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