⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡤⣒⣲⣶⣒⡢⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢷⡀⠀⠀⠀⠀⣎⣾⣏⣷⣮⢻⣿⡞⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣰⠈⢿⡀⠀⠀⠀⢏⠿⠿⣸⡿⣸⣿⣇⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣟⠀⠀⢻⣆⢠⣴⣲⠒⠒⠒⠒⠶⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⡏⠀⠘⣧⠀⠀⠀⠀⠉⠉⡽⣵⣿⢏⠞⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣿⠀⠀⠀⢻⣆⠉⠉⠛⢶⣄⠀⠀⠀⠈⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⢰⡇⠀⠀⢻⡄⠀⠀⠀⠀⢨⢱⡿⡵⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢹⡄⠀⠀⠀⢿⡄⠀⠀⠀⠉⢷⣦⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠈⡇⠀⠀⢸⡇⠀⠀⠀⠀⢠⡾⠧⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⢻⡀⠀⠰⣾⣧⠀⠀⠀⠀⠀⠙⣷⡀⢀⡾⠃⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⡏⣿⣿⣾⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⢳⣤⡀⡇⣿⠀⠀⠀⠀⠀⢀⣸⣧⣾⣷⣶⣶⣦⣤⣄⣀⣿⡃⠀⠀⠀⠀⠀⢸⡄⣠⢸⡇⠀⠀⠀⠀⠙⠯⠽⠚⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢀⣀⣽⡿⠷⠛⢷⣴⠶⠾⠿⠿⣥⡬⣿⣟⠲⢦⡶⢶⣇⠉⠛⢿⣟⡒⠦⣄⡀⠸⣿⢇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣤⠶⠚⢉⣡⠤⣖⡭⣷⣿⣐⠲⢄⡀⣰⠏⠙⠳⢦⣤⡟⠀⠀⠉⠓⢦⣟⠈⠙⢶⣼⠛⠳⣯⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢟⣩⠤⣖⣺⠭⣚⣫⡵⠚⢉⡟⠉⠛⠲⢭⣏⠀⠀⠀⢠⡟⠙⠶⣄⡀⢀⡞⠉⠳⣤⣠⡏⢻⣦⠈⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡒⢒⣋⣭⠶⠞⠋⠁⠀⠀⣸⠁⠀⠀⠀⡾⠈⠙⠲⣤⡞⡒⠤⣀⡈⠙⠛⠀⠀⠀⡼⠟⠰⡈⡎⠻⠃⢹⡈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⡦⣼⠇⠀⠀⠀⠐⣄⡇⠀⠀⠉⠓⢤⡀⠀⡰⠁⠀⠀⠙⠁⠀⠀⠈⣇⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣧⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠀⠀⠀⠙⠴⠁⠀⠀⠀⠀⣴⡀⠀⢀⡿⣆⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢧⡀⠀⠀⢸⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠯⣷⠤⣼⠧⠽⣆⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣾⠬⠷⣤⠖⢿⢒⣒⣛⣳⣤⣀⡀⠀⢰⣦⠀⢀⣤⣿⣷⣶⣾⠿⠿⠿⣿⢿⡄⠀⠈⢿⢷⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⣷⣶⣶⠿⠿⠿⠿⠿⢿⡿⠃⠈⠉⠙⠛⠈⠛⠋⠀⠀⢻⡄⠀⠀⠀⠀⢹⡄⢷⠀⠀⠸⡎⠻⣶⣄⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡟⢹⡆⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠸⡇⠀⠀⣷⠀⠈⠛⢷⣤⡀⠀
⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁⠈⣧⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⣸⠇⠀⣿⠀⠀⣾⡄⠀⠀⠀⢈⣿⠂
⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢻⡄⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⣤⡶⠟⠀⠀⣿⠀⢀⡿⡇⠀⠀⢀⣾⠏⠀
⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠙⠶⣦⣤⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⣼⠃⣿⠀⣠⣾⠃⠀⠀
⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣸⣇⠀⢻⡾⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠙⠻⠶⣤⣄⣀⡀⢸⡆⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⢹⠀⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠈⣿⠦⣄⣀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣼⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⣿⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠃⠀⣸⠃⢿⡀⠀⠀⠀⠀