Bird Dot Art

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠋⠙⢿⣿⣦⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣤⣤⣾⣿⡿⠟⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⢤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀ ⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠙⠻⠿⠿⣿⣿⣿⣿⣿⣯⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠛⠻⢿⡿⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠒⠒⠒⠶⠦⠤⠴⠒⠚⠉⣰⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⣤⣄⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⣰⠞⠁⠀⠀⠀⢠⣤⠀⠀⠀⠀ ⠀⠀⢠⡟⠸⣿⡿⢀⠤⢄⠀⠐⣷⣿⣿⡷⠀⠀⢻⠀⠀⠀⢀⡴⠋⠘⡇⠀⠀⠀ ⠀⠀⢸⠈⠲⡬⢠⡏⠀⢀⡷⠀⠨⣭⠭⠖⣇⠀⣾⠀⠀⡴⠋⠀⠀⠀⣧⠀⠀⠀ ⠀⠀⢸⣷⠞⠁⠀⠳⠖⠋⠀⠀⠀⠙⠶⠶⠃⡼⢿⣠⠎⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀ ⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢠⠃⠀⠀⠄ ⢀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠉⠲⢄⡀⢀⣠⡷⠀⠀⢠ ⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠧⠤⢾⢀⠏ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠏⠀ ⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀ ⠈⢷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢀⣤⡏⠀⠀⠀ ⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠶⠶⠖⠊⠁⣴⠇⠀⠀⠀ ⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⣠⣎⡀⡀⠀⠀⣀⣰⢶⠶⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠛⠉⡙⠛⢛⣷⠖⠒⢖⣾⠟⢛⠛⠺⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣥⣶⣦⡙⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠋⢐⡛⢿⣿⣿⣿⣿⣷⡘⢿ ⣿⣿⣿⣿⣿⣿⠇⡆⡇⡸⢸⣿⠟⣛⣛⠻⢿⡆ ⣿⣿⣿⣿⣿⡏⣼⣷⣶⣶⣿⡟⣸⣿⣿⣿⡆⠁ ⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣧⡙⣿⣿⡿⣸ ⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⠁⣾ ⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡆⣿ ⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿ ⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿ ⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿ ⣿⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿ ⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣩⣭⣶⣶⣮⣭⡙⠿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⡃⠄⠹⡿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣷⡌⢿⣿⣿ ⣿⣿⣿⣿⣿⠐⣠⡶⣶⣲⡎⢻⣿⣤⣴⣾⣿⣿⣿⣿⣿⠸⣿⣿ ⣿⠟⣋⡥⡶⣞⡯⣟⣾⣺⢽⡧⣥⣭⣉⢻⣿⣿⣿⣿⣿⣆⢻⣿ ⡃⣾⢯⢿⢽⣫⡯⣷⣳⢯⡯⠯⠷⠻⠞⣼⣿⣿⣿⣿⣿⣿⡌⣿ ⣦⣍⡙⠫⠛⠕⣋⡓⠭⣡⢶⠗⣡⣶⡝⣿⣿⣿⣿⣿⣿⣿⣧⢹ ⣿⣿⣿⣿⣿⣿⣘⣛⣋⣡⣵⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸🦢🦢🦢🦢🦢🦢🦢

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⠀⠀⣀⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣿⣿⠫⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⡿⠂⠁⠦⣀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠏⡐⠬⢃⢬⠓⣽⠦⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣽⣿⠐⣂⠤⢒⠩⠙⡺⠷⣅⣴⣶⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⢐⣂⣈⡉⠴⠋⠐⢺⣿⣿⣿⣶⣶⣬⣧⣽⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀ ⢸⡿⠀⠐⠂⠒⠒⠀⠀⢸⣿⣟⡙⢿⣿⣿⣿⡟⠿⣿⣯⣹⣿⣧⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⠆⠻⢿⣿⣿⣶⣬⣭⣟⡽⣿⣾⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⠿⠛⠉⠉⠉⠀⠀⠉⠑⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⣙⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣏⠯⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡼⢣⢽⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠭⣇⣺⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣕⣻⣿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⡮⣷⣿⢻⣏⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣏⠷⡵⣻⣯⢳⡬⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣟⣟⡞⡼⣛⠖⣿⡚⣯⢱⡳⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣟⡾⣼⡳⣍⠺⢣⡝⣶⠡⣟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣾⣽⢲⡽⣋⢼⢣⡟⣞⡼⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣷⣽⣮⣵⣿⣞⣽⣿⣯⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣩⣭⣶⣶⣮⣭⡙⠿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⡃⠄⠹⡿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣷⡌⢿⣿⣿ ⣿⣿⣿⣿⣿⠐⣠⡶⣶⣲⡎⢻⣿⣤⣴⣾⣿⣿⣿⣿⣿⠸⣿⣿ ⣿⠟⣋⡥⡶⣞⡯⣟⣾⣺⢽⡧⣥⣭⣉⢻⣿⣿⣿⣿⣿⣆⢻⣿ ⡃⣾⢯⢿⢽⣫⡯⣷⣳⢯⡯⠯⠷⠻⠞⣼⣿⣿⣿⣿⣿⣿⡌⣿ ⣦⣍⡙⠫⠛⠕⣋⡓⠭⣡⢶⠗⣡⣶⡝⣿⣿⣿⣿⣿⣿⣿⣧⢹ ⣿⣿⣿⣿⣿⣿⣘⣛⣋⣡⣵⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣩⣭⣶⣶⣮⣭⡙⠿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⡃⠄⠹⡿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣷⡌⢿⣿⣿ ⣿⣿⣿⣿⣿⠐⣠⡶⣶⣲⡎⢻⣿⣤⣴⣾⣿⣿⣿⣿⣿⠸⣿⣿ ⣿⠟⣋⡥⡶⣞⡯⣟⣾⣺⢽⡧⣥⣭⣉⢻⣿⣿⣿⣿⣿⣆⢻⣿ ⡃⣾⢯⢿⢽⣫⡯⣷⣳⢯⡯⠯⠷⠻⠞⣼⣿⣿⣿⣿⣿⣿⡌⣿ ⣦⣍⡙⠫⠛⠕⣋⡓⠭⣡⢶⠗⣡⣶⡝⣿⣿⣿⣿⣿⣿⣿⣧⢹ ⣿⣿⣿⣿⣿⣿⣘⣛⣋⣡⣵⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠿⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⣀⣀⣀⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣾⣿⣿⠿⠿⠿⠿⠿⢶⣶⣶⣤⡀⠀⠀⢻⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠉⠉⠉⠉⠛⠿⣷⡄⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠹⣿⠀⠀⠈⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣰⣿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣀⣀⣴⣾⠟⠀⠀⠀⢻⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣴⣶⣶⡿⠿⠿⠿⠿⠿⣷⣦⣄⠀⠈⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣾⡿⠿⠟⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⣠⣴⣿⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀ ⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠙⠻⠿⢷⣶⣶⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣶⣄⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣯⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡏⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠟⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣾⣿⣿⣿⣷⣿⣿⣦⣠⡏⠙⠿⠿⢿⣷⣦⣄⠀⠀⠀⠀⣼⣿⣿⣧⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠉⣿⠛⢻⣿⠛⠂⠃⠀⠸⣿⣿⡿⠻⣿⡆⠐⢏⡛⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣟⣿⡄⠘⠀⣾⠿⠀⢠⡀⠀⠰⣿⣰⡄⠀⣿⡇⠀⠸⢇⣸⣿⣿⠿⠛⠛⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠈⠉⠩⣿⣾⡿⠈⠛⠛⠋⠛⠛⠿⠿⠿⠼⡿⠇⣀⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠿⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖⣲ ⡶⠲⠶⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⣾⠃⠀⠀⠀⠀⣀⡤⠔⠚⠛⠙⠛⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣭⣭ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢈⡶⠞⠛⠋⠉⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⢠⡆⣠⣾⣿⣿⣿⣦⣀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠈⣿⠿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢡⡀⠀⠀⠀⠀⣽⡟⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⠙⠻⠿⢷⣶⣤⣄⣀⣀⣀⣠⣼ ⢻⣧⡀⠀⢠⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿ ⡟⠛⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢷⣦⢤⣤⣤⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿ ⣷⡤⠴⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢝⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣿⣿⣿⡭⣿⣿⣿⠽⢏⣹⣿⣿⣿⣯⡿⡻⠟⣿⣝⢻⠿⢿⢋⠹⡿⠽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⡸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠁⢠⣤⣤⣤⣤⠀⢠⣤⣤⣠⣤⣄⠀⣤⣤⣄⣠⡄⠀⣤⣀⣤⣤⣀⣄⢀⣤⠄⣤⣀⣤⣄⠀⣤⠀⢠⡄⢀⣤⠀⢠⣤⣄⣠⣤⣤⣤⣄ ⠀⠀⠀⢠⣿⠀⣿⠶⢾⣿⣿⣿⢷⣭⡰⣿⠀⣹⣿⣇⢀⣿⣿⡁⢈⣹⣿⣿⡁⠀⣿⣿⡷⣯⡀⣿⡶⢾⣇⣾⣿⣷⣾⡷⠿⢿⡷⠿⠋⢿ ⠀⠀⠀⠈⠛⠀⠛⠀⠘⠉⠛⠙⠛⠋⠀⠛⠛⠋⠀⠙⠛⠁⠈⠛⠋⠉⠋⠈⠓⠀⠙⠉⠛⠋⠀⠛⠀⠘⠛⠋⠀⠙⠛⠃⠀⠘⠃⠀⠀⠸ ⠀⢰⣤⣴⣶⣶⣶⣶⣶⣶⣤⣴⣦⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣴⣶⣤⣤⣴⣤⣴⣶⣶⣤⣤⣤⣤⡤⠤⠤⠤⠤⠤⠶ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣽⣟⣿⣷⣿⣻⣿⣿⣿⣿⣿⣿⣷⣭⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣟⡟⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠉⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡿⠿⠟⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣶⣾⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⣷⣦⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣿⣿⣿⣿⡿⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⣯⡙⠛⠿⠿⠿⣿⠿⠿⠿⠛⠋⣁⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠿⣿⣿⣷⣶⣶⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠿⠷⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⢀⣀⡀⠙⣷⡀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠘⠿⠃⠀⢸⣿⣿⣿⣿ ⠀⣠⡿⠛⢷⣦⡀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟ ⢰⡿⠁⠀⠀⠙⢿⣦⣤⣤⣼⣿⣄⠀⠀⠀⠀⠀⢴⡟⠛⠋⠁⠀ ⣿⠇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀ ⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀ ⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀ ⠀⠹⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠉⠙⠛⠿⠶⣶⣶⣶⣶⣶⠶⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠚⠉⠉⠉⠙⢯⣢⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⠊⠀⠀⣀⠀⠀⠀⠀⢱⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣮⠃⠀⠀⠘⠛⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⢀⣼⠒⣺⣻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠛⠃⠀⠀⠀⠀⠀⠀⢞⠁⠈⠉⡿⡿⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡴⠊⠁⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⣹⣖⠀⠀⠀⠀ ⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣧⠀⠀⠀ ⠀⠀⣎⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀ ⣠⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠈⠳⡅ ⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⢞⣁⣀⣀⡀⢀⡀⣀⡀⠓⠉⠒⠦⡀⠀⢱ ⡾⠀⠀⠀⠀⠀⠀⠀⢰⠛⠉⠀⠀⠀⢰⠛⠛⠛⠁⠈⠙⠛⠛⡇⠀⠀⠀⠈⠛⡄ ⢻⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⡀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣀⣀⣠⠃ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠁⢠ ⠸⡽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼ ⠀⠙⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡞⠀ ⠀⠀⠀⠀⠙⢲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⡦⠶⠶⣾⠏⠉⠉⠉⠉⠉⠉⢉⢿⣿⣷⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⡸⠷⣶⣴⣶⣦⡀⠀⠀⢀⣤⣤⣴⣵⡿⢞⠿⡶⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⠤⠿⠧⠶⠶⠤⢧⠃⠀⠀⠙⠾⢟⣛⣁⣒⣻⣅⣙⡾⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠛⠁⢰⣧⡈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣇⣼⡀⠻⠟⠁⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⣹⠙⣧⡀⠀⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⡴⠋⠀⣀⣴⣿⡷⠴⠞⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣁⣀⡤⠾⠛⠁⣸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⢿⣶⠶⠿⠟⠿⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠈⠙⠛⠿⠶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣠⣤⣤⣤⣤⣤⣀⠀⠉⠙⠳⢦⣄⡀⣀⣤⣀⣀⡄⠀ ⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⠻⢶⣀⠀⠀⠈⠉⢁⠈⠏⣿⣁⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⡴⠁⠀⠀⢙⣿⡾ ⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣀⣠⡾⠟⠃ ⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡔⢊⣵⠞⠋⠁⠀⠀⠀ ⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠳⠶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣴⠊⣁⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⡷⢶⡶⠶⠤⠔⢺⠃⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢰⡇⠀⡇⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣤⣭⠿⠟⣃⣾⠋⠀⠀⢠⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠙⠛⢋⣿⣙⣶⣾⡿⢷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠻⠧⠶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⠛⠚⠛⠻⠟⠛⠓⠟⠻⠓⠐⠚⠒⠛⠁⠀⠀⠸⠓⠇⠞⠛⠚⠙⠲⠀⠐⠞⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣏⣹⣿⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠋⢠⣷⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠛⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢾⣿⣿⣿⡟⠿⠿⣿⣿⠿⠿⠛⠋⣁⣴⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⠻⠷⣶⣤⣤⣤⣤⣶⣾⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣤⣤⣤⣤⣤⣴⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠙⠛⠻⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⣠⣴⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⢀⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⣼⣿⠋⠉⢹⣿⣿⣿⣿⣿⡄⠀⠀⣾⣿⢁⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠙⢿⣷⣤⣀⣹⣿⣿⣿⠟⠀⠀⠀⠈⠛⠛⠛⠛⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠁⠀⢀⣠⣴⣶⣶⣶⣶⣶⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⠉⣉⠉⠉⣽⣏⠛⠿⣿⣿⣶⣤⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠁⠀⠀⠺⣿⠇⠈⠻⠛⠀⠀⠀⠈⠙⠛⠿⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣿⣿⣶⣦⣤⣤⣤⣤⣤⣶⣶⣾⣿⡿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⡿⠛⠉⠉⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