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⠀⠀⠀⠀⡆⠁⠀⠀⠀⠀⣀⣴⣾⣿⣿⣷⣶⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣧⠀⠀⠀⠀⣼⣿⣿⣿⠿⠟⠛⢛⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣤⣄⢀⢻⠀⠀⠀⠀⣿⡟⠉⠀⠀⠀⠀⢈⣄⣱⣀⠀⠀⢀⡀⣀⢀⠀⠀⠀⠀
⠉⠉⢸⢸⢸⠀⠀⠀⠀⠹⡇⢀⢤⣤⡴⠺⡟⠿⠻⢹⡄⠀⢨⡏⣞⢱⠃⠀⠀⠀
⠀⠀⡌⢸⡌⠀⠀⠀⠂⢰⣻⠐⠛⠛⡡⢄⣙⠶⡤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡇⣸⡇⠀⠀⠀⠀⠈⢧⣷⡐⢬⣤⠾⠽⢓⡇⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡇⣿⡟⡽⣻⠗⠀⠀⠀⠐⢧⠈⠉⠀⠭⠜⣀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⠀⣿⡏⠃⠘⠀⠀⠀⠀⠀⠸⡄⢄⢤⣤⣤⣿⣽⡿⠉⠂⠀⠀⠀⠀⠀⠀⠀
⠀⢸⠀⠛⠛⠉⠭⠴⠶⠶⠶⢖⡶⢺⠀⠀⠉⢁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
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🟥🟦🟦 🤍
🟥🟥🟥🟥🔪 ⚪️
🟥🟥🟥🟥 🟩🟩🟩
🟥 🟥 🟩 🟩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⠑⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⡀⠀⠀
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⣼⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⢰⠃⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⡇⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⣷⠀⠀⢺⣿⣿⠂⠀⢠⡄⠀⠀⠀⠀⠀⠀⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⢠⠏⠀⠀⠀⠉⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀
⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⣰⠃⠀
⢿⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢀⠀⠀⠀⡼⠁⠀⠀
⠈⣇⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠈⠀⠀⣼⠁⠀⠀⠀
⠀⠘⣆⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠁⠀⠀⣿⠀⠀⠀⠀
⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡵⠀⠀⠀⠀⣿⠀⠀⠀⠀
⠀⠀⠀⠈⡇⠀⠰⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⢀⣤⠞⠁⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠻⡄⠀⠀⠀⠘⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢿⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⠤⠤⠴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠶⣤⠀⠀⠀⠀⢳⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⠀⠚⠋⠉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠛⠛⠉⠉⠉⠉⠙⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠋⠉⠉⠛⢷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⡄⠀⢀⣠⣾⠟⠛⠛⠛⠋⠀⠀⣀⣀⣀⣀⣀⠈⠉⠛⠛⠛⠛⠛⠿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⣾⣛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢿⣯⣉⠉⠉⠙⠛⠶⣤⣀⠀⠀⠀⠀⠉⠛⠷⢦⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⡏⠉⠛⢶⣤⣀⡀⢀⣀⣀⠀⠀⠈⠉⠛⠳⠶⠦⣤⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢹⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠶⠶⠶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⡆⢀⣤⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⠶⠶⠶⠶⣼⣿⠿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣷⣦⡀⠀⠀⠀⠀⠙⠷⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣇⠘⠁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠷⢦⣄⠀⠀⠀⠀⠀
⠀⠀⠀⡿⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠶⢦⣤⣄⠀⠀⠀⠀⠀⢶⣶⡛⠲⠶⢤⣤⣀⠀⠀⠀⢰⣶⡖⠲⣦⣄⡀⠈⠁⠀⠀⠀⠀
