Turning Red Text Art

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

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