⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠒⢶⣄⡞⠋⠁⠀⠈⢳⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡟⠀⠀⠀⠀⠀⢸⡏⠁⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⡇⠀⠀⠀⠀⠀⡼⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⠶⠶⣤⠾⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡬⠷⠦⠝⠒⠦⠤⢤⣰⡃⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣰⣿⣀⡴⠾⣮⡾⢻⣷⣦⣄⣀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢼⣯⣉⡾⠤⠼⣋⣼⣿⡿⣧⣠⡿⡇⠀⠀⢀⣴⡿⠉⢀⣀⣀⡀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠨⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣹⡿⣷⠤⠼⣻⡿⠿⡁⠀⣽⠀⣧⣀⣀⣾⠏⢀⣾⠝⠚⠓⠫⣧⠀⢰⠃⠀⢀⣀⡤⠤⣀⠀⠀⠘⣎⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣯⣯⡏⠉⢩⠥⣄⠀⢹⣶⠃⣸⣟⣯⣼⠏⠀⢸⠇⠀⠀⠀⠀⣽⠀⡜⠀⢠⠟⠉⠉⠙⢮⢇⠀⠀⢹⡌⣷⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠹⣿⢤⣳⣴⢋⣠⡞⠃⠀⠈⣳⣾⡿⠀⠀⢸⣄⡤⣄⣀⡴⠃⠀⠀⠀⣼⠀⠀⠀⠀⠈⣿⠀⠀⠈⡇⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠳⣮⡉⠉⠉⠉⠁⠀⡴⠋⣞⡇⠀⠀⠀⠀⣀⡤⠤⣀⡀⠀⠀⠀⠈⠉⠉⠙⠒⠲⠇⠀⠀⠀⣿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⢸⠁⢠⢿⠀⠀⠀⠀⠰⡟⠋⠙⠒⠯⠷⠶⠮⠭⢍⣲⡄⠀⠀⠀⠀⠀⠀⠿⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⢸⠀⢸⢸⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠇⠀⠀⠀⠀⣀⣤⣾⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡀⢸⢸⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣠⠼⠋⠀⠀⠀⣠⠞⣡⢾⡟⠛⠙⠛⡶⠋⣻⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⢸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠉⠁⠀⠀⠀⠀⢠⡇⢰⡃⡏⠀⠀⠀⠀⠑⠒⠛⣞⣻⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢾⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⡇⠸⡄⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢀⡏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣸⡄⢸⠀⢸⠇⠀⣀⡀⠀⠀⠀⠀⢸⣇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣇⣟⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢀⣀⣤⢶⣺⣿⠀⢸⠀⣸⡄⠀⢹⠇⠀⢰⠆⡆⠸⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠛⠒⠯⠭⠵⣶⣲⣶⣶⣲⣄⢀⣼⡿⠒⠋⠉⠀⠈⠓⠓⠚⡏⠳⠤⣏⣀⣠⠏⣰⢃⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⣄⣀⠀⠀⠀⠀⠀⢀⣙⣿⣿⣟⣅⠀⠀⠀⠀⠀⢀⣀⡼⡇⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡄⠀⠉⠉⠓⠒⠒⢲⣟⠉⠉⠉⠉⢉⣷⡒⠒⠚⠉⠉⠀⢠⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠁⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠿⣅⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠚⠉⣁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠒⠚⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