Panties Emojis & Text

Copy & Paste Panties Emojis & Symbols 👙🩲🟥

⢀⣶⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣶⡀ ⢸⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁ ⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀ ⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀ ⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀ ⢀⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣄⣀⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⡀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡇ ⠀⣿⣇⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⣸⣿⠁ ⠀⣿⣿⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣿⣿⠀ ⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢰⣿⠇⠀ ⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀ ⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀ ⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⠾⣝⠣⣌⡲⣷⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣶⣭⣶⣉⠛⠳⠄⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡛⠿⣿⣿⣶⣶⣤⣄⣀⡈⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠤⠚⢰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠈⠙⠧⣍⠙⠛⢻⠿⠿⣶⣶⣤⣤⣦⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡽⠋⠉⠁⠀⡄⠀⡾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠈⢳⡀⠀⢦⠀⠀⠙⠉⠛⠛⢿⣷⣷⣦⣤⣀⡀⠀⠒⠒⠒⠩⠄⠂⣀⠀⣀⣽⣧⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⡏⠛⢿⣿⣶⣶⣤⣉⡉⠓⠙⠛⡒⠉⢿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢹⡇⠀⡀⢀⠷⣄⣀⣤⠀⠀⠀⡀⠓⢤⣀⣼⠿⠿⠛⣿⡿⠟⠓⠒⠀⠀⠀⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡼⢁⠎⢠⣿⣿⠇⡀⢀⡔⢁⡶⠚⠉⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⣠⠔⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠎⠀⣿⡿⠈⢸⣇⡼⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⠀⣼⣿⠃⠀⢸⠏⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⡽⠈⠀⠀⡿⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢸⠁⠀⠀⢰⡇⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢨⠇⠀⠀⠀⡏⠀⠀⠀⡼⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢸⠀⠀⠠⣸⠀⠀⠀⣰⠃⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢀⣿⡇⠀⢠⠇⠀⠀⣼⠇⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⣀⣾⢻⣥⢀⡾⢀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣃⣀⣠⡾⠋⠀⢸⣿⣾⣧⣸⠻⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣧⣀⣀⣠⣾⣿⣿⡿⠁⠀⠀⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠿⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⡄⢈⣉⣙⡛⠛⠿⠶⢤⣤⣴⣺⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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