My Melody Text Art

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⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⠟⠛⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠛⢷⣄⢀⣠⣤⡶⠾⠟⠛⠛⠛⠛⠛⠛⠻⢷⡄ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿ ⠀⠀⠀⢰⣿⠀⠀⢰⣆⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏ ⠀⢀⣤⣼⣿⠶⣦⡄⠛⢷⣤⣤⣀⣀⣴⡿⢶⣦⣤⣤⣤⣤⣶⣶⡶⠾⠟⠛⠁⠀ ⢰⣟⠁⠉⣁⠀⢼⣇⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠙⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡶⠈⠛⣀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⣶⡾⠛⠛⠋⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⣿⠃⠀⠀⠀⠀⣀⣤⡶⠟⠛⠋⠉⠉⠉⠉⠉⠛⠿⣦⡀⢸⡇⠀⠀⠀⠀⠀ ⠀⠸⣿⠀⠀⠀⣠⡾⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⢹⣧⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⢻⣆⠀⢰⡟⠁⢸⣿⠀⠀⠀⠀⣴⡄⠀⠀⠉⠁⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣦⣿⣇⠀⠈⠉⠀⠀⠀⢰⣶⡾⠇⠀⢀⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢿⣷⣤⣄⣀⣀⣀⣀⣠⣤⣴⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣴⣶⣶⣶⣄⠀⠀ ⠀⠀⠀⣀⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⢇⠠⣏⡖⠒⣿⣿⣿⣿⣿⣿⣿⣧⡀ ⠀⠀⢀⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⢸⣿⣿⡿⢋⠁⠀⠀⠀⠀⠉⡙⢿⣿⣿ ⠀⠀⠘⣿⣿⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⣿⡿ ⠀⠀⠀⠈⠙⠷⠤⣀⣈⣓⣃⣀⣠⠤⠾⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠁⠀⠀⠀⠈⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀ ⠀⠀⠀⠀⠀⣠⠎⠉⠀⠀⠀⠉⠑⠲⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠀⠀ ⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⡧⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠈⣧⣀⣀⣠⠴⣋⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡧⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⣟⠀⠀⠈⠋⠀⠀⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠘⠀⠀⠀⠀⠀⠙⠲⠤⠤⠴⠛⡬⠂⠀⢼⣷⠐⠀⢎⠀⠀⠀⠀⠀ ⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⣀⠤⢄⡀⠀⣸⣆⠀⠀⠀⠀ ⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠹⡄⠀⠀⠀ ⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠋⠉⠉⠉⠉⠉⠓⠢⣄⠀⠀⡇⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠈⢆⢀⡇⠀⠀⠀ ⠸⡀⠀⠀⠀⢀⠞⠀⣶⣦⠀⠀⠀⠀⡠⠄⢄⠀⠀⠘⠛⠁⠀⣸⡞⠀⠀⠀⠀ ⠀⠳⡀⠀⠀⢸⠀⠀⠻⠟⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⣠⡼⠋⠀⠀⠀⠀⠀ ⠀⠀⠙⠢⣄⣘⣄⠀⠀⠀⠀⠀⠀⠑⠒⠒⣁⡠⣪⣯⢀⢀⡼⣶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠛⠒⢲⠖⠒⠚⢻⣏⡉⡡⡅⣻⠄⠻⠉⠀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡶⠤⣄⡎⠁⠈⢳⠈⢾⡄⠀⢀⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠴⠶⢤⡷⣄⣀⣀⡄⠠⠞⠄⢄⣉⣓⡁⡴⠚⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠁⠈⠉⠉⠐⢄⠠⠊⠁⢈⡆⡟⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠣⢄⣀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠇⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣄⣀⠀⠀⠀⠀⢀⣏⣀⡠⠫⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠒⠒⠒⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⣄⣤⣄⡀⠀⣠⡶⠚⠉⠙⠲⣄⠀⠀⢀⠸⣆⠀⣀⡀⠀⠀⠀⠀⠀⢀⡾⡁⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠈⢹⠏⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠀⠁⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀ ⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢀⣤⠞⠛⠛⠲⢄⠀⠀⣰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⡞⠁⠀⠀⠀⠀⠈⣇⠰⢧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠊⢳⡦⠸⡇⠀⠀⠀⠀⠀⢠⡟⠀⠀⢹⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⣴⠋⠀⠈⠙⠦⣄⣀⣠⠴⠋⠀⠀⠀⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡀ ⠀⠀⠀⠀⠀⠀⠿⡀⠀⠀⠀⠀⠀⢸⡷⣄⡀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⣹⠦⠤⠤⡤⠞⠋⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣄⣀⣀⣀⣠⠴⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⠤⠤⠤⠤⢤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⢿⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡄⠀⠀⢸⡿⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⡀⠀⣿⡇⢀⣠⣾⡿⠟⠛⢻⢷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣴⣤⣤⣄⠀⠀⢸⠀⠀⠀⠀⣦⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⡀⠘⣧⠘⠟⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠀⠛⠋⠃⠀⠀⠩⠛⣿⣦⢼⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣀⠀⠀⠀⣀⡤⠔⠒⠒⠲⢤⡀⢀⣠⠴⠒⠒⠒⢤⡀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠛⣶⠞⠁⠀⠀⠀⠀⠀⠀⠙⣏⠀⠀⠀⠀⠀⠀⠈⢧⣀⣤⣶⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢻⡅⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠹⣄⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢀⡼⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠈⠓⠢⠤⠤⠖⠋⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠤⠴⠚⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
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⠀ ⠀⠀⠀⠀⣾⣿⣿⣷⣄ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣴⣶⣶⣶⣄ ⠀⠀⠀⣀⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠀⠀⢇⠠⣏⡖⠒⣿⣿⣿⣿⣿⣿⣿⣧⡀ ⠀⠀⢀⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⢸⣿⣿⡿⢋⠁⠀⠀⠀⠀⠉⡙⢿⣿⣿⡇ ⠀⠀⠘⣿⣿⠀⣿⠇⠀⢀⠀⠀⠘⣿⠀⣿⡿⠁ ⠀⠀⠀⠈⠙⠷⠤⣀⣀⣐⣂⣀⣠⠤⠾⠋⠁ ⠀⠀
⢆⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢆⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠠⠄⡀⠀⠀ ⠀⠀⠣⡀⠀⠀⢀⣀⡀⠀⢡⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠈⢂⠀ ⠀⠀⡰⠉⠉⣱⠁⡀⠈⡆⠉⠉⠁⠀⠀⠁⠀⠸⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠳⣀⡌⠀⠀⢰⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⡁⠈⠐⣆⣁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⢀⠆ ⠀⠀⢠⠋⠀⠉⠀⠀⢀⡀⠤⠤⠤⠄⢀⡀⠀⠀⠀⠉⠓⠒⡆⠁⠀ ⠀⠀⡆⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢀⠀⠀⠀⢹⠀⠀ ⠀⠀⠇⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⢸⠀⠀ ⠀⠀⠘⡄⢇⠴⠛⠉⠒⠀⠀⠀⡄⠀⠀⠠⠶⠒⢦⣀⠀⢀⠇⠀⠀ ⠀⠀⠀⠈⠺⣆⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⢠⡠⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⠵⢢⠔⠈⠉⠑⢔⠉⠀⠑⢄⢤⠒⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢇⣠⠆⠀⠀⠀⠀⡘⠀⠀⠀⠈⣄⣵⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡘⠄⠀⠀⠀⡐⠱⡀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠈⠀⢒⠈⠀⠀⠈⠐⠒⠊⠸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣤⠶⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⣴⣤⣄⡀⠀⠀⠀⠀ ⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡄⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀ ⠀⠀⠈⠻⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀ ⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠶⠿⣿⣦⠗⠛⠒⣦⣀⠀⠀⠀⠀⠀⠐⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡇⠀⢠⡇⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠘⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣇⠄⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠐⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠹⣤⡀⢰⠞⠉⢳⡄⠠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠛⢶⣤⣀⣀⣀⣤⡴⠟⠃⠀⠀⠀⠀⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠠⡏⠀⠈⠓⡶⠊⠀⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠰⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣧⣀⣀⣠⡾⢦⣤⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠀⠈⠉⠁⠀⠀⠀⣀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡴⠒⠒⣞⣁⡠⠽⠭⢄⣈⣳⣊⡉⠲⣄⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀ ⠀⠀⠀⠀⢸⡇⠀⡴⠋⢙⡵⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠳⢤⣀⣳⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠐⢺⡇ ⠀⠀⠀⠀⢸⡇⡮⢇⡾⠁⢠⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⢹⣄⡀⠀⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⠸⣿⡁⣼⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠈⠳⣄⢹⠦⠀⠀⠀⠀⠀⠀⣟ ⠀⠀⠀⠀⠀⠻⡟⢿⠀⠀⠈⠛⠉⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠙⣎⠳⡄⠀⠀⠀⢸⢰⡏ ⠀⠀⠀⠀⠀⠀⠱⣜⣆⡤⠦⠤⣄⠀⠀⠀⠀⠛⠒⠋⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⢸⣤⠇⠂⠀⢠⢄⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠐⣾⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⠃⡃⠁⠠⣠⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⣼⣦⣤⣠⠦⢄⠙⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡞⣡⣤⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠸⣿⠉⠀⣹⣀⣙⣿⠏⠁⡽⠶⠤⣤⣤⣤⣤⣤⣴⡾⠅⠚⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠈⠛⣿⠿⣌⡝⠝⡍⣘⣧⣀⣀⣀⣀⣤⣴⣶⣾⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣳⡶⢻⠷⣮⣤⣤⣽⣥⣬⣭⣿⣿⢿⡖⠋⠉⠉⢳⡝⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⢺⣥⣧⣽⢂⡄⠀⠓⠀⠈⢻⡄⠀⠀⠀⠀⣿⣭⣧⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⠴⢺⠥⠚⠁⠀⠘⠦⣽⡒⢤⣄⣀⣼⢳⣤⡀⠀⠼⠃⣠⣷⡗⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠯⠜⠉⡏⠀⠀⠀⠀⠀⡄⣧⠉⠙⠲⣾⣯⣯⣏⣳⣶⣴⣾⣻⣉⣽⣵⡦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣿⢄⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⡶⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠟⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡀⠙⠒⠢⢴⣉⡦⠔⠚⠋⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⠽⣉⣙⣟⠛⣛⠻⢿⠞⠿⡟⠿⣻⠛⣧⠀⠀⠀⠀⠁⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣉⣉⣻⣿⣃⠙⢍⣫⣁⠉⠉⠉⣉⣩⣿⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣉⣉⣿⡀⠉⠛⠛⠧⠜⠛⠛⠛⠉⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠾⠶⠶⠶⠶⠞⠳⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀୭ 🧷 ✧ ˚. ᵎᵎ 🎀
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discord.gg/UUZkkhe5ws ⠀⠀⠀⠀⣾⣿⣿⣷⣄ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣴⣶⣶⣶⣄ ⠀⠀⠀⣀⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠀⠀⢇⠠⣏⡖⠒⣿⣿⣿⣿⣿⣿⣿⣧⡀ ⠀⠀⢀⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⢸⣿⣿⡿⢋⠁⠀⠀⠀⠀⠉⡙⢿⣿⣿⡇ ⠀⠀⠘⣿⣿⠀⣿⠇⠀⢀⠀⠀⠘⣿⠀⣿⡿⠁ ⠀⠀⠀⠈⠙⠷⠤⣀⣀⣐⣂⣀⣠⠤⠾⠋⠁
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣦⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⢸⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⣶⡆ ⠀⠀⠀⢸⡁⢴⠎⣹⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡏⠀⠘⠋⠀ ⠀⠀⠀⢼⣿⣤⡞⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⠀⠀⠀ ⣴⣿⠀⢼⣿⣿⠀⣼⣿⠀⢀⣄⠀⢾⣷⠄⣽⣿⡟⠀⠀⠀⠀ ⠈⠁⠀⠈⠻⣿⣦⣌⣉⣀⣈⣁⣀⣸⣩⣴⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣶⣿⡶⢿⡿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣯⣿⣯⣯⣷⣿⣳⣆⣤⣤⣤⣤⣤⣶⣾⣿⡯⡄⠄⢸⣿⡿⢺⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠋⢴⣿⣷⢀⢈⢹⣿⣶⣿⡿⠿⣿⣿⠁⠿⡿⠟⡀⠀⣀⢂⢿⡏⠉⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣾⢿⡎⠛⠓⠋⣉⠁⠹⣿⣗⣿⢅⣠⡌⢻⣶⠶⠶⠧⢡⣾⠿⠇⢹⣇⠀⠀⠀⠀⠈⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⠟⠉⠀⠈⣿⡀⠰⣿⡟⣃⠛⢯⠉⢿⣧⡛⣫⣿⠃⢀⣤⣤⡄⠐⠰⢠⡌⣿⡆⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⡟⠁⠀⠀⠀⠀⣿⣧⣀⠀⠘⠚⠁⠀⣴⣶⡿⣟⠛⣟⢷⣬⣿⢯⠇⠀⠸⣿⠇⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⠀⠀⠀⠀⠀⠀⣿⠟⠯⡀⣿⡷⠮⣎⣿⢿⡿⠃⠀⠈⠛⢿⣟⣻⡶⢶⣶⠶⢾⣿⡵⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀ ⠸⣿⣄⠀⠀⠀⠀⠀⡿⣦⣌⣡⣶⣵⣿⣿⣷⣿⣴⠶⠶⠶⠶⠶⠶⠾⣿⣿⣙⠛⠋⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀ ⠀⠈⠛⠿⠿⠿⠿⠿⠟⠓⠛⣿⣷⠋⣫⡿⢛⣥⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣄⡀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣾⠏⢰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠘⠿⠿⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣄⠘⢿⣄⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠈⠢⠀⠀⠀⢸⣋⢙⡆⠀⠀⠀⠀⢰⣿⣿⣿⡆⠈⢻⡄⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⣽⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⢀⣀⣩⠉⠁⠀⠀⠀⠀⠈⢿⣿⠿⠀⠀⠘⣿⠀⠀⠀⠀⣰⡿⠙⠿⣶⣤⣀⣀⣀⣴⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⡾⠛⠉⠙⢷⡄⠀⠀⠀⠀⠀⠀⠐⠢⡄⠀⠀⣿⠆⠀⣠⣾⠟⠁⠀⠀⠀⠉⠉⠋⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢨⣿⡾⠿⠷⣶⣤⡀⠀⠀⢁⣠⣾⣯⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠖⢀⣴⠟⠁⠀⠀⠀⠀⠉⠛⢿⠟⢿⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⣟⡁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣉⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣉⠛⠻⠶⣶⡶⠟⠛⠋⠉⠉⠉⠉⣻⣯⡤⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣤⣤⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠟⠉⠉⠉⠙⣦⡀⠀⠀⠀⢠⡾⠋⠉⠉⠙⣲⡀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣷⠀⠀⣰⠏⠀⠀⠀⠀⠀⣽⣷⠀ ⠀⠀⠀⠀⠀⢿⠀⠀⢀⣤⠤⣄⣻⣄⣀⡏⠀⠀⠀⠀⠀⢀⣵⠃⠀ ⠀⠀⠀⠀⡴⠛⠛⣳⣿⡤⠀⠈⣏⠉⠉⠁⠀⠀⠀⠀⢠⣼⠋⠀⠀ ⠀⠀⠀⢸⡁⠀⠉⢹⢿⣀⣀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀ ⠀⠀⠀⢠⡟⠲⠒⠋⣠⡬⠟⠛⠛⠛⠛⠛⠓⠦⣤⡀⠀⠀⠀⢿⡀ ⠀⠀⠀⣾⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠈⣧ ⠀⠀⠀⢿⠀⠀⣸⠁⠀⣴⣦⠀⠀⠀⠀⠀⣶⣦⠀⠀⢸⡆⠀⠀⡿ ⠀⠀⠀⠈⢧⡀⠹⣄⣀⠙⡋⠀⠀⠁⠀⠀⢝⢁⠠⠀⣸⠃⠀⣰⠃ ⢀⣄⣴⡄⠀⠙⠶⣽⣶⣤⣤⠖⠲⣄⡼⢛⡳⣆⣠⡴⢋⣠⡾⠃⠀ ⠀⠙⠛⠁⠲⢤⡴⣏⡀⢠⡏⠀⠀⣼⡇⠐⠃⠘⣇⠀⠈⣹⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡟⠛⠀⠀⠀⠈⠁⠀⠀⠀⠘⠞⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⣀⣀⣰⣶⣂⣀⣀⣀⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⣛⠛⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢋⠦⡙⢦⢡⢋⡔⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢣⠜⡡⢎⡱⢊⢆⠣⡜⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠶⣲⠛⠶⢶⣤⣀⠀⠀⠀⠀⢀⡴⢏⠲⡡⢎⡱⢊⠴⣉⢎⡱⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⢡⢋⠴⣉⠞⡰⢢⡙⡳⣄⠀⢠⡞⡍⢎⡱⡑⢎⠴⣉⠖⡡⢎⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡇⡎⡜⢢⡑⢎⡱⢡⢎⠱⡩⢷⣟⡰⣉⠦⡱⣉⢎⠲⡡⢎⣱⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡷⡘⡜⣷⣜⢢⡑⢣⢌⢣⡑⣚⣿⡐⢆⢣⠱⡌⢆⢣⣱⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⠱⡘⣌⠻⣷⣬⣃⣎⢆⣱⣾⢏⡜⡌⢆⠳⡘⣌⠻⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡠⠜⠧⠟⠋⠉⢷⢨⢛⡹⢛⡍⢣⠎⡴⢉⢎⡱⠱⣌⢣⢃⢎⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡄⠀⡠⠒⢦⠀⢾⡂⢧⡘⢥⢊⡕⢪⠔⡩⢆⡱⢃⢆⠣⢎⡌⢳⡘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠁⠉⠒⡁⠀⢀⡟⡤⣙⢢⠣⢜⡡⢎⣑⣊⣴⣉⣎⣱⢊⡌⢣⠜⣌⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠦⡴⡚⡝⣋⠛⡜⡰⣡⣶⠟⠛⠉⠉⠉⠁⠀⠀⠉⢉⣉⡛⢧⣞⠤⢫⡇⢀⣤⣀⠀⠀⠀⢀⣀⡀⠀⠀ ⠀⣿⡘⠴⡱⡘⢤⢋⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠙⣮⢱⡇⢸⡀⠀⠉⠒⠚⠉⠀⣈⠀⠀ ⠀⢻⣌⢣⠱⣉⢦⡿⠃⣾⣿⡆⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⠙⠋⠀⠀⣿⣼⠁⣸⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠈⣷⣈⠳⢌⢾⠁⠀⠻⠿⠇⠀⠀⠀⠀⠑⠚⠁⡀⠀⠀⠀⠀⠀⣠⡿⠃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀ ⠀⠀⠈⢷⣍⠎⡼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⣠⣄⣀⡤⠞⠉⠀⠀⠉⠓⢲⣦⠀⠀⢀⡤⠤⠶⠚⠃ ⠀⠀⠀⠀⠈⠛⠶⣽⣷⣄⣀⠀⠀⣀⣀⣀⣠⣤⣴⣶⠛⠀⠙⡄⠀⠀⠀⠀⢀⡴⠋⠘⣇⣠⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠒⠉⠀⠙⣟⢻⡟⠋⠉⢿⡡⢆⡍⣛⣦⠀⡀⡇⠀⠀⠀⣠⠊⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢫⣴⣤⡴⠋⢻⠀⡀⡀⠘⣷⠛⠚⠉⠙⣯⠵⣅⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠋⠀⠀⢱⡀⠈⠓⠓⠚⠒⠋⠑⠦⣄⡄⠀⠀⢀⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢄⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠙⠤⠠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠠⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⠈⡆⠀⠀⠀⠀⠀⠀⠀⣸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⠦⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⣟⡯⣟⣻⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡹⠞⡩⠰⡑⡌⣡⢉⠳⢾⡽⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⡽⢊⠴⢡⡑⠣⠜⡰⢄⡃⢎⠢⡝⣷⣳⡄⠀⠀⠀⢀⣤⢶⡻⡝⢯⠛⠮⠽⢽⣹⣞⣦⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢯⡟⡓⢪⡐⠣⢌⡑⠣⠜⡰⠘⣌⠱⣠⠙⣷⣻⠀⣡⣾⣻⠼⢋⠱⡘⢢⠙⣌⠱⢂⠆⡍⠺⣏⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⡟⣡⠙⡄⢎⡑⡊⠬⣑⠩⡔⢩⢄⠳⣀⢋⢳⣟⣾⢻⡜⠱⣈⠣⢅⡃⢣⠩⢄⢣⡉⠲⢌⡱⢘⢾⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣽⠣⡰⢉⡔⢊⡔⡉⢦⠡⡒⠬⣁⠎⢢⠅⠎⣜⡿⣼⢋⠔⡃⠦⣉⠦⡘⣡⠚⡐⢆⡡⢋⡔⠢⢍⡸⣞⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⠇⡑⢆⠣⡘⢆⠢⢍⠢⠥⢡⠓⠤⡙⣂⠎⡑⣾⣽⡃⣌⠚⡌⡱⢐⢢⠱⢄⢣⢉⠦⡘⡡⢌⠓⠬⡐⢻⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣳⠏⡜⢨⠑⡌⠦⣉⠦⡑⣊⠥⢊⡅⢓⠤⢊⡱⣟⡾⡐⢢⠱⡘⡰⢉⠆⡱⢊⠔⡊⠴⢡⡑⢊⡱⢊⠱⢸⣻⡀⠀⠀⣀⣄⡀⠀⢀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⡘⣬⠂⠓⠸⡔⣂⠖⡡⠒⢬⢡⠘⡬⠌⡥⢸⣯⠷⢨⡑⢢⠱⢡⣞⡾⡕⡡⢎⢡⠓⢢⠜⡡⢆⠩⡌⢳⣽⠁⠀⠈⣟⣲⡵⣼⡳⣽⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠿⢼⠁⠀⠀⠀⢸⡔⡈⠖⣉⠆⢎⠒⡰⢩⠰⣉⠹⠌⡥⢌⡑⣊⠅⢎⢿⣝⢶⡈⢆⠹⡐⣊⠔⣊⠱⣸⡿⡞⠀⠀⠀⠘⢵⣫⡗⠗⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡠⠀⠄⠀⠀⠀⢛⠄⣚⢤⣹⣤⢧⡷⣴⣭⢶⣱⢦⣵⣐⣪⡌⢆⠻⣭⣟⢦⢧⡱⣤⢯⣴⣿⠯⠋⠀⠀⠀⠀⠀⠀⣉⣁⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠁⠦⠊⠀⠀⢀⣸⢿⣹⠯⠓⠛⠚⠉⠉⠚⠋⠚⠛⠊⠛⠳⢟⣯⡶⣦⣉⢛⡚⢳⢙⡚⢻⣯⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡟⣱⠀⠀⠀⠀⣴⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣻⣶⡜⢄⠣⢎⠣⢯⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⡣⠍⠦⢄⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣮⢑⢊⡱⢼⡷⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣾⣻⢄⠹⣜⣿⡽⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣷⠊⡔⣊⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣸⠟⣧⠀⠀⠀⠀⣷⣻⠌⡒⣼⢷⠃⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡆⠀⠀⠀⢸⢾⣁⠎⣡⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣳⢎⡽⣟⡼⠀⠀⠀⠀⢳⢯⣗⠡⣟⣿⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⡤⠀⢢⠀⠀⠀⠀⠰⣿⣿⣿⣿⠀⠀⠀⢸⣻⡸⡘⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠚⠓⠁⠀⠀⠀⠀⠀⢻⣮⣧⡹⣞⣧⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠙⠐⠈⠀⠀⠀⠀⠀⠙⠻⠿⠃⠀⠀⠀⢿⡝⣑⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣝⠿⣼⢻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡾⣝⡾⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠯⢷⣫⡟⣞⠷⣶⢶⣤⣤⣤⣤⢤⣤⢤⣤⡤⣤⢤⡦⣖⣶⣻⣽⣳⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣛⣾⣷⣶⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⣾⠟⠉⡖⠈⢦⠹⣿⣶⣶⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⣾⠟⠁⠀⠀⠣⣴⡰⠃⣿⡇⠀⠀⠈⠉⠉⠙⠛⠻⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⡿⣻⣿⢅⡋⣵⡄⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠶⢦⣴⠖⠶⣦⣶⣿⣟⡛⢉⣀⣸⣷⡟⠀⠿⠿⠟⠁⠀⠀⢰⣏⡦⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡞⣻⣿⣷⠾⠿⠿⠛⠿⢿⠷⢶⣼⣷⡿⠋⠉⠙⣿⣆⣤⣶⣶⠶⠄⠀⠈⠉⠁⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⢹⣾⠟⠉⡌⠉⢲⡀⠀⠀⢸⣁⡀⡏⣿⡄⠀⣠⣄⠘⣿⡏⠁⠀⢀⣀⣀⠀⠀⠀⣀⣰⡀⠙⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣄⠀⠀⠀⠀ ⠀⠸⣿⡀⠀⢍⡧⠽⠃⠀⠀⠈⢉⣭⣶⡿⣷⣄⠿⠦⢀⣿⡇⠀⠰⣋⠀⢄⡇⠀⠀⠹⠿⠇⢀⣿⠏⣷⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣷⣄⠀⠀ ⢀⣾⡿⣿⣄⠀⠀⠀⡀⠀⠀⠀⠟⠋⠀⠀⠙⠿⣷⣶⠿⢻⡿⣷⣦⣭⣌⣈⣀⣀⣀⣤⣤⣶⢿⡯⠾⠋⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀ ⣿⠟⠀⠘⢿⣆⠀⠀⠤⠄⠀⠀⠀⠀⠀⢠⢞⣹⡿⣻⠀⠈⠛⠷⠿⣯⣙⣻⣿⣟⣛⣿⢯⣤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿ ⠋⠀⠀⠀⠈⣿⣆⠀⡀⠀⠀⠀⡀⠀⠀⠸⣰⣿⣵⠟⠀⠀⠀⠀⠀⠀⠉⠉⢀⢉⣉⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⢹⣿⢢⠀⠀⠀⣿⣼⠀⢀⣴⡿⢡⡿⠀⠀⠀⢀⣠⣤⡶⠾⠟⠛⠛⠋⠉⠉⠙⠛⠛⠻⠷⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⡎⠀⠀⠀⠠⢆⣴⣿⢿⡟⠋⢀⣀⣤⡾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢷⣤⡀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⣿⢿⣶⣤⣶⡾⠟⣿⠖⠛⠁⢀⣶⠟⢁⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡉⠻⣦⡀⠀⠀⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣷⣶⣾⣿⣷⠟⠉⠀⠀⣰⡿⠃⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠈⢿⣆⠀⠀⠀⣾⣿⠈⠻⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀ ⣄⣀⣀⣤⣴⣶⡿⠟⠋⠁⠸⣿⣆⠀⠀⢰⣿⠁⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠈⣿⡄⠀⢀⣿⡏⠀⠀⠀⠉⠛⠿⣷⣶⣦⣤⣤⣶ ⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠹⣿⣦⡀⠸⣿⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⢾⡋⠀⣹⡇⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⣿⠇⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣻⣧⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣼⣿⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀my melody ᯓ★ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⠟⠉⠉⠙⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⣤⡾⠟⠋⠉⠉⠛⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠹⣷⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⢶⣾⠟⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⣀⣀⣤⠀⠀⠘⣿⡄⠀⠀⣼⡟⠁⠀⠙⣿⡄⠀⣀⣾⠏⠀⠀⣤⣤⣀⣠⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣯⠁⠀⠀⠀⢹⣗⢀⣼⡟⠀⠀⠀⠀⠘⣿⡄⢸⣿⠀⠀⠀⠀⣹⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⢀⣾⡟⠻⠟⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣄⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀ ⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⢀⣠⠤⢄⡀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⢠⠞⠉⠉⠑⢶⠉⠀⠀⠀⠹⡄⠀⠀⠓⠒⠒⠐⠒⠒⠒⠚⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀ ⠀⠀⠀⢠⡏⠀⠀⢀⡴⠚⠀⠒⢄⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠈⠳⣄⡀⡎⠀⠀⠀⠀⢈⡆⠓⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠳⢄⣀⣀⣠⠞⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀ ⠀⠀⠀⠀⠻⡄⠀⠀⠀⢀⡿⢤⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⣨⠏⠁ ⠀⠀⠀⠀⠀⡟⠓⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠶⠤⢤⡔⠚⠁⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠋⠉⠉⠉⠉⠉⠉⠐⠒⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠀⠀⠀⠀ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⢰⡇⠀⠀⠀ ⠀⠀⠀⠘⡆⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢸⠃⠀⠀⠀ ⠀⠀⠀⠀⢹⡀⠸⡇⢀⣤⣾⠟⠛⠶⠦⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⡇⠀⠀⢸⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠳⡀⢱⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠉⠉⠀⠀⠋⠿⠗⡇⠀⢀⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣀⠀⠀⣀⡤⠤⠤⠤⣄⠀⡠⠔⠒⠢⢄⡀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢹⠖⠁⠀⠀⠀⠀⠈⠹⡀⠀⠀⠀⠀⠘⢦⠶⢶⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠈⢇⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⣻⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠸⣷⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⡄⠀⠀⠀⠀⠀⢀⠜⠉⢆⠀⠀⠀⠀⠀⠀⢰⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠘⠦⣀⣀⣀⠤⠊⠀⠀⠈⠢⢀⡀⠀⢀⡠⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⠶⠶⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⢀⣀⣀⡤⠴⠴⠦⠴⠶⠶⣤⣄⠀⠀ ⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡄ ⠀⠀⢸⣧⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇ ⠀⠀⣾⠘⠀⢀⣀⠹⢦⣄⡀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠞⠋⠀ ⠀⣀⠿⠦⡞⠉⠉⢹⡄⠉⠛⠛⠛⠛⠋⠀⠛⠛⠶⠶⢶⣶⠶⠖⠛⠛⠋⠁⠀⠀⠀⠀ ⠀⣇⠀⢠⠖⢲⡄⠺⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⡇⠈⠓⣊⡀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠷⠤⠶⠋⠉⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀ ⢠⡟⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠋⠉⠉⠉⠉⠉⠉⣙⡳⣦⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⢸⡇⠇⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠈⢻⡀⣸⠇⠀⠀⠀⠀⠀⠀ ⠘⣧⠀⠀⢀⡾⠡⣿⣿⡀⠀⠀⠀⢠⠤⢄⠀⠀⠀⠉⠋⠀⣸⣷⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣆⠀⢸⡃⠀⠙⠛⠀⠀⠀⢀⣌⣛⡡⠀⠀⠀⢀⣠⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠷⣮⣷⣄⣀⡤⣤⡤⣞⡦⣄⣤⣤⡤⠶⢾⡟⠉⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣆⣛⣷⢿⣭⣿⠃⠀⠈⢻⣴⠟⣸⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣘⣷⣦⣽⣘⣻⣸⠩⣽⡆⠀⠀⢸⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡟⠁⠀⣨⠿⣄⣀⣠⣄⣤⠏⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢧⠀⠀⡟⠀⠈⠉⢹⢱⡱⠄⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠙⢻⡀⠀⠀⠀⠀⠀⠰⡆⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠰⣧⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣄⣀⣀⣼⣤⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠋⠉⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠳⣤⡀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠈⢷⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀ ⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀ ⠀⠀⠀⠸⡇⠀⠀⠀⠀⣀⣤⠤⣤⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⢿⡶⠛⠳⢾⡃⠀⠀⠀⠙⣇⣸⣇⣤⡤⠤⠤⠤⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⢀⣠⠽⢤⡄⠀⢤⣿⣋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢘⣦⡄⠸⢧⣤⡴⠋⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡟⠁⠀⠀⢠⡷⣤⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠙⠷⠤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠛⠉⠉⠉⠉⠉⠙⠛⠛⠲⠤⣄⡀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⣀⣴⠞⠉⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⡛⢦⣄⠀⠀⠈⣷⠀⠀⠀⠀ ⠀⢠⣿⠀⠀⠀⠀⢀⡾⠋⠀⢠⣾⡏⠁⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠈⢳⡆⠙⢧⠀⠀⢿⡄⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⢠⡟⠀⠀⠀⢾⡟⣷⣦⣴⣿⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣦⣴⣿⡇⠀⠈⣇⠀⢸⡇⠀⠀⠀ ⠀⢀⣿⣦⣀⠀⡿⠁⠀⠀⠀⠸⣿⣿⣷⡿⠃⠀⣰⣀⣀⣙⣃⣀⣀⠈⠻⢷⣿⡿⠁⠀⠀⣿⡄⣼⠃⠀⠀⠀ ⣼⠋⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣽⣏⢛⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣿⠟⠛⠓⢦⡀⠀ ⡇⠀⠀⠀⠀⠀⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢷⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⠻⢯⣿⡿⠟⠃⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢸⠀ ⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀ ⠀⠀⠈⠷⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣶⢦⣤⣀⣀⠀⢀⣀⣠⣤⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀ ⠀⠀⠀⠀⠘⠶⣀⠀⠀⠀⠀⠀⠀⠘⢧⠻⠶⣿⡿⠃⠀⠈⢿⡽⠿⠋⣽⠇⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠘⣇⣴⠟⠁⠀⠀⠀⠀⠙⢦⣴⡏⠀⠀⠀⢀⣴⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣇⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣉⣩⣍⡙⠻⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣶⣿⣿⣿⣿⣿⡆⢹⣿⡇⠁⡀⠤⡤⢉⡿⠟⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠃⣰⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⢠⣴⣇⣃⠀⣼⡗⠠⠀⠁⠐⠀ ⣿⣿⣿⣿⣿⣿⡿⠿⣿⠏⠛⠻⡅⠀⠀⠘⣿⣿⡏⣰⣿⣿⣿⣿⣿⠟⠛⣉⣀⣉⡙⠻⢿⣿⣧⣴⣿⣧⣀⣄⠂⠀⢀ ⣿⡟⢉⢙⡥⠶⠖⠸⣿⡆⠸⠠⠄⠆⠰⠀⣿⣿⠁⣿⣿⣿⣿⠟⢠⣶⣿⣿⣿⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣷⣾ ⣿⣷⠰⠈⣇⣀⣠⡄⢻⣿⣴⣤⣷⣶⣾⣿⣿⠿⠀⢻⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣇⣸⣿⣿⣿⣶⣾⣿⣿⣿⣿⡿⠛⣉⣤⣶⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⠋⣼⣿⡟⢰⣿⡟⣩⡙⠟⣛⠻⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣉⣉⣉⣤⣾⣿⣏⠁⢾⣿⡇⢿⣷⣜⡟⢁⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠻⠁⣼⣿⣿⣿⠿⠛⣋⣉⣭⣍⣙⣛⠻⠿⣿⣿⣿⣿⣿⣿⣷⣄⠻⣿⣦⣭⣉⣥⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣀⣶⡌⣩⣉⠡⠞⠉⠙⣿⣿⣿⣿⣿⣿⣷⣦⣍⠻⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠟⣡⣆⠹⠿⠟⣡⣿⣧⠸⠀⠀⣸⣿⣿⠿⣿⣿⣿⣿⠟⠛⢳⡌⢿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠇⣼⠋⣭⢹⣿⣿⣿⣿⢿⣇⠹⢚⢛⠻⣧⣄⣼⣿⢿⣟⠀⠀⢸⣷⡘⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠰⣿⣦⣥⣾⠿⣿⣿⡁⠶⢘⣷⣦⠘⢄⢶⣦⣴⠄⡞⡻⣷⣶⣿⣿⣇⢻⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡄⢻⣿⣿⡇⠶⢈⣿⣿⣶⣿⣿⣿⣷⡄⣎⣛⣫⣆⢳⡶⡛⢿⣿⣿⣿⡆⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣇⠸⠿⠟⡛⠿⠿⢋⣙⠻⠟⣉⠙⣛⠃⣈⣛⠛⠿⠿⠦⣴⣿⣿⠿⢟⣸⣿⣿⠿⢁⣿⡏⣠⡙⠟⣛⠛ ⣿⣿⣿⣿⠟⠻⣷⠰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣶⣾⣄⡛⠒⠂⣠⣤⣤⣬⣭⣭⣭⣤⣴⣿⣿⣧⡘⣧⣾⠟⢀ ⡟⠉⣭⣁⣾⠇⣸⣆⠹⠿⠿⠿⠿⠿⠿⠿⠟⢃⣴⣾⣶⣶⣿⣿⣿⣷⠨⡍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿ ⣿⣄⣙⣋⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣶⡈⠻⣿⠏⡉⢽⣿⣿⡟⢐⣃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣩⣤⣾⣄⡙⠛⣋⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠲⡌⢥⢊⣵⣿⡿⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣯⣢⡑⢎⠰⣁⠎⡰⢁⠎⡰⢁⠎⡰⢈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡓⡜⣢⢽⣾⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣾⣌⡓⢤⠚⡄⢣⠘⡄⢣⠘⡄⠣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡴⢣⣾⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⡱⢌⢣⡘⢄⠣⡘⢄⠣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣣⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣘⢢⠜⡠⢃⠜⡠⢃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⢣⠱⢌⠢⡑⠌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠻⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣮⢘⠆⡱⢈⠜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣦⠀⠀⠀⠉⠻⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠹⣿⣇⢎⡱⢈⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣄⣀⣀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⡶⠾⠿⠋⠁⠀⠀⠀⠀⠀⢿⣿⠢⣅⠋⡌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⡀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡓⠬⡑⢌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢦⣀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡃⠧⡑⢌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠛⠿⣿⣿⣶⣤⣶⣶⣿⣶⣶⣶⣦⣤⣄⡀⠉⠙⠓⠚⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡉⢖⡉⢆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⡭⢏⡽⣙⠻⠿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠣⡜⢢⠜⢢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⢦⢡⠋⢖⡡⢎⡛⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢣⠱⡌⢣⢎⣱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠠⢇⠚⢤⠘⢢⡉⠖⡬⢛⠿⣿⣿⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠻⣤⢣⣳⣼⣷⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡓⢬⡉⢆⡉⠆⠬⡑⠦⣉⠶⢨⢍⡛⠻⠿⠿⡿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣿⠿⠟⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣍⠲⡌⢢⠘⡌⢢⠑⡒⠤⢊⢅⠢⣉⠱⣉⢎⠱⢒⠬⠥⣋⠭⣍⢫⡝⣻⣿⣿⣿⡛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠈⠙⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⢲⢡⠣⡘⢄⠣⡘⢄⠣⢌⠢⡑⠤⢃⠔⡨⢊⡒⢌⡒⣡⠒⣌⠲⣜⣵⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠈⠛⠿⣿⣶⣤⣄⣀⡀⠀⠀⢿⣿⣧⡎⡱⡡⢎⠔⣡⠊⡔⡊⡔⢡⠎⡐⢎⡑⢆⡩⢒⠼⢤⣻⣼⣿⣿⣿⣿⠿⣟⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣿⠿⣿⣿⣿⣿⣿⣥⣓⣎⠚⡤⢓⡜⠴⣘⠆⡎⠵⢪⣜⣦⣵⣿⣾⣿⠿⠛⠉⠙⢿⣿⣝⣮⣽⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⢀⣼⣿⠿⠟⠛⠉⠉⠉⠛⠻⢿⣿⣦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠞⠁⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⢀⠤⠠⢄ ⠀⡘⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠈ ⠀⠇⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠎⠀⠀⠀⠀⢸ ⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⡌⠀⠀⠀⠀⢀⠃ ⠀⠈⡤⠤⡖⠐⢆⣇⡀⠀⣰⠀⠀⠀⠀⢀⠆⠀ ⠀⠀⣣⠰⢭⠂⢘⠆⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀ ⠀⡰⠣⠄⠊⠉⠁⣀⡀⠀⢀⣀⡀⠀⠀⠱⠀⠀ ⠀⡇⠀⢀⠤⢊⡥⠄⠀⠀⠀⠀⡤⢕⢤⠀⡇⠀ ⠀⣅⠀⠎⠀⢻⣷⡞⢀⠀⠄⡘⢷⡾⠀⢃⡸⠀ ⡏⠀⠙⢆⠀⠀⠀⠀⢿⣿⣽⡇⠀⠀⢀⠎⠉⢠ ⠣⡀⠀⠀⠁⠢⡀⠀⠀⠉⠉⠀⣠⠔⠁⠀⠀⡸ ⠀⠈⠢⡀⠀⠀⢩⢛⡟⠀⢺⡛⡏⠀⢀⠄⠈⠀ ⠀⠀⠀⠈⢢⠀⠀⠉⠀⠀⠀⠈⢰⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀
