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