⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⡞⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡾⠀⠀⠀⠀⠀⢀⡴⢊⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⣸⠃⠀⠀⠀⢀⡴⠋⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠙⢦⡀⠀⠀⡞⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠏⣶⠂⣴⠀⠀⠀⠙⢦⣼⠁⠀⣸⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠻⠞⠋⠀⠀⠀⠀⠀⠃⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢸⡄⣷⡄⠀⠸⣇⠀⠀⢀⠀⠀⠀⠀⠘⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣤⣄⣿⠀⠀⣤⣄⠀⠀⠈⠛⠃⠀⠀⠀⠘⢧⡀⠘⣷⣄⠀⠀⠀⢹⡌⠳⡄⠀⠀⠀⠀ ⠀⢀⣿⣿⣷⠟⠃⠀⢸⣇⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠻⣆⣿⠸⡄⠀⠀⠀⢻⡀⢹⡄⠀⠀⠀ ⠀⠘⡿⢻⠋⠀⠀⠀⠀⠙⠷⣄⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠈⢻⡀⢻⡄⠀⠀⠈⣧⠀⢻⡀⠀⠀ ⠀⢠⡇⣼⠁⠀⠀⠀⠀⡶⣤⡉⠳⣆⡀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠻⣎⣷⣀⣀⣀⣿⠀⠨⣇⠀⠀ ⠀⢸⠁⡟⠀⠀⠀⠀⢸⡇⠀⠙⢦⣌⠙⣦⣀⣀⣈⣷⢦⡀⠀⢀⡀⢙⣷⡀⠉⡄⠀⡄⠀⢻⡄⠀ ⠀⣸⢰⡇⠆⠀⠀⠠⢸⣇⣀⣀⣬⡽⠶⠟⠛⠋⠉⠉⠈⠓⢦⣈⣷⣾⠙⣇⠀⢷⣴⠇⠀⠈⣇⠀ ⠀⣿⢸⡇⠀⠀⠀⠀⢲⡛⣯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⡟⠀⠀⠀⠀⠀⠀⡟⠀ ⠐⡟⢸⡇⠀⠀⠀⠀⢸⡛⠛⠛⠒⠒⠶⠦⠤⠤⢤⣤⣤⣄⣀⣠⣤⣤⣤⣄⣀⣀⡀⠀⠀⣰⠃⠀ ⠀⡟⢸⡇⠀⠀⠀⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠮⣍⡓⠦⢤⣄⣀⣿⠀⢰⡏⠀⠀ ⠀⢻⡀⠻⣄⣀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⡉⠁⠀⠘⢧⡀⠀ ⠀⠀⢻⠳⠦⣭⣉⡓⠺⠧⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⣿⠀ ⠀⠀⢾⠀⠀⠀⠈⠙⢳⡶⠦⣤⣉⡙⠛⠒⠶⠦⠤⣤⣤⣄⣀⣀⣀⣀⣠⣄⣸⣿⠴⠖⠀⣠⡏⠁ ⠀⠀⣸⠄⠀⠀⠀⠀⢸⠇⠀⠀⠈⠉⠙⠓⠲⠦⠤⢤⣤⣤⣄⣄⣀⣈⣭⣽⣥⣤⣤⣴⣶⠋⣿⠆ ⠀⠀⠛⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡇⢸⣿⣿⣽⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠛⢻⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣸⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡞⠀⠀⠀⠀⠀⠀⣠⠔⣺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠃⠀⣸⠁⠀⠀⠀⠀⣠⠊⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠳⡀⠀⠀⠀⡜⠁⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡸⢣⡄⢀⡀⠀⠀⠘⢦⡀⡼⠁⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠁⠈⢧⠜⠀⠀⠀⠀⠀⠙⠃⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⡄⢀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⡀⢸⠀⠀⠀⡀⠀⠀⠀⠹⠼⠃⠀⠀⠈⢳⡀⠀⢠⣄⠀⠀⠀⠀⢿⠳⢤⠀⠀⠀⠀ ⠀⠀⣼⣏⣯⡭⠟⠀⠀⡞⠉⠲⢤⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⡏⢧⠀⠀⠀⠈⣇⠈⢧⠀⠀⠀ ⠀⠐⣿⠿⠛⠁⠀⠀⠀⠙⢤⡀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠈⠳⡧⠈⣇⠀⠀⠀⠸⡄⠈⢧⠀⠀ ⠀⠀⡏⢠⠄⠀⠀⠀⠀⢠⡀⠑⢦⡀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠙⣆⠸⡄⠀⠀⠀⢿⠀⠘⡆⠀ ⠀⢰⡇⣾⠀⠀⠀⠀⠀⣾⠓⢤⡈⠑⢦⡀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠹⣄⠧⢤⣤⡤⠾⠀⠀⣇⠀ ⠀⢸⢀⡇⡀⠀⠀⠀⠀⣇⠀⠀⠙⠲⣄⣙⣦⡤⠤⠶⠟⢦⡀⠀⢠⠀⣨⢳⠀⠀⡀⠀⡄⠀⠹⡄ ⠀⣿⢸⠇⠀⠀⠀⠈⢀⡿⡴⢶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠳⣌⡳⠋⠈⡇⠀⠳⠞⠁⠀⠀⡇ ⢀⡿⢸⡄⠀⠀⠀⠀⢨⡷⣿⣯⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠁⠀⠀⠀⠀⠀⠀⡇ ⠈⡇⢸⡂⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠓⠶⣖⡖⠶⣶⡒⠒⠶⠶⠤⡄⠀⠀⡼⠁ ⠀⣇⠸⣇⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣉⡙⠲⠤⣤⡇⠀⢸⠁⠀ ⠀⠙⣦⣈⡓⠶⠤⣄⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢆⠀⠀⠀⠈⢳⡀ ⠀⠀⣿⠈⠉⠙⠲⢤⣉⡉⠛⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡷ ⠀⠀⣷⠀⠀⠀⠀⠀⢸⡉⠙⠲⠦⢤⣄⣉⡉⠙⠒⠒⠶⠦⠦⠤⠤⠤⣤⣴⣤⠼⠷⠚⠁⠀⣴⠃ ⠀⠀⡿⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠶⠶⠶⠤⠤⠤⠤⠶⣤⠴⣶⣖⡟⠉⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢾⡽⣆⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠛⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡜⠀⠀⠀⠀⠀⢀⡠⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢸⠀⠀⠀⠀⢀⡔⠋⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⢣⡀⠀⠀⢠⠎⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠏⡄⠀⡀⠀⠀⠘⢦⣠⠎⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⠹⠔⠁⠀⠀⠀⠀⠉⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆⢠⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀ ⠀⢀⡤⠤⢤⡗⠀⢀⠤⣀⠀⠀⠘⠋⠀⠀⠀⠘⢦⡀⠐⣦⡀⠀⠀⠈⣏⠑⣄⠀⠀⠀ ⠀⣾⣶⣿⠋⠁⠀⠸⡀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠱⣄⡇⢣⠀⠀⠀⠘⡄⠙⡄⠀⠀ ⠀⡟⢉⠀⠀⠀⠀⠀⠉⠢⣀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠈⢧⡀⢇⠀⠀⠀⢻⠀⠹⡀⠀ ⢀⡇⣾⠀⠀⠀⠀⢰⠓⢤⡈⠳⢄⠀⠈⠑⢤⡀⠀⠀⠀⠀⠳⣸⠀⣀⣠⠼⠀⠀⡇⠀ ⢸⠀⡇⠀⠀⠀⠀⢸⠀⠀⠉⢲⣄⣹⡤⠤⠴⠟⠲⣄⠀⢠⠀⡝⣆⠀⣀⠀⣦⠀⠹⡄ ⣿⢰⠃⠀⠀⠀⠀⡼⢖⢺⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠑⠤⣛⠁⢸⠀⠘⠚⠁⠀⠀⡇ ⣟⢸⠀⠀⠀⠀⠀⡼⠺⠧⠤⠤⠤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢠⠇ ⡧⢸⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢯⡙⠻⢭⣉⠉⠉⣧⠀⢀⠏⠀ ⢳⡈⠳⣄⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⡉⠓⠋⠀⠸⣄⠀ ⠀⡿⠓⠦⢭⣙⠒⠫⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⠀⠀⠀⠘⡆ ⠀⣟⠀⠀⠀⠀⠙⡗⠒⢤⣄⣉⠙⠒⠒⠤⠤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣯⡤⠆⠀⣠⠃ ⠀⣯⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠙⠒⠒⠠⠤⠤⠤⢤⣀⣄⣩⡭⣄⣤⣤⣤⡖⠛⡄ ⠀⠁⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣯⢇⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠛⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