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𝓻𝓮𝓼𝓹𝓮𝓬𝓽𝓯𝓾𝓵𝓵𝔂 𝓼𝓽𝓯𝓾 <3 ⠀⠀⣀⣤⠶⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⣴⣤⣄⡀⠀⠀⠀⠀ ⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡄⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀ ⠀⠀⠈⠻⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀ ⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠶⠿⣿⣦⠗⠛⠒⣦⣀⠀⠀⠀⠀⠀⠐⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡇⠀⢠⡇⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠘⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣇⠄⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠐⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠹⣤⡀⢰⠞⠉⢳⡄⠠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠛⢶⣤⣀⣀⣀⣤⡴⠟⠃⠀⠀⠀⠀⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠠⡏⠀⠈⠓⡶⠊⠀⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠰⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣧⣀⣀⣠⡾⢦⣤⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠀⠈⠉⠁⠀⠀⠀⣀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡴⠒⠒⣞⣁⡠⠽⠭⢄⣈⣳⣊⡉⠲⣄⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀ ⠀⠀⠀⠀⢸⡇⠀⡴⠋⢙⡵⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠳⢤⣀⣳⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠐⢺⡇ ⠀⠀⠀⠀⢸⡇⡮⢇⡾⠁⢠⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⢹⣄⡀⠀⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⠸⣿⡁⣼⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠈⠳⣄⢹⠦⠀⠀⠀⠀⠀⠀⣟ ⠀⠀⠀⠀⠀⠻⡟⢿⠀⠀⠈⠛⠉⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠙⣎⠳⡄⠀⠀⠀⢸⢰⡏ ⠀⠀⠀⠀⠀⠀⠱⣜⣆⡤⠦⠤⣄⠀⠀⠀⠀⠛⠒⠋⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⢸⣤⠇⠂⠀⢠⢄⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠐⣾⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⠃⡃⠁⠠⣠⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⣼⣦⣤⣠⠦⢄⠙⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡞⣡⣤⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠸⣿⠉⠀⣹⣀⣙⣿⠏⠁⡽⠶⠤⣤⣤⣤⣤⣤⣴⡾⠅⠚⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠈⠛⣿⠿⣌⡝⠝⡍⣘⣧⣀⣀⣀⣀⣤⣴⣶⣾⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣳⡶⢻⠷⣮⣤⣤⣽⣥⣬⣭⣿⣿⢿⡖⠋⠉⠉⢳⡝⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⢺⣥⣧⣽⢂⡄⠀⠓⠀⠈⢻⡄⠀⠀⠀⠀⣿⣭⣧⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⠴⢺⠥⠚⠁⠀⠘⠦⣽⡒⢤⣄⣀⣼⢳⣤⡀⠀⠼⠃⣠⣷⡗⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠯⠜⠉⡏⠀⠀⠀⠀⠀⡄⣧⠉⠙⠲⣾⣯⣯⣏⣳⣶⣴⣾⣻⣉⣽⣵⡦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣿⢄⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⡶⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠟⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡀⠙⠒⠢⢴⣉⡦⠔⠚⠋⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⠽⣉⣙⣟⠛⣛⠻⢿⠞⠿⡟⠿⣻⠛⣧⠀⠀⠀⠀⠁⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣉⣉⣻⣿⣃⠙⢍⣫⣁⠉⠉⠉⣉⣩⣿⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣉⣉⣿⡀⠉⠛⠛⠧⠜⠛⠛⠛⠉⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠾⠶⠶⠶⠶⠞⠳⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠟⠛⠛⠶⣦⣄⣠⣴⠾⠛⠛⠛⠳⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⡟⠁⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠈⠻⣧⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠉⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣄⠀⠀⠀ ⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀ ⠀⣠⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀ ⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⢿⡄⠀⢀⣴⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⣠⡿⠀ ⠈⠻⣶⡟⠁⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⣼⠷⣤⣤⣴⠾⠛⠷⠶⠶⠾⠛⢷⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠉⢻⣿⠁⠀ ⠀⣸⡟⠀⠀⠀⠀⣾⠃⠀⠀⢰⣶⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠙⣷⣄⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠹⣧⠀ ⠀⣿⠀⠀⠀⢀⣼⠏⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡄⠀⠀⠘⣷⡄⠀⠀⠀⢹⡆ ⠀⢿⣄⣀⣠⡾⠋⠀⣤⣴⣿⠃⠀⢠⡞⠉⠳⡄⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣴⠋⠙⢦⠀⠀⠈⢻⣶⠦⠀⠈⢿⣦⣀⣀⣾⠃ ⠀⠀⠉⠛⠹⣧⡀⠀⠉⡀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⢀⢀⣠⡿⠉⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠈⠛⠿⠿⢷⣄⣙⣷⣤⣀⠀⠀⠀⠀⠀⠀⠲⠤⠤⠶⠂⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⣀⣼⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠙⠻⠶⠶⣤⣤⣤⣤⣀⣀⣀⣤⣤⣤⣤⠶⠶⠟⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀ ⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀ ⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢸⠀⠀⢀⡤⠖⠒⠒⠢⢄⡀⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠙⢧⡀⠀⠀⢸⠀⡰⢃⡴⠛⠲⡤⠖⢦⣹⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡆⠀⣠⠴⠒⠒⢾⡃⠀⠀⠀⠀⣻⠚⠙⠉⠀⡇⠸⡄⠀⠀⠀⠀⢠⢿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢱⣰⠃⠀⠀⠀⢀⠔⠒⠢⡀⠠⢧⡀⠀⠀⠀⢳⡀⠙⢦⡀⢀⣴⠏⣸⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣧⡀⢀⠀⡏⠀⠀⠀⣹⠀⠀⢹⡄⠀⠀⠀⠙⠢⢤⣈⣩⠤⠞⠁⠙⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⡿⢻⠟⠀⠘⠢⠤⠔⠁⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⣄⠀⠀ ⠀⠀⠀⠀⢠⠞⠁⢸⡀⠀⠀⠀⠀⣸⠖⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀ ⠀⠀⠀⢠⠏⠀⠀⠀⠳⢤⣀⣀⠴⠋⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⢹⡄ ⠀⠀⢀⠏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡠⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⣧ ⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢻ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⣇⢸ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠾⠛⠋⠛⠀⢹⡟ ⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢠⡾⠋⠁⠀⠈⠉⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⣽⠃ ⠀⠀⠈⢷⠄⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠴⠊⠀⠀⠀⠀⠀⣰⡋⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠞⠁⠉⠓⠒⠦⠬⢷⣦⣄⣀⣠⠤⢤⣤⣄⣀⣀⡤⠴⠖⠛⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⡷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⠋⠀⠀⠉⠓⠒⠒⠒⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀ ⣀⣰⡹⠃⢀⣀⣀⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⡀⠀⠀⣀⣀⣸⡇⠀⠀⠀⠀
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⠀⠀⠐⠀⠄⠀⣀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⣀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠰⣀⣔⠖⢡⣖⢿⡖⢤ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠱⢤⣀⣀⣘⣧⡀⠀⠀⠀⠀⣷⢧⠀⠈⠛⠿⣿⡘ ⠑⠤⣀⠀⠀⠀⠀⡎⠀⡈⠧⢄⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣦⡄⠄⠚⠃⠀ ⠀⠀⠀⠈⠹⣲⠒⡞⠀⠣⠤⠜⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡇⠁⠀⠀⠀⡠ ⠀⠀⠀⠀⠀⠀⡴⠉⠒⠒⠉⠁⢉⡀⠤⠄⠀⠂⠀⠤⢀⠀⠀⠀⠘⡒⣶⡾⠟⢃ ⠀⠀⠀⠀⣀⣴⠁⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢰⠐⠂⠈⠀ ⠀⠀⠀⢈⡷⠛⠀⠀⠀⡜⢠⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣶⣌⠄⠀⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⠀⠀⠸⠀⢺⣿⣿⠟⠀⠀⠀⠀⠐⠀⠀⢻⣿⣿⢸⢐⠁⠀⠀⠀ ⠀⠀⠀⠀⡀⢀⡡⡀⢲⠀⠀⠈⠁⠀⠀⠀⣰⠒⢲⡆⠀⠀⠉⠁⠘⡜⠀⠀⠀⠀ ⠀⠀⢀⠂⠀⠀⠈⠘⠦⣢⡀⠀⠀⠀⠀⠀⢯⣀⡼⠁⠀⠀⢀⡴⠛⠠⠀⠀⠀⠀ ⠀⠀⠀⢆⠀⠀⠀⠀⠀⠈⢏⠒⠠⠄⣀⣀⣀⣀⣀⠀⠤⡔⠉⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⢀⣁⠢⠄⡀⣀⣀⡀⠡⣀⠀⡠⠊⠀⠀⢆⠀⡰⠁⠀⢀⡠⠚⠁⠀⠀⠀ ⠀⠀⠀⠠⠐⢄⡀⠡⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡐⢲⠌⣀⣀⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⠉⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠫⣉⣀⣉⠁⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠁⠁⠀⠈⠉⠉⠛⠳⢦⣤⡀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⣸⠀⠀⠀⠀ ⠀⣾⡋⢹⣷⣤⣤⣀⣀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣼⡀⠈⠉⡿⠓⡀⠁⠀ ⠀⠈⠛⢻⣿⣻⡟⠛⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣿⡷⠶⠛⠛⠋⠉⠉⠉⠉⠉⠙⠛⠳⢶⣄⡀⠁⠰⠦ ⠀⠀⠀⢸⣿⣿⠇⠠⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣄⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠉⠻⣦⡀⠀ ⠀⠀⠀⢸⣿⣿⣇⢈⣘⡀⡈⠿⣿⠿⣷⣦⣄⣀⠀⠀⠀⢰⡟⣉⡽⣿⡅⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠊⠉⠉⠀⠀⠀⣉⣭⠐⠢⡈⠻⣆ ⠀⠀⠀⠀⣿⣿⣿⣶⣾⣤⣴⣴⣴⣠⣴⣿⣿⣿⠛⠛⣿⡿⢿⣯⣥⣼⠇⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠈⠢⣹ ⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠸⠟⣿⣟⠉⠉⠉⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠶⠶⠶⢶⣏⣠⠇⢱ ⡄⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⣿⣿⢿⣿⢹⡿⣿⣷⣤⣠⣿⠉⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣿⣄⠀⠀⠀⠀⠀⢀⣴⠟⠉⠘⠿⠀⢹⣬⣿⣿⠛⠛⢿⠇⠀⠀⣰⠃⢀⣀⣤⣤⣴⡦⠀⠀⠀⢈⣡⡶⠶⢶⣦⣀⣀⡀⠀⠀⠀⠀⠀⢀ ⠿⣿⣦⠀⠀⢀⣴⣿⡱⢾⠗⠀⠀⠀⢦⣿⣿⠇⠀⠀⢸⡆⠀⠀⡇⠚⠛⠋⢉⣽⠟⠁⠀⠀⢰⣿⣭⣄⣠⡿⠉⠀⠈⠙⢦⡀⠀⠀⠀⣸ ⠀⣽⣿⡆⣰⣿⠻⠟⠛⢶⣤⣶⣦⣿⣿⣿⡟⠀⠀⠀⣸⣇⠀⠘⡇⢀⡴⢶⡿⠋⠀⠀⠀⢀⡾⠋⠀⠈⢻⣇⠀⠀⠀⠀⠈⢿⡄⠀⣴⠏ ⠀⣿⢸⣿⣿⢹⡟⠒⣶⣾⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠿⢻⣆⠀⢣⠘⠦⠞⠁⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⢿⠿⣧⡀ ⡀⣿⣾⣿⣿⣿⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠇⠀⠀⠙⢷⣄⠳⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢸⣧⡈⠻ ⣿⣿⣿⣿⣿⡟⠀⢀⣀⣠⣤⣄⠀⠀⠀⠀⠈⠋⠁⠀⠀⢀⣤⠀⠙⠳⣿⣶⣤⣀⡀⠀⣀⣿⠀⠀⠀⠀⠀⢠⡟⢷⡀⠀⠀⠀⠀⠙⢷⡀ ⣿⣿⣿⣿⣿⡇⠚⠛⠿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣠⡾⠃⣠⣴⠾⠛⠩⠭⢯⠛⠛⠛⣿⠀⠀⠀⠀⠀⢼⣧⠈⠻⠆⠀⠀⠀⠀⠀⣿ ⠉⠁⣿⣿⣿⣇⠀⠀⠀⠈⠻⣿⣿⡿⠀⠀⠘⠓⠚⠛⠉⢠⣾⠋⠁⣀⠤⢒⣋⡙⠆⠀⣀⣿⡀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠸⣿⣿⢿⡄⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⣳⣿⠾⠟⠻⣦⢀⣾⠿⠃⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⢻⣷⣿⣿⣄⠀⠀⡞⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠿⠋⠀⠀⠀⠀⢸⡟⢹⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⣉⣩⣥⣶⣶⣶⣾⣿⣶⢶⣶⣶⠞⠁⠀⠀⠀⠀⠀⢀⡿⢀⡞⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇ ⢀⣤⣤⣄⣀⣀⠉⣙⣿⣿⣿⣿⣋⣿⣟⡈⢻⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣀⣴⡟⠡⠞⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀
⠀⠀⣀⣤⠶⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⣴⣤⣄⡀⠀⠀⠀⠀ ⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡄⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀ ⠀⠀⠈⠻⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀ ⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠶⠿⣿⣦⠗⠛⠒⣦⣀⠀⠀⠀⠀⠀⠐⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡇⠀⢠⡇⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠘⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣇⠄⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠐⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠹⣤⡀⢰⠞⠉⢳⡄⠠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠛⢶⣤⣀⣀⣀⣤⡴⠟⠃⠀⠀⠀⠀⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠠⡏⠀⠈⠓⡶⠊⠀⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠰⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣧⣀⣀⣠⡾⢦⣤⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠀⠈⠉⠁⠀⠀⠀⣀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡴⠒⠒⣞⣁⡠⠽⠭⢄⣈⣳⣊⡉⠲⣄⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀ ⠀⠀⠀⠀⢸⡇⠀⡴⠋⢙⡵⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠳⢤⣀⣳⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠐⢺⡇ ⠀⠀⠀⠀⢸⡇⡮⢇⡾⠁⢠⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⢹⣄⡀⠀⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⠸⣿⡁⣼⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠈⠳⣄⢹⠦⠀⠀⠀⠀⠀⠀⣟ ⠀⠀⠀⠀⠀⠻⡟⢿⠀⠀⠈⠛⠉⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠙⣎⠳⡄⠀⠀⠀⢸⢰⡏ ⠀⠀⠀⠀⠀⠀⠱⣜⣆⡤⠦⠤⣄⠀⠀⠀⠀⠛⠒⠋⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⢸⣤⠇⠂⠀⢠⢄⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠐⣾⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⠃⡃⠁⠠⣠⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⣼⣦⣤⣠⠦⢄⠙⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡞⣡⣤⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠸⣿⠉⠀⣹⣀⣙⣿⠏⠁⡽⠶⠤⣤⣤⣤⣤⣤⣴⡾⠅⠚⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠈⠛⣿⠿⣌⡝⠝⡍⣘⣧⣀⣀⣀⣀⣤⣴⣶⣾⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣳⡶⢻⠷⣮⣤⣤⣽⣥⣬⣭⣿⣿⢿⡖⠋⠉⠉⢳⡝⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⢺⣥⣧⣽⢂⡄⠀⠓⠀⠈⢻⡄⠀⠀⠀⠀⣿⣭⣧⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⠴⢺⠥⠚⠁⠀⠘⠦⣽⡒⢤⣄⣀⣼⢳⣤⡀⠀⠼⠃⣠⣷⡗⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠯⠜⠉⡏⠀⠀⠀⠀⠀⡄⣧⠉⠙⠲⣾⣯⣯⣏⣳⣶⣴⣾⣻⣉⣽⣵⡦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣿⢄⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⡶⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠟⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡀⠙⠒⠢⢴⣉⡦⠔⠚⠋⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⠽⣉⣙⣟⠛⣛⠻⢿⠞⠿⡟⠿⣻⠛⣧⠀⠀⠀⠀⠁⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣉⣉⣻⣿⣃⠙⢍⣫⣁⠉⠉⠉⣉⣩⣿⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣉⣉⣿⡀⠉⠛⠛⠧⠜⠛⠛⠛⠉⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠾⠶⠶⠶⠶⠞⠳⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⣠⣤⣶⡶⠶⠶⣶⣤⣄⡉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢁⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠙⠿⣶⡄⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣠⡿⠋⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠈⢿⣆⠘⠦⠔⠊⣉⣠⣤⡴⠶⠦⣤⣤⣄⣉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠏⢰⡿⠁⠀⠀⢀⡼⢃⠀⠀⠿⣇⠀⠀⠀⠀⠀⢻⣇⣠⣶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠷⣦⡈⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠀⣿⠁⠀⠀⠀⠸⣇⡻⠦⢄⣠⡟⠀⠀⠀⢀⡔⣼⡿⠋⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣆⠘⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢸⣯⠀⠀⠀⠀⠀⠙⠛⠓⠛⠋⠁⠀⠀⣠⢫⣾⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⢠⢧⡿⠽⠁⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢱⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠀⣠⠞⢉⣸⠎⢻⡆⠀⣎⣿⠃⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⠀⠀⠀ ⠀⢀⡠⠤⠀⠀⠀⠀⣿⢘⣬⣭⣷⡞⠡⠶⠋⠁⠀⢸⣇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀ ⡰⢉⣤⣶⡖⠒⠒⣶⣾⣾⡈⡆⡻⣋⢻⣆⣴⣶⠀⠈⢻⡄⠸⣿⡀⠀⠀⠀⠀⠀⢼⡅⣞⠀⠀⠈⡗⠀⠀⣰⡆⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀ ⡇⢸⡇⠷⠖⠛⠉⠩⣟⠡⠇⣾⣷⣁⢾⡏⠉⠀⠀⠀⠈⣿⡄⠻⣧⡀⠀⠀⠀⠀⠠⠿⣷⣗⡶⠾⢃⣴⡾⠋⠀⠀⠀⠀⠀⢈⡿⠀⡄⠀⠀ ⢳⡈⢿⣄⠀⠀⣠⢴⣟⢿⣷⡿⣵⣿⣼⣧⣤⣤⣤⣠⣤⣾⠇⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⣀⣤⡾⢟⠋⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠱⡀⠀ ⠀⠱⡀⢻⣆⠀⠉⠉⠀⠈⣻⣟⡟⠀⠀⠀⢀⣀⣉⡁⣠⡶⠿⠶⣦⣤⡼⠟⠛⠿⣿⣿⠿⠿⣯⣴⣣⣤⣄⡀⠀⠀⠀⠀⠀⠀⠉⣿⡄⢳⠀ ⠀⠀⢣⠈⣿⡀⠀⠀⣠⡾⠋⠈⠀⠀⢠⣴⠟⠋⠙⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠉⠈⠙⢿⣦⠀⠀⠀⠀⠀⢸⣸⣧⠀⡇ ⠀⠀⠈⢆⠘⢿⣴⣾⠋⡄⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⡀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⣶⡀⠀⢨⠀⣿⠀⡇ ⠀⠀⠀⠀⠑⡆⠸⣿⢸⠀⠀⢀⣤⣾⠛⠀⠀⠀⠀⣀⣄⣴⡟⠋⠻⠶⠾⠟⠙⠛⠛⠙⠛⢷⣤⣤⣄⡀⠀⠀⠀⠀⠀⠈⣿⣸⢰⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⢱⠀⣿⡌⠣⠔⣿⠃⠀⠀⠀⢠⣤⣾⣿⣭⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣷⣬⡛⠛⣏⡄⠀⠀⠀⠻⣧⠀⢸⡿⠀⡀ ⠀⠀⠀⢀⡀⠈⡆⠹⣷⡆⠀⣿⡀⠀⠀⣠⡿⢃⡾⠁⢀⣨⣧⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣼⣅⣀⠀⢳⡀⢻⣾⣆⠀⠀⠀⣿⢠⣿⠃⡸⠁ ⠀⢀⣀⢸⡇⠀⠘⢆⠙⢿⣤⡏⠀⠀⠐⣾⣄⢸⣿⣛⣿⣡⡟⠀⠀⠀⠀⢿⣿⠆⠀⠀⠀⢻⣄⣽⣉⣿⠃⣠⡾⠆⠀⠀⠘⣿⡿⠃⡰⠁⠀ ⠀⠈⠉⢱⡌⠛⠀⠈⠳⡀⠻⣷⣀⠀⠀⢼⣿⠃⠈⠙⠛⠉⠀⠀⠀⠀⣀⣀⣦⠀⠀⠀⠀⠀⠉⠙⠋⠁⠀⣿⡎⠀⠀⣀⣼⡏⢀⠞⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣦⠉⢛⣦⣀⡀⢛⣷⣦⣀⠀⠀⢠⠖⢶⣾⠋⢹⣟⢦⣴⣤⣄⠀⠀⠀⣀⣴⢾⣏⣀⣀⣼⡟⠉⢠⠋⠀⠀⠀⠀ ⠀⠀⠀⠈⠁⠀⡠⠒⢉⡉⢀⣴⡟⠈⠉⠙⠛⠉⠈⠻⣿⣻⣿⣦⣤⣿⠢⣾⡿⡇⠀⠀⠙⠿⣟⣿⠟⠃⠈⠛⠋⠉⠁⢻⣦⡈⢉⡉⠒⢄⠀ ⠀⠀⠀⠀⠀⢰⠁⣾⠋⠙⠛⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣫⠿⣯⣿⡿⠻⠓⠶⠃⠀⠀⠀⢀⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⠉⠙⣧⠈⡆ ⠀⠀⠀⠀⠀⠸⡄⠻⢦⡄⠠⣻⡆⠀⠀⠀⠀⠀⣾⠋⠉⣡⡗⠙⠉⠀⢀⡀⠀⠀⠀⠀⠀⣯⠛⢿⣦⡀⠀⠀⠀⠀⠀⢰⡟⠇⢠⣴⠟⢀⠆ ⠀⠀⠀⠀⠀⠀⠈⢦⡘⠛⢧⣪⣿⣄⠀⠀⠀⠀⠙⠻⣿⡏⠁⣤⢾⣟⠋⠛⠛⠻⢶⣄⡀⠹⣧⣤⣪⡇⠀⠀⠀⠀⣠⣿⣅⡼⠛⢃⡴⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⢄⠘⠻⠿⣶⣤⣤⣤⡾⠟⢷⣿⣇⡻⠟⠀⣴⡄⠘⣿⡏⣧⣀⡶⠿⢷⣤⣤⣤⣴⠾⠟⠃⣀⠤⠞⠁⠀⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⠀⠀⠀⠀⠐⢤⣈⡉⠛⠶⠶⢯⣥⡴⠶⠚⠿⠛⢁⠄⠤⡀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⡄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠸⠀⠀⠀⠀⠀⠀⠃⠀⠀ ⠀⢃⠀⠀⠀⠀⢀⡠⢼⠀⠀⠀⢀⢔⣆⣀⣒⣼⠀⠀⠀ ⠀⠘⡄⡠⠒⠲⠇⠀⠀⡑⠒⠃⡆⢇⠀⠀⢨⢳⠀⠀⠀ ⠀⠀⠱⣇⠀⢰⠁⠈⡆⠑⡄⠀⠘⠄⣑⣒⡡⠒⢄⠀⠀ ⠀⠀⢀⠟⡏⠀⠑⠒⡁⠠⠃⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀ ⠀⢠⠃⠀⠑⡤⠠⠞⠀⠀⠀⣀⠠⠤⠤⠤⠄⡀⠀⠀⢣ ⠀⠆⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠑⢆⠸ ⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠄⣦ ⠀⡆⠀⠀⠀⠀⠆⠀⠰⠏⠉⠉⠀⠀⠀⠚⡀⠀⠀⠀⡟ ⠀⠘⢄⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⢀⠜⠀ ⠀⠀⠈⡱⠤⢀⣑⢄⡀⠀⠀⡀⠀⠀⢀⣀⢤⠂⠁⠀⠀ ⠀⠀⡸⠄⡀⠀⠀⠈⣉⡩⠅⠋⠉⠉⠁⠀⠀⢇⠀⠀⠀ ⣠⡞⠀⣀⣀⠉⠉⢀⣀⣀⣀⣀⣀⢀⡀⠀⠀⢀⡆⠀⠀
