Zk Emojis & Text

Copy & Paste Zk Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⠶⠶⠶⠖⠚⠛⠛⠛⠛⠓⠶⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⠶⠶⠶⠖⠚⠛⠛⠛⠛⠓⠶⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⠀⠀⢀⣀⣠⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠛⠛⠛⠿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⣠⣶⡿⠟⠋⣉⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠿⠿⢿⣿⣟⡻⢦⠀⠀⠀⠀ ⠀⠀⢠⡿⠁⠀⠀⣠⣾⣿⡿⠋⢀⣴⠿⠋⠉⠉⠉⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣴⣾⣿⠟⣷⠀⠀⠀⠀⠀ ⠀⢠⣿⠃⠀⠀⠚⠋⠙⠉⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠈⠛⠋⠀⣼⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣶⣶⣦⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⡖⠀⣰⣿⣃⠀⠀⠀⠀ ⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠴⢿⣇⠘⣿⣿⠿⠃⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠘⢿⣦⣄⣀⣀⣠⣴⣤⠾⠛⠙⠛⠻⣶⣄⠀ ⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⣀⣀⣀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⡤⢿⡿⠁⣤⡿⠛⠶⣦⠀⠹⣦ ⢸⡇⠀⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣼⠟⣿⢳⢶⡾⣧⠀⣿ ⢸⡇⠀⠱⣀⡀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢠⡟⠒⠛⠛⠚⠓⣿⠀⣿ ⢸⣇⠀⠀⠘⣇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠸⡇⠀⠀⠀⠀⢠⡟⣸⡇ ⠈⣿⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢐⡷⠀⠀⠀⢀⡿⠀⣿⠀ ⠀⢻⣧⡀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⢸⡇⠀⣿⡀ ⠀⠀⠙⢷⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⡀⣸⠇⣼⠧⠤⣄⡀⠈⣷⡀⢸⡇ ⠀⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠉⠂⠄⠀⣠⡟⠀⡟⠀⠀⠀⠙⣦⣸⡇⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⠛⠉⢹⡶⣄⠁⢸⡇⠀⣿⢻⣟⣿⢻⠉⣿⠁⢸⡇ ⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣿⠁⠀⠙⣾⡇⠀⢻⣏⠉⠙⢛⡿⠃⠀⣾⠃ ⠀⠀⠀⠀⣰⡾⠛⠁⠀⠀⢀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣨⣿⣄⠀⠈⠛⠛⠋⠁⣠⡾⠃⠀ ⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⢸⣇⣀⣀⣾⠟⠉⠉⠛⠛⢻⣆⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⣾⠏⠀⠈⠛⠲⢶⠶⠶⣿⡋⠀⠀⠀ ⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣇⡀⢀⣿⠀⠀⢹⣇⠀⠀⠀ ⠀⠀⣰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢨⣿⠀⠀⠀ ⠀⣰⡟⠀⠻⢶⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣀⣴⣄⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀ ⢠⡟⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠳⠶⠤⠤⠤⠤⠴⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠉⠉⠙⠻⠶⠶⠟⠋⠁⠀⠀⠀⠀ ⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀
⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿
⡩⢍⢩⠉⡍⢩⠩⢍⠉⣩⠉⡉⢉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠒⡌⢢⠑⢌⠢⣉⠂⠐⠤⠃⡐⠠⠈⠄⢂⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣠⣤⣤⡤⣶⣿⣿⣷⣶⣶⣦⣥⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠐⠀⡐⠈⠄⡑⢈⠠⠑⡀⠄⠀⢀⠀⢂⡁⠂⠀ ⢣⠐⢂⠩⢄⠣⠄⡁⠈⡜⠁⠀⠁⠂⠀⢂⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢁⠂⠐⡀⠀⠡⠀⠀⠠⠀⠐⠠⢀⠡⠀ ⢂⠉⠄⠃⠌⡐⢂⠀⠐⡌⠠⠁⠈⠀⠄⠈⠄⠀⠀⠀⠀⠀⠀⠀⠠⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢁⠀⠀⠡⠀⠀⠀⠀⠀⠁⡀⠀⠀ ⠂⠌⠠⠁⢂⠐⡀⠈⠠⠘⡀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⡐⣾⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠉⠉⠉⠛⠛⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠡⠐⠀⠁⠀⠂⠀⠠⠁⡑⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢯⠱⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⠘⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡿⡄⢇⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠘⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡧⢋⣴⣿⡶⣶⣤⠀⠀⠀⠄⠶⣶⡒⠳⣄⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣇⠻⢵⡿⢿⠝⢿⡳⠀⠀⠘⢿⣻⡋⠟⠀⠀⡟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣎⡳⣀⠈⠉⠀⢃⠰⠅⠀⠀⠀⠀⠀⠀⠀⠀⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡔⣡⠂⠀⣔⠿⣤⣆⢠⡄⠈⠀⠀⠀⠀⢐⡇⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⣿⣷⡥⢚⠀⣾⣿⣿⣻⢟⣶⣤⡄⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⣿⣾⣯⣄⣿⡟⣧⣬⣦⠌⠉⢻⢀⣠⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣶⣤⠞⡋⢐⣌⣿⣾⣻⡿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⢿⣿⣿⣿⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⢿⣿⠿⣿⠿⢛⠋⠁⣼⡇⢸⣿⣯⣷⡿⣯⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠁⢅⠈⠉⠁⠀⣰⣿⢣⣈⢿⣯⣿⣽⣿⢿⣿⣯⣿⢿⣽⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢶⠠⠠⡀⢀⣰⢟⡟⢵⠋⢿⣿⣾⣳⣿⣿⡿⣟⣿⣿⢿⣻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡀⢄⡃⠞⣋⣾⠇⠘⠀⢸⣿⣯⣿⣯⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠰⡌⢎⢳⡎⠀⠀⠆⡨⣿⣿⣾⣿⣻⣿⣯⣿⢿⣯⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⠨⠼⠀⠀⠊⠇⡀⣿⣿⣿⣿⣯⣿⣿⣽⣿⢿⣳⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡀⢸⡢⡆⠀⠀⠀⢧⣿⣿⣿⣿⣿⡟⠟⠛⢾⣿⣿⣟⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⠈⡇⠀⠀⠀⢃⠈⣿⣿⣿⣽⣿⡧⠰⠠⢃⢛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⠀⠀⠤⡚⡿⣽⣿⣿⣿⣿⣧⣤⣶⣽⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⡀⠀⠀⢰⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⢀⠀⠀⠀ ⡒⣄⠢⢄⠠⣀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⣠⠤⠚⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠀⠀⠀ ⠳⣌⠚⡬⢱⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠁⠀⠀ ⠳⡌⡜⡰⢃⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣀⣛⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀ ⢳⡘⡰⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⡖⠷⡟⠷⣦⣌⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⢧⡘⢡⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⣠⠟⠁⢹⣦⠀⠙⠢⢄⡀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣧⠀ ⣆⠙⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠐⠉⠀⠀⠀⡞⠉⢹⣶⡄⠀⠀⠀⠀⠀⠀⠈⣿⣷⢿⣷⣿⣿⣿⣿⣷⣿⣿⡏⠀ ⡜⢢⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢼⣿⢿⠿⠦⠄⠀⡀⠀⠀⣿⣿⣿⣻⣽⣿⣿⣟⣿⣿⠋⠀⠀ ⡜⢣⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡄⢀⢀⡀⠐⣠⣿⣿⣿⣶⡄⣁⠢⢌⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⡜⢣⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠄⡀⠐⣈⠡⡘⠬⣅⣡⣾⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⡀ ⡜⢣⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣻⣵⣶⣭⣿⣴⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠀⠀⠀⠀⠀⡀⢀⠂⠀ ⡞⡥⢋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠆⡁⠀⠄⠀ ⡳⡜⢭⡚⣥⢋⡟⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢈⠰⡁⠌⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠔⠊⠉⢱⠀⠀⢰⠉⠁⠒⢄⡀⠀⠀⠀⠀ ⠀⠀⠀⡠⣎⠀⠀⠀⢀⡜⠀⠀⠀⠣⣄⡀⣀⡽⢦⡀⠀⠀ ⠀⢀⠎⠀⠈⠑⠒⣾⡍⠀⠀⠀⠀⢠⣴⡀⢀⠔⠋⠑⡄⠀ ⠀⡞⠉⠉⠑⢄⠐⣀⠑⠑⠤⠤⠞⠉⢉⡡⢺⠀⠀⠀⢸⠀ ⢰⠀⠀⠀⠀⠘⡆⡜⠒⢢⠀⠀⢀⡠⠤⠤⢀⠓⠤⠐⠋⡇ ⠀⢦⡀⠀⢀⡼⠈⢧⠀⢰⠀⡴⠁⠀⠀⠀⠀⢱⠀⠀⡰⠁ ⠀⠀⠉⠁⠛⠒⠒⣶⣿⣳⣖⢓⡦⠤⣤⠄⠒⠚⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡿⣯⠋⣿⠏⢹⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡃⣟⠀⢸⡄⠈⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡎⣿⣿⠀⠈⠃⢹⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⣿⣿⡀⣤⣄⣼⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀ ⢾⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣴⣶⣿⣿⣿⣿⡇ ⠈⢿⣿⣿⣿⡛⠛⠈⠳⣄⠂⠀⠀⠀⠀⠀⣠⠞⠉⠛⢻⣿⣿⣿⡟⠀ ⠀⠸⣿⣿⣿⠥⠀⠀⠀⠈⢢⠀⠀⠀⠀⡜⠁⠀⠀⠀⢸⣿⣿⣿⠁⠀ ⠀⠀⣿⣿⣯⠭⠤⠀⠀⠀⠀⠃⣰⡄⠌⠀⠀⠀⠀⠨⢭⣿⣿⣿⠀⠀ ⠀⠀⠹⢿⣿⣈⣀⣀⠀⠀⠠⢴⣿⣿⡦⠀⠀⠀⣀⣈⣱⣿⠿⠃⠀⠀ ⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠘⣻⣿⣶⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⢂⠀⠀⠀⠀⠘⢸⡇⠆⠀⠀⠀⢀⠰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣷⣿⣆⡀⠀⠀⠁⠈⠀⠠⠀⠀⢀⣶⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣷⣴⡜⠀⠀⠀⠀⣦⣤⣾⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠛⠿⠿⠛⠁⠀⠀⠀⠀⠘⠿⠿⠿⠿⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣎⠁⠀⣀⣀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢿⡀⠀⠘⠛⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠤⠚⠉⣀⣠⠔⣻⡆⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣤⡶⠿⠛⠋⠉⠉⢹⢷⠆⠀⠀⠀⠠⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⡀⠀⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠙⣶⠁⢻⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⡀⣠⠏⠀⠈⠀⢠⡷⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢄⣀⣀⣀⠤⠴⠒⠚⠉⠉⠉⠀⠀⠀⠀⠀⢀⡴⠛⢛⣿⣿⡯⠀⠀⢀⡴⠋⣠⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⡠⠋⠀⣰⠃⠀⠀⠀⡠⢾⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠖⢚⣷⡤⠞⠁⠀⠀⠀⠔⠒⣻⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⢡⡀⠀⠀⠀⠀⠀⠀⠀⡰⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠋⢀⠀⠈⠉⢉⣹⠇⠀⠀⠀⠀⠀⢤⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⠈⠣⡀⠀⠀⠀⠀⠀⠀⡇⠈⣦⠀⠀⠀⠀⠀⣀⡠⠔⡋⣀⣀⣀⡴⠃⠠⠤⠒⣻⠃⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠓⠄⠀⠀⡀⢀⡠⠞⠁⠀⠉⣠⠖⠥⠤⠔⡾⠁⠀⠀⠀⢠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣄⠀⠸⢦⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⠤⠬⠽⠤⠤⠼⠿⠭⠤⠤⠤⠖⠋⠀⠀⢀⠸⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠬⠷⢄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠤⠤⣄⣽⠲⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠠⠇⠀⠈⢩⠏⡿⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⢀⡼⠀⠀⠀⡼⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠤⠤⠔⠒⠊⢀⣠⠴⠒⠁⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡁⠀⣀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⠿⠛⠿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠄⣀⡤⢤⣤⣈⠁⣠⡔⠶⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠄⠄⠄⣼⣿⠁⡀⢹⣿⣷⢹⡇⠄⠎⣿⣿⣿ ⣿⣿⣿⠿⠛⠉⠁⠄⠄⠄⠄⠄⠄⠄⠹⣇⣀⣡⣾⣿⡿⠉⠛⠒⠒⠋⠉⢸ ⡿⠋⠁⠄⠄⢀⣤⣤⡀⠄⠄⠄⠄⠄⠄⠈⠙⠛⠛⠉⠄⠄⠄⠄⠄⠄⠄⠈ ⠄⠄⠄⠄⠄⢹⣧⡈⠿⣷⣄⣀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⣠⢄⣾ ⠄⠄⠄⠄⠄⠈⠻⢿⣶⣌⣙⡛⠛⠿⠶⠶⠶⠶⠶⠖⣒⣒⣚⣋⡩⢱⣾⣿ ⠄⠄⠄⠄⠄⠄⠄⠄⠈⠉⠛⠛⠛⠻⠿⠿⠟⠛⠛⠛⠉⢉⣥⣶⣾⣿⣿⣿ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠒⠶⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠈⠻⣿⣿⣿⣿⣿⣿ ⣿⡿⠛⠛⠛⢻⣿⠿⠛⠛⠛⢿⣿⣿⡿⠛⠛⠛⢻⡟⠛⣿⡿⠛⣻⣿⣿⣿ ⡟⠄⣼⣿⣿⣿⡇⠄⣾⣿⣧⠄⢻⡏⠄⣼⣿⣿⣿⡇⠄⡟⢀⣴⣿⣿⣿⣿ ⡇⠄⣿⣿⣿⣿⡄⠄⣿⣿⣿⠄⢸⡇⠄⣿⣿⣿⣿⡇⠄⣀⠈⢻⣿⣿⣿⣿ ⣿⣄⠈⠙⠛⢻⣧⡄⠙⠛⠉⣠⣿⣷⣄⠈⠙⠛⢹⡇⠄⣿⣧⠄⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⣤⣶⣶⣄⠀⠀⣻⣿⣿⣿⣿⣿⣿⣷⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠻⠿⠿⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇ ⠘⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣶⣶⣶⡄⠀⠈⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⢿⣿⣿⣿⣿⣿⣿⡀⠀⠘⠻⠿⠿⠟⠁⠀⢀⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⠈⢿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀
⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⣋⣼⣽⣾⣽⣦⡀⠀⠀⠀ ⢀⣼⣿⣷⣾⡽⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⡿⢿⣟⣽⣾⣿⣿⣦⠀⠀ ⣸⣿⣿⣾⣿⣿⣮⣤⣤⣤⣤⡀⠀⠀⠻⣿⡯⠽⠿⠛⠛⠉⠉⢿⣿⣿⣿⣿⣷⡀ ⣿⣿⢻⣿⣿⣿⣛⡿⠿⠟⠛⠁⣀⣠⣤⣤⣶⣶⣶⣶⣷⣶⠀⠀⠻⣿⣿⣿⣿⣇ ⢻⣿⡆⢿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⣠⣶⣿⣿⣿⣿⡟ ⠈⠛⠃⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⡤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠿⣦⣤⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠉⠓⠦⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀ ⠀⠀⣠⠞⠁⠀⠀⣀⣠⣏⡀⠂⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆ ⢀⡞⠁⠀⣠⠶⠛⠉⠉⠉⠙⢦⡸⣿⡿⠀⠀⠀⡄⢀⣀⣀⡶⠀⠀⠀⢀⡄⣀⠀⣢⠟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⡞⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⢳⢀⣠⠀⠀⠀⠉⠉⠀⠀⣀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⣀⣤⠞⠁⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠁⠀⢀⣀⣀⡴⠋⢻⡉⠙⠾⡟⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠀⠀⠀⠀ ⠘⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢉⣹⣯⣍⣿⠉⠟⠀⠀⣸⠳⣄⡀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠒⠒⠒⠒⠚⠋⠁⠀⡴⠋⢀⡀⢠⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡾⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠉⠋⠻⣄⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⠳⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⠤⠶⠋⠙⠳⣆⣀⣈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠤⣶⣶⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢦⣤⡄⠒⠋⠁⠀⠀⢻⡝⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⡏⠀⢀⡀⠀⠀⠀⠀⠀⢷⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⣸⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠁⠉⢳⣴⢻⣽⣟⢦⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠋⠐⠉⠙⣿⢿⡇⠀⠀⣀⡀⠀⠀⢀⡴⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣄⠀⠀⠀⠀⠀⣰⠟⣽⠁⠀⣀⠓⠃⠀⢠⡞⣱⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣧⣦⣤⣤⡔⢋⠈⠁⠀⠀⠀⠀⠀⠀⠏⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢸⣻⣿⣿⣯⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⢠⡀⢠⡄⠀⢀⡾⡯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣡⡾⢋⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣸⢸⢠⡆⠀⠀⠀⠀⠀⠰⠞⠁⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡽⠛⠘⢿⣥⣤⣤⣤⣀⠀⠤⠠⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠶⣿⡛⠁⠀⠉⠉⠉⠙⣿⣦⢠⣰⠚⣋⣉⣁⣀⣤⠤⣶⣫⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠚⠿⠯⠭⠭⠭⠤⠼⠏⢹⢾⠿⠿⠟⠓⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⣼⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⢠⡏⠀⠘⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⣤⠏⠀⠀⠀⡿⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡶⡦⢤⣀⡴⠋⣥⣍⡻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢿⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣾⣷⣷⣶⡝⠂⠈⠀⠘⠓⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣔⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠹⣆⠀⢠⡆⠀⢀⡀⠈⠁⠀⢸⠐⣿⣿⡀⠀⠀⠀⠀⢀⢠⣶⣟⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠫⢘⢧⣼⣷⣂⡈⠉⠀⢀⣀⡌⢧⠻⣿⣷⡀⠀⠀⠀⠨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢉⣿⡟⠿⠥⣶⣟⣉⣁⣠⡤⠴⠖⠙⠟⣴⣀⠀⣽⡿⣳⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣈⣨⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣄⣀⣀⠀⢀⣀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣼⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣶⣶⣦⣤⣤⡀⠀⠀⢿⣷⣄⣹⣿⣿⣿⣿⣿⡿⠟⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣤⣤⣅⣀⣀⣀⡀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⢻⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣧⢿⣿⠏⠀⢸⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠿⠁⠀⠀⠀⠀⠈⠿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⡎⠟⠀⠀⠈⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣶⣶⣶⣿⣿⡿⢟⣫⣭⣟⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣵⣮⣭⣷⣾⣿⣿⣿⣿⣷⡜⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⡎⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉⠀⣴⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⡇⠈⠙⠻⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢰⣿⣿⣿⠟⠁⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠢⠤⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀(Ignore for z00phile rights, Like for YIPPEE) ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠦⠀ ⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⡇⠀⠀⠀⢀⡶⠛⣿⣷⡄⠀⠀⠀⣰⣿⠛⢿⣷⡄⠀⠀⠘⣿⠀ ⠀⡇⠀⠀⠀⢸⣷⣶⣿⣿⡇⠀⠀⠀⢻⣿⣶⣿⣿⣿⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠈⠛⠻⠿⠟⠁⠀⠀⠀⠈⠛⠻⠿⠛⠁⠀⠀⠀⢸⠀ ⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁ ⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⡁⠀⠀ ⠀⠀⠀⠀⠈⠙⠒⢢⡤⠤⠤⠤⠤⠤⠖⠒⠒⠋⠉⠉⠈⢙⢨⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⣿⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⠘⡆⠀⠀⢸⣀⡰⠋⣆⠀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠼⠀⠘⠤⠴⠃⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⠀⡀⠄⡒⠈⠭⠭⠥⠈⠐⣚⣛⠛⠛⠛⡲⢦⣀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠔⡨⡢⠑⠈⠉⠁⠉⠄⠀⠀⠀⡲⠀⠀⠐⢄⠀⠈⢷⠀⠀ ⠠⣤⣿⣛⡛⠛⣻⢿⣛⣟⡻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⢿⣿⣿⣿⡟⢦⡀ ⡴⠛⢡⡶⠒⡖⠦⢭⣿⣮⣱⣎⣿⣿⡿⠏⠀⠙⡿⠷⠿⣾⢿⣿⢭⡞⡐⣷ ⡇⠀⢺⠠⢾⡟⠲⢤⣀⡀⠠⠤⠄⡖⢂⣀⠀⠀⠙⣦⣄⠉⠉⢰⡄⠠⢃⣿ ⠹⣎⡪⠀⠀⢷⡦⣄⣯⡉⠓⠲⣤⣵⣉⣀⡀⠶⠞⠁⣀⣨⣴⢿⣷⠈⣰⠃ ⠀⠈⢳⡀⠀⠀⠻⣌⡟⠛⠷⣶⣧⣄⣀⣹⣏⣉⣻⣉⣉⣧⣸⣷⣿⠀⣿⠀ ⠀⠀⠀⠳⣄⠀⠀⠈⠳⢤⡀⣸⠉⠉⠛⡿⠻⠿⡿⠿⣿⢿⡿⣿⡟⠀⣿⠀ ⠀⠀⠀⠀⠈⠳⣅⡪⢔⡠⢉⡛⠲⠦⠤⠧⣤⣤⣧⡴⠧⠾⠖⠛⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣅⡒⠡⠶⠀⣠⡤⠤⠤⠤⠤⠤⠐⢁⠠⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⡀⠀⠉⠉⠉⠉⠀⢀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠚⠉⠁⠀⠀
⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⣿⣁⢈⠉⠉⣉⣉⡧⠀⠀⣼⠋⠁⠀⠘⠢⡾⠋⠉⠉⢳⠀ ⠐⠛⢻⣯⠀⢠⠋⠉⠀⠀⢸⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇ ⠀⠀⢸⡿⠀⢸⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⢴⣯⣉⣁⣀⡈⠒⠒⡀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⡠⠊⠀⠀ ⠈⠉⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠢⡠⠒⠁⠀⠀⠀⠀ ⢰⣖⠒⡀⠀⢠⣴⠒⡂⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⠈⢄⡾⠃⡜⣴⠟⢉⢥⡈⢢⢶⣯⢀⠁⠀⢰⡯⠉⡇ ⠀⠀⠈⢿⡬⢁⠌⢠⡿⠁⠆⠈⡇⢸⣿⣇⢸⠀⠀⢸⡇⠀⡇ ⠀⠀⠀⢸⡯⢻⠀⢸⡇⠀⡀⢸⠇⢸⣿⠃⢈⠀⠀⣿⡀⠀⡇ ⠀⠀⠀⣾⠁⠘⠀⢸⣧⠀⠈⠁⢀⠎⣿⠀⢺⠀⣰⡿⠀⢠⠁ ⠀⠀⠀⠛⠒⠃⠀⠈⠛⠳⠶⠖⠋⠀⢿⣄⡀⠉⠁⠀⡠⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡱⢌⢢⡑⢂⡒⡐⢂⡒⡐⢂⡒⡐⢂⡒⡐⢂⡒⡐⢂⡒⡐⢂⡒⠰⡈⢆⠱⣊⠽⣿⣷⣄⣴⣾⣿⢟⡫⢒⠥⢒⡐⢂⡒⡐⢂⡒⡐⢂⡒⡐⢂⡒⡐⢂⡒⡐⢂⡒⡐⢢ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣎⠖⡌⠱⢠⠡⢃⠔⡡⢃⠔⡡⢃⠔⡡⢃⠔⡡⢃⠔⡡⢃⠌⡱⢈⠆⡓⡌⢮⢹⣿⣿⣿⢟⡱⢊⠴⡉⢆⠣⡘⠄⢆⡉⢆⠰⣁⠣⡐⢡⠃⡔⢡⠃⡔⢡⠃⡔⢡⢂ ⣀⣴⣿⣿⣦⣄⠀⠀⠀⠀⠀⢀⣠⣶⣿⣷⣤⡀⠀⠀⠀⠀⠀⢀⣤⠾⠿⣦⣄⠀⠀⠀⠀⠀⠀⣠⣾⠿⣿⣿⣿⣯⡜⣡⠣⡜⢢⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⡄⢣⠘⡄⢣⠘⡴⣉⠞⣾⣿⡟⢣⠎⢲⠉⢆⠱⡈⢆⠱⡈⢆⡘⢄⠣⢄⠣⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢄⢊ ⠟⠟⠀⠀⠉⠛⠿⢷⣾⣶⠿⠿⠛⠉⠀⠀⠙⠻⢿⣶⡷⠾⠛⠋⠁⠀⠈⣿⠟⠳⠶⠶⠶⠶⠛⠉⠀⠀⠀⣹⣿⣿⣿⣔⣣⠜⣢⠘⡤⢃⠜⡠⢃⠜⣠⢃⡜⠬⡱⠱⣌⣣⣓⣬⢡⠳⡰⣥⣿⡿⢏⡜⡡⢎⠡⠚⡌⢢⠑⡌⢢⠑⢢⠘⡄⠣⢌⠢⡑⢌⠢⡑⢌⠢⡑⢌⠢⡑⢌⠢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠆⠀⠀⠀⠀⠀⠀⢿⡃⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠛⠛⠛⠻⢿⣿⣦⡹⣄⠣⢜⢠⠣⣘⡐⠦⣜⣵⣿⡿⠿⠛⠛⠻⢿⣷⣿⣿⡿⡙⢦⡘⢡⠊⡔⢣⠘⡄⢣⠘⠤⡉⢆⠱⣈⠱⡈⢆⠱⡈⢆⠱⡈⢆⠱⡈⢆⠱⣈⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣦⡙⢦⠁⡞⢤⢚⣷⣿⠟⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⢡⡙⢆⢌⠡⢊⠔⡡⢊⠔⡡⢊⠔⡡⢊⠔⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠄⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠐⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣯⢆⡹⣐⢣⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⢧⠘⡌⢢⠉⢆⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢄⠣⢎⠔⡣⠘⣄⠣⡘⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣴⣭⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡜⢢⠱⡈⢆⡉⢆⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢬⡑⢮⣾⡇⠱⢂⠱⣈⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡃⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠉⠛⠻⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣎⢇⠲⣁⠦⡘⠤⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢄⠣⡘⢢⡑⢭⣢⣽⣿⢋⡜⡡⢍⠒⠤⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⣻⣿⣆⠀⠀⠀⠀⢀⡠⢤⣤⣾⠏⠀⠀⠀⠀⠀⠈⣿⣷⣤⣤⣄⡀⠀⠀⠀⠀⣾⣿⣿⣎⡕⢢⢆⡑⢢⠑⣌⠢⡑⡌⢢⡑⢌⢢⢑⡊⢥⣑⢣⣞⣷⣿⡟⢥⢃⠦⡑⢌⡘⠰⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⢀⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⣾⡟⠀⠈⠉⠁⠀⠀⠀⠘⢿⣿⣿⣿⣾⣇⢦⡙⢦⢩⣄⠳⡰⢌⡥⣘⠬⣆⢣⣞⣶⣾⣿⣿⢟⡡⢚⡔⢊⠔⡡⠢⢌⡑⠢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⡀⣀⣠⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡻⢿⣿⣿⣿⣾⣶⣮⣷⣽⣾⣶⣷⣿⣿⣿⣿⡿⠿⡙⢆⠎⡔⢣⠘⡄⡊⠔⡡⠢⢌⡑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢨⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⢿⢿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢦⢍⡛⢻⠻⡟⠿⠿⠿⡟⢿⠻⢟⢫⢋⠵⣈⠧⡙⠤⢋⠔⡡⢊⠔⡡⠚⡄⢃⠆⡘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏⡞⣡⠚⡜⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢏⠲⡌⠜⡡⠣⢍⡩⢃⢇⡙⠢⡍⠎⠦⣉⠦⡁⠦⣁⠓⡌⢢⠑⡌⢢⢁⠣⡘⢄⡊⢅ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⣤⣤⣤⣤⣶⣿⢟⠻⣄⠳⣈⠔⠣⠜⣌⠛⣿⣿⣶⣤⣤⣀⣀⣤⣴⣿⡿⣋⠬⠓⡌⡑⢢⠉⢆⠒⡡⠢⢌⠱⡈⠜⡰⢠⢂⡑⠢⢄⠣⡘⢄⠣⡘⢄⠊⡔⢡⠂⡜⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⢛⠟⣛⢏⠫⣍⠲⢌⢣⠰⢡⠒⡌⢃⡚⢄⠫⡔⢬⣙⠻⢟⠿⠿⠿⡛⡍⢲⢁⠎⣑⠢⡑⢢⠉⢆⡑⢢⠑⡌⢢⢁⠣⠔⡡⢂⢌⠱⡈⢆⠱⡈⢆⠱⡈⠜⡠⢃⠜⡠⢃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢟⡰⢋⡜⠰⣊⠱⡨⠜⡂⢆⡑⢢⠑⡌⢢⠘⡄⠓⡌⢆⠢⢍⠪⡙⣌⠣⠱⠌⣅⠊⡜⢠⠃⡜⢠⠉⢆⡘⢄⠣⡘⢄⠊⠴⡁⠦⡁⢎⠰⡁⢎⠰⡁⢎⠰⣁⠚⡄⢣⠘⡄⢃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⢣⠎⡔⠣⢌⠱⣀⠣⠔⡡⡘⠤⡘⢄⠣⡘⢄⠣⢌⠱⡈⢆⡑⢊⠔⡡⢂⡙⠰⡉⢄⠣⡘⢄⠣⡘⠤⡉⢆⡘⢄⠣⡘⠤⡉⢆⡑⢢⠑⡌⢢⠑⡌⢢⠑⡌⠒⡄⢣⠘⡄⢣⠘⠤ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠲⡌⢥⢊⣵⣿⡿⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣯⣢⡑⢎⠰⣁⠎⡰⢁⠎⡰⢁⠎⡰⢈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡓⡜⣢⢽⣾⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣾⣌⡓⢤⠚⡄⢣⠘⡄⢣⠘⡄⠣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡴⢣⣾⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⡱⢌⢣⡘⢄⠣⡘⢄⠣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣣⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣘⢢⠜⡠⢃⠜⡠⢃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⢣⠱⢌⠢⡑⠌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠻⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣮⢘⠆⡱⢈⠜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣦⠀⠀⠀⠉⠻⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠹⣿⣇⢎⡱⢈⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣄⣀⣀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⡶⠾⠿⠋⠁⠀⠀⠀⠀⠀⢿⣿⠢⣅⠋⡌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⡀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡓⠬⡑⢌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢦⣀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡃⠧⡑⢌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠛⠿⣿⣿⣶⣤⣶⣶⣿⣶⣶⣶⣦⣤⣄⡀⠉⠙⠓⠚⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡉⢖⡉⢆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⡭⢏⡽⣙⠻⠿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠣⡜⢢⠜⢢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⢦⢡⠋⢖⡡⢎⡛⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢣⠱⡌⢣⢎⣱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠠⢇⠚⢤⠘⢢⡉⠖⡬⢛⠿⣿⣿⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠻⣤⢣⣳⣼⣷⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡓⢬⡉⢆⡉⠆⠬⡑⠦⣉⠶⢨⢍⡛⠻⠿⠿⡿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣿⠿⠟⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣍⠲⡌⢢⠘⡌⢢⠑⡒⠤⢊⢅⠢⣉⠱⣉⢎⠱⢒⠬⠥⣋⠭⣍⢫⡝⣻⣿⣿⣿⡛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠈⠙⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⢲⢡⠣⡘⢄⠣⡘⢄⠣⢌⠢⡑⠤⢃⠔⡨⢊⡒⢌⡒⣡⠒⣌⠲⣜⣵⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠈⠛⠿⣿⣶⣤⣄⣀⡀⠀⠀⢿⣿⣧⡎⡱⡡⢎⠔⣡⠊⡔⡊⡔⢡⠎⡐⢎⡑⢆⡩⢒⠼⢤⣻⣼⣿⣿⣿⣿⠿⣟⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣿⠿⣿⣿⣿⣿⣿⣥⣓⣎⠚⡤⢓⡜⠴⣘⠆⡎⠵⢪⣜⣦⣵⣿⣾⣿⠿⠛⠉⠙⢿⣿⣝⣮⣽⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⢀⣼⣿⠿⠟⠛⠉⠉⠉⠛⠻⢿⣿⣦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠧⠤⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠃⠀⠀⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡿⠙⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣠⡶⠤⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢲⣤⠮⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣾⡿⣫⢾⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⣩⠞⣫⡾⣡⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⣉⡴⠋⣡⡾⢋⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⣁⡴⠞⠉⣠⠞⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁⣠⠴⠚⠉⢀⡰⠞⠁⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢷⣦⡀⣀⣠⣤⡶⠶⠛⠋⠉⣹⠇⠀⠀⠀⣀⣠⡤⠖⠒⠋⠉⠀⣠⡴⠒⠉⠀⢀⣠⠖⠋⢀⡤⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠀⠀⠀⠀⠀⢠⡟⠒⠊⠉⠉⠁⠀⠀⣀⣤⠔⠚⠉⠁⠀⢀⣠⠖⠋⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⢀⣠⣤⠤⠒⠚⠉⠁⠀⠀⠀⣀⠴⠚⠉⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠉⠁⠀⠀⠀⠀⠀⣀⣠⠴⠒⠉⠁⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣀⣀⡤⠴⠒⠋⠉⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣞⠉⠉⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠻⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠈⠻⡛⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣥⡀⠀⡈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢠⡾⠋⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡾⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡄⠀⠀⠀⡀⠀⠀⠀⠀⠘⣧⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠙⠶⠶⣿⠋⠀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢶⣄⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣿⡋⠀⠀⠀⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠙⠷⠞⠛⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀ ⠀⠉⠙⣇⣰⠓⠚⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠶⣾⡇⠀⠀⠀ ⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣤⣤⡀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢯⡄⢠⣽⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣼⠟⠒⠒⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠏⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡄⠀⠀⠀ ⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀ ⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀ ⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢹⡄ ⡏⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇ ⣿⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⡇ ⢹⡆⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣾⠀ ⠈⢷⡀⢸⡇⠀⢀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣤⣄⠀⠀⣿⠀⣼⠃⠀ ⠀⠈⢷⣼⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡾⠃⠀⠀ ⠀⠀⠈⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠘⢿⣿⣿⣿⣿⡿⠃⠀⢠⠀⣄⠀⠀⠙⢿⣿⣿⣿⡿⠏⠀⠀⢘⡇⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⠉⠀⠀⠀⣴⣿⠀⣿⣷⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣟⠳⣦⡀⠀⠀⠀⠸⣿⡿⠀⢻⣿⡟⠀⠀⠀⠀⣤⡾⢻⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⢻⠻⣆⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⢀⡾⢻⠁⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⡆⢹⠒⡦⢤⠤⡤⢤⢤⡤⣤⠤⡔⡿⢁⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⠀⢣⢸⠦⣧⣼⣀⡇⢸⢀⣇⣸⣠⡷⢇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠺⣄⣇⢸⠉⡏⢹⠉⡏⢹⢀⣧⠾⠋⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠈⠉⠙⠓⠚⠚⠋⠉⠁⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠦⣤⣤⣤⡤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⠄⠀⢀⣠⣤⣴⣶⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿ ⠐⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰⠟⠉⠛⢻⡏ ⠀⠀⢀⡀⢠⣤⣤⣤⣄⣠⠀⠀⠀⢀⠀⠀⠀⠀⢄⣤⣴⠮⠁⠀⠀⠀⢡ ⢴⠞⠛⠋⠩⣀⠀⣼⣿⣿⣷⢲⠶⠊⠁⠀⠀⠀⣿⣏⣠⠶⠚⠛⣻⣿⠃ ⠀⠀⠢⠴⣤⣤⣤⣤⠴⠶⠂⠀⠀⠀⠀⠀⠀⠀⠈⠓⡯⢬⣥⣌⣛⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠤⠭⠟⠿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣀⡀⠀⢀⣀⡠⣀⣀⠄⠀⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠿⢿⣿⣿⣿⣤⣴⡗⠁⠀⠀⡾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠌⠙⠛⢧⣀⡴⠋⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⢀⡠⠄⠤⠀⢀⣀⣠⣤⣤⣄⣀⡴⢦⣶⣾⡿⠀⠀⠀ ⠀⠀⠀⣴⣶⣶⣬⣥⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⢦⡈⡍⠛⠻⣿⠿⣿⣿⣿⣿⣭⢿⣯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠠⢀⠀⠈⠛⠉⠀⠈⠟⢛⣻⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⡀⡈⠀⢬⢵⣖⣒⢲⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣋⡇⠉⠹⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣯⣤⡯⠿⢽⣷⡈⣬⡟⢦⡀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⡴⢺⣙⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⣛⡟⠢⢄⣱⡈⢣⣤⣶⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣏⢻⣟⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⣷⡖⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣯⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣟⠣⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣯⣽⣿⣿⣿⣹⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠀⠀⠈⠈⠉⠙⠉⠉⠙⠿⣿⣏⣿⣷⣿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡿⠛⢻⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⢠⠾⠋⠀⠀⠘⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⠛⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⡀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢹⠿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢺⣿⣿⣿⣿⣿⡇⠹⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣀⣀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⠶⢶⣦⡀⠈⠛⠉⠂⠀⠀⠘⠛⠉⠉⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⡎⠐⣋⡴⣟⠳⢿⣿⣿⣿⣿⣿⡿⠸⡄⠐⠢⢤⡈⠻⣆⠀⠀⠀⠀⢠⣶⣴⠶⠶⣦⣀⣿⣿⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠸⠒⠠⠁⢸⣿⣿⣿⣿⣿⡇⠀⣿⣿⣳⡂⣸⠀⠁⠀⠀⠀⠀⣸⣻⡔⠀⠀⣈⡿⣿⣿⣿⠃⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠑⠒⠒⢻⣿⣿⣿⣿⠿⠰⣦⣈⢛⣛⣉⠁⠀⠀⠀⠀⠀⠀⠀⠸⠁⣠⠿⢻⡇⣿⡿⠃⢸⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣀⣼⣿⣿⣿⣿⡀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠢⢭⣡⢤⣿⣷⠟⠁⠠⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⢠⢼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣟⠲⢄⣀⠀⠀⠀⠀⠀⠀⢀⠠⠚⠁⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⣸⣿⡿⣟⣿⣿⣿⣿⣿⠋⠙⠢⢌⣉⣲⠤⠤⢖⡾⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠤⠒⠊⡟⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣻⣿⣿⣽⣿⣶⣤⠀⡿⠘⣧⣴⡿⠧⣤⠔⠚⠛⢉⣼⠟⢡⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠃⣼⣿⣿⠃⠀⠀⠉⠒⠢⣌⣀⡀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠊⣉⣉⠉⠉⠉⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠐⢿⣿⣿⣦⡀⠀⠀⠀⠱⢄⠀⠀⠀⠀⡄⠶⠛⠙⠛⠉⠒⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⣈⣅⣤⡤⠶⠒⠛⠛⠳⢯⡷⠶⢶⣾⣷⣆⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡶⠶⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠉⠉⠙⠷⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠃⠀⠀⠄⠀⠀⠻⢧⡀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠉⠳⢦⣄⡀⠀⠀⢰⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡐⠀⠀⠁⠀⠄⠀⠀⢀⠈⠀⠀⠄⠀⠀⡀⠀⠀⠂⢀⠀⠀⠉⠉⠛⠳⠛⠻⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠠⠀⠁⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠠⠀⢀⠀⠂⡀⠐⠀⠤⢠⡁⠚⢷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⡀⠂⠠⠐⠀⠄⠂⢀⠊⠀⣃⢦⢡⠉⠄⠛⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠁⡀⠐⡀⣀⠁⢠⢡⡌⣀⢆⡄⡌⡰⣈⠆⣻⠜⡂⠑⠬⢿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢃⣀⠀⠠⠀⠀⠄⠀⡀⠠⣀⢐⡈⣠⣄⢦⡵⢴⠮⠿⢶⠿⣾⣿⣶⣝⣷⣑⢪⡕⣏⡒⠈⢈⣹⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢻⣿⣿⣷⣿⡶⠿⠾⠓⠚⠋⠉⠁⠈⣀⠤⣄⣆⢳⡬⡶⢤⢠⢉⠋⠻⣽⢦⣹⣿⢡⠂⠀⢼⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⢶⣰⠾⣶⣷⡾⢿⣾⣸⢷⣹⢿⣿⢷⡏⣰⠀⡀⠰⠈⠱⠀⢀⠸⣾⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣦⣜⣦⣻⣞⣷⣯⣶⣷⣿⣷⣿⣾⣟⣾⡝⣧⢟⡾⣿⣿⣿⢧⡝⣦⣒⢤⣀⣦⣠⢾⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣹⢯⣝⣮⢻⡜⣿⣿⣿⣿⣳⣯⣾⣿⣿⢿⣯⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢏⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣻⠶⣭⡗⣞⢧⣿⢿⣿⣿⣿⣿⣿⣿⣟⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣎⠜⣧⡻⣽⢿⣿⣿⣿⣿⣽⣿⣎⣿⣦⣽⡞⣮⢼⣛⢾⡹⢯⣿⣿⣳⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⣰⢻⣭⣛⢿⣯⢿⣿⣟⣯⣟⣼⡷⣯⣝⢮⣳⠻⣬⣛⣿⣼⣿⣽⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⠠⠙⣯⠓⢮⠛⣾⡹⣷⡻⣯⣟⣾⡷⣟⡷⣯⢯⣷⣻⡷⣿⣾⡿⣟⣿⢸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⡿⠁⠀⠁⠰⣯⠈⠤⡙⢤⠳⣵⣟⡿⣾⣻⣽⣟⣿⣿⣿⣿⣯⣿⣿⣯⣿⡻⢾⡉⢇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢨⣴⠋⠀⠀⠀⠀⠀⣿⠀⡄⠑⢢⢱⡏⣾⣽⢳⡝⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣯⡝⢻⡄⢩⢻⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣀⣴⡟⠉⠀⠠⠁⠀⠀⠀⠘⢷⣄⠑⢢⠙⣼⢣⡽⣻⢷⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣭⢳⠽⢀⠡⢈⠙⢧⠀ ⠀⠀⠀⠀⢀⣠⡶⠞⡉⠆⡍⡒⠠⢀⣠⣆⠀⠀⠀⠀⠀⠀⠙⠷⣦⣑⠮⣳⢟⣽⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣞⠯⠊⢄⠘⡠⠈⠊⡷ ⠀⠀⠀⣤⠟⡉⠐⡀⢂⡱⢊⣥⣿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠾⢷⣿⣼⣷⣟⣿⣿⣿⡿⠿⠛⠋⠌⠤⣉⠂⠄⠡⢀⠁⡗ ⠀⣠⡊⢀⢂⠤⣱⣸⣿⣿⣝⠨⣁⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠂⠀⠄
⠀⠀⠀⠀⢀⣠⡤⠴⠶⠒⠒⠛⠛⠛⠉⠉⠛⠫⠍⣉⠉⠉⠛⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⢠⠖⠋⠁⢈⠩⠭⠀⣀⠀⠀⠀⠀⠄⠀⠉⠥⢐⡩⡒⢄⠀⠈⢷⡀⠀⠀⠀ ⠀⠀⡿⠀⠀⠐⠁⠀⠀⠀⠂⠀⠀⠀⠘⢀⣠⣤⣤⣄⡈⠪⠀⠀⠀⠀⢷⡀⠀⠀ ⣠⠞⡡⠤⠤⠐⠾⠿⢿⣷⣦⣀⠀⠀⢶⣋⣥⠼⣿⠿⠿⠧⠐⠄⣀⣀⠶⢿⣦⡀ ⣯⢃⠫⠶⠲⣦⣀⡄⠀⠀⣽⠀⠀⠀⠀⠉⠀⠀⠘⠳⠦⠴⠖⠋⣩⠉⠻⡄⢩⢳ ⢿⢌⠂⢠⣷⠀⠀⣀⣴⣏⠁⠀⢀⣀⣘⢳⡖⠂⠀⢀⣀⣤⠶⠛⣹⠷⠆⡇⠈⢸ ⠘⣧⠈⢸⡿⣷⣬⣀⡀⠘⠷⡖⢀⣀⣈⣼⣵⠶⠛⠉⣩⣇⣤⣶⠟⠀⠈⢕⣡⠏ ⠀⢸⠀⢸⣧⣷⣀⣏⣉⣙⣏⡉⣹⡏⣀⣀⣸⣦⣶⠿⠛⣏⣰⠋⠀⠀⢀⡾⠁⠀ ⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠟⠛⠉⣿⠀⢀⡤⠟⠁⠀⠀⢠⡞⠀⠀⠀ ⠀⢸⠀⠀⠳⣧⣽⣌⣧⡀⣻⡀⠀⣸⣀⣀⣤⠼⠟⢋⠠⢀⠠⣀⡴⠋⠀⠀⠀⠀ ⠀⣾⠀⡄⠐⢄⡀⠉⠉⠉⠉⠉⠉⠉⠉⡀⠠⣐⠪⢕⣪⡵⠞⠉⠀⠀⠀⠀⠀⠀ ⠀⢿⡀⠈⠒⠤⠤⠭⠭⠭⠍⠉⠒⠒⠀⢉⣡⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⢤⣀⣀⣀⣀⣀⣀⣠⡤⠶⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⡿⢿⣇⠀⠀⠀⠀⣠⠤⢄⣀⣀⣠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠳⠾⠿⣿⣿⣾⣭⣉⣹⠉⠓⡞⡿⠤⠤⢄⣉⣉⡙⢲⡋⠉⠑⣒⠲⠴⣥⣴⣉⣀⠀⠀⠀⠀⠉⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠧⠧⢄⣀⣀⣀⣀⡀⢉⠉⢱⠏⠉⠛⠛⠻⠶⡆⠸⡉⠉⠓⣲⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠽⢿⡤⣤⣀⣀⣀⠀⠛⠤⣉⣿⡆⠙⠙⡷⠶⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢩⠇⢀⢞⣯⡏⣻⣿⣿⠧⠤⣤⣀⣧⠀⠈⠉⠉⠙⠓⠲⠦⠤⣤⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡠⠃⢀⠎⣼⠏⠉⢻⠓⢿⣕⢆⢻⣇⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠚⢁⡠⠊⠀⡠⢃⡾⠁⠀⠀⠻⣷⣄⢽⡌⡌⢏⢧⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡎⠁⣀⠴⣪⡴⠋⠀⠀⠈⠀⠀⣄⠀⠀⠿⠶⠾⠼⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⠵⠛⠁⠀⠀⠀⠀⠀⠀⠀⠹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⠶⠻
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢉⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⡱⠖⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠆⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠒⢴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢨⠀⣰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢹⡀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⢠⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⣀⣀⣀⡠⠋⠀⠀⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣄⠊⠁⠀⠀⠀⠀⠀⢀⡨⢦⠀⠀⠀⠀⠀⠀⠀⠘⠒⠤⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠔⠊⠁⢀⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⡀⠄⠂⠉⢀⡀⢰⠁⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢊⠠⠒⣁⠤⠐⣀⡁⠤⢤⠃⢀⣀⡠⢄⡀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⡪⢐⡡⢐⠩⠐⠊⠁⠀⠀⠀⠚⠉⠉⠀⠀⠀⠙⠢⣀⡇⠀⠀⠀⠀ ⠀⠀⢠⡪⡪⡲⠕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⣰⣿⠞⠉⠀⠀⠀⠀⠀⡄⡰⡆⠀⠀⠀⠀⠀⠀⢐⣌⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⡐⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠤⠔⠒⠒⠒⠒⠒⠒⠒⠦⢄⣀⠀⠀⠀⠀ ⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀ ⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀ ⢸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠈⡇ ⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡇ ⠘⡆⢸⠀⢀⣀⣤⣄⡀⠀⠀⠀⢀⣤⣤⣄⡀⠀⡇⡸⠀ ⠀⠘⣾⠀⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⠀⡗⠁⠀ ⠀⠀⣿⠀⠙⢿⣿⠿⠃⢠⢠⡀⠙⠿⣿⠿⠃⠀⡇⠀⠀ ⠀⠀⠘⣄⡀⠀⠀⠀⢠⣿⢸⣿⠀⠀⠀⠀⠀⣠⠇⠀⠀ ⠀⠀⠀⠀⡏⢷⡄⠀⠘⠟⠈⠿⠁⠀⢠⡞⡹⠁⠀⠀⠀ ⠀⠀⠀⠀⢹⠸⠘⢢⢠⠤⠤⡤⡄⢰⢡⠁⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠣⣹⢸⠒⠒⡗⡇⣩⠌⢀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢧⡀⠀⠉⠉⠉⠉⠁⠀⣀⠜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⠤⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠛⠛⠛⠉⠉⠉⠛⠛⢷⣤⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⡟⢠⣴⠾⠛⢋⣉⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣻⣯⣭⣭⣽⣶⣦⠙⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡞⣠⣤⣼⣿⣿⣿⡿⣿⡦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢻⡿⣿⣿⣿⣿⣿⡿⣿⡅⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣻⣿⣿⣿⣿⣿⣭⣿⠇⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣌⣻⢿⣿⣿⣷⢏⡇⠘⡄⢒⣿⣷⠄ ⢠⣤⠄⣽⢿⡹⣿⣿⣿⣿⣫⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠒⠚⠁⠀⠙⠁⢀⡏⠀ ⢻⡈⠑⠺⠈⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀ ⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀ ⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀ ⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢢⡼⣆⠀⠀ ⠀⠀⢀⣽⣀⠀⠀⠀⠀⢠⣤⣄⠀⢀⡀⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠀⠀⠀⠀⢀⡞⠁⠀⣿⠀⠀ ⠀⠀⣾⣧⠈⠙⡆⠀⠀⠀⠀⠉⠛⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⡼⢧⠀⢀⡿⠀⠀ ⠀⠀⢹⡟⠦⠀⡿⢆⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠈⠙⠋⠀⠀⠀ ⠀⠀⠀⠈⠓⠚⠁⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠾⠿⠟⠛⠉⠉⠉⠛⠛⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⣠⣶⣿⠟⠛⠿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⢀⣴⡾⠟⠉⠉⠉⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠜⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⢠⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣿⡟⠀⠀⠀⠀⠀⡀⠀⠀⣼⣿⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⣸⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢸⣿⡇⠀⠀⠀⠀⠀⣷⡄⠀⢿⣿⠀⠀⣾⡿⠀⢀⣼⣇⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠘⣿⠁⠀⠀⠀⠀⠰⣿⡇⠀⢸⡿⠀⢠⣿⠇⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢠⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⢿⣧⠀⠀⠀⠀⠀⠋⠀⠀⣹⡇⠀⢸⣿⣇⠀⠘⢿⠃⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⣼⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡈⣻⣷⣄⣀⠀⠀⠀⢀⣸⣿⠀⠀⠘⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⢀⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⢿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠻⣿⣧⣄⣀⣀⣀⣀⣠⣴⠟⠋⠀⠀⢠⣾⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣍⠙⠻⠿⠛⠃⠀⠀⠀⠀⠀⠀⠠⢤⣝⡻⠿⣿⣯⣿⢟⡥⠀⠀⣠⡼⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠾⡶⠒⢂⣠⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⢠⣾⣏⣠⣾⣿⣟⣛⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⢿⣿⢿⡟⠉⠀⡿⠉⣡⣿⠁⠠⠉⢛⠛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⠈⠷⠀⠀⠷⠀⠈⠁⠀⠀⠀⠘⣷⡿⢷⣶⠦⠤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣧⣸⡏⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠒⠶⢶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⡀⠀⠈⢉⡉⠉⠛⠲⠶⢦⣤⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⡴⠟⣰⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠠⠴⠦⢤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⢀⣠⡴⠞⢋⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⢀⡄⠀⠀⣿⡟⠛⠿⠶⠶⣦⣤⣭⣭⣍⣉⣙⣛⣛⣓⣛⣛⣩⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢷⣤⣀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠠⠤⠤⢤⠤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⢀⠠⣒⠨⠅⢀⡀⠉⠭⠄⠐⠀⠈⠭⠭⠓⠦⣄⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⠀⢂⢕⠜⠊⠁⠀⠀⠈⠆⠀⠀⠀⡌⠉⠉⠐⢂⠀⠈⣇⠀⠀ ⠀⠀⣠⣾⠥⠄⠀⢤⢄⣶⣿⢿⣿⣉⠳⣄⠀⢀⣀⣥⣶⣶⣶⠄⠤⠀⣘⢦⡀ ⠀⡞⡍⣠⠞⢉⡝⠲⠤⠤⠴⠊⠀⠈⠙⠁⠀⠀⢹⡏⠀⠀⣀⣠⢤⠦⠕⠡⣿ ⠘⣇⠃⢿⠰⢻⡉⠓⢦⣤⣀⠀⠀⢲⡚⣃⣄⠀⠀⢉⣷⠄⡀⠁⣸⡄⢐⣱⡟ ⠀⠙⢮⡂⠀⠈⢻⡶⢤⣧⣉⠙⠓⡶⠥⢤⣀⣀⣳⣋⣀⣠⡤⢾⢻⣷⠁⡞⠀ ⠀⠀⠀⠹⡄⠀⠀⠙⣤⡏⠙⠻⢿⣧⣤⣤⣼⣤⣤⣿⣤⣤⣧⣼⣾⡿⠀⡇⠀ ⠀⠀⠀⠀⠻⣄⠀⠀⠈⠛⢦⣄⡞⠀⠀⠉⡟⠛⢛⡿⢛⡿⣻⢿⣿⠇⠀⡇⠀ ⠀⠀⠀⠀⠀⠈⠓⢮⣔⡩⢐⡨⢉⠛⠒⠶⠷⠶⠾⠷⠾⠷⠛⠛⡉⢀⠀⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣅⠘⠓⠰⠄⢀⡀⡀⠀⠒⣒⣈⠠⠘⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠦⢤⣀⣀⡀⠀⠀⠀⢀⣀⡴⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⢌⡛⠒⢦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠚⠁⠀⣀⡠⠒⠚⡄⠑⠀⠈⠳⡄⠀⠀⠀ ⠀⢀⡞⠁⠠⠦⠀⠀⠀⠀⠸⠠⠀⠀⢀⠤⠜⣆⠀⠀ ⢀⡎⠀⠀⠡⡀⠀⠐⠂⠀⠈⠀⠀⠀⣁⠀⣀⣸⡆⠀ ⢸⠀⡤⡀⠀⡧⠀⠀⠀⠀⠠⠤⠀⠨⠀⠀⠀⠀⢧⠀ ⠀⢧⠀⠈⢀⠆⣤⣤⣶⣶⣦⣤⠁⢀⠔⣢⣴⣶⢨⠇ ⠀⠘⡆⡄⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⣼⣿⣿⣿⡏⠀ ⠀⠀⢻⠀⠇⠀⠙⢿⣿⣿⡿⢿⠀⠁⠻⠿⠿⢿⡅⠀ ⠀⠀⢈⡷⢼⠈⢈⣀⠠⠀⠐⠊⢀⣾⡟⣦⠤⠼⠁⠀ ⠀⠀⠘⣆⠅⣽⠉⠘⡆⠆⠀⢀⠛⠓⡁⢻⠀⠀⠀⠀ ⠀⠀⠀⢺⠐⠙⢦⢀⡧⣈⣘⣈⣀⣢⣣⣾⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⢌⠈⠛⢷⣓⡜⢤⠧⡗⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠉⠍⠉⡀⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠤⠴⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠦⠴⠤⠀⠤⠤⠆⠤⠤⠄⠰⠀⠲⠴⠦⠀⠀⠀
⠀⠀⠀⢀⡴⠋⠉⢉⠍⣉⡉⠉⠉⠉⠓⠲⠶⠤⣄⠀⠀⠀ ⠀⠀⢀⠎⠀⠪⠾⢊⣁⣀⡀⠄⠀⠀⡌⠉⠁⠄⠀⢳⠀⠀ ⠀⣰⠟⣢⣤⣐⠘⠛⣻⠻⠭⠇⠀⢤⡶⠟⠛⠂⠀⢌⢷⡀ ⢸⢈⢸⠠⡶⠬⣉⡉⠁⠀⣠⢄⡀⠀⠳⣄⠑⠚⣏⠁⣪⠇ ⠀⢯⡊⠀⠹⡦⣼⣍⠛⢲⠯⢭⣁⣲⣚⣁⣬⢾⢿⠈⡜⠀ ⠀⠀⠙⡄⠀⠘⢾⡉⠙⡟⠶⢶⣿⣶⣿⣶⣿⣾⣿⠀⡇⠀ ⠀⠀⠀⠙⢦⣤⡠⡙⠲⠧⠀⣠⣇⣨⣏⣽⡹⠽⠏⠀⡇⠀ ⠀⠀⠀⠀⠀⠈⠙⠦⢕⡋⠶⠄⣤⠤⠤⠤⠤⠂⡠⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⠤⣄⣀⣀⣀⣠⠔⠁⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠉⠙⠓⠦⣄⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠛⠛⠛⠶⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣀⣠⠤⣄⣀⠈⣧⡤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⢴⣟⠉⢀⣀⣀⣀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⠀⠀⣠⠎⠁⠀⠀⢠⡞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣇⠀⠀⠈⢳⡄⠀⠀⠀⠈⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⠀⠀⡏⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⡤⠤⠤⣤⡀⠀⠀⠀⠀⠀⢀⡔⠋⠉⠉⠓⢤⡈⢳⡀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠀⠀⠀⢷⣀⢀⡜⠁⠀⠀⢀⡴⠋⠁⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠙⣄⠙⣆⣰⡇⠀⠀⠀⣼⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢉⡟⠀⠀⠀⣠⠏⠀⠀⠀⣀⠤⣤⡄⢸⡀⠀⠀⠀⠀⡇⠀⣰⣶⡖⣦⠀⠀⠘⣧⠘⣯⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⡾⠁⠀⠀⣰⠇⠀⠀⠀⢸⢿⣿⣿⡇⡼⠀⠀⠀⠀⠸⢧⠀⣿⣿⣿⣿⡇⠀⠀⠘⡆⠘⡖⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⣿⠀⠀⠀⠀⠘⠾⠯⢟⣷⠃⠀⠀⠀⠀⠀⠈⢷⡈⠻⠿⠟⠁⠀⠀⠀⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⠶⡄⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⢀⣴⠟⠁⢀⡤⠖⠒⠒⠒⢦⡀⠙⠦⣄⣀⠀⠀⢀⡴⠃⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣇⠀⠹⣄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠊⠉⠀⠀⠀⢫⡀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⡄⠈⢦⡀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠣⣀⠿⢆⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⣼⠃⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⡈⢧⡈⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠶⠷⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⣄⠹⣎⠉⠙⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠞⠉⠁⠀⠈⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠏⠳⡈⠳⣄⠀⠀⢠⡌⠉⠙⠒⠲⠦⠤⠤⠤⠤⠤⠖⠒⠒⠚⠉⠉⠉⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢙⣦⠬⠷⠤⠿⣄⡀⠀⠀⠀⠀⣀⡤⠴⠦⠶⠶⠶⠦⠤⣤⣀⡀⠀⠀⠈⣆⠀⢀⣀⡤⠤⠀⠀⠘⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⣭⣲⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀⣼⠖⠉⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣍⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣗⡿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⠋⢐⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣴⣲⠄⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠘⢺⣤⡟⣙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠠⢯⡷⠀⠀⠀⢀⣠⡾⣁⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⠉⠛⠿⣏⠉⠀⠉⠣⡀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⣶⣶⠞⠛⠉⠉⠉⠉⠙⢶⡀⠀ ⠀⠀⠀⠀⠀⡴⠋⠀⣠⣤⡴⣶⣶⣤⣀⠈⠳⣄⠀⠀⠘⢦⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⣀⣤⣴⡶⠶⢤⣄⠀⠀⢹⡄ ⠀⠀⠀⠀⣼⠃⢠⠟⢩⡿⢧⣻⣄⡇⠈⠙⢦⡈⢳⡀⠀⠀⠹⣤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣣⡴⠋⢱⣇⣀⣷⠤⢄⠈⢳⠀⢨⡇ ⠀⠀⠀⠀⢿⡀⣾⢀⣘⣧⠼⠃⣀⠤⠶⠦⡄⠙⢆⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⣠⠖⠒⠲⣄⠻⢤⣞⣀⢸⢀⡼⠁ ⠀⠀⠀⠀⠈⢷⡸⣼⣀⣹⠀⡴⠁⠀⠀⠀⣸⠀⠈⢿⣿⢤⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣠⠴⢾⡿⠀⠐⣇⠀⠀⠀⠈⡆⠸⣀⡼⣾⠞⠁⠀ ⠀⠀⠀⠀⠀⠈⠻⣽⣍⠁⠀⠳⣄⣀⣠⠖⠁⠀⠀⠀⣻⠀⠀⠈⣉⡉⠉⠉⣉⣁⣀⣤⣄⣀⣀⢸⡇⠀⠀⠘⠶⠤⠤⠞⠁⢀⣸⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠒⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠙⠻⢦⣄⣀⣠⣤⣤⠶⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⢉⣉⠛⠓⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢁⡤⣄⠈⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⢤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠖⠁⠀⠀⠑⢄⡀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣶⣄⡀⠈⠳⣄⠀⢀⣼ ⠀⠀⢀⣀⠀⠀⠀⠀⣀⡤⠖⠉⡠⠊⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠉⠓⠲⣆⣠⣴⣶⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⢷⣿⣿ ⠀⢰⠛⠬⠭⠭⠭⢭⠥⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢈⣠⣴⣾⣿⣿⣿⣿⣿⣿⣶⣿⣧⣭⣽⡿⣿⣿⣿⣿⣿⣿⣿⣆⣸⡿⠁ ⠀⠘⡟⠲⢤⡀⠀⠈⢷⣜⡄⠀⠀⠀⠠⠀⠒⠊⠉⠉⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⡟⣿⢛⣿⣿⣿⠀⠀ ⣇⠀⠘⢦⡀⠀⠀⠀⠈⢿⣿⣦⣤⣀⠀⠀⢀⣠⣶⣿⣿⣿⣿⠿⠟⠁⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡄⠀ ⠘⣧⣄⡀⠙⠢⣀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣽⡿⣿⠛⠁⣾⣏⠀⠀⠀⢠⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀ ⠀⠘⢿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣯⣍⠀⠈⠛⠛⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⡏⠉⠉⣹⠋⣸⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⠀⠀⣈⣉⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣿⢶⠋⠁⠀⢸⣇⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠘⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⡛⠋⠉⠀⠀⠀⠀⣼⣿⠃⣰⣿⣿⠋⣿⣟⢘⠋⣿⣽ ⠀⠀⠀⠀⠀⠐⠛⢹⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⡅⢿⣿⣿⣿⢵⣿⣿⣿⣧⡄⠈⠻⠂⠀⠀⠀⠀⢘⣿⠃⢐⣿⡿⢧⠀⣿⣿⣿⣷⣿⣿ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣄⠀⡀⠀⢠⣿⣷⣼⣿⣿⣇⠘⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣠⡿⣁⣴⠟⠁⠀⠀⢹⣿⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣦⠙⢤⣀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠈⠀⠀⠀⠀⣠⣤⣴⣾⠿⢛⣿⣿⣿⠟⢷⣦⢼⣿⣿⣿⣿⡟⠐ ⠀⠀⠀⠀⢀⣨⠽⠛⠉⣽⣿⣿⣿⣿⣆⠀⠀⢹⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣿⣿⣿⣿⠆⠀⣿⣸⣿⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⢻⡏⠉⠉⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠃⠀⠐⣻⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠿⣷⡾⠁⠀⢰⣿⢿⣿⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⣿⣿⣿⣿⣿⣇⠀ ⠀⠀⠀⠀⡿⣿⠑⠒⠾⣋⣁⢠⡋⠀⠀⠀⠀⢿⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢁⠀⢿⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠀⢧⣈⣷⡄⠀⠀⠉⠢⣈⠳⢄⠀⠀⢸⢿⠃⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠙⢮⣷⣾⣿⣿⣹⠈⠻⡄ ⠀⠀⠀⠚⠋⠉⠀⣹⡄⠀⠀⠀⠈⠣⡀⠑⢄⣾⡄⠀⣼⠃⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡇⠀⠈⠙⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠐⢶⡦⣄⡐⣿⠀⠀⠀⠀⠀⠙⢄⠀⠙⢿⡆⠙⢦⣴⡾⣷⡤⡀⠀⠀⢀⡠⠤⠄⠒⠊⠉⢨⢷⣿⠇⠀⠀⠀⢾⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣦⠻⣾⡇⠀⠀⠀⠀⠀⠈⢣⡀⣸⡇⠀⠘⣯⢷⡟⡇⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣠⣊⠀⢀⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣧⠘⣧⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⣄⠀⡿⠈⠧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠴⠢⢸⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠻⣟⠳⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠻⣿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⡀⠀⠀⠀ ⠀⠀⠀⢹⢱⣿⣿⣿⣿⣿⣿⣿⣇⢀⡠⠤⠖⠒⠒⠒⠂⠀⠀⠀⠀⠀⠘⠐⠿⠿⢧⣐⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀ ⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⣿⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣏⣼⣿⣿⣿⣿⣿⣿⣿⡌⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⣯⠄⢀⣐⣒⣂⡐⠤⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠤⣴⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⠋⣲⢿⡿⣿⢍⡙⠻⣷⡄⠀⠀⠀⠀⠀⠉⣥⣾⢿⠛⠶⣦⣍⠠⡈⢻⣿⣿⣿⣿⣿⣿⠿⠦⠄⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⠱⡿⢛⣀⠇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠃⡀⠬⣽⢧⠈⢻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠛⠒⠮⠭⣶⡃⠈⣠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⡻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠘⠀⢿⡿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣧⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀ ⠀⠀⠀⠈⠁⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛ ⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⡗⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⢻⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣯⣸⢿⣿⣿⣿⡇⠀⠉⠓⢤⣀⡀⠀⠀⠀⣀⡠⠔⠊⠀⣼⡿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢟⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣧⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⣿⡿⠋⢹⡇⠘⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣶⣿⡿⣿⣿⣿⣿⣶⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⡈⠻⢶⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣸⣿⣟⡿⢷⣿⣿⣿⣿⣿⡐⢩⢛⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠁⠚⠀⠄⠀⠀⠸⠻⣿⣤⣿⡟⢿⣿⣿⣿⣿⣿⣿ ⣠⣴⣏⢁⣠⣟⠀⣠⣿⣿⣿⣿⣿⣿⣾⣎⣩⣙⡛⣦⡀⠀⠀⢀⣠⢴⣏⢁⣂⣀⣀⣤⣠⠍⢀⣠⡃⣀⣠⣿⠟⠳⣾⣿⣿⡇⠙⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠙⢦⡀⠀⠀⠀⢀⡴⠋⠁⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣦⣤⡤⢤⣄⣀⣀⣠⡷⡄⠈⠙⠦⣄⣰⡏⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠷⠚⡑⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠚⠛⠛⢒⡶⠋⠁⣀⡤⠤⠖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢉⡉⠉⠓⠒⠒⠒⠒⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠈⠁⢠⠴⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠤⡤⠤⠖⠒⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⢀⡤⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡙⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠒⠉⠉⣩⠟⣰⠋⠀⢠⠇⠀⢠⠏⠀⠀⠀⡼⢁⡔⡸⠀⠀⡆⠀⢤⠀⡄⠰⣧⠀⠹⣄⠉⠒⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣡⠖⢁⠞⣠⡏⠀⢠⠏⠀⠀⢀⡞⣠⠞⢠⠇⠀⢠⣿⠀⢸⡆⢷⠀⢻⢦⡀⠈⠣⣀⠀ ⠀⠀⠀⠀⠀⠀⠴⠾⠛⠉⣇⡴⠋⡴⢋⡇⢀⡞⠀⣠⢇⣾⡼⠁⠀⡜⠀⢠⠎⢹⢀⡇⢁⢸⠀⢸⠀⠉⠓⠤⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡤⠞⣠⠾⡄⡼⠀⣴⣯⣾⣿⣿⣷⣰⠃⣠⢿⣶⣾⣿⣶⣼⡘⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠤⠾⡏⠙⡟⣡⠞⢹⣿⣿⣿⣿⣿⡿⠖⠧⣾⣿⣿⣿⣿⣿⣧⣧⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⡇⢧⠀⠘⢿⣿⣿⣿⡿⠁⠀⠀⠘⣿⣿⣿⣿⠟⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢦⡄⠀⠀⠉⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⣠⡤⢤⣄⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⡇⠀⠀⠀⠀⠓⠲⠒⠋⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡬⢍⡙⡻⣖⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⣸⣏⢳⢱⠀⠀⣤⣴⡖⠶⠒⢦⣠⣀⣠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⡛⢟⡾⡀⣞⠛⠈⠁⠀⢀⡀⠀⢯⠖⣫⣭⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣜⣷⣷⣯⣀⣰⣄⣳⠞⠙⢦⣊⣷⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣹⡟⣷⡼⣧⣀⠀⣠⠷⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡼⠉⠙⠲⢦⡈⢫⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠙⠓⠤⣀⡀⠀⠉⢉⣻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠦⣄⡀⠀⠀⠈⠙⠛⠛⠻⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠏⡅⡏⠀⠀⠉⠉⠉⠀⣶⣦⣄⣴⢿⣧⣽⢿⣿⣿⣿⢷⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢠⡁⠁⠀⠀⢶⠀⠀⠀⣸⠟⠛⠷⣄⣉⣨⣿⣿⣿⣷⣄⠙⢦⡙⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠔⢲⡀⠀⠀⠀⡴⠁⠀⠀⠀⢀⡇⠀⡀⠀⣀⣀⣠⠔⠁⠀⠀⠀⠀⠀⣿⣿⣿⠉⠉⠉⠑⠦⠼⣿⣷⣦⠀⠀⠀⠀ ⠀⢠⣔⣊⣁⣀⣀⣉⣹⠶⣾⠁⠀⠀⠀⢀⡼⠻⠞⠉⣡⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⣀⣠⡄ ⠀⠀⠀⢀⣀⣀⠜⠁⠀⠘⠁⠀⠀⢀⣾⠏⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠀ ⣤⠖⠉⠁⢀⠁⢀⣀⣀⣀⣒⠾⠓⠛⠛⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⢀⣀⠤⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠖⠛⠓⢶⡄⠀⠀⠀⠀⢠⡶⠚⠛⠓⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⡤⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢤⣀⠈⠙⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡞⠁⢀⡴⠋⠀⠀⠀⣰⠏⠀⠀⠀⠀⠹⣦⠀⠀⠀⠘⢷⡀⠈⠻⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⠟⠀⢀⡞⢁⡄⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⠙⢷⠀⠀⢠⡀⢳⡄⠀⠹⣆⠀⠀⠀ ⠀⠀⢠⠏⠀⢠⣾⣿⡞⢁⠄⠀⠙⣦⠀⠀⠀⠀⠀⠀⣴⠋⠀⠠⡄⢳⣿⣿⡄⠀⠹⡄⠀⠀ ⠀⢀⡞⠀⢠⡾⠻⣿⣧⡎⢠⠀⣴⠋⠀⠀⠀⠀⠀⠀⠙⢧⠀⣄⢹⣼⣿⡛⢿⡆⠀⢻⡄⠀ ⠀⣸⠁⠀⣼⠃⢀⡏⣿⣧⣏⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣸⣾⣿⢹⡄⠈⣧⠀⠈⣧⠀ ⠀⡇⠀⠀⡿⠀⣼⠀⡭⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⢩⠀⢷⠀⢻⡀⠀⢸⡄ ⢸⡇⠀⢸⠳⣴⣇⢰⠇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠸⡆⢸⣷⠞⡇⠀⢸⡇ ⢸⡇⠀⢿⣾⣹⢻⣿⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣿⣏⣧⣷⣿⠀⢸⡇ ⢸⡇⠀⡿⠋⡟⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢻⠉⢻⠀⢸⡇ ⠀⣷⠀⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⢸⠀⢸⠀⣾⠀ ⠀⢹⡄⡇⡄⣗⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣸⣦⣸⢀⡏⠀ ⠀⠈⣧⢹⣻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⣸⠁⠀ ⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠒⠒⠶⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀ ⠀⢠⠋⠀⠀⠀⠀⣀⣀⣤⠤⠶⠖⠒⠒⠛⠉⠙⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀ ⠀⡇⢀⣠⡴⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀ ⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠦⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠀⣠⠖⣿⠿⢦⡀ ⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠙⣆⠀⡞⠁⡞⠉⢆⠀⡇ ⠀⢻⠀⠀⠀⠀⠀⢀⠀⢲⠀⣠⣠⣴⡿⣿⣿⣿⣶⣮⡥⠴⠀⠀⠀⠀⠘⣦⡇⢸⡏⠲⡌⣧⡇ ⠀⠸⣦⣴⣶⣦⣤⣼⡆⠀⠙⠛⢿⠯⠼⠛⠛⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⣷⠀⠈⣼⠀ ⠀⠠⢟⣻⣿⣿⣿⡿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⡀⠘⡝⠀ ⠀⠀⠈⢿⢛⠻⠉⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⡰⠁⠀ ⠀⠀⠀⢸⠀⠁⠀⠀⠀⢸⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠒⠊⠀⠀⠀ ⠀⠀⠀⠘⡆⠀⠀⠀⢀⡟⠀⠀⠀⠀⣘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⡄⠀⠀⠸⢧⣀⣀⣰⠿⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢠⠤⠤⠒⣉⡽⠷⣶⡶⠂⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠸⢿⡉⠉⠁⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⣠⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠉⢉⡽⠗⠒⠂⠒⠈⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⣀⡤⠤⠖⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠛⠲⢦⣄⡀⢀⣠⠿⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠙⠿⣥⡀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡏⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠉⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⣀⣀⣀⣤⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⡻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⠉⢉⣽⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣶⣌⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠿⠟⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⠷⣽⣯⠻⠖⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡈⠻⠷⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠘⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠹⣟⠷⣤⣀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠉⠛⠶⣆⣠⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠷⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣀⣀⣀⡀⡀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⢘⣛⣛⡛⢛⡛⣟⣛⣛⣛⡟⠛⠛⢻⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⣉⣉⢉⢉⢉⣉⣙⣛⣛⣛⣛⣛⣛⢛⣛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠖⠒⠒⠛⠋⠉⠉⠉⠙⠛⠓⠒⠲⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠀⠀⠀⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡿⠹⣿⠀⠀⠀⣾⠏⢿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⠟⠋⠀⠀⢻⡇⠀⢸⡟⠀⠀⠙⠻⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⣸⠇⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⠿⠟⣻⣽⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣤⣤⣬⣉⠛⠻⠿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠘⣇⠀⠀ ⠀⠀⣿⠀⠀⠀⢀⣴⡾⠿⠟⢿⡏⠉⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣼⡇⠀⢸⣷⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠉⢹⣿⠻⠿⠿⣦⡀⠀⠀⠀⣿⠀⠀ ⠀⠀⣿⠀⠀⠀⠁⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⣿⣿⣿⣿⠛⣿⣿⣿⣿⠀⠀⠀⣸⡿⠀⠀⠀⢿⣇⠀⠀⠀⠀⣿⣿⣿⠛⣿⣿⣿⡇⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠈⠁⠀⠀⣿⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣰⡿⠁⠀⠀⠀⠈⢿⣦⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠶⣤⡈⢿⣿⣿⣿⣿⣿⠟⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠈⠿⣿⣿⣿⡿⠋⢀⣤⠶⠻⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣹⣶⣌⣉⣉⣉⣥⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⣀⣀⣤⣴⣏⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀ ⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⠶⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠷⠶⠶⢦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳ ⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⢤⣀⣀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡏ ⠸⡄⠀⠀⠀⠀⠀⣀⡤⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣈⠳⣤⡀⠀⠀⠀⠀⢠⠇ ⠀⢷⡄⠀⠀⣠⡿⠋⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠊⢿⣆⠀⠀⠀⡾⠀ ⠀⠈⢻⡄⠀⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⢠⡞⠁⠀ ⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠤⢤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡤⠤⠶⠚⠋⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⢏⢙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⠉⠑⢄⠈⠳⣄⠀⢀⣀⣀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣶⣧⣤⠄⠀⠉⠢⡈⠋⠁⠀⠀⠉⠓⠦⣄⡀⣦⣀⡠⠤⣄⠀⠀⠀⠀⠀ ⠈⣟⢯⣇⠁⠀⠀⠀⠈⢶⣆⠀⠀⠀⠀⠀⣴⠽⠚⣉⣠⠇⣾⠀⠀⠀⠀⠀ ⠀⠙⣆⠹⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠀⠀⠠⠔⠋⣡⠋⢘⡏⠀⠀⠀⠀⠀ ⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠋⠀⢀⢾⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⣼⣋⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⢀⢰⣇⠀⠀⠀⣺⠆⠀⠀⠀⠀⠙⠢⣄⠀ ⠀⠀⠀⠀⠀⢸⢠⠀⢀⠀⠰⡄⠀⡷⡇⠀⠀⠉⠁⠀⠀⠀⠀⢐⠚⠻⣍⠀ ⠀⠀⠀⠀⠀⠾⠛⡦⡿⡷⢷⡟⠢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠂ ⠀⠀⠀⠀⠀⠀⠀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢋⣉⣉⣉⣉⣉⣉⣙⠛⠻⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣤⠔⠚⠉⠉⠀⠀⠀⠀⠈⠉⠙⠓⠦⣬⡉⠻⡟⠉⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠈⠙⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣟⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠛⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⠤⠤⠤⠤⠬⢿⣦⡀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠤⠤⣤⣤⣀⣈⣙⢷⣄⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⣉⣥⠴⠖⠚⠒⠒⠒⠲⢶⣤⣄⡀⠙⢦⣤⡴⠖⠛⠉⣉⣁⣠⣤⣤⣤⣤⣤⣄⣉⠉⠉⠛⢷⣄⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⠤⠶⠟⢉⣠⠶⠋⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠉⣉⣳⡾⣏⡤⠶⠚⠉⣉⣉⣠⠤⣤⣤⣤⣦⣬⣯⠭⢽⣲⡦⣿⣄⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣶⠶⠿⠴⠖⠛⠉⠀⠀⠀⣀⣠⠤⣶⡾⠻⣿⣿⣿⣿⣿⣆⠀⠀⠉⢻⠶⠖⠛⠋⠁⠀⢀⣾⡿⠟⣿⣿⣿⣿⣿⣆⠀⠙⠛⢿⡂ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠛⠓⠲⠦⣤⣤⡤⠴⠒⠛⠁⠀⣾⣿⣧⣾⣿⣿⡿⠛⢿⣿⣧⠀⠀⣸⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⡄⠀⠀⢸⡇ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⢷⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣆⡴⣯⣄⡀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣧⣴⣿⣿⣧⡦⣶⠏⠁ ⠀⣼⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣈⡉⠓⠶⠿⣿⣷⣽⣿⣿⣿⣷⣿⡿⠛⢁⡰⠏⠈⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠛⠉⠁⣼⠿⠋⠀⠀ ⣸⠃⠘⠻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠦⠤⢭⣍⣉⣉⣁⣤⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠃⠀⠀⠀⠀ ⡏⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⢀⣀⣠⣤⣴⡖⠋⠁⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⠉⠉⠁⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⡀⠀⠀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⠶⠶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣾⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀⠀⠀⢻⡀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⢤⡾⠋⠁⢠⡄⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷⡀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢰⣸⡃⠀⠀⠀⣿⡀⠀⠀⠀⠘⢿⡿⠯⢭⣍⣙⣛⠻⠻⢿⠿⠿⠿⠿⡇⠿⠿⠿⠿⠿⠿⠿⠛⢛⣉⣭⠴⠞⠋⠉⣳⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠘⠷⣄⡀⠀⠉⠙⠓⠺⠾⠷⢤⣄⣀⣀⡈⢳⡀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠋⠉⠀⠀⠀⠀⣀⣴⠟⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠈⠙⠳⢦⣤⣀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠛⠒⠒⠦⠤⠤⣤⣤⣤⣄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠴⠒⢾⡋⠁⠀⠀⠀⠀ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠉⠉⠙⠓⠶⠶⠦⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀ ⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠚⠒⠒⠒⠲⠶⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⠤⠤⠶⠛⠁⠀⠀⠀⠀⠀⠀ ⣶⣾⣟⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣶⣯⣙⠗⠶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣈⡉⠙⠛⠛⠒⠶⠦⠤⠤⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣀⣀⣁⣠⣤⣴⣾⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠰⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⢰⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣆⡀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⠀⣠⣾⠃⠀⣀⠀⠀ ⠠⠂⠉⠉⠑⢈⠙⠻⠿⠛⠁⠀⢰⠀⠀⠀⠀⣶⠀⠀⠈⠛⠛⠋⠡⠂⠁⠀⠈⠠ ⠂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⢧⡼⠿⡾⠏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⡀⠌