⠀⠀⠀⡇⢦⡀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⣀⠀⠀⠀⠉⠛⠶⣦⣤⣈⣉⠳⣦⡄⠀⠈⠙⠓⠾⢿⠷⠀⠀⠀⠀⠀⠀
⠀⠲⠶⠷⠦⣭⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠳⢦⣄⡀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢸⡆⢿⡏⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⡤⠶⠖⢻⠋⠉
⠒⠚⠛⠳⠾⢿⣏⣁⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣳⠶⠛⠉⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡀⢰⡶⣾⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⢂⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⡗⠋⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣋⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣦⠀⠀⠐⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⢀
⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⣾⣷⡟⣦⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠒⠛⠛⠛⢛⣿⣿⠛⠛⠛⠻⡲⠶⠤⣄⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠿⠷⠖⠚⠛
⢬⡿⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠛⠛⠁⠈⠳⠶⠖⠚⠛⠉⣿⢞⣧⠀⢀⣀⣀⣀⣙⣿⣛⣀⠀⠀⠀⠀⣗⢛⡟⠉⠛⠲⣄⣀⣀⣀⣤⡤⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀
⡞⠁⠀⠈⠙⠲⠦⢤⣤⣄⣀⣀⣠⣤⡴⠟⠀⠀⢠⣤⣶⡄⠀⠀⠀⢀⣼⡿⠗⠛⠋⠉⠛⠋⠉⠉⠉⠙⠫⢿⣶⠶⣽⣿⠁⠀⠀⠀⢈⣹⣉⠁⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⢲⣤⣤⠤⢤⣤⣀⠀⠀⡶⢶⡀⠀⠀⠀⠀⠐⢻⣿⡿⠇⠀⢀⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣶⡀⢰⣿⣡⡟⠀⠀⢘⣧⠀⠀⣀⣀⣠⣤⣤⠶⠚⠛
⢰⠟⠁⠀⠀⠀⠀⠈⠉⠛⠳⠾⠧⢴⣶⣶⡶⠶⠾⣍⠀⠀⠀⠸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⢀⣶⠖⠛⠉⠉⠙⠛⠿⢭⣭⣿⡛⡇⠀⠀
⢸⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠓⢈⣳⣄⠀⠀⢙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⢀⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢦⣤
⠈⠻⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠾⠃⠀⠀⠰⢝⢦⣲⣏⣹⠟⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡅⠀⠀⢀⡾⠋⠛⢷⣶⠤⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠉⠙⠒⠒⠲⠒⠒⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠑⢍⠻⣥⡀⠀⠀⠉⠛⠓⠶⠤⣤⠤⠤⠶⠖⠚⠋⠁⢻⣍⣽⣠⣴⠟⠁⠀⠀⠀⠉⠳⣤⢨⣿⡟⠛⠛⠒⠒⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⣿⣩⡇⠀⠀⠀⠀⢀⣀⣤⠶⠟⠙⢿⡷⢦⣀⠀⠀⠀⠀⠈⠻⣏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠉⢉⡟⠉⠉⠉⠙⠓⣶⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠒⠒⠒⠚⠋⠉⠻⡄⠀⠀⠀⠈⢷⣼⣿⣿⣦⣄⣀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣁⡀⠀⠀⠀⣸⠃⠀⣼⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠘⣿⣟⣿⡟⠄⣻⡟⠶⢤⣄⣘⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⢤⠇⠀⣼⠁⠀⠀⠀⠈⣹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⢸⣿⡟⠁⣴⡿⠃⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠢⣤⣀⢰⠏⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠉⢣⠀⠀⠀⠀⢠⣾⠇⠙⠳⢦⣼⡏⢠⣾⡟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⢦⣀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⡾⠀⠀⠀⣴⡿⠃⠀⢠⣶⣶⠉⢀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⠤⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⡾⠁⠀⠀⣸⡟⠀⠀⣀⣾⣿⡿⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠚⠋⠀⠀⠀⢀⣿⣠⡴⠛⠁⠈⠻⣆⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠿⢿⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠋⠁⠀⠀⣀⣤⣤⠤⠴⠒⠀⠀⠀⠀⠤⠤⠤⣍⠛⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⣿⠟⠁⠀⠀⢠⡔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀⠀⠀
