⡄⠀⠀⠀⠀⢠⠏⠀⠀⠀⣾⢸⠀⠀⢀⣠⣾⣇⣇⣀⡇⠈⠑⠦⡀⠀⠀⢠⣇⠀⠀⠀⡇⡄⡇⠀⣏⢳⣄⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠤⣀⠤⠤⠤⠾⠒
⠁⠀⠀⠀⢠⠋⠀⠀⠀⠀⡇⣼⡤⡾⠛⠉⡙⡇⡇⠀⡇⠀⢸⠀⢈⠓⢤⣸⢹⠀⠀⠀⡇⣇⡇⠀⢹⠸⡏⠳⣄⠀⠀⠈⠛⠷⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⡇⣿⠎⠀⠀⠀⡇⡇⡇⠀⡇⠀⢸⠀⢸⠀⢸⣿⢸⠤⣀⣿⡇⢸⣿⠀⠘⡄⣷⣤⠈⡗⢦⡀⠀⠀⠀⠙⠻⠵⢦⣄⣀⣀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠟⡡
⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⡗⣿⠀⢰⠀⠀⡇⠃⡇⠀⣿⠀⢸⠀⢸⡀⢸⣿⠈⡆⠈⣿⣿⠀⣾⠀⠀⣧⡟⣿⣆⡇⠉⠏⠗⠦⠄⣀⠀⠀⠀⠈⠉⠉⠉⠐⠒⠓⠛⠃⢉⡁⠴⠊⢱
⢇⠀⢸⠃⠀⠀⠀⠀⢠⠋⢿⣿⠀⢸⠀⣀⡇⢸⣇⠀⣿⠀⢸⡆⢸⡇⢸⣿⠀⣧⡀⢸⣿⠀⠹⠈⠁⢀⣠⣠⡶⢶⣯⣭⣷⠶⢾⡷⠏⠙⠒⠒⠒⠒⠒⠒⠒⡖⠊⠉⠁⠀⠀⠐⢀
⣞⢆⢸⠀⠀⠀⠀⣠⠃⡀⠸⠿⢀⡸⠀⠛⠓⠘⠛⠒⠛⠃⠸⢷⣸⡇⢸⢹⠀⢹⣧⣾⢻⠀⠀⠿⣿⢻⣏⢹⡍⣤⣒⣲⢼⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀
⡹⢯⣻⡆⡀⣄⡰⡁⡆⣧⣇⣲⣷⣼⣷⣼⣷⡚⣟⡿⣿⣷⡄⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢰⣍⡷⣤⣤⡴⢞⣡⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠙⡇⣇⢹⠁⢻⢿⣿⣷⢸⢻⡋⠷⢄⢸⡞⠭⣻⡇⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⣽⣿⣷⣶⣿⣿⣳⠿⡇⠀⠀⠒⠤⡀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀
⠘⢆⠀⢰⢿⡟⡆⣘⣼⣿⣿⠀⠛⣧⡀⢷⣄⣉⣉⣥⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⣰⣴⡶⠀⠀⠈⠓⢤⡀⡗⠒⠒⠒⢤⢤⡤⠤⠤
⠀⠸⠁⠀⠻⠹⣿⣿⡟⠈⣏⠀⠀⠟⠻⠶⠾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣄⡿⠶⠆⠀⠀⠀⠀⣇⠁⠀⠀⠀⠈⣿⣇⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠈⠁⢀⡜⠀⣷⣄⡤⠒⠒⠂⢤⡀⠀⠀⠀⠀⠀⠠⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣧⠃⠀⠀⠀⠀⠀⢀⠀⣿⠀⠀⠀⠀⠀⠸⣟⡆⠀
⠀⠀⠀⠀⠀⣀⠤⠒⡟⡽⠈⢠⣼⠿⢄⡀⠀⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⣿⢀⡏⠀⠀⠀⠀⠀⠀⢻⣵⡀
⠀⢀⡠⠖⢩⠃⠀⡼⣱⡵⢂⠀⠀⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣿⢸⠃⠀⠀⠀⠀⠀⠀⠈⣯⢇
⠒⠁⠀⢠⠃⠀⣰⢡⠃⠀⢸⠀⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠸⡟
⠀⠀⢀⠇⠀⢰⢣⠏⠀⠀⡎⡤⠘⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠊⠙⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣧⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⢀⠎⠀⢠⢇⠎⠀⠀⠀⢃⡇⠀⢣⠀⠈⠑⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⢻⢁⡇⠀⠀⠀⠀⠀⠀⣿⢹⢻⠸⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⡜⠀⢠⠎⡞⠀⠀⠀⢸⡼⡇⠀⠀⠀⠀⠀⠀⠀⠈⠹⠶⡶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠋⠁⠀⠀⠘⣾⠁⠀⠀⠀⠀⠀⢠⡟⡟⠈⡆⢧⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣡⢀⡞⡜⠀⠀⠀⠀⡾⡇⡇⠀⢰⠀⠀⠀⠀⡀⠀⡄⠀⠀⠈⠀⠀⠀⠉⠉⠛⠒⠒⣺⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢸⣷⠁⠀⢹⠘⡄⠀⠀⠀⠀⠀⣀⠤
⡛⣇⡜⡰⠁⠀⠀⠀⠀⣧⠀⠇⠀⢸⠀⠀⠀⠀⡇⢠⠇⠀⠀⠀⠀⠀⠀⢀⢰⡶⠚⠉⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣿⢏⣀⠀⠀⡇⢳⢀⣠⡴⠚⠉⠀⠀