⠀⠀⠀⠀⠈⠉⠉⠲⢌⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠂⠤⣀⢀⠞⡴⠋⠀⣠⠤⠤⠤⢄⠀⠉⢆⠀⠀⠀⣠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⣄⠀⠄⠀⠀⠀ ⠀⠀⠀⠔⠒⠒⠢⢄⠀⠳⡈⠆⢆⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡉⠺⡀⢠⢊⠴⠚⠉⠓⢤⠱⡄⡨⢃⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⡠⠊⠉⠉⠓⡌⢢⡠⢃⠞⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠈⠢⣉⠡⡎⠀⠀⠀⠀⠀⢧⢈⡴⠋⠀⠀⠀⢀⠄⠂⡀⠀⠄⠀⠠⠠⣉⠑⠢⢄⠀⠀⠀⠀⠀⠀⠁ ⠀⠘⡇⠀⠀⠀⠀⢸⢀⡴⠃⠀⠀⢀⡠⠒⣁⠤⠂⠐⠀⠀⠦⢌⡑⠢⢄⠀⠀⠀⠈⢦⠑⡄⠀⠀⠀⡰⢃⠎⠀⠀⠀⡠⢊⡡⠒⠉⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡑⢤⠀⠀⠀⠀⠀ ⠀⠀⠈⢆⠀⠀⢠⢃⠎⠀⠀⢀⡔⢃⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡑⡄⠀⠀⠀⢣⠘⡄⠀⡰⢡⠏⠀⠀⢠⠎⡰⠋⠀⠀⠀⣀⠤⠤⠤⠠⠤⣀⠀⠀⠀⠙⢄⠑⡄⠀⠀⠀ ⠀⠀⠀⠈⠆⢀⢃⠎⠀⠀⢠⢊⡔⠁⠀⠀⡠⠔⢒⣒⣒⠒⠢⢄⡀⠀⠀⠱⡈⢆⠀⠀⠀⢣⠸⢠⢃⡇⠀⠀⢠⢃⠞⠀⠀⢀⠔⣉⠤⠒⠉⠉⠑⠒⢤⡉⠦⡀⠀⠀⢣⠘⠀⠀⠀ ⠀⠀⠀⠀⠘⠊⠼⢄⣀⣠⢃⠎⠀⠀⡠⢊⡴⠊⠉⠀⠀⠈⠑⠦⠘⢆⠀⠀⣹⠀⢓⣂⡭⠥⠴⠤⠤⠈⣩⣵⣧⣮⢤⣄⣠⣃⠜⠁⢀⡠⠤⠤⠤⢄⠀⠙⢆⠱⡀⠔⢋⡤⠗⠀⠁ ⠠⠀⠂⠈⠀⠉⠀⠂⠔⢣⡘⠢⢄⡰⢡⠋⠀⣠⣶⣦⢶⡶⣻⠟⠛⠿⣶⢾⣤⣤⡭⣤⣤⡤⣤⢤⡴⣿⣛⡞⣶⡹⣞⡼⣫⢟⡶⣦⣥⡔⠊⠁⠒⢄⠱⡀⡠⢃⡴⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣜⣠⣇⣤⣟⢿⣣⡼⠟⠻⣇⣀⠀⠀⣸⡟⣼⢣⡟⣧⡜⣧⢻⡜⣧⢇⡿⣸⣇⢿⡸⢧⡻⣜⢧⣇⣟⡻⣧⣄⡀⠘⡇⠘⣣⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠄⣀⠀⣀⣤⢶⠾⣝⡞⣶⡹⢮⡟⠀⠀⠞⠁⢠⠃⠈⢙⡿⣜⢧⣛⢶⡹⣎⢷⡻⣜⢯⡞⣵⣿⣯⣽⢳⡝⣮⢳⡞⣼⢳⣭⢳⢯⣳⢷⣞⡁⠀⠀⢀⠤⠒⡠⠐⠀ ⠠⠐⠀⠂⠈⢀⣴⣾⢻⡻⣜⢯⡻⣼⡹⢶⣹⢳⣷⠔⠀⠓⠊⡁⢀⣠⢾⡹⣎⠿⣜⢧⡻⣝⢮⡳⣝⡮⣝⢮⣻⢿⣿⣧⡟⣵⢫⢾⡱⣏⣆⡟⣮⢳⢯⣝⡻⣶⣴⣋⠴⠋⠀⠀⠀ ⠀⠀⠀⢠⣞⢿⡹⣎⠷⣝⣮⢳⡝⣶⡹⢧⣏⢷⣹⣦⣀⣀⣼⢻⡽⣹⢎⣷⠭⠿⠚⠓⠛⠚⠳⠿⢼⣳⡽⣎⢷⣫⢟⡿⣿⣷⣫⢷⡹⣞⡼⣹⢎⡟⡾⣜⡳⢧⢯⡽⣟⢶⣄⠀⠀ ⠀⠀⣰⣯⣛⢮⡳⣭⢟⡾⣜⢧⣛⢶⣫⢗⣾⣽⣿⣿⡻⣝⢮⣳⡽⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣽⢎⡷⣹⢻⢿⣾⣵⣫⢞⡵⣛⢾⡱⣛⡽⣫⢞⡵⣫⢞⡿⠀⠀ ⠀⠁⠀⠳⣯⡳⣝⢮⡻⣼⡹⢮⡝⣮⣳⣿⠞⣿⡿⢧⣛⣮⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣱⢯⡞⣽⡈⠙⠾⢽⣝⣮⢳⣝⡳⣝⣮⣳⡽⡟⠀⠀⠀ ⠀⠀⢠⡠⠼⢝⡻⢮⠷⢧⡿⢷⡻⠟⠁⠀⠀⣿⣝⣳⡻⠃⠀⠛⠳⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⠟⠛⠃⠘⣯⡞⣽⣹⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠓⢤⠁⠀⡀⠄ ⠀⣤⠋⠀⠀⠀⠙⡌⡒⢋⡴⠋⠀⠀⠀⢀⣸⡗⣮⣳⠁⠀⠀⣴⠶⠛⠋⠁⠀⠀⠀⣠⣤⡀⠀⠀⠀⠉⠛⠻⢶⣤⠀⠀⠘⣟⡲⢧⣗⢉⠐⢋⡙⡒⠒⢤⣀⠀⠀⠀⠀⠙⢄⠡⠀ ⠐⠘⠄⠀⠀⠀⢀⠟⡰⠋⠀⠀⢀⠴⢊⡥⠖⣟⡶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢻⣝⣯⠇⠀⠀⠀⠀⠉⠑⠢⢄⡓⢤⠀⠀⠀⠀⠐⠠ ⠀⠈⠄⠀⠀⢀⡎⡼⠁⠀⠀⡔⢫⠔⠉⠀⠀⢻⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡹⡾⠀⠀⠀⠠⢄⣀⠀⠀⠀⠙⢄⠓⣄⠀⠀⠀⠐ ⠀⠀⠈⡄⢠⠞⢼⣀⡀⢀⠞⡴⠃⠀⠀⡠⠖⣙⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷⡽⣓⠥⠂⠓⠈⠦⢌⡑⠦⡀⠀⠀⢫⡘⡀⡀⢄⡐ ⠐⠄⠃⠈⠀⠚⠐⠢⠍⣱⡞⠀⠀⣠⠎⡴⠋⠁⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣠⣿⣿⠛⠁⠀⣠⣤⣄⣀⠀⠙⢦⠙⣄⠔⣋⡴⠃⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⡡⢎⠀⡠⢚⣩⠥⣌⡛⢷⢤⡀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣀⡤⠞⠫⣅⠣⣀⠴⢚⠴⠒⠂⢦⡑⣄⡠⠇⡼⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⡀⢀⠠⣄⣀⠀⠀⠀⠀⠑⢎⡙⣴⠋⠀⠀⠀⠙⣄⠒⣩⠟⠒⠢⣤⢤⣭⣭⠽⣭⣭⣤⢤⡴⠒⢿⡅⠀⠀⠀⠈⠲⡰⢸⠁⠀⠀⠀⠀⢳⡘⣡⠞⠀⠀⠀⠀⡀⠀⡄⡐ ⠂⠉⠀⠁⠈⠈⠀⠲⠬⡙⠢⡀⠀⠀⠀⠱⡌⢆⠀⠀⠀⡰⢉⡼⠁⠀⠀⣄⠈⣓⣏⣿⣷⡿⢛⡏⠈⠀⠀⠀⠙⣷⣄⠀⠀⠀⠙⢆⠳⡀⠀⠀⢠⠎⡴⠃⠀⠀⢀⠴⣉⠴⠁⠀⠀ ⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠳⡌⢦⡀⠀⠀⠹⡌⢆⠀⣰⠑⣸⠁⠀⠀⠀⢈⡟⠉⠀⠈⢻⡴⠚⠑⠲⣶⠛⠀⠀⠘⡇⠳⡀⠀⠀⠈⢖⢱⡀⢠⠇⡾⠁⠀⠀⡰⢩⠔⠁⠀⠀⠀⠀ ⠀⢠⠐⡄⠊⢩⡍⠒⣤⠀⠀⠈⣦⢱⠀⠀⠀⢹⠘⣶⠃⠃⡇⠀⠀⠀⠀⣼⠀⠀⠀⠀⢠⠁⠀⠀⠀⢸⠀⠀⠀⠀⣷⢣⢹⡄⠀⠀⢨⡆⠓⡎⣼⣥⠀⠀⡜⢡⠋⠀⠀⠀⠀⠐⠂ ⠈⠀⠀⠀⠀⠀⠉⠲⣌⠦⡀⠀⢘⡆⠳⡀⣌⣡⠎⠐⠌⢸⡇⠀⠀⠀⠀⡽⠀⠀⠀⢀⠾⡀⠀⠀⠀⢸⠃⠀⠀⠀⡏⠘⢆⠡⡐⠄⠢⠘⠠⠑⠀⠆⠩⢙⠡⠻⣄⠀⢠⠚⠈⠁⠀ ⣦⣴⣶⣶⣶⣶⣶⣤⣾⣶⣿⣴⣷⣦⣥⣤⣤⣤⣤⣤⣄⡴⠿⠀⠀⠀⠀⢾⣳⣎⡉⠧⣀⣩⠖⣦⡤⡞⠂⠀⠀⠰⠿⣾⣶⣷⣶⣶⣶⣶⣶⣶⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠸⣿⣯⡝⡿⣿⣴⡻⢿⡽⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⠀⠀⠀⠀⢀⡞⡽⠈⠉⠉⠉⠉⠉⠉⢷⡆⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢠⠟⠂⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡒⠉⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠤⣶⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣝⣣⣿⣢⣓⣖⣲⣒⣖⣲⣖⣲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⢀⡤⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠋⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⢤⡀⠀ ⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢻⠀ ⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀ ⠀⠀⠸⡆⠀⠀⠀⢀⣀⣀⡀⠀⣧⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀ ⠀⠀⠀⢻⠖⠒⢶⡉⠀⠀⠹⣄⣯⠤⠤⠤⠤⠼⡇⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀ ⠀⠀⠀⢺⡀⠀⡶⠛⣲⠀⠚⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀ ⠀⠀⠀⣸⡟⠀⠉⢹⣅⣀⣀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⠀⠀⠀⠀⠀ ⠀⠀⣰⠛⠦⠤⠖⠋⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀ ⠀⢀⡇⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠀⠀⠀⠀⠉⠉⠙⠲⢤⡀⠀⠀⢸⡄⠀⠀⠀ ⠀⣸⡇⠀⠀⠀⣠⠞⠁⣰⡞⠒⢦⠀⠀⠀⠀⠀⠀⢀⡴⠒⢦⡝⢦⡀⠀⣇⠀⠀⠀ ⠀⢹⠁⠀⠀⡼⠁⠀⢸⡟⣷⣤⣾⠀⠀⠀⢀⡀⠀⢸⣷⣤⣾⡇⠀⢳⠀⢸⠀⠀⠀ ⢀⡼⠷⢤⣼⠃⠀⠀⠀⠻⠿⠟⠃⢀⣶⣤⣬⣥⣤⡀⠙⠻⠛⠁⠀⢸⣆⣟⡀⠀⠀ ⡏⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣾⣿⡇⠀⠀⠀⠀⢀⡞⠁⠀⠈⢧⠀ ⣧⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠟⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸⠀ ⠈⠲⣄⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⣠⠞⠀ ⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⢻⡻⣯⣿⡶⠂⠐⣶⣾⡿⣻⠃⠀⠀⠀⠀⡠⠊⠀⠀⠀ ⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⢳⣠⠟⠁⠀⠀⠘⠦⣠⡏⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠐⡦⠖⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠋⠑⠒⠠⠤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢃⢀⣴⣋⢀⣯⠷⡍⣪⠉⠉⠒⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡸⠇⠰⠵⢀⡹⠽⠕⠛⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⠠⠮⠂⠉⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀ ⢰⠉⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢰ ⠀⢁⡶⢲⠈⠁⠀⡤⢚⠒⠒⠢⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠒⠉⠀ ⠐⠉⠀⢸⡄⠀⡹⣴⣿⡇⠀⠀⠀⠀⠉⠒⢲⠀⠀⠀⢠⠀⢃⠇⠐⠠⠄⠀ ⠀⠀⠀⠀⢣⣀⠇⠈⠛⠁⠀⠆⠀⠀⣼⣿⡆⢱⠢⠀⢸⠀⠈⢂⠀⠈⡄⠀ ⠀⠀⠀⢀⢴⠓⠳⢄⡀⠀⠐⠄⠀⠀⠙⠿⠃⠜⠆⠀⠈⢆⠀⢀⡆⠀⡇⢈ ⠀⠀⠀⠀⠢⠀⢠⠃⠈⠒⠤⠀⣀⠀⠀⢀⡜⠀⠀⡠⠂⠁⠉⠉⠁⠀⠈⠂ ⠀⠀⠀⠀⠀⠉⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠴⠥⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠤⣑⣦⡄⢦⣀⠀⠀⠀⡀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡿⠭⠰⡒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠁⢀⣀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⣠⢖⡫⡝⢭⢛⢦⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⡴⣋⠳⡬⣑⠎⢧⡚⡼⡆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠂⠀⢀⣀⣀⠀⠀⠐⠢⢀⠀⡰⠃⠀⣴⢋⡖⣩⢣⠕⣎⡹⢆⢳⢹⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠂⠀⣴⠺⣍⠭⢭⣙⠳⢦⣄⠀⠉⠀⣠⠻⡌⣇⠮⣑⢎⡹⢤⢓⢎⣣⡟⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡖⠀⢰⢫⡱⢊⢮⡑⣎⡹⢲⡘⠷⣄⣴⠫⡕⠳⣌⠞⣡⢎⠵⣊⢭⣲⠏⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⢸⢇⣣⢻⣤⠫⣔⠣⣇⠭⡓⡽⣎⠧⣙⠳⣌⠞⣡⢎⡣⣍⡶⠃⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⠀⠸⣎⠖⣩⢛⣷⣌⠳⣌⠳⣉⢶⡟⣌⢇⡳⢜⢪⠕⣮⠕⠋⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠜⠀⢀⣧⣛⡴⠿⢴⡹⣛⠾⢳⢻⡚⠵⣊⡜⢲⡩⢎⠞⣩⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⢰⠁⠈⢉⣀⡀⢀⡷⣡⢋⢧⠲⣉⠧⡓⣜⢣⡱⢋⡼⢡⡛⢦⡙⢷⡀⠈⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠀⠈⡲⠀⠧⡤⠇⠈⢳⢥⢋⢦⠛⣌⠧⡹⢤⢣⠣⢏⡴⢣⡙⢦⡙⢦⠻⡄⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⡀⠈⣇⣀⣀⡶⢦⢴⠺⡜⢪⣌⣏⡦⠟⠓⠋⠉⠉⠉⠙⠓⠻⢦⣝⢪⡕⣳⠀⠀⠁⠐⠠⠤⠐⠈⠀⠀⢂⠀⠀ ⢀⡇⠀⣯⡙⢦⠓⣎⠎⢧⣹⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣦⠈⠳⣜⣹⠀⢸⠓⠢⢤⣠⠤⠒⡹⠀⢰⠀⠀ ⠈⡇⠀⣧⡙⢦⢛⡤⢛⡞⠁⣴⣄⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠻⠟⠀⠀⣟⡼⠀⢘⠀⠀⠀⠀⠀⠀⡇⠀⢊⠀⠀ ⠀⢧⠀⠹⣜⠣⠞⡬⡟⠀⠘⣿⡟⠀⠀⠀⠀⠳⠤⠃⡀⠀⠀⠀⠀⠀⣠⡟⢁⡴⠋⠀⠀⠀⠀⠀⠀⠘⢄⠀⠱⠀ ⠀⠈⢄⠀⠹⣍⡳⢱⣇⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠒⠀⣀⣀⢀⡠⠜⠁⠀⠈⠓⠂⣤⡀⠀⢀⡤⠄⠠⠚⠃⠀⡀ ⠀⠀⠀⠢⡀⠈⠓⠧⣞⣧⣄⣀⡀⠀⢀⣀⣀⣠⣤⡄⡶⠓⠈⠳⡀⠀⣴⠟⠁⢀⠔⠁⢣⣠⠎⠀⡠⠄⠀⠀⠂⠁ ⠀⠀⠀⠀⢰⠀⢀⡄⠒⠊⠉⢻⡝⡿⠛⠛⢯⢲⣡⠛⡵⣦⠀⡀⡇⠀⠉⢀⡴⠁⢀⡀⠈⠁⠀⠔⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢄⠀⠹⣅⣄⣀⠎⠙⡁⡄⡀⠘⣷⠒⠛⠉⢉⡩⠴⣁⠀⡠⠊⠀⡠⠂⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠇⠀⡎⠁⠈⠉⡄⠀⠑⠛⠚⠓⠉⠑⠦⣤⡀⠀⠀⢀⣹⠁⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡆⠀⢃⡀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⢠⠃⠑⠤⠤⠞⠁⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢀⡀⠀⡹⣄⠀⠀⠀⠀⠀⠀⠠⢺⠁⢠⡤⠄⠀⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⢠⡁⢸⠀⠀⠀⠀⠀⠀⠀⡸⢄⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠄⠀⠑⠺⢄⣀⣀⣀⣀⣀⡀⣀⣠⠃⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠄⠀⣀⡀⠀⠀⠉⠉⠁⢀⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠉⢳⡀⠀⠀⣀⡤⠴⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡽⢿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀ ⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣼⠋⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣾⡟⢡⡾⣿⢷⣾⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣟⣿⡆⠀ ⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⣠⣿⣿⠧⠯⠟⠃⡇⣟⣇⣿⣿⣆⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣤⣤⣿⠇⠀ ⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⣯⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⣰⣿⢏⣿⣴⣿⣹⣷⣷⣿⣿⣧⣿⡏⣠⣴⣾⣿⢛⣿⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢹⡆⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢹⣇⢠⣿⣿⣧⣿⣿⣿⣿⣿⣶⣿⣏⣽⡟⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢿⡀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢠⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡿⣦⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢸⡇⠀⢀⡴⠒⢦⣀⣠⠿⠗⠛⠛⠛⠛⠓⠲⠦⣄⡘⠦⣀⣀⣀⣴⠟⠁⠀⠙⣿⣿⣿⣿⣿⡿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣏⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀ ⠀⠘⣷⠀⢈⡷⣴⠚⣇⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⠉⠁⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣴⡆⠠⣶⢘⣿⣿⣦⣿⢁⣸⣿⣿⣿⣿⣿⡟⣿⣇⣀⣼⣿⠀⠀ ⠀⠀⢹⣇⠸⣄⣈⣟⠉⣹⠀⣀⣤⣴⠶⠶⠶⠶⢦⣤⣀⠀⠙⣦⠀⠀⠀⠀⠀⠀⢀⣾⠟⠙⠻⣷⣴⣴⣴⣿⡿⠿⢿⣿⣷⣵⠉⢏⣯⣿⣽⣷⣿⣿⣷⡿⠋⠀⠀ ⠀⠀⠀⣻⠎⠀⠀⠈⣩⣷⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⠸⣧⠀⠀⠀⠀⠀⢸⡏⡀⠀⠀⠀⠉⠋⠉⠀⠀⠀⠀⠀⠙⢿⣄⠆⠘⠟⢿⡟⣿⡍⠁⠀⠀⠀⠀ ⠀⠀⣺⠏⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡙⢧⢻⠀⠀⠀⠀⠀⢸⡇⢿⣶⣤⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠘⣿⣿⣻⠀⠐⠛⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⣸⠃⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠸⣿⢀⣀⡞⢹⡆⡿⣃⣸⣿⡿⠀⠀⠀⠀⠀⢿⣿⣿⣿⠛⠀⢹⣷⠇⠄⢀⣢⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⣿⡄⠀⠀⣿⠀⠈⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠒⣿⠘⠲⠽⣿⡀⢧⡴⠃⠙⠁⣴⣲⡄⠀⠀⠘⢿⣿⠟⠤⡄⣸⣿⡀⣤⣾⡿⠃⠰⣿⠹⠶⢳⡆ ⠀⠀⠘⣷⡄⠀⣿⠀⣔⠒⢙⠿⠇⠀⠀⠀⢰⣚⡶⠀⠀⠀⢉⣵⠏⣀⣠⠶⣟⣻⣶⣿⣦⣤⣠⡬⠭⢴⡏⠀⠀⠀⠈⠓⠒⣷⣿⣿⣿⠿⠋⠀⠀⠀⠈⠻⠶⠛⠁ ⠀⠀⠀⠈⠙⢦⣜⣧⡈⠉⠉⠀⠀⠀⠀⠀⠀⠈⢻⣭⣍⣓⢿⣏⢰⢫⡴⠶⣭⡥⣤⡙⣿⢟⣵⣾⣿⣯⣽⣄⣀⣀⣀⣴⣿⣿⣿⣿⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⣠⣤⣄⣤⡤⣌⠙⢛⡷⠲⠦⠤⠤⠤⢤⡤⠴⠚⠛⠉⠀⣷⡘⣮⢿⣧⡤⢤⣀⣨⣧⠯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠧⠿⠀⠀⠀⠀⠀⠀ ⠀⢿⣄⠈⠁⣰⡟⠀⢸⣧⡀⠀⠀⠀⣠⡾⠻⢦⣀⣀⣀⣼⢿⣿⣧⡄⠈⠀⠈⠙⢏⣺⡇⢸⣿⠟⠓⠲⡝⣿⣿⣿⠿⠿⢿⣏⢻⡄⠀⠀⠀⣤⣤⣤⣄⣀⠀⠀⠀ ⠀⠀⠈⠛⠛⠋⠀⢠⡞⠉⢙⡷⠞⠛⠛⢦⢀⣴⠟⠛⢿⣧⠸⣧⣉⡥⠦⠀⣀⣀⣀⡇⠀⣘⡇⠀⠀⠀⢹⠈⡟⠀⠀⠀⠀⠹⣆⢿⣦⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⣀⣠⣄⣀⣠⣿⠀⡴⠋⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⢹⡆⣿⠉⣳⠂⣴⣿⠉⣹⢤⣾⡏⠀⠀⠀⢀⣾⠀⣇⠀⠀⠀⠀⠀⠛⢸⡿⣷⠀⠻⠿⢛⣿⣿⡆⠀⠀ ⢠⡟⠁⠀⠀⢈⡟⢿⠀⠀⠀⠀⠀⠀⠀⣸⠸⣧⠀⠀⠀⢸⡇⢹⡇⡞⣯⠽⣼⢦⣇⠤⢯⢷⣄⣀⣠⡾⠁⠀⠙⢦⡀⠀⠀⠀⠀⢸⡇⣿⣷⣶⣶⣾⣿⣿⡇⠀⠀ ⢸⡇⠀⠀⠀⢸⡇⠈⠣⣄⡀⠀⣀⣤⠞⠁⠀⠉⠳⣤⣠⡿⠃⠈⣿⡀⢹⡙⢹⢹⡏⢒⡾⠀⠉⠹⣇⠀⠀⠀⠀⠀⠙⠓⠶⠤⠴⠟⢁⣿⢿⣿⣿⣿⠿⠋⠀⠀⠀ ⠀⠙⠧⣤⣠⣼⣧⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠸⣧⠀⣇⢸⢸⡇⣾⠇⠀⠀⣴⠟⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⣄⣀⣀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠹⣧⢸⠸⠿⢰⡟⠀⣠⡾⠋⠀⠀⠀⠀⣿⣹⠆⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢹⣧⡖⣦⣿⣰⡟⠉⠀⠀⠀⠀⠀⣤⡿⠋⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⣸⣷⣄⠀⠀⠀⣰⡿⠀⠀⠀⠀⣰⡟⠻⠥⠽⠚⢿⣷⣄⣀⠀⢀⣀⣾⠁⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⠤⠞⠋⠀⠉⠓⠲⠚⠋⠀⠀⠀⠀⠰⣿⣼⣚⣒⣂⣄⣌⣿⡄⠉⠉⠉⠉⠙⠦⣄⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⡠⠄⠈⠈⠀⠐⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠄⠀⠀⢀⠠⡐⡔⢪⢔⠢⡔⢠⠈⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣎⠀⣄⠣⢎⡱⣱⢪⡑⢮⡱⢌⡣⣙⠦⣠⠡⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣘⢀⠲⡌⢧⢣⢓⡆⢧⡙⢦⡓⡭⢲⠥⡳⢥⡓⢦⢠⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⣬⠳⣍⠶⡩⠖⡼⡡⢞⡱⣜⡱⢣⢏⡵⢣⡝⣮⢣⢖⡀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣌⠿⣌⠷⣩⢝⡲⡹⣌⢳⣌⠳⣭⢚⡼⢣⣛⡴⢫⡞⡴⣂⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢺⡹⢶⡹⢶⡍⡞⣥⢣⡝⢮⣙⠶⣩⢞⡵⢎⣻⡱⣎⡳⢇⡟⢦⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣹⢯⡽⣣⢟⡝⣦⢳⡚⢧⡹⢞⡥⣏⢞⡹⢶⡹⣜⣭⠻⣜⢯⡳⢤⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣟⣞⡷⣏⡿⣜⢧⡳⣝⣣⢯⡝⡼⢎⡽⣭⢳⡝⣞⡼⢻⡜⣧⢻⡭⢖⡈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢀⠠⡐⢄⠒⣌⡐⢢⠰⢄⠂⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣼⣛⣾⢳⣏⣯⢳⣝⡺⡼⣩⢗⣫⢞⡼⢣⡟⣼⣩⠷⣹⢎⡷⣹⢏⡶⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠠⢄⠣⢌⠢⡑⡌⢎⡰⢌⢢⠱⣈⠎⡔⢣⢊⠴⡀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠧⣟⣾⣛⣮⢷⡻⣜⣳⢽⡱⢯⡜⣮⢓⡯⣜⠶⣣⢻⠵⣫⢞⡵⣫⢞⡳⡌⢆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢨⡑⢌⠲⣈⠵⡘⠤⣃⠖⡌⢆⠳⣠⠓⣌⢣⢚⢦⡙⣆⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⢹⢾⡽⣞⣯⣽⢻⣼⢣⡟⣧⢻⡜⣝⡲⣭⢳⡭⢳⣋⢷⣫⢞⡭⣏⢷⣱⡈⢄⠀⠀⠀⠀⠀⠀⠀⠠⢀⠧⣘⠢⢓⢌⠲⣉⠖⣡⠚⡜⣌⠳⣄⢫⡔⢫⡜⢦⡝⢦⣃⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢆⢯⢿⡽⣾⣝⡿⣼⢻⣜⢧⡻⣜⠧⣝⠶⣫⡜⣧⢛⡮⣵⢫⡞⡽⣎⠷⣜⠄⠂⠀⠀⠀⠀⠀⢠⠃⣘⠦⣅⠫⡜⣌⠳⡌⢎⠥⣋⠴⣊⠵⡘⡖⣜⢣⢞⣣⢞⡳⣎⣇⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠂⢯⣟⡷⣯⣟⣳⡟⣮⢏⡷⣭⣛⡼⢭⣓⠾⣡⢟⡼⣣⢟⡼⣳⢭⡻⣼⢩⠌⣄⠀⠀⠀⠀⠇⠰⣌⠳⣌⢳⡘⣤⠳⡜⣩⠞⣡⢏⠲⣍⠳⡜⣬⢳⣎⢧⣏⢷⣏⡞⡆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡘⡾⣽⣳⢯⣷⣻⠽⣞⡵⣳⢎⡞⢧⡭⢏⡳⢏⡾⡱⣏⢾⣱⢫⠵⣎⢧⢣⠘⡄⠀⠀⢘⠠⣓⢮⣛⡜⣦⠝⣦⢛⡴⢣⢞⣡⢎⡳⣌⣳⢹⣬⢳⣎⠷⣞⣯⢾⣝⡆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⡘⢷⣯⣟⡾⣽⣻⢽⣺⢵⣫⢞⡧⣻⠭⣝⣣⠷⡹⣜⢲⢣⢏⣳⢚⡬⣓⢂⠡⠀⠀⠈⡄⢫⡞⣵⢻⣬⢻⡜⣧⣝⡳⣎⢧⣏⢷⡹⣖⢯⡲⣏⣾⢻⡽⣞⡿⣞⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠉⣾⣽⣻⠷⣯⣟⣮⢷⡹⢮⡱⢇⣛⠦⣇⢯⡱⢎⠧⣋⠞⣰⢋⠶⣩⠖⡀⢇⠀⠀⢻⠨⣽⢞⣧⢯⣗⣻⠶⣭⣳⢏⡿⣼⣏⡷⢯⡾⣽⣻⣞⣯⢿⣽⣻⡗⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠡⠱⣯⢷⣻⢷⣫⣞⢧⡻⢵⡙⢮⡜⠳⡜⢦⡹⢌⠧⣃⡛⡔⢫⠜⣡⠚⣁⠈⠀⠀⠀⠀⢾⣻⣞⡿⣾⣽⣻⣳⡽⣯⣟⡷⣾⣽⣻⣽⣳⣟⡾⣽⣻⣞⣷⣻⡅⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠡⡘⣯⣻⡽⣳⡽⣺⡝⢮⡙⢦⣙⢣⡝⢢⠧⣩⠚⢥⢊⡑⢣⠘⠤⡑⢄⢊⠴⠡⢎⠰⣉⠱⢫⢟⡷⣯⢷⣯⣟⡷⣯⣟⡷⣯⢷⣯⠷⣯⣟⢷⣛⣮⢷⣳⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢯⣽⣳⡽⣣⢟⡣⡝⠦⡍⠶⣈⢇⠚⠤⣉⠆⡒⡌⢆⡍⢲⠡⠎⡜⢢⡙⣌⠳⢌⡓⢢⠎⡜⣩⠛⡞⢭⢛⠳⣩⠛⡡⢃⡜⠭⣓⢮⡛⣼⢣⡿⣭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌⢶⢻⡼⡝⠮⣑⠩⣒⠉⡖⢡⢊⡌⢣⠒⡬⡑⡜⢢⠜⡡⢎⡱⢌⠣⡜⢤⢋⠦⣙⢢⠱⡘⡤⡙⡌⢦⡉⢖⢡⠚⣄⠣⢌⠒⡌⢢⡙⣌⠻⡜⢧⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠀⣏⠖⡩⠒⡌⣒⠡⡍⡔⢣⠒⡬⢡⠓⡴⠱⣌⠣⢎⡱⢊⡴⢋⠵⡘⢦⡉⡖⣡⢎⡱⢅⣣⠱⡘⢆⠭⣘⠢⡍⢤⠓⡬⡑⢬⠡⡜⢤⠓⡼⡑⢦⠌⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⢠⠘⡔⠬⣁⠳⠰⡌⡱⢢⠍⢦⡙⡔⢣⡙⡔⣣⢌⠳⣘⡔⢫⠔⣩⠒⣍⠦⣑⡚⡔⢪⠔⡣⢆⠭⡱⢊⢖⡡⢓⡜⠢⡍⠴⡑⣊⠦⣉⠦⡙⡴⣙⠎⡵⣂⠀⢄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡄⢃⡚⢄⡓⠤⢋⠲⣁⠳⣌⠚⡤⢓⡌⢧⡘⢦⡑⢎⡱⢆⢎⡱⢊⡥⢋⡔⢣⡜⠴⣉⠖⣩⠒⣍⠲⣉⠇⡎⠴⢣⠜⡱⣌⠳⡘⡔⢢⡑⢎⡱⡚⡴⢋⡶⣩⠞⡤⠳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢀⡰⢌⠣⡜⢢⠜⣡⠋⢖⡡⢓⡌⡣⢕⠣⡜⢢⡙⢦⡙⢦⠱⢎⢦⢣⣍⠲⣍⠼⣡⢎⠳⡜⡬⢥⢫⠴⣉⠦⣙⡌⢇⣣⢚⡱⢌⠣⡕⢪⠱⣘⠬⣱⢣⡝⣣⠞⣥⠻⡴⣁⠱⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠊⢀⠦⣑⢎⡱⢌⢣⠚⡤⢋⠦⡙⢦⠱⣉⢎⡕⡪⢵⡘⢦⡙⢦⠛⡜⢦⢣⠎⡵⣊⠵⣊⡜⡣⢧⡙⢦⢋⠶⣉⢮⠱⣌⠳⣤⢣⡜⣌⠳⣌⢣⠓⣬⢣⢓⠮⣜⣥⠻⣜⡽⣱⢣⢣⡘⡄⠀⠀⠀ ⠀⠀⠀⠀⢀⠈⢠⢚⢤⣋⠼⣡⠞⣌⢲⠡⠞⣤⢓⢬⡒⣍⠞⣡⠳⣌⠳⣌⠳⡜⣲⢱⢪⢜⠲⢥⠛⣔⠫⣕⢣⠎⡵⣊⠞⣔⢫⡜⢦⡙⢦⡍⣎⡱⣙⢦⡙⣎⠶⣉⢎⡞⣴⢫⡝⡶⣹⢵⣫⢞⡮⣅⠑⡀⠀⠀ ⠀⠀⠀⢀⠆⢠⢃⣏⠲⣌⠳⡜⡼⣘⠦⢫⡹⢤⣋⢦⠳⡬⣙⢆⡛⡴⢋⡬⢳⡱⢎⠲⡡⠎⠙⠬⠙⠈⠑⠈⠂⠙⠐⠉⠘⠌⠦⠙⠦⢙⠦⣙⢦⠳⣍⢶⡹⡜⢮⡱⣏⠾⣜⢧⡻⣜⢧⡻⣜⢯⡖⣧⢆⢱⠀⠀ ⠀⠀⠀⡜⠀⡎⡞⡴⢫⡜⣣⠳⡜⣆⢏⡣⣕⢣⠞⣬⢳⡱⣍⢮⠱⠍⠓⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠲⠹⣝⢣⡟⣼⢻⡜⣧⢻⡼⣳⢽⡹⣮⢽⡺⡜⡄⠅⠀ ⠀⠀⢀⠇⡸⣜⡱⣭⠳⡜⣥⠳⣍⠶⣩⠖⣭⢚⡜⢦⢣⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢎⡷⣹⢞⣧⢻⡵⣫⢷⣫⡗⣯⡝⣆⠸⡀ ⠀⠀⠈⣐⠳⣌⡳⣜⣣⠟⣴⡛⣬⡓⢧⡛⢦⣛⠼⠓⠁⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠉⠳⣏⣞⢯⢾⡝⣧⢷⣫⣗⣻⡼⡀⢃ ⠀⢸⠀⢮⡝⢮⠵⣓⢮⡝⡶⣙⢶⣩⠧⣏⡷⠉⢀⡀⠀⣙⣿⣿⣿⡿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣿⣿⣃⠀⣀⠈⢞⣯⡳⢿⣹⡞⣧⢯⣳⣝⢧⠐ ⠀⢸⠈⣞⡼⣫⢽⡹⣞⡼⢳⡹⣎⢧⣻⠌⠀⠀⠀⢻⣿⡿⠿⢻⠛⠀⠈⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠙⠿⠻⣿⣿⠋⠀⠀⠸⣛⣯⢷⣻⣭⣟⣳⡞⣧⠘ ⠀⢸⠀⣾⡱⣏⢾⣱⢏⣞⡳⣝⢮⣳⠁⠀⠀⠀⠀⣸⣿⣧⣀⠼⣦⡀⣤⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⡠⣴⠳⣀⣾⣿⡆⠀⠀⠀⠘⣽⣞⣳⡽⣞⣷⢻⡖⢸ ⠀⢸⢠⢳⡝⣾⡹⣎⠿⣼⡹⣎⠷⡏⠀⠀⠀⠀⠀⣿⣿⣿⠂⠀⢹⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⠁⢉⣿⣿⡧⠀⠀⠀⠀⣻⣼⣳⢿⡽⣞⡿⡼⢸ ⠀⢸⠀⢿⡼⣳⡽⣫⡟⣵⢯⡝⡿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⣶⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣶⣾⣿⠿⠁⠀⠀⠀⠀⠘⣧⣟⣯⢿⣽⡳⡏⢸
