Boykisser Emojis & Text

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⠀⢸⠂⠀⠀⠀⠘⣧⠀⠀⣟⠛⠲⢤⡀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢹⡀ ⠀⡿⠀⠀⠀⠀⠀⠈⢷⡀⢻⡀⠀⠀⠙⢦⣰⠏⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⢀⣻⠞⠛⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠛⠓⠒⠓⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⡟⠀ ⠀⠘⣇⠀⠘⣿⠋⢹⠛⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⢳⠉⠀⣠⡾⠁⠀ ⣦⣤⣽⣆⢀⡇⠀⢸⡇⣾⡇⠀⠀⠀⠀⣿⣿⡷⠀⢸⡇⠐⠛⠛⣿⠀ ⠹⣦⠀⠀⠸⡇⠀⠸⣿⡿⠁⢀⡀⠀⠀⠿⠿⠃⠀⢸⠇⠀⢀⡾⠁⠀ ⠀⠈⡿⢠⢶⣡⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣴⣧⠆⠀⢻⡄⠀⠀ ⠀⢸⠃⠀⠘⠉⠀⠀⠀⠠⣄⡴⠲⠶⠴⠃⠀⠀⠀⠉⡀⠀⠀⢻⡄⠀ ⠀⠘⠒⠒⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⠛⠒⠛⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠸⣟⠓⠒⠂⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢧⡀⠀⠀⢰⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠙⢦⡀⢸⡏⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠙⠺⡇⠀⠀⠙⠳⠦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡖⠶⠶⠒⠒⠒⠒⠓⠂⠀⠀⠀⠀⠀⠐⠒⠚⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⣰⠏⢉⣼⣧⠀⠀⠀⢠⣿⣅⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⢸⣿⣿⠀⠀⠀⣾⣿⣿⠀⠀⠀⣷⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⢀⠈⠁⠀⢸⣿⣿⠀⠀⠀⢹⣿⣿⠀⠀⠀⠉⠀⠀⠀⠈⠛⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢸⣧⣴⣀⣄⠉⣁⠐⣳⢀⣨⣟⠋⠀⠀⣀⣴⣠⠀⠀⠀⢀⡼⠃⠀⠀⠀⢰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⡎⢳⣌⡉⠀⠀⠙⠻⣯⣉⢉⣿⠄⠀⠀⢉⣬⡿⠃⠀⠀⢾⡀⠀⠀⠀⠀⣸⠃⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⡈⠙⠛⢳⡶⣤⣤⣭⣽⣭⡴⣶⠛⣿⣥⡄⢠⣤⣤⣼⡇⠀⡄⣾⠀⣿⠀⠀⠀⠀⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡟⠛⠺⠷⢤⣤⣿⣿⣿⣤⡾⠟⣃⡿⠀⠀⠀⠀⠀⠀⠘⠃⡿⢀⡗⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢸⣏⣌⡙⡇⠀⠀⠺⣦⠀⠀⠀⠀⠀⠀⣼⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⠀⠀⠀⠛⠛⠛⠁⠀⠀⣾⠁⠀⠀⠀⠀⠀⢰⡟⢹⣆⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⠀⠀⠀⠀⣤⠀⠀⠀⢰⣾⠀⠀⠀⠀⠀⣠⡟⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡟⠛⠛⠀⣠⡟⠀⠀⠀⢸⢹⡄⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⢸⠸⣇⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢼⣰⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⠛⠋⣿⠀⠀⢠⡏⠀⠀⠀⠀⡿⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⡿⠾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠿⠀⠀⠀⣿⠀⠀⣸⠃⠀⠀⠀⢠⡏⠀⠀⠀⠀⢹⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠁⠀⠀⠀⠀⢶⣿⠀⢠⡟⠀⠀⠀⠀⢸⠅⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠘⣿⢀⡾⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢦⣄⡀⠀⠀⠀⠀⡏⣼⠃⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠓⠤⡀⠈⠹⣦⡀⠀⠐⣷⣷⡇⠀⢠⡄⠀⣼⣃⣀⣀⣀⠀⠀⡇⠀⠀⠀⠲⣄⡀⠀⠀⠀⣈⡽⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠿⠅⣀⠀⠀⠈⠳⡄⠸⣧⠀⣠⡿⠿⢷⢤⣬⣿⡾⠛⠉⠉⠉⠉⠷⣴⡇⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡾⢁⡀⠀⠀⠑⢄⠀⠀⠸⣄⣿⠟⠉⠀⠀⠀⠀⠀⢸⣇⠤⠤⠦⠤⠤⢀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠋⠀⠀⠈⠑⢄⠀⠀⢣⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡏⣴⠉⠑⣢⣄⠀⠀⢳⣀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠿⣏⠀⠀⢿⠀⣳⣤⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⡀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠋⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠓⠢⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⣀⣀⡀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢰⡇⠀⠀⢿⢑⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣀⣤⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡆ ⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠛⠛⠿⢿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠁ ⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠈⠉⠻⠿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆ ⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⣤⡀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣇⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣄⠀⠀⠀⣰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀ ⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣧⠀⠀⠀⠀⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣶⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀ ⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣄⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡆⠀⣠⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⠉⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀ ⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀ ⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀ ⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀ ⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⢿⣿⣿⡟⠻⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⣿⣿⣿⣿⡟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⢰⣿⣿⡏⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⡀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣏⣀⡀⠀⠀⠀⠀⠀ ⣀⣀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⡀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣷⣶⣤⣤⣤⣤⣼⣿⣿⣿⣿⣆⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⢿⣿⣿⠟⠛⠛⠋⠉⠉⠉⢉⣿⣿⣿⠀ ⠻⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠏⠀ ⠀⢿⣿⣿⣧⠀⠀⠈⠉⠉⠉⠙⢿⣿⡿⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠏⠀⠀ ⠀⠈⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠁⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣤⣶⣶⣶⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣤⡼⠿⢿⣧⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣦⣄⡀⠀⢀⣀⣀⣘⢿⣿⠏⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⢀⣼⣿⣧⠀⠀⠀⠀⢠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠛⣻⣾⣿⣿⣿⣿⡆⠀⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣣⣾⣿⣿⡿⠀⠀⠀⠀⠸⠿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⢸⣿⣿⡟⣹⣿⣿⣧⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠀⠀⠀⠙⠛⠃⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⢻⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣶⣶⣤⣄⣠⣶⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣤⣴⣿⣿⣿⡿⠛⠛⠻⢿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⢀⣶⣄⣀⣤⣼⣿⣿⣧⡄⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣦⣄⣀⣀⣿⣷⣶⣤⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣷⣶⣦⣤⣤⣤⣾⣿⣿⣿⣿⣿⡿⠿⠟⠃⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⣿⣿⣿⠿⠋⣿⣿⠿⠿⠿⠿⠿⠟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⢿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢩⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⠀⠈⠙⠛⠻⠿⠛⠻⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠁⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠛⠛⠛⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠲⣄⠀ ⠀⠀⣠⡟⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⢽⡄ ⠀⠀⡿⠀⠀⠀⠀⠀⠉⠷⣄⣀⣤⠤⠤⠤⠤⢤⣷⡀⠙⢷⡄⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠈⡇ ⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠹⣦⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡗ ⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇ ⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠂ ⠀⢿⠀⠀⠀⠀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⣸⠇⠀ ⠀⠘⣇⠀⠀⠀⠀⠉⠉⠛⠛⢿⣶⣦⠀⠀⠀⠀⠀⠀⢴⣾⣟⣛⡋⠋⠉⠉⠁⠀⠀⠀⠀⣴⠏⠀⠀ ⢀⣀⠙⢷⡄⠀⠀⣀⣤⣶⣾⠿⠋⠁⠀⢴⠶⠶⠄⠀⠀⠉⠙⠻⠿⣿⣷⣶⡄⠀⠀⡴⠾⠛⠛⣹⠇ ⢸⡍⠉⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣬⠷⣆⣠⡤⠄⢀⣤⠞⠁⠀ ⠈⠻⣆⡀⠶⢻⣇⡴⠖⠀⠀⠀⣴⡀⣀⡴⠚⠳⠦⣤⣤⠾⠀⠀⠀⠀⠀⠘⠟⠋⠀⠀⠀⢻⣄⠀⠀ ⠀⠀⣼⠃⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⢻⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀ ⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠧⠿⠿⠟⠀⠀ ⠀⣾⡴⠖⠛⠳⢦⣿⣶⣄⣀⠀⠀⠀⠀⠘⢷⣀⠀⣸⠃⠀⠀⠀⣀⣀⣤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⠻⠦⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢲⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀
pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
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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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⠀⠀⠀⠔⠢⠀⡄⠢⡀⠀⠀ ⡠⢄⡰⠀⠀⣦⠁⠀⡇⡠⢄ ⢇⠀⠱⠣⡴⠥⢦⡔⡎⠀⢸ ⠈⠒⡸⠎⠀⠀⠀⠱⢕⠐⠁ ⠀⠠⡀⠀⠀⠀⠀⠀⢀⠆⠀ ⠀⠀⠑⠠⠔⠒⠢⠤⠊⠀⠀
𖣂🐻✨🌻♡ cute, ,,bear this so funny ngl like ur all fighting over this shitt hahahahehehe≽´ܫ´≼

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i didnt think there would be so much lore on an emoji website 😨
⠀⠀⠀⠀⠀⣠⣄⠀⠀ ⠀⠀⠀⣴⣾⣿⣿⣶⡄ ⠀⠀⠀⣼⣿⣿⣿⣿⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⠀ ⠀⠀⣽⣿⣿⣿⣿⡿⠀ ⠀⠀⣽⣿⣿⣿⣿⡇⠀ ⠀⠀⣿⣿⣿⣿⣿⠁⠀ ⠀⠀⣼⣿⣿⣿⠇⠀⠀ ⢀⣤⣿⣿⣿⣿⣦⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⢿⣿⣿⣿⣿⣿⣿⡿⠀ ⠈⢿⣿⣿⣿⡟⠁⠀⠀ ⠀⣾⣿⣿⣿⡇⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠊⠀⠔⠀⠡⠀⠀⠀ ⠀⢀⠐⠀⠀⠀⠀⠀⠀⠐⠄⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠈⡈⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠇⠀⠀⠇⠀⠀ ⠀⠀⠡⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠐⠀⠈⢍⣢⠀⠀⠀⠀⢀⡨⠐⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠈⠋⢀⠠⠄⢀⢉⠉⠌⠁⠀⣀⠁⠀⠀ ⠀⠔⠀⠁⠠⢀⠖⠈⠀⠐⠄⠠⠒⠀⢄⡒⠈⠀⠊⠀⠁⠀ ⠀⠀⠀⡀⠀⢠⢠⡈⣤⣤⡀⣨⣄⢠⡀⣍⡀⣀⠀⠀⠀⡀ ⠈⠂⠀⠴⠐⣶⣼⡇⣿⣿⡗⡏⢹⣿⡇⣿⣿⢉⡇⠀⠈⠀ ⠀⠀⠀⠀⠀⠿⠀⡀⠿⢈⢇⣻⣟⡈⢻⣏⣻⠟⣃⠀⣀⡀ ⠀⠀⢰⣿⠿⠿⢿⣿⠀⣿⣿⣿⣻⣿⢻⣟⣻⡧⣿⣄⣿⡇ ⠀⠀⢸⣿⣿⠀⢸⣿⠀⣿⣿⣿⢿⣿⢸⡿⢿⣧⠘⢿⡟⠁ ⠀⠀⢸⡟⠀⠀⠈⢿⣿⠟⠸⡟⠀⠿⠸⠇⠘⠿⠀⠸⠇⠀ ⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠒⠂⠉⠀⠂⠀⢦⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡤⠔⠈⠀⠈⠂⠀⠀⠀⠀ ⠠⣀⣀⣀⡀⠉⡴⠉⣀⡎⢀⡀⣀⣀⠀⠀⢆⣀⣠⡆ ⠀⠀⠈⠁⢰⡞⠠⠂⠈⠀⠨⠐⠢⢄⠀⠀⠀⠹⠟⠀ ⠀⠀⠀⠀⢢⠀⠀⡆⠀⠀⠀⡆⠀⠀⠂⠀⠠⠀⠐⡨ ⠀⠀⠀⠀⠀⢀⡆⢀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣈⠀ ⠀⠀⠀⢄⣶⣏⠀⠈⠀⠀⠀⣀⣤⣴⣾⣿⣿⣾⠁⠀ ⠀⠀⠀⠀⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⢐⣿⡿⢿⠛⠁⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠍⠀⠀⢁⠀⠀⠀⠀⠀⠉⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠂⠄⠊⠄⠤⠐⠒⠒⠀⠀⠐⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡾⢻⣇⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠟⠋⠀⢸⣿⠀⠀ ⠀⠚⠛⠛⣿⡿⠛⠛⠉⠀⠘⠿⠿⠛⠋⣁⣠⣾⠗⠀⣸⡟⠀⠀ ⠀⠀⠀⠀⣿⣇⣀⣀⡀⠀⠀⠀⠰⠾⠟⠛⠉⢀⡀⢠⣿⣿⣤⠀ ⠀⣀⣤⣾⣿⣿⡍⠉⢻⣦⣀⡀⠀⠀⠀⠀⠀⠙⡷⠻⣿⣿⣿⠀ ⣿⣿⡟⠉⠀⠘⠁⠀⠐⠋⠉⠁⠀⠀⠀⠰⠶⠟⠃⢠⣿⣿⡿⠀ ⠸⣿⣆⠀⣀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿ ⠀⠻⣿⣟⡛⣉⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠙⠿⠿⠿⠿⠛⣿⣷⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣟⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀

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⣿⣿⡇⠀⢀⡤⢪⠡⠀⡘⡿⠀⠀⠹⡔⡀⠀⠘⣥⠀⠀⢂⠱⠀⢻⡀⠠⠠⠀⢰ ⣿⣿⢑⣴⠁⠀⠀⠇⢀⡹⠀⠀⠀⠀⣡⡽⡘⠀⠰⣣⡀⠣⠳⢧⡘⣇⠀⢇⠲⢺ ⣿⡿⠁⣿⠀⠀⣠⠀⣨⠃⢀⣠⠴⠋⠈⣇⢡⠀⠀⠹⣷⢄⠀⠀⢆⣻⡀⢸⡆⠀ ⣻⡇⠀⢱⡇⠀⣹⢀⡟⠊⠁⡀⠀⠀⠀⠸⠌⡷⡄⠀⠘⢧⢁⢶⣩⣽⣇⠀⠁⠀ ⣿⠁⢸⢸⣧⠀⣿⠁⣃⠀⠤⠤⠤⣤⠀⠀⢋⢤⠈⠒⢄⣼⣿⣿⣿⠈⣻⡟⣶⠀ ⣿⠀⠈⠈⢹⣦⣿⣾⣿⣿⣿⣿⢿⡙⠓⠀⠀⠎⠆⠀⠸⠻⣿⣿⡟⠤⣿⡇⡏⠀ ⡏⠀⠀⣤⣼⠟⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠄⠀⠈⡆⢀⠴⣿⣿⠄⣰⣽⢃⡇⠀ ⠃⠀⠈⢿⡙⠤⠰⣿⡿⢿⡿⣃⠀⠢⡀⠀⠀⠀⠀⢹⣄⠁⠈⠁⠀⣸⢃⢾⠃⠀ ⠀⠀⠀⠸⡹⡄⠀⠀⠒⠛⠋⠓⠄⠀⠁⠀⠀⠀⠀⠀⠛⠆⠀⠀⡠⠷⢹⡮⠀⠀ ⠀⠀⠀⢠⢗⣌⡢⢄⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⣠⣾⡟⣅⠀⢀ ⠀⠀⠀⠀⢾⣝⠛⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡰⣰⣵⠿⠊⢌⢞⣐⠂ ⠀⠀⠀⢰⠀⢠⢉⠠⣴⢻⢿⠵⠂⣀⣀⣤⣤⣴⣷⠀⡠⠟⠉⡀⠀⣀⠜⣣⠃⠀ ⠀⠀⠀⠀⠀⢸⣦⣴⡜⠻⡄⠀⠀⠀⠀⢘⡿⢟⣵⣯⣤⡤⢤⣖⠨⠔⢛⠇⡀⠀ ⠀⠀⠀⠀⠠⡿⣿⣯⣽⠓⠾⣵⣂⡤⠤⣮⡞⠛⠻⣧⡀⠁⢶⢷⣤⣠⢊⡴⠅⠀ ⣀⠔⠁⢈⡩⠓⠺⣟⣿⡄⠀⠼⠟⠛⠛⠉⢀⣀⠜⠉⠛⠔⠀⠵⠖⢓⣁⠀⠀⢀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢪⡔⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠨⠌⠑⠲⡒⢺⢈⢰⢘⣤⣄⠀⡦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢒⠗⠒⢆⠬⢢⡀⠘⢿⢸⢘⡷⣾⣷⠑⡇⠡⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣂⠥⠐⣈⠉⣣⡀⠑⡕⡾⡘⠀⠙⠀⢁⢢⠛⠀⠃⢠⠄⠀⠀⠀ ⠠⠴⠦⢧⠕⡺⠛⡓⠤⠄⣀⡱⡀⢿⠱⠁⡀⣔⡀⢘⡄⢣⢀⠗⣱⡠⠀⠀⠀ ⠀⠀⢀⢂⠼⡴⢬⡤⢐⢊⠝⠉⠀⣿⣷⠌⣾⠉⢩⡗⡷⢀⣧⠼⣉⠢⢄⠀⠀ ⠀⢀⣾⣃⡟⢀⡴⡏⣧⠁⠀⡀⠀⠈⠁⠰⢙⠓⠻⠋⣔⣹⣃⣔⠒⠭⢒⠵⠄ ⠀⠈⠉⠀⠁⣨⢀⠀⡇⢻⡏⢀⡀⠀⠀⠀⠀⠀⠀⠮⣮⠊⣇⠀⠙⡑⣥⡄⠀ ⠀⠀⠀⢠⣶⣏⢞⣠⢷⣾⠂⢿⣿⣷⠀⠀⠀⠀⠀⢀⠀⠀⡇⠁⠢⠬⠧⠑⠀ ⠀⠀⠀⣾⣪⡭⠐⠁⠀⠸⣿⣿⡽⠋⠀⠀⠀⠀⠀⡘⠀⢰⡏⢄⣦⢾⠀⠀⠀ ⠀⠀⣄⣶⣷⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠠⠁⠀⡧⢼⠳⢼⣩⠂⠀⠀ ⠀⠀⢿⣿⡏⠄⡴⣶⡇⡰⠁⠀⠀⠀⣀⠠⠄⠊⠀⠀⠀⠘⣦⠳⡀⡏⠀⠀⠀ ⠀⠀⠀⠙⠵⢥⣭⣭⢎⣀⠤⠰⣾⣥⣀⣀⠀⠀⠀⠀⠀⠀⠈⠊⢛⣲⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠻⣷⡅⠀⠀⣀⣠⠄⠠⠖⠚⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠆⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠠⠄⡀⠀⠀⠀⠀⠀⣀⣒⡤⠤⠂⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢤⠀⡠⠙⡹⠁⠀⡞⠀⠀⠀⠀⠀⢀⡆⠈⠓⢌⠑⠢⣀⡈⡁⠒⠀⠄⡀⠀⠈ ⠀⠠⠺⠁⢰⠃⠀⠠⠁⠀⠀⠀⠀⠀⢸⢰⣀⠠⠀⠱⣄⠈⢗⠨⡉⠲⢂⠠⢁⠂ ⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⢸⠈⠣⠱⠀⠐⢂⠀⢡⠀⠀⡀⠑⢄⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠀⠀⢣⢡⡀⠀⡆⠀⠆⠄⠘⣆⠀⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⡒⠒⠂⢓⠛⡉⠹⡄⢰⡸⡄⠘⡿⡀ ⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⢾⠀⣳⣒⣒⣾⣂⠒⢠⡱⢸⢡⢯⣆⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠌⢉⣠⡤⠶⢺⣾⣻⢿⣿⡉⠋⢠⠃⢸⢾⣼⣢⣉⡄⠀ ⠀⢀⣴⡤⠀⡣⠀⠀⣇⠰⠀⠁⠀⢠⠈⠺⡈⡉⠀⣠⢀⣠⠨⣃⢌⢯⢹⠉⢢⠀ ⠀⠸⡿⢿⢰⠁⡆⢠⠛⡄⢃⠀⠀⠀⡰⢤⠞⠣⣀⠔⠁⣁⣎⢔⠕⢉⢼⠆⠈⠀ ⠀⠀⡀⣸⣁⣼⡇⢸⠀⠘⡄⢆⡀⠀⢹⠈⢓⠪⠀⠉⠻⠋⠔⢑⢕⠕⡉⣧⠀⠀ ⠄⠠⠚⣾⣿⣧⠇⢸⠜⢄⡰⠘⠳⡄⠀⠣⡙⢆⠀⠀⠀⠀⠀⣠⣵⣶⠀⣟⡳⠄ ⢀⠀⡈⡏⠏⠸⡇⡌⣸⣶⣦⣇⢣⡙⢦⠀⠀⠀⠉⠂⢄⠀⣜⡿⠿⠧⠰⣬⣷⣉ ⠸⣤⢡⡧⣀⣺⡇⢣⢿⡟⣏⣿⢎⣿⠦⠝⣦⡀⠀⠀⠀⠑⢿⣎⠐⢲⣤⡈⠘⣧ ⠀⠁⠆⠁⢱⠻⡇⢸⢸⡇⠏⢻⠈⣿⠀⠲⢹⡻⣦⣀⠀⠀⠀⢩⣣⣚⡉⠁⠀⢸

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀ ⠀⠀⢠⡶⠶⣒⡦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠿⠉⣭⡈⣷⡄⠀ ⠀⠀⢸⣦⡶⠛⠛⠛⠓⠻⢿⣗⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⠿⠚⠋⠉⠙⣧⢸⣷⠀ ⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠈⠙⠶⢼⣛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢸⣤⣿⡆ ⠀⠀⡿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠇⡇ ⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠿⠿⠭⠙⣻⣷⣶⣶⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇ ⠀⠀⣇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠁ ⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⡟⠀ ⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀ ⠀⠀⠀⢨⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⡿⠃⠀ ⠀⠀⠀⡾⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀ ⠀⠀⢰⠇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⠒⠲⣄⠀⠀⠀⠀⠀⠀⢀⣠⢤⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀ ⠀⠀⡾⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣇⠀⢀⣾⣆⠀⠀⠀⠀⢀⡏⠀⢀⣽⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀ ⠀⢰⠳⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠘⣿⣧⣽⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣅⣼⣿⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⡆⠀ ⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠈⠻⠿⠿⠿⣻⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠿⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣷⠀ ⠀⡟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⣀⣀⡠⢔⣾⣿⠟⠀⠀⠀⠀⠈⢿⣦⣀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀ ⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠶⠟⠁⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⢸⣿⡇ ⠰⡇⠸⡄⠀⠀⠛⢿⣷⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⣿⣿⡿⠀⠀⣿⣿⡇ ⠈⣿⣆⠙⣦⡀⠀⠀⠙⢿⣦⣍⣳⢶⣤⣀⡀⠀⠀⠀⡀⣠⡄⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⢛⣩⣾⠟⠁⠀⠀⠀⣠⠏⣿⡇ ⠀⠈⠹⢿⣟⢿⣶⣄⡀⠀⠉⠻⢿⣽⣛⠿⢿⣿⣿⣛⣿⣟⠛⠺⠋⣤⣤⣶⠶⠾⠟⣉⣁⣤⣴⣾⡿⠟⠁⠀⠀⠀⣠⣾⣋⣾⠟⠀ ⠀⠀⠀⠀⠙⠻⢿⣥⣉⠓⠦⣄⣀⠈⣩⣿⣷⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⣹⣿⠟⠛⠉⠀⠀⢀⣠⣴⣾⣫⡿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣭⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣶⣶⣶⣾⣻⡽⠾⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⢀⣠⣴⢛⣉⣁⣀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣶⣶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⢿⣶⣾⡿⣻⣿⢟⣫⠽⠿⠟⠓⠒⠶⢤⣤⣄⣀⣤⣤⣄⣀⣤⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⣿⠛⢿⣦⣀⣹⡿⠒⠶⠖⠒⠚⣿⣿⣿⣿⣿⣿⣿⣴⡟⠡⣶⣶⣶⣦⣬⣭⣅⣤⣶⡿⠋⠁⠀⠀⠈⢻⣿⣿⠋⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⠀⠈⣿⣿⡏⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣍⣉⠍⠙⢻⣯⣥⣤⣤⠀⠀⢀⣴⣾⣿⣃⠀⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣷⢶⠽⠋⠁⠀⠀⢀⣴⣿⣿⣿⡟⣻⣿⣿⣿⢿⣿⡏⣁⠉⠉⠙⠿⢿⣏⠛⠻⢷⣄⡀⠤⠀⠁⢀⡴⠛⠫⢄⣼⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⢠⣾⡿⢯⣼⢟⣿⣿⣿⣿⠇⣾⡎⣿⣿⣷⣴⣦⡀⠀⠙⢷⣄⠀⣀⣛⢦⣀⠀⡏⠉⣀⣠⡾⢻⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣷⣿⣶⡀⢐⣿⠟⣠⣿⣿⡿⣽⣿⡿⣿⡆⢻⠀⢾⡟⢷⣝⢾⡝⠷⣤⡰⣿⣷⣍⠛⢿⡿⣦⣵⠸⡏⠁⢠⠞⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠨⣷⣾⣿⣾⣻⠎⡿⢠⡏⢰⣻⣿⡇⣿⡇⢸⡆⠘⣷⡀⠙⣷⡙⢧⡈⠻⣮⠳⣟⠃⠀⠙⢮⢻⣾⠷⣶⡒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣼⡿⣁⡞⠀⡾⢰⢏⠏⣿⢰⠋⡃⠘⣇⠀⢹⢷⣄⠀⠙⢧⡝⣦⡀⠳⣌⢧⡀⠀⠸⣧⡻⣆⢸⡏⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠤⠖⠉⢸⣟⣾⢻⡇⠀⢡⣯⠟⣼⢻⠸⡆⢣⡀⠙⠀⢸⣷⠙⢷⡤⡀⠹⣶⣝⢶⣌⣾⡷⡄⠀⢿⣷⡽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⡼⠁⢸⡇⠀⣿⣟⡼⡁⢸⣷⣿⠀⠳⣄⠀⠈⣿⣆⠀⣙⣿⣅⠈⠿⣿⣾⣿⣷⠻⡀⠀⢿⣿⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠴⠋⣿⡇⠀⠸⡇⠰⢹⣿⣧⣤⣀⣿⡈⣧⠀⠈⠳⣄⢻⢹⡆⢨⣵⡿⢛⣻⣿⣿⣿⣿⠀⢱⠀⠘⢹⣿⣿⢬⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡟⢧⠀⠀⢷⡀⢾⠟⠛⢿⣷⣿⣿⠿⣷⣄⠀⠀⠘⡇⠹⣬⣷⣿⣿⣿⡟⠁⣸⢿⠀⡾⠀⠀⣸⣿⣿⡄⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⣧⠘⣧⠀⠈⢧⡘⡿⣦⡀⠻⢿⣿⡿⠿⠌⠻⢦⡀⢻⡄⠙⠿⠟⢛⣛⣡⡴⠋⢸⣴⠃⢠⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⠈⢧⡀⠈⢳⡕⠈⠛⠲⠤⢤⣤⠀⢀⣀⠀⠉⣿⣧⡄⢈⣩⠭⠍⠁⠀⢀⣾⡿⠀⣠⣿⣿⣿⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢸⠛⢦⠀⢹⣶⡀⣀⣠⣄⡈⠁⣍⣻⣷⣦⣾⡉⠰⢁⣠⠴⠋⠀⢒⢿⣷⣷⣾⣿⣿⣿⣿⠀⠀⠉⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣿⣦⣻⡿⠁⠀⠀⠈⠓⠼⣏⣁⣀⣸⡆⠀⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢹⣿⣿⣿⣆⢀⡀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠈⠓⣦⣼⣿⣿⣿⣤⣾⣷⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣧⣿⣿⣿⣿⣄⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣠⡿⣻⣿⣿⣿⣿⣿⣿⣿⣮⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⢹⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠈⠀⣀⡤⠞⡯⢀⣿⣹⡾⠻⢿⣿⣿⡁⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⣹⡏⠀⡙⢿⣿⣿⠉⢻⠹⡗⠦⣤⣀⡤⠶⠞⠉⠀⢸⡇⠘⢻⡏⣧⠀⠈⠻⣿⣇⢸⡟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⣤⣴⣾⠏⢯⠀⢠⣿⣷⠀⠙⠻⣿⣿⡇⢸⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⢸⡇⣿⠀⠀⠀⠉⢻⣿⠃⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣾⠿⣿⣿⡏⠹⣦⠘⣧⡈⠻⣿⣧⠀⠀⠻⢻⣷⣸⡇⠀⠹⡄⠀⠀⠀⠀⠀⠈⠁⣠⠤⡺⠁⡿⠀⠀⠀⣠⣼⠋⠀⣀⣿⡿⣧⡆⠀⠀⠀⠀⠀⠀⠀ ⢴⣿⣿⠟⢉⣿⣿⣿⠦⣌⡷⣾⣷⡀⠙⠻⣷⣄⠀⠙⢿⣿⢿⠀⠀⠀⠀⢠⠀⣀⡴⠞⠉⠀⣠⠇⡸⠃⢀⣴⠞⠉⠀⣀⣴⣿⠟⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣠⢸⣿⣿⣿⠀⢈⠙⠛⠿⣷⣄⠀⠈⠛⠿⣦⣜⠿⣿⣇⠈⠙⠓⠚⠋⠁⠀⠀⠀⣰⣁⣼⡷⠞⢋⣀⣤⣶⠿⠛⢁⣠⡴⠾⠛⣻⣦⣀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⡀⠀⠀⠈⠛⢷⣦⣤⡄⣨⡙⢷⣽⣿⣇⠀⠀⠀⠀⢒⣶⣴⢿⠟⠋⢀⣠⣶⣿⣛⣯⣥⣶⣾⠟⠉⠀⠀⠀⣼⠿⣿⣷⣦⣄⠀⠀ ⠀⠈⠙⠻⣿⣿⣿⣿⣷⣀⡃⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣾⣿⣿⣿⣦⣤⢶⣛⣛⣁⣁⣠⣴⣶⣿⣿⠿⠛⠉⠉⣠⡾⠋⠀⠀⠀⠀⣼⣿⣴⣾⣿⣿⣿⣷⡄ ⠀⠀⠀⠀⠀⠉⠛⠿⣿⣽⣛⠿⢶⣤⣄⡀⠀⠀⠀⠀⡍⠐⠪⢹⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢶⣴⣭⡙⠳⠶⠦⡄⠀⠀⠀⠈⠁⠶⠆⠠⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣦⣤⣄⡀⠀⠀⠀⠉⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣤⡾⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠛⠛⠲⢶⣤⣤⣤⣶⣶⠶⠒⠂⠒⠚⠋⠉⠙⠛⠛⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⣸⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠀⠀⠀⠀⠀⠈⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣱⠟⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀ ⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠘⣏⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢰⠋⣀⡠⢴⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠙⡸⡆⠳⣄⠀⠀⠀⠀⠀⠀⣀⣤⢄⣀⠤⠤⠤⠤⠤⠤⠤⠾⠵⠒⠒⠛⠉⠉⣠⡞⠀⠀⢼⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⣸⠀⠀⠀⠀⢠⠀⠀⠹⣄⠀⢹⠀⠈⢳⡀⠀⢀⡴⢚⡽⠛⠉⣠⡤⠤⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣠⡾⠋⠀⠀⠀⣸⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⡟⠀⠀⠀⠀⣿⠰⡄⠀⠈⢧⠀⡇⠀⠀⠙⣤⠎⣠⠏⣠⠖⠉⢀⣀⠴⠶⠿⢥⣒⣉⠉⠉⠓⠻⢯⣀⠀⠀⠀⠀⣰⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⢻⠀⠙⣆⠀⠈⢇⢸⡄⠀⠀⠸⣻⣟⣾⣡⠴⠞⠉⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠈⠻⢤⠠⠞⣡⠆⠀⠀⢰⠇⠀⠀⠀⠀⠀ ⠀⠀⢿⠀⠀⠀⠀⠈⣇⠀⠈⢣⡀⠈⣼⡇⠀⠀⠀⠘⠙⢿⠛⠲⠤⠤⠤⢤⣤⠤⠤⠤⣖⣒⣒⣚⠛⠒⠲⠤⣌⢷⡘⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠘⣦⡀⠀⠹⣄⠻⡇⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠉⢷⣀⠀⠀⠙⢷⣿⣿⣶⣄⡀⠈⢻⡇⠀⠀⣠⢾⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡄⠀⠀⠀⠀⠀⢨⢳⡦⠀⠘⢮⡇⣠⠆⠀⠀⢀⣤⣸⣷⡀⠀⠀⠀⠀⠀⢻⣦⠀⢲⣿⣿⡿⣿⣿⣷⣆⠀⡇⣠⡜⠁⣜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡄⠀⠀⠀⠀⠈⠳⣝⠦⠄⢀⡿⠁⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠘⣿⣇⠈⠀⢉⣿⣟⠉⠽⢿⣾⠟⠁⠀⣰⢿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣟⣄⠀⠀⠀⠀⠀⠀⠙⠲⡞⠀⠀⣽⡿⢟⠋⣩⣲⠓⠇⣙⣫⣿⣦⡀⠀⠹⣿⣇⣠⣿⣿⠿⣿⡅⠛⠁⠀⠠⠞⠁⣸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⡌⠳⢤⡀⠀⠀⠀⠀⣸⠃⠀⣼⠫⢾⣴⣿⣿⣿⢿⣶⡄⠀⠈⠻⣿⣷⣤⣿⣿⣿⣟⡋⡀⠈⢿⡴⠂⢀⡤⠀⣴⣯⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡄⠀⠉⠓⠲⠤⢼⡏⠀⠀⠉⣮⣿⣿⣿⡯⠹⠀⠙⢿⡆⠀⠀⠀⠙⢿⡿⣿⣿⣿⡿⠁⠀⠈⣧⠐⠛⠋⠬⣷⣾⣥⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⠆⠀⠀⠀⠀⠘⣇⠀⠀⢀⣾⣿⣿⣿⣤⠀⢦⠀⠀⢧⠀⠀⠀⠀⠀⠁⠸⣿⢟⠁⡄⠀⢀⣯⣤⣤⡀⠀⠀⠈⠉⠉⢹⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣈⣻⡶⠆⢀⡤⠴⣿⣆⠀⢸⡏⢻⣿⣿⠿⠀⡎⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⠻⠾⣅⣠⠞⠁⠀⠀⢳⡀⠀⠀⢀⣠⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⢒⣿⣯⠘⠛⢓⡘⠃⣀⣼⣿⣌⠳⠴⠃⡰⠃⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠈⡇⠀⣀⣴⣋⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠈⣇⣰⠇⠀⢀⣙⣷⣶⠯⣁⣀⡠⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠲⢤⡉⠳⣿⠛⠋⠁⡼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⡼⠋⠀⠀⠀⠀⠀⢻⠃⠀⡴⠋⠀⠀⠈⠉⠳⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⢀⣀⣤⠤⠒⠂⡇⠀⢸⠀⢀⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠿⣄⠀⠀⠀⠀⠀⠀⠘⡆⠀⠇⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⢹⣤⡤⣭⣤⣤⡤⣴⡾⠃⠀⢸⣷⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣁⣀⣀⡀⠹⣆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⡾⠋⢀⡀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣛⠛⠻⠾⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣁⣀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢶⣦⣙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣟⡷⠲⣖⠛⢿⣿⣾⣿⣯⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠙⢮⣤⢤⡈⠳⢤⣹⣿⡟⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠶⠉⢻⣿⣶⣦⣤⣀⡀⠀⠈⠙⠻⠿⠟⠊⢉⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠉⠓⠿⣝⣻⠿⠿⢶⣶⣶⣶⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣶⣶⡞⠾⠃⡀⠀⠀⠀⠀⠀⠙⠛⠙⠲⠄⢴⢽⣿⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⢿⣏⣛⡷⠆⢀⡤⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣸⣷⢤⣲⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠚⠉⠀⠀⢀⣠⣽⠿⠗⣦⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢭⣿⣯⣀⠉⠑⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠶⠟⠉⠀⠀⠀⠀⠀⣨⠉⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠪⡙⢦⣀⠀⠀⠈⠉⠓⠲⢤⣀⠀⠀⠀⠀ ⠀⠀⢀⠞⠉⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢩⡃⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢇⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⡞⢀⣉⠁⠀⠈⠁⠘⠠⡀⢸⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⣞⠄⠒⠈⠉⠉⠐⠂⠀⠀⠈⠙⡀⠰⡀⠀⠀⠀⠀⠀⢀⣠⡴⣞ ⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠼⠤⠤⠀⠐⢊⡴⠊⠀⣼ ⠀⠀⠮⢤⢒⠒⣒⠒⡲⠖⣒⡒⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⡿ ⠀⠀⣤⠚⠁⡜⢁⢞⣙⡠⠊⠀⠀⡴⠟⠻⢷⣦⡀⠀⠀⢀⢧⠁⠀⠀⡜⠇ ⠀⢼⠁⠀⢸⠀⠈⠸⣺⠁⠀⠀⠈⠀⠀⠀⠀⠙⢻⡆⢀⠌⠎⠀⢀⢎⠎⠀ ⠀⢸⠀⠀⣀⠣⠼⠤⠁⠀⠀⡀⢀⣆⣀⣀⠀⠀⡄⣇⡝⠹⠤⠒⡡⠂⠀⠀ ⠀⠀⢷⠭⠤⠀⣀⡀⠀⠀⠀⠉⠋⠉⠛⠿⣷⣄⠃⠹⣄⣀⡠⠾⠃⠀⠀⠀ ⠀⠀⢎⢦⡀⠀⠀⢈⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣢⢬⡶⡉⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⢀⠠⢺⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠁⠊⠀⠈⠱⠒⠂⠉⣀⠠⠤⠐⠒⠉⠁⢀⣶⠗⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢫⠗⢄⣀⠔⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠰⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠟⠉⠙⠀⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⣤⠑⠤⠤⢤⣤⣀⡀⠀⠀⠀ ⡰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠒⠤⢀⣀⣠⠏⠀⠀⠀⠀⠀⠉⢶⡀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀
⠀⠀⠀⠀⠀⣦⢀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡀⣿⣼⣣⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠲⠶⢶⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣖⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠚⣿⣿⡄⠀⣠⠶⢮⣽⠛⠋⠉⠛⠓⣶⡾⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⣿⢻⣿⡅⠻⣴⡿⠂⣄⠀⠀⠀⣈⣿⣶⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⡟⠀⠘⠙⣄⣈⣳⣖⣻⣶⣉⣼⣟⡿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢷⡆⠀⠤⣾⠏⠉⢏⡉⢽⣤⠍⢁⡀⠀⣙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠐⠚⠁⢤⣤⡀⠙⣦⣀⡴⢁⣤⣔⡪⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢦⠄⡴⢋⡟⣙⣦⠈⠉⢠⢻⣿⡣⣕⢭⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠈⠀⡨⠋⠀⠀⢾⠈⠧⢳⡦⠒⠛⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⠚⠁⠀⠀⠀⠈⢧⡀⠈⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⣆⠀⢀⡀⠀⠀⢀⣄⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢹⢄⢀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡀⠀⠸⡄⠀⠀⠀⠀⠀⣿⡆⠀⡾⠈⠛⣿⣿⣿⣿⣿⣧⣤⣠⣴⣾⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⠒⠒⢳⡀⠀⠀⠀⣰⠛⠃⣸⠃⠀⠀⠈⠙⣟⣽⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠈⠓⣲⠊⠁⠀⣰⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣴⠇⠀⢀⣼⠃⠀⠀⠀⠀⢰⣿⡿⣿⣿⣯⣿⣿⡿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠏⡏⠀⠀⡇⠀⠀⢿⣇⠰⠋⣏⠀⠀⠀⠀⠀⠸⣿⣇⢈⣾⣷⢹⣿⣇⠹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠀⡇⠀⠈⠇⠀⠀⠸⡟⢄⠀⢻⡆⠀⠀⠀⠀⠀⠙⣼⣀⣿⣓⣾⣿⢯⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡄⠀⠀⠀⠀⠀⢸⡀⠀⠀⠙⢄⠀⠀⠀⠀⡼⠁⠇⠰⢶⣿⣿⣟⣿⣿⣶⣶⣤⣤⠤⠤⠤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣵⡀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⠳⣶⣔⡊⠀⠀⠀⠀⡀⠙⢿⣿⣿⣿⣿⣿⣆⠈⠳⣦⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠃⢳⡀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠙⣿⣟⠛⠛⠒⠀⠉⠲⢶⣿⣿⣿⣿⣿⠿⣷⣄⣈⢷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢹⣄⢀⢸⡾⡀⠀⠀⠀⠀⠀⠀⠘⣿⣭⣤⠀⠀⠀⠀⠚⢻⣿⣿⣿⣿⣷⣄⠀⠉⠙⢯⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢷⠛⠛⡇⠳⡄⠀⠀⠀⠀⠀⠀⢿⣏⡀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠘⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠈⣗⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠑⠥⠖⠛⣛⠛⠿⢿⣿⣿⣟⠛⠋⠉⠉⠒⠢⠴⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠘⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⢤⣀⣀⡀⠀⠀⢹⣣⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡏⢳⡀⠀⠀⠀⠀⢈⡽⣿⣿⣿⣿⣷⣪⠉⠁⠀⢠⠀⠱⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠉⠓⠢⠄⠒⠒⠉⠉⠀⠀⠀⠉⠙⢦⠀⠀⠱⡳⣄⠱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢸⠀⡖⢇⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠹⣟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠈⣶⠇⠘⢧⠀⠀⢸⣿⡟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠘⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠒⠒⠢⢿⠀⠀⠈⡇⠀⠸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⡇⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠰⠁⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠀⢀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢸⡄⢸⡄⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⢸⣧⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣶⣦⣤⣤⣄⣀⡀⠀⠀⠀⠈⠙⢶⣤⡀⠀⠀⠀⠸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠹⣿⣷⣄⠙⣶⡝⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠚⠛⠉⠁⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣷⡈⢿⣞⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣴⣀⣤⣶⠆⠀⠀⠀⠀ ⣴⣿⣿⣿⣿⣿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤ ⣿⣿⣿⣿⣿⣿⣷⣷⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⣿⣿⣿⣿⣿⣿⣿ ⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠉⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣭⣉⣉⣙⣛⣛⣋⣻⣯⣭⣶⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣼⡟⠁⠈⣿⣿⣿⣿⣿⣿⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣥⣴⣟⠋⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡟⣿⡿⠛⣿⣿⣿⡏⠀⠀⠀⠈⠉⠉⠛⠛⠛⠓⠲⢼⣿⣿⣿⣿⠄⢻⡿⢀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡁⠀⢣⢸⠃⠀⢀⣼⡿⠋⠀⢧⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⢤⡀⢿⣿⣿⣿⠀⢸⣷⡀⠁⢀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠟⣹⣿⡍⠛⠿⣷⣾⣾⡀⠀⣸⠋⠀⠀⠀⡞⢧⠀⠀⢀⠔⠉⠀⠀⢀⣀⣠⠿⠛⢻⣿⣿⠀⠘⠃⢹⣏⠁⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣋⠀⣸⠟⠈⠙⠳⣶⣞⣿⣿⠄⠒⠚⠷⠤⢄⣀⡇⠸⣄⣴⣷⣶⡶⠿⠿⢿⣿⣿⣷⣶⣾⣿⡇⠀⠀⠀⠈⢯⢣⡀⠀⠀⠀ ⣿⣿⣿⣿⠛⣥⢰⠃⠀⠀⠀⢀⣠⠿⠋⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠙⠧⢤⣤⣤⣤⣴⣿⠾⠿⠟⠁⠀⢸⠀⠀⠀⠐⡄⠘⣧⣣⡠⠀⠀ ⣿⣿⣿⣿⣼⣿⢸⠀⢠⠴⠻⢟⣡⡤⣤⣀⣀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢡⠀⢹⣹⠃⠀⠀ ⣿⣿⣿⣿⣿⠁⠘⡶⠁⠀⠰⣿⣷⣦⣤⣤⣬⣿⣦⡴⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡀⠀⢸⠀⣸⠃⠀⠀⠀ ⡿⢻⣿⣿⠘⢆⠀⠰⡄⠀⠀⠹⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⡠⠴⢖⣶⠟⠚⠛⠀⠀⠀⠀⠀⠀⣼⠀⠀⡇⠀⢸⣷⠏⠀⠀⠀⠀ ⠀⢸⣿⣿⠀⠈⠳⡀⠙⣆⠀⠀⠈⠙⡍⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡸⠀⠀⡼⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⠀⠀⠀⠈⠢⡈⢆⢺⡏⠉⠙⠒⠤⣄⣀⣀⣀⢀⣀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣰⠁⠀⡴⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⡀⠀⠀⠀⠀⠙⢮⡈⠳⣀⠀⠀⠀⠀⠈⠙⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⣴⣇⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠈⠲⣌⣵⣶⠒⠒⠒⠒⠒⠋⠉⠉⠉⠉⠉⠉⠉⣿⠛⠂⠀⠀⠀⠀⢀⡜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠟⠛⠻⣦⡀⠀⠀ ⠀⠀⢸⡟⠈⣹⣷⣦⣭⣛⡳⠦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣞⣿⠾⣟⣉⣥⣤⣿⣷⠀⢿⣧⠀⠀ ⠀⠀⢸⢻⢸⠛⠉⠀⠈⠈⠙⠛⠿⣬⣝⡛⠿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣟⣽⣟⣫⡷⠞⠋⠉⠀⠀⠈⠻⣧⠸⡿⡆⠀ ⠀⠀⣸⡜⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣽⡛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⡇⣷⠀ ⠀⢸⣿⠗⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣟⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⡇⣿⠀ ⠀⢸⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⣷⣦⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⡀⢀⣼⢱⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀ ⠀⠘⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠶⠶⠶⠶⠶⠶⠾⠿⢿⣿⣿⣟⣋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣿⠀ ⠀⠀⣇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡏⠀ ⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣿⠁⠀ ⠀⠀⢨⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀ ⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⡇⠀⠀ ⠀⠀⠀⠀⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣩⡿⠃⠀⠀ ⠀⠀⠀⣰⡟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣶⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀ ⠀⠀⢀⡿⢁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡅⠀⠀⠀⠀ ⠀⠀⣸⠃⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠋⠀⠈⠹⣆⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⢻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀ ⠀⠀⡏⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢹⣿⣿⣷⣄⣀⣀⣼⣿⡄⠀⠀⠀⠀⠀⠀⣾⡀⠀⢀⣴⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣿⡀⠀⠀ ⠀⢸⠡⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⢸⣿⣧⣨⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣏⣀⣿⣿⡿⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⣇⠀⠀ ⠀⣼⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡇⠀⠀⠻⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣿⠀⠀ ⠀⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣧⠀⠀⠀⠀⠉⠛⠛⣉⣴⣿⣿⠃⠀⠀⠀⠀⠈⣿⣿⠛⠛⠛⠛⠁⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀ ⢀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡠⠤⣤⠤⠖⣋⣽⣿⡟⠁⠀⠀⠀⠀⠀⠀⠹⣿⣷⣤⡀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀ ⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠶⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⢸⢿⣿⠀ ⣸⡇⢻⣄⠀⠀⠀⣶⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⣿⣿⣿⡇⠀⠀⣿⢸⣿⠀ ⢼⣇⡀⢻⣆⠀⠀⠀⠈⠻⣿⣯⣙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⣩⣾⡿⠛⠛⠋⠀⠀⢀⡿⢸⣿⠆ ⠘⢿⣷⣀⣹⣦⣄⠀⠀⠀⠈⠻⢿⣷⣶⣬⣝⣛⠶⣤⣤⣀⡀⠀⠀⢤⣀⣶⣦⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠖⠛⠉⣡⣴⣿⡿⠋⠀⠀⠀⠀⠀⢀⡾⢃⣿⡿⠀ ⠀⠀⠙⢿⣯⡛⢿⣷⣦⣀⠀⠀⠀⠉⠻⢿⣯⣝⡛⠿⢿⣿⣿⣽⣟⣟⣿⣓⠉⠻⠿⡁⣦⣶⣶⣶⡾⠿⠿⠉⣉⣠⣤⣴⣶⣿⣿⠟⠋⠀⠀⠀⠀⠀⣀⣴⡏⣡⣾⡿⠁⠀ ⠀⠀⠀⠀⠉⠻⢷⣯⣛⠉⠛⠶⣤⣀⠀⠀⠈⠉⣛⠿⣶⡄⠈⠉⠉⠛⠛⠛⠛⠻⠿⠷⠶⠶⠶⠶⠶⠟⠛⠛⢛⣯⣿⠿⠛⠋⠀⠀⠀⠀⠀⣀⣴⣾⢟⣽⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣤⣍⡛⠶⣶⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣖⣀⢀⣀⣀⣠⣤⣶⠿⣋⣭⣶⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⠷⠶⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣭⣭⣭⣭⣭⠷⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃ ⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣶⣶⣤⣤⣤⠤⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⠤⣄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⢸⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⠟⣩⣾⣿⣿⣷⣶⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀ ⣿⣷⣤⣀⠀⠀⠀⠀⢲⡦⠤⣄⣀⣠⣿⡿⣡⣾⠿⠟⠫⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢻⣆⡀⠀⣀⡀⢀⠀⠀⠀⣅⠀ ⠉⠉⠉⠉⠉⠉⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⣀⠀⠛⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠃⠈⠙⠒⢦⡿⠛⠒⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠙⢦⣀⠀⠀⠀⠀⠀⠈ ⠀⠀⢤⣤⡤⠤⠴⠶⠒⠉⠉⠁⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡷⢦⡈⠳⢤⣀⠀⠀⠀ ⠀⠀⠈⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠤⢤⡀⠘⣇⠀⠀⠀⢀⡀⠀⠀⢀⣼⣿⣿⣿⣿⡟⣠⣾⣿⣷⣄⠉⠓⢦⡀ ⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⡀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢽⠀⠀⠀⠀⠙⢦⡀⣼⣿⣿⣿⣿⡿⠀⣿⣿⣿⣾⣿⢷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⣠⡤⠒⢋⡏⠀⡼⢀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠙⣿⡋⠀⠀⠈⡇⠀⣿⠙⠛⠻⢿⣦⠙⣦⠀ ⠀⠀⠀⠀⠀⠀⠴⠋⠁⠀⠀⠀⠀⢸⠇⢸⠃⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠈⢳⣴⠀⠀⢷⡀⢻⡀⠀⠀⠀⠈⠛⠻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⣾⠀⣼⣇⣤⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠈⢇⠈⢷⡄⠀⠀⠀⠀⣼⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠘⢧⠈⢻⣤⠀⣠⡾⠻⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡏⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⣳⣄⢹⡾⠋⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠂⠀⣿⡇⢰⢋⣙⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣿⣷⣶⣤⣀⣠⡾⠇⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠟⠋⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⣠⠎⢁⡄⠀⣿⡇⢸⣾⠉⠻⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⢐⣮⡷⠿⣛⣉⡉⠛⠿⣿⣧⣄⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠁⠀⠀⠀⠀⠐⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢸⠁⢀⠟⣷⡼⣿⣦⣴⡟⢻⠆⠀⠀⠀⠀⠀⠀⢰⠟⠋⣠⣾⣁⡀⠙⢧⠀⠈⢻⣿⣧⡀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⡇⠀⣸⠀⠹⢷⣝⣛⠚⢡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠀⠟⠛⡇⣧⠀⠀⠹⣿⣿⣤⣤⣇⣀⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡇⠀⣿⠀⠀⠀⠈⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠘⣆⣠⡞⢁⡏⠀⠀⣰⣿⡿⠛⢻⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣇⣰⣿⠀⠀⠀⢴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠤⠤⠴⠛⠀⣠⣾⡿⠋⠀⠀⡸⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⢤⡀⠀⠙⣄⠀⠀⣽⠁⢻⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⠛⠉⠀⠀⠀⣠⠞⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⢤⣈⠳⣄⣸⠀⠈⣇⠀⠀⠰⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠒⠀⠀⠀⣀⡤⠚⠁⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢹⠾⢽⣆⠀⠸⡆⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠑⠒⠋⠉⠁⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠈⠉⠀⠙⢆⠀⠀⣿⢯⣑⠒⠲⠦⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣀⡀⠀⠀⢀⣀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠳⣄⠀⠀⠀⠀ ⠠⡤⠀⣤⣤⣤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⠁⠀⠈⢙⠖⠢⠤⣤⣀⣨⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠈⠓⢦⣄⠀ ⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⢹⡀⠀⠀⠘⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠿⢦⣄⡈⠓ ⠀⠀⠀⠀⠉⠓⠶⢤⣤⠴⠖⠋⠁⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠾⠟⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠿⠷⠒⠒⠂⠈⠙⠛⠲ ⠀⠀⠀⠀⠀⢀⡴⠋⠁⣰⡄⠀⠀⠀⠀⠀⠀⠀⣸⠇⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣎⡉⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⠴⢋⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠋⠀⢠⠞⢹⡇⣠⢴⣶⣶⢖⣞⠉⠄⠐⢫⠿⣄⣀⣤⡤⠤⣶⣾⣿⣿⣿⣿⣿⡏⠙⠒⣤⢞⣿⠇⠀⠀⠀⠀⠀⣠⠴⠋⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠋⠀⠘⡇⠈⠁⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡦⢞⣵⣾⠇⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠄⠀⠀⠀⢰⠃⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠈⣯⠀⠙⢿⣿⣿⣿⣫⣶⣿⣿⡟⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⣠⠔⣋⡴⠃⠀⠀⢀⡀⢀⣀⣠⣤⠴⠦⢤⣰⣄⠀⠰⣤⣀⡀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⡏⣇⠀ ⠀⣠⠖⣫⡴⠚⢿⠶⠤⠖⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⢧⡈⠓⢤⡀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⡄ ⣼⣵⠞⠁⠀⠀⠈⣳⣄⡀⠀⠀⠀⠠⡀⠀⠀⠀⢀⡤⠔⠒⠈⠉⠑⠒⠤⣀⠀⡝⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡄⣧ ⠘⢿⣶⣶⣶⣿⣿⣿⣿⠿⠋⠁⢀⡠⠑⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠃⢿ ⠀⠀⠀⠉⠉⠉⢠⠞⠁⠀⢠⠖⢉⠄⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡞⠁⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢰⣿⣿ ⠀⠀⠀⠀⠀⣰⠃⠀⠀⡴⠃⠀⡾⠀⡼⠀⠀⢀⣀⡤⠄⠀⢀⡤⠖⣠⣿⣶⣶⣤⡈⢦⡀⠀⠀⠀⠀⠀⢀⣾⠤⠀⠉⣽ ⠀⠀⠀⠀⢀⡟⠀⠀⡼⠁⠀⢠⠃⠀⣇⡤⣾⠟⠁⠀⣀⡴⠋⣡⡶⢫⡏⠀⠀⠉⠻⣆⠈⢢⡀⠀⠀⢀⡾⠃⠀⠀⣰⡟ ⠀⠀⠀⠀⠸⡇⠀⣸⠃⢀⠀⡏⠀⣰⢋⠞⠁⢀⣠⣾⣯⠴⠚⠁⢀⣿⣿⣿⣷⣦⡀⠙⡆⠀⠱⣄⣠⠋⠀⠀⢀⠞⢱⠃ ⠀⠀⠀⠀⠀⢣⠀⡏⠀⢸⠀⠁⢰⣷⠋⢠⣴⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⡿⠿⡟⢿⡄⠹⡀⠀⠙⡇⠀⠀⠘⠁⣠⠋⠀ ⠀⠀⠀⠀⠛⠿⢷⣿⡀⠘⡀⢀⣿⠃⣠⢿⡛⠟⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣶⡄⠈⣿⠀⠱⡄⠀⡇⠀⠀⣠⠼⠓⡾⠀ ⠀⠀⠀⠀⣠⠔⠋⠙⣷⡀⠱⢸⡇⣸⠁⢀⣽⣿⣿⣿⣷⣶⣤⣄⣯⡓⠛⠉⡽⠁⠀⢸⡆⠀⢿⠆⢹⠀⠈⢁⣴⣮⢤⠆ ⠀⠀⢀⠜⠁⠀⠀⠀⡿⠛⠲⣜⣷⣿⠟⠁⠘⠿⣿⣿⣿⣿⠟⠀⠙⠏⠛⠉⠀⠀⠠⢿⠃⠀⢸⠀⣏⡤⠒⠉⢀⣤⠎⠀ ⠀⢠⡯⢤⡤⠤⠀⢸⣥⣼⣷⠀⠉⠁⠀⠀⠀⠀⠈⡏⠁⠀⠀⠀⠀⠀⠸⡖⢲⣶⡄⡀⠻⢇⣼⠫⠿⢤⣀⣙⣛⣓⠞⠀ ⠀⠰⣶⠋⠀⠀⠀⠸⡜⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠿⠿⠂⣸⣷⡄⠈⠩⣌⠙⢏⠁⠀⠀ ⠀⠀⠈⠑⠦⣀⠠⠀⢳⣦⠟⣀⠀⠀⠀⠀⠀⠀⣀⣶⣤⣀⠀⠀⠀⠀⠀⠀⣠⣶⡄⢰⣾⣿⣾⠇⠀⠀⠈⢷⣆⢧⠀⠀ ⠀⠀⠀⠀⠰⠾⣍⣀⠀⠙⢆⣩⡀⠀⠀⠀⠀⠻⢿⡟⠛⢻⣿⠇⠀⠀⠀⠀⠛⠛⠀⢸⣿⣿⡇⠀⠀⠀⠀⠈⡏⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢿⣦⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⡿⠛⢙⣦⡀⠀⠀⢀⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⠿⣿⣁⠀⠀⢻⣿⣦⢀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡛⠲⠤⠤⠤⠤⠶⠶⠛⠋⠁⠀⣸⣧⡀⠀⠈⠉⠒⠦⠧⠙⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠖⠋⣙⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣽⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⢴⣲⢭⡿⠃⠀⢠⡖⠠⢼⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠉⣯⠿⠟⠉⠛⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡴⠉⠰⠟⠚⠉⢰⡄⠀⣀⢵⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠻⠇⠙⠶⣄⠀⠀⠀⠀ ⠀⢸⠁⠀⠀⠀⠀⠀⡹⠂⠉⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢿⣦⠀⠀ ⠀⢸⠀⠀⠀⠀⠠⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠐⠹⣧⠀ ⠀⢸⡀⢚⣥⡄⢘⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⢲⡀⢹⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⡏⣉⡐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠐⠚⢁⣴⣄⠐⢮⣪⠀⠀⠀⠀⠀⠈⢓⢄ ⠀⠀⠀⠀⠀⠀⠀⡄⢰⠀⠰⢁⠴⣟⠿⠃⣿⣷⠯⠀⠀⠀⢀⠂⠀⠀⡎ ⠀⠀⠀⠀⠀⠀⠈⢷⣿⡆⣰⠛⠒⣜⠀⠀⢈⣷⡀⠀⢀⠔⠁⠀⠀⠀⢇ ⠀⠀⠀⠀⠀⠀⠀⠘⢖⡋⢻⡄⢀⢻⡙⣥⣍⡠⠃⠀⠁⠀⠀⠀⠀⡜⡘ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣸⡮⠡⢠⢱⠹⠑⢴⠀⠀⠀⠀⠀⡠⢊⠔⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⢸⡸⡠⣄⢜⠀⠀⣀⡤⣺⡵⠂⠀⠀ ⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⣠⠿⠀⠘⠙⠓⣷⡞⠈⠉⢀⡻⠁⠀⠀⠀⠀ ⠀⢀⠀⠈⠢⣿⣦⡠⠔⠚⠆⠃⠦⠤⠠⡲⢿⣷⡫⣖⣋⡀⠀⠀⠀⠀⠀ ⠀⠢⠌⠉⠙⠋⠎⢀⠠⠄⠼⣰⠀⠠⣱⢗⠟⠙⠋⠀⠀⡈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡆⡀⠂⠉⠀⠀⠑⢎⠆⡄⠀⠀⠀⠀⠀⢁⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡔⣿⣀⠀⠀⠀⠀⠀⠀⠑⡥⡤⠔⣮⣧⠔⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢡⠿⠇⡉⣔⠠⠄⠀⠀⠀⢸⡀⠤⠘⠁⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⡀⠀⢠⣻⠀⢧⡏⠙⠢⠄⣀⣀⠠⠃⠀⠁⢄⠠⢄⠀⠀⠀⠀⠀⠀ ⠈⠉⠁⠂⠉⠹⠄⢘⣞⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠬⠊⠚⠷⠀⠀
⢧⡠⠊⡔⠃⠀⣆⡴⠚⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡰⠁⢀⣠⣤⣤⣤⣀⠐⢂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠈⠀⠙⢦⡙⠓⠶⣤⣠⣀⠀⠀⠀⠀⠄⠀⠀⠀⠀ ⠜⢁⡌⠀⢠⣴⠋⠀⠀⠀⠀⠂⠀⠀⠀⠐⠐⠀⠀⠀⠁⠀⡂⠀⠀⠀⠀⢐⠀⠀⠀⢐⠀⠀⠀⠀⠀⡂⡂⠀⠀⠀⢙⠳⣤⡀⠀⠀⡀⡈⢿⣗⢦⣤⡈⠙⢳⡄⠀⠀⡀⠀⠄⠀⠀ ⡰⠋⠉⣶⠏⣀⣀⣤⠤⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣂⠀⠀⠀⢙⠳⣄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⡀⠹⣿⡉⣠⣾⠋⠀⠀⠀⠀⠀⡀⠀⠀ ⢀⣤⠾⠛⠋⠉⠠⢀⣀⡤⠤⠄⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⢼⣆⠀⠀⠠⠠⠈⠛⢦⡀⠀⠄⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠛⣦⠀⠀⠀⠙⣿⣅⠠⠀⠀⠀⠀⡀⠀⠀⠀⡀ ⠟⠀⠀⠀⠠⠀⣴⠟⠁⣠⠏⠅⠀⠀⣆⠠⠠⠀⠀⠠⠀⠀⠄⠀⠙⣿⣆⠠⠀⠀⠀⠠⠀⠙⢷⣤⣀⠄⠄⠈⠓⠤⡘⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⢳⡄⠀⠀⠀⠀⠂⠀⠀⠀⠀ ⠀⠀⠠⠀⢀⣰⠣⢀⡼⠁⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢻⣿⣧⠀⠠⠀⠀⠀⠀⠀⠝⢿⣗⢦⣄⠀⣀⡀⠀⠀⠀⠄⠀⠁⠀⠀⠐⢦⡀⠈⢻⡆⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⢐⠀⠀⣿⢀⡞⠁⠀⢀⡀⠀⠀⢹⡄⠀⠀⠀⠀⠁⠀⠀⠁⠁⠈⢿⡌⢻⣌⠀⠀⠀⢠⡀⠅⠀⠙⢶⣌⠻⢾⡳⣄⠀⠀⠁⠁⠀⠀⠁⠀⠈⠹⣆⢨⣿⣦⣠⣤⠤⠥⣥⣄⡀ ⠀⠀⠀⠀⢀⠃⠈⠃⢀⡞⢸⡇⢀⠀⣸⣗⢀⠀⠀⢀⢠⠀⠸⣴⠀⠀⠘⢷⡀⠙⣦⢀⠐⡁⠀⠀⠀⡀⡀⠙⢷⣄⣙⣾⣷⣄⠀⠀⡀⡀⢀⠀⠀⠀⢈⢳⡜⣷⣄⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢸⡇⠀⠀⠸⣿⣆⠀⠀⠀⣟⢧⡀⠙⡇⠀⠀⠘⢷⡀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⠙⢛⢻⣦⡀⠂⠀⠀⠀⢀⠀⠐⠀⠹⣾⣿⢶⣦⣀⣀⠀⠀ ⠀⠀⠠⠀⠀⠀⠠⢠⡇⠄⢸⡇⠀⠀⠀⣧⢹⣤⠀⠀⣿⣄⣵⣤⣿⡄⠀⠀⠘⢳⡀⢀⣼⢷⡄⠄⢀⣠⣤⣴⣤⠴⢼⣦⠀⠙⢿⣷⡀⠀⠂⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠈⠙⢓⡴ ⠀⠀⢀⠀⠀⠀⠀⣾⠇⠀⢼⡇⠀⠀⣯⢿⡄⠹⣆⠀⢿⡽⣞⠏⠉⠀⠀⠠⠀⠈⢻⣌⠁⠀⠙⣧⡾⣛⣭⣭⣭⣀⠀⠈⠀⠀⠀⠙⢿⡄⠀⠀⠈⠠⠠⠀⠀⠀⠘⢷⡀⠀⢀⠞⠀ ⠀⠀⠀⠀⢀⠀⢀⡟⠀⢀⢻⣇⠀⠀⠈⢸⡇⠀⠘⣦⠘⣷⠘⣦⡀⠀⠀⠀⠀⠀⠀⠹⣦⡈⠾⣩⣾⣿⣉⣉⠉⠙⠻⢷⣦⣀⠀⠀⠈⢿⡌⠀⠀⠀⠈⠀⠀⠈⠀⠁⢷⡀⠇⠀⠁ ⣀⡤⠖⠛⠛⠳⣾⠇⠀⠀⢸⣿⠀⠀⢀⠈⣿⠀⠀⠈⢷⣽⡇⠈⠳⣄⠀⠀⢐⠀⠀⠀⠈⠳⣤⣿⣿⡟⠻⣿⣷⣦⡀⠀⠙⢿⣷⡄⠀⠈⣿⡄⢀⠀⠀⢀⠀⠀⡀⠀⠀⣿⡀⠀⠀ ⠉⠀⠀⢀⣤⠞⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⣇⣀⣀⡀⠙⢿⡄⠀⠙⢦⡀⣀⡤⠶⠚⠛⠋⠉⠈⢿⣇⣴⣿⣿⣿⣿⣆⠀⠀⢿⡿⠀⠀⠘⣷⡀⠀⢀⠀⠀⠀⠀⢶⡀⠘⡇⠀⠀ ⠀⣠⡴⠟⠡⠀⠀⠀⠁⠀⢼⠉⡇⠀⠀⠠⠀⠹⡏⠉⠉⠀⠈⠛⢦⡀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢹⣿⠀⠀⢸⠇⠀⠀⠀⢹⣿⡠⠠⠀⠀⠀⠀⠄⢷⡀⢻⡄⠀ ⡾⠁⠀⠀⢀⠀⡀⠀⠀⠀⣹⠀⣿⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣾⠃⠀⠀⣰⣶⣴⡤⣤⠈⣿⣿⡌⠀⠀⠀⠀⠁⠙⣧⢸⣇⣀ ⠇⠀⠐⠀⠀⠀⠐⠀⠀⣀⣸⣧⡿⣆⣤⠶⠶⠶⠶⠛⠁⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠉⠁⠀⠀⢀⣿⡇⠇⡇⣿⠀⣿⣿⣿⣈⠀⠀⠀⠀⠀⣿⣿⡇⠀ ⢸⠀⠠⠀⢀⣀⡤⠖⠛⠉⠉⠉⠙⣿⡇⠀⠀⠀⠀⢀⣠⣭⣥⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⡀⠀⣿⢏⡇⠀ ⢿⢀⡠⠖⠋⠁⠀⠀⠀⢀⣠⡴⡚⠉⠀⠀⠀⣠⣾⣿⠿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡼⣇⠀⠀⠀⠀⢀⡿⢸⡇⠀ ⠿⠋⠁⠀⠀⠀⢀⣤⣶⠛⠉⢻⣇⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⡇⠀⠀⠀⠀⣹⠇⠘⡇⠀ ⠀⠀⠀⣠⡴⠛⠉⠀⠛⠳⢶⣬⣿⡆⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡏⠀⠀⠁⢤⡟⠀⠀⢰⠀ ⣠⣴⡋⠁⠀⠀⠀⠀⠀⠀⡘⣷⡀⠀⠀⠘⠿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣿⡇⠀⠀⢠⡟⠀⠀⠀⠀⠣ ⠁⣿⢀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠻⣆⡀⠀⠀⠀⡠⣴⡼⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⠀⠈⠙⠻⣿⣇⠀⠀⠀⠀⠀⢀⣿⡴⢻⠇⠀⢠⡿⠀⠀⠀⠀⠀⠀ ⠀⢸⡀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⢀⣽⣦⡀⠀⣷⡏⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⣼⡟⠀⢸⠐⠀⣾⠃⠀⠀⠀⠀⠀⡜ ⠠⠸⡇⠀⠀⠀⣿⡀⠀⠀⠀⠀⠠⡟⠉⣿⣿⣦⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠠⣼⡟⠀⠀⢸⡄⢀⡇⠀⠀⠀⠀⠀⠘⣄ ⠀⠈⡇⢀⡎⠀⡟⣧⠀⠀⠁⠀⠈⣧⠀⢿⣿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠀⠀⠀⢀⣼⡟⣀⡀⠀⠈⣧⢸⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡇⣼⡇⠀⣿⠸⡆⡀⠀⠀⠀⠘⣧⡈⠻⣷⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣆⣀⠀⠀⠀⠀⣀⣠⠶⠛⠁⠀⠀⠀⢀⣾⡏⠉⠉⠻⡄⠀⠸⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡿⠛⣇⠀⢻⡀⣻⡖⠀⠀⠀⠐⠈⠻⣦⣬⣛⣻⡝⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⣰⣿⢻⣇⠀⠀⢠⡇⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀ ⣠⡿⠉⠀⢹⡀⠘⣿⡽⢻⡄⠀⠀⠀⠀⠀⠀⠻⣍⡛⠛⣎⢿⣻⣶⣤⣀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡿⠟⠁⠀⠀⠀⠀⠀⢠⣼⡟⠇⠈⢿⣄⣀⠀⠀⠀⠀⠀⠹⣆⠀⣀⣠⡀⢀⣀ ⠋⠀⠀⠀⠈⢻⡁⢿⡀⠂⣹⣦⡀⠠⠀⠀⠀⢠⣌⠷⣤⠈⠳⣿⣌⠉⠉⠛⠓⠒⣶⣦⣾⣽⣯⣅⣀⡀⠀⠀⠀⠀⢀⣴⡿⠋⠘⠀⠀⠈⢻⣿⡟⠳⣦⡴⠖⠒⠛⠉⠁⠀⠉⠻⣯ ⠀⠀⢀⠀⣠⡞⠻⢮⣷⡇⠀⠈⠛⢦⣈⠀⠀⠀⠻⣟⠿⢽⣦⣝⡮⣗⡶⠴⣷⣺⠿⠚⠁⠀⠀⢿⣯⡉⠙⠛⠛⠛⠛⠋⠀⢀⠇⠀⠀⠀⠀⠙⢿⡆⠸⡟⠿⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⡋⠀⢀⡄⢙⠻⡇⠘⠀⠠⠿⠳⣦⣀⠀⠘⢧⡀⠀⠉⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢸⡧⡚⠷⣄⣼⠋⣷⡀⠀⠀⠀⠀ ⢀⣼⣻⠁⠀⠀⠀⢀⠀⠀⠘⠓⣚⠟⠀⠁⠉⠋⠓⠶⣤⣛⢦⣤⡀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⣠⢾⣧⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⢠⣟⢀⣿⣆⡰⠀⠀⠛⠳⢤⣁⠀⡠

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠇⠀⢰⣿⠉⠓⠲⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡏⠀⠀⣠⡯⠤⠒⠒⠀⠉⠢⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠃⢸⠟⠉⠀⣠⣶⣄⠉⠉⢲⣤⡙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣝⠢⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡴⠁⠀⣠⣾⣿⣿⡿⢓⣦⣴⣍⣿⠟⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢆⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⣼⠀⠀⣼⠁⡰⠚⢾⣿⠛⠛⠀⠸⣿⣿⡿⠛⠓⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⢸⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣸⣿⣆⠀⢻⣼⠿⠶⣄⠙⠇⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢸⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⡛⣏⣷⣼⠁⠀⠀⠈⣷⣤⣄⣀⢠⣴⡾⠟⢧⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢀⡇⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡖⠋⡹⢻⣆⠀⠀⢰⠛⣏⠹⣄⣩⢏⢀⡠⠋⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⡜⢀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡉⢀⢼⣟⠓⠒⠁⠀⠙⡗⢾⡿⣍⠙⢆⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⠎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⠾⣿⠳⠤⠂⢰⡄⢱⠀⢣⠀⠱⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣠⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⡀⠀⠀⠘⡇⢸⠀⣸⠀⢀⣿⠀⠀⠀⠀⠀⢀⣠⣾⡕⣆⠜⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⣷⡄⣴⢉⣤⠊⣸⠀⣀⣠⠤⠶⢿⣙⡶⠟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢠⡿⢳⠀⠀⠐⠓⠟⠚⢻⣿⣺⠋⠉⠀⠀⠀⣈⢲⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠢⡀⢸⣿⡀⠀⠀⠀⢀⣠⣴⠋⢣⠘⡗⠀⠀⠀⠀⣀⣸⣭⣿⢒⡲⢤⣀⣲⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⢈⢲⣻⣯⣲⡴⠚⠉⠀⠈⢆⠀⡆⠙⠒⠒⠋⡟⢡⠋⣻⣿⡿⣉⢻⣯⣏⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠹⠿⠃⡰⠋⠀⠀⠀⣀⡀⠘⡄⡇⠀⠀⢀⡜⣰⣷⣾⡿⠏⠹⠟⠉⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⡇⢀⠔⠊⠉⣁⡠⠍⠓⢶⡀⠀⢈⠜⡿⠁⠎⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⡠⠊⠁⠀⠀⠀⠀⠀⠉⠺⡁⠰⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣧⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⢣⠀⠀⠀⢀⣀⢤⡖⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⡿⡷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⢒⡾⠟⠙⢷⣾⣟⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⣇⣿⠂⠈⠑⡲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠘⡏⠀⣀⢀⡨⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠈⢸⠙⣶⢼⡷⡞⠀⠉⠑⠀⠀⠀⠀⠀⢠⠛⠦⣈⠉⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡎⣽⠀⠀⣧⣿⠀⠉⠛⠦⣄⣀⠀⠀⠀⢀⡴⠃⠀⠀⠈⠳⣄⠀⠱⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠿⠿⠿⠑⣀⡴⠾⠿⣿⠀⠀⢸⣿⣦⣄⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠉⠒⢶⡒⢶⣶⣤⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠧⠐⢄⣿⣈⠳⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠊⠉⠉⢙⡛⠃⠀⠀⠀
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