Stick Man ASCII Art

Copy & Paste Stick Man ASCII Art Emojis & Symbols

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

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

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

Warning: This item may contain sensitive themes such as nudity.

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠚⠉⠉⠀⠀⠀⠉⠙⠓⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⣰⠋⠀⣀⣠⣤⣤⣤⡄⠀⣤⠤⠤⢿⣦⠀⠀⠀⠀⠀ ⢰⠇⠀⠰⡅⠀⠰⢆⡼⠀⠀⠳⢤⡼⠟⠈⣧⠀⠀⠀⠀ ⣼⠀⠀⠀⢉⣉⣉⣩⣤⠤⠤⠤⠶⢶⠒⠀⢸⡄⠀⠀⠀ ⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⠀⢀⡼⠀⠀⢰⠀ ⠘⢷⣀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡴⢃⡴⠋⠀⠀⣰⢉⠇ ⠀⠀⠉⣳⠦⢤⣤⣤⣤⠤⣮⠶⢻⡏⡀⢤⣲⠝⠚⠁⠀ ⠀⠀⣰⠃⢠⠴⣚⡭⠖⠉⠀⠀⢸⡧⠚⠉⠀⠀⠀⠀⠀ ⠀⢠⡏⠀⠐⠋⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠛⠛⠛⠓⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠈⠳⣤⣀⠀⠀⠀⣀⣠⠴⠛⣁⣠⠴⠖⠋⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠉⠙⠛⠛⠛⠓⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⠀⠀⣤⣤⡤⠖⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠒⠶⣤⣤⣄⠀⠀⠳⢦⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣠⠞⠋⠁⣀⡴⠺⢟⡿⣷⣦⣀⠀⠀⠀⢰⡆⢶⠀⠀⠀⠀⣠⣶⡿⣿⠻⢷⣄⠀⠀⠙⢳⣄⣤⣄⣀⠀ ⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠉⠙⠲⣤⣾⡿⠀⠀⢸⠃⠈⠙⢿⣶⣤⡀⢸⡇⣾⠀⣀⣴⣿⡟⠉⠀⢻⡄⢸⠙⣷⣤⠶⠋⠁⠀⠀⠉⢧ ⠀⠀⠀⠀⠀⠀⣿⢇⢤⣤⣀⣀⠀⠀⢨⣷⠁⠀⠀⢸⡀⠀⠀⠸⣟⡿⢿⣾⡇⣽⣾⠿⣟⣿⠃⠀⠀⣸⠇⢈⠃⢸⡇⠀⠀⣀⣀⣤⡄⣸ ⠀⠀⠀⠀⠀⠀⢿⡞⣄⠀⠉⠛⣷⣦⣿⣽⡀⠀⠀⠈⠳⣄⡀⠀⠀⢀⣤⣾⣃⣛⡧⣄⡀⠀⠀⣀⡴⠛⠀⣸⣀⣠⣧⣴⣾⠋⠉⠀⣠⢻ ⠀⢠⣴⢶⣦⠀⠀⢻⣌⠢⡀⢸⡉⢹⣿⣏⣩⣿⣶⡶⣦⣬⣭⣿⣿⣯⣟⣩⣭⣭⣿⣿⣽⣿⣿⣿⣶⣶⣿⣯⢿⣿⣿⠋⢹⡇⢀⡔⣣⠏ ⠀⠸⣧⢸⣏⣇⠀⠀⠙⠶⣌⡺⣍⣸⣿⡿⣿⣿⣿⣶⣿⣿⣿⣛⣿⣿⡿⣽⣽⣫⢿⣿⣿⣙⣿⣿⣥⣤⣿⣿⣻⣿⡏⠀⣨⣖⣫⠞⠋⠀ ⢀⣴⢟⣫⣭⣟⢿⣶⣖⣶⣾⢽⡛⠻⣿⣧⣿⣸⣿⣿⣯⣭⡿⢿⣿⣯⠽⣿⣿⣿⢭⣿⣿⢿⣿⣯⣽⣿⣏⣿⣹⣿⠗⠛⠛⠉⠁⠀⠀⠀ ⣼⢱⣿⣿⣿⣿⣷⢽⢻⣻⣯⡯⢿⣦⠈⠷⣿⣿⣍⣝⣿⣿⢿⣾⠿⣿⣾⣽⣿⣯⣿⣿⣿⣶⣿⣿⡏⣻⣿⡟⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡸⣿⣿⣿⣿⡿⣸⣿⠏⣷⣧⡈⣯⣇⠀⠈⠻⢿⣽⣿⣯⣾⣿⣶⣿⡟⢻⣿⢿⣿⣿⣽⣿⣯⣽⡿⣽⣿⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡷⣬⣛⣛⣫⡴⣫⢟⣰⢛⣯⢇⣇⣿⠀⠀⠀⠀⠙⢻⣧⣿⣟⣹⣿⣷⣿⣿⣶⣿⣟⣹⣿⢏⣿⣷⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢷⡸⣟⣿⣖⣛⣡⣾⢷⣿⣩⣾⡽⠃⠀⠀⠀⠀⣴⠋⡾⢻⢿⣿⡟⣻⣿⣼⣿⣛⣿⣿⣿⡿⣟⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠻⠭⣽⡿⠟⣿⠚⣿⣿⣯⡀⠀⠀⠀⢀⡾⠃⣸⢇⠇⠀⠙⠳⣿⣞⣻⣿⣟⡿⠟⠉⡇⢻⡦⣀⡈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣧⠀⣿⢔⣿⡏⠉⢻⡄⠀⢀⡞⠁⢠⡟⡸⠀⠀⠀⠀⠙⣷⣾⠟⠋⠀⠀⠀⢣⠀⣷⢬⣝⡲⣄⠈⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢯⣦⡼⠛⠛⣧⣤⣾⠳⠶⠋⠀⣰⢻⢃⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠀⢸⡀⠈⣧⢸⠀⠘⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⡾⠟⣿⣿⣦⣀⣀⠜⣡⣿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢸⡇⠀⣿⠘⡄⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣶⣾⡿⠟⠷⠬⠵⠾⠃⢸⠛⠓⠶⠤⣤⣀⣀⣀⣀⣀⣀⣀⣤⡴⠷⠚⢋⡇⠀⣿⡀⡇⠀⢻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢸⠇⢠⡿⡽⠁⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣼⠀⡇⠀⠀⢠⡄⠹⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣷⣲⠿⣤⣵⠀⠀⣾⠃⠀⢹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠈⠳⢦⣄⣀⣀⣀⣀⣀⣀⣤⠶⠛⠉⠀⢸⣧⡴⡽⠃⠀⣰⣯⡀⢀⣼⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⠋⠉⠉⠉⠉⠉⢿⡄⠀⠀⠀⠀⣿⣜⠁⢀⣴⠏⠈⣠⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸⡟⠿⢯⣥⡤⠾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣀⡀⣿⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⠇⢀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠈⠉⠙⠻⠷⣤⡀⠀⠀⢻⣆⠀⠀⠀⠀⠀⣾⠃⠀⠀⣀⡴⠟⠛⠉⠉⠀⠀⠀⠈⠉⠳⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠹⣆⠀⠀⢀⡾⠁⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄ ⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠹⣆⢀⡾⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳ ⠀⠀⠀⠀⠀⢸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠈⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠸⣆⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⠤⢤⣤⣄⣀⣀⣀⣀⣠⣤⡤⠤⠴⠖⠋⠀⠀⠈⠓⠶⠤⢤⣭⣭⣦⣤⣀⣠⣤⣤⡤⠤⠤⠴⠒⠚⠉⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠟⠛⠛⠛⠋⠙⠛⠛⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠃⠀⠀⢰⡶⠾⠿⠿⠛⠛⠻⣿⠋⠀⠀⢸⡟⠉⠉⣭⣍⢹⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠃⠀⠀⠀⣿⡀⠀⠀⠰⠿⠆⣠⡿⠀⠀⠀⠈⢷⣤⣀⣼⡿⠟⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⠀⠀⠀⠀⠘⠿⣶⣤⣤⣶⠾⠟⠁⠀⠀⠀⠀⠀⠈⠉⣁⣀⣀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡶⠶⠶⠶⠶⠖⠛⠛⠛⠛⣿⠋⠉⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⣺⡇⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣼⡇⠀⠀⠀⣤⡄⠀ ⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢠⡿⠁⠀⣠⣾⠏⠀⠀⠀⢀⣿⣇⠀ ⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⠟⠁⣠⣾⠟⠁⠀⠀⠀⠀⣿⠉⣽⠂ ⠀⠀⠈⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣹⣿⣴⡿⠋⠀⠀⢀⣠⣤⣶⣿⡽⠞⠁⠀ ⠀⠀⠀⠀⠀⣸⡿⠻⠿⢶⣶⣶⣶⣶⣶⠶⣛⣷⡾⠛⠉⣿⣁⣠⠴⢞⣫⡵⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠀⠀⢀⣤⡴⠟⣋⣥⡶⠚⠋⠁⠀⠀⠀⣿⣋⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡿⠀⠀⠐⣋⣤⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠃⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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