⣿⢏⡇⣀⠂⠰⣀⠒⡐⢂⠒⡐⢂⠒⡐⢂⠒⡄⢢⠐⠤⡀⠘⢽⣻⣟⣿⣻⠿⣝⣯⢻⡝⣯⣟⢯⡛⡱⢋⠖⣩⢒⡱⢊⢖⡩⠛⠽⢫⣏⢷⣫⣟⡿⣿⣟⣿⡹⢯⡝⣯⣟⡿⣽⣻ ⣯⢟⡶⡀⠌⡐⠠⠘⢠⠃⡱⢈⠅⡊⠔⡡⢊⠔⡡⢊⠔⠰⢠⠀⢳⣟⡾⣽⣻⣝⡮⣗⢯⢷⡉⠔⡬⢱⡉⢎⠤⢃⡜⡡⠎⠴⡉⡔⡀⠙⢮⣳⡽⣟⣷⣻⢮⡽⢧⣻⠶⣯⢿⣵⣻ ⡿⣎⢷⣹⠀⡄⠡⠘⠠⢈⠰⢁⠎⡰⢁⠆⡡⢊⠔⣁⠊⡔⡁⠆⡀⠻⣽⣳⣟⣮⢗⣯⣛⠎⠀⣍⠲⢡⡘⢌⠲⣁⠦⡑⢪⠑⡴⢐⠡⢂⠈⣷⣻⢯⣿⣹⡟⣞⢯⡞⣽⢯⣟⢾⣽ ⣿⣹⣎⢷⣣⠀⠡⠈⠄⡁⠢⠌⢂⠱⡈⢆⠑⠢⠌⡄⠣⡐⢌⠰⣀⠀⠹⣷⣻⣎⢿⡲⣏⠀⡜⢠⠓⠢⠜⣈⠖⡐⢢⠡⢃⡜⢠⠃⡜⢠⠂⠑⣯⣟⣾⣳⢟⡽⣲⢻⣼⣻⣾⣻⢾ ⣷⢳⡞⣯⢳⣇⠀⢁⠂⠄⠡⠘⣀⠣⡐⠌⡌⠱⡈⠔⡡⢘⠠⢒⡀⠎⠀⠹⣷⢫⣗⣻⠂⠠⡘⠤⢩⠑⣊⠴⣈⠬⡁⢎⢡⠘⡄⢣⠈⢄⠂⠀⢼⣻⢾⣽⣫⢗⣯⢳⡞⣷⢯⣟⣯ ⣯⡳⣽⢣⣟⣾⣡⠀⠈⠄⠡⠁⡄⢂⠱⡈⠔⡡⠘⠤⡑⢌⠢⡁⢆⠩⡐⠀⢯⡟⣮⢳⠀⢁⢂⡑⠢⡉⠔⢢⠐⢢⠉⢆⠢⡑⠌⠄⠊⠄⢨⠀⢸⣯⣟⡾⡽⣞⡼⢧⣻⣽⣻⢾⡽ ⡷⣝⡾⣹⢞⣼⣻⢆⡀⠌⠠⢁⡐⠈⠤⡑⢌⠰⡉⢆⠱⡈⢆⠱⡈⢆⢡⢃⠈⢽⢳⣏⡆⠀⠠⠐⢡⠈⢒⠠⠉⠄⠊⠄⠒⡈⠐⡈⠡⠈⠄⠂⢸⡷⣯⢿⣽⢺⡝⣧⢻⡶⣯⢿⣽ ⣟⢮⡳⣝⣞⣳⣯⣟⡦⠀⡁⠂⠄⡉⠔⡈⢆⠱⡈⢆⠱⡈⠦⡑⠸⣠⠒⣌⠢⡌⡑⣎⢳⡀⠀⢁⠂⠌⡀⢂⠉⠄⠡⢈⠐⠠⠁⠐⡀⠡⠐⠀⢸⣿⣹⢿⡼⢧⡻⣞⣽⣳⢯⣟⡾ ⡿⣜⢧⣻⡸⣇⡿⣼⣻⢇⠀⠃⠄⡘⠠⢃⠜⡠⢃⠜⠤⢃⠤⢛⢣⡀⢟⡀⢧⠸⣠⠠⢄⠣⢄⡀⠀⠄⢀⠀⡘⢀⠃⠀⠘⠀⡄⢃⠀⡃⡘⠀⢼⢧⣟⡿⣸⡟⣧⢻⣤⡟⣿⡼⣻ ⣝⢮⡳⢧⡝⣾⣹⢷⡻⣞⡦⠀⠂⡐⢡⠊⡔⢡⢃⠎⡜⢡⠚⡌⢆⡉⢆⠍⣢⢑⠢⣉⢌⡃⠎⠴⡉⡔⡠⢄⠤⣀⢆⠲⣉⠖⡰⢈⠆⡁⠐⠀⡘⣿⡼⣻⡵⣻⡜⣳⢞⣽⣳⡽⢯ ⢞⢧⣛⣥⢻⡵⣛⣮⠽⣽⠶⣔⠀⢀⠣⡜⢌⠲⡌⠜⣨⠑⢪⠰⣁⠚⡌⢜⠠⢎⠱⡐⢢⡘⢌⠣⠜⣠⢑⡊⠴⣁⠎⢲⢁⢎⡱⢡⠚⠤⢃⡀⠳⢯⢷⣳⡽⣱⠞⣥⢻⣎⢷⣫⣟ ⢏⡞⢦⢣⢇⡻⣹⡜⡻⣜⡋⠀⣄⠊⡵⠘⡬⠑⣌⠚⠤⡙⡄⢣⠘⡔⡘⡌⠲⣈⠦⡑⣡⠘⡄⢣⢉⡔⠢⢌⡱⢄⠋⡆⢍⠢⡜⢡⡙⢂⠇⠤⣀⠈⠳⣧⢻⢥⡛⣬⢳⡞⣯⠶⣯ ⣾⡽⣞⡷⣞⣷⣳⣟⢷⠈⢀⡜⢠⢋⠔⣩⠰⡉⢤⡉⠖⡡⠜⢢⡑⠬⠰⢌⠱⡠⢆⠱⡀⠇⡜⢢⠡⢌⡑⢆⠒⡬⠘⣌⠂⢇⠜⠢⣌⢡⠚⡰⠠⢌⡀⠸⣷⢮⡵⣮⢷⣞⣶⡽⣶ ⣷⣻⣽⣻⡽⣞⡷⣏⠃⢠⠃⣌⠣⡘⠬⢄⠣⠜⠤⡘⢢⢑⠊⡥⢘⡰⢉⠆⠣⠔⣊⠱⢨⠑⣌⠢⠱⣈⠔⡊⠴⡁⢇⢢⠙⡌⠬⡑⢤⢂⠣⡐⢅⠢⡐⠄⠙⣯⡿⣽⣻⢾⣽⣻⣽ ⣟⡷⣽⢧⡿⣽⣛⠀⢀⠆⡩⢄⠣⢌⡱⢌⢊⡑⡊⢅⠣⡌⠱⡄⢣⡐⢣⢘⡡⢃⠆⣍⠢⡱⢠⢃⡃⢆⠎⡑⢢⢉⠒⡌⠜⡐⢣⠑⠢⢌⠢⡑⢌⢂⠱⡈⠄⠑⣟⡷⣯⣟⣾⣳⢿ ⣯⣿⣭⡿⣽⡳⢂⠜⡠⢃⠜⡠⢃⡒⢰⡈⠒⡌⠱⣈⠒⡌⠑⠈⠂⠘⣀⣦⣱⣬⣼⣤⣗⣶⣣⣦⡵⣮⣬⣥⣀⣁⠊⠐⠡⠘⠤⣉⠒⠌⣂⠱⢈⢂⠒⡈⢄⠀⠩⣟⣷⣻⢾⡽⣯ ⣛⣜⡣⢟⡳⢃⠌⢢⠑⡌⢢⠑⢢⠑⢢⠘⡡⠌⠑⢀⣠⣤⣶⣶⢿⡿⣿⣻⣿⣽⣯⣿⣽⣶⣿⡽⣟⣿⣳⣟⣿⣭⣿⣟⡶⣦⣤⡀⠉⠔⡀⠎⡐⢂⠡⠐⠂⠌⠀⢹⡞⣭⢏⣻⡹ ⣳⠮⣝⢧⡋⠔⡘⢄⠣⡘⠤⡉⢆⡉⠆⡑⢀⣠⠘⠫⢿⡻⠯⣿⣿⢿⣿⣟⣯⣿⣽⣿⣯⣿⢯⣿⣻⣽⣯⢿⣞⣯⣷⣟⠟⡓⣯⡙⠃⢀⡀⠂⢁⠢⠌⢂⠉⠄⠂⠈⣞⡵⣎⢷⡹ ⣧⢻⡜⣯⠆⢩⠐⡌⢂⡑⠢⠑⢂⠜⠀⣰⡄⠛⠃⠀⠀⠀⠀⠀⠙⣿⣟⣾⣿⣯⣿⣾⡿⣽⡿⣿⢿⣳⣿⣻⢯⣟⡇⠈⠀⠀⠀⠀⠀⠘⠈⢆⡀⠂⠌⠠⠌⢂⠁⠀⢮⡳⣎⢷⣹ ⣽⢣⡿⣜⠂⡡⠒⡈⠔⣈⠡⣉⠂⢀⡾⣯⡇⠄⠀⢠⠀⠘⡳⠀⠀⢻⣯⡿⣿⣾⣟⡷⣿⣻⣽⣿⣻⣽⣞⣯⣿⠾⠘⠀⠀⢛⠄⢠⠀⠀⢸⢯⡖⡀⠈⠡⠈⠄⡀⠁⣺⢵⣛⡮⢷ ⣾⡹⣞⡽⠀⡐⠠⠁⡌⠄⠒⡀⢀⡇⣿⣽⠀⠀⠀⠀⡤⠀⠀⠀⢀⢺⣷⢿⣻⢾⣽⣿⡻⡓⠟⢷⣟⣷⣻⢷⣻⣿⡴⠀⠀⠀⠀⡤⠀⠀⠈⣷⡹⡥⠀⠀⠡⢂⠐⠀⢼⣣⢟⡼⢯ ⣶⢫⢷⣹⡀⠀⠐⠡⠐⡈⠡⠀⣸⢷⣫⣟⡆⣆⠀⠀⠁⠀⠀⣠⡼⣟⣯⣿⣻⢯⣟⡾⣷⣄⣨⡼⣟⡾⣯⣟⡷⣾⢽⣣⡄⠀⠀⠀⠀⢀⣤⢗⡯⢳⠀⠈⡐⠠⠀⠀⢸⢧⣛⠾⣽ ⣳⢏⡷⣣⢗⠀⠈⠠⢁⠐⠡⠀⢏⡾⣱⢎⡝⣎⠳⣔⡲⢶⣞⡷⣻⡽⢯⢷⡫⣅⠈⠑⠃⠙⠃⠛⠉⠃⠀⣽⢾⡹⣞⡳⣝⢧⡲⡔⡴⢣⠜⡪⢝⡣⠂⠀⠠⠁⠀⢰⣫⢞⡭⣟⣞ ⣯⢞⡳⣝⢮⣃⡀⠀⠂⠌⡐⠀⠘⣧⠓⡎⢴⣈⠳⣌⢳⢫⢞⡵⡳⢏⡟⣮⢳⢯⡄⠐⢌⡒⠰⢌⠂⢠⡝⢯⠞⣵⣋⠷⣙⢎⡳⢍⢖⡩⢎⡕⠣⡜⠀⠀⠀⠀⣠⡟⢮⣻⡜⣷⢺ ⢳⡏⣷⣭⠛⣧⢱⠀⠀⠐⢠⠁⠀⠊⢳⡜⢡⡎⢱⠊⣧⠋⣮⡕⢫⡝⣮⣵⠋⣶⠙⡆⠀⠘⠀⠀⣴⢫⡜⣭⡞⢱⠊⢳⠉⡎⠑⡎⣬⠀⠁⡎⠁⠀⠀⠀⠀⣶⡝⣾⡏⣷⢹⡎⣿ ⡿⣜⢧⣏⠿⣭⢏⣻⡤⡀⠀⠐⠀⠈⠂⢅⠣⠘⢄⠋⡔⢩⠢⠙⠬⡑⢎⠲⡙⢆⡛⣌⠃⢦⠘⡱⠢⢍⠲⠱⡈⢇⠚⢄⠣⠌⡑⠰⡈⠌⡑⠈⠀⠀⢀⡤⢞⡵⣫⢗⡹⣎⠷⣹⢎ ⠳⣎⠳⣬⢓⢮⡹⢶⣽⣿⣷⡦⣄⣀⠀⠀⠀⠂⠠⠈⠐⠤⢈⡁⠆⡑⡈⠤⠑⢂⡐⢈⠡⢂⠱⠠⠑⣈⠰⢁⡘⠠⠌⠄⠢⠄⠁⠂⠀⠀⢀⣠⣴⡾⣿⣛⣮⢵⡳⣎⠷⢮⡝⡶⣭ ⣷⣼⣳⢶⣫⣶⢯⣻⢞⡷⣞⡿⣿⢿⣿⣷⣶⡄⢄⣀⣀⢀⡀⣀⡁⣀⢁⡈⠒⣀⠒⣈⢂⠐⢂⡑⢂⢀⡀⡁⣈⠁⣄⢠⠠⠤⠤⢰⣚⣿⣿⣻⣟⡿⡳⢏⡞⣧⢻⣜⡻⣧⡻⣵⣳ ⣟⡾⣽⢯⡷⣯⢿⣬⣋⠹⢭⢻⡝⣯⢾⣽⢾⣿⣤⡐⠨⢆⡱⢂⡑⢆⠒⣌⠱⡠⠃⢠⣿⣷⡀⠘⠰⡊⢔⡑⠢⡍⡔⢢⠌⢃⣴⡾⣿⡻⣞⡱⢎⠓⣙⣬⣛⡼⣓⢮⡝⣞⡳⢧⣛ ⣯⢿⡽⣯⢿⣹⣟⣾⣽⣳⢶⣦⣜⣆⡛⢞⣻⢾⣽⡿⣶⣤⣈⠁⠘⠤⢋⢄⠣⠁⢀⣿⡿⣿⣷⡄⠐⠱⣈⢌⡑⠒⢈⣡⡴⣿⣏⡟⠧⢋⡴⣑⢮⡙⣑⢮⡱⡩⣍⢎⡱⢬⡑⢣⡘ ⣉⠞⣩⣑⠫⡜⡌⢧⠛⣌⠳⡬⢜⡬⣙⠎⣜⠳⣎⡿⣿⣽⢿⣿⣶⣤⣀⣈⣐⡈⣼⣿⣟⣿⣿⣿⣀⣀⣁⣠⣴⣾⢿⣯⢿⣱⠎⣝⠨⠖⠐⠈⠲⢔⠋⡶⡑⢳⠤⠋⠘⠦⣜⠣⡝ ⢌⡛⢤⢣⠳⡜⣱⢊⡝⣨⠳⡱⢎⡲⢍⡚⣌⢳⣹⢿⣻⣯⣿⣿⣾⣟⣿⣟⣿⣿⣿⣯⣿⣿⣾⣻⣿⢿⣻⣿⡿⣽⣟⡾⢯⡧⠅⡠⠄⠀⠀⠀⠀⠀⠉⠀⠉⡡⡐⣄⢃⠤⣈⠒⡉ ⢢⡜⡌⢆⠳⣌⡱⣍⢲⢡⠣⠵⣉⢎⢧⡹⢜⡲⢯⣟⡿⣷⡿⣷⣿⣿⣻⡿⣿⣽⣾⣿⢿⣾⡿⣟⣿⣿⣿⣟⣿⣿⣽⣻⣭⢟⡃⣵⢩⠀⠀⠀⠀⠀⠀⠀⠀⢲⡱⡌⠎⠲⡡⠏⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡞⠁⠀⠀⠙⠒⠉⠉⠓⢄⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⠖⠉⠀⠙⢆⠀⠀⢸⠀⠀⠀⠀⠓⠒⠒⠒⠒⠤⠤⣀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣓⡞⠁⠸⡀⠀⠀⢀⠞⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢁⣿⡁⠀⠀⠈⠁⠈⠁⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣡⡟⣹⡿⠦⠤⠴⠦⣀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⣰⠋⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⡼⠋⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠋⢠⢏⡟⢁⣼⠏⠀⠀⠀⠀⠀⣀⡤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⡎⡞⢠⠎⡸⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡇⢸⢻⠀⡏⠀⡇⠀⠀⣠⠎⢠⣶⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣾⣿⠀⢰⢀⡇⠀⣰⠃⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣄⠙⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡋⢙⣷⣤⣾⣿⣤⣠⡇⠀⠸⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⠘⣆⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠈⣟⣿⣾⡡⠟⠉⠉⠛⢷⣄⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠰⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠸⡄⠀⠀⠀⠀ ⠈⠑⠢⣄⡀⠀⢫⣿⡿⠃⠀⠀⠀⠀⠀⢹⡿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁⠀⠀⣇⠀⠀⠀⠀ ⣀⠀⠀⠀⠉⠢⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⡇⠘⢿⣆⠀⠀⠀⠀⠀⣸⠿⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀ ⠀⠈⠉⠻⢶⣒⠿⣏⠀⠀⠀⠀⠀⠀⠀⢠⡿⣆⢀⡿⣷⢄⠀⠀⠀⢿⠀⠀⠀⠀⡈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠈⠙⢿⡀⠀⠀⠀⠀⠀⠀⡼⠁⡿⣿⣄⠈⠻⣷⣄⠀⠸⣷⡀⠀⠀⢿⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⣠⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⢾⣅⠀⣇⠈⠙⢿⢦⡈⢿⣆⠀⠈⠙⠒⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⣀⡴⠿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠈⠙⠻⣶⣤⣸⡄⣷⣼⡯⠉⣶⠒⠒⠂⡤⠤⣄⣀⣀⣀⣀⣠⡴⠶⠟⠒⠒⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢄⡀⠀⠀⣀⡀⠻⡙⠷⢿⠞⠁⢰⠻⠀⠀⠀⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠇⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⠉⠐⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⢀⣠⠄⠠⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⡀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⣶⡾⠋⢠⣶⠶⣾⣿⡖⢦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⢋⣿⠟⠁⠀⠈⢿⣿⣴⣿⣿⡆⡻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠤⠒⠷⣦⣀⣀⣀⣀⣈⣿⣦⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⣦⠀⠀⠀⠀⠉⠛⢻⣿⣡⠇ ⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠈⢱⡇⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠿⣤⣀⣀⣀⣠⡴⡿⠇⠈⠆ ⠀⠀⠉⠓⠢⠤⣄⣀⡀⠀⠀⠀⢧⡀⠀⡴⠋⠉⠉⢢⡤⠼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⡽⢲⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣟⣻⡉⠒⡾⠉⠈⠓⠤⣀⠤⠊⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠉⠀⠀⠀⡀⠀⠀⢀⡴ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣠⠳⢄⡀⠀⣀⠞⠦⠤⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣀⣀⣤⣶⣿⡃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⠀⠀⠉⠉⠁⠀⠀⠀⠀⣀⠤⠐⠒⠂⠈⠉⠉⠉⠉⠑⠒⠢⢤⣀⠀⠀⠀⠀⠀⠹⣍⣹⡿⠿⠟⠋⢉⡠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⢹⠀⠠⠤⠒⠊⠁⠀ ⠀⠀⠀⠀⠀⠀⣠⡄⣺⡟⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⡟⡇⠀⠀⠀⠀⠀⡸⠃⢀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣦⡈⢆⠀⠀⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠁⠀⡇⠀⠀⠀⠀⢰⠃⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⣿⣿⣿⣷⠘⡄⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⡎⠀⠀⠹⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⣿⣿⣿⡿⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠠⡇⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⢀⡴⠶⢤⣤⡀⠀⠀⠀⠈⠛⠛⠁⠀⡇⣸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠒⠁⠒⠦⣙⢦⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⣼⣠⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠈⠙⠷⣦⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣰⠟⠀⠀⠀⠀⠀⠀⢀⣼⠟⠓⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠉⠑⠒⠠⢤⣤⣄⣀⡀⠀⣀⣠⠤⠤⠒⠒⡻⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⡽⠋⠀⠀⠈⢧⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠲⠴⠒⠁⠉⠱⡒⠒⠠⢤⠤⠀⠀⠈⠳⠤⠤⠴⠊⠀⠀⠀⠀⠀⠈⢦⣀⡴⡇⠀⠀⣀⡀⠤⠚⠁⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠴⠒⠦⠄⠀⠀⠳⣄⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠉⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀ ⠀⠀⠀⠀⠀⠐⠒⠒⠒⠚⠉⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⡖⠭⢿⣟⣿⠶⠗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠑⠤⣄⣀⣀⣀⣀⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠙⡆⢰⡵⣖⡢⢀⡀⢀⡀ ⠀⠀⠀⠀⠀⢀⡀⣤⣤⡀⠀⡜⠀⠀⠀⣀⣠⣇⣘⠁⠩⠇⢼⢾⡿⡇ ⠠⣲⢪⢭⡇⢹⣽⠯⠯⠇⢰⠃⠀⢠⠎⠁⠀⠀⠈⢳⠀⠀⠀⠀⠉⠀ ⠀⠻⠈⠁⠚⠀⠀⠀⣠⠔⠚⠁⠀⢸⡀⠀⠀⣠⠀⢸⠀⡤⢄⢀⡀⠀ ⠀⠀⠀⠀⠀⢄⢠⠞⠀⠀⢀⣀⣀⣀⠉⠒⠋⠁⠀⠣⡀⠣⣈⡰⠃⠀ ⠀⠀⠀⠀⢀⡞⠛⡖⢢⢪⣧⠀⠀⠀⠈⠑⠢⡀⠀⠀⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⡔⡡⡕⠒⠁⠈⣞⣋⡀⠖⠄⠀⣰⣷⠘⡀⠀⠀⠇⠀⠀⠀⠀ ⠀⠀⠀⡅⠁⠡⢄⠐⠭⠊⠙⢿⡉⣩⠱⠌⠁⠀⢣⠀⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⢇⣀⢌⣈⠤⢀⡠⡤⢼⠬⣄⣁⣛⣀⣀⠜⠀⣀⠇⠰⢆⡠⡀ ⢀⢀⠖⡆⢇⠀⠀⠀⠀⠈⡢⠄⠤⠑⠒⢯⣉⠉⠉⠉⠁⠀⠘⠬⠔⠃ ⠙⠂⠚⠁⠀⠉⠉⠉⠉⣏⢣⣀⡖⠀⢀⠼⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣟⣿⣻⣟⣿⣻⣟⣿⣻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠄⠀⠂⠄⠁⠂⠀⠀⠀⠐⣿⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⡀⠂⠄⠈⠀⢁⡐⣀⡀⠸⣷⣟⣾⣽⣳⣯⡷⣟⣾⢷⣻⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣻⢯⣟⡿⣷⣦⠀⠀⠀⠀⠀⠀⠠⠁⠰⠀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⠄⡀⢂⠦⢤⡾⣙⢦⡝⢦⡻⣿⣞⡷⣯⡷⣟⣯⣟⣯⢿⡾⣽⣧⠀⠀⠀⠀⠁⠀⠀⠠⣴⣿⢿⣯⣟⣯⡿⣯⢿⣽⣻⣷⡄⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠢⠔⠄⠀⠀ ⠀⠀⠀⠀⠄⠂⠅⠘⣷⡹⢦⡹⢆⡳⡹⢯⣿⣳⢿⣯⣟⡾⣯⡿⣽⢯⣿⣆⠀⠀⢀⣌⣀⠀⣸⣿⢯⣿⣾⡽⣾⣽⣻⣟⡾⣷⣻⣿⠀⠀⠀⠁⢃⡇⡁⠀⠀⠀⠸⠡⠨⠈⠀ ⠈⠀⠒⠀⡀⠀⠑⡄⠑⠻⣖⡹⣎⠵⣙⡼⠛⣿⣻⢾⣽⣻⣷⡿⢯⣿⣞⣿⡄⠠⣿⢯⣟⣿⡿⣯⡿⣽⣷⣟⡿⣞⣷⢯⣿⣳⣟⣾⡇⡄⠚⠉⠀⠁⡉⠑⢦⡐⠁⣀⣀⠀⣀ ⠀⠀⢠⠀⡀⠀⠂⠀⠀⠠⠀⠉⠊⠝⠁⠀⠀⣈⠿⠿⢾⠏⠀⠀⠀⠘⣿⣞⣿⣴⣿⣿⣾⣿⡽⣷⣻⢯⣿⣞⡿⣽⣾⣻⢷⣯⣟⣾⣗⠠⣀⠦⣙⠶⣩⢻⢤⡳⣭⠳⣭⢻⡜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢀⠤⢄⡀⠀⠀⣿⡿⣼⣟⣧⢿⡼⣧⣿⣻⣟⡿⣿⣟⡿⣿⣼⣻⢿⣼⣻⣼⡇⢧⣘⢧⢻⢼⢣⡟⣜⠧⣇⢿⡠⢇⠿ ⠀⠀⠀⠠⠀⣠⠤⢤⠀⣀⡀⡄⠀⠀⠀⠀⢃⠀⠀⢰⠁⠀⠀⠈⡄⠈⠙⣿⢷⣻⣾⣻⣽⢷⣯⢷⣻⣽⢯⣿⢿⣳⣯⣟⡿⣾⣽⡿⠜⣦⢹⡎⢯⢞⣣⡝⣮⢻⡜⣧⠻⣭⢛ ⠀⠀⠀⠀⠂⣧⣋⡌⢳⢡⢋⣤⠀⠀⠀⠀⠀⢱⡄⠘⢄⡀⢀⡰⠃⠀⠀⢸⣿⣳⣯⢷⣯⢿⣞⣿⣻⢾⣻⡽⣟⡿⣷⢿⣿⡓⠋⠀⠙⡦⣛⢼⢫⡞⣥⢻⡜⣧⡝⣎⢷⣣⢯ ⠀⠀⠀⠀⠀⠈⠳⢜⡣⢏⠖⠡⠁⡂⠀⠀⠀⣸⡀⠀⠀⠀⢀⣦⣤⣤⣴⣿⣳⣟⣾⢯⣟⡿⣞⣷⣻⢯⡿⣽⣻⣽⢯⣿⣞⣿⣄⠀⠀⠀⠜⣮⢳⡝⣮⢳⣝⡲⣽⡸⣎⠷⡫ ⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣰⣿⣷⢦⣤⣴⡿⣿⡽⣞⣷⢯⣷⣻⡽⣯⢿⣽⣻⢷⣻⢿⣽⣻⢷⣯⢿⡾⣽⢯⣿⡀⠀⠀⠀⠉⢷⡻⣵⣏⠾⣵⣣⠿⠘⠋⠀ ⠀⠀⠜⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣟⡾⣯⡷⣯⣟⡷⣟⣿⠾⠛⠓⠛⠛⠛⠛⠚⠛⠻⢽⣟⣾⡽⣟⣾⢿⡽⣯⣟⡿⡇⡀⠀⠀⠀⠀⠙⢳⠞⠛⠉⠀⠀⠀⠀⠀ ⠀⠈⢂⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡷⣯⣟⡷⣿⣽⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣯⣟⣯⢿⣳⡿⣽⡗⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⠀ ⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣳⢿⣽⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣟⣯⢿⣽⡇⠃⠀⠀⠀⡇⡀⠀⠀⠀⠘⣿⣻⣟⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣽⣻⡾⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢹⣟⣾⢯⣿⠁⠀⠀⠀⠀⠃⢣⠀⠀⠀⠀⠈⠻⠊⠁⠀ ⠀⠀⠀⠀⠀⡄⠀⠁⠀⢳⠀⠀⠀⠀⠀⠐⢻⣷⣟⣇⢀⡻⠭⠭⠭⡛⠀⠀⠀⠀⠠⣀⡄⠀⠀⠀⠰⢟⠩⠭⠽⡁⢸⡿⣽⣿⠃⠀⠀⠀⠀⠈⡆⡜⠀⠀⠀⠀⠀⠈⠂⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⡐⠝⣿⣻⣆⠄⠒⡐⠴⠃⠀⠀⠀⠀⢄⠀⡰⠀⠀⠀⠀⠧⠂⡓⠀⣤⣿⣿⡝⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢒⣠⣀⡝⠻⢦⣄⠀⠀⠀⠀⢀⣀⠀⠀⢀⡠⠤⢄⡀⠀⠀⠀⢀⣴⡾⠟⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠌⠐⠀⠘⠻⡿⠇⠀⠀⣼⣿⢿⡟⠉⠀⠀⠉⡖⠁⠀⠀⠀⠘⢶⣿⢿⡿⣧⠀⠀⠀⠀⠀⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣸⣿⣽⣻⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡿⣯⣟⡿⣧⠡⡀⠀⠀⠀⠀⠀⢀⠤⢀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⠚⠛⡄⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠘⠛⠛⠛⣿⣿⡇⠐⠀⠀⠀⠀⠐⢠⠒⣮⢻⣭⢳⡝⣶⢹⢻⡄⠀⠀⠀ ⠀⠀⠈⠀⠆⠁⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⡀⢤⣀⠈⠸⢿⣿⣄⠀⠀⠀⠀⠀⡠⠉⠢⡀⠀⠀⠀⠀⠀⢀⠔⢩⡛⠁⠀⠀⠀⠀⠄⢣⡹⢞⡭⣞⡽⣎⠷⣭⣛⣮⠃⠀⠀⠀ ⠀⠀⠠⠃⡆⠀⠀⠀⣠⠞⣭⢳⡹⢲⡰⣲⡔⢦⡀⠣⡄⠀⠀⡏⠑⠂⠒⠂⠉⠀⠀⠀⠀⠉⠐⠒⠒⠈⠁⠀⠰⡇⠀⠀⠀⠐⠄⢀⠘⢵⣫⢞⡵⣺⢭⡻⣵⣫⠎⠀⠀⠀⠀ ⠀⠐⠀⠁⠀⠀⠀⠀⣏⡞⢦⢣⡝⣣⢳⢇⣯⢳⡝⡄⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢀⠠⠡⠀⠄⡑⢻⣞⡷⣫⠗⠋⠁⠄⠀⠀⠀⠀ ⠀⠀⡀⢀⠀⠒⠁⠀⠳⣚⢥⠳⡜⣥⢛⣎⠞⡵⢮⡵⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠁⠀⠀⠀⠈⠄⠈⡉⠁⠀⠀⠀⠀⠀⠀⢠⣜ ⠀⠀⠈⠠⠃⠀⠀⠀⠀⠈⠛⢧⡝⢦⢫⣜⣫⡽⠊⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠧⠮⠃⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠃⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣸⠀⠇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⢿⡿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⢫⡝⢦⠳⡜⣭⢛⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⢣⠳⣜⢣⡛⡜⢦⢫⡜⢿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⡿⣙⢧⡛⣬⢣⡝⣜⢣⠳⣜⡹⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡷⣩⢖⡹⢆⡳⡜⡬⢇⡻⣔⢣⣿⣿⣿⣷⣠⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢱⡹⣎⠵⣋⠶⡹⣜⢣⠳⣌⠷⣞⣿⣿⣿⣿⡿⡻⢟⠿⣻⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⢦⣻⣌⠳⣍⢞⡱⢎⢧⡛⣬⢓⣿⣿⡿⢫⣍⢳⡙⣎⢳⡱⢎⡵⣻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠦⡿⣌⢗⣎⢮⡱⣋⢮⡕⣎⢧⣿⡿⣱⢣⢎⢧⡹⣌⢧⠳⣍⠶⣩⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡘⢷⡩⢞⡜⢦⡹⢥⡛⡼⣸⣾⣿⡱⢣⡝⣎⠶⡱⢎⣎⠳⣌⠳⣥⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⠳⣌⠳⣜⡱⢎⡳⣌⠳⣥⢫⣿⣿⢣⢎⡵⡹⢆⠷⣜⡹⢆⡛⢦⣙⢮⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣳⣜⡹⣦⣿⣾⣷⣮⣷⣌⢳⢺⣿⣗⡎⢶⡹⣍⠞⣦⡙⢮⣽⣿⢿⣋⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡿⠛⠛⠛⣿⡿⠛⠉⠁⠉⠙⣿⣿⡌⣏⠿⣿⣿⣦⣳⣌⣻⣴⣿⡿⢿⡙⢦⡙⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡟⠀⠀⣠⣶⣿⣧⣀⣀⣀⣀⣴⣿⡟⡼⣘⠞⡴⣛⠿⡻⢟⠿⡻⢭⡙⢦⡝⢮⡱⢾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣏⠀⣀⣼⣿⣁⣼⡿⠋⠉⠙⠻⣿⣷⣝⠲⣍⢞⡱⣍⢞⡱⣋⢞⡱⢣⡝⣦⢹⢦⡙⢦⡙⣿⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⢠⣼⣿⡿⠟⠋⠉⠙⣿⡏⠀⠀⠀⠀⠀⣼⡿⣌⠳⡜⢮⡱⢎⢮⡱⣍⢮⡱⢳⡜⣥⢋⡶⣩⢧⡙⢦⡹⢿⣿⣷⡀⠀⠀⠀ ⠀⢠⣾⣿⣿⡀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⣴⣿⡟⣬⢳⡙⢦⣙⢎⠶⡱⢎⠶⣩⠳⡜⢦⡛⡴⢣⢎⡝⢦⣙⢎⢿⣿⣿⣄⠀⠀ ⣠⣿⣿⣿⣿⡇⠀⠀⢀⣴⣿⢻⣿⣶⣶⣾⣿⣿⡿⠾⠷⠿⠷⠿⠾⠿⠿⠿⢿⣶⣽⣜⣣⠝⣜⢣⠞⣜⢣⠞⡜⣎⢻⣿⣿⣄⠀ ⣿⣿⡟⡭⢿⢿⣶⡾⣿⣛⢦⣷⣾⠿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠿⣿⣮⣧⢛⡬⢣⡛⡼⣌⢏⣿⣿⣿⡆ ⣿⣿⡟⣜⢣⠞⡴⢣⢧⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣜⡣⣝⠲⣍⠞⣾⣿⣿⡇ ⣿⣿⣟⡬⣇⠻⣜⣳⡿⠋⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⢿⣷⣎⠳⣌⠯⣽⣿⣿⡇ ⣿⣿⣧⠳⣌⠗⣾⣿⠁⠀⠀⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⡄⠀⠈⢻⣯⢳⣌⠳⣿⣿⣿⡇ ⠘⣿⣿⡿⣌⢏⣿⣿⠀⠀⠀⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡃⠀⠀⣸⣿⢣⢎⣽⣿⣿⡟⠁ ⠀⠈⢿⣿⣗⢮⡜⣿⣦⠀⠀⠹⣿⡿⠟⠀⠀⠀⠀⠀⠀⣾⡿⠿⣿⣆⠀⠀⠀⠀⠀⠙⣿⣿⠟⠁⠀⢠⣿⢯⢇⣿⣾⣿⠟⠀⠀ ⠀⠀⠈⠻⣿⣷⣮⡝⢿⣷⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟⠋⠀⠀⠀⠀⠀⠐⠋⠁⠀⢀⣴⣿⠟⣮⣾⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⠻⣿⣿⣾⣽⣿⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣽⣾⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡿⢿⡻⢟⡿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿⡿⢿⠿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣵⣣⠝⣎⠶⣩⠞⣭⢻⣿⡇⠀⠀⠀⠀⢹⣿⡩⣍⢧⢣⢳⡙⣎⢳⣭⣻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠿⢿⣷⣿⣴⣯⣶⣿⣿⠇⠀⠀⠀⠀⢸⣿⣷⣼⣮⣧⣧⣿⡾⠿⠻⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⠛⠉⠁⠀⢀⣶⣌⣉⣉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⡉⣉⣷⣄⠀⠈⠉⠙⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣸⣿⠿⠿⠿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠷⠿⢿⣿⡀⠀⠀⠀⣽⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⡀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠉⢻⣦⡀⠀⠀⠀⠀⠀⣠⣾⠏⠁⠀⠀⠀⠀⠘⢿⣄⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣀⣀⣠⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣤⠀⠀⠀⣀⣤⣾⣿⠟⠈⠉⠀⠀⠙⠛⢿⣦⣄⠀⠀⠀⣠⣴⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⣰⠋⠉⠀⠀⠈⠉⠑⠲⣌⣧⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡀⠀⠀ ⢠⣖⣶⣤⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⢀⣀⣀⣀⣠⣇⠙⠗⡀⡀ ⠀⠈⣿⣿⢛⢻⣿⣄⠀⠀⠀⠀⠀⢀⡀⣀⣰⠴⠛⠉⠉⠀⠀⠀⠀⠈⠙⠲⣄⠉ ⠀⠀⢿⣿⠨⡇⡝⢿⠳⣦⣄⣀⣀⣏⡭⣯⠀⠀⠀⡀⠤⠒⠊⠉⠁⢈⡽⠐⢌⢣ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣏⠠⢿⡟⠛⠋⡠⠐⠁⠀⠀⠀⠀⠀⠴⠯⠤⢔⣐⠹ ⣄⠀⠀⠈⠙⣻⠟⣿⢻⣹⣿⠷⣾⠁⢀⠌⠀⢀⣀⠀⠀⠲⣛⣀⡀⠀⠀⠀⠀⠀ ⢿⣆⠀⣠⣾⠷⠆⠀⣨⣿⠏⠀⢧⠀⡈⠒⠛⣹⠏⠀⢠⣮⢥⡼⠉⠉⠲⡀⠀⢰ ⢸⢿⣾⢫⠍⣩⣿⠿⠟⠛⠀⠀⡿⡄⢡⢘⡹⠁⠀⠀⡞⠀⠀⢳⠀⠀⠀⢹⣴⡃ ⣬⣿⣿⡗⠋⠁⠀⠀⠀⠀⡴⠎⠀⠘⢶⣣⡀⠀⠀⠀⡇⠀⠀⠈⣧⠀⠀⠀⢧⡙ ⣿⣿⣿⡇⠲⢾⣿⣦⠀⠀⠀⢀⣠⢃⣠⠞⠻⢗⠒⢺⡇⠀⠀⢸⡏⠣⠀⠀⠀⢱ ⠀⢹⣿⣇⠀⠀⠙⠛⠁⠀⠉⠉⠀⢯⡀⢲⣭⢿⡁⣲⡇⠀⠀⠠⠇⠀⠀⠀⠀⢸ ⠀⠈⢷⣿⣆⠀⣎⡠⠀⣀⣀⣀⠀⢀⠝⠉⠀⠀⡹⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢀⣀⣀⡙⢻⣷⣶⣟⣿⠹⣿⣿⡟⠁⠀⠀⢀⡴⡣⠓⠁⠀⠀⠀⠀⠀⠀⠀⢠⠃
