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