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣶⣖⢶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⡀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣶⣤⡀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⣿⣿⣟⣛⣛⣛⡿⣿⣿⣷ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣶⡿⣿⣿⣿⣟⣾⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣽⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣯⣻⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣿⣿⣿⣽⣿⣿⣿⣿⡿⢫⠟⠻⣯⠿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣽⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣿⡇⣿⣿⣿⡿⠿⠿⠉⠛⣁⣀⣀⣼⣿⣿⣿⣾⣿⠻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣧⣿⣿⡟⠀⠀⠀⣰⣿⢿⣿⣿⠋⠁⠈⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿ ⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⠀⠀⠀⠀⠻⢀⣠⣿⣧⣄⣴⣿⠿⡿⢛⣷⣯⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⣼⣿ ⠀⠀⠀⠈⠉⠛⠛⠛⠛⢛⣿⣿⣿⣿⣿⣸⣿⣷⡕⠀⠀⠀⠀⢠⠁⣰⣿⣿⣭⣌⠂⠐⠡⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⣿⡿⣿⣿⣿⣿⣏⣾⣿⣿⣿⢹⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡀⠀⠀⠀⢰⣿⠏⣠⡤⠉⣷⠀⣸⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⡿⣽⣿⣿⣿⡇⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣯⣿⣿⣿⣿⡏⣉⠻⣷⣁⠀⠀⠀⢼⡿⣧⣉⠏⢁⣿⡶⠟⢻⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣭⣭⣿⣯⣭⣿⣷⣾⣿⣿⣿⣿⣿⡇⣼⣿ ⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⡻⢅⣿⡇⠀⠀⠀⢸⣟⣜⣿⡿⠟⢋⣀⠀⣸⣋⡈⢹⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣇⡿⠿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠚⠛⠛⠛⣭⣽⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⡷⠀⠀⠀⡜⠛⡋⢀⣤⣾⡿⣿⣻⠛⠟⣟⣿⣿⣿⣿⣿⣿⣽⣿⣟⣿⣿⣿⣿⡿⠋⠀⢠⠤⢄⡀⠙⠻⣿⣿⣿⣿⣿⣿⣿ ⠀⣠⣠⣤⣄⣀⣴⣶⣿⢹⣿⣿⣿⣿⣿⣿⣿⣶⣿⣍⠛⠀⠀⠀⠀⠰⢁⣾⡟⢥⣼⣮⢿⡦⢬⣿⠃⣽⣿⣿⣿⣯⣿⣿⣿⣼⣿⣿⣷⡅⠀⢠⠚⠒⠲⡄⢀⠀⢹⣿⣟⣿⣻⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⡿⣿⣿⣿⡟⢹⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣼⣻⣷⣿⡿⠿⠥⠞⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣶⡈⠓⠀⠀⠃⠀⠀⢨⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣷⠚⣟⣿⣆⠀⠀⠀⠀⢸⡻⠿⠾⠿⠛⠉⠀⠀⠐⢶⣿⠿⠟⠁⢹⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⢾⣿⣿⣿⡇⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⡀⠉⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣼⣿ ⣿⣿⣿⣻⡿⣾⣿⣿⣿⣿⣿⣟⣭⣿⣿⣿⣿⣿⡇⠀⠚⠀⠀⠀⠀⠀⠘⠻⣿⣿⡿⢛⡙⠻⣿⣿⣶⣄⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿ ⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠸⠿⣄⣹⡇⣿⣿⡆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣽⣿⣿⣿⣿⡎⢹⠙⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣿⡶⢿⢾⣕⢿⣿⠀⢠⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢸ ⣾⢿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⢉⣵⣿⡿⠋⣰⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿ ⠁⠀⠙⢿⣷⣟⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⠓⠚⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠿⠛⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣄⢹⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣯⣿⣿⣿⢿⣻⣿⣿⣿⢿⣿⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⡇⣿⡇⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣿⢸⣿⣿⣿⣵⡿⢟⣯⣷⣿⢹⣿⣿⣿⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⣶⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⠙⢻⣿⣿⣿⣿⣿⣷⣿⣇⣿⣿⣿⣿⣿ ⢀⣴⡾⣿⣽⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⢹⠇⢠⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣯⣻⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿ ⢿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡶⡤⠴⠖⠚⢉⠁⠀⠀⢠⠏⢠⠎⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡠⠤⠏⠩⡽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣽⣿⣿⣿⣿⡇⣿⣿⣹⢦⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⢀⡤⡟⢿⢿⣿⣿⣿⣿⣿⣿⣟⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣳⣿⣿⣿⣿⣿⣷⣿⣿⣿⡞⠷⡄⠀⠀⢠⠏⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡶⣅⢛⠣⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢇⠈⢣⠀⠀⠀⠀⣀⠄⠊⣩⣾⣿⠟⠋⣿⣿⣿⣿⣿⣿⣿⠯⢢⠾⠆⣠⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣵⣾⣿⣿⣿⣿⣿⠃⠀⣇⣰⠀⠀⣠⠖⠋⠁⢀⡼⠛⠉⠀⠀⢀⣿⣿⣿⣿⣟⣿⣿⡤⢫⣱⣿⣿⣿⣿⡿⣏⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣽⣾⣿⣟⣹⣿⣿⣿⢹⠏⠀⠀⢸⡿⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣟⠈⣿⣁⣴⣿⡿⠿⠿⠛⠉⠠⣿⣦⣻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸⣷⣿⣿⣿⡟⠀⡤⠞⣉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣻⣿⣿⣿⣿⣦⣧⡿⡉⢱⢰⠀⠁⠡⢀⣾⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⣤⣤⣴⡯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⣀⡼⣻⠏⠀⢹⡏⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣶⣶⣤⠤⣄⣀⣠⠟⠁⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣼⡟⢶⣄⣙⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣷⡈⠓⠦⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⢻⡇⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣷⣄⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠚⣯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡆⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⣤⠤⣄⠀⠀⠀⢰⠀⠀⠀⠀⣰⠟⠁⢹⢰⠄⢧⡀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣧⢿⠀⠈⠳⣄⠀⠀⣧⠀⠀⣴⣿⡇⠀⡞⣼⠀⠈⠛⢿⣟⠒⠦⠼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣯⢿⣧⠀⠀⠙⣷⣄⣹⣠⠞⠙⣿⣧⡴⣿⠃⠀⠀⠀⠀⠉⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡄⢻⣷⣄⣀⣽⡷⣿⡗⠓⠒⠛⢉⣤⡞⠀⠀⠀⢀⣤⣤⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡀⠻⢦⣀⠀⠀⠀⠀⠀⣠⣴⡿⠛⣀⣴⣶⡷⠟⢧⡄⠙⢦⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠉⣹⠗⠒⢾⠛⢿⠉⢷⣾⣻⣾⠛⠻⣆⠀⠙⢦⡀⣷⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢠⡏⠀⠀⢸⠀⠈⠳⣰⡟⠀⠙⢧⡀⠈⢧⠀⠀⠀⣸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠀⠀⠀⠸⡄⠀⠀⢳⣷⡇⠀⠀⠓⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⢀⡇⠀⢀⣴⣿⣇⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⡶⠒⢦⣀⠀⢀⡼⠋⣽⣷⠶⠋⠀⠀⣿⠲⣜⣾⣧⣤⣶⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠟⣩⠿⢻⣦⣀⣿⠻⣯⣀⡞⢹⠀⠓⡶⢤⠀⣿⣶⢼⣁⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡞⢁⠔⠛⣉⡿⣿⡄⢈⣻⡄⢸⠀⠀⡇⠘⡆⠈⡏⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣧⡜⠀⡞⠁⣀⣽⣹⠟⠉⠀⣾⠀⢰⠃⠀⢧⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⠮⣥⣤⣿⠿⠁⠀⠀⠀⡇⠀⢸⠀⠀⢸⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⠀⠀⠀⣧⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣼⠁⠀⣼⣄⡀⠀⢻⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠾⠤⠤⠿⠒⢙⣦⣨⡇⠀⠸⣗⡒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⠒⠀⠀⠀⠀⢻⡿⣅⠙⠒⠒⠋⢁⣰⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⠳⡶⠤⣤⠤⢾⣡⡟⠉⠉⠉⠈⢉⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠟⠉⠙⢆⠀⠀⠀⢳⠀⠀⠀⢸⡆⢙⣶⡶⠚⠋⠙⠓⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠟⠁⠀⠀⠀⠘⡄⠀⠀⢸⡆⠀⠀⣠⣷⣿⠏⠀⠀⣀⣀⣀⣀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡞⠁⠀⠀⠀⠀⠀⠀⣷⠀⢀⣨⣧⣴⣺⡽⠟⡟⠀⡴⠉⠉⠀⠀⠉⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠿⣶⡦⠤⠤⠤⠤⣶⣟⣯⣭⠿⠛⠋⠉⠀⢸⡇⡼⠁⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠳⢤⣀⣀⣀⣀⣀⣀⣾⡇⠀⠀⠀⢘⣿⣿⣿⣽⣿⣱⣾⣸⣻⣿⠀⣋⣯⣿⠯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⡛⢲⠶⠶⠶⠶⠾⠟⠋⠀⠀⠀⠀⠀⢀⢁⠀⠀⠀⠀⠀⣉⢉⢉⠀⠀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣯⣭⣭⠭⠭⠭⠭⢍⣙⣛⠒⠢⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠑⠒⠢⢤⣀⡉⠉⠁⠒⠂⠉⠉⠓⣦⢴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢦⣀⠀⣿⠉⠉⠉⢸⣇⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⠋⣁⣠⠤⠶⠒⠚⠉⠉⠉⠉⠉⠉⠒⠶⠤⣀⣀⠀⠀⠀⠀⠀⠀⠈⠹⣿⡆⠀⢀⡞⠈⢷⡈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⡏⢹⠀⡸⠁⠀⠀⠉⠳⢦⣈⠻⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣸⠁⡜⢠⠇⠀⣀⣠⣤⣤⣒⣺⣷⡒⠓⢿⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⠃⠈⣷⣿⣿⣯⣍⣁⠀⠀⠉⠙⢷⡆⠙⢯⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠖⠋⠉⠀⠀⠀⠉⢳⡀⠀⠀⡼⣷⡀⠀⠙⢮⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣤⠿⠷⠟⠻⠿⣶⣤⡙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⣤⠀⠀⠀⠘⢿⢇⠀⠳⣟⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⣠⡞⣿⣤⢤⣈⣿⣧⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⡾⠛⠋⠉⠉⠙⣮⠉⠀⢷⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣄⠀⠀⢀⡼⠀⠀⠀⢹⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣴⡿⢷⣶⣲⡦⣄⡹⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡋⣹⠟⠉⠀⠀⠉⠳⡝⠻⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⢰⠏⠀⠀⠀⠀⠀⠀⢹⡀⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⣇⠀⠀⠀⠀⠀⠀⣸⢰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣌⠷⣄⣀⣀⣠⠶⠁⠸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⠤⠤⠶⠦⢄⡧

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