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⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡸⠁⢰⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠂⠄⠀⠁⠀⡲⠀⡠⠀⠀⠆⠘⠄⠀⠀⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⠀⢠⠂⠐⡄⠢⡀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⠘⠤⠠⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡛⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀ ⠀⠀⠎⠙⣯⠃⠀⠀⢀⠤⠐⠊⠉⠉⠉⠁⠒⠠⢀⠀⠀⠀⠀⢃⠀⠀⠁⠀ ⠀⠀⠀⠈⡧⢮⢛⢖⣴⣦⠀⠀⠀⠀⠀⠀⠀⣴⣦⡑⡀⠀⠀⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠩⢀⠿⣸⣿⣿⠃⠀⠀⡀⡀⠀⠀⣿⣿⡇⡸⠄⣠⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⡐⠁⠀⠀⡆⠀⠀⠀⢰⠒⠂⠀⠀⠀⠀⠜⠀⠀⠈⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⡅⠀⠀⠀⡷⠂⠀⠄⠀⠠⢀⠀⠀⠐⠒⣡⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⢡⠀⠀⠀⠈⠦⡀⠀⢠⠆⠘⡄⠀⠀⠔⠉⠀⠀⠀⠌⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠄⠀⡐⠀⠉⠒⠂⠀⠀⠈⠒⠊⠀⢃⠀⠠⠂⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⡀⢀⠠
⡄⣈⡳⠀⠀⠀⢠⠎⠁⠀⠉⢣⡈⠈⡹⠿⠍⠩⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡯⠒⠛⢕⠄⠘⠀⠀⠀⠀⠀⢣⠀⣾⡏⠉⡇⡍⣏⣿⡿⠋⠁⠀⠉⢿⣿⣿⣿ ⡟⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠸⡄⣿⣇⣀⣇⡁⣟⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠧⣢⠤⢤⣪⠆⢸⠀⠀⠀⠀⠀⠀⣧⢹⣿⡟⠛⢻⡏⠀⠀⠀⠀⠀⢀⡿⢿⣿⣿ ⠀⠀⠀⠈⠁⠀⢠⠆⠠⡔⠁⡄⠀⡷⠒⠛⠉⠉⡙⠀⠀⠀⠀⠀⠀⣜⠤⠤⠁⠀ ⠀⠀⠀⠀⠀⠀⢸⣦⢎⢀⠍⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⠟⠤⠌⠁⠉⡠⠐⠒⠢⢄⠀⠀⠀⠀⠀⠀⢾⡸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣠⠮⠄⠒⠒⠂⠠⠍⣦⡀⠀⠀⠀⠀⢻⡈⠂⠀⠀⠀ ⠀⠀⠀⠀⢀⡜⠀⠀⡠⢊⣤⡀⠀⠀⠀⠀⠀⢀⣤⣅⢄⠀⠀⠀⠈⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠁⠀⠔⠀⣿⣿⡇⠀⢠⡄⠀⠀⢸⣿⣿⠆⢢⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢆⠘⡄⠀⠈⠉⠀⠀⢀⡀⠀⠀⠀⠉⠉⠀⡌⡇⠀⢀⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⢌⠲⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠔⢀⠴⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠗⠦⣉⠀⡲⠲⢖⠒⠒⢀⡥⠮⠊⠁⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠆⠉⡆⠉⠉⠁⠀⠀⢣⠐⠊⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⡔⠛⡄⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⢠⣴⡟⠁⡀⠆⡐⢈⠌⡐⠠⢈⠂⣁⠂⡐⡇⠀⣿⣿⡇⠀⠀⠀⠘⠻⠶⠿⠋⠀⠀⢐⣿⣿⠃⡐⠀⢂⠡⢈⠐⠈⠶⣯⣴⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡐⢈⠀⠌⠐⡀⠄⠡⠌⣿⣧⠀⠀⢰⠰⠀⠀⠙⣿⣿⣿⡟⠁⠀⠀⠀⠀⠉⠿⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡿⠋⢀⠂⡐⠠⢁⠢⠐⠠⢁⠂⡡⢀⠒⡀⠅⢂⢸⡿⣿⣄⠀⢀⣠⡄⠀⠀⠀⠀⠀⣸⡿⢆⠡⠠⢁⢂⡐⠠⣸⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠙⢿⣶⡌⢀⠂⠄⡐⢀⠂⢼⣿⠄⠀⠸⠀⠀⠀⣼⣿⣿⠟⣦⡀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢦⣀⡀⠀⠀ ⠀⠀⠀⢀⣴⠟⠀⡀⢂⠐⠠⢁⠂⡰⢉⠐⠂⠌⡐⠠⢂⠐⡈⠄⡀⠡⢈⣿⣿⣿⣿⣄⡀⠀⣀⣠⣾⡿⢃⠌⡀⠂⠄⣀⣤⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠉⢿⣦⠈⠠⠐⠠⠀⠌⣿⡇⠀⢀⠀⣄⣼⣿⣿⠏⠀⠈⠙⢷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦ ⠀⠀⣠⣿⠋⠀⢂⠁⢂⠌⡐⠠⠘⡀⠆⡘⠠⠁⡄⠃⢄⢂⠐⠠⠐⢠⣶⣿⣿⣿⣿⢿⣿⣿⠿⠛⡍⢀⠃⡐⠢⢁⣼⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠻⣧⡑⠈⠤⢁⠀⣿⡇⠀⠚⢀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠉⠙⠣⠄⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠃⢀⠐⠠⠌⢂⠐⠠⡁⢁⠢⠐⠠⢁⠂⠄⡁⠢⠀⠌⢠⣸⣾⢿⣿⡿⢹⣇⠢⡌⠐⡀⢃⠰⢀⠐⡀⢂⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢹⣧⠁⡀⠂⠀⣿⡇⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀ ⢠⡟⠁⡀⠂⠌⠒⡈⠄⡘⠠⠠⢁⠂⠡⢁⠂⠌⡐⠠⠑⠨⣰⡷⠿⣧⣿⠏⠀⣿⠇⠰⠤⢁⠠⢀⠆⠈⠐⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⡆⠄⠁⠠⣿⡇⢠⣿⣳⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⣀⠀⠀ ⡿⠁⠠⠁⡌⠠⠁⠄⢂⠐⠠⢁⠂⠌⡐⠠⢈⠐⠠⠁⣌⣳⣷⣾⣿⣿⢋⣀⠀⣿⠀⢂⠐⠠⠀⠌⢂⠁⢲⡿⠁⠀⠀⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠹⣱⣿⣧⣿⣳⡟⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀ ⡗⠀⡀⢣⠠⢁⠘⡀⠂⠌⢀⠂⠌⡐⠠⢁⠂⡉⢄⣣⣶⣿⣯⣾⠟⠁⠀⠀⠀⣿⠌⠠⠌⠠⢁⠂⡄⣸⣿⠁⠀⢀⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣿⣿⣿⣽⠏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠁⡀⠄⠂⠄⡈⠄⡁⠂⠄⡈⠐⡄⢁⠂⢄⢳⣼⣿⣿⣿⠟⠁⠀⠀⢀⠀⣀⣿⡇⠐⡈⠐⢢⠀⠼⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢀⣼⣿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢁⠐⠌⡐⠠⢈⡐⠠⢁⠂⠄⢁⠐⢤⣸⣾⣿⣻⣿⠟⢁⡀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢀⠁⠂⠌⣸⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢞⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣁⣼⣿⢫⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⡄⢈⡐⠠⠁⠆⠠⠁⠀⡈⢔⣢⣾⣮⣻⣷⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠌⡐⠃⣽⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠽⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣿⣣⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣷⣦⡐⠠⠁⠌⡐⢌⣂⣱⣿⣿⡿⠟⠉⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡈⠐⠠⠀⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣟⣩⣿⣻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠛⠿⠿⠿⠿⠿⠟⠛⠋⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠁⢢⠁⢻⡇⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠁⠀⠀⠈⠙⠻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠠⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⠡⠀⠀⠀⠀⠻⣷⣀⠁⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣤⡀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⡿⡟⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣏⢾⡱⣟⡿⣿⣿⣿⣿⣿⢟⡹⣛⠻⡛⢽⠻⡿⢯⣿⣫⣝⡻⠛⠭⡙⠆⠆⡑⣎⡷⢘⢯⠛⣿⡽⣿⣿⣌⠛⢶⣤⡀⢞⠻⣟⣦⡘⡀⢩⢯⠁⠀⣰⠧⠔⠊⠉⠁⡀⠀⠀⠄⠠⠀⠄⠠⠀⠄⢀⠂⠠⠀⠄⢀⠂⠄⠠⠐⠠⠉⢈⠉⠡⠁⠀⠄ ⡽⣹⢻⠿⣿⢿⣿⣿⣿⣿⣿⣭⣿⣿⣾⣽⣳⣝⣾⣱⣭⣾⣿⣿⣿⣿⠟⢦⠱⣌⣣⣭⣆⡣⢛⣿⡭⡙⣿⡐⢩⣂⣥⣼⡶⠟⢋⠱⠊⢊⠱⢬⣣⡙⢷⣯⣷⣿⣦⠇⠨⡀⢌⠠⠡⢤⠟⠊⡀⠀⠀⠀⡀⠐⠂⠐⠀⠂⠐⡀⠂⡐⠀⠂⠔⠂⠀⠂⠐⠂⠐⠂⠐⠀⠂⠂⠐⠐⠀⠂⠐⠐⠂⠆ ⣝⣣⢯⢻⡵⣏⡶⣳⢽⡺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣌⠻⣄⠣⢛⢽⣶⣝⢷⣬⣿⢿⡔⢻⣧⠒⠉⠁⣀⠂⠤⢃⠘⡑⡈⠄⠻⣇⠧⣌⢁⠭⠀⡄⠠⢀⠂⠌⢌⠸⡵⡀⠂⢀⠂⠀⠂⠐⡈⠄⠠⠁⡈⠐⡠⠁⠠⢁⠈⠄⠠⠈⠐⠀⠂⡀⠂⠀⠁⢈⠀⠈⡀⠐⠀⠀⠀⠀⠀ ⢧⣓⢯⢳⣞⡱⡷⡹⣎⢽⢣⠯⣽⣻⣿⢿⣿⣿⣿⡿⡿⢿⣫⠅⣏⠰⡱⢌⢲⣉⣌⣿⣯⢿⣾⡿⠼⡟⢋⡥⠶⣒⠩⠥⠴⢿⣎⣤⠴⠟⣀⠂⠌⠛⠖⣒⠦⠅⠀⡋⢀⠐⠈⠐⡄⢳⡜⣦⣁⠠⠁⡐⠠⠀⠄⠀⠂⠄⠆⠡⠄⠐⠂⠡⢂⠐⠀⠡⠀⠂⡀⠄⠀⠀⠀⠠⠐⠀⠀⠀⠂⠀⠀⡁ ⢞⡬⢧⢏⢶⣻⣵⣯⣙⠾⣿⣟⡟⣿⡭⢣⡓⢮⣱⣭⣷⠗⣰⣛⡿⠁⠍⣋⣍⣚⣼⣹⣿⣏⣏⣡⠤⢺⣽⠬⠗⣉⣥⣴⣾⠽⡶⢶⣦⣤⣤⣊⠌⡌⠰⢀⠢⢀⠒⢀⠄⠈⠀⠄⠈⠢⢝⠢⣽⡳⣦⡀⠡⠀⢂⠁⠄⠠⠀⠁⠠⠁⢂⠠⠀⠐⠀⡁⠐⠀⠀⠄⠐⠀⠁⠀⠀⠄⠀⠀⡀⠀⠀⠄ ⣮⡙⣎⢞⡻⣿⣿⣽⣿⣜⣿⣿⡷⣸⣿⡱⢜⡛⢿⣿⣿⡿⢟⡱⡔⣂⠨⢍⠖⠣⢢⢙⡒⢎⠒⠒⠊⣉⢰⣴⡾⠟⢩⠐⠠⠒⡈⠢⢐⡈⠍⠻⢿⣦⡂⠄⡁⠂⡀⠢⠠⠓⠺⠶⢶⣦⣅⡛⠤⣛⢮⡟⢷⣤⣄⣈⠐⠠⠄⠁⢂⠀⠂⠀⠂⢈⠀⠐⡀⠈⠀⠄⠈⠐⠀⠠⠀⠀⠀⠁⠀⠀⠀⠂ ⡶⡹⡜⢮⡱⡝⣿⣿⢷⣏⣿⠳⣿⡔⢿⣷⢨⠞⡲⣬⢇⢜⣽⣿⣧⣉⣄⣤⣾⠿⠛⣟⠻⡛⠿⠾⣦⣴⡾⠋⠔⣉⠰⡈⢡⠑⡌⡑⢢⠐⡌⠂⢆⡉⢻⣷⡰⠡⠈⢆⠡⢊⠡⠐⡠⠀⢍⠛⢷⣮⡒⠮⣗⡲⢭⣟⣛⠳⡶⢶⣤⣌⡐⠀⠌⠠⠀⢂⠀⠄⠁⡀⠀⠄⠀⡀⠠⠀⠠⠀⠈⠀⠀⡃ ⢷⡱⡝⢮⡱⢭⣹⣿⣎⠿⣟⠱⣻⣿⡘⣿⣶⣍⣷⢣⣚⡾⠟⣉⣷⡿⢫⠍⢢⠱⠱⣠⠓⡭⢌⠱⠌⡩⠤⣉⠒⡌⠰⡁⢆⠣⡐⣁⠃⡔⢂⣩⣀⡒⠤⠐⠤⡁⢍⠰⢈⠂⢢⢁⠂⡉⠄⡀⠂⡈⢿⣆⠊⢉⠋⠖⡫⢭⠽⢟⡲⢭⣿⢷⣦⣄⠡⢀⠈⠀⡀⠄⢂⣀⠐⡀⠀⠀⠁⠀⠐⠈⢀⡁ ⢧⡛⣜⣣⠽⣑⣮⣿⣿⣷⢎⡳⣴⣿⡿⢞⡿⣛⢥⢫⢏⡜⣩⣿⠟⣈⢇⡚⡄⡋⠵⡰⣍⠲⡌⣃⢎⡑⠦⡑⠬⣐⠣⡙⡄⠓⢌⣢⣶⢿⣛⢯⢿⣻⠿⣷⣬⡐⢊⠌⣃⣬⣴⣦⣴⣥⣔⡂⠌⡐⠀⢿⣧⣤⣮⣶⣶⣦⣬⣐⡃⠧⢌⡙⠺⣝⡷⣤⠈⢀⠐⢰⠟⡉⠷⣄⠂⠀⠁⠀⠈⠀⠀⡃ ⣧⡛⡴⣍⠾⣡⡛⡵⢣⣎⡝⢦⣧⠚⢛⣘⣢⠧⢚⡱⣉⢶⣿⡃⠳⡌⢦⡑⢦⠙⡴⡑⢦⡙⠴⣡⣦⣱⣼⣬⣑⢢⢡⠱⢨⢩⣶⢿⣡⣧⣫⠮⠗⣭⢛⣶⣟⣟⣿⣿⡻⣝⣳⢾⡷⣯⠽⣻⢷⣬⣀⠊⣁⢂⠂⠄⠄⡐⠨⢍⠩⡐⢤⣎⠱⢈⠳⣟⣷⡀⠀⡿⠈⢄⠃⠺⣽⣦⡁⠀⠐⠈⠀⡁ ⢧⣝⢳⣜⢻⠴⣍⣳⢣⣶⠾⣛⡤⢖⣋⡭⠪⡜⣃⣦⣡⣿⡇⣎⠵⣉⢦⠙⡦⢹⠰⣉⠦⣩⢚⣾⣟⡿⣿⣿⣟⣯⣿⣿⢷⣟⣿⣎⠞⡋⠤⢉⠒⡄⡉⢲⣹⣾⢿⣝⡯⢛⠟⠏⠖⢯⣺⣵⡿⣼⣿⣆⣡⢶⠶⣾⢶⣬⣄⣂⠆⡙⠠⡙⣿⣧⣦⡼⢯⣱⣠⡷⣴⡌⠒⢉⢖⣈⣳⣄⣂⠈⠐⠀ ⡞⡝⢮⣙⡞⡴⡝⡭⣮⠏⣔⡫⢳⢜⢉⣥⣶⣷⢿⢻⣛⢏⣱⡉⢦⡹⢌⠶⢡⢎⠲⣍⠦⣩⣾⡿⣽⣳⠿⠟⠿⢿⣿⣿⢾⣿⡻⠋⡔⢡⠂⡜⢠⠡⡑⡼⢋⢹⡞⢛⡡⢊⠐⣂⠂⢌⢉⡉⠳⢿⢿⣽⡯⣜⡦⢏⠾⣝⡛⢿⣆⠑⢂⠱⡍⢿⣯⢥⡸⣏⣯⡱⠛⣇⣀⣬⡸⠝⠭⡻⣿⣶⠀⠀ ⢽⣹⣣⢽⡘⣧⢫⡷⢣⢛⡴⡝⢣⣾⣿⠛⡕⣎⠜⡲⢌⣎⠲⡩⢖⠩⢎⢥⠣⢎⡳⣈⠖⣽⣿⣻⡭⡑⢊⡑⣊⠔⢢⡇⠭⢄⡢⠑⢌⠰⡈⢄⠃⠆⣼⢃⠌⢢⡇⢂⡐⠠⠃⠄⡘⠀⠆⣰⡇⢊⢛⠛⠖⣭⢾⠋⠞⡲⣿⡯⢿⡍⠄⢂⠐⡈⣿⣧⡟⣭⣳⣻⣯⣄⠙⢢⡐⠉⠲⠡⣟⡏⠐⠀ ⢧⡳⢞⣲⣙⢮⡽⡝⣽⢎⣳⢩⣿⡟⣲⠹⡜⢬⢭⢣⡛⣬⠳⣙⢎⡣⣍⢆⣏⣦⣵⣬⣾⣿⡿⡽⠤⡉⢦⠑⡌⠸⣈⣧⠱⢂⢷⡉⢢⠑⠂⣌⠘⠤⠉⠎⠌⣼⢇⠢⠄⢃⠑⢂⠑⡨⢢⡟⢨⠐⠄⣼⠟⠡⣸⡏⡐⢀⠛⣴⢻⣷⠨⠐⠤⠁⣸⣿⠙⢿⣷⡛⢻⣽⣿⣦⡈⠑⢦⣴⠟⠀⢀⠀ ⢯⡝⡯⢶⡹⡾⣏⣽⢹⣚⡴⣿⡟⡔⣣⢣⠝⣎⡞⣱⡝⣦⢛⡜⣪⣵⣾⣿⣟⣿⣿⣿⣿⣟⠿⣥⡓⠜⡠⢃⢌⡱⠠⣟⠒⡡⢚⣧⣡⣌⣥⣤⣮⣤⣵⣬⣦⣯⣤⣌⣌⣀⣪⠀⢂⢡⡿⢁⠂⡌⣬⡿⢶⣧⣏⠠⠐⢠⠐⡘⣦⢿⣷⣕⡠⠑⡸⠿⠶⢿⣦⣿⡻⢷⣽⢫⡿⢧⡐⠀⠀⠄⠂⠀ ⣟⡼⣓⢯⣓⢷⡿⡼⡷⢮⣽⣿⡜⡥⢣⢮⡹⢮⡱⢗⡞⡱⢮⡽⣾⣿⣻⣿⣿⣿⣿⠻⠽⣏⡔⡌⠽⣆⣑⣪⣴⣴⠿⡟⢻⡐⡩⠍⠭⡐⡌⢢⠑⡌⢄⠣⡌⠡⣉⠩⠍⡙⣙⠛⠿⠾⣷⣦⣥⣼⠟⢤⢃⡌⠻⢶⣜⡀⢂⠂⢿⣿⣾⣻⣿⡿⣶⣶⣐⠄⠂⡙⢻⣾⣏⠠⠙⢮⡽⡄⠠⢀⠀⠀ ⡾⣱⢏⣞⣽⣻⡜⣳⡟⣭⣻⣿⡶⣩⢓⠮⣵⢳⡹⢞⡼⣱⠳⣎⢿⣷⠟⣍⠱⣂⠦⡙⢴⠝⣾⣼⣼⠿⢛⠫⡑⠦⡉⢴⠁⠦⡑⡘⠤⡑⢌⠂⠥⡘⢠⠒⠄⢃⠰⣀⠒⠡⣀⠁⢒⠠⠌⣈⣽⠯⡘⡤⠣⡔⡡⠌⠛⣿⣄⠡⢈⣼⠿⣽⣿⣿⣿⢾⣛⣷⡈⠠⠄⡈⢿⣧⠡⠈⣷⡹⡀⢀⠀⠀ ⡳⣝⣾⣾⣣⢿⣼⡓⣞⣵⣿⣿⣗⢣⠯⣝⡲⢏⡽⣚⢼⢣⡟⣬⣛⣿⣮⣐⠳⣈⠖⣩⣶⠿⡛⢍⡒⠜⡌⢣⠘⡤⠉⢆⣙⢀⢃⣑⣂⣑⣂⣃⣒⡐⣁⡂⡊⠄⠡⠐⡈⠡⠄⠌⡐⠠⠒⣼⠧⢏⡔⣣⢣⡘⢔⡘⢂⠌⢻⣼⡟⠁⢂⡉⢉⡉⠛⢾⢟⣹⣇⠠⢁⠂⠌⢻⣷⡁⠈⣧⢳⠀⠀⠀ ⣝⡾⢿⠿⣿⣖⣷⣿⣿⢿⣙⡖⣮⢫⢯⠵⣛⢮⢳⡹⢎⡳⡞⡭⣞⢽⣿⣶⣱⢬⡾⡟⣅⣓⣼⣦⣼⣶⢾⡶⠿⠟⢿⢛⣛⡛⢻⢛⡛⡛⡝⢻⢙⡛⣛⢛⡛⠿⢿⠳⠶⠳⢊⠔⢄⡡⣼⡿⢸⢢⠱⡎⡔⣿⢛⡻⣦⣌⣿⡙⡛⠿⣶⣤⣐⠠⢁⣂⣼⡿⡁⠢⠁⡌⠄⡂⢹⢴⢈⢹⢫⠀⠐⠀ ⣿⣾⣿⣿⣾⣻⣿⡿⣓⢮⣚⡼⣵⡛⢮⢏⡧⢏⡶⡝⡯⣕⣫⢗⡭⢖⡳⢾⡵⡿⣟⣻⢻⡹⢭⡙⡲⢬⡒⡵⢩⡝⢢⡃⢦⡘⢣⢢⡰⠥⣘⠆⣃⢆⡑⢆⠱⠌⢆⡱⢨⢓⢊⠌⢆⠂⣿⡏⢦⣉⠖⡱⠚⣩⠻⢶⣮⡿⢧⢣⡙⢆⡒⢌⣻⠟⡟⢋⡝⢛⢙⠻⠻⠶⣦⣅⣎⣎⠘⢸⣯⠀⠀⠀ ⡿⣽⣾⣿⣿⣿⡟⡼⢱⣎⢧⡳⢮⡝⣫⢾⣱⢻⢼⡹⢵⡫⡞⣭⠺⣭⡙⢦⡣⡝⣢⡕⣦⠫⢦⡙⡱⢣⠱⣊⢓⡜⢢⡙⢆⡙⠲⣈⠴⡑⣢⠩⠔⡒⣘⠢⡙⠌⢥⡘⢢⡐⠭⡈⠦⡙⠾⣿⣤⣬⣈⣅⣚⣀⣡⣨⣞⡝⢆⠳⡨⠱⡈⣽⠏⣼⣈⡶⢠⡃⢌⡐⠆⠱⡀⣽⣿⡟⠠⠸⡟⠀⠀⠀ ⡿⣷⣿⣶⣿⡿⣍⢜⡳⣬⠳⣍⠷⣚⡵⢳⢮⡟⣮⣝⣣⢷⡹⢎⡷⣡⡟⡼⣱⡹⡔⡞⡴⣙⢎⡜⣱⢣⠳⢥⢣⢎⣃⠞⡬⣘⠣⡜⡰⢅⠲⡑⢥⡑⠦⡑⢜⡨⢆⠸⡐⢌⡒⡑⡰⢁⠦⠘⢌⣁⢋⠭⢩⡉⡡⢘⠙⣻⢾⣇⣅⠣⣼⠟⣯⣴⣫⣽⡇⡜⣠⠑⢊⠤⣱⣿⣿⠣⠂⢀⣗⠀⠈⠀ ⣿⢷⣯⢿⣿⡷⣘⢮⡱⢎⡳⣍⢯⡱⡞⣯⣙⢮⣓⢮⡵⡞⣭⢳⣙⢦⡝⡲⡥⢳⡜⡭⠖⣭⢚⡜⢦⠣⡝⡎⣜⠲⢌⡚⡴⢡⢋⠴⡡⠎⡥⢙⠢⡜⡰⡉⢆⡐⣊⠱⡈⠆⣐⢂⠡⠡⠥⡉⠢⡔⠨⡈⠦⠐⡂⢅⠒⠠⡙⢋⠽⡿⣿⡠⢇⠮⢭⢹⢠⠍⡤⢙⠄⣢⡿⠻⣿⣦⡡⡀⢿⠠⠀⠀ ⡭⣞⠾⣽⣿⣿⢎⢧⡹⢎⡵⣊⣶⣿⢿⢫⡵⢫⡞⣏⡞⡽⣎⠷⡭⡞⢞⢧⣋⠷⣘⢧⡛⡴⣋⠼⣡⠛⡴⣍⠶⣉⢇⠳⡌⢇⡚⠵⡑⣙⠰⣃⠚⠤⡱⢌⡒⠌⡤⢃⡘⡐⣂⠊⠆⠫⣀⠋⡔⡠⣑⠐⡡⢃⡘⢂⢁⠓⠌⠆⡜⠠⢛⣿⣄⡱⣈⠖⡡⢊⡐⢂⣼⡟⢁⠂⠌⣿⣧⠀⠸⣇⠂⠀ ⣷⢫⢿⣱⢿⣿⢎⢮⣼⣵⣿⢟⡻⣌⡻⣜⡺⢭⢞⣱⢾⡳⣭⣛⡵⢏⢯⣒⢏⡞⡭⡖⣭⠳⣬⢳⣩⡝⡲⢌⠶⣡⡎⡳⣌⢣⡙⡔⢃⠎⡱⢢⡙⡰⣉⠔⡌⡒⣐⠢⠔⢡⢄⠊⣌⠱⡀⠎⡐⡡⠐⡌⠔⢡⠐⣂⠊⢔⠈⡆⠰⢉⠂⣅⠻⣷⣄⠒⠄⢡⣴⡿⢋⠁⡊⠄⢂⠘⣿⠆⡀⢿⡀⠀ ⣭⢧⡻⣜⣯⣿⣷⣿⡿⢫⣜⢣⡹⢆⡷⢣⡽⣝⣾⣟⡫⢞⡵⣋⢷⢫⡗⣫⢎⡳⣝⡜⡲⣝⢢⠳⠴⣜⠱⣉⠖⡥⢒⠵⠸⡰⢱⡘⡉⢎⡌⢃⡜⠰⡐⣌⠒⡡⢂⠕⢌⠃⡌⠌⠤⢃⠜⡐⠌⡐⠡⡘⠄⡅⡘⠤⢈⠂⢊⠄⡱⣈⠒⢠⠂⡍⠹⢷⠾⠟⡉⢢⠠⠁⠔⢈⠀⠂⣿⣇⠠⢸⠄⠀ ⣯⢞⡵⣏⣾⣿⡟⣯⣙⠳⣬⠳⣍⡗⡺⢏⣶⣿⡿⠼⣍⡟⣴⢫⢯⣧⢻⡱⣋⢧⠳⣜⠳⣬⠣⡏⠵⡌⡗⡡⠞⡌⢇⠺⡱⢡⠣⣐⢛⣦⠘⠤⢊⠕⡰⣀⠓⡈⠥⢪⠈⡜⢠⢉⠣⠔⠢⡑⢌⡢⠑⣨⠐⢂⡑⠤⠡⢘⡀⠎⡐⢄⡘⢄⠢⢡⠉⠤⠙⡈⠰⢀⠂⡉⢐⠈⠄⢂⣿⡧⢀⠸⠌⠀ ⢧⡟⣽⢾⣿⡻⡜⣦⢫⢳⡍⣷⢚⣽⣳⢯⣿⡿⣍⣻⢬⡻⣜⣫⢳⡜⢧⣹⣽⡊⢗⡭⢓⡴⢩⢲⢣⣼⡟⣐⣣⣜⣬⣑⣄⣣⣴⣾⠟⡻⣷⣎⣈⠄⠅⠤⠃⢌⣂⣥⣧⠰⢄⠂⠥⢊⠑⡨⡐⢠⠡⠄⠊⡄⠌⢄⢃⠤⠁⠆⡡⢂⠰⠠⠌⢡⠉⢌⠰⠁⠆⡁⠢⡁⠄⠡⠈⣼⣿⢁⠂⡍⠀⠀ ⢿⡜⣯⣿⢣⡳⡝⡖⡯⢧⣛⢦⢏⣾⣹⣿⣿⡳⢇⡗⣮⢓⣳⣏⣳⠞⡵⢣⣮⣽⣊⣴⣩⣴⣷⡾⢟⠱⡘⢤⠈⠭⠹⠛⢛⡩⢩⠀⢣⠐⠌⡙⢛⠿⢿⠿⠿⠟⢛⠋⠻⣿⣄⠊⠔⡁⢊⠰⠐⢂⡁⢣⠉⡄⢃⠆⠢⠐⣉⠒⣀⠃⡅⢂⢉⠰⡁⠆⡉⠆⠰⣷⣅⡐⠈⠅⣲⣿⡗⠂⣰⠁⠐⠀ ⣟⢾⣿⡇⣧⢛⣞⡹⣝⠧⡞⣭⡿⣼⣿⡿⡸⣝⠮⣝⡖⣯⢕⡮⡥⢟⠬⣛⣿⡝⡛⡟⡛⢭⠚⡌⢣⠃⡜⢠⡙⠢⢍⡘⠤⢢⠱⠈⢆⠉⠆⡈⠆⡰⠠⠌⢂⠔⣀⠊⠡⢈⠣⠌⣤⣴⣆⣆⣁⣦⣴⠀⠆⡑⢈⠤⣁⠣⡀⢢⡐⡰⠠⠌⢸⣇⢐⠢⡐⠂⠔⡘⠻⣷⡅⢾⣟⠷⠡⢲⠧⠀⠠⠀ ⣞⣻⣿⡝⣦⢛⡬⢟⣜⡫⣜⣳⣾⣿⣛⠶⣭⢣⡟⡼⣹⣌⢯⡱⢭⢣⢇⣿⡿⣡⢣⠱⣉⠦⢍⡜⣥⣧⣬⣡⠌⡑⠢⠜⡠⡁⢆⡉⢆⡘⠠⡑⡐⠄⡑⠈⡄⠂⠄⠌⠠⢁⠢⠐⡈⢉⠛⠛⠛⢹⣿⡂⡁⠆⡁⢢⠀⣂⠌⡁⡐⠤⠑⡨⢸⣿⠈⡐⢠⠉⠢⡐⢈⠙⣿⣧⠘⡌⠴⢸⢳⠀⠀⠀ ⣽⢳⣿⣿⣶⣭⣚⣭⣲⣽⣾⣿⣛⢦⠯⣝⢮⢳⢺⡝⡲⢎⡞⣱⢋⣯⣿⠿⡑⢎⢎⡱⢌⡚⣦⣿⣿⣿⣿⣿⣆⠩⡑⢢⠑⡌⠰⡐⢢⠐⡡⢒⠀⡒⢌⠐⠠⠈⠆⡘⠀⠆⡁⠂⠔⠂⠌⠠⠈⢀⠻⣷⣄⢡⠐⢂⠢⡀⠌⠒⢌⠂⠥⠐⢸⣿⠆⡂⡁⠎⡐⠡⡈⠔⡈⢿⣧⡃⠆⢸⡿⡀⠐⠀ ⢯⣻⣾⣟⣿⣿⣿⣿⣿⣿⣯⠲⣍⠾⣝⢮⢳⣫⢞⡼⣵⣿⣾⢿⣿⠻⡥⢣⡙⡜⣢⡑⢣⣼⣿⣿⣿⣿⣿⣿⣿⠡⡘⢄⠊⡔⢡⠘⡄⢂⡁⢆⠘⣀⠢⠌⠡⠘⠠⢀⠁⠆⢠⠁⡘⢈⢀⣷⣿⣿⣷⣌⠻⣶⣤⣀⣑⡀⢡⠉⡄⠊⡄⢁⠲⣿⡇⠐⠠⢁⠂⡅⠐⢂⠐⠘⢿⣿⠃⡬⣧⢣⠀⠀ ⣮⢻⠿⣿⢿⣯⣿⣿⣯⢿⣿⣶⡝⢦⡝⡞⢮⡹⢼⡱⢯⡹⢭⠞⣿⣦⠣⢎⡱⢣⢋⡕⣊⢿⣿⣿⣿⣿⣿⣿⡟⡄⢓⡘⠤⡑⢌⠢⡑⢌⠃⡜⢠⠉⠢⠐⢂⡐⢂⠘⡀⠆⡈⢂⠑⠌⣾⣿⣿⣿⣿⣿⡆⢙⠻⠿⣿⣷⢈⠂⠑⡂⠡⠘⡀⢿⣇⠢⡐⠌⢂⠑⣀⠊⠔⠂⠸⣿⡆⡇⢽⡚⠄⠀ ⢯⣏⣿⣿⣻⣷⣿⡹⣿⡾⣹⢿⣿⣧⣻⡜⢧⡛⢮⡱⢧⡙⣎⢣⢻⣿⣇⢣⠕⣣⠣⣜⠰⢺⣿⣿⡽⣿⣿⣿⠱⡈⠦⡑⢢⠁⢎⡰⢌⠢⣁⠎⠠⠃⠔⡁⢢⠐⠄⢊⠀⠆⣁⠂⠌⢸⣿⣿⣿⣾⣿⣿⣿⠂⡠⠁⣼⣿⠀⠌⠰⢀⡑⠤⠐⠸⣿⡆⠰⠈⢄⡈⠀⠐⠠⡁⢂⢻⣷⡄⠠⣿⡀⠀ ⣟⡾⣱⣿⡗⣿⣿⣽⣮⣻⣷⣛⠿⣿⣿⣿⣿⣷⣷⣷⣧⡽⣌⠧⣃⠾⣿⣧⡛⣔⠣⣌⠳⣡⢙⠻⡿⠽⢟⠡⡑⢌⢒⠡⢢⠉⢆⠰⢌⠒⠤⣈⣵⡾⠷⢦⣦⠈⠌⡂⠌⠂⢄⠘⢈⠘⣿⣿⢿⣿⣿⣿⡟⢀⠠⠡⠘⣿⣦⠘⡐⠠⠐⠠⢁⠆⠹⣿⣄⠉⠄⠄⡡⠄⠁⡀⠂⢼⣿⡔⠀⢿⡀⠀ ⣟⡾⢧⣟⣿⣷⣻⣿⣟⣿⣾⣫⡿⣝⡿⣿⣿⣿⣿⡿⣿⣿⣎⠶⡙⢦⢍⡻⣿⣮⡱⢌⠳⡌⢎⠲⡌⡓⣌⠣⡑⢊⡄⠳⣈⠱⣈⠒⠬⡘⡐⢸⣿⡐⡭⣡⣽⡇⢂⠡⠌⡁⠢⠌⠠⠌⡙⢯⣯⣷⣿⠟⡀⠂⠰⢀⠁⡈⣻⢿⣶⣌⣌⡐⡈⢄⢡⠝⣿⣦⡈⡐⡐⠠⢁⠄⠠⣸⣿⣢⠁⡞⠄⠀ ⣟⢾⣛⡾⣽⣷⣿⣻⣿⣿⣻⢿⣟⣮⢹⡟⣿⢿⣿⣽⡻⣿⣿⣾⣝⣎⠲⣕⠪⢿⣿⣮⣕⡸⢄⠳⢰⢁⠦⣁⠧⡑⢌⠱⣀⠣⢄⡉⠦⡑⢌⠢⠌⡙⡛⢏⠥⠐⢂⠜⢠⢀⡁⢂⠡⠒⡀⠢⢈⠅⠠⡀⠄⠡⡁⠄⢢⣾⠏⢄⠐⡉⠉⡄⠘⣀⠢⡌⠀⠟⣿⣶⣤⣁⢂⣀⣶⣿⡿⠋⠄⠧⡄⢂ ⣯⠷⣯⣝⣯⢿⣷⣿⣞⣿⣯⣿⣿⣿⣧⡙⣮⢛⡼⣮⢽⡳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣥⣃⠎⠴⣁⢆⠩⢆⠣⢌⠒⡔⢘⠢⡑⡈⠔⣨⣿⣷⢐⠂⢅⠊⡐⡀⠆⠨⠄⢂⠑⠠⢁⠆⢈⡐⠠⠉⢂⣤⣿⡿⠛⢈⠠⢈⠤⢁⠢⢁⢂⢠⣡⣷⡞⠄⡩⡙⡛⡿⣻⡿⡺⠡⢘⠈⠰⠈⡅ ⣯⢟⡾⣼⡞⣿⣻⣿⢮⣽⣳⣿⣿⣿⣾⠳⣍⣏⢶⡳⣏⣿⣿⡿⢿⠟⡿⣛⢻⢻⣿⣟⣱⣬⣿⡿⡿⢿⡶⣶⣬⣒⠌⡒⢌⡘⠤⢃⠆⡱⠘⡰⢈⡛⡉⢄⠊⡄⢊⠐⣠⣌⣤⡅⠂⣬⣴⣤⣦⣤⣤⣡⣾⡿⢿⣿⠂⣰⣾⣶⣦⣤⣦⣴⣿⡿⢿⣿⡁⠔⠨⠄⡱⢨⡵⡏⠎⢠⡝⠠⠀⢁⠂⡌ ⣿⢮⢷⣛⣞⡷⣫⣿⣿⡶⣯⢗⣯⣟⣿⣹⢿⣬⢣⣿⣿⣛⠴⣏⢮⢫⡕⢧⢋⠶⣽⡿⢯⣳⣣⣽⢾⡷⣕⡫⡝⣻⣷⣾⣦⣥⣎⣔⣨⣐⡑⢄⠢⠔⡠⡂⠅⠒⣾⣟⣛⢉⠁⢂⠑⠄⠢⢈⠨⠭⠍⢉⠙⢛⣿⣧⣾⣿⢯⣽⣿⣿⣿⠟⠙⣷⣄⠉⠛⢯⡆⡑⢜⡒⢯⠰⢸⠞⠀⠀⠁⡀⢂⠠ ⣿⣯⢞⡽⢮⠿⣵⡻⢿⣿⣷⣟⡾⣽⣟⣮⣿⡶⣿⡟⠶⣭⡛⡼⢎⢧⡹⢎⣯⣾⢿⣹⣟⣷⣿⣾⡿⣿⣿⡷⣙⣦⡿⠿⣿⢏⡟⡿⠿⠿⣿⣿⣿⠿⠿⢻⢛⠟⣻⣏⠛⣛⠻⠿⠷⠾⢶⡷⠶⠆⢶⡾⠻⠛⢻⣿⠟⣿⣿⣽⣿⡿⠃⠌⡐⠈⠿⣷⣌⠐⣈⠺⣧⡄⢌⡲⢺⣇⠌⢀⠂⡀⠀⠂ ⣿⣞⡯⣞⢯⣻⠵⣯⢯⣻⢿⣾⣿⣿⣻⣿⡿⣽⣿⣹⡳⢥⣛⣼⢏⡮⣹⢾⣿⣯⣟⣿⢯⣷⣿⣻⢿⣿⣽⣿⡿⢋⠜⡡⢆⣺⣿⣷⣭⣾⣿⣖⣿⡻⢯⣕⠫⡜⢼⣷⠘⢄⠊⢤⢁⢎⢢⠈⡵⢈⡐⢤⡚⠅⣿⣿⣿⣾⣿⣿⡿⠱⣌⠰⣈⠑⡄⠚⠿⣧⠀⠂⡉⢿⣤⠉⢦⠻⣕⢄⠢⠐⠡⠁ ⣷⢯⣷⡹⣎⢯⠿⣭⡻⣝⡿⣿⣿⢯⣿⣳⣻⣿⣏⣶⣹⣖⢯⣿⣿⣞⣵⣺⣿⢺⣿⣿⡿⣿⣿⣿⣿⣿⣿⢣⠌⠥⠣⣱⣾⠛⡅⢆⡛⣿⣏⠉⣿⣷⣅⠫⣓⠜⡸⣿⣬⣄⢊⣿⡆⠎⣔⠩⢌⠇⡎⡤⡝⣈⣿⣿⣿⣿⣿⡿⢁⡲⢚⠒⣆⢉⢄⢃⠔⠂⠹⢦⣄⡀⠹⢿⣚⣧⠻⣿⣆⠁⠁⠂ ⣯⠿⣽⡳⣝⢯⣛⡶⣽⡹⣞⣿⣽⣾⣽⣿⣾⣿⣷⢺⣿⢿⣿⡟⣽⣿⢛⣻⣷⡿⣿⢻⣿⣿⣿⣿⣽⡿⣁⠖⡘⢬⣵⡟⠥⡓⡌⢆⡡⢻⣯⣈⣼⣯⣻⣧⣥⣚⣴⣿⣶⢩⡍⣋⠝⡩⢦⣯⠿⡍⡝⣱⡏⣿⣿⠠⠙⣿⡟⣠⠗⠠⢃⠜⡰⣊⠤⢊⡌⡰⣁⠢⡙⠻⣶⣬⣻⣾⢇⢹⣾⠀⠀⠀ ⣾⣻⢗⣿⢼⣫⡝⣾⣱⣛⢾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣼⣽⡏⡞⠴⣋⣷⡹⢿⠿⣯⣿⢿⡿⡑⢢⠎⣱⣾⢟⡙⠴⡑⡸⢀⠇⡍⢻⣿⣿⣿⡿⠾⢟⠻⢋⡝⣿⡔⡧⡔⡅⣃⢷⣧⢗⣸⡒⣼⣀⣾⣇⣠⣡⡿⣰⠋⡌⢱⢊⠦⡑⢎⡩⢣⢒⡰⢠⠁⠆⡑⣠⣽⡿⠟⡀⡾⠃⢠⠠⠄ ⡷⣯⠾⣽⣧⢷⡹⣶⢳⣛⡾⣽⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⣭⣿⠵⣉⠞⡩⣿⣯⣝⡫⢗⣿⣿⠣⡙⠴⡘⣾⠟⡤⢍⠲⣡⡃⡎⠲⡨⢹⡿⠟⣷⣮⣍⣮⢶⠩⡔⢿⣧⣹⡌⡸⡭⢶⡯⠞⣌⢧⡟⣸⣿⢋⠛⢿⣵⠃⡱⠘⡔⣪⠑⡍⡖⡌⠥⢎⡔⠣⣌⣢⣾⣿⣿⠛⢢⡝⠀⢋⠠⠐⡀ ⣿⣩⢟⡾⣽⣖⡻⣼⢳⢯⣽⣳⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⢽⣟⢮⡱⢎⠵⡹⣿⡿⢿⣿⢾⣿⣡⠑⡊⣜⡝⡹⢰⢉⠲⣄⠲⣉⢜⣤⡿⢋⠜⡠⢘⢿⣷⣈⠖⢩⠚⣿⠼⣇⠇⡔⢢⡗⣝⠞⣹⢏⣿⠻⠳⠿⣦⣽⣥⡐⣡⠩⠔⣩⠰⡘⣤⠟⣂⣴⣷⠿⢛⠱⣿⠃⣴⠋⠀⠐⠀⠄⢁⠀ ⡷⣭⠾⡽⣽⣧⠿⣜⣯⣛⣮⣷⣟⣻⢿⡹⣏⣿⣿⣽⣿⣿⢣⣾⣿⡦⣙⠎⡞⢥⠻⣿⣖⡰⠣⡝⡻⢿⣶⣿⣼⣵⣧⢊⡱⠌⣕⣨⣿⠏⡐⡡⢂⠥⡁⢆⣿⡿⣾⣤⣃⢻⣷⣯⣎⣈⡡⣯⣌⣂⣼⣴⡡⢌⡑⠒⡄⠢⠍⢻⢷⣄⠣⢄⡧⣓⣵⣾⠿⡭⣐⡂⠣⡘⡥⢸⣿⠀⢈⠀⠌⠀⠂⡁ ⣟⡼⣫⢗⡿⣼⡿⣵⢾⣹⢾⡽⣧⢻⣧⢟⣞⣿⣿⣿⣿⣿⣿⢛⣿⣷⢩⠞⣱⢊⡵⢩⠿⣷⣷⣰⠑⢎⡰⢣⢙⢡⠃⣿⣿⡿⢿⡟⠿⣷⢶⣥⣮⣴⣾⣾⣿⣄⣣⢍⢛⠿⢿⣭⣽⣉⣟⢋⢋⠭⢙⢨⠑⠤⢡⠋⡄⠓⡌⠡⠌⡛⠷⣿⡾⠟⠻⢧⣈⠐⢉⠖⣥⡠⢱⢻⣷⡆⢀⠂⡄⢁⠂⡅ ⡟⣼⡹⣞⡽⣯⣷⣏⢾⡷⢯⣟⣿⢧⣿⣫⢾⣿⣿⣽⣷⣿⣷⣿⡿⣿⣎⢳⢌⣆⠣⣇⣾⣷⠿⠻⣿⣶⣶⣥⣎⣂⠓⢆⢛⡛⡛⡡⢋⡐⢢⠙⣿⡶⠿⡁⢍⠛⣿⣾⣮⣬⣒⠆⠣⠝⢛⡛⠷⠾⣬⣤⣍⣊⢒⠰⠜⠴⠈⠥⣃⠰⢡⡨⢄⠣⡱⢈⠙⣷⡀⠌⠺⢿⣎⡷⢸⣽⠀⠄⡐⠀⠂⡄ ⣟⢶⣹⢞⣽⣳⢿⣞⣻⡼⣟⣯⣻⣧⢻⣷⢫⢿⣿⣾⣟⣿⣿⣿⡷⣹⣿⣧⡚⣤⢓⣿⣿⣿⣿⣷⣶⣿⣯⡟⡛⡟⠿⢿⡶⣾⣶⣵⣶⢬⠧⢉⠶⠶⡷⠿⠟⢻⣿⡝⡬⢹⢛⡿⣿⣾⣦⣼⣌⣱⡄⡌⠜⣉⢋⣛⠓⣋⠟⠶⢖⠮⠶⢦⡶⢥⠶⠅⡑⠫⠑⡐⢨⣸⣿⣚⡥⣿⡂⠈⢄⠈⡁⠆ ⣏⢾⣱⢟⣾⣹⢯⣷⣫⢿⡵⣾⣳⢿⣏⢷⢯⢷⣛⡿⣿⣿⣿⢿⣷⣿⣛⣿⣿⣤⢣⠽⡻⢟⢿⣿⣿⣿⣿⢇⡓⢬⡙⢢⠔⡰⢂⠆⡔⢢⡑⢌⣊⠱⡐⣿⣿⣳⣿⣧⡑⡡⢎⡴⣇⡶⣽⣿⣿⢿⣿⡿⢿⣶⣷⣶⣦⣥⣌⣒⣉⡘⠡⢆⠒⣡⢊⣅⣩⣴⣥⣼⡾⣟⣧⡿⢃⡇⢁⠂⠢⠐⠠⡁ ⡾⣭⣛⠾⡶⢯⡿⣽⣟⡻⣞⡵⢯⣟⣿⢮⡿⢮⡵⣛⢿⣿⣿⣿⣿⣿⣿⣿⣝⡻⣿⣷⣝⣸⠢⡝⡻⡿⢋⠖⣩⢆⢣⢃⢎⡱⣉⠦⡙⢤⠘⡰⢀⠣⠘⢿⡿⣿⣿⡿⣷⡇⣿⣿⣿⣟⢿⠻⢞⡿⣿⣿⣧⡲⡔⢦⣡⢋⣼⢍⢯⣁⢧⣘⢬⡝⣫⣯⣹⣭⣟⣼⣷⠿⢋⡡⠊⠄⠠⠂⡐⢈⠀⡄ ⡷⢮⡝⣯⡽⣯⣟⠷⣿⢵⣫⣞⣿⢾⣻⡎⣽⣷⣋⣧⣿⣿⣿⣿⣳⣿⣿⣿⣷⣳⣿⠯⣼⣟⢷⣾⣵⣌⣣⣙⡒⢬⠲⢍⠆⡖⣡⠲⡉⢆⢓⠤⢉⠢⠡⢈⣙⣫⣾⢷⣾⣿⣿⡟⡍⠛⠿⣉⡢⢭⠖⣿⡅⠉⠜⡡⣉⠍⠒⣋⠚⣊⠓⢋⢚⡉⢓⡋⢉⠩⢉⠔⠂⡀⠁⠠⠐⡐⠐⠠⠐⠠⠂⡄ ⡷⣎⢷⣭⢳⣽⡻⣶⣻⣞⣯⡽⣏⣾⣿⢳⡽⣯⢻⣽⣿⣿⡟⡿⣿⣿⣿⣿⣿⣿⣿⣔⣿⣿⡜⣻⡿⢻⢿⣿⣷⣾⣶⣼⣴⣥⣯⣄⣧⣘⣌⣴⣬⣤⡶⠾⣿⠛⢉⣬⣿⢿⣿⣷⡇⠂⠰⠏⡱⢜⣶⣻⢗⠠⠀⡡⠉⢀⠂⠉⠠⠉⠠⢈⠈⠁⠈⠁⠌⡀⠌⠄⢀⠡⠐⠂⢄⠁⡐⠂⡐⢀⠀⡃ ⡿⣜⣳⢮⡟⣼⡻⢷⣯⢿⢾⣳⣯⣿⢮⢳⣿⡹⣿⣿⣿⡿⡼⡹⣜⠻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣮⣿⣷⣮⣿⣭⣍⣻⣿⣭⡙⢭⣿⢍⡡⢹⣿⣰⣹⣷⣾⢿⣯⢞⣿⣼⠆⡡⠜⢌⣘⡜⣳⡿⠇⠠⡁⠄⠂⠄⠐⠠⡁⠄⠂⠄⠂⠁⠠⢀⠐⠠⠀⡐⠠⠐⡁⠅⡐⠈⠔⠀⠰⢀⠂⠅ ⡿⣜⣣⡟⣾⣳⣟⣻⢞⣿⡿⣼⡷⡯⢏⡿⣾⣽⣿⣿⣿⣷⣿⣿⣷⣟⢮⡳⣎⢼⣿⣿⣿⣿⣼⣻⣿⣿⣿⣿⣿⣿⣟⣿⣿⠿⣟⠻⣿⣾⣿⢿⢿⡿⣿⣿⣫⣽⣿⡟⣿⣿⢏⡟⠷⢶⣾⣶⢷⠷⢛⡁⢎⠡⢄⠃⠬⢐⠡⡁⠔⢠⠈⡐⢄⡁⠡⣀⠢⢁⠂⠄⡡⠐⡈⠔⢈⠌⠄⢈⠐⠠⢈⠆ ⡽⣎⠷⣹⢧⢷⠾⣝⣞⣞⣿⣼⢿⣛⣽⣛⢯⣿⣿⣿⣿⣿⣿⣻⣿⣿⣶⣷⣾⣿⣿⣯⣻⣿⡿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣵⡪⣴⣭⣿⣿⣷⣾⣶⣿⡿⣻⣿⣛⣶⡿⢟⣋⠞⡁⠇⢒⡈⢋⠔⣂⠂⠔⢌⠰⠁⠎⠡⢂⠒⠌⡐⠂⡑⠈⠄⡀⢃⠀⢂⠆⠡⠌⡀⢃⠐⢃⠂⠰⢈⠂⠌⡐⠁⡂ ⣿⣾⡝⣯⢟⣾⢫⡽⣎⣷⣻⣾⢿⣏⣾⣹⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡝⣶⡣⡟⣽⣿⣿⣿⣿⣷⣹⡷⡽⣿⣿⣿⣯⢿⣽⣯⣟⣷⣿⣿⣿⢛⠩⠕⠠⢋⡀⠎⣰⠉⢆⡙⡂⠌⡔⠨⣑⠔⡂⠍⡐⠡⠂⠌⡐⢀⠃⠄⢃⢂⡘⠠⠈⡄⠌⡐⢂⠡⢈⡐⠄⡈⢁⠂⠌⠐⠠⠁⠆ ⣿⣿⣿⣞⣻⣼⡻⣜⣻⣼⣳⢿⡿⣟⣼⢣⣏⢾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⣵⣻⣧⣿⣽⣞⡶⣿⣿⣿⡿⣿⣿⣽⣿⣿⣿⣿⣷⣿⢿⣼⡿⢟⠯⠂⡅⠂⠌⢐⠠⡘⠴⣀⠚⢄⠒⢌⢡⠂⡡⠄⠒⡐⠤⠑⡈⠌⡐⢈⠄⡈⠌⡀⠆⢠⠁⠒⠠⠐⣀⠂⠂⠡⢀⠂⡐⠠⢈⠐⡈⠄⢁⡃ ⣸⣿⣿⡷⣛⡶⢯⡝⣮⢷⡻⣯⣿⣳⡭⡗⡞⣌⣿⣿⣿⣿⣿⣿⣵⣻⢿⣻⣷⣻⣿⣿⡿⢷⣹⣿⣻⣼⢻⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⣯⣿⣿⡿⢋⡴⡩⢀⠡⠈⡄⢃⡘⡔⢌⡉⠦⡉⢌⢂⠩⢐⠈⡔⠡⢂⠡⠐⠂⠌⢂⠐⡈⠔⠌⡐⠂⠅⡨⠁⠒⠠⠐⠡⠌⢀⠂⠄⡁⠂⠄⠐⡈⠄⡁ ⣿⣿⣿⡽⣹⣞⡯⣽⢳⣏⣿⣳⣿⡷⣻⣽⡜⣮⢿⢫⢝⡻⣿⣿⣶⣝⣾⢷⣿⣿⢟⢻⣼⢻⣿⡟⣷⣚⠯⣿⢿⣿⣯⣿⣹⣯⣿⢾⡹⣿⣿⡾⢔⣓⠪⡔⢖⡲⣑⠘⣄⢣⢘⡰⢌⠰⡈⡌⡐⠌⠤⡁⢌⡐⠡⢂⠡⠌⠠⡁⢌⠐⡐⠰⢀⠊⠄⡐⠄⠃⡠⠁⠆⡐⠨⠐⡈⠐⡈⢀⠂⠄⢂⣸ ⣿⣿⢻⡜⣷⢺⠷⣭⢷⣺⢳⣟⡾⣿⣹⢷⣻⢧⣯⡽⢮⠷⣣⢯⣽⣿⣿⢿⡿⣿⣾⣟⡮⣗⣺⢿⣶⣙⣞⣲⡍⣞⡻⣿⣽⢩⢧⡳⣯⡽⣛⣷⣮⣴⢍⡜⢆⠱⢌⢢⠆⡂⢇⠰⡈⢆⡉⠔⡈⠜⠠⣁⠢⢀⠣⠐⠂⠌⠡⡐⠠⢂⠡⠐⡁⠌⡐⠐⠠⢁⠐⡈⠐⢀⠁⠂⠄⠡⠐⡀⢈⠀⡶⢉ ⡻⣼⢣⡟⢮⣛⣯⢷⢯⣽⣻⣞⡿⣽⣿⣹⣯⢏⣿⣟⣿⣻⢽⣿⣿⣿⣿⣯⣝⣿⣿⡻⣝⡾⣽⠻⣿⣷⡞⣽⢻⢶⠿⣿⣿⢿⡞⣟⡱⠜⣬⢩⢿⣷⡥⠚⣌⡱⠌⢢⠘⡡⢊⠣⡁⢆⢊⡌⠰⠌⡡⢄⠢⢁⠆⡱⠈⡌⠡⠌⠒⠠⢂⢁⠊⢐⡀⠃⢈⠂⡐⢁⠐⢂⠈⠄⢊⠐⠡⢀⠂⡼⠁⠂ ⣝⢧⣟⡾⣭⠿⣼⡻⣞⡧⢿⡞⣽⣻⢷⣳⢽⣺⣿⣯⣷⣻⣞⣾⣿⣿⣿⣻⢯⣿⣿⣷⣾⣿⣿⣷⣿⣧⣛⡼⣹⢯⢿⢲⣛⣷⣽⢰⣱⢫⠴⢣⠎⡽⣿⡽⣦⡒⠜⡠⣃⣑⣂⣅⣌⣰⣦⣬⣬⣴⣤⣦⣡⣬⣐⣠⣉⣄⣁⡊⠥⢁⠡⠈⠔⠠⠀⠌⠠⢈⠠⢀⠂⠄⠂⠈⠀⠂⠌⠀⠸⠀⡈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡿⡁⠰⣀⠙⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡧⢇⠡⠄⢊⠡⡘⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⡾⠷⠷⠾⣬⣆⡡⢐⠡⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠃⠤⠑⡨⠐⡄⢊⠛⣷⣆⠡⠚⣷⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡇⡎⡐⢡⠐⡡⠐⡌⠰⢀⠽⣧⠑⡸⣟⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡁⠗⡈⢶⣥⠐⡡⠄⢃⠌⡠⢿⡃⠤⠹⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣵⠟⠓⣦⣙⠻⢶⣬⣦⣦⡵⠟⡠⠑⡈⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⣶⠉⠁⡔⠲⡄⠈⡿⢀⠢⠐⡄⠢⢡⠐⡡⠌⠌⠻⣷⡀⠀⠀ ⠀⠀⣠⡿⣶⠀⠙⡊⠀⢸⠉⡄⠢⢑⠠⠑⢂⠔⡐⠨⠌⠡⠌⣻⣆⠀ ⠀⢠⡿⢁⠜⠛⢋⠙⣛⣭⡴⠶⠷⠚⠒⠛⠶⠶⢬⣅⡊⣁⠒⠠⢻⣅ ⠀⣿⡃⠎⣀⠣⣼⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡌⣁⠚⣿ ⠀⣿⡁⠆⡉⣴⠋⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡈⢳⡍⡐⣿ ⠀⢻⣇⠢⢁⡏⠀⠸⣿⠇⠀⠀⠀⠀⢠⡒⡄⠀⠀⠹⠿⠃⠀⡇⣼⡟ ⠀⠀⠻⣷⣌⢷⡀⠀⠀⠀⠀⠀⠀⢠⠤⡤⠀⠀⠀⠀⠀⠀⣸⣷⠟⠁ ⠀⠀⠀⠈⠙⢻⣿⣦⣤⣄⣀⣀⣀⣀⣉⣀⣀⣀⣀⣤⣴⡿⠛⠁⠀⠀ ⢠⡤⢤⣤⣀⡸⠿⢦⣄⠰⣈⡿⠉⠉⠉⠙⢯⣉⡿⠺⠛⠉⠙⣧⠀⠀ ⢸⣆⠘⠈⠈⠀⠀⢀⡌⠙⠛⠁⠀⠀⠀⠀⠈⣍⣀⣀⣀⣠⡴⠏⠀⠀ ⠀⠈⢓⡖⠒⠒⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣧⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠛⢿⡄⠀⠀⠀⠀⠀⢢⠀⠐⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠠⠬⡇⠀⠀⠀⠀⠀⠾⡀⠐⠺⡤⠤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣜⠆⠀⠀⠙⠶⠦⢤⣀⣀⣠⣧⣀⣤⠇⠀⠀⠘⡆⠀⠀⠀⠀ ⠀⠀⠀⠈⠒⠤⠄⢠⡀⠀⡀⠀⠀⠀⡀⢀⢀⡄⡤⠠⠜⠁⠀⠀⠀⠀
