⠀⠀⠀⠀⠀⠀⢀⠞⡰⠁⠀⡼⠀⠀⠀⣰⠇⣸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡄⣂⠀⢞⡤⡄⠀⣧⠀⠠⡄⠀⠀⠘⡞⠿⠹⣞⢮⠻⡝⢦⠀⠀⠀⠀⠀⠀ ⠀⢤⣀⣼⣁⣀⡞⡸⠁⠀⢰⠃⠀⠀⠀⠛⢀⠟⠁⠀⠀⢸⡇⠀⠀⠀⣸⠀⠀⠀⠀⢸⢸⠻⠀⠈⠃⡇⠀⢸⠀⠀⢧⠀⠀⠀⢹⡀⠀⠁⠀⢣⡹⡌⠳⡀⠀⠀⠀⠀ ⠞⠉⠀⣐⠆⠈⠑⠣⡄⠀⡞⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣸⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠨⠀⠀⠀⠀⢳⠀⢸⡆⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⢱⡹⡄⠙⣅⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠈⠂⡇⢰⠃⠀⠀⠀⠀⠀⡏⠀⠀⠀⢠⣿⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⢸⢧⠀⠘⡇⠀⠀⠀⢸⠀⠀⢦⠀⠀⢣⢱⠀⠙⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡧⡾⠀⠀⠀⠀⠀⠀⡇⠀⠰⢤⣸⡇⠀⠀⠀⡾⢳⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢸⠀⢸⢸⠀⠀⣿⣠⠄⠀⢸⠀⠀⢸⠀⠀⡌⡎⣇⡁⠹⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠃⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⡏⠓⠲⢤⣇⣸⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡼⣀⣾⣼⡖⠋⡏⡇⠀⠀⢸⠀⠀⠈⡇⠀⢹⣹⢸⢣⠀⢳⠀ ⣻⠗⠲⢶⣒⡒⠲⡏⢹⠁⠀⠀⠀⠀⠀⠀⣇⠀⠀⢰⠃⢹⠀⠤⢼⠓⠛⣯⠍⠃⠀⠀⢻⡆⠀⠐⡾⡟⢻⠗⠚⡇⢠⠇⢹⠀⠀⢸⠀⠀⠀⣷⠀⢸⡏⡎⣟⠀⠈⠃ ⠀⠠⠚⠁⠀⠈⡇⢱⣼⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣠⣼⣒⠾⢽⣒⡲⢼⡄⠀⠀⠀⠸⡇⠀⠀⣸⡵⣞⡭⠬⣯⣺⠤⠘⡄⠀⢸⠀⠀⢀⢹⠀⢸⢸⠇⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⢸⡽⠀⠀⠀⠀⠀⠀⠀⡟⡆⣠⢿⣋⢭⣷⠖⢾⣦⣝⣷⠽⡄⠀⠀⠀⣇⠀⢀⣿⣿⣵⣶⡶⡷⣾⡙⢆⡇⠀⣿⡇⠀⢸⢸⠀⣸⠘⡄⣿⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠆⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⣹⣣⢾⢱⣋⣾⣄⣸⠈⣧⠙⠂⠹⡄⠀⠀⢸⡄⠘⡿⢱⣣⣾⣿⣿⢹⡙⣎⣷⢰⡇⣇⠀⡼⡞⢀⡏⠀⣿⡇⠀⠀⠀ ⠤⣀⣈⣀⡤⠴⠒⠁⡇⠀⠀⠀⠀⠀⠀⠀⡇⣇⣿⣸⣞⣩⣿⣷⣿⢭⣹⠀⠀⠀⠙⢦⠀⠀⢧⡞⠁⣾⣭⣿⣿⡯⣽⠇⢸⣾⡾⠀⢸⢠⠇⠁⡼⠀⠀⡟⡇⠀⠀⠀ ⠀⠀⠀⢀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡇⠹⠆⠻⢹⡃⠙⠻⢟⠀⡿⠀⠀⠀⠀⢠⢗⣄⡈⣇⠀⢹⣀⠙⠯⡄⡿⠀⠘⢸⡇⠀⢸⡎⢀⣼⡇⠀⠀⠀⠈⠀⠀⠀ ⠀⠀⠀⢸⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠙⠚⠀⠘⠚⠁⠀⠀⠀⢠⠿⠋⠀⠙⠺⠆⠀⠙⠒⠒⠊⠀⠀⠀⣼⠀⠀⢸⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢺⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣰⠆⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⢿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡰⠃⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⢸⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠦⠤⠤⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⢀⠜⢹⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⢸⢧⠀⢰⠀⠀⠀⠀⠀⣇⡇⢨⠗⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⡇⠀⢸⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⡇⠀⠀⠀⡏⢸⠀⢰⠀⠀⠀⠀⠀⣿⣁⡼⠤⠖⢻⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⡟⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢀⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢃⠇⠀⠀⢀⡇⢸⠀⠚⡆⠀⠀⠀⠀⣿⠹⡀⠀⠀⢸⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⣀⡴⠚⠉⠉⣳⢧⡀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢼⠀⠀⠀⢸⠀⠈⡆⢸⣇⠀⠀⠀⠀⣷⠀⠈⠓⠢⠼⣄⣀⣀⠀⠀⠈⠙⠻⢶⣶⣿⢿⣡⠤⠖⠊⠁⢸⠃⠀⡇⠀⢸⠀⠀⠀⠀⡇⣸⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠀⠀⠀⡞⠀⠀⡇⠈⣿⡀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠢⢄⣀⡴⠋⠀⠀⠀⠀⠀⡾⠀⠀⢻⠀⢸⠀⠀⠀⢸⠁⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⡇⠀⠀⢰⠃⣀⣀⣳⠀⣧⣇⠀⠀⠀⢹⢽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢰⣋⡉⠳⣼⣤⣼⠀⠀⠀⣼⢠⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠃⣠⡶⠟⠛⢉⣉⣹⡄⢻⣘⡆⠀⠀⢸⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡏⠁⠙⢦⣀⣀⣸⠀⠀⢠⡟⢸⠙⠻⣅⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⡾⠋⢀⠔⠋⠁⠀⠀⣇⢸⠀⠸⡄⠀⢸⡀⠀⠘⢮⡙⠢⢄⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⢆⡄⠀⠀⠀⠀⠀⡇⠀⢀⡏⡇⡏⠑⢦⡈⢷⡀⠀⡀⠀⠀⠀ ⢠⡿⠁⡴⠃⠀⠀⠀⠀⠀⢸⣼⠀⠀⠹⡄⠘⡇⠀⠀⠀⠙⠢⣄⠈⠙⠲⠤⠄⠀⠀⢩⠀⠀⣠⠞⡵⡻⠃⠀⠀⠀⠀⠀⡇⢠⠎⠀⣷⠁⠀⠀⠙⢦⠻⡀⠀⠀⠀⠀ ⡿⠁⡼⠁⠀⠀⠀⡆⠀⠀⠀⠻⠀⠀⠀⠹⣄⡇⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠈⡇⠉⠀⢼⠜⠁⠀⠀⠀⠀⠀⢸⡵⠋⠀⠸⠏⠀⠀⠀⢠⡌⢣⢳⡇⠀⠀⠀ ⠁⡼⠁⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⢸⠀⠀⢣⢧⠀⠀⠀ ⠐⠃⠀⡀⠀⠀⠀⠘⡆⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢸⠀⠀⠈⢿⡆⠀⠀ ⠀⠀⠀⢻⠀⠀⠀⠀⢷⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢀⠘⣿⡀⠀ ⠀⠀⠀⠈⣇⠀⠀⠀⢸⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡏⠀⢀⡏⠀⢹⣇⠀