⠀⠀⠀⠀⣼⡿⠁⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀
⠀⠀⠀⣼⡿⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀
⠀⠀⣰⣿⠁⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀
⠀⢀⣿⠇⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⢸⣿⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⣾⡇⣀⣼⣧⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⣀⣶⣾⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⢸⣿⣿⣿⣯⣀⣨⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣾⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⠻⣿⣄⠀⠀⠀⠀⠀⠀⢸⣿⠃
⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⠀⠀⠀⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⡿⠀⣸⣿⠀⠀⠀⠀⠀⠀⣸⡿⠀
⢸⣷⠀⠙⠻⠿⣿⣛⣛⣉⣁⣴⡿⠋⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⡿⠿⠟⣋⣠⣶⠿⠁⠀⠀⠀⠀⠀⢠⣿⠇⠀
⢸⣿⠠⣆⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀
⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀
⢸⣿⡄⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀
⠈⣿⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀
⠀⢹⣿⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀
⠀⠀⢿⣧⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢿⣧⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢿⣷⡀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⣿⣦⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣿⠟⠁⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣾⡟⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣼⣿⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣙⣿⣷⣆⡀⠀⠀⠀
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🍆🍑🍑🍑🍑🍑🍑🍑🍑🍆
🍆🍑🍑🍑🍑🍆🍆🍆🍆🍆🍆
🍆🍑🍑🍑🍆🍌🍌🍌🍌🍌🍌🍆
🍆🍑🍑🍆🍌🍌🍌🍌🍌🍌🍌🍌🍆
🍆🍆🍆🍑🍑🍆🍌🍌🍌🍌🍌🍌🍌🍌🍆
🍆🍑🍑🍆🍑🍑🍆🍌🍌🍌🍌🍌🍌🍌🍌🍆
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🍆🍑🍑🍆🍑🍑🍑🍑🍆🍆🍆🍆🍆🍆🍆
🍆🍑🍑🍆🍑🍑🍑🍑🍑🍑🍑🍑🍑🍑🍆
🍆🍑🍑🍆🍑🍑🍑🍑🍑🍑🍑🍑🍑🍑🍆
🍆🍑🍑🍆🍑🍑🍑🍑🍑🍑🍑🍑🍑🍑🍆
🍆🍑🍑🍆🍑🍑🍑🍑🍑🍑🍑🍑🍑🍑🍆
🍆🍑🍑🍆🍑🍑🍑🍑🍑🍑🍑🍑🍑🍑🍆
🍆🍑🍑🍆🍑🍑🍑🍑🍑🍑🍑🍑🍑🍑🍆
🍆🍆🍆🍑🍑🍑🍑🍑🍑🍑🍑🍑🍑🍆
🍆🍑🍑🍑🍆🍆🍆🍆🍑🍑🍑🍆
🍆🍑🍑🍑🍆 🍆🍑🍑🍑🍆
🍆🍑🍑🍑🍆 🍆🍑🍑🍑🍆
🍆🍆🍆 🍆🍆🍆
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⠛⠛⠿⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠴⡿⠿⠿⣿⣗⡠⠤⢀⡁⠒⠙⣿⣿⣿⣿⣷⠀⠀⠀
⠀⠀⢀⢔⠕⠀⠀⠀⠀⠀⠀⠉⠙⠓⠾⣕⣢⣼⣿⣿⣿⣿⡁⠀⠀
⠀⠠⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠙⠻⢿⣿⣿⣿⣿⣷⣄
⢀⠃⠃⠀⠀⢀⣠⡴⠃⠀⠀⠀⠀⠈⠉⠉⠳⠆⠀⠙⣿⣿⣿⣿⣿
⢸⠀⠀⠀⠉⣉⠉⣀⣀⠀⠀⠀⢀⣀⠀⢀⠀⠀⠀⠀⢸⠀⠉⠉⠁
⢸⠀⠀⠀⠀⠛⠛⠛⠋⠀⠀⠀⠈⠒⠛⠛⠁⠀⠀⠀⠸⠀⠀⠀⠀
⠀⠆⠀⠀⢀⡠⠄⠒⠂⠈⠉⠉⠀⠒⠒⠤⣀⠀⠀⢀⠆⠀⠀⠀⠀
⠀⠈⢄⠀⠉⠉⡙⠋⡟⠀⠒⠶⡒⠒⠒⠒⡱⠃⢀⠎⠀⠀⠀⠀⠀
⠀⠀⠈⠪⣉⠳⣄⠀⠀⠀⠀⠄⢈⡑⠒⠈⢀⠜⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⡆⠀⠀⠀⠈⢁⡢⣄⠄⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠒⠢⡙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⠀⠀⠀⠀⡔⠉⠂⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣄⠀⢀⡀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