⣶⣦⣤⠀ ⢰⣶⢶⡾⣿⣿⢿⣻⣿⣿⣿⣽⣿⣿⣿⣦⣭⣿⣿⣷⣶⡾⠿⠿⠿⣿⣿⣿⣿⣿⠿⢯⣩⣽⡿⠟⠁⠀ ⢰⣿⣿⡦⢬⣉⣸⣦⣍⣀⣬⡍⢸⣯⣀⠀⣉⣉⠙⠋⣡⠤⣴⣖⣾⣿⣯⣽⡟⣻⣷⣶⣧⣽⠃⠀⠀⠀ ⠀⠀⠹⣷⣶⣯⣭⣿⣤⣼⡿⣧⡾⢿⣿⣷⣤⣼⣷⣶⣿⣶⣿⡿⠛⠛⢿⠛⠿⣿⣿⣿⠿⢿⡇⠀⠀⠀ ⠀⠀⢰⡟⣿⠛⣻⢋⢉⣻⠛⠋⢀⣠⣿⡿⠾⢿⣿⣿⠿⠛⠛⠷⣄⠀⠀⠀⢀⡿⢁⣿⣶⣿⣷⠀⠀⠀ ⠀⠀⠈⠳⣼⣿⡿⡿⣿⢿⣷⣶⣿⣿⣿⣦⣴⣶⣇⣼⣶⣿⣿⣤⣘⣿⣷⣶⣿⠿⣾⡶⠟⠉⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣛⠋⠉⠛⠛⢿⠉⣩⢿⣿⣿⡿⠟⠉⠉⠉⠙⠋⠉⣻⣿⠿⠁⣀⣞⣿⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣽⠛⣷⣧⣦⣀⣻⠀⠁⠈⣯⠟⠁⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⠿⠿⠛⢁⣴⣿⣦⡀⣀⠀ ⠀⠀⢀⣼⣿⣿⣿⣽⡟⢻⣿⣿⣄⠀⢀⣿⣾⣿⣿⣿⠛⣛⣉⣠⣤⣄⣀⣴⣦⣶⣶⣿⣿⣿⣯⠹⣟⠁ ⠀⠀⠸⣧⡭⡄⠽⣿⢿⣿⣤⣟⠛⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣛⣿⣿⣿⢿⣭⣥⠥⠤⠿⠇ ⠀⠀⠀⠘⣦⢳⡞⠻⣄⡈⠉⢉⣉⣩⣿⣿⣿⣏⣭⣿⣮⣶⣀⣴⡾⠿⠿⠿⠋⣁⣠⣤⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⣷⣶⣼⣏⣉⡉⠉⠛⠛⠛⢻⣿⣿⣿⠟⠋⠁⢀⣀⣀⣶⣾⣿⣻⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣶⣶⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢩⣋⡄⠀⠀⡷⢣⢹⢳⡀⡆⡇⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⣠⢡⠀⠀⠀⠀⠀⢳⡈⢎⣿⣢⣀⣿⣄⣙⣄⠑⡁⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢫⡾⢂⢡⠀⠈⠀⢹⢉⣪⢾⣦⣤⡄⠷⢣⠀⡖⣷⠇⠀⠀⠀⠘ ⠰⢠⠇⠀⠄⠀⢸⣷⢶⣦⣗⢄⢄⠙⢟⠑⠋⢩⣵⣮⢳⣄⣦⠀⡜⡀⠀⢀⡇⡮ ⠀⢫⡴⣀⠳⡄⠈⢿⠰⢿⡎⠂⠑⠪⠙⠁⠀⠘⠌⣋⡌⢁⣏⣬⣮⡖⣠⣿⡞⠀ ⠀⠀⠑⠹⣀⠜⢢⣲⡦⠥⡅⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⢸⠾⡾⠋⡇⣇⠀ ⠀⠀⠀⠒⠓⢚⡷⢧⣇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡌⠀⠀⠇⢃⣴ ⠀⠀⠀⠀⠀⠁⠀⡇⢿⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⢀⠃⢀⠋⠻ ⠀⠀⠀⠀⠀⠀⠀⡇⠘⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢘⠂⢸⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⢷⣄⠘⠨⣉⠀⠀⠀⠀⠀⠀⢀⡞⡇⠀⡌⠀⡼⠊⠀ ⣀⠀⠀⠀⢀⡤⠀⢐⠀⠀⠈⡇⡧⠀⠀⠀⠀⠀⢀⡤⠞⢉⣧⡇⠰⠀⢰⠁⠀⠀ ⣿⣿⣶⣶⣿⡷⠀⠀⠀⠀⠀⡇⡇⠑⠤⠄⠒⠚⡟⠀⠀⢰⣾⡧⠁⠀⣟⠠⠐⠂ ⣿⣿⣿⣿⣿⡇⠀⠀⠇⠀⠀⠇⡇⠀⠀⠀⠀⠀⠸⡀⢀⣞⡿⠁⠀⣰⠃⠀⠀⠀ ⣿⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⡇⡇⠀⠀⠀⠀⠀⣀⡧⢾⠞⠀⠀⣠⠏⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡷⠀⠀⠈⡀⠀⣇⠇⠀⠀⠀⣀⠞⠁⢀⠌⠀⢀⣴⣏⠀⠠⠤⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿⣶⣦⠄ ⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣾⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀ ⠒⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⢟⣵⠻⣿⣿⣿⣿⣿⣿⣿⣶⡦⠄⠀ ⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣷⠋⠀⠸⠟⠀⠁⠨⡟⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠶⣿⣿⡐⣽⠸⣀⡀⠐⠀⠂⢀⣰⢨⢇⣿⣿⡦⠤⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⣿⣿⣿⣿⣷⣻⡀⢸⡫⢀⡰⣤⣮⠍⣖⣼⣍⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⢿⣷⡸⡯⢉⣒⡇⠝⡏⡟⡩⠁⠈⠢⡀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⡆⢿⢫⡑⠭⣽⡘⡄⡇⡔⣱⣶⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⣼⣿⡿⠛⠉⢻⢿⣿⣿⡎⠸⣿⣦⡞⢈⠃⢁⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣮⠂⢄⠜⢰⠈⢏⣰⠀⢿⣿⣧⡈⠀⣸⢸⠉⠁⠀⣇⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣿⠠⡂⠀⡎⠀⢸⠛⡈⠙⠿⣿⣿⣶⣴⣿⣷⠤⢄⠎⡄⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⡄⠈⠀⠰⡇⡸⠊⠀⡠⠊⢹⠿⡿⣿⡿⠋⠒⠄⠁⡇⠀⠀⠀⠀⠀ ⠀⠘⢿⣿⣷⡘⡀⠀⠈⠁⠀⠁⣀⢔⣥⣦⣸⢄⠡⡀⠀⠀⠠⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⠀⠀⠀⠀⢿⣦⠀⠀⠀⣠⣾⡟⠀⠀⣀⣀⠀⠀⠀⠀⠀⠠⣀⣀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢯⡙⠦⣤⡄⠘⣏⢧⠀⡜⣷⠋⠀⠀⠀⠀⠀⠉⠉⠉⠳⠒⠒⠚⠛⠛⠓⠲⠦⢤⣉⡒⠒⠶⠶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠲⣌⠳⣄⢹⡈⡟⢰⠃⢀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠠⠤⢤⣴⢀⠂⣼⠀⠀⠀⠀⠀⠀⠀ ⣦⣀⣀⠀⠘⢦⡘⢾⣇⠁⣏⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠠⢄⡀⠙⢢⡤⠉⡸⢸⣼⡿⠲⠤⢤⣄⠀⠀⠀ ⢧⣙⢿⣷⢤⡀⣹⣌⢿⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠢⡀⠀⠀⠀⠈⠑⢾⣿⣿⢁⣿⡏⠀⠘⡄⠀⠀⠀⢦⡀ ⠶⣍⠛⠻⣿⣿⡍⠈⣾⠋⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣆⠀⠀⠙⣄⠀⠀⠀⠀⠀⢹⣿⡿⠁⢱⠐⠀⠹⡀⡠⠞⠁⢙ ⣤⣬⡷⠿⢀⣼⣿⡶⢁⡜⠁⠀⠀⡀⠀⡴⠁⠀⠀⠀⠀⡄⠀⠀⠘⡄⠀⡟⡄⠀⠀⠈⢦⣄⣀⠂⠤⣾⣋⡀⡠⢤⣴⡷⠚⣋⣀⡤⠖⠁ ⢉⡽⠀⣸⣿⣿⡿⢁⠎⠀⡜⠀⡰⠁⣰⠁⠀⠀⠀⠀⢰⣷⠀⠀⠀⢷⠀⢹⠸⡀⠀⠀⠈⢷⠶⠶⠶⣿⣤⣄⣈⣉⣉⡭⠝⠛⠉⠀⠀⣴ ⣶⣿⣿⣿⠿⣿⢁⠎⠀⡸⠀⢰⠃⢰⡏⠀⠀⠀⠀⠀⣸⣹⠸⡀⠀⢼⣇⠈⡆⢧⠀⠀⠀⠈⢧⠀⠀⠘⣿⣍⣭⣽⣿⣿⣶⣤⣤⣶⣾⠟ ⣿⣿⣿⣯⢾⠇⡼⠀⢠⠃⠀⡇⢀⣿⡇⠀⠀⠀⠀⢀⣧⢽⣄⣇⣀⣾⣿⣄⣣⣾⡀⠀⠀⠀⠘⡗⢻⣿⠿⣟⠛⣼⣿⡏⢙⡿⡿⣿⣥⣾ ⣿⣿⣿⣿⡸⢠⡇⠀⢸⠀⢸⠀⢸⣿⡧⠤⠒⠒⠉⠁⣀⣠⡀⣀⣤⠼⠿⢯⣹⣿⡇⠀⠀⠀⠀⢷⣿⣿⣛⢛⠦⠍⣻⣇⣸⣿⣡⣾⠿⠻ ⣯⣿⣇⣿⡇⢸⡇⠀⢸⠀⣸⠖⠋⠁⣀⠤⠤⠔⠒⠚⠛⠑⡿⠋⠀⠀⣠⣤⣠⣭⣿⡄⢠⠀⠀⢸⣫⣷⠌⠑⠢⢄⡀⢻⣿⣿⡟⠁⠀⠒ ⣿⣿⣻⣿⡇⢸⣇⣠⡼⠋⠀⢠⡶⠛⠓⠒⠲⠄⠀⠀⠀⠀⠀⣠⣶⠿⠟⠛⠛⠛⢻⡇⢸⡆⢀⣸⡟⡙⠓⢄⠀⠀⢱⠈⢿⣏⢿⡄⠀⠀ ⣺⣿⡏⣸⠀⠈⠉⣿⣷⣀⣶⣯⣷⣤⣴⣦⣤⣀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⢸⡇⢸⡇⢸⡦⠝⠓⠲⡈⣇⠀⠀⢇⠈⢿⣦⣻⣆⠀ ⣫⣿⡿⢻⠀⢆⠀⣿⢿⣿⡿⠟⠋⠁⢒⣁⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⣿⠋⡟⠳⣄⠀⠘⢿⡀⠀⠘⡄⢸⣿⡟⢿⣷ ⡘⣿⣷⣿⡀⢸⠀⣿⡸⣿⡀⢀⠀⡶⠁⠀⢈⣵⣎⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⢸⣿⡿⢁⡞⠀⠀⠹⡄⠀⠈⡇⠀⠀⡇⢸⣿⡇⠀⠉ ⣧⠹⣿⣿⡇⢸⡆⣿⣷⣝⡷⢢⠊⠀⠀⣰⠟⠁⠀⢉⡦⠤⡀⠀⠀⢀⡤⠊⠀⠀⣿⣿⣥⠎⠀⠀⠀⠀⣿⠀⠀⢇⠀⠀⡇⢸⣿⡇⠀⠀ ⣽⣶⣿⣿⣷⢸⣿⡿⢿⠛⠒⠒⠒⡶⠾⣀⠀⠀⡰⠋⠀⠀⢈⡷⠮⡁⠀⠀⠀⢀⣿⣠⠋⠀⠀⠀⢂⣼⠟⠀⠀⠘⠀⠀⠃⢸⢸⠃⠀⠀ ⠿⠛⠉⠀⠈⣿⠃⡰⠃⠀⠀⠀⡸⠁⠀⣨⠗⢬⡀⠀⠀⣠⠞⠁⠀⣸⡆⠀⠀⣸⣿⡇⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠃⢠⠃⠀⠀⠀⢠⠇⠀⡜⠁⠀⣸⠉⠓⢄⡁⠀⠀⣼⡿⠁⢀⣶⣿⣿⡇⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣀⡞⠀⠀⢀⡇⠀⠀⠀⢹⢦⣼⣏⣥⣶⠿⢻⣿⣿⡇⡾⡇⢀⣀⡤⠒⠊⠋⠉⠑⢦⣴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⣸⠀⠀⠀⢀⡏⠀⠉⣿⣿⠇⢀⣿⣟⣿⣷⣿⠋⠉⢸⠀⠀⢳⡀⠀⠀⠀⠘⢿⡶⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠈⠑⢄⡀⢀⡞⠀⠀⣸⣿⡏⣠⣾⣿⣿⡟⢻⡇⠀⠀⣜⠈⠋⡉⠛⠲⢤⠀⡆⠀⢱⠀⠉⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣀⣠⣶⡟⠀⠉⣻⣿⠿⢿⠁⢹⠉⢸⣶⠿⠘⣖⠛⠲⢄⣀⠈⡇⢀⣸⠀⠀⠀⠱

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⡽⠋⠕⠢⡠⣄⣤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢁⠠⠊⠀⠡⠀⡀⢱⢄⠀⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢵⣟⣍⠆⣶⠖⣷⡷⡼⢀⢆⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⡣⡀⣃⡀⢠⣿⠗⠁⡜⡌⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢈⡭⡟⠉⡟⠒⣄⠁⠚⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⡇⠤⡤⡡⠐⠉⣇⡆⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢋⡎⢈⡟⠁⠀⣄⠤⡸⠃⠀ ⢀⣶⢶⢛⡆⡀⠀⠀⠀⢀⠔⠁⠈⣣⢌⡧⠄⡰⠁⢠⡇⠀⠀ ⣸⢷⡂⣀⠕⣤⠉⠐⠨⢄⡀⡠⠊⢸⢃⠡⠊⠀⠠⠃⡇⠀⠀ ⠈⠙⠒⠂⠉⠀⠀⠀⠀⠀⠀⠁⠒⠽⣅⠀⢀⠔⠁⠀⢳⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⡖⡻⠔⠈⣀⣀⠴⡾⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⣴⣶⣶⣶⣶⣦⣴⣿⡻⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣻⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣧⣬⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿⣿⠿⠟⠛⠉⠛⠛⠋⠁⠿⠿⣿⣿⣿⣿⣿⡟⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⢻⡀⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣀⣨⡷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣏⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠗⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⡆⠀⠉⣼⣿⢿⣭⡁⠀⠀⠀⢰⣿⣿⡛⠳⡄⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡧⠀⠀⠈⠿⠾⠻⠟⠀⠀⠀⢿⣿⣿⡿⠇⠀⣼⣗⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⡟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢷⠀⠀⠀⠀⠀⠲⣼⣖⣶⣤⠄⠀⠀⠀⢀⣾⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢤⣠⣤⣤⣈⣉⡀⠀⠀⠀⠀⢸⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠈⣝⠛⢭⣽⣿⠓⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠱⢄⡀⠀⠀⠀⠀⣠⣴⡾⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠉⠉⠉⢉⣴⣿⠿⠿⣟⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣿⠀⠀⠀⣀⣠⣤⣶⠟⠋⠁⠀⠀⠈⢿⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠚⣡⣮⡽⠒⠚⠉⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠱⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⢁⣾⣈⣿⠀⣠⠅⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡋⢙⣿⣭⠒⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠉⠠⣿⡇⠇⢀⡠⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣄⣴⢢⣿⠃⠀⢤⠆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⢿⣭⣧⢃⣿⠿⠦⣶⠆⢀⣈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠏⡈⠉⢛⣾⡟⠀⠠⠆⠀⠈⠰⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣉⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡎⢠⠜⢰⣀⡛⠀⠀⠀⠀⠀⠐⠒⠻⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡜⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⠿⣿⠿⠗⠲⠖⠒⠐⠒⠒⠀⠐