Family Guy Evil Monkey Dot Art

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⠀⠀⠀⠀⠀⠀⢀⣴⠾⢶⣶⣶⣾⣿⣿⣿⣷⠶⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡟⣡⢄⡀⠈⠙⠛⠛⠉⠀⠀⢀⡀⠈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⡜⠁⠀⠉⠒⢶⠀⢠⠴⠒⠋⠉⠑⡄⢹⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⣤⣸⣇⣧⠶⠦⠾⣆⡼⠀⢿⣀⣀⣀⣤⠀⣸⢀⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⣼⠟⢩⠝⠋⠉⠉⠉⣖⠊⠉⠀⠀⢨⣦⣤⠤⠭⣽⣃⣼⣿⣿⣿⣿⣄⠀⠀⠀⠀ ⣿⣠⠃⠀⠀⠀⠀⠀⠀⠑⠴⠚⠓⠊⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠿⠛⠛⠻⣶⡄ ⢸⣿⠀⠀⠀⣀⡤⠴⡖⠒⠒⢲⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠘⣇⠔⠫⡉⠁⠈⣿ ⠸⣿⡄⢠⢚⢷⠀⡰⠹⡄⢠⠟⡇⠀⣸⡌⠑⢄⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣰⡟ ⠀⣿⠠⣷⣸⠈⢦⠇⠀⠷⠃⠀⣧⠜⠁⡇⢀⣴⣳⠀⠀⠀⠀⣸⣦⣤⣶⠾⠋⠀ ⠀⢿⣄⠳⠿⠤⠒⠒⠛⠛⠛⠒⠢⠤⣀⠗⠁⢸⣇⠇⢰⢀⣰⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⠶⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⡉⠒⠚⠋⣠⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣤⣀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⣠⡾⠿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⢠⡾⠋⠀⠀⠀⠉⠻⢶⣤⣀⡀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠟⠛⠙⠻⣧⡀⠀⠻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⢨⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢹⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⣿⣀⣀⣀⣀⣀⣰⣶⣆⠀⢀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣴⣾⣿⣿⣷⣶⣿⣿⣇⣹⣏⠉⠉⠉⠉⠙⠛⢻⣶⡾⠏⠀⠀⢸⣧⣤⣤⣤⣤⣤⣼⣿⣿⡀⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⡿⠛⠉⢉⣹⡿⠟⠛⠋⠉⠛⠛⠷⣦⣤⡶⠟⠛⠉⠀⠀⠀⠀⠀⢻⣅⠀⠀⠀⠀⠈⠉⠉⠛⣷⡿⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⡏⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣽⣶⠶⠶⠿⠿⠷⠶⠾⢿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⡀⠀⠀⠀⠀⠀ ⣿⣿⡃⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⣤⡶⠶⠦⣴⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀ ⢿⣿⣇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠈⠙⢿⣿⣷⡀ ⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠁⢀⣤⣶⡟⠛⠛⠃⠀⠀⢹⣿⣧ ⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣴⠶⠟⠛⠉⣩⡅⠀⠀⠀⠀⢀⣭⡉⠉⠛⠛⠷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣴⠟⠉⠉⠻⡆⠀⠀⠀⠀⢈⣿⣿ ⠀⢹⣿⡇⠀⠀⠀⢀⣴⡾⣻⣇⠀⠀⠀⣼⠟⣿⡀⠀⠀⠀⣾⢿⡇⠀⠀⠀⠀⣴⡌⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏ ⠀⢸⣿⣷⡾⠀⢠⡾⠁⣰⡟⣿⠀⠀⣸⡏⠀⠸⣇⠀⢀⣾⠃⠈⣿⠀⠀⠀⣼⢿⣧⠀⠀⠈⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁ ⠀⢀⣿⣿⠃⢠⣿⡇⢀⣿⠀⢹⣇⢀⡿⠀⠀⠀⣿⣠⡾⠁⠀⠀⢻⡆⢀⣾⠋⠀⣿⠀⠀⠀⢀⣼⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⣀⠀⣀⣀⣤⣶⣿⡿⠋⠀⠀ ⠀⢸⣿⣿⠀⢸⡏⢿⣼⡏⠀⠀⠹⣾⡇⠀⠀⠀⠸⠟⠀⠀⠀⠀⢸⣷⠟⠁⠀⠀⣿⠀⠀⣰⠿⢻⡇⢻⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀ ⠀⠈⣿⣿⡀⠀⢻⣌⣻⡇⢀⣀⣀⣬⣤⣴⡶⠶⠶⠶⠶⠶⢶⣤⣬⣁⠀⠀⠀⠀⣿⣤⠞⠁⠀⢸⡇⠸⡇⠀⠀⡆⠀⠀⠀⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣿⣷⣄⠀⠉⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⢦⣄⡉⠁⠀⠀⠀⢸⡇⣸⡇⠀⢸⡇⠀⣀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠛⢿⣶⣶⣦⣴⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣤⣤⣿⡿⠋⠀⢀⣾⣷⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣶⣶⣾⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠙⢦⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢉⠑⡀⠀⢀⡞⡠⠖⠚⠢⡀⠉⠻⠿⠿⠿⠿⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⣇⣇⣀⢸⣜⡀⠀⣀⠀⢸⠀⡄⠀⠀⠀⣀⠤⣀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡖⠋⠀⠀⠈⠙⠺⣉⣲⣍⣀⡼⢀⠜⠒⠒⠉⠉⢢⡀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠫⡄⠀⠀⠠⣸⡤⠤⠤⣰⣆⢀⡇⠀⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⠤⠤⣤⠤⠤⣈⡉⠙⠚⠉⠙⠒⠢⠤⣤⠏⢀⣼⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠆⡔⡹⡇⢀⡜⡏⠀⠀⣠⡟⠑⠦⡀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡧⠔⠒⠒⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢰⠃⡇⡎⢠⠃⢀⠔⢡⠃⠀⢠⡟⠢⡀⠀⠀⠀⠀⠀⠘⣿⠋⢀⡠⣴⠒⠂⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⢇⠀⠛⠤⢿⣀⢸⣠⠊⠀⡞⠀⡰⢹⠃⠀⣵⡀⠀⠀⠀⠀⠀⢸⡴⠉⠀⠘⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠈⠓⢤⣤⣤⣤⣍⡓⠤⣰⡵⠊⢀⠎⡠⠊⡏⢱⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⡌⠑⢤⠾⠊⢀⡜⢀⢾⢀⠀⠀⠀⠀⢸⠳⠤⠤⠤⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠑⢤⣾⠚⣁⠞⢀⠇⠀⠀⢀⠇⠀⠀⠀⠀⢀⣀⡠⠐⠒⢄⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠉⠀⢀⡜⠀⣀⠴⠃⠀⠀⠀⠀⣞⠕⠒⠧⢆⠀⢈⢦⠀⠀⠀⠀ ⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⡄⠀⠀⠀⠀⠀⡠⠞⠒⠂⣀⠴⠊⠁⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡇⢰⠠⠊⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠁⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠣⣹⡀⠀⠀⠀⠀⣤⡀⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣧⠀⢀⡀⣰⣿⣿⣏⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠧⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠛⠛⠀⠙⠃⠀⠈⠻⣿⣿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠒⠉⠀⠀⠙⠻⠿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣷⣦⣤⣤⣤⣾⣿⣿⣿⣿⡏⢦⡀⠀⠀⠀⠀⡔⠀⠀⣾⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠀⡠⠋⠀⠀⡴⠀⠀⠀⠀⣀⠤⠖⠒⠒⠒⠒⠒⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠛⢇⠘⠉⠁⠀⠀⡜⠀⠀⢰⠋⢧⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀ ⠀⠀⠀⠱⣰⡃⠀⠀⣸⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⡴⣅⣀⡤⠋⢀⣨⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀ ⠀⠀⠀⠀⠀⠑⠒⠚⠙⠒⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣀⣀⡤⠒⠉⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⣀⣀⠤⠊⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡊⡑⠿⠛⢋⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢤⣿⠀⠤⠂⡁⢠⡀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠁⠀⡈⠂⢀⠉⠉⠉⠻⣟⡓⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣶⣿⣶⡄⠀⢸⢐⢦⠊⡐⢁⠸⢠⠀⠀⣇⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⡟⠙⣿⣿⡀⠘⠨⢤⠁⠀⠁⢊⠼⢠⣴⣷⣶⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀ ⠘⣿⡿⠀⢻⣿⡇⠀⣴⡿⠁⠀⠀⢼⣿⣿⠿⣿⣿⣿⣿⣿⡟⠉⠙⠓⠒⠒⠤⢄ ⠀⠀⠀⠀⢸⣿⡇⣼⣿⠁⠀⠀⠀⠀⢿⡇⠀⠀⠈⠉⠙⠻⢇⡈⠠⣁⡱⠒⠶⠞ ⠀⠀⠀⣀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⠀⡀⠀⠀⠀⠀⠀⠉⠒⠒⠃⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡬⠟⢻⣿⣿⣄⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣗⣑⠠⡈⠈⠉⠉⠻⣶⠒⠒⠋⠠⢄⠀⠀⠩⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⣡⣈⠠⠂⠉⠒⠊⠀⠀⠀⠀⠀⠑⠲⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⢀⣠⣾⣷⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣾⠟⠉⠉⠉⠉⠉⠉⠛⠿⣟⡛⠉⠁⠈⠉⠉⠉⠉⠉⠙⠛⠶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣀⣤⣽⡿⣦⣄⠀⠀⠀⠉⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣶⣿⠿⠿⠿⢶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣴⡟⠉⠉⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠉⠛⠿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡾⠋⠁⢀⣀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠃⠀⠀⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⣀⠀⠀⠈⠉⠛⠛⠿⠶⠶⠦⠤⠴⠶⠿⠿⠷⢶⣦⡀⠀⠀⠀⠀⠀ ⢀⣿⠇⠀⠾⠟⠙⣷⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⢸⡟⠛⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠁⠀⠀⠀⢠⣤⣀⠀⠀⢀⣀⣠⣤⣶⣶⣶⡄⠉⣿⡆⠀⠀⠀⠀ ⢸⡏⠀⠀⠀⣴⠟⢿⡇⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⢘⣧⡀⠀⠀⠈⠙⠻⠷⣦⣤⣀⡀⣠⡿⠀⠀⠀⠀⠀⣠⡿⠟⠛⠿⠿⠛⠋⠁⠀⠹⣷⡀⠀⣿⡇⠀⠀⠀⠀ ⢸⣇⠀⠀⠀⠿⠀⢸⡇⠀⢀⣠⣿⣿⠿⠟⠃⠀⠐⠋⠉⠉⠙⠛⠛⠶⠶⣦⣄⣀⣉⣹⣿⠟⠁⠀⠀⠀⠀⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣶⠟⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⣸⣷⡾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢩⡶⢶⣦⣄⣀⣠⣤⣼⣿⠿⢿⣤⣄⣀⠀⠀⠀⠀⠀⠈⣿⣧⣀⣀⠀⠀⠀⠀ ⠸⣿⡄⠀⢀⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢠⣦⣍⠉⠉⠀⠈⢿⣦⣀⠀⠉⠙⠛⠳⢶⣦⣄⣼⣿⠋⠙⠛⢿⣦⠀⠀ ⠀⠙⠷⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⢶⣿⡖⠲⠶⠶⠦⢤⣄⣀⡀⠀⠀⠀⠈⠉⠀⠀⠙⣷⡀⠀⢀⣬⣝⡛⠛⣷⣶⣤⣄⣀⣈⣽⡿⠁⢀⣀⣀⠀⠙⣷⡄ ⠀⠀⢀⣿⠃⣀⠀⠀⠀⠀⣀⣴⠞⠋⠁⠀⠀⢸⡟⣷⡀⠀⠀⠀⠀⠀⠉⠛⠷⣄⠀⠀⠀⠀⠀⠀⠘⣿⠷⠛⠉⠉⠙⢷⣾⠋⠉⠉⠛⠻⢿⣤⣴⠛⠿⠟⠁⠀⢸⣿ ⠀⠀⢸⣿⠟⠁⠀⠀⣠⣾⡏⠁⠀⠀⠀⠀⠀⣸⠇⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣿ ⠀⣰⡿⠁⠀⢀⣴⣿⡟⢹⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠦⣤⣀⣀⣀⣤⣤⡤⠤⠤⠤⢤⣤⣀⡀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⢰⡿ ⢰⣿⠁⠀⣠⡞⢡⣿⠀⠘⣷⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⢠⡟⠀⣿⡀⠈⠉⠉⠁⢠⣿⣇⠀⠀⠀⠀⠈⠉⣿⣦⡀⠀⠀⠀⠀⠘⣿⠀⣠⣿⠃ ⣾⡇⠀⢀⡿⠀⢸⡏⠀⠀⢿⡄⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢠⡿⠁⠀⢸⡇⠀⠀⠀⠀⣾⠋⣿⠀⠀⠀⠀⠀⢠⣿⣯⠙⣄⠀⠀⠀⠀⢻⡿⠟⠁⠀ ⣿⡇⠀⠘⣇⠀⣾⡇⠀⠀⠘⣷⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣰⠟⠀⠀⠀⠸⣷⠀⠀⢀⣼⠇⠀⢻⡄⠀⠀⠀⢀⣾⠋⣿⠀⠘⣆⠀⠀⢠⣾⡇⠀⠀⠀ ⣿⡇⠀⠀⢻⣄⣿⡇⠀⠀⠀⢹⣧⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⣿⡀⣠⡾⠋⠀⠀⠀⠀⠀⣿⠀⢀⣾⠃⠀⠀⢸⡇⠀⠀⢀⡾⠁⠀⢿⠀⠀⢹⡆⠀⢸⣿⡇⠀⠀⠀ ⠸⣿⡀⠀⠀⠉⠛⠷⣤⣄⣀⣀⣹⣿⣿⣄⣀⣀⣀⣀⣀⣀⣠⣸⣿⣏⣀⣀⣀⣀⣀⠀⠀⣿⣶⠟⠁⠀⠀⠀⢸⡇⠀⣠⡟⠁⠀⠀⢸⡇⠀⠀⣿⠀⠈⣿⡇⠀⠀⠀ ⠀⠙⢿⣦⣄⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠿⠿⣦⣤⣀⠀⠀⢸⣿⣼⠋⠀⠀⠀⠀⢸⡇⠀⠀⣽⡇⠀⢸⣧⠀⠀⠀ ⠀⠀⠀⠉⠛⠿⢿⣷⣶⣶⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠿⣿⣁⠀⠀⠀⠀⠀⣼⡇⣠⡾⢻⡇⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⢀⣿⡾⠋⠀⣼⠇⠀⢸⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣀⠀⠉⠻⢿⣤⣀⣼⠏⠀⢀⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⣦⣄⣀⠀⠀⠀⢀⣰⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠛⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠶⣶⣶⣶⣦⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⢿⣷⣾⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⡂⠍⠲⢶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⢾⢄⡄⡅⡄⠠⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⣀⠃⠀⠰⠖⣒⠢⢀⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢐⠟⠐⠃⡠⠃⢠⡀⠀⠈⠻⡿⠃⡒⠂⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣦⣄⡀⠀⠘⡘⠒⠠⡄⠘⠀⡅⣰⡀⠀⠀⠳⠁⠁⠀⠇⠀⠀⠀ ⣴⣿⣿⡿⠟⠛⠿⣿⣿⡆⠀⣼⣿⣿⣷⣕⠔⢂⠠⡇⠀⠀⠔⠀⠀⠊⠀⠀⠀⠀ ⢿⡿⠋⠀⠀⠀⠀⢈⣿⣿⢀⣿⣿⣿⣿⣿⣷⣁⣈⣠⡀⠈⠀⠀⡖⠋⢄⠱⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⡀⠊⠀⠀⠀⠀ ⠀⠀⢀⣴⣶⣶⣶⣼⣿⣿⣿⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣦⣬⣶⣀⣠⣷⡆⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⢿⣿⣿⣿⡿⡿⢿⣿⣿⣿⡿⠿⠏⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⢿⡿⠇⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⢊⠀⠀⠉⠋⠉⠥⠬⠭⠛⠛⠓⠚⠛⠛⠇⠓⠀⠠⠀⡘⡄⠀⠀⠈⠠⡀⠀ ⠀⠈⠂⠤⠣⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡒⢂⠀⠒⠄⠀⠀⠀⠈⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠒⠦⣤⠤⠒⠇⠒⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⢀⣰⣄⡀⠑⠢⣀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀ ⢀⡴⠛⠛⠛⢻⣿⣿⡇⠀⢰⣏⠀⠀⠉⠢⢀⠀⠙⠲⠤⢤⣀⣀⠱⠤⣀⠀⠀⠀ ⢸⠀⢋⢽⠀⠈⣿⣿⡇⠀⢹⠉⠒⠦⣄⡀⢀⡏⠀⠀⢲⠤⠤⠴⠒⢷⠀⡷⠀⠀ ⢻⠀⠈⢈⣦⠴⠛⠉⠀⠈⠉⠉⠉⠑⠢⢾⣋⣀⢀⣀⡿⣆⡀⠀⠀⠈⣗⡁⠀⠀ ⠸⢄⡔⠋⠀⠀⠀⣀⢠⡤⠤⠀⣀⠀⠀⠘⠀⠲⡄⠀⣳⠤⣌⣉⠒⣶⠋⠉⠳⡄ ⠀⢸⠔⠀⣠⠔⠉⠀⢠⠛⡄⠀⠀⠈⠓⢄⠀⠀⢸⠉⠁⠙⠋⠈⠉⠓⢎⠉⠀⢹ ⢰⠃⡠⢾⠉⡇⠀⠀⡸⠀⠹⡀⠀⠀⠀⡞⡇⠒⠒⢲⡒⠒⠒⢤⡀⠀⠀⢣⢀⡜ ⡏⠀⡇⡞⠀⢣⠀⢀⠇⠀⠀⢇⠀⢀⠜⠀⢱⠀⢠⠏⡇⠀⠀⡼⡏⢆⠀⣸⠏⠀ ⢣⠀⠑⢧⣀⡈⣧⣎⠀⠀⢀⣸⣴⣋⠀⠀⢸⡠⠋⠀⢀⢀⠜⠀⡇⠈⡆⢹⠀⠀ ⠈⠓⠦⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠂⠤⢼⡊⠀⠀⡇⣠⠇⠈⡇⠀ ⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠐⠤⣟⣁⠇⢰⠃⠀ ⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠶⠤⠤⠴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠲⠶⠤⣤⣤⠤⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠚⢉⣩⣭⡭⠛⠓⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠃⢀⡴⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⠀⠀⡾⠁⣠⠋⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⠀⠀⠀⣸⠁⢰⠃⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀ ⠀⠀⠀⡇⠀⡾⡀⠀⠀⠀⠀⣀⣹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⢸⠃⢀⣇⡈⠀⠀⠀⠀⠀⠀⢀⡑⢄⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⢸⠀⢻⡟⡻⢶⡆⠀⠀⠀⠀⡼⠟⡳⢿⣦⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⣸⠀⢸⠃⡇⢀⠇⠀⠀⠀⠀⠀⡼⠀⠀⠈⣿⡗⠂⠀⠀⠀⠀⠀⠀⠀⢸⠁ ⠀⠀⡏⠀⣼⠀⢳⠊⠀⠀⠀⠀⠀⠀⠱⣀⣀⠔⣸⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀ ⠀⠀⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀ ⠀⢸⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⠀⠀⠀⠀⠀⣾⠀⠀ ⠀⣸⠀⠀⠹⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠸⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⡏⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⡇⠀⠀⢰⡀⠀⠀⠀⠀⠀⡇⠀⠀ ⢰⠇⡄⠀⠀⠀⡿⢣⣀⣀⣀⡤⠴⡞⠉⠀⢸⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣧⠀⠀ ⣸⠀⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢹⠀⠀⢸⠀⠀⢀⣿⠇⠀⠀⠀⠁⠀⢸⠀⠀ ⣿⠀⡇⠀⠀⠀⠀⠀⢀⡤⠤⠶⠶⠾⠤⠄⢸⠀⡀⠸⣿⣀⠀⠀⠀⠀⠀⠈⣇⠀ ⡇⠀⡇⠀⠀⡀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠸⡌⣵⡀⢳⡇⠀⠀⠀⠀⠀⠀⢹⡀ ⡇⠀⠇⠀⠀⡇⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⢧⣀⣻⢂⠀⠀⠀⠀⠀⠀⢧ ⣇⠀⢠⠀⠀⢳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⣆⠀⠀⠀⠀⠀⠘ ⢻⠀⠈⠰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⢮⣧⡀⠀⠀⠀⠀ ⠸⡆⠀⠀⠇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⢢⡀