⡿⠟⠋⠉⠙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣧⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣷⣄⠀⠀⣸⣿⠿⣿⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠋⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣦⣠⣿⡟⠀⠈⠉⠛⢻⣿⡿⠿⠿⢿⢿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠁⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⣿⣷⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠆⠀⠀⠛⠿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠉⠻⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾ ⠀⠀⣿⡍⠛⠲⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠉⣠⡞⠀⠀ ⠀⠀⠘⣽⢷⣦⣌⣈⠋⡚⠿⣦⡀⠀⠀⣴⣶⡄⠀⠀⣠⡶⠚⠛⣙⣭⠠⣤⣶⣯⠆⠀⠀⠀ ⠀⠀⠀⣼⣷⣀⠀⠀⠈⠀⠀⠀⢻⡇⠺⡿⠛⣿⡅⠀⢿⠀⠀⣼⠿⣫⣭⣠⣤⡶⠂⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⠿⣹⣾⠔⠃⠀⠈⠳⠾⠏⠀⠻⣷⡺⠋⠀⣤⣸⣷⣶⡾⠖⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠒⠷⣿⡻⣞⣀⣄⣀⣀⡄⠀⠀⣠⣄⣸⡿⣾⣿⡽⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠯⣽⢿⡿⠃⠀⢀⣿⡙⠑⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣦⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢩⡿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣎⠁⠀⣀⣀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢿⡀⠀⠘⠛⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠤⠚⠉⣀⣠⠔⣻⡆⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣤⡶⠿⠛⠋⠉⠉⢹⢷⠆⠀⠀⠀⠠⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⡀⠀⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠙⣶⠁⢻⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⡀⣠⠏⠀⠈⠀⢠⡷⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢄⣀⣀⣀⠤⠴⠒⠚⠉⠉⠉⠀⠀⠀⠀⠀⢀⡴⠛⢛⣿⣿⡯⠀⠀⢀⡴⠋⣠⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⡠⠋⠀⣰⠃⠀⠀⠀⡠⢾⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠖⢚⣷⡤⠞⠁⠀⠀⠀⠔⠒⣻⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⢡⡀⠀⠀⠀⠀⠀⠀⠀⡰⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠋⢀⠀⠈⠉⢉⣹⠇⠀⠀⠀⠀⠀⢤⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⠈⠣⡀⠀⠀⠀⠀⠀⠀⡇⠈⣦⠀⠀⠀⠀⠀⣀⡠⠔⡋⣀⣀⣀⡴⠃⠠⠤⠒⣻⠃⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠓⠄⠀⠀⡀⢀⡠⠞⠁⠀⠉⣠⠖⠥⠤⠔⡾⠁⠀⠀⠀⢠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣄⠀⠸⢦⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⠤⠬⠽⠤⠤⠼⠿⠭⠤⠤⠤⠖⠋⠀⠀⢀⠸⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠬⠷⢄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠤⠤⣄⣽⠲⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠠⠇⠀⠈⢩⠏⡿⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⢀⡼⠀⠀⠀⡼⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠤⠤⠔⠒⠊⢀⣠⠴⠒⠁⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡁⠀⣀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡤⠊⢉⠖⠉⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠋⠌⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⡎⠀⡠⠒⠈⠉⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⢰⡒⠠⠤⢄⡜⠀⠀⠀⣠⣀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡄⠀⠩⣁⠒⠤⠌⢱⠀⠀⠙⠋⠀⠀⠀⠀⠸⠤⠤⠤⠤⣀⠀⢀⡠⣦⠴⣆⡀ ⠀⠹⡄⠀⠀⠉⢦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠙⠁⠚⢡⠞⡱⠇ ⠀⠀⠘⢆⠀⠀⠈⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡰⠁ ⠀⠀⠀⠀⠙⠦⢀⡜⠀⠉⠀⠀⠀⠀⠀⡄⠀⠔⢹⠤⢢⠤⠊⢱⠀⠀⠀⡎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠁⠀⢀⠇⠀⠀⢠⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⢀⠴⠃⠀⠀⢠⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠉⠒⠒⠈⠁⠀⠀⢀⡴⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⣀⡀⠀⠀⠀⠀⣀⣀⠠⠔⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠉⠁⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢽⣿⡀⠤⠃⠀⢀⡀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⡛⠗⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢡⢸⡧⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠎⠝⣄⢀⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣒⣁⡴⠚⡏⠉⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⣰⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠋⠀⠀⠈⣧⠴⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠃⠀⠀⠀⠀⠈⠢⠀⠀⠀⠈⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀ ⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠑⢦⡀⠈⢉⡉⢻⡇⡀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠊⠀⣀⡾⠁ ⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢆⡵⠋⠁⠀⠀ ⠀⠀⠀⠉⠳⠤⣄⣀⡀⠀⠀⠀⠀⣀⡔⣃⡤⠚⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠟⡖⠒⠊⣇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣯⣵⢞⣳⠒⠀⣰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠼⢼⣛⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠤⠴⠤⠤⠤⠴⠠⠤⠄⠀⠢⠴⠤⠤⠠⠄⠴⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢏⠑⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣶⢸⠆⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠣⢠⡞⠺⡧⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠸⡀⠈⠧⣀⠈⡤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡒⠉⠀⠀⠀⠀⣀⣀⣈⣉⣑⡺⢄⠈⠢⠋⠁⠀⠑⢄ ⢀⣀⠈⠙⠻⢒⡶⠟⣪⡥⢤⣤⡤⠤⠤⣀⠀⠀⠀⠀⠒⠨⢍⠊⢔⠒⠀⠀⠀⢸ ⣤⣭⣵⠞⠫⠭⢍⠑⠢⠄⣉⠁⠊⠉⠁⠀⠈⠀⠀⠀⠀⠀⢈⡆⠀⡀⠀⠀⠀⡜ ⠐⠶⠭⣭⡭⠥⢸⡄⠀⠀⠀⠉⠐⠢⠤⣀⣀⠀⠀⣀⣀⠠⠊⠀⠀⢱⠒⡖⠉⠀ ⠀⠈⠣⠤⠐⠒⠉⠙⠦⣤⣀⣄⠀⠀⠀⠀⠀⢨⡅⠀⠀⠀⠀⠀⣠⡦⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⠀⢀⡀⠾⣬⣦⣤⠤⠖⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢇⢗⣲⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⠤⣖⣏⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⡛⠛⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠹⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢀⡀⠀⢧⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡄⠀⣿⣿⠀⢸⠇⠀⢼⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⡁⠀⠉⠻⠃⡞⡀⢀⡞⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢷⡀⢠⡄⣾⠓⠃⢸⣧⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠙⠸⣇⣯⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠸⡽⣄⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣦⣤⣀⣀⠀⠀⠀⠻⣄⠀⠀⠀⢱⡝⠷⣦⣀⣀⣸⡏⠲⢦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⣤⣹⣧⡀⠀⠀⠱⣄⠀⣿⠉⠉⠀⠀⠀⠉⠻⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠒⢋⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⡈⠙⠿⣦⡀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄ ⠀⠀⠀⠀⠀⠐⠶⣦⣤⣤⣤⣤⣀⣀⣠⠾⠛⣉⡴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢀⡉⠉⠙⠓⠲⢬⣙⠦⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠯⣍⣛⠛⠯⠭⣝⣛⡓⠲⠤⠤⣤⣶⣖⠒⠒⠒⠒⠶⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⠶⣤⡀⠈⠛⢦⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻ ⠘⠛⠿⠿⣿⣓⣒⠲⠶⠶⠶⠤⠿⠿⠦⣄⣀⠀⠉⠙⠓⠶⠤⢤⣉⡙⠛⠳⠦⢤⣄⣀⠀⠉⠛⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣀⣀⣠⣤⣦⠾⠿⠿⠿⠶⢶⣦⣄⣀⠀⠀⠉⠛⠶⢦⣀⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟ ⠉⠛⠒⠶⢶⣶⣶⣤⣤⣤⣤⣄⠈⠉⢹⠆⠀⠀⠀⠀⠈⠉⠓⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠣⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⣠⣾⠋⠀ ⠀⠸⣶⣛⡋⠉⠉⠁⠀⠀⣈⣉⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠃⠀⠀⠀⠀⠀⣷⠲⠖⠒⣲⠟⠋⠀⠀⠀ ⠀⠀⠈⠉⢉⣙⣿⠿⠟⠛⠛⠉⠁⢀⣸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠤⢤⣤⣀⣀⣀⣀⣠⡤⠤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⣾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣍⣀⣀⣀⣀⣠⣤⠶⠟⠋⠘⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⣴⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣤⣤⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡷⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠈⠳⣄⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣦⣤⣦⠀⠀⣄⣠⡴⣿⣷⣶⣶⣬⣭⣷⣶⣶⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸⡇⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢿⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣈⣇⠀⣿⠻⢿⣿⣟⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⢹⠀⠈⠓⢒⣚⣻⣿⣏⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣆⡀⠀⠚⠒⠒⠢⣴⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡙⡛⠛⠶⢦⣽⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠁⣀⣀⣀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⡀⠘⡆⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⠉⠉⠉⣹⡆⠀⠀⣿⣿⣿⣿⡇⠀⢀⣀⡿⠀⢹⠀⠀ ⠀⢀⣀⣠⡬⠿⠿⠟⠓⠚⠛⠉⠉⠉⠙⢲⡈⠉⠉⠉⠉⠉⠉⠀⠀⠀⢸⡆⠀ ⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠉⠓⠶⠶⣶⠶⠶⠶⠖⠒⠒⠒⠒⠒⢦⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠈⠓⠒⠶⠶⠶⠶⠶⡶⠶⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⢀⡴⠖⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⣹⠖⠋⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⢹⠏⠀⠀⠀⠘⠁⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⢠⠏⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⣤⣄⣀⠀⠀⢠⡇⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡇⠀⠀⠳⣄⡀⠉⠑⠚⠳⠤⣇⡀⠀⠀⠀⠀⢀⣶⣶⡀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⡀⠀⠀⠻⣍⠓⠲⠤⣄⣀⡀⠙⢦⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⣷⣀⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⢀⣤⣄⣠⣤⡄⠀⠀ ⠀⠘⣧⠀⠀⠀⠈⠓⠤⣄⣀⣀⣉⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⣠⠞⢩⡾⠛⢁⣴⠿⣷⠀ ⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⣠⠞⢁⣴⢿⡄ ⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⢁⡼⠁ ⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢈⡷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⡾⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠠⡴⠛⣻⣠⠴⣄⣀⡴⠚⠙⣧⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠴⠛⠀⣰⠟⠁⠀⠀⢠⡏⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣏⠉⠉⠉⠉⠉⠉⠉⣿⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠾⠀⣿⠀⠀⠀⠀⠀⠀⠀⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠽⣿⣿⠀⣀⣤⠟⠀⠀⠀⠀⠀⢀⣀⡗⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠉⠉⠀⠀⠀⠀⠀⣐⣶⣟⣁⠀⢀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣀⠐⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⢟⢻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠻⣿⣿⣿⣯⣿⣽⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⣶⣤⠀⢀⣸⣗⣿⡚⣻⣿ ⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣷⣾⣷⣾⣿ ⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠚⠻⣟⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢳⣦⢄⣈⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢻⣿⣿⣿ ⣿⣿⣿⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿ ⣿⣟⡿⡟⣻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣧⣿⣿⣿⣿ ⡿⣿⣿⣿⣿⠟⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⣯⣿⣿⣿⣿⣿ ⣿⠿⡟⠋⢂⣠⣶⣿⣿⣶⣄⣀⣄⠤⠀⠀⠀⠤⣂⡠⣴⣷⣾⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡯⡿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡏⢨⡓⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣰⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⣧⣞⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣯⠔ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⡛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣶⣾⠿⠛⠉⢽⣿⣿⣿⣿⡿⠍⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠟⠋⠉⠀⠀⢀⣀⣼⣿⣿⣿⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢹⣷⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣶⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⣁⣠⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣀⣠⣤⡶⠟⠁⠀⠀⠀⠀⠀⠐⢶⣾⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠻⠿⠋⣠⣷⣿⣿⣿⣿⡟⠷⣤⣀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⠻⢶⣦⣤⣤⣶⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⢻⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⣄⠙⠻⠿⠛⠃⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠀⢙⠂⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠙⢷⣄⠐⢿⣿⣿⣿⣷⣶⣦⣄⣸⣿⣿⠛⠀⠘⣦⡀⠀⠘⢿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠹⣿⣦⣍⠛⠻⢿⣿⣿⣿⡟⠛⠁⠀⠀⠀⢻⣿⡄⠀⠻⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣶⣤⣍⡉⠉⠁⠀⠀⠀⠀⠀⠀⠉⢃⡀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣾⣿⠿⠋⠁⠀⠉⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⢀⣰⣶⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣦⣶⣤⣴⣶⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠀⠀⢀⠀⢠⣽⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⢿⣿⣿⣧⣠⣤⡌⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⣀⣸⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠉⠙⠻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⡀⣠⣾⣿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣟⣰⣼⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⢶⣿⣿⣿⣿⡿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠞⠋⣥⠞⠽⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡏ ⣀⡀⢀⣠⣤⣤⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣀⣤⣶⣿⣿⣿⡟⠀ ⠉⠙⠛⠻⠿⢿⣿⣦⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⢀⣴⣾⣿⣿⣿⣿⣿⣿⠏⠁⠀ ⠀⠀⠀⠀⠀⠀⢻⣟⣧⣀⣸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⠛⠛⠛⠛⠷⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠃⠀⣀⣀⣀⣀⡀⠀⠀⢀⣭⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠁⠀⣼⡏⢉⣿⣿⣿⡆⠀⣾⢡⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠃⠀⠀⠸⣷⣄⣻⣿⡿⠁⠀⠙⠛⠛⢻⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⠉⢀⣴⡾⠿⠿⢿⡿⢷⣤⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢰⣿⠉⠀⠺⠇⠘⠃⠀⠉⠙⠛⢷⣄⠀ ⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠘⠿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠂ ⠀⠀⠀⠀⠀⣹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢉⣹⡿⠷⢶⢶⡶⠶⠛⠛⠁⠀ ⠀⠀⢠⣶⠟⠋⠙⠛⠀⠀⠀⠀⠀⠀⠈⢿⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠘⣧⠀⠀⠀⠀⠀⠀⠀ ⢸⣷⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⢿⡄⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣄⠀⠀⣰⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣧⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣧⣀⡿⠉⠛⢷⣶⠶⠤⢦⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠟⠃⠀⠀⢸⡇⠀⠀⢸⣇⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⡶⠀⠘⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠙⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡯⢤⡀⠀⠀⠀⠀⠈⢧⡀ ⠀⠀⠀⠀⠀⠀⣸⢹⢸⢇⡇⠀⣠⠤⠤⣄⡀⢹ ⠀⠀⠀⠀⠀⢰⠃⠈⠉⠉⠀⢠⠇⠀⠀⠀⢹⣾ ⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢀⠇ ⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣾⠁ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢹⠀ ⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂ ⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀wot doing??⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠉⠀⠀⠉⠳⣄⠀⠀⠦⢭⣓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⠔⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠈⠳⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⠁⠐⠁⠀⠀⠀⣠⠀⠀⠀⠀⠀⢳⠸⣦⣀⠀⠀⠀⠀⢘⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⢀⡔⢹⠀⡄⠀⠀⠀⢸⠀⢻⠈⠛⠲⣄⠀⠀⢻⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠁⠰⠁⠀⢀⣤⠔⠋⠀⠸⣄⠑⠀⠀⠀⣸⣀⡿⠀⠀⠀⠘⣦⠈⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⠇⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠘⠦⣀⢀⣆⣿⡿⠁⠀⣀⣀⣀⣺⣷⡜⢿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⣼⢠⠀⣠⣇⡜⠀⣠⣤⣤⠄⠀⠀⠀⠀⠉⠉⢙⣄⠀⠀⠉⣿⡿⠀⣿⣷⣆⠛⣿⠂⠀⠀⠀ ⠀⠀⠀⢹⣿⢠⢿⠻⡇⠀⠀⠿⠟⠁⠀⢀⣴⠚⠉⠉⠉⠉⠉⢲⣄⣈⣀⣀⣠⡾⢿⡆⣿⠀⠀⠀⠀ ⠀⠀⣰⠋⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⢀⣿⣯⡀⠀⠀⠀ ⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡏⠱⡄⠀⠀ ⢰⠃⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢀⡠⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢱⡀⠀ ⣼⠀⠀⠀⠀⢀⣜⣁⣀⣀⣠⠤⠖⠊⠁⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢧⠀ ⢻⠀⠀⠀⠀⡜⠀⣼⡏⠁⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀ ⠈⣇⠀⠀⢸⠁⠀⢻⣇⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡇ ⠀⠈⢆⣠⡧⠀⠠⠤⠜⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠳⣄⡼⠀ ⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⠔⠢⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠾⢍⣈⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⡶⠒⠒⠶⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠉⠁⠀⠀⠉⠻⣦⡀⠀⠠⠤⢬⣉⡛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⢁⡤⠀⠀⠀⠀⠀⠀⠀⠐⢬⣧⠀⠀⠀⠀⠈⠙⣶⡈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⡄⠀⠀⠀⡀⢹⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠊⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⣿⠀⢿⢦⣄⠀⠀⠀⠀⠀⠈⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⡇⢣⠀⠀⠀⠀⠀⣼⠀⠘⡇⠈⠛⠳