⣻⢭⡻⣭⢏⡯⣽⡹⢿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠄⡠⢀⠄⡰⢀⢂⠰⢀⠰⠀⠆⡐⠄⠢⡀⠆⡐⠄⢂⠄⣂⠐⡄⠠⣿⣿⣿⡿⣟⣿⣻⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣿⣾⣿⣾⣷⣽⣧⣿⣿⣿⣷⣿⢿⣯⣿⣟⣷⡿⣟⣿⣾⣟⣾⣿⣽⣏⠀⠒⡀⢂⠂⠔⢠⠂⠤⢁⠢⢁⠆⠰⠈⡔⢠⠂⠤⢁⠆⠰⢀⠂⡐⠀⣿⣿⢯⣟⡽⡾⣽⢯⣿⣿⣿⣿⡿⣿⡽⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⡉⢉⠈⡉⢉⠉⠛⠻⢿⣿⣿ ⣿⢸⡽⣺⡝⣯⣻⢯⣿⣿⣿⣿⢿⣿⡿⣯⣷⡿⣯⣿⢿⣻⣾⣟⣿⣾⣿⡇⢘⠠⠘⠠⢈⠰⠀⢌⠐⡠⠂⠤⢈⠄⡡⠐⠠⢈⠔⠠⠈⢄⠡⢂⠁⡂⢿⣿⣻⢞⣽⣻⣭⣟⣿⣿⣿⣿⣿⣿⡽⣯⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⡠⠈⠤⢁⠰⢀⠂⡁⠂⠌⠠⡁⠤⢈⠙ ⣯⠾⣽⢳⣽⢳⣭⢟⣮⢟⣿⣿⣟⣿⣿⣟⣷⡿⣿⣽⡿⣿⣽⣾⣿⣳⣿⡇⠠⢂⠉⠔⠂⢄⠃⡄⢂⠄⠡⠒⡀⢂⠄⡑⢂⠡⢈⠂⡉⠄⠒⠠⠁⡄⣻⣿⣽⣛⣮⢷⣛⡾⣿⣿⣿⣿⣷⣿⣻⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠄⣈⠒⡀⡁⠊⠄⠢⠀⠅⢂⠡⢈⠡⠐⡠⠂⠂ ⣗⣻⡵⣻⡼⣫⣞⡽⢮⣻⠼⣿⣟⣾⣿⣿⡽⣿⣻⣽⡿⣯⣷⣿⣻⣽⣿⡇⠐⠡⣈⠂⡉⠄⢂⠰⢀⠊⠤⢁⠐⠂⠔⠠⠂⠔⠂⢌⠐⡈⠌⠄⠡⡀⣽⣿⢾⡽⣞⣯⠿⣽⣻⣿⣿⣿⣯⣿⢷⢯⣟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠠⠄⢃⡐⡀⢂⠐⠠⠁⠌⡐⠉⠤⠁⠌⡀⠆⠡⠄⢡⠈ ⢯⢾⣱⢯⣳⢽⣺⡝⣯⣳⢻⣽⣿⣯⣿⣟⣿⢿⣽⣷⢿⣟⣷⣿⣻⣽⣿⡇⢘⠠⢀⠂⡡⢈⠄⠒⠠⡁⢂⠌⡈⠤⠉⠄⡡⠘⣀⠊⡐⢈⠰⢈⠡⠀⢾⣿⣯⣟⡽⣞⡿⣳⣿⣿⣿⣿⣿⡿⣯⣟⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠟⢀⠂⢡⠈⠤⠐⡀⢂⠌⠡⢉⡐⠈⢌⠠⠉⡄⠡⠘⠠⡁⠢⠐ ⣯⢟⣮⠿⣜⣯⢞⣽⢣⡿⣹⣾⢿⣯⣿⣿⢯⣿⣟⣾⢿⣯⣿⢾⣿⡽⣿⣧⠐⡐⠠⠒⡀⠆⠨⠘⠠⢁⠂⠔⡈⠄⠃⡌⠠⢁⠄⠢⢐⠈⡰⢀⠂⡁⢾⣿⣿⡾⣝⣻⡼⣷⣿⣿⣿⣿⣿⣟⡷⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⢠⠂⡘⠠⠈⠄⠡⠐⣀⠊⠄⡡⠀⡅⠢⠐⡡⠠⢁⠊⠄⣁⠢⠁ ⣟⣾⣱⢿⡹⣎⣟⢮⡟⣼⣳⣿⣻⣿⣿⣻⣿⣻⣾⣟⣯⣷⢿⣯⣷⣿⣿⣷⠀⡄⠃⠔⡐⢈⠐⠡⠘⠠⠌⠰⠀⠎⠡⢀⠑⠂⠌⡰⠈⠄⣁⠂⡐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠃⠄⠒⠠⠁⠌⡐⠡⠌⠠⢈⠔⠠⢁⠤⢁⠒⠠⢁⠢⠁⠌⣀⠂⡅ ⣟⢶⡻⣎⢿⣱⡞⣯⣽⣷⣿⡷⣿⣿⣿⣽⡷⣿⣳⣿⣻⢾⣿⣽⡾⣿⣾⣿⡇⠠⠑⡀⠂⠄⠃⠌⢂⠡⢈⠂⢡⠈⠔⡈⠄⡡⠂⠄⡑⠐⣀⠂⠤⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠠⢉⠈⠄⠃⢄⠑⡐⢈⡐⢈⡐⠤⢈⡐⢂⠐⡠⠈⠔⠂⠄⣉⠐⡀⢂⠰ ⡟⣞⢷⣫⠿⣼⣹⣶⣿⢿⣽⣾⣿⣿⣟⣷⣿⣻⣽⣷⣯⣿⡿⣞⣿⢿⣽⣿⣧⠂⡡⠐⡉⠄⡡⢈⠐⠄⠂⠌⠠⢈⡐⠠⠒⠠⢁⠊⠄⡡⠄⢂⠰⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⡌⠰⠠⠈⡄⠉⠄⠂⠌⠠⠐⠠⠐⡐⠠⠐⠠⢁⠐⡁⢊⠌⡐⢀⠂⡐⠠⣼ ⣿⡿⣿⢿⣟⣿⣟⡿⣽⣿⣿⣿⣿⣯⣿⣻⣾⢯⣷⣿⣳⣿⢿⣻⣯⣿⣻⢾⣿⣄⠁⢂⠐⠠⣐⣠⣌⣠⡉⠄⣁⠂⠄⡡⠌⡐⠡⢈⡐⠠⠈⠄⠒⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠠⠡⠄⡁⢂⠡⡀⠅⡘⠈⢄⡁⢃⠁⡂⠔⠡⢁⡘⠠⠌⢠⠁⢂⠐⠄⠂⠄⣱⣿ ⣿⣽⣯⣿⣾⣿⣾⣿⣿⣿⣟⣿⡿⣾⢷⡿⣽⣿⣳⣿⣽⣿⣿⣿⡿⠿⠿⢿⣿⣿⠄⠂⣼⡾⠛⠉⠉⠉⠿⣿⡄⠐⡈⠐⣀⠂⡁⠂⠤⢁⠉⠄⡁⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠡⢀⠃⡐⢂⠐⡀⠆⠠⡁⡐⢁⢂⠐⡠⠘⠠⢈⠔⠂⠄⡁⢂⠂⢌⠠⠌⣀⠃⣰⣿⡿ ⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⢯⣿⡿⣽⣿⣻⣟⣾⣽⣟⣾⣿⡿⠋⠀⠀⠀⠀⠙⠻⣷⣾⠛⠀⠀⠀⠀⠀⠀⠸⣷⠈⠄⠃⠄⠂⠌⡁⠆⠄⢊⠐⠠⣿⠿⠿⠛⠛⠛⢉⠋⡉⢉⠉⢉⠉⢉⠉⡉⠙⣿⡟⠂⡐⢀⠒⠀⠆⡐⠤⠈⠄⡡⠐⠠⠂⠌⠠⠁⠆⡁⢂⠡⠌⠐⠂⠌⡀⠆⡐⠠⣰⣿⡿⣽ ⣿⣿⢿⣻⣿⡿⣿⣟⣿⣿⣼⣿⢿⡿⣼⣟⣿⣼⣻⣟⣿⣿⠃⠀⠀⠀⠀⣀⣸⣤⣟⣀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢃⠘⡘⠄⠃⠄⠠⠘⢄⠠⠘⠠⠀⠄⠠⠘⡀⢃⠄⡠⠀⠇⡘⢀⡘⠀⠄⡀⢻⡿⠀⠠⡘⢀⠘⠄⠤⠀⠄⢃⠄⡀⢃⠄⢃⠘⢃⠘⠄⠠⠄⠠⠘⠸⠘⠠⠀⢄⠠⣸⣿⣿⣻⢧ ⣿⣯⡿⣿⣽⢽⣿⣽⣳⣟⣾⣿⣻⣟⡿⣾⣻⣞⣿⡽⣿⣿⣀⠀⠀⣠⣿⠛⠉⡈⢩⡻⣷⡀⠀⠀⠀⠀⣠⡿⠃⠠⠒⠠⠈⠌⡐⡁⠊⠄⢂⠁⠆⡁⢊⠁⢂⢁⠂⡐⠠⠑⢂⠘⠠⠠⢁⠂⠴⣿⠃⡈⢂⠐⠂⠌⡐⠠⢉⠐⡈⠄⡰⢈⠐⡈⠄⡡⢈⠂⡡⢈⠡⠘⠠⡁⠡⠃⡀⣶⣿⣿⣷⣿⣿ ⣿⣳⣿⣟⣾⣻⣿⣞⣿⢯⣿⣾⣻⢾⡿⣽⣷⣻⣿⣽⣿⣿⣿⠄⢰⡟⠁⢀⠂⠠⢀⠀⣿⡇⠀⣤⣴⠾⢋⠡⢈⠡⠘⠠⢁⠒⠠⠐⠡⡈⡐⢈⡐⠐⢂⠘⡀⢂⠐⡠⠃⡈⠄⡘⠠⢁⠂⠌⠠⢁⠂⡐⡈⠌⡈⢐⠠⢁⠂⠒⡀⠒⡀⢂⠂⡐⠂⠔⠠⢁⡐⢂⡁⢊⠄⡁⢂⢡⣼⣿⣿⣿⣛⡾⣼ ⣿⢯⣷⢿⣧⣿⣷⣻⣾⣻⣯⣷⢿⣻⣽⣟⣾⣯⣷⣿⠋⠁⠀⠀⢸⣯⢄⡠⠄⠁⢠⢨⡿⠀⠀⠙⣿⡤⠂⠤⢁⠂⡁⢂⠡⠈⡄⢉⡐⠠⠐⠡⢀⠡⠂⠌⠠⢁⠂⢡⠐⠠⠁⠤⢁⠂⠌⠌⠰⠀⠆⡐⠄⢂⠁⠢⠐⡈⠤⢁⠰⠁⠌⡀⠆⠌⡐⠌⢠⠁⠰⠠⠐⢂⠐⡈⣤⣿⣿⣟⡟⣶⢏⡷⡽ ⣿⣟⣯⣿⣼⡿⣾⡽⣿⣽⡿⣞⡿⣽⣞⡿⣞⣯⣿⠃⠀⠀⠀⠀⠀⠻⢷⣭⣧⣥⡾⠟⠁⠀⠀⠀⠘⣿⣀⠒⡀⠆⠐⡀⢂⠡⠐⠂⠄⡡⠘⠠⢁⠂⢡⠘⡀⢂⠌⠠⠌⡀⢃⠐⠠⢈⠐⠌⡠⠁⠆⡐⠈⡄⠌⡐⠡⠐⡀⠆⢠⠁⠢⠐⣈⠐⠠⠌⠠⠌⣁⢂⠡⡈⢐⣼⣿⣟⡷⣺⠽⣞⢯⡞⣽ ⣿⢾⣽⠾⣽⣿⣳⣿⢷⣿⣽⣻⣽⣟⣾⣻⣽⣻⣿⡀⠀⠀⠀⠀⠀⠀⠀⣄⡡⠁⠀⠀⠀⠀⠀⠀⢀⣿⢙⠠⠐⡈⠐⡀⢂⠐⠠⢁⠂⠄⡁⢂⠡⠈⠄⠂⠄⡁⢂⠁⢂⠐⠠⢈⠐⠠⢈⠐⠠⢁⠂⠄⡡⠐⠠⠠⢁⠂⡐⠈⠄⡈⢁⠂⠄⠌⡐⢈⠰⠀⠄⠂⢄⣰⣿⣿⣟⡮⢷⣏⡟⣮⢗⣻⢼ ⣿⣻⣞⡯⣟⡷⣯⣿⢾⣟⣾⣽⣳⣯⢷⡿⣽⣷⣻⣷⣄⠀⠀⢀⣠⣴⡾⠟⢻⣧⣢⠀⠀⠀⠀⣀⣾⠋⠀⢄⣡⣀⣡⠐⡠⢈⠐⠠⢈⠐⡀⠂⠄⠡⠌⡐⢈⠐⠠⠈⠄⡈⠔⠠⢈⠰⢀⠁⢂⠄⠨⠐⡀⢁⠂⡁⢂⠐⡈⠄⠡⠐⠠⢈⠐⡐⠠⢁⠂⠌⠐⢨⣼⣿⣿⣿⢳⣏⠿⣼⡹⣎⡟⣮⢳ ⣿⣳⣯⢷⣻⣟⡷⣟⣾⣿⣳⢯⣷⢯⡿⣽⣳⣯⣿⣿⣿⣿⣿⠛⠋⡁⠠⠐⣀⠨⢝⠛⠿⠾⠛⢋⣥⣶⣿⣿⢿⡿⣟⣿⣷⣶⣬⡰⠀⠂⠄⠡⢈⠐⠠⠐⠂⠌⠠⢁⠒⠠⢈⠐⡀⠂⠄⢊⠀⢂⠁⠂⠔⡀⢂⠐⡀⠆⠐⡈⠄⡁⠒⠠⠁⠄⡁⢂⠐⣈⣼⣿⡿⣟⣾⣿⡹⣎⡿⣱⢏⡷⣹⣭⣛ ⣿⣳⡟⣾⣻⢾⣽⣯⡿⣾⣽⣻⢾⣻⣽⣻⡽⣷⣿⣻⣿⠋⢀⡐⠐⢠⠁⢂⠄⠠⠀⠌⡐⣠⣽⣾⣿⠿⣽⣞⣯⢿⡽⣾⡽⢯⡿⣿⣿⣦⣅⠂⠡⢈⠄⠡⠈⠄⡁⠂⠌⡐⢀⠢⠀⠅⡈⠄⠨⠀⠌⡐⠂⡐⠀⠆⡐⢈⠐⡀⠂⠄⡡⠈⠤⠁⡐⠠⣰⣿⡿⢯⣽⣻⢾⣿⣹⢧⡻⣝⣮⣝⡳⢮⣝ ⣿⣳⣏⡿⣽⣻⢾⡵⣿⣳⢯⣟⣯⣟⡾⣷⣻⣯⣿⡟⠁⡐⢠⠀⠅⢂⠈⠄⡈⢄⠁⣶⣾⣿⣟⡿⣺⣟⣳⣟⡾⢯⣽⣳⢟⣯⡟⣷⣫⢿⣿⣿⣥⡀⠂⠤⠁⠂⠄⡁⢂⠐⢂⠠⠁⠌⡐⠈⠄⣁⠂⠄⠡⢀⡁⢂⠐⡀⠂⢄⠡⠈⠄⡁⢂⢡⣴⠿⢻⣿⣿⣛⡾⣽⣻⣿⡞⣧⢟⡼⢶⣭⣛⠷⣎ ⣿⣳⢽⣻⡽⣯⣟⡾⣷⣻⢯⣟⣾⣽⣻⢷⣿⣿⠋⠄⠒⢀⠂⠌⡐⠠⠈⠄⢠⣶⣿⣿⣻⢞⡾⣽⣳⢯⡷⡾⣽⣻⢾⣭⣟⡾⣽⣳⢯⣟⡶⢯⣟⣿⣧⡔⡈⢁⡐⢀⠂⠌⡀⢂⠁⢂⠄⡁⠂⠄⡈⠄⡁⠂⠄⠂⠄⠡⠈⠄⠠⢁⢂⠐⡀⠛⡉⠐⡀⢻⣿⣯⡽⣞⣷⣻⣯⡳⢯⡝⡷⢮⣝⡻⣼ ⣿⣭⣟⣷⣻⢷⡯⣟⡷⣯⢿⡽⣞⡷⣯⣿⡿⠃⡐⢈⠐⠠⠈⠄⠠⢁⢂⣼⣿⣿⢻⣼⣏⣿⣽⣾⣷⠿⠷⠿⠷⠿⢷⠿⣾⣽⣷⣯⣟⡾⣽⣻⢾⣹⣟⣿⣿⣤⡀⢂⠈⠄⡐⠠⠈⠄⠂⠄⡉⠐⡀⢂⠡⠈⠄⠡⠈⡄⠡⢈⠐⡀⢂⠐⠠⠁⠄⠡⠐⡀⢻⣿⣿⣷⣯⣷⣿⣿⡳⢯⡽⣣⣏⢷⣣ ⣿⢶⣻⢾⡽⣯⢿⣽⣻⡽⣯⣟⣯⢿⣻⡿⠁⠆⠐⡀⠊⠄⠡⢈⢐⣼⣿⣿⣻⡾⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢷⣯⣷⣞⣷⢻⡿⣿⣄⡈⠄⡐⠠⠁⠌⢂⠒⠠⢁⠐⡀⢂⠡⢈⠐⠡⠐⡀⢂⠐⡀⠂⠌⠠⢁⠘⠠⢁⠐⡀⢿⣿⣿⣿⣿⢯⡿⣿⣷⣝⣳⢮⣳⢭ ⣿⣫⣟⣯⢿⣽⣻⣞⣷⣻⢷⣻⣞⣿⡿⠡⠈⠄⠡⠠⢁⠘⢀⣼⣿⣿⡿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣾⣯⣿⡽⣿⣷⣆⠀⠡⢈⠐⠠⢈⠐⡀⢂⠐⠄⠂⠄⠌⠠⢁⠐⡀⠂⠄⢡⠈⡐⠈⠄⡁⢂⠐⠠⠘⣿⣿⣿⣿⣯⢿⣽⣻⢿⣷⣯⣞⢧ ⣟⣷⣻⣞⡿⣞⣷⣻⢾⡽⣯⢷⣯⣿⠁⠆⠁⠌⠠⢁⠂⣨⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣷⣿⣿⣷⢀⠂⠌⢀⠂⡐⠠⢈⠐⡈⠐⡈⠄⡁⢂⠐⠠⢉⠐⡀⠂⠄⣁⠂⠔⡈⠄⡁⠂⢹⣿⣿⣿⣟⣞⣳⣽⢻⡾⣽⣻⣿ ⡿⣞⡷⣯⢿⡽⣾⡽⣯⣟⣽⣻⣾⢇⠂⠄⠡⢈⠐⢠⣾⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣂⠈⠄⠂⠄⢁⠂⡐⠠⠁⠄⢂⠐⠠⢈⠐⡀⠂⠄⡁⠂⠄⢂⠐⡀⠂⠄⠡⠀⣿⣿⣿⣿⣿⣳⣞⣯⣽⣻⢷⣿ ⣿⣯⣿⣽⣯⣿⣷⣟⣳⡟⣾⣻⡏⠨⢀⠌⡐⠠⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣆⠐⠁⡈⠠⠐⢀⠡⢈⠐⠠⢈⠐⡀⠂⠄⡁⠂⠄⠡⠈⠄⠂⠄⠡⠈⠄⢁⢸⣿⣿⣿⣿⣿⣿⣾⣷⢯⣿⣿ ⣿⣻⢿⣿⡿⣿⢿⣯⢷⣻⢷⣿⠡⢊⠠⠀⠄⣼⣿⣿⡏⠀⢀⣴⣶⣾⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣯⡀⠡⠐⢈⠀⠂⠄⡈⠐⡀⠂⠄⡁⠂⠄⠡⠈⠄⡁⢂⠡⠈⠄⡁⠂⠌⠠⣿⣿⣿⣿⣟⣿⣽⡿⣿⣿⣿ ⣷⢯⡿⣽⣻⣽⣻⢞⣯⢿⣻⡏⡄⠄⠂⢐⣼⡿⣿⡏⠀⠀⣿⡿⠟⠉⠉⠙⠻⢿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠈⠄⡈⠐⠠⢀⠡⢀⠁⠂⠄⠡⠈⠄⡁⢂⠐⠠⢀⠡⠂⠠⢁⠈⠄⢹⣿⣿⡻⣟⣿⣿⣿⣿⣿⣾ ⣯⢿⣽⣳⣟⡶⣯⣟⡾⣯⣿⠇⠇⣀⠃⣼⣿⡽⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠁⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠐⠀⡁⠂⠄⠂⠄⢊⠐⡈⠄⡁⢂⠐⡀⠌⠐⡀⢂⠁⢂⠐⠠⢈⠘⣿⣷⢻⡽⣿⣻⣿⡽⣯⢿ ⣟⡿⣮⢷⡾⣽⣳⢯⣟⡷⣿⠁⡂⠀⣼⣿⢧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣬⣽⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣷⣶⣾⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠹⣿⣏⡐⠠⠈⠐⠈⡐⠀⠂⠄⠂⡐⠀⠂⠄⡈⠐⡀⠂⠌⠠⢈⠐⠠⠈⣿⣿⣯⣿⣿⣿⣿⣟⣿⣻ ⣿⣽⣳⢯⣟⡷⣽⢯⣾⣽⣿⠀⡀⢿⡿⣿⡾⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠻⢿⣿⣦⡀⠀⠀⠀⠀⠀⢹⣿⣷⣀⠡⢈⠐⠀⠡⢈⠐⠠⢀⠡⢈⠐⠠⠁⠄⠡⢈⠐⠠⠈⠄⠂⣹⣿⣟⣯⣿⣽⣷⣿⣿⣿ ⣿⣾⣽⣿⡾⣽⢯⡿⣷⣻⣿⠄⢐⣿⣃⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⢿⣿⣿⣔⠀⠄⢁⠂⠄⡈⠐⡀⠂⠄⡈⠐⡈⠐⡀⠂⠌⠠⢁⠂⠐⢸⣿⡿⣽⣾⢿⣽⣾⣟⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡆⢼⡟⣌⠲⡹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠁⠀⠀⠀⠀⠀⢹⣯⣟⣿⡧⢈⠀⡐⠠⢀⠡⢀⠁⠂⠄⠡⢀⠡⢀⠡⢈⠐⠠⢀⠡⠐⣿⣿⢯⣿⣟⣿⣾⣻⣽ ⣿⣿⣿⣷⣿⣯⣿⡿⣽⡷⣿⣿⣾⡏⡔⢣⡑⡚⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣟⣼⣿⡆⠐⠠⢁⠀⠂⠄⠊⡐⢈⠐⡀⠂⠄⠂⠤⢈⠂⢀⠂⢘⣿⣿⣻⣿⣾⣿⣽⣿⣻ ⣿⣿⣷⣿⣿⢯⣷⣻⢯⡿⣽⡻⣿⡗⣌⠣⡜⣑⠺⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢶⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣮⢿⣿⡀⠅⠠⢈⠐⢈⠐⡀⢂⠐⠠⠁⠌⡐⢀⠂⠌⢀⠂⣼⣿⣿⣿⣷⣿⣿⣿⣿⣿ ⣿⣾⢳⣿⡞⣯⣷⣿⢻⣿⣷⢻⣽⣿⣦⠓⡜⣤⠓⡌⢻⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⡞⣽⣿⡇⢠⠁⠂⠈⡄⠂⠐⢠⠈⡄⠁⠂⠐⢠⠈⡄⢠⠀⣿⣿⣿⣿⣿⡟⣿⢻⣿⣿ ⣿⣞⡿⣾⣽⣻⢾⣽⣻⣾⢿⣷⣿⣿⢿⣶⡱⢌⠲⣉⢎⡹⢿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⣟⣼⢻⣼⣇⠃⠤⢈⠐⢀⠈⠄⠂⠐⠀⠡⢈⠠⢀⠢⠐⢀⣾⣿⣿⣿⣿⡿⣽⣻⡿⣾⣻ ⣿⣽⣻⢷⣯⣟⣯⣟⡷⣯⢷⣿⣿⠃⠀⠻⣿⣾⡱⢌⠦⣑⠣⢛⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢫⣞⡽⢾⣏⠂⠐⡀⠈⠄⣈⣤⣾⠿⠛⠛⠛⠛⠛⠿⣶⣿⣿⣿⣟⣿⣿⣿⣻⢷⣿⣻⣽ ⣿⢾⣽⣻⢾⡽⣾⣹⢯⡽⢯⣿⣿⠀⠀⠀⠘⠿⣷⡾⡰⢡⡙⣌⠳⣉⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣝⢯⡞⣽⣿⠃⠨⢀⣰⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣻⣿⣿⣷⣻⣯⣷⢿⣻ ⣿⣻⢾⣽⣳⣟⣳⢯⡿⣽⢳⣻⢿⡆⠀⠀⠀⠀⠘⠻⢿⣦⠵⡨⠱⣌⢚⠲⣙⢻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣽⣛⣮⢿⣿⠃⢤⣱⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣻⢷⣻⣿⣻ ⣿⣽⣻⢾⡵⣞⣯⢿⡽⣞⣯⢷⣻⢿⣄⠀⠀⠀⠀⠀⠀⠙⠿⣶⣓⠬⢆⠳⢌⠎⢦⡙⢛⠿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣟⡳⣧⣿⣼⡟⢃⣼⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣯⣟⣯⡿⣞⣿ ⣿⢾⡽⣯⢿⡽⣾⢯⡿⣽⣞⣯⣗⣻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣮⣚⣌⠚⡴⣈⢇⡚⢤⢩⡙⣛⡻⠷⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣯⣾⡿⣿⡿⠋⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡷⣯⣷⢿⣻⣽ ⣿⢯⡿⣽⣳⠿⣭⣟⣾⡳⢯⣞⡧⣿⡽⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣯⣴⣌⠦⣙⢂⠣⡜⠤⣣⣾⠟⢡⢋⢿⣯⣛⡹⣛⠿⠿⢶⢶⡶⢶⡶⢶⠶⡶⢶⠶⡶⠾⠟⣟⡛⢫⢍⣱⣶⠟⠉⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣿⣿⣟⡷⣯⡿⣿⣽ ⡿⣯⢟⡷⣯⣟⡿⣞⣷⣻⣟⣾⡻⣷⣻⣳⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⠷⢾⣷⡼⠿⢋⣡⡾⠟⠛⠛⠻⣷⣶⣡⠚⡔⢣⢢⡙⠴⣘⢢⠓⡜⢢⡙⣌⢣⡙⢤⣪⣵⠿⠋⢀⣤⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣾⣿⣿⡾⣽⣻⣽⣷⣻ ⣿⡽⣯⢿⣼⣳⢿⣹⣞⣧⣟⣾⣹⣟⢷⡯⣟⣾⣻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠁⠂⢂⠐⠀⠆⢠⡿⠀⠀⠀⠀⠀⠘⣯⠛⣷⣬⣃⠦⣙⢢⡑⢎⡙⠬⡱⣘⣰⣦⡿⣟⣩⣴⡶⢿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣟⣾⣿⡿⣿⣽⣳⣯⢿⡾⣽ ⡿⣽⣳⣟⣮⡽⣯⢷⣻⡼⣞⣧⢻⣞⣯⣽⢻⣞⡷⣯⢿⡿⣷⣦⣄⡀⠀⠀⠀⢸⡇⠠⠁⠌⢀⠐⠈⡐⠈⣿⣄⠀⠀⠀⠀⣸⡟⠀⡀⠉⠛⢷⣮⣤⣍⣦⣭⣶⣷⠿⠿⠛⠛⠉⠉⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⢿⣟⣿⣿⣿⣷⣻⣞⡿⣿⣽ ⣿⣳⢟⣞⣧⢿⣽⣳⢯⣽⣳⣏⡿⣼⣳⣞⣿⣼⣻⡽⣾⣝⣯⣿⣿⠛⡷⣶⣤⣸⡇⠐⠈⠄⠂⠄⡁⠄⠐⠈⠛⢶⣦⡴⠾⠋⠐⡀⠄⠡⢈⠠⠀⠉⡉⠉⠉⠄⢀⠂⠠⠁⠂⡁⠌⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⣟⣾⣿⡿⣿⣻⣿⡿⣿⣞⡷⣯⣟⣷⣻ ⣷⡹⣞⠾⣜⡳⣞⡼⣳⢮⡗⣮⢵⣳⢳⡞⣶⢧⡷⡽⢶⣹⣾⣿⠃⣇⠲⢡⢩⢹⣿⠀⡁⠐⡀⠂⠄⠂⢈⠰⢠⣶⠶⠶⢶⣤⠂⠠⢀⠁⠠⠀⠂⢁⠐⠈⠠⢈⠠⢀⠡⠀⡁⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⣿⣽⣿⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣽⣻⢷⣯⡿⣽ ⣷⡹⣎⡟⣜⡳⣝⡺⣕⢯⣞⣱⢏⣞⣳⡝⣧⣻⢼⣹⢏⣷⣿⠇⡽⢠⢃⠇⡎⡔⣿⡆⠀⠡⠐⠈⢀⠂⡀⣲⡟⠀⠀⠀⠀⠹⣿⠀⠂⠌⠀⡁⢈⠀⠄⠁⠂⢀⠂⢠⢄⣁⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣤⡶⠟⢹⣿⣻⣛⠷⣯⣻⣝⣯⣛⣧⣻⣜⣳⣮⣳⣽⣶⣛⣾⣳⣻⣳
⠀⠀⢀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠙⡄⠀⠀⠀ ⠀⡴⠏⠀⠀⢸⡵⢤⠖⢢⡀⠀⣰⠋⠀⠀⠀⢀⡇⠀⠀⠀ ⢸⠀⠀⣠⠆⠘⡦⠨⠕⢘⡗⠤⠃⠀⠀⠀⠀⡼⠀⠀⠀⠀ ⠘⠢⠚⠙⢤⠀⠓⢒⣋⡉⣀⣀⣀⣀⠀⠀⠼⣁⠀⠀⠀⠀ ⠀⠀⢀⡴⠋⡴⠊⢡⡄⠀⠀⠀⠀⣼⡙⢦⡀⠀⢱⠀⠀⠀ ⠀⠀⡎⠀⣞⡠⠤⢾⠇⠀⣀⡀⠀⠻⠁⠀⢹⠀⣸⠁⠀⠀ ⠀⠘⣇⠄⡿⡀⠀⢨⠃⠀⠟⠀⠀⠈⠈⢀⣼⡴⠋⠀⠀⠀ ⠀⠀⠈⠙⠻⣳⣀⠀⠳⡤⠤⣤⠤⠤⠖⠋⡹⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠋⠹⣆⠀⠈⢉⡏⠢⣀⠀⡰⠱⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢙⢆⣠⠞⠒⠒⠛⢦⡀⠈⣭⠁⠀⠹⣤⡀⠀⢠ ⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠈⠉⢇⣀⣀⠤⠻⠤⠴⠊
⠀⡰⢸⠿⣽⣏⠿⣭⢯⡽⣭⢯⡽⣭⢯⡽⣭⢻⡝⣯⣛⢿⣧⡂⠄⠠⠀⠄⣀⠢⠐⡄⢢⠐⠠⡐⢤⢎⡴⣩⠖⡭⢎⡵⡩⢖⣤⣂⡔⠰⡈⠔⠠⢀⠀⠠⠀⢆⡐⢢⠐⠠⢀⠂⠄ ⠐⡠⢉⢿⣳⢯⣟⣧⡟⣼⢎⡷⣺⢵⣫⢞⡵⣫⢞⡵⣫⣏⡟⣿⡌⠠⢁⠂⠄⠢⢑⠨⡐⡈⢶⣫⢓⡎⢶⡱⣛⡼⢣⢞⣱⣋⢶⢫⢿⣦⡑⠌⢂⠠⠈⠄⡑⢂⡘⠄⣉⠐⡀⠊⠄ ⢀⠱⡈⠆⣿⢻⣞⣧⣟⡷⣏⡾⣱⢏⡾⣹⢞⡵⣫⠾⣵⢫⢾⣹⢿⣄⠂⠌⠠⠑⡨⠐⠤⣱⣿⠲⣍⡞⢧⡳⣍⠾⣙⢮⡕⣮⢋⡯⣞⡽⣷⠈⠄⡐⠀⠆⢠⠡⡐⢡⠂⡐⠠⡁⠂ ⠀⠆⠱⡈⠜⣿⣞⣷⣻⢾⣝⣳⡽⣎⢷⡹⣮⣝⣳⢻⣜⢯⡳⣏⠿⣿⣆⠈⠄⠱⡀⢍⠰⣿⢣⡟⣬⣝⣣⠷⣩⢯⡝⣞⡼⢣⡟⣼⢣⡟⣽⣮⠐⠠⠁⠌⡠⢂⠍⡄⠃⠄⠁⠄⡁ ⠈⡌⢡⠐⡌⠸⣿⡾⣽⣻⣞⣧⠿⣜⢯⣳⢳⣎⢷⣫⢞⡧⣟⡭⢿⣱⣿⣆⠈⡔⠨⠄⣽⣟⢧⣛⡖⣮⠵⣋⠷⣓⢾⡱⡞⣧⢻⡜⣷⡻⣽⣿⡃⠄⡁⠂⠔⡨⠐⡌⢡⠈⡐⠠⠐ ⠐⢌⠂⡜⠠⠁⠞⣿⣷⣻⣞⣾⢻⡽⣎⢷⣫⢞⣧⣛⢮⡳⣝⢾⡹⣖⢯⣿⡐⢠⠑⡌⣿⡾⡽⢮⣝⢶⣫⡝⣯⡝⣶⡹⣝⢮⣳⣻⣵⣻⡗⣿⡇⠐⠠⢁⢂⠡⢃⡘⠄⠂⠄⡁⢂ ⢈⠢⢁⠆⡡⠃⠄⡹⢿⣳⣟⡾⢯⣷⣛⢮⡳⣏⢶⡹⣎⢷⡹⣎⢷⡹⡞⡼⣷⡂⡌⠰⢹⣿⣟⣯⡞⣷⡭⣟⣶⣻⣵⣻⣭⢷⣯⢷⣞⣷⣻⣽⡇⢈⠐⡀⠂⡅⢢⠘⡄⢉⠐⡀⠂ ⠠⡑⢌⠢⠡⠌⠐⠠⢙⣿⢾⣽⣻⢶⣫⢷⡹⣎⢷⡹⣎⢷⣙⢮⣇⠟⣭⠳⣝⢳⢮⠱⡌⢿⣿⡾⣽⣳⢿⡽⣶⣻⣞⡷⣯⣟⣾⣯⢿⣞⣯⣿⡇⠀⠆⡀⢃⡘⢄⠡⠂⠌⡐⠠⢁ ⢀⠣⡘⠄⢇⠸⢀⠃⠄⡸⣿⣼⣻⢧⣟⡼⣣⢟⡼⣣⣛⡼⣛⡤⡜⢿⡠⢿⡘⣇⠟⣟⡻⣜⡻⢿⣿⣻⡿⣿⢧⡿⣼⣿⣧⣿⢻⡼⣿⢼⢧⣿⡃⡘⠠⢀⠇⢠⠘⡄⠛⢠⠀⢃⠄ ⠢⡑⢌⡘⢢⠁⠆⡈⢄⠡⢙⣿⣽⢯⡞⣵⢫⡞⡼⣱⢣⡞⣥⢳⡹⢶⡹⣲⠝⡮⣝⠶⡳⢼⣱⣋⢶⢫⢟⡻⣛⠿⡹⣍⠶⣩⢏⡷⣹⢾⣯⣿⢧⠀⢃⠄⢊⠄⢣⠌⡡⠂⠌⢂⡐ ⡡⡘⠤⠚⡄⢊⠤⠑⣂⠂⣉⠫⣿⡿⣜⢣⡳⣍⢳⣣⠗⣮⡕⣏⠾⣥⢳⡣⣟⡱⣎⢯⡝⢧⡳⣜⣣⠟⡮⢵⣋⠾⣱⡍⡾⡱⢎⡞⣥⣛⡼⢿⣌⡐⡈⠌⢂⠎⣡⠚⡄⠱⡈⠔⠠ ⡰⢡⡙⡜⡸⢄⠆⢣⢄⠣⢴⣿⠻⣵⢊⣧⢓⣮⠳⣥⣛⢦⢻⡜⣧⢫⢧⢳⣍⠷⣙⢮⠞⣧⢻⡜⡶⢫⣝⡳⢎⡻⣴⢹⡲⣝⢣⡞⢦⡽⣸⣛⠿⣷⣌⠘⡄⡚⢤⠓⡌⢡⠐⣉⠐ ⠁⢂⠡⢈⠡⠈⠌⠠⡈⣷⡿⢣⡟⡴⣫⠖⣏⢶⡛⢶⣩⢞⣣⡝⢮⣓⣏⡳⣎⢟⡹⣎⢿⣸⢣⡝⣞⡳⢮⡹⣭⢓⣧⠳⣽⡸⣣⣝⠳⡞⣥⢏⣟⡳⢿⣇⠈⡑⢊⠑⡈⠡⠉⢂⠉ ⠈⠄⠂⠄⢂⠡⢈⠰⣼⡟⣼⠳⣜⢧⣓⡻⣜⣣⣛⢧⡝⡮⣵⢚⡧⢏⡶⣹⣜⣫⠵⣎⡗⣮⠳⣝⣎⠷⣫⢵⣋⢾⡸⡝⣦⢳⣓⢮⡛⡽⣜⢯⡺⣝⢯⣻⣦⠐⢀⠂⠄⡁⠂⠄⠂ ⠠⢈⠂⡘⢀⠂⠤⣿⡿⣹⢖⡻⣜⡳⢎⡳⡵⢮⢵⡺⣜⢳⣎⢻⡜⢯⡜⡧⢞⡼⣹⠲⣝⢎⡟⡼⢼⡹⣱⢮⡝⡶⣭⢳⣣⢯⡜⣮⣝⡳⣝⢮⡳⡽⣎⢷⣻⣮⠠⢈⠐⠠⠁⠌⡀ ⠐⠀⠒⢀⠂⢌⡽⣣⢟⡼⣣⢟⡼⢭⡏⢷⣭⢳⣎⠷⣭⢳⣮⣷⣽⣧⠿⠙⠎⠓⠃⠛⠨⠉⠜⠙⢊⠑⠓⠚⠿⠾⣵⣯⣞⣧⣛⠶⣭⣳⠽⣎⡷⡽⣭⢷⡻⣿⣖⠠⠈⠄⡁⢂⠐ ⠤⠣⢜⡠⢌⡼⣳⡝⣮⢳⡝⣮⡝⣮⡝⣧⢞⣳⣮⡿⠟⠛⠉⠉⡀⢀⠀⠄⠀⠂⠐⠀⠂⠉⠀⢂⠠⠀⠌⠠⠀⠒⠀⠠⢉⠙⠛⢿⣶⣫⢿⣱⢯⡽⣞⣯⣽⣳⣿⡆⢡⠒⡰⠄⢆ ⠌⣑⠢⡘⢴⣫⢧⡻⣜⢧⣛⢶⡹⢶⣹⢮⡿⠟⣧⣔⡀⢄⣐⠀⠀⡀⠀⠠⠐⠀⠂⠀⠐⠀⡐⠀⠄⠂⠐⡀⠡⠐⠈⠠⣠⢬⠐⢦⣼⡿⢿⣽⡾⣝⣳⡽⣶⣻⣽⣷⠡⢊⠱⡈⢆ ⠘⡄⢣⠐⣹⡖⣯⢳⡽⢮⣝⣮⡽⣣⣿⠏⢻⣤⣼⣿⣿⣿⣿⣿⣦⠀⠠⠁⠀⠐⠀⠁⢀⠂⢀⠀⡀⠌⠀⠄⡐⠠⢸⣷⣿⣿⣿⣿⣿⣧⣷⡹⢿⣽⣳⣟⣳⡽⣾⣿⡑⢌⠱⡈⠆ ⠂⡜⢀⠣⣽⢞⣭⢷⣫⠷⣞⠶⣽⡿⢁⠐⢸⣻⣿⡟⣿⣧⢌⣿⣿⡄⠐⢀⠀⠁⠠⢈⠀⠄⠂⠀⠄⠂⠡⠐⠀⣁⣧⣿⣿⡤⣻⡟⣿⣿⡇⡐⢩⢿⣷⣞⣷⣻⢿⣾⠅⡊⠤⢑⡈ ⠁⢆⠡⢂⣿⢯⣟⣾⢳⣻⣭⢿⡿⢸⠀⠂⣿⣿⣿⣿⢛⣿⣿⣿⡿⡅⠈⡀⠄⡁⠂⠀⢄⢬⣠⡈⠠⠈⠄⡈⠄⠀⢋⣿⣿⣿⣿⢛⣿⣿⣷⠈⢆⢚⣿⣿⣞⡽⣯⣿⡃⠜⡠⢃⡐ ⠉⡔⡈⠆⢿⣿⣯⣞⣯⢷⣞⣿⠇⡈⠔⠠⢹⠹⣿⣿⣾⣿⣿⠟⢃⠠⠐⠀⠄⡐⠠⢁⠈⠻⠗⢃⠠⢁⠐⠠⢈⠁⡂⠜⢻⣿⣿⣿⣿⡿⠛⡨⢐⡌⣿⣷⢯⣟⣿⣿⡇⡘⠤⣁⠂ ⠌⡰⢈⠜⡨⣿⣷⣟⡾⣯⣞⣿⡰⢁⠎⡱⢢⠱⣌⠫⢍⡉⠡⢈⠄⢂⡐⡈⢔⠺⣷⣮⣼⣦⣼⣤⣶⣼⣿⠂⡁⢆⠡⢌⠢⡘⢍⢫⢋⡜⣣⢕⡢⢜⣽⣿⣟⣾⣿⡏⠔⡡⢒⠠⠡ ⠐⡡⢌⠢⡑⠼⢿⣿⣽⣳⢯⣿⣧⠘⣬⢱⡋⠷⣌⠳⡌⡔⡡⢊⢌⡰⢠⠑⡌⡐⢻⣯⡳⢭⣏⡳⣽⡟⢢⡐⣡⠊⠴⣈⠦⡱⢌⡲⡩⢖⡱⢪⣜⢣⣿⣿⣿⣿⠟⢠⡑⠄⢣⠈⡅ ⡌⢰⠈⠒⣤⠘⡎⣿⣿⣯⡟⣾⣿⣵⡌⢣⡞⢱⡎⣵⠘⣴⠑⢪⡔⢢⠑⠊⣴⠉⣦⢹⣿⣧⣿⣿⠋⡔⢣⠒⢡⡎⣵⡌⣶⢱⣮⢱⠓⣿⣾⢱⣾⣿⣿⣿⣿⠉⢢⠁⢰⠈⡆⢱⠀ ⢀⠣⡘⠰⣀⠒⡰⠄⢛⢿⣿⣯⣿⣷⣽⡺⣜⣧⡻⣴⢫⡖⣝⣦⣓⢮⡱⣍⢦⡹⢤⠳⣼⡙⣧⢎⣝⡲⣍⣎⢷⡸⣥⡻⣜⣳⢮⣏⢷⣳⢮⣷⣿⣿⡿⢛⡡⢊⠔⡨⢆⠱⣈⠆⡱ ⣌⠱⣌⠓⡬⡑⢆⡉⠂⠀⠈⢙⠻⠿⣿⣿⣿⣽⣟⣷⣯⣛⡷⢾⣹⢮⢷⣛⣮⡽⢯⡷⣞⡽⣎⣟⣮⠷⣏⡾⢧⣟⣳⣻⣝⣻⣾⣽⣿⣿⡿⠟⠋⢁⠀⠤⠑⡊⢌⠱⣈⡑⢢⢉⠒ ⠈⠃⠌⡉⠔⠉⡐⠄⡡⢈⠡⢀⠀⡀⠀⠈⠉⢻⡻⠿⠿⡿⢿⠿⢾⠿⡾⢷⣭⠿⣭⠷⡽⣯⡽⢮⡽⡿⢿⢾⠷⣾⠻⡟⣟⣛⣛⡏⠥⠀⠀⠄⠠⢀⢌⡰⢡⠘⡄⠣⢄⠘⢄⠊⠌ ⠠⢁⠂⡐⢈⠐⡀⠓⠴⣆⡒⡄⢢⠐⡁⠂⡁⠀⠛⢯⣗⡹⢎⡽⢮⡹⣭⠳⣎⢟⣼⡟⠀⠈⢿⣧⣏⢵⡫⢮⣝⢲⢫⡝⣳⡼⠋⢁⠀⢄⠡⢎⡱⣬⠦⠓⠤⢃⠬⡑⢢⠡⢌⡘⠤ ⠐⡀⢂⠐⡀⠆⠠⠁⠂⠌⡉⠙⠣⠹⢤⡡⠄⡁⠂⢀⠉⠛⠷⣾⣧⣛⡴⡻⣜⣾⡿⠀⢀⠀⠈⢻⣯⣎⠷⡳⢮⣭⡷⠞⢋⠀⠰⢠⣘⡴⢋⠮⡑⢦⠮⡑⢎⢖⠲⡱⢎⡓⢮⡜⢧ ⠶⣡⠖⠮⣔⢣⢳⡘⣤⠳⣌⢓⡣⢓⠦⣱⠣⣌⠱⢀⠀⠂⡀⠀⠉⠛⠿⠷⠯⢷⠃⠀⠠⠀⠀⠀⠿⠿⠾⠟⠋⠁⡀⠐⡀⠎⣱⠢⣗⣩⣯⣷⣍⡫⣴⢉⢮⡌⣛⣴⣧⣙⠣⣜⢢ ⡳⢤⡛⡜⣌⢣⠎⡵⢢⠗⣌⢎⡱⢍⡲⢥⠳⡌⠆⡀⠄⠐⠀⠀⠁⠠⠀⠠⠀⠀⠀⠐⠀⠀⠁⠄⠀⡀⠄⠀⢀⠂⠠⢁⡐⢘⣺⢟⣻⣿⣿⣿⣿⣿⣶⣿⣶⢞⢯⠻⡼⣛⠷⣭⢶ ⡝⢣⢳⡹⣌⠳⢎⠲⡍⡞⣜⣊⠶⡱⡘⢆⡣⢍⡐⠠⢀⠈⢀⠈⠀⠀⠄⢀⠀⠂⠁⠀⡀⠁⢀⠠⠀⠀⠀⠠⠀⠀⠂⠄⠒⡠⢼⠊⡖⣿⣿⣿⣿⣿⣿⣿⣿⡍⢎⢳⣱⣍⢞⣰⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠓⠦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠘⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄ ⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⠤⠶⠶⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀ ⠀⣴⠋⠁⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⠋⠉⠉⠉⠉⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀ ⢸⠃⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⢀⣀⣠⣤⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠋⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠚⠋⠉⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⡤⠤⠖⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠈⣇⣤⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠩⠀⠀⡀⢀⡟⣼⡿⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠓⠦⣤⣀⣀⣀⣀⣀⣀⣠⡤⠴⣿⠀⠀⢸⣿⡇⣀⠀⠀⡤⠤⠒⠂⠀⠀⠀⠂⠀⢐⣵⣟⣁⡼⠣⡀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⡎⠸⣻⢱⠀⠀⠀⠀⠀⢀⡤⡴⠋⠉⠉⠀⢀⠏⠉⠳⣧⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢦⣌⣀⣠⢧⣏⡤⠤⢶⣒⣿⣥⣶⡧⣲⠤⢄⡠⠋⠀⠀⢀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡯⣯⣾⡷⡯⠓⠒⠙⠫⠦⠘⣚⠶⠫⢠⠀⠀⢠⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⡟⠓⢦⣧⣀⣀⡠⢤⠒⠋⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠑⠒⠚⢲⢭⢱⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⣞⣆⣤⢾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⡤⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢑ ⠑⢲⠷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⡟⠉ ⠀⠸⡇⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⡇⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠈⠙⣲⣀⠄⠠⠄⠒⠢⠤⠠⢴⠋⠁⠀⠀⠀⠀⠀⢸⠇⠀ ⠀⠀⣧⠀⠀⠀⠀⠀⣀⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⢳⡀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⢸⠀⠀⠀⣠⣾⠀⠀⠀⣂⡠⠤⢤⣤⠬⠤⢄⣰⠀⠀⠈⣷⡀⠀⠀⡾⠀⠀ ⠀⠀⠸⢦⣀⣼⠋⢏⢀⡜⠊⠁⢠⣾⣿⣿⣿⣦⠀⠈⠑⠶⡀⣹⠹⡦⠖⠃⠀⠀ ⠀⠀⠀⠀⢸⠃⠀⠀⠉⠀⠀⠀⠸⣁⣼⣿⣇⡸⠀⠀⠀⠀⠈⠁⠀⢻⡀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⣠⡴⠒⠉⠓⠲⢼⣈⠯⠒⠋⠙⠲⣄⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⢹⠀⠀⣰⠋⢲⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠋⢳⠀⠀⢸⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⣧⠀⣏⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠈⡇⢠⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣿⡀⠀⠀⠀⠀⠀⢶⡶⠆⠀⠀⠀⠀⢀⣼⡶⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⣀⠽⠓⠲⠤⢤⣤⣤⣤⣄⣠⡤⠤⠶⢯⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠣⠸⠛⠒⠒⢲⡀⠀⣀⡬⠦⣄⠀⢠⠖⠒⠒⠻⣀⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢑⠋⠁⠀⠀⠀⢹⠉⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠀⠀⠈⠙⢿⣆⠀⠀⠀⡻⢷⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢰⡟⡟⣻⣬⣌⢩⠟⢠⣤⣶⡀⠀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣸⠛⠁⠻⠶⡟⣿⠀⢠⡿⣩⣿⣾⢻⣝⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣀⠠⡞⣿⣟⢷⡀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⣤⣄⣈⠀⠀⠀⠰⣾⠇⠀⠸⢿⡿⣽⡯⣽⣿⡿ ⠀⠀⠀⠀⠀⣠⣴⠶⠶⡟⠀⠐⢿⡟⣛⣶⣷⢿⣟⢿⡟⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣰⡾⠟⠉⠁⠀⠀⠀⠉⠙⢿⣦⠀⠀⠀⠀⠀⠀⠈⠁⠈⠛⠳⡿⠁ ⠀⠀⣿⢻⡗⢡⡤⡵⡖⣷⡀⠀⠸⣧⣿⡄⢿⣾⣽⠼⠷⠀⠀⢸⡇⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣎⣷⠘⠿⠞⠛⣺⣇⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⢀⣀⣼⣧⠆⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡅⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠛⠉⠉⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⢰⡟⠀⠀⣠⠴⢤⡀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⣀⣀⣠⣴⠾⠋⠀⠀⣄⡿⠁⠀⠀⣧⠀⠈⣿⡁⠈⣹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠙⢷⣆⠀⠀⠹⣦⡀⠀⣁⣾⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣼⡋⠀⠀⠀⠀⣀⣤⠶⠚⠛⠛⠉⠉⠛⠓⠒⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠈⠉⠛⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠿⠉⠙⣷⠶⠶⣾⡋⣤⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⣧⠀⠀⠀⣠⡟⠀⠀⣿⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠻⣆⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⣤⣌⡛⠛⠛⠉⠀⠀⠀⠘⣿⠛⠛⠁⠀⠀⢰⡖⢶⡄⠀⠀⠀⢠⣿⣿⣿⠀⠹⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡏⠀⣾⡁⣸⡇⠀⠀⠀⠀⢀⣤⣄⠻⣦⣾⣳⢚⣧⣀⣉⣉⣀⣀⡄⠀⠙⣿⣿⠟⠀⠀⣿⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠁⠀⣀⡀⠀⠀⢿⣐⣸⠇⠀⠈⢿⣼⢹⡀⠉⠉⠉⣼⢰⡶⡄⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⣏⠉⢹⠄⠀⠀⠉⠁⠀⠀⠀⠀⠉⣿⠳⣄⣠⠞⠹⡄⠉⣁⣀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⢀⠉⠉⠉⠀⣤⡀⠀⠀⢀⣤⣀⣀⣀⣽⣄⣀⡀⠀⠀⠉⠐⠧⠞⠃⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀⡿⠀⢀⣴⢦⡄⠀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠷⡤⠶⠛⠻⠶⠶⠞⠋⠙⠛⠛⠛⢡⡟⠉⠙⠷⢬⣉⣻⡟⠿⠶⣦⣤⣤⣤⣤⣤⡴⠛⠁⠀⣀⣠⣴⠿⠃⠀⠸⣇⠀⢻⡞⠋⢹⣷ ⠀⠀⠀⠀⢀⡴⠶⣦⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣀⣀⣀⣀⣈⠛⠶⠶⠶⣿⠃⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠹⣦⡈⢀⣰⡾⠏ ⢀⣴⠚⠳⢾⠁⢀⣼⠀⠘⣧⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁⠀⠀ ⠀⢿⣤⣀⣠⣤⠿⠋⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⢩⡟⠓⣷⡀⠀⠀⢠⣤⣤⠀⠀⠀⠀⢸⣏⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡈⣻⣦⣤⣿⡀⠙⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠘⠛⠷⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀⣀⡀⠀⢀⣴⣾⡿⠛⠛⠛⠋⠛⠛⠛⠛⢻⢿⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢿⠻⣍⡻⣜⢣⣏⠽⣩⢏⡝⢯⢟⡿⢿⣿⣿⣯⣥⣐⢷⣤⡀⠠⢀⠠⠀⠰⣏⢇⢮⡙⡛⠿⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⠀⠀⠀⠀⢠⣾⡿⢯⡹⢎⡳⢭⠶⣩⢳⢬⢳⡓⢾⣘⠧⣮⢱⢏⠶⣹⡛⡿⣿⣿⣿⣿⣄⠀⠠⠐⠀⠛⢮⡦⠝⠁⢀⠀⠈⠛⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⠿⣿⣿⣿⣶⣶⣿⡟⡭⢧⡹⣎⠽⣭⢚⡵⣋⣎⢧⣋⠷⣊⡷⢬⠳⢮⡝⢶⣙⠶⣡⢏⡽⢿⣿⣦⠀⠐⠠⠀⢀⠀⠀⠌⠀⡀⠂⡀⢀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⢊⠐⠠⠀⠄⢸⣿⡟⡼⣱⢣⡝⣎⡳⢬⡛⣴⢫⣿⣶⢭⣚⠵⣚⡭⣛⠶⣩⠗⣮⢹⡱⣎⡵⢫⠽⣿⣧⠀⡀⠁⡀⠂⢡⡞⡵⢲⣄⠀⠄⠂⠠⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⡁⠂⠌⠠⠁⠌⣾⣿⡹⢲⣍⠮⣕⢮⡙⢧⣙⢦⡳⣹⣿⣧⣋⣞⡱⢮⡕⣫⡕⣏⢖⡫⢵⡚⣜⢧⡛⡼⢿⣷⡄⢀⠐⢀⠈⢳⡵⢃⣾⠁⠀⠠⠁⠐⢠⡟⡜⢻⢿⣷⣄⠀⠀⠀⠀⠀ ⠄⡉⠄⡑⠈⠄⣿⡷⣍⠷⣜⢻⣘⢮⡙⢧⡹⢆⣗⡣⢿⣿⡞⡴⢭⢳⡼⣱⡚⡼⣪⢝⡣⣝⢎⣳⢹⡜⣭⢻⣿⣧⣤⡀⠀⡘⠮⠝⠁⠀⠌⠀⠌⠀⠄⢟⡼⠇⠊⠙⠿⣷⣤⡀⠀⠀ ⠂⠔⠠⢈⠐⡈⣿⣿⣌⢳⢎⡳⡜⢮⡝⢮⣙⡳⢬⢳⣹⣿⣟⡼⢣⡳⡜⣥⢛⡴⢭⢞⡱⢮⡝⣲⢭⡚⢶⡙⣖⢻⢻⢿⣷⣶⣄⣀⠐⠈⢀⠐⢀⠈⡀⠀⢀⠀⠄⡀⠀⠈⠛⢿⣷⣦ ⠡⠌⠐⡀⠂⠄⢻⣿⡬⣓⢮⠳⣍⠳⣎⢷⡡⢯⡙⣦⣹⣿⡟⣜⡣⢗⡹⢲⡍⣞⡱⣎⡳⢣⣞⡱⢮⡹⢮⡱⣞⢣⣏⠞⣭⢫⠿⣿⣷⣤⡀⠀⠂⢀⠀⠁⠠⠀⠄⡀⠂⠁⠠⠀⠀⠉ ⠡⢈⠐⠠⠁⠌⡘⣿⣷⡭⢎⡳⢎⡽⣸⠲⡝⢶⡙⣦⣽⣿⣛⢬⠳⣍⢗⡫⣜⢥⣓⢮⡱⢏⠶⣭⢣⡝⣣⠽⣌⣷⣬⣿⣴⣿⣷⣷⣿⣿⣿⣆⠀⢂⡴⢞⣄⣄⡀⠠⠀⡁⠐⠀⡁⢺ ⡁⠂⠌⠠⢁⠂⣰⣾⣿⣿⣌⡳⣍⠶⣣⢛⡜⢧⡹⣼⣿⠷⣩⢎⡽⡸⢎⡽⣘⠦⣏⠶⣙⢮⠳⣎⣳⣼⣷⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣧⠈⣗⠭⣒⠬⡗⠀⠐⢀⠠⠁⠀⣎ ⠄⠡⠘⢀⢂⣿⣿⢯⡹⢻⣿⣶⣭⣞⣥⣫⣼⣧⣿⣿⣋⠷⡱⣎⢶⡙⢧⡚⣭⠞⣜⢣⡏⣎⣷⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠸⣿⡆⠈⠓⠋⠉⠀⡈⠠⢀⠠⠀⠁⠈ ⠌⡠⢁⢂⣾⣿⣋⢶⣩⠳⣜⡹⡻⢟⡿⢟⡟⢯⢳⡱⣎⢳⡱⢭⣲⠹⣖⡹⢆⡻⣌⣳⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠂⠠⠐⠀⠠⢀⠀⠀⠂⠁⠄ ⢂⠐⢠⣿⣿⢣⠞⣦⢣⡛⡴⣣⡝⣣⠞⣥⣛⢎⢧⢳⡜⣣⡝⣣⠮⣝⡲⣍⡳⣱⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡿⠏⠀⠀⡀⢀⣿⡇⢀⠁⠄⠠⠈⣠⢴⡲⢶⡁⠈⠀ ⠀⢬⣿⡿⢎⢧⣛⢬⡣⣝⠶⣱⣚⢥⣻⣴⢣⢏⣎⢳⡜⡵⣚⢥⠻⣔⡳⢬⣳⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠠⠁⠄⣸⣿⠁⠀⠄⠂⠐⠀⢏⠖⣩⢲⣱⠀⠁ ⣠⣿⡟⢧⣋⢶⡩⢖⡹⣌⡳⡱⢎⡖⣿⣿⣓⠮⣜⢣⢞⡱⡭⢎⡳⢎⡵⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠈⠀⠂⢁⠠⠀⢀⠙⠒⠃⠈⠀ ⣿⣿⡛⢦⡍⢶⡙⢧⢳⡜⡵⣋⠞⡜⣿⣿⢎⡳⢬⣛⢬⠳⣭⢳⡙⣮⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢡⢤⡢⢦⡔⠀⡀⠌⠀⠠⠀⡐⠈⠀ ⣿⣣⠝⡶⣩⢧⡙⢧⢳⡜⡲⣭⢚⣭⣿⣟⠮⣝⡺⢜⡎⠷⣌⢧⡝⣵⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⣭⢲⣉⢖⠟⠀⠀⠄⠁⠂⠐⠀⢈⠀ ⣏⢧⡛⣴⢣⢎⡽⣊⢷⡸⡕⣎⢳⣺⣿⣿⡜⡲⣭⢓⢮⡛⡼⢦⡹⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⢠⡄⠀⠀⠀⢰⣿⠇⠀⢀⠉⠊⠁⡀⠌⢀⠈⡀⣰⢠⡬⢀⠀ ⣎⢧⣙⢦⡛⡼⢲⡝⢦⡳⡹⢬⣫⣾⣿⣿⣧⠳⣎⢏⢶⣩⢳⠥⣏⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⢀⠂⠠⠐⠀⠠⠀⢂⠀⢠⣏⠵⣨⢃⠆ ⡝⢮⣜⠲⣍⠳⢧⡚⢧⢳⣍⢳⢲⣿⡇⢹⣿⡷⣘⢮⢳⡜⣣⢛⡴⢿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣴⣾⠿⢿⣶⣴⣿⣿⣿⠀⠀⠂⠀⡐⠀⢈⠀⠂⠄⠐⠘⠮⠖⠁⠈⠀ ⣏⠷⣌⠳⣍⡻⢎⡝⣎⠳⣬⢳⣿⡟⠀⠀⠹⣿⣧⢞⡣⠽⣬⠳⡜⣿⣷⠀⠀⠀⢀⣤⣾⠟⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠈⢻⣿⣿⡟⠀⣠⣀⠶⡱⢆⠀⡐⠀⠂⡀⠂⠀⠄⠈⡀⠂ ⣎⠷⣪⡝⡼⣱⢫⡜⣎⢳⡜⣽⣿⣷⣶⣶⡶⠿⢿⣾⣷⣿⣶⣽⣜⣲⢻⣧⡀⠀⠀⣠⣤⣶⣶⣬⣤⣤⣿⣯⠀⠀⠀⠀⠀⠀⠁⢹⣿⡐⣇⢎⢳⢡⠟⠀⠠⠀⠁⡀⠄⠁⢀⠂⠐⠀ ⡝⣮⠱⣎⡵⢣⠳⡼⣌⢧⣽⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣿⣷⣦⣿⠟⠉⢡⣽⡿⢿⡏⠙⣿⣄⡀⠀⠀⣀⣴⣿⣶⣿⣿⣯⡉⠙⠋⠀⠌⠀⠌⠐⠀⢀⣌⣀⠀⠌⠀ ⡝⣖⢫⡖⡭⢳⣋⢶⣍⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡇⠀⠀⠻⣷⣶⠆⠀⠀⠀⠛⣻⣿⡿⠟⠛⠁⠀⠀⠀⢻⣿⠀⢀⠂⠄⠈⡀⠐⠀⡿⣌⡜⣲⢲⠀ ⣿⣎⠳⡜⣭⢓⣮⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠄⠀⠂⢀⠡⠀⠘⠴⠺⠤⠋⠀ ⠙⠿⣿⣿⣾⡿⠟⠋⠙⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣶⣶⣶⡾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠌⠀⠡⠀⡀⠂⠐⠀⠁⡀⠄⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠠⠈⠐⠀⡀⣄⡀⠁⡈⢀⠠⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣷⣶⣦⣤⣤⣤⣄⣀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣴⣾⡟⠁⠀⠂⠁⠠⢀⡿⢜⣹⡀⠀⠄⠀⠂⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⢹⣿⡇⠀⠌⢀⠡⠀⠸⢎⡵⢢⣻⠆⠈⡀⠁⡀ ⠛⠛⠻⠷⠶⣶⢦⣤⣤⣠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠠⢀⠠⠐⠀⡀⠉⠁⠁⢀⠠⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠳⠶⠶⢶⣦⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠠⠀⠂⢁⠀⢂⠈⠠⢀⠠⠀⠡⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠿⠶⠶⢦⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣄⡂⠈⠀⠠⠀⠂⠐⠀⡀⠂⠐⠀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⠉⠉⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢣⣀⠀⠀⠀⣀⡤⣔⡿⢏⡉⠒⠂⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡽⠓⠻⠿⠒⠋⠁⠀⠀⠙⠒⠶⠖⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀ ⠀⠀⠀⣠⠎⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑ ⠀⠀⡼⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣦ ⡞⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠒⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⠿ ⠹⡄⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢦⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⣄⣹⣄⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠁⠙⢾⣧⡀⠀⠀⠀⠀⠀⠈⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⢟⣹⣷⠶⠶⠶⠶⠶⠶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣴⠾⠛⠋⢉⣿⡟⢷⣾⡇⠿⣦⡀⠀⢀⠠⠐⢠⢀⡉⠛⠻⣶⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢻⣿⢛⣿⢻⡶⣤⣸⣾⣯⣽⣾⣨⣿⠀⣿⣷⡄⠠⠀⠀⠂⡐⠌⡑⢢⢀⠉⠻⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⣿⣴⣉⣧⣛⣼⣿⢿⣯⡋⢻⣱⣞⣦⢝⣿⡇⣤⣿⡄⠀⠈⠀⡀⠠⠈⠐⡈⠆⡁⠘⣿⡄ ⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⢹⣿⣏⡉⢧⣎⣻⡖⣿⡿⠟⠳⣭⣿⡼⠟⠛⣻⣾⠛⢷⣤⣂⠀⢀⠁⠈⠀⠐⠐⠱⣸⡇ ⠀⠀⠀⢀⡼⠏⡀⠐⠈⠀⠀⣾⡧⢉⣿⠋⣿⠖⡿⠀⢀⠠⢀⣈⣉⣍⣯⣏⣆⣀⠀⡈⢙⣿⠶⠶⣤⣥⣦⡾⠾⠋⠀ ⠀⠀⢠⡟⡁⠒⡄⠁⠂⢈⠀⢼⣿⡁⣾⡟⣡⠞⢁⣴⠶⠛⠋⠉⠉⠀⠀⠀⠈⠉⠛⣶⡸⣻⠷⠲⠀⠀⠈⣧⠀⠀⠀ ⠀⢠⡟⣨⠔⠃⠄⡁⠀⠐⢨⣿⠈⠛⠿⢿⣳⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⢷⣦⡶⠂⢸⣇⣿⣠⣄⠀⠀⠀⣹⠀⠀⠀ ⠀⣿⠁⡜⢨⠁⠂⠀⡀⢦⣾⠃⠀⠀⢤⡿⠋⠀⢀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣾⡿⠋⠁⠀⠀⠀⠘⢿⡄⠀⠀ ⢸⡏⠀⡎⡀⠆⠀⡀⣰⣿⡇⠀⠀⢁⣾⠁⠀⢀⣾⡆⠀⠀⠀⢾⣉⡿⠀⠀⢀⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀ ⠸⣷⠀⠕⢄⠠⠐⣰⡿⠋⢿⣤⠀⠈⣿⡀⠐⠛⠋⠀⠀⠀⠀⣈⣽⣧⣖⠛⠛⢯⣽⣛⡶⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀ ⢸⡿⢷⣬⣤⣶⠿⠋⠀⠙⠉⠙⢻⣶⣬⣷⣦⣤⣤⣤⣤⢶⣾⠏⠈⠁⣹⣆⣠⡀⠀⢹⡆⠀⠀⠀⠀⠀⠰⠀⣼⠀⠀ ⢸⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠺⠋⠉⠀⢀⣠⠞⠋⢁⣰⠏⠀⠀⣴⠞⢏⣭⣯⣓⡶⠾⢥⣄⠀⠀⠀⠀⠀⣴⠇⠀⠀ ⠈⢷⡀⢀⡄⠀⠀⠈⠑⢦⡀⠀⡀⠔⠉⠈⠹⠶⠦⠷⠿⣤⣤⠾⠧⢷⡿⠉⠀⠈⣷⠀⠀⠹⡆⠀⠀⢰⠟⠁⠀⠀⠀ ⠀⠈⠛⢾⡇⠀⢠⢀⢄⠊⠙⠢⣄⡀⠀⠀⠀⠀⠚⠶⣤⣿⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣿⠀⢠⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢷⡋⠉⠳⣀⢀⠀⠀⠀⠉⠂⠀⠀⠀⢠⣤⣏⣿⡀⠀⠀⠀⠀⠀⠀⣸⢷⡀⠀⢀⣟⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣄⠀⠈⡉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠤⠽⢦⣀⣴⠏⠀⢉⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠲⠮⣥⣤⣼⣦⡀⠀⠀⠀⠀⠀⠀⣀⣶⣀⣀⣀⣀⣀⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠛⠉⠁⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣤⣶⣾⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⢿⡟⢯⣛⡭⣛⡬⢧⡹⢭⡛⣟⡻⢿⣿⣿⣶⣮⣟⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⢿⢻⢻⣙⠯⣝⢫⣛⠽⣛⠿⣿⣿⣿⣿⣶⣾⡳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⡿⣹⣙⢮⣳⢚⢧⣓⡞⣥⢟⣮⣓⠯⡽⢶⣹⠲⣭⢻⣟⢿⣿⣿⣦⣽⡷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡟⢯⡹⡬⢧⣛⡼⣊⢷⡩⣗⢎⣳⠭⣞⣱⣫⣝⠻⡿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⣟⢧⠻⣇⢿⣘⠧⡟⢼⣣⠼⣃⠿⣿⣟⡼⢻⣇⡜⠿⣄⡿⡼⣿⡘⢿⢿⣿⣿⣇⢻⣤⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⢿⡻⢤⡻⢇⢧⣻⣧⣟⣼⣿⣜⣿⡟⣜⡣⢟⣤⢻⣧⡜⣿⣧⣛⡛⢿⣿⣿⣿⣄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⢟⣭⠳⣭⢞⡳⣭⣫⣾⣷⣮⣿⣷⣯⢯⡷⡷⢮⣹⣻⣿⣯⣿⣵⣺⢵⣧⣿⡬⣳⢹⣿⣿⣷⣌⠻⣦⡀⠀⠀⣀⣴⣿⣿⡿⢏⡼⢲⢭⠳⣽⣽⣾⣿⣿⡿⣿⣿⣿⣿⡿⣜⡱⣏⣖⣫⡝⣞⣴⡿⣷⣟⣖⠺⢿⣿⣿⣿⣌⢣⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⣜⣚⢖⡻⣦⢯⣽⣿⣿⣿⡿⣿⣟⣿⣿⣧⡝⣼⣻⣿⣿⡿⢿⣻⠿⣿⣿⣾⡵⣻⣥⠳⣌⡟⣿⣿⣷⣌⠃⢀⣴⣿⣿⡟⢯⣙⠮⣵⢫⢞⣹⢲⣌⠿⣻⣿⣷⣿⣿⣹⣿⣽⢎⡳⣽⣲⢿⣯⣽⣿⣿⣿⣿⣿⣿⢣⠖⣭⢻⣿⣮⡙⢿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣏⡽⣚⡼⣍⢷⣿⣿⡿⣟⡾⣽⢳⣭⣟⢮⣿⣿⣿⣾⣿⣯⡳⣝⢯⡞⣽⡳⣭⢿⣿⣿⣝⡳⣭⣜⢲⢿⣿⣿⣦⣿⣿⣿⣳⢚⢧⣭⢳⣎⡟⡼⢣⣗⢮⢳⡥⢿⣿⣿⣿⣿⣿⣻⢫⡵⣛⣧⣟⣾⣿⣿⣿⣿⣿⣿⣿⠭⡞⣥⠳⣜⢻⣿⣌⢿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣓⡳⣜⡳⣜⣿⣿⣿⣿⣻⢽⣾⣽⣻⢶⣭⠷⣞⣯⣿⣿⣿⢻⢿⣭⣟⡾⣳⢯⡽⣚⢿⣿⣷⣝⡚⣿⣯⡞⡽⣿⣿⡿⡻⢥⡓⢯⣚⡴⣫⠶⣹⢭⢳⣎⠟⣮⢿⡶⣩⣿⣿⣿⣿⣿⡧⣽⡹⣞⣼⣿⣿⣿⣿⣿⣿⣿⣿⠯⡵⣋⠷⣩⠞⣿⣿⡄⢻⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣇⠾⣱⢫⣼⢳⣿⣿⣿⣳⢯⣟⣾⡿⣽⢿⣞⡿⣽⣿⣿⣿⣧⡟⣾⣛⡾⣽⡳⣯⣳⢯⣻⣿⣿⣎⠷⣱⢞⡿⣿⣿⣿⡳⣝⡣⢟⣭⠳⣍⢧⢏⢷⣏⢾⣯⡝⣲⡍⣿⣷⣿⣿⣿⣾⣿⣿⣾⣷⣛⡿⣿⢿⣿⣿⣿⣿⣍⠶⣏⡵⢫⣝⡱⢯⡜⣿⣿⣄⢿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣻⣬⣛⡵⢫⡞⣿⣿⣿⣞⣭⢿⣞⡷⣿⣯⣟⡾⣽⣯⣿⣻⣿⡳⣽⣻⣯⣷⢯⣽⣳⢯⣳⢿⣿⣿⣿⣽⣹⣿⣿⣿⣿⣿⣷⣣⠯⣝⡲⢻⡜⣯⢞⣾⣯⣾⣿⣜⣧⣾⣿⣿⡿⠿⢟⠻⢿⣿⣯⣿⣿⡿⠿⣿⣿⣿⣿⣛⣿⡾⡴⣋⠷⣬⢋⡷⢼⡹⣿⣿⡼⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⡶⣱⢮⡹⣇⢿⣹⣿⣟⣾⣿⣿⣾⣽⣿⣷⣫⢿⡿⣿⣿⣿⣿⡝⣧⢟⣿⣿⣟⣮⢿⣹⢧⡿⣿⣿⣿⣯⢿⣿⣿⡟⣻⣻⣿⣷⣿⡬⢽⣧⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⡟⣥⢎⡙⡤⣉⠆⡻⢿⡛⢣⠜⣩⢙⠻⡙⣿⣿⣾⣿⣷⣿⣳⢞⡭⢞⣣⠳⡽⣿⣶⢻⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡹⡵⣣⠷⣹⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣷⢫⣗⣿⣾⣿⡽⢾⣹⠾⣽⣞⣭⢿⣭⠿⣽⣻⣿⣿⣷⢫⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⡏⢣⠜⡳⡔⢪⡑⠭⡑⢧⡚⣤⢋⠖⣡⠹⢏⢛⣻⠿⡿⣿⣾⣱⢏⡖⢯⡱⢿⣿⣾⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣯⢳⡵⣋⣾⣵⣾⣿⣿⣿⣿⣿⣷⣿⠿⣿⣯⣻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣽⡾⣭⣟⣳⣿⣿⣿⣿⣣⢽⣙⡞⢶⢫⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣼⣿⣿⣿⣿⣷⣃⠎⡵⡈⠷⣩⠒⣭⢚⠵⢪⡝⡺⣔⢣⢎⡬⡑⢎⡱⣿⣿⣿⣿⡾⡥⢏⣿⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⢳⣾⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣽⣿⣿⣿⣿⠿⠁⠠⣾⡿⠿⣿⠉⠀⠉⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡘⣞⡼⣚⣭⢳⣿⣿⣿⣿⣿⣿⣿⣭⣹⣿⣗⣼⣿⣿⣿⢳⠂⢥⠻⡟⢰⠛⡰⢡⠍⡤⢋⡜⣡⢚⠱⢎⢣⠚⡔⣩⢚⠤⡙⣞⣿⣿⣿⣗⢯⢾⣿⠹⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⠿⣿⣶⣿⠿⠿⠿⠏⠸⣿⡇⠀⢠⣤⠀⢿⣇⢠⣿⠃⢀⣸⣿⠁⠛⣿⡟⢦⣽⣿⣿⣷⣽⣚⡴⣫⢖⣿⣿⣿⠿⣷⣿⡿⣿⣿⣿⣿⣿⣿⡏⢲⡟⢢⠙⣄⣳⣯⣴⣿⣐⢣⣚⣤⣧⣶⣥⢊⡕⣊⢦⡙⠴⣁⠻⣮⡙⡟⢻⣿⣿⣯⣎⣿⡿⢘⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢹⣿⣧⣄⠀⢴⣦⠀⢹⣧⣄⣿⣿⣀⢸⣿⣤⣅⣆⡠⣿⠇⠠⣿⠏⢀⢠⣿⠟⠛⠻⣿⣿⢷⣩⢞⣴⣿⣿⣼⣟⣿⡧⢼⣿⣿⣿⡃⠼⣾⣷⣿⣿⣾⣿⡿⠉⠉⣿⡿⢿⣿⠟⠉⢹⣿⣷⣺⣽⣶⣽⣦⣙⠣⡜⣣⠝⡢⢾⡿⣿⣷⣿⣿⢸⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣾⠟⠈⢿⣷⣀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣀⡀⡿⠃⢀⣤⣾⣿⣿⣯⢖⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⠟⠋⢰⣿⡟⠉⢠⣀⢴⣿⡅⢨⣿⠁⣠⣼⣿⠙⢻⣿⣿⡍⢹⣿⣶⣙⠷⣮⣱⣾⢳⣿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣰⣾⣿⣿⣿⣻⣟⡿⣿⡾⣽⣾⡽⣞⡷⣯⡷⣯⢿⣻⣿⣿⣿⣿⣷⣼⣟⣋⣹⣿⣿⣿⣯⣓⣿⣿⣿⣿⡕⢎⠶⣁⣺⣿⣧⡀⡀⣶⣤⣄⣿⣷⣦⣾⣿⠀⣿⣿⣮⣥⣴⣻⣿⡷⣉⣾⠟⣁⣿⣾⠿⢿⣿⣿⣙⣛⣬⣃⣿⣿⡿⢹⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣾⣳⢯⣿⢿⣽⣳⢯⣻⡝⣯⢷⣻⡽⣟⣳⢯⢿⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡉⢿⣎⣶⣭⣾⠟⠉⠿⣷⣼⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣠⣼⣿⠇⣆⣤⣾⣿⡿⢛⠛⣿⣿⣿⣦⣻⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣭⣟⣾⣹⣶⣯⣯⡳⢿⡵⣯⣳⢯⡽⣏⡿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⣡⣯⣽⣿⣿⡡⢀⣴⣿⣿⡿⢋⡍⢡⠢⠔⡢⠍⡆⣍⠣⡜⡡⢎⡔⢢⢩⡙⠟⣿⣷⣧⣼⣿⣻⣽⣿⣧⣯⠒⡍⢛⠻⣿⣿⣷⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⠿⠿⠿⠿⢿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣯⣆⠱⡨⢔⠣⣍⠻⡱⢋⡜⡰⡛⢧⡝⢯⡞⢧⢣⡜⡱⣂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠯⠀⠀⠋⠉⠀⠂⠈⠘⠀⠀⠈⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⢻⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣷⢱⡪⢕⡪⠵⣩⣳⡼⢧⡙⢦⡘⠦⣘⢣⠳⣌⡳⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣾⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣵⡆⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣬⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟⡌⣿⣿⣿⣿⣿⣿⠿⡿⢋⢧⣵⣮⣵⣧⣿⡿⣿⣷⣾⣿⣿⣿⣦⣧⣿⣶⣷⢋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣭⢼⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡟⠿⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠄⠀⠠⠄⠈⣤⣀⡐⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠱⣊⢿⣿⣿⣿⣿⣿⣍⢳⣹⣾⣿⣿⠛⠛⣯⠁⠀⠠⠀⠀⠈⠁⠈⡉⠉⠉⠛⣿⣿⣬⣾⣿⣿⣿⣷⣿⣿⡟⣦⢍⢢⢻⣿⣾⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣃⠀⠀⢠⣻⣿⣿⣿⣯⠉⠹⣿⣿⣿⡿⠃⠀⠀⠠⠄⣸⣿⣿⡅⠀⠀⠀⠀⣿⣿⣿⣿⣿⡋⠅⣺⣿⣯⣿⣿⣿⣿⡟⣿⣟⢦⣹⣾⣿⣿⣿⣿⡏⣼⣿⣿⢻⣿⣿⣿⣆⣩⠀⠀⠀⡀⠀⣄⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣾⡿⢃⠎⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣤⣶⣿⣿⣿⣿⣿⣿⣄⡄⠛⣯⠥⠀⠀⠀⠀⠀⠀⠘⠿⠟⠋⠀⠀⠀⠀⠀⠈⣻⣿⠏⡁⢲⣿⣿⣿⣿⣿⢿⡱⣞⠾⣿⣷⣿⣿⣿⡿⣿⠟⣷⣿⣿⠉⢹⣿⣿⣿⣿⠟⠀⠀⢀⡀⠀⠈⠀⢀⠀⢿⣿⣿⣿⣿⠏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣽⣿⡙⠿⣿⣿⣿⣦⡀⣀⠒⠀⢀⠀⠀⠀⠀⠰⢠⣤⣶⣶⣶⣄⠀⣀⢋⣁⣠⣴⣿⣿⣿⠿⣯⢛⣦⠻⣜⢧⣛⢧⣛⡞⣿⣿⣶⣿⣾⣝⣿⣿⣆⣻⣿⠿⠁⠊⠀⠀⢸⣿⣰⠁⠠⠀⠀⠙⣻⢿⣿⡟⣀⣶⣿⣿⣿⣿⣿⣿⣿⠿⠏⠍⡽⣿⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣿⡿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠻⣴⢫⣖⣻⣜⢧⣏⢾⣡⠟⣽⡳⢿⣿⣿⣿⣷⣾⣿⣿⣿⣤⣴⣶⣶⣶⣆⣐⡄⣀⣀⣀⣄⣘⣵⣿⣿⣿⣿⣿⣽⣿⠿⣻⡿⠟⠿⢿⣷⣤⣴⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣷⣶⣶⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠘⠿⣿⣿⣿⡿⣿⠿⣷⢹⡜⣻⠴⣏⢶⡹⣎⠷⣎⢷⣫⡝⣶⡹⣳⢬⣻⡟⣽⣻⣿⡿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⡉⢀⣲⣿⣷⡀⠀⠀⣹⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣦⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣾⣿⣿⣝⡮⣝⡼⢣⡽⣣⢟⣮⢳⡝⣮⢻⡜⣧⢳⡝⣶⡹⣥⣛⢦⣻⣿⣿⣿⢱⠎⡴⣈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣙⣿⣿⣿⣿⣿⣿⣷⣾⡿⣿⣻⣷⣶⣾⣿⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡈⣻⣷⣿⣿⢿⠿⠟⢍⣿⡿⠋⢉⣿⡏⢉⢻⣿⡙⠿⣿⡹⢿⣿⣴⢫⡜⣧⢻⡵⣫⢎⡷⣹⢎⡷⣹⢎⡷⣹⢶⡹⡖⡽⡺⣜⡻⢿⣿⣯⣜⣤⢣⣿⣿⣿⠛⠛⢻⣿⠛⠻⣿⡻⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣟⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠉⠂⠠⠀⢻⣯⠀⠌⡀⣿⡅⢺⣴⣿⡆⠘⢻⣷⠀⠛⣿⣷⡝⣎⠷⣹⢵⣫⢞⡵⣫⢞⡵⣫⢞⡵⣫⢳⡝⣳⡝⣦⢻⣯⣿⣿⣿⡿⠿⣿⡿⠃⠜⢠⢸⣿⠌⡠⣿⡇⠈⠿⣿⣼⢿⣯⡄⠒⠉⠀⠙⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣸⣿⠏⢀⠠⠠⢁⠈⠍⠃⡀⢂⠀⢉⠴⣀⠘⠿⠓⠠⠌⢣⠆⢼⣘⣿⣿⣎⢻⡱⣎⢧⡻⣜⢧⡻⣜⢧⡻⣜⢧⡻⣜⡳⢞⣷⣿⣾⡿⢻⠏⡐⠸⢋⠁⠌⡀⠂⡉⢉⠒⡀⠻⠃⠌⡀⢋⡙⠀⠻⣿⣆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⣀⣀⡀⢐⡀⠌⠐⠠⠐⠀⠌⢠⠘⡀⠂⠔⡀⠡⠐⠠⢈⠀⣉⣼⣿⣿⣧⡝⣮⠳⣝⢮⡳⣝⢮⡳⣝⢮⣏⢷⡹⣜⣫⣿⣿⣿⣼⣿⣤⣔⡈⠄⠊⡄⠐⠁⠄⣁⠊⡐⡀⢀⠀⠆⡁⠠⢀⢊⣹⣿⣾⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣐⣤⣈⡄⠐⣠⣱⣦⣽⣦⣷⣦⣵⣶⣿⣿⣿⣿⣣⢞⣱⠻⣜⢧⡻⣜⣧⢻⡜⣳⢺⢬⣓⢮⢵⣾⣿⣿⣿⣿⣿⣿⣿⣶⣥⣔⠈⣐⠂⠠⣐⣤⣷⣬⣶⣦⡠⢴⣬⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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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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