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⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⢠⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡸⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⣠⠤⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢠⢶⢟⢻⣗⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢠⠇⠈⠒⠊⠑⠚⠓⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀ ⠀⣀⡤⣄⠀⢸⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣦⠀⠀⠀⠀⠀ ⡜⢁⣠⣶⠷⣼⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀ ⢳⡾⠋⣠⣤⣿⠀⠀⠀⠀⠀⠀⠸⡀⠀⡀⠀⠀⠀⠀⠀⠀⢻⡿⠋⢠⣴⡒⠲⡄ ⠀⠉⠓⠛⡿⡿⢢⡀⠀⣀⣀⡀⠀⠳⣄⢹⠿⣶⣶⠒⠒⠒⠋⡀⢀⣯⡈⢿⡆⢸ ⠀⠀⠀⠀⢻⡵⢻⠑⠐⠓⠒⢮⠀⠀⠈⠩⣛⣒⣾⡀⢀⣠⣿⣽⣟⡿⠧⠼⠟⠃ ⠀⠀⠀⠀⠀⠳⣙⢷⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⢣⢏⢩⡾⠗⢈⡼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⡒⠒⠶⠥⠋⠀⠀⠀⠀⠀⠀⠻⣦⠴⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠖⠁⠒⢤⠀⠀⠀⠀⠀⠀⢈⣼⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣿⣇⣀⣀⣀⠠⠜⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡃⠀⠀⠀⢸⠁⠀⡟⠀⠀⠀⠰⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣅⣆⣀⣀⡼⠀⠀⠳⣄⣀⣀⣆⣾⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣵⣶⣤⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⢻⣻⡛⠛⠛⣛⣛⡛⢹⣿⡿⠍⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣜⠁⠀⠙⡤⣎⠀⠀⠙⡍⠉⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠖⠙⢄⠔⠒⠃⠹⣀⣀⠔⠁⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠃⠀⠀⠘⣄⣀⣠⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡘⠀⠀⠀⠘⠒⠀⠀⣴⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⡠⠤⠤⠼⠿⠯⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀ ⠀⠀⠈⡇⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀ ⠀⠀⠀⣷⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀ ⠀⡠⠊⠈⠆⠀⠀⢧⡀⠀⣠⡀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢ ⡜⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⠈⢷⠀⠰⡆⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⣟⠀⠀⠈⠀⠀⢹⡄⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣰⠛⠀⣠⡞⠀⠀⢀⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠻⣆⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⡼⠃⢀⡴⠋⢀⣤⣾⣿⠟⣁⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⣿ ⣷⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⣀⣀⠀⢼⡷⣄⠈⠳⣤⣀⠀⠀⠀⠀⣰⣿⣿⣟⣡⠴⠯⠴⠿⠿⢿⣿⣟⣋⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾ ⠛⢧⠀⠀⠀⢤⣻⣦⣀⠀⠀⠀⠈⡛⠒⠤⢤⣙⣻⣭⣿⡿⠿⠛⠛⠛⠲⠬⠭⠟⠛⠛⠛⠩⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⡿⠿⠟⠛⠒⠒⠀⠀⠀⠈⠛⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣀⣀⣈⣉⣑⣲⡶⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣠⡀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⠐⢶⡄⣤⣀⣀⡀⠉⠙⠻⣿⣿ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⣿⣧⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⡟⣶⡽⣯⣭⣽⣿⣿⣿⣿⣿⣿ ⠷⠄⠀⠀⠀⠀⢀⡶⠚⠋⠉⣩⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠰⡆⠘⠇⠀⣇⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣤⣤⠀⠀⠀⣴⡟⢁⣴⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣾⣿⡀⠀⢠⣿⠿⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⢠⣾⣿⣴⣿⣿⣷⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠉⢻⠃⠀⠈⡇⠀⠀⠉⠃⠀⠀⠀⠀⢀⣀⣠⡤⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢁⣴⣿⣭⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⡇⠀⠀⣀⣤⣤⡶⠖⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣵⠿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠷⠿⠿⢿⣶⣀⠀⠁⠀⠀⠀⢀⡼⠛⢉⣠⡤⢶⣶⣖⣒⣲⡭⢵⣶⠶⠀⠀⣸⢡⢷⠘⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠱⢟⣿⣿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣒⣚⡳⢦⣄⠀⠀⠀⠀⢀⡞⣤⣿⣿⣷⣾⠿⣟⣿⣶⠋⠁⠀⢰⡆⠀⠀⣷⣿⠸⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠸⢿⡇⢀⡀⠙⠻⣿⡇⠀⠀⠀⠀⢀⡠⢤⣤⣶⡿⢷⣾⣿⣿⣷⣆⠙⠾⠏⠀⠀⠀⠀⠀⠀⠘⠋⣽⡟⠁⠀⠻⠿⠟⠀⠀⣠⡿⡤⢀⣴⣿⡙⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣧⢸⡟⢦⡀⠹⣿⠀⠀⠀⠀⢦⢦⡀⠁⠀⠀⠀⣿⣿⡟⠉⠙⢦⡀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠹⠄⢀⣀⣀⣀⣠⣴⣶⡿⢳⠃⣼⢠⠉⣧⠇⢠⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⠘⠇⣌⠿⣆⠸⣆⠀⢀⡀⠨⣻⡙⢦⡀⠀⠀⠀⠀⠀⢀⣀⠀⠉⠂⠀⢀⣤⣤⣾⣧⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢚⡟⠛⣠⡏⡜⣼⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢻⡄⠀⡇⠀⢸⡇⠉⠀⠀⢳⡄⢳⠹⢦⡭⠷⠶⠖⠚⠉⠁⠀⠀⠀⢀⣴⡿⠟⠛⢹⠿⠿⠷⠦⠤⠤⠤⠄⠀⠀⠀⠈⠙⠋⠙⡿⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠘⣇⠀⢿⣄⠈⢷⡀⢀⠀⠸⣿⣘⢛⣛⠧⠀⠀⠀⠀⠀⠠⠤⠤⠴⠛⠉⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠹⣆⠀⠙⢦⣀⠙⢾⣄⣴⡿⠻⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠈⠉⠛⠿⡜⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⡏⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⢹⡽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢱⠁⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣴⣾⣷⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠀⠀⠰⣼⣟⠏⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⣷⣿⣷⣄⠀⠀⠀⢀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠤⠖⣒⣻⠽⠛⠁⠀⠀⢀⣾⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠙⣯⠻⣟⠻⣷⣄⠀⠀⠀⠉⠉⠛⠛⠻⠯⠭⠥⠤⠤⠤⠴⠚⠋⠀⠀⠀⠀⠀⣠⣾⣯⠏⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⢹⡆⠈⠳⣍⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠆⠀⠀⠀⢀⣴⡟⣵⠇⠀⢸⣏⢳⣄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⠁⠀⠀⠀⠀⠀⠘⣿⡀⠀⠈⠳⣌⠙⢿⣦⡀⠀⠀⣀⡀⠉⠉⠙⠋⠉⠁⢀⣀⣠⣿⣿⠿⢏⣾⡿⠀⠀⢸⠈⢷⣝⢷⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠹⣿⢦⡙⠿⣿⣿⣿⣷⡀⢻⣇⠀⠀⠀⢸⡏⣸⠋⠀⣠⠟⢈⡇⠀⠀⢸⠀⠀⠙⢶⣝⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢀⣤⣿⣿⣿⣿⣁⡠⠤⠖⠒⠚⠛⠲⢤⣤⣿⡆⠀⠀⠀⣿⡄⠙⠷⣬⣁⠀⠀⠙⢦⠻⡄⠀⠀⠸⠠⠇⣀⡼⠃⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠈⠛⠧⠀⠀⠀⠀⠀⠀⠀⣠ ⣠⣤⣼⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⣤⣿⣿⡀⠀⠀⠉⠳⠦⣤⣤⣤⣤⣤⣤⡴⠶⣻⠟⠀⠀⠀⢸⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠽⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠏⢻⣿⣧⠀⠀⠀⠀⠀⠈⢻⣟⠂⠈⠁⢠⣶⠋⠀⠀⠀⢀⣼⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢸⠀⠈⢻⣿⣇⠀⠀⠀⠀⠀⠀⠻⣷⣄⣠⡿⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢹⣾⠀⠀⠀⢻⣿⡄⡀⠀⠀⠀⠀⠀⠻⣿⡟⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠙⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠛⠉⠙⠛⠛⠲⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠙⢶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⣀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⠤⣤⣤⣤⣤⠤⠴⠺⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡟⠀⠀⠀⠈⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣤⣀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠁⠀⠀⠀⠀⣼⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⣀⣀⣀⣀⡉⠳⡄⠀⡰⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡇⢠⡀⢀⡴⠋⣁⣀⣀⣉⣻⣦⡀⠀⠀⠀⠀⣸⠛⠉⠉⠉⠉⠉⠉⠉⠉⢻⡿⠵⠊⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⠀⠲⢽⡿⠚⠉⠉⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠸⣿⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀ ⠀⢀⡇⠀⠀⠸⡇⠀⠀⠀⠀⣿⠆⠀⠀⢸⠇⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀ ⠀⣸⠀⠀⠀⠀⣳⡀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀ ⠀⡏⠀⠀⢀⡼⠁⠙⠲⢤⣤⣤⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀ ⢸⠃⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀ ⢸⠀⠀⡼⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀ ⡟⠀⢰⠇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀ ⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⢿⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁ ⢸⡄⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⠞⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀ ⠀⢧⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠹⠃⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀ ⠀⠘⣆⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀ ⠀⠀⠘⣆⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⡀⠀⢀⣠⠴⠒⠲⢤⣤⣀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢧⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣉⠉⠉⠀⠀⣀⣀⡤⠴⢪⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⡀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⣉⠉⠉⢀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡈⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣌⡙⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣃⣤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠬⣭⣛⣲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠂⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠃⠀⣧⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⢰⠓⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⡞⠀⠀⢸⡄⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⡇⢀⡠⠤⣷⣀⣔⣁⣀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣧⠊⠀⠀⡼⠋⠁⠀⠈⢳⡄⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠃⠀⠀⡜⠁⠀⠀⠀⠀⠀⣧⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠉⠙⠻⣦⢀⣠⣴⣾⡿⠿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡟⠉⠉⠉⠙⠛⠿⣷⣦⣤⣤⣶⣶⣶⣶⣶⣶⣶⣾⠋⠀⠀⠀⠀⠀⠹⣿⠛⠉⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠉⠉⠉⠉⠉⣽⠃⠀⠀⠀⣠⣤⣤⣀⣹⣇⣀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣼⡏⢀⣿⠟⠉⠉⠙⠻⣦⣶⠶⠶⠿⠿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠘⢷⣾⡇⠀⠀⠀⠀⠀⢻⣧⣀⠀⠀⠀⠈⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⣀⣀⣀⣽⣧⠀⠀⠀⠀⢀⣾⠏⢹⡇⠀⠀⢠⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠙⠷⣦⣤⣶⡿⠻⠶⠟⠁⠀⢀⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠇⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣙⣻⣿⣟⡋⢹⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡀⠀⠀⠀⠀ ⣀⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠃ ⠈⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠁⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀ ⠀⠀⠰⠾⠟⠛⣿⣿⣿⡿⣋⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢿⣄⣠⡿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣯⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⡶⠟⠛⢿⣦⣌⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⣠⣾⡿⠋⠉⠛⠿⢶⠀⠀⠀ ⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠉⠻⢿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⣿⣶⣦⣄⣀⣀⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠙⠛⠛⠛⠉⠙⠿⡿⣿⣿⣶⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠒⠢⡄⠀⠀⠀⠀⠀⠠⣄⠈⠙⢿⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠆⠀⠀⠀⢹⠀⠀⡤⠒⠒⠲⣄⠱⠀⠀⠹⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠈⠦⢄⣀⡤⠃⠀⢸⠶⠀⠀⠀⢸⠆⠀⣀⣴⣿⡿ ⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⢀⡠⠞⠁⢀⣀⠈⠣⢤⣠⠤⠊⠀⠀⣿⣿⡟⠃ ⠀⠀⢀⡔⠁⠀⠀⠀⠀⢀⠖⠊⠉⠀⠀⠀⠀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠫⡯⠀⠀ ⠀⣠⠋⠀⠀⠀⠀⠀⢴⠂⠑⠦⠤⠤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡅⠀⠀ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠙⢲⠤⢤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠶⣦⣤⣄⣀⣀⣀⣀⣈⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⢇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠉⠛⢿⣛⡿⣻⠟⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀ ⠀⠈⢦⡀⠀⠀⠀⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀ ⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠦⢤⣤⠭⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣠⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠦⢤⠴⠒⠒⠚⠛⠒⢶⠤⠤⠤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠴⣒⠉⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠹⡝⠒⠤⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣶⡾⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢒⣒⣒⡒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⠃⢠⡄⠙⢿⣿⣷⣤⡀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠈⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠣⣈⣀⠀⠀⠙⠻⣿⣿⣶⣄⠀⡞⠀⠀⢰⣶⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⢍⠉⠒⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⡄⠀⠀⠀⠈⠻⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢀⣄⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⢸⣆⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣯⣶⣶⣾⣷⣶⣤⣤⣤⣈⣆⠀⠀⠀⠀⣼⣟⣤⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢸⣿⣿⠿⠛⠛⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣋⣀⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣶⣾⣿⣿⠃⠀⠀⠤⠊⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⢹⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣠⢋⠟⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠢⢄⣀⣀⢆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⣀⣠⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠁⠀⠼⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⢳⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣴⣯⣴⣶⣶⣮⠕⠢⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⡀⠀⠀⢀⣏⠙⢒⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⠿⠿⠿⠿⠟⠛⠁⣰⣿⣿⣿⣿⠿⣟⣧⣤⣶⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣮⣽⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣶⡦⠤⠤⢤⣤⣤⣤⡤⠤⣤⣶⣶⣾⣏⠁⠀⠀⠀⠀⠀⢀⠤⣴⣿⣿⣿⣻⣷⣿⣿⣿⣟⣁⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⡼⠁⠑⢤⠊⠈⢦⣿⣿⣿⣿⣿⣿⣦⣠⣤⣶⢶⠁⢀⠀⡟⠛⢻⠉⠉⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠃⠀⠀⣤⢣⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⡀⣸⣏⠑⡲⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣤⣭⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⠿⠿⠿⠿⢻⠿⢿⣿⣿⠟⢟⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠿⢸⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢺⢤⡼⠿⠿⠦⠬⠆⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡀⠙⠶⠿⠿⠉⢻⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠉⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⢀⣾⣿⡿⠁⠀⡇⠘⣦⠀⠀⠀⠀⠀⠀⠓⣢⣤⠝⠻⣿⣶⣄⢀⠀⠀⡠⡠⣠⢄⢄⣀⣢⣢⣦⣄⣔⣤⡢⡠⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⣿⣿⠃⠀⣼⣿⡄⠈⣧⠀⠀⢀⣴⣦⠞⠁⠀⠀⠀⠀⠙⠻⠷⣇⣬⢼⣾⣴⣿⣻⣿⠿⠿⠿⠿⠿⢿⣟⣿⣷⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⡼⠀⣿⡄⠀⠀⠀⠀ ⠀⣠⣿⣿⡿⠃⠀⣼⣿⣿⣿⡄⢸⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠮⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⡇⠀⣿⢷⠀⠀⠀⠀ ⣼⣿⢻⠟⠁⠀⣼⣿⣿⣿⣿⣿⣾⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⣿⣿⡄⠀⠀⠀⢧⠀⢹⡸⡇⠀⠀⠀ ⣿⡇⠋⠀⣠⢾⣿⣿⣿⣿⣿⣿⡟⠁⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠙⢿⣿⣿⣿⣆⠀⠀⢸⠀⣿⡇⣧⠀⠀⠀ ⣿⣷⣤⣤⣴⣿⣿⣿⣿⣿⣿⣯⠀⣠⠞⠁⠀⠀⢀⠔⠁⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢣⠈⠻⣿⣿⣿⡄⠀⢸⠀⢻⡇⠸⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣽⣿⡴⠁⠀⠀⠀⢠⠊⢀⡔⢠⠞⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡆⠀⠙⢿⣿⣳⠀⠈⡇⢸⡇⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢧⡟⠀⠀⠀⠀⣰⠃⢀⡼⢠⠟⠀⠀⠀⠀⠀⢀⣴⠟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⠀⠀⠀⠹⡿⡄⠀⡇⠸⣄⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⡸⠃⠀⡸⢁⡏⠀⠀⠀⠀⢀⡴⠋⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣇⠀⠀⠀⢇⢱⡄⣧⡀⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣰⠃⠀⢰⢃⣾⠁⠀⠀⢀⡴⠋⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⢸⡀⢻⡍⢻⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⢠⠇⠀⠀⡜⣼⠇⠀⠀⣠⠋⠀⣠⡤⠤⠤⣧⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⣿⠀⠀⠀⠀⣇⠈⡇⢀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠋⠀⠀⠀⣧⡏⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⢷⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠸⡇⠀⣹⠀⠀⢀⠀⠈⠀⢷⡾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡜⠉⠒⠦⢤⣀⠀⠀⠀⠀⣸⠁⠀⠊⠲⣄⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡰⠦⠤⣄⡀⣰⠃⠀⢷⠀⣿⠀⠀⡸⠀⠀⠀⢺⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠖⠀⠀⠀⠀⠈⠙⠲⠤⣄⣇⣰⣷⣤⣶⣿⣿⣿⣦⣤⡀⠀⠀⢳⠀⣤⠀⠀⠀⠀⠀⡰⠃⡼⠁⢀⣤⠀⡸⠓⢤⠀⢸⢰⠃⠀⢰⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⣀⣀⣠⣴⡾⠛⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⠿⣿⣿⣿⣿⣿⣿⢿⣿⣦⠀⠈⣇⢻⡀⠀⠀⠀⣼⡥⠈⠀⣠⠞⢁⡼⠁⠀⠀⠀⢸⡸⠀⠀⡞⠀⡀⠀⠀⡜⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠛⢦⠀⣏⠓⢦⣤⣤⡤⠴⠒⠋⢹⣿⠇⣸⠻⠻⣿⣿⣿⣿⠀⣻⠻⣷⠀⠘⡎⡇⠀⢀⣾⠟⢁⣴⡾⢁⣴⣯⣤⣄⠀⠀⠀⣼⠇⠀⡼⠁⢀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀ ⣿⣋⠻⣿⠀⠈⢧⢸⡄⠀⢳⠀⠀⠀⠀⠀⠈⣿⠀⡇⠀⢴⣿⣿⡏⠙⢿⡏⠀⠙⠂⠀⠈⢳⣴⣿⡯⠖⣻⣿⣿⣿⣿⠿⠻⣿⣷⠤⢤⡟⠀⡴⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⣩⣦⡙⢧⡀⠀⠈⣇⠀⠸⣇⠀⠳⡄⠀⠀⢱⡀⢧⠀⠀⠉⠉⠀⢸⡿⠁⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢩⣿⣿⣿⣿⣦⣀⠘⣿⣧⣼⢃⠞⠁⠀⢰⠇⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀ ⡤⠋⣿⠙⠦⣉⡓⠄⠸⡀⠀⢻⡄⠀⠙⢆⡀⡀⢳⡌⣇⡀⣀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢸⣿⣿⠿⣿⡏⠀⣸⣿⠃⠈⠀⠀⠀⡎⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣶⢾⡀⣄⡀⢻⡛⠲⠷⠄⠸⣻⡄⠀⠀⠱⡬⣦⣙⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠻⡛⢠⠟⠀⡰⣿⠃⢀⡀⠀⠀⠘⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠈⣧⣏⣿⢿⡷⡄⠀⠀⠀⢻⣿⣦⠀⠀⢻⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⣀⣤⠎⠀⣠⢞⣡⠖⠋⠀⣠⠞⠀⣠⠿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⣄⡼⡇⠙⣦⡀⠀⠈⢿⡈⠻⣦⣄⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠀⠉⣹⠏⠀⢀⣠⠞⢁⣠⢞⣉⣉⣠⣬⠗⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣬⣿⣅⡇⠀⠋⠻⣦⣄⡈⢳⡀⢸⣮⠙⠛⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⣴⣚⢁⣀⣈⣽⡷⠊⠻⣍⠁⢠⣶⣶⣶⣾⣾⣷⣶⣶⣶⣶⣶ ⠀⠀⠀⢨⣫⠴⠛⣧⠀⠀⠀⢹⡌⠉⠛⢛⠞⣿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⠉⠉⠹⣷⠀⠀⠈⢦⣿⣿⡋⠉⠋⢉⡉⠙⠉⠉⠉⠋ ⠀⠀⣠⠟⠁⠀⠀⢹⡄⠀⠀⠀⢧⠀⠀⠸⡄⢹⣄⠈⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⡆⠀⠀⢻⡄⠀⢲⣿⣿⡏⠉⠀⡀⠈⠁⢀⠀⠉⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢆⠀⠈⠀⠀⠀⠻⡀⢯⠓⠦⣄⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠁⠀⣷⠀⠀⠘⡇⡀⣾⣿⣿⠃⣀⠀⠁⢀⡀⠈⠀⣀⢀⣿ ⠁⠆⠀⠀⠀⠀⠀⠀⠸⡆⠘⡆⠀⠀⠀⠀⠀⠹⣌⢧⠀⠀⠙⢦⣀⠙⣿⣷⣶⠶⠶⢶⡶⠶⠖⢲⣾⡏⠉⠁⢷⠀⠀⠀⢰⢸⡄⠀⠀⢷⢸⣿⣿⣯⡀⠀⠀⡀⠀⠀⢀⠀⠀⣼⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠹⣄⠸⣦⡀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠉⠳⣬⣿⡟⠀⠀⢸⣟⣔⡁⠈⠛⣿⣄⠀⠈⡇⠀⠀⢸⠀⣇⠀⠀⢸⣾⣿⣿⠁⠀⡄⠀⠀⢠⡄⠀⠀⣴⣿⠏ ⠂⠀⠀⠀⠂⣀⠀⠀⠀⠀⠚⢧⣷⡙⠦⣈⢦⣄⠀⠀⠉⠛⠦⣄⣀⠀⢘⣧⡀⠀⠀⣿⣫⡯⠀⠀⠀⠘⡿⣆⠀⢳⡄⠀⣸⠀⢸⠀⠀⢸⣿⣿⡟⠤⠄⠀⠀⠄⠀⠀⠠⢰⣿⡿⠀
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⣠⣤⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀ ⣿⣿⣿⣿⠿⠟⠃⣾⣿⣶⣄⣾⣿⣄⣸⣿⣷⣁⣤⣁⣶⣶⡆⢰⣿⣿⣤⣾⣿⠇ ⣿⣿⣿⣧⣤⡄⢠⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⡇⠀⠻⣿⣿⡿⠃⠀ ⢹⣿⣿⣿⠛⠃⢸⣿⡿⣿⣿⣾⣿⡟⠟⣿⣿⢸⣿⣿⢿⣿⣷⣶⠀⣿⣿⡇⠀⠀ ⠸⣿⣿⣿⠀⠀⠸⠿⠇⠸⠛⠉⠛⠁⠀⠘⠛⠈⠉⠉⠾⠿⠿⠛⠀⠛⠛⠋⠀⠀ ⠀⠉⠉⠉⠀⠀⣠⣴⣶⣶⣶⣤⣤⡆⠀⣤⣤⣴⣶⣄⢠⣶⣦⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⠟⠛⠛⢻⣿⣷⣀⣿⣿⡿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣀⣛⣿⡿⣿⣿⣿⣿⡿⠁⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⡿⠇⠈⠉⠛⠉⠀⠀⠘⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠉⠉⠉⠉⣉⣩⠭⠭⠉⠉⠩⠭⠉⠉⠉⠙⠛⠛⠛⠻⢿⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⣀⠤⠒⣉⠤⠔⠒⠒⠒⠋⠙⠒⠒⠂⠤⠤⠤⠤⠤⠤⠤⠄⠒⠒⠮⠙⠻⢷⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⢀⠤⠊⡡⠖⡩⠔⠂⠉⠉⠉⠉⠉⠹⡄⠀⠀⠀⠀⠀⠠⢒⠒⠒⠀⠒⠢⣄⠀⠀⠀⠙⢿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠠⠊⠴⠋⠀⣀⣀⣤⣤⣤⣀⡀⠀⠑⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠸⣷⠀⠀⠀ ⠀⠀⠀⣠⣾⣟⣀⡀⠀⠀⠀⣀⡀⢠⣶⣿⣿⣿⣿⣿⡋⠙⠻⢷⣄⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠻⣧⣄⠀ ⠀⢠⣾⣻⠋⠉⣡⣤⣤⣤⣌⡉⠔⠈⠛⠛⠉⢉⣭⠉⠛⠻⣶⣶⡿⠃⠀⠀⠐⢾⣿⡿⠿⠛⠛⠛⠋⠉⠀⠀⠉⠉⢍⡳⢌⢻⣦ ⣰⡿⢱⠃⢠⡾⠋⠁⢰⣌⠙⠛⠷⢶⣶⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣄⣀⣴⡶⠶⠶⣶⠹⠀⢳⣿ ⢿⡇⢸⠀⣿⠃⣀⣤⣾⠿⢷⣤⣀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣤⣤⡤⠀⠀⠀⠀⠀⠘⠻⣦⣄⠀⠈⠙⠛⠋⢠⣇⠀⠀⢠⠇⣸⣿ ⢸⣧⠘⡆⢹⣇⠉⠉⢿⣆⠀⠈⠙⢿⣷⣦⣤⣉⡁⠀⠀⠸⣿⡀⣶⡶⠶⠄⠀⠀⠀⣠⣿⠿⠗⠦⣄⠀⠀⣼⣿⡇⢀⣣⠴⣿⠏ ⠀⠹⣧⣘⠲⠅⠀⠀⠘⢿⣿⣶⣤⣸⣿⡀⠈⠙⠛⠿⢶⣦⣭⣅⣀⡀⠀⠀⠐⠷⡾⠟⠁⠀⠀⢀⣠⣴⣿⢿⣿⣷⠈⠀⣼⡟⠀ ⠀⠀⠈⠻⣿⡀⠀⠀⠀⠈⢻⣦⠉⢻⣿⣿⣶⣦⣄⣀⣸⡏⠉⠉⠉⠛⢿⡿⠿⠶⢶⣶⠶⠿⠛⢿⡏⠁⣿⣄⣿⣿⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠙⢷⣼⡟⠀⠉⠛⠻⢿⣿⣷⣶⣤⣤⣤⣼⣧⣤⣤⣤⣿⣤⣤⣤⣾⣷⣴⣿⣿⣿⣿⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠛⢷⣤⡀⠀⠀⣸⡟⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⢀⡀⠀⢀⠀⠉⠻⣷⣴⣿⠁⠀⠀⠀⠀⢸⡇⠀⠀⠈⣽⡏⠉⢹⣿⠋⣽⡟⢸⣿⡿⠃⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣌⡓⠦⣍⠒⠤⣀⠉⠙⠛⠿⠶⢶⣤⣾⣧⣄⣀⣠⣿⣄⣠⣾⣧⣴⡿⠷⠿⠋⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣉⠒⠦⢍⣑⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⡆⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣤⣀⡉⠑⠒⠩⠭⠍⢐⣒⣒⠒⠂⠐⠒⠒⠒⠒⠒⠉⠀⢀⡤⠚⠀⠀⣹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣠⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡩⠝⠲⢖⠀⣀⣐⠒⠤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⠀⣀⠀⢠⠋⠀⠀⠙⡄⠀⠉⠉⠙⢆⠀ ⠀⠀⠀⢀⠔⠂⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠒⠂⠹⡀⠐⠂⢀⠇⠀⠀⠀⠀⠈⡆ ⠀⠀⣰⣥⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠊⠁⠀⡀⠀⠀⠀⠀⢁ ⢠⠞⣡⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸ ⡾⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠤⠔⠁ ⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀ ⠀⠙⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠉⠒⠒⠂⠠⠤⠤⠤⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⣤⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⠟⢄⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⢈⡋⠛⠛⠻⠿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠈⡆
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⣠⣀⣤⣄⣤⣀⣤⡀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⠼⠟⠚⠉⠉⠀⠀⠀⠀⠀⠀⠉⠙⠲⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠒⠶⠿⢟⡻⠍⠉⢉⡶⡦⠴⢲⣀⣀⣁⠒⢄⠀⠐⠿⠀⣀⠀⠀⠀⢀⠀⠀⠀⠹⣆⠀⠀⠀⠀ ⠀⠀⣾⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠀⠀⠀⢀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠹⡀⠃⠘⣶⠆⠛⠁⠀⠀⠁⠀⠀⠀⠀⢯⠀⠀⠀⠀ ⡤⠤⢬⣷⣄⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠶⠖⠛⠛⠙⠋⠁⠀⠀⠈⠓⠾⠦⠶⢤⡀⠀⡐⡾⠦⠀⠀⠀⠀⠀⠀⠀⠩⢉⠀⠀⠀⢸⠀⠀⠀⠀ ⣤⣀⠀⠀⠉⡟⠙⢆⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠉⠉⠙⠢⡀⠀⠀⠀⣠⠴⠒⠒⠤⣄⠈⠛⠉⠋⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀ ⣀⣉⣛⠲⣄⢳⣄⠀⠓⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣶⠀⠀⠀⢳⠀⠀⡞⠁⠀⢀⠀⠀⠈⢳⡀⠀⠀⠀⠀⣀⣀⡠⠏⠉⠁⠑⠈⠉⠐⠚⢃⠀⠀⠀⠀ ⣍⡉⠉⠙⢻⡟⠀⣠⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢀⣠⠞⠁⢸⠀⠀⠀⠛⠃⠀⠀⠀⡇⠀⠀⢀⡤⠧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠈⠉⠛⠲⣄⠀⠀⢻⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣲⠶⠋⠁⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠓⡄⢀⣤⡀⠀⠀⠀⠀⠀⢀⣤⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⢿⢦⡀⠀⠑⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠈⣲⡀⠑⢦⠤⠤⠴⠊⠁⠀⠀⠀⠀⠓⠃⠄⣸⠀⠀⢀⣄⡔⠛⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⢠⠞⠉⠁⠳⡀⠈⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢰⢚⡡⠾⠿⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⡀⠀⠀⠳⣶⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠙⢦⣀⡀⠀⢀⣀⡀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡄⠀⠀⣼⠁⠑⢄⠀⠀⠀⣿⠀⠀⠀⠀⢠⡇⠀⢀⠀⠀⣀⣀⣈⣩⣿⣿⣿⡇⠀⠀⢰⠀⠀⣇⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠹⣄⣴⠃⠀⠀⠀⠑⢦⡀⠘⠷⣤⣤⡴⠞⠙⠓⠚⠛⡶⣏⣉⢉⣿⡟⣹⠋⠀⠀⠀⡜⠇⠀⢹⡄⠀⢹⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣤⠟⠁⠀⠀⠀⠀⠀⠀⣹⡦⠤⠤⢤⣀⡀⡖⣦⠀⣸⣿⣿⣿⣿⣿⠴⠁⠀⠀⠀⢰⠁⠀⠀⠀⣷⠀⢸⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠸⠛⠳⡿⠿⠷⣿⠟⠛⠉⠁⠀⠀⠀⠀⢠⠧⠀⠀⠀⠀⡟⠀⠈⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠿⠤⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣠⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠈⠦⣄⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠷⠶⠶⠖⠚⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠁⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠙⠉⠉⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣶⣿⣿⣶⣤⣤⣤⣶⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠼⠟⠛⠛⠛⢧⣄⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠈⠹⣿⠛⠻⠶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣍⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠛⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠳⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠐⠟⣧⡀⠀⠀⠀ ⣰⡟⣛⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣠⣄⡀ ⢿⡀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠶⠶⢯⣝⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⡶⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⡉⣷ ⠘⢷⣤⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⣤⣤⣄⣀⣀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⣙⣧⡀⠀⠀⠀⠀⠀⠀⣀⠋⣠⡿ ⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠉⠛⠙⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢸⣯⣤⠶⠶⠾⠿⠛⠉⠹⣷⠀⠀⠀⠀⢀⣼⠛⠛⠋⠀ ⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣠⡟⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠸⣏⠉⠛⠛⠛⠛⠛⠛⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠈⢻⣟⠛⠋⠉⠉⠉⣉⡿⠁⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠙⠷⣤⣀⣀⣀⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡀⠀⠀⠀⠀⠙⠳⠶⣶⡶⠾⠋⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⡀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⠶⠚⠛⠛⢻⡿⠾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠦⢤⣤⣤⣤⣄⣀⣀⣠⣤⣤⣤⡤⠶⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣄⠀⠀⠀⠀⠀⢀⣤⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀ ⢴⣾⣿⣿⣿⣏⣉⣉⣉⣛⣛⣻⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠙⢷⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣛⣛⣋⣉⣉⣉⣿⣿⣿⣿⣶⠄ ⠀⠙⢿⣿⣿⣿⡁⠀⠀⣉⡿⠋⠉⠉⠙⠛⠻⢿⣦⣄⠀⠀⠀⠀⠘⣇⠀⢀⡟⠀⠀⠀⠀⢀⣤⣾⠿⠛⠋⠉⠉⠉⠻⣏⡉⠀⠈⣹⣿⣿⣿⠟⠁⠀ ⠀⠀⠀⠙⣿⣿⣟⠉⠉⣙⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀⠀⠀⢹⠀⣸⠃⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⣿⡉⠉⠹⣿⣿⡟⠉⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣟⠉⢉⣿⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠸⡇⡿⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⣍⠉⠙⣿⣿⡯⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⣿⠉⠀⠀⣀⣨⡟⠛⠛⠒⠒⠤⢄⣀⠀⠙⢿⣆⣷⣧⣾⠟⠁⠀⣀⠤⠄⠒⠚⠛⠛⣯⣀⡀⠀⠉⢹⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⠉⣀⡤⢷⡦⠄⠀⠀⠀⠀⠈⠙⠢⣌⣻⣿⣿⢋⠤⠚⠉⠀⠀⠀⠀⠀⠠⣶⠷⣄⡈⠙⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣁⡤⠾⣷⣤⣴⠶⢶⣒⡻⠿⠿⢛⣿⣿⣿⣟⠛⠽⠿⢓⣲⠶⢶⣦⣴⡟⠦⣄⣹⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⢛⣉⠥⠒⠉⠁⠀⣀⠔⢈⠔⣽⣿⣿⡝⢌⠒⢄⡀⠀⠉⠑⠢⢍⣙⢻⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⠀⢀⡤⠊⠀⡴⠋⣼⡟⣿⡟⢿⡄⠳⡄⠈⠢⣀⠀⠀⠀⠈⢻⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⢽⣀⠀⣀⣴⡏⠀⢀⡞⠁⣸⡿⠀⠉⠀⠘⣿⡀⠙⣆⠀⠘⣷⣄⡀⢀⡸⢯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⡶⠋⡿⠋⣽⠷⣶⡟⠀⢰⣿⠃⠀⠀⠀⠀⢹⣧⠀⠘⣷⡖⢿⡍⠻⡏⠳⣶⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡞⠀⢠⡇⢰⡟⠀⠀⣾⡏⠀⠀⠀⠀⠀⠈⣿⡆⠀⠘⣧⠀⣷⠀⠹⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⡟⠙⣿⡀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⣹⣟⠙⣷⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⡿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠉⠉⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣧⠀⠀⠀⠀⠀⢀⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣸⠿⢋⢧⡀⠀⠀⣰⡟⣡⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢶⣽⣦⣴⠏⣸⠛⡉⠙⠻⣿⣤⡀⠀⠀⠀⠀⠀⠀⣀⣽⡀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣏⣰⣿⢀⣚⣛⣻⣶⣿⣷⣄⠀⣀⣤⣤⣾⣿⠿⢿⣀⣠⠴⣿⣿⣿⣿⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠉⠻⢿⣼⣿⣇⣹⣿⠟⠋⠉⢻⣿⣿⣿⡿⣄⠀⢈⡴⠋⠉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⠀⠀⠀⠀⢉⣩⠙⠆⠀⠀⠀⠀⠙⠿⢽⣓⡛⠑⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⣾⣶⣶⣶⣿⣯⣴⣷⣄⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢤⠶⢾⡿⣿⣄⠀⠈⠉⠙⠻⠿⢿⣶⠶⠶⠛⠛⠿⣦⣄⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⢀⣀⣴⣿⡇⢸⠀⢸⡇⠸⣯⠛⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⡇⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠻⣿⣿⣿⣿⣿⣧⠸⣄⢀⣿⠛⠛⢷⡝⠲⢤⡈⠉⠑⠒⠒⠒⠒⠒⠛⠉⠘⠃⢰⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣧⠙⠚⣿⡆⠀⠈⢷⡐⠆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣶⣶⣶⣦⡀ ⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣴⣿⠇⠀⠀⢸⣇⣀⣀⡴⠂⠉⠀⠠⣄⠈⡆⠀⢀⣴⣿⣿⣿⣿⣿⠛⠁⠀⠈⠁ ⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⣀⣬⠿⠁⢠⣾⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣴⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣹⣿⣿⣏⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⠟⠋⣥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⣀⣀⠀⢀⡰⠞⠛⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣤⣿⣿⣧⡤⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⢀⡠⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣟⣷⡆⠀⠀⠀⠀⠀ ⠀⠀⣼⠁⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠃⠀⡀⠀⠀⠀⠀ ⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠖⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⣶⡟⠛⠛⠿⠿⠿⠿⠖⠒⠛⠓⠦⣄⡀ ⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠐⠀⢿⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣀⣤⣶⡾⠿⠟⠿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣄⣠⡄⢢⣰⡜⠿⣿⠁⠉⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⡾⣟⣿⡶⣌⡞⠀⠀⠀⠀⢸⣿⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠖⠒⠂⠉⠋⠉⠐⠲⠶⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠜⠁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⠀⠀⠀⠛⢄⠀⠀⠀ ⠀⠀⣰⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠀⠀⠀⠈⢧⠀⠀ ⢀⡰⠁⠀⢀⠖⠉⠉⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠉⠳⡀⠀⠀⠀⠀⠷⠄ ⢏⠂⠀⠀⢸⠀⠀⠂⠀⢸⠀⠀⢀⠄⠀⠀⠀⠐⡁⠀⠐⠀⠀⡇⠀⠀⠀⠀⣉⠜ ⠀⠙⡄⠀⠈⠶⣒⣒⡲⠊⠀⠀⠪⠀⠀⠀⠀⠀⠱⢖⣒⣒⠖⠁⠀⠀⠀⡰⠁⠀ ⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⣀⠀⠦⢶⣤⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀ ⠀⠀⠀⠀⠑⢤⡀⠀⠀⡞⠙⣷⠰⠚⠻⠟⢺⠟⢿⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⡶⠓⢤⣿⣀⠀⠀⠀⢸⠤⠼⣧⡤⠔⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⢠⣿⣿⠛⠛⠛⢻⣿⢆⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⡟⢻⣀⣀⣀⡿⢻⡄⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣷⣾⣿⣿⣿⣷⣾⣷⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀
⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟪⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟪🟪⬛⬛⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛ ⬜⬜⬜⬜⬛🟪🟪🟪⬛⬜⬛🟪⬛⬜⬛⬛⬜⬜⬜⬛⬛🟪🟪⬛ ⬜⬜⬜⬜⬛🟪🟪🟪🟪⬛🟪🟪⬛⬛🟪⬛⬜⬛⬛🟪🟪🟪⬛⬜ ⬜⬜⬜⬜⬛🟪🟪🟪⬛🟪🟪🟪⬛🟪🟪⬛⬛🟪🟪🟪🟪🟪⬛⬜ ⬜⬜⬜⬜⬜⬛⬛🟪🟪🟪🟪🟪🟪🟪⬛⬛🟪🟪🟪🟪🟪⬛⬜⬜ ⬜⬜⬜⬜⬜⬛🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛⬜⬜ ⬜⬜⬜⬜⬛🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛⬜⬜⬜ ⬜⬜⬛⬛🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛🟪⬛⬛⬜ ⬜⬛🟪⬛🟥🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛⬜ ⬛🟪🟪⬛🟥⬛🟪🟪🟪🟪🟪🟪🟥🟥🟪🟪🟪🟪⬛🟪🟪⬛⬜⬜ ⬛🟪🟪⬛🟪🟪🟪🟪🟪🟥⬛🟥🟥🟪🟪🟪🟪🟪🟪⬛🟪🟪⬛⬜ ⬜⬛⬛⬛⬛🟪🟪🟪🟪🟪🟥🟥🟪🟪🟪🟪🟪🟪🟪🟪⬛🟪🟪⬛ ⬜⬜⬜⬛⬜⬛⬛🟪🟪🟪🟪🟪🟪⬛⬛🟪🟪🟪🟪🟪🟪⬛⬛⬜ ⬜⬜⬜⬜⬛⬜⬜⬛⬛⬛⬛⬛⬛⬜🟪🟪🟪🟪🟪🟪⬛🟪⬛⬜ ⬜⬜⬜⬜⬛🟪⬜⬜⬜⬜⬜⬜⬜🟪🟪🟪⬛⬛🟪🟪🟪⬛⬜⬜ ⬜⬜⬜⬜⬜⬛🟪⬜⬜⬜⬜🟪🟪🟪🟪🟪🟪🟪⬛⬛⬛⬛⬜⬜ ⬜⬜⬜⬜⬜⬛⬛🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛🟪⬛⬜ ⬜⬜⬜⬜⬜⬛🟪⬛⬛🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛🟪🟪⬛ ⬜⬜⬜⬜⬜⬜⬛🟪🟪⬛⬛🟪🟪🟪🟪🟪🟪🟪🟪⬛🟪⬛⬛⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬛⬛⬛🟪🟪🟪🟪🟪⬛⬛⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟪🟪🟪⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜
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⠀ ⠀ (\__/) (•ㅅ•) Don’t talk to _ノヽ ノ\_ me or my son `/ `/ ⌒Y⌒ Y ヽ ever again. (  (三ヽ人  /  | | ノ⌒\  ̄ ̄ヽ ノ ヽ___>、__/ |( 王 ノ〈 (\__/) /ミ`ー―彡\ (•ㅅ•) / ╰ ╯ \ / \>
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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠳⡀⠀⠀⣰⣫⣴⠶⣤⡀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⢬⡖⠒⠁⢉⣠⣤⣬⣿⣶⡀⠀⠀⠀⣀⣴⣾⣇⠀⠀⡜⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠐⢶⣯⣿⣶⡾⣿⣿⠷⠶⣿⣿⣿⣷⡦⢈⠒⢊⠤⠾⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣄⡀⢀⣀⣠⡾⠁⠀⠀⠈⠉⢉⡽⠋⠀⠀⠀⠈⠻⢿⣿⣽⡾⢶⡁⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⢹⠿⣿⣿⠁⠀⠀⣤⣶⣾⣿⣿⣿⣦⣀⠀⠀⢀⣰⡄⠀⠀⠀⢹⣷⢿⣿⣿⠀⠀⠀⠀⠀⣠⠔⠒⠒⢄ ⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣿⣿⣸⣸⣿⡇⠀⢀⡾⠋⠁⠀⠀⠉⠙⠻⣿⡿⠛⠋⠙⠻⣶⣄⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⢻⡄⠀⠀⠀ ⠉⠳⠤⠊⠁⠀⠉⢦⠀⠀⣿⣯⣿⣿⣿⠃⠀⢸⠑⢶⣾⣿⢻⠶⣶⣤⣀⣀⣀⡀⠀⠀⠙⣿⠀⢸⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣆⠀⠀ ⠀⠀⠀⠀⠀⣀⡴⠏⠀⠀⣿⣿⣿⣿⣿⡄⠀⠘⢠⠸⣿⣿⣿⣶⣧⣀⣏⣉⣏⣽⣿⠗⠀⠁⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄ ⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡀⠀⠈⢧⠙⣿⣍⠙⠛⠿⠿⠿⣿⡿⢋⡔⠀⠀⢠⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣠⠞⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠳⢌⡙⠓⠶⠤⠴⠞⢋⡤⠋⠀⠀⣰⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣟⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣾⣷⡄⠀⠀⠀⠉⠓⠒⠒⠒⠋⠁⠀⠀⣠⡾⢃⣾⣿⣿⡟⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⣠⣾⣿⣿⣿⣧⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⣠⠤⢤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠠⠶⠤⠶⠛⣉⣴⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠒⠉⠉⠙⠒⠢⠤⣠ ⣡⠖⠊⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣯⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠻⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⢿⣿⠿⠟⠛⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢙⣿⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣤⣤⣶⠟⠋⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀
N   O     O      o      o       o      o      。     。    .    .     .     .