⢦⡀⠀⠐⠘⣿⣻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠁⢠⠃⠀⠀⠀⡀⢀⡴⠋⠀⠼⡇⠘⣆⠀⠀⠀⠀⣿⠄⢰⡇⠀⠀⠀⠈⢻⡄⠀⢲⣜⣷⢿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠀⠀⠋⠀⠀⠀⣴⠛⠉⠀⠀⠀⠀⠹⣄⠀⠀⠀⣀⠀⣿⣼⣾⠃⠀⠀⠀⠀⠀⢻⡆⠘⣿⣾⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠃⠀⠀⠀⡀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣿⣹⣿⠟⠁⠀⢀⣀⣀⣤⡤⠽⢿⣷⡈⢻⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⢠⠀⢀⢰⡇⢸⠃⢀⣀⣀⣴⡤⠦⠀⠀⠀⠀⠀⠀⠉⠁⠓⣆⠀⠀⠀⠀⣿⣿⡿⠀⣻⣿⣷⣆⠙⢿⣿⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⢸⠀⢸⣿⢳⣿⠀⠀⠀⣿⣿⡟⠀⠀⠀⢀⣤⠴⠒⠚⠛⠛⠛⠛⠦⣄⠀⠘⠙⠀⠀⠉⣠⣿⣿⡆⢸⣿⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⣟⣧⡏⠿⠀⠋⠀⠀⠀⠈⠉⠀⠀⠀⠀⠿⣧⣀⣀⣀⣀⣀⣀⣤⡤⠞⠉⠒⠒⠓⠒⠒⠻⠋⠈⣇⣼⠇⠀⠀⠀⠀ ⠀⠀⢠⡟⠀⠈⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⢶⡀⠀⠀⠀ ⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠀⢻⡄⠀⠀ ⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢻⡀⠀ ⣼⠁⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⣀⣤⠴⠚⠉⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢷⠀ ⣿⠀⠀⠀⠀⠀⠀⣰⠯⠤⣤⣤⡤⠴⠒⠛⠉⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⡇ ⣿⡀⠀⠀⠀⠀⢰⠃⠀⡞⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿ ⠘⣧⠀⠀⠀⢠⠟⠀⠀⣧⣧⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿ ⠀⠘⣄⠀⠀⡼⠀⠀⠀⠈⠛⣳⡤⠤⠤⠤⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣄⠀⠀⣿ ⠀⠀⠸⠦⢾⡓⠒⠖⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠙⠦⠼⠏ ⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⠒⠓⠲⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣤⠿⢧⣤⣤⠽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣇⣀⣿⣿⣷⣶⣶⣶⣶⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⣿⣿⣟⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⠛⠋⠉⠙⠛⠻⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠘⣿⣿⣆⣀⣀⣀⣀⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣾⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⠀⠀⣠⣿⣿⠟⠀⠉⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠀ ⠀⣰⣿⣿⠋⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠿⠿⠋⠁⠀⠀ ⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣄⣀⣀⣀⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⢿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⠶⠦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠒⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀ ⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣶⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠈⠉⠛⢻⣶⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⢰⣿⠂⠀⢀⣤⣼⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⣠⣶⠿⡛⡜⢿⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⢀⣾⡿⠿⠿⣷⣼⣢⢻⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠘⠻⣿⣤⣿⡃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠈⠻⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣶⢶⣦⣤⣀⣀⣀⣄⣠⣤⣤⣤⣤⣤⣴⡾⢿⡄⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⠏⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⡀⢀⣀⣤⠾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⢿⠉⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣽⣻⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⢷⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣯⣿⢾⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⡽⣟⡿⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⡽⣯⠇⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⡀⠀⠀⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣶⣶⣿⡟⠉⠛⠛⣶⠛⠛⢻⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢩⡙⣿⣄⠀⠀⠀⠀⠀⠀⣾⣏⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢢⠱⡩⢿⣆⠀⠀⠀⠀⢸⣿⢄⠫⡹⠟⠿⣻⣷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣋⠬⢥⢣⡑⢎⣿⣦⠀⠀⠀⠀⠻⣯⣶⣡⢋⠖⡡⣾⣾⠗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⣴⣿⣶⡣⣼⣦⣙⣿⡆⠀⠀⠀⠀⠈⠛⠿⣾⣼⣷⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠘⠿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀

૮ :7 \ ) = rotate your phone | |

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