⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠙⠲⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠸⣧⠈⠙⠳⢶⣤⣄⣀⣀⠀⠀⡈⢻⡄⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⣿⠀⠀⠀⠀⠀⠉⠉⣛⡛⠛⠛⣄⠹⢷⣤⣄⣀⣀⣙⣻⣶⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠉⢻⣄
⠀⠀⠀⠀⠀⠀⢀⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠸⣧⣿⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠸⣧⠀⠈⠉⠙⠻⣯⡋⠉⠉⠁⠀⠉⠉⠉⠉⠙⠛⠷⣦⣄⢹⣆
⠀⠀⠀⠀⠀⠀⢸⡇⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣿⡿⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡿⢷⣿
⠀⠀⠀⠀⠀⠀⣾⠁⠀⢻⣆⠀⠀⠀⠀⠀⠀⣼⠏⠀⢠⡿⠁⠀⠀⠼⠷⠶⠶⠾⠿⠿⠷⠂⠀⠀⢿⡆⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⢠⡞⠋⠉⠁⠀⢸⠟
⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠻⣧⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⢸⡇⠀⠀⠀⣰⠿⢤⣤⣄
⠀⠀⠀⠀⢿⣿⠿⠷⠶⢶⣦⣽⣷⣀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢀⣠⣤⡶⠿⠶⠶⠶⠶⢤⣝⠦⣤⣀⣹⣦⣤⠤⣍
⡀⠀⠀⢀⣾⠃⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡉⠉⠉⠁⠀⢸
⣷⡀⣠⡾⠃⠀⣀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠓⠶⠶⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠤⣄⠰⠛
⠘⢿⡋⠀⠀⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢀⣠⠟⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠈⣷
⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⢀⣠⡶⠾⠛⠉⠉⠉⠉⠙⠛⠷⣦⣄⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⡆⠀⢻⡄
⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢺
⠀⠀⠐⣦⣀⠈⠙⠷⢦⣤⣤⡄⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠈
⠀⠀⠀⠈⢿⡷⢦⣤⡶⠾⠋⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⡀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⡼⠁⢠⡷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠻⣦⡀⠀⠀⠀⠀⠀⠀⠙⠛⠷⣦⣤⣄⣀⣳⣀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠈⠛⠷⣤⣄⣀⡀⠀⠀⠀⠀⢀⣀⣭⣽⣟⠹⣄⠀⢉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⢹⠉⢙⣿⠟⠛⠛⠋⣽⠉⣿⣿⣶⣄⢹⣤⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⣼⢳⡏⠀⠀⠀⠀⠀⢻⡄⢸⣻⡿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⣠⡾⢃⣿⠀⠀⠀⠀⠀⠀⠀⠙⠿⠾⢿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢀⢀⣼⡟⠁
⣀⣤⡾⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⡶⣿⣿⣿⠋
⠋⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠈⠙⣿⣿⣶⣶⣤⣤⣄⣀⣀⠀⠀⢠⣤⣿⣶⣿⣿⣟⠀⣿
⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⣀⣠⣴⠟⠁⢻⣿⣿⣿⡟⢿⣿⠃⠀⠀⠘⢿⡿⠛⢻⡏⠉⠙⠛⠿⢷⣶⣿⣿⣿⣿⣿⣿⣾
⠀⠀⠀⠀⢀⡖⠙⠛⠶⠶⠶⠛⠛⠋⠉⠀⠀