⠀⠀⠀⠀⠀⣠⡟⠉⠁⠀⡴⠃⠀⠀⠴⡔⢀⡴⠋⠁⢀⣴⢞⣿⠋⠁⠀⠀⠀⢀⡠⢀⣴⠞⠁⠀⠀⠀⠀⣀⠄⢀⣾⣤⣶⠟⠉⠁⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠟⠀⠀⠀⣰⠁⠀⠀⠀⣠⣰⠟⠀⢀⡴⠛⢡⡞⠁⠀⠀⠀⣠⠚⢡⣶⣿⠋⠀⠀⠀⣠⡴⢛⣽⡶⠋⣱⠟⠁⠀⠀⢀⡤⢀⡾⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠐⠄⠀⠀ ⠀⠀⠀⣼⠏⠀⠀⠀⢰⡇⢀⡴⠀⢰⡟⠁⢀⡴⠋⣠⣾⠏⠀⠀⣠⠶⠊⣡⠾⢋⣼⠃⠀⠀⣠⢾⡵⠟⣩⠟⣠⠞⠁⠀⠀⢀⡴⠋⢀⡼⠁⠀⠀⠀⠀⣤⢸⠇⠀⠀⠀⠀⠈⢄⠀ ⠀⠀⣼⠋⠀⠀⠀⠀⡎⠀⡜⠁⢀⣏⠀⣠⣟⣴⠟⣽⠃⣀⣀⣴⣁⣠⡞⠁⠀⡾⠏⠀⣠⢞⡵⠋⠀⡴⢃⡴⠃⠀⠀⢀⣴⠟⠀⠀⣼⠃⠀⠀⠀⠀⢰⢣⡟⠀⠀⠀⠀⠀⠀⠈⣆ ⠀⣸⡏⠀⠀⠀⠀⢰⠃⡼⠁⢠⡟⢀⣼⡿⠟⠁⣸⠃⢀⣴⠋⢀⡽⠋⠉⠛⣿⡟⠦⠤⣥⣋⡀⠀⣼⢡⡞⠁⠀⢀⣰⣿⠋⠀⠀⢰⠏⠀⠀⠀⠀⣰⢁⡞⠀⠀⠀⠀⢠⡇⠀⠀⠘ ⢠⡿⠀⠀⠀⠀⠀⡼⡼⠁⠀⢻⢠⡾⠛⠁⠀⣼⠃⣠⡾⠁⣠⠟⠁⠀⠀⢰⢻⠃⠀⡜⠃⠉⢉⣿⣿⣿⣦⣤⣴⣿⣟⣁⣠⣤⢴⡟⠀⠀⠀⠀⢠⣧⡞⠀⠀⠀⠀⢰⣾⠀⠀⠀⠀ ⢸⢻⡆⠀⢀⠀⢠⣿⠁⠀⠀⢸⠟⠁⠀⠀⣼⢃⣴⡟⢀⡾⠙⠀⠀⠀⠀⡞⡌⠀⣸⠌⠀⢀⠞⣿⠏⠀⠀⣠⡾⠉⠉⠁⢀⡄⣾⠃⠀⠀⠀⢠⣿⡾⠁⠀⡀⠀⢀⣯⡇⠀⠀⠀⠀ ⡟⢸⣷⠀⠈⠛⢾⣇⣀⡄⣠⣏⣠⣄⣤⣼⣿⣿⣿⣤⣏⠀⠀⠀⠀⠀⢸⠇⣇⢾⠏⠀⢠⠏⣰⠃⠀⣠⣾⠏⠀⠀⠀⣠⠞⢳⡇⠀⠀⠀⠰⣞⣾⠁⢀⡾⠁⢀⣿⣿⡇⠀⠀⠀⠀ ⡇⠀⢹⣷⠤⣤⣾⣧⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣽⢸⣯⡟⠀⢠⠏⢠⠏⠀⣰⣿⠏⠀⠀⠀⣠⠏⢀⣾⠁⠀⠀⠀⣼⣿⣁⣠⣾⠁⠀⢠⡾⣿⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣆⣾⢿⠏⠻⠾⣿⣿⣟⠛⢹⡿⣿⡿⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣟⠃⢀⣎⢀⡏⢀⡾⢱⡏⠀⠀⠀⣰⠃⠀⣼⡏⠀⠀⠀⢠⣽⢟⣿⣿⠇⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⡏⠀⠀⠀⠈⠉⠛⠷⣾⣱⣟⠀⠀⠀⠀⠀⠀⢿⡍⠙⢻⣿⣿⣷⣆⠈⡿⣄⡟⠁⣾⠃⠀⠀⡸⠁⢀⡾⣿⠃⠀⠀⠀⣿⡿⠋⢠⡿⣦⢠⣾⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣹⡄⠀⠀⠀⠀⠀⠀⠛⡹⠉⠉⠛⠲⠶⢤⣀⡀⢳⣄⣼⠃⣹⣿⣿⣾⢀⠾⡇⢸⠏⠀⠀⠀⠁⢀⡞⢀⡟⠀⠀⠀⣸⡟⠁⢀⡿⠀⢨⢿⣱⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠺⣿⣛⠹⠁⠙⢷⠟⠀⡇⡟⠀⠀⠀⠀⢠⡟⠀⢸⡇⠀⠀⢰⣿⣁⣤⣼⠁⣰⠋⠀⣻⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⠉⢿⣟⣆⠀⡄⠀⠀⠠⢚⡡⠄⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⡞⠀⠀⢷⡇⠀⠀⠀⢀⡟⠀⠀⣿⠁⠀⣐⣿⣯⣿⣾⣿⣿⣷⣦⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⠈⢿⡜⠆⣧⠀⠀⠔⠋⠁⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⣠⠄⢸⡀⠀⠀⠀⡾⠀⣠⡴⣿⠀⠾⢻⡟⢻⣿⡿⠿⣍⠉⢻⣿⣿⣤⡄⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠸⣧⠀⠘⣷⡀⠹⠂⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⢋⠤⠒⢹⢤⠄⣀⣼⣥⠞⠉⠀⣿⠀⠀⣼⣷⣿⡏⠀⠀⣿⠀⣼⣿⢻⣿⣇⣄⡄⠀⠀⢀⢻ ⢻⡀⠀⠀⠀⠻⡄⠀⠈⢳⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡷⠋⢁⡟⠁⠀⠀⠀⣿⠀⢠⣿⠉⠘⠦⠤⠶⠋⠘⠉⣠⡾⣿⣷⠟⠀⠀⣰⠋⡞ ⠘⣷⡀⠀⠀⠀⢳⡄⠀⠀⠳⡵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⡇⠀⠀⠀⠀⢻⡀⢸⣻⡛⠲⢤⣀⠀⡀⣠⠴⠉⢁⣿⡿⢦⣀⡴⠃⡼⠁ ⠀⣿⠿⣦⣄⠀⠀⠳⡄⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡸⡇⠀⠀⠀⠀⠈⡇⡎⢸⡇⠀⠀⣨⠿⣿⣁⡀⠀⣡⣿⣧⡴⠋⠀⡼⣡⣿ ⣷⣬⡃⠐⠙⠷⣦⣀⠙⢦⡀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢤⠄⠀⠀⠀⠹⣿⡄⢱⡔⠊⠀⠀⠈⠑⠒⣻⡿⢻⡇⠀⢀⣾⣿⣷⣷ ⠉⢻⣿⠀⣀⠀⠀⠈⠙⠳⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣵⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣠⠞⢣⣿⡿⠁ ⠀⣼⣿⠀⠘⣆⠀⠀⠀⠰⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡿⠞⢁⡴⠋⡾⠁⠀ ⠀⣿⡇⠀⠀⠘⡆⠀⠀⠀⢳⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠰⠋⠀⢸⠃⠀⠀ ⠀⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣿⠀⠀⠀ ⢰⣿⠃⠀⠀⠀⡇⠀⡆⠀⠀⠘⣿⡄⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢀⠈⣧⡀⠀ ⢸⡿⠀⠀⠀⠀⣇⠀⣀⠀⠀⢀⡾⣿⠉⠉⠁⢀⡈⠉⠉⠓⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠘⣆⠈⠻⢦ ⣾⡇⠀⠀⠀⠀⠈⠉⠁⠀⠀⢸⣄⣬⡽⠶⣾⠋⠙⢷⣤⡤⠤⠤⣄⣉⣓⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡀⠀⠀⠀⠀⣿⣄⠀⠀ ⠟⢀⡀⠀⠀⢦⠀⠀⠀⠀⠀⠘⣿⠋⠀⠀⣿⠀⠀⠀⣷⠀⠀⠀⠀⠈⣿⠅⠉⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⣰⠟⣼⡇⠀⠀⠀⠀⣿⠀⠉⠉ ⠁⠈⢻⡀⠀⠈⡆⠀⠀⠀⠀⠀⠻⣤⣀⣤⣿⠀⠀⠀⢹⠀⠀⠀⠀⠀⣿⠀⠀⠘⢦⠀⠉⠛⠶⣤⣤⣀⣀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠃⠀⠹⣷⠀⠀⠀⠀⣿⠀⠀⠀ ⡀⠀⢸⡙⡄⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⢀⡇⠀⡯⠀⠀⠀⠈⠙⠦⣄⠀⠀⠈⠉⠉⠛⠒⢿⣄⡀⠀⠀⠀⠀⠀⠀⣰⡘⣷⠀⠀⢀⣿⠀⠀⠀⣰⠇⠀⠀⠀ ⡇⠀⠀⠻⣞⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⢸⡇⠀⡇⠀⡀⠀⠀⠀⠀⠈⠳⢶⡶⣄⡀⠀⠀⠀⠈⠛⢦⣄⠀⠀⢀⡴⠿⠤⠿⠀⠀⣼⠋⠀⣠⡶⠏⠀⠀⠀⣀ ⣷⠀⠀⠀⠹⣦⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⣿⡇⠀⠃⠸⣧⡀⠀⠀⠀⢀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠈⠛⠷⣏⡀⠀⠀⠀⡤⠾⠧⠴⠛⠋⠀⠀⠀⠚⠉⠀ ⢸⠀⠀⠀⠀⠈⠳⣄⢹⣄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠀⠀⣿⡃⠀⠀⠈⣹⡇⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠉⠳⢦⣶⣀⠀⠀⠈⠛⢶⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
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