Lumine ASCII Art

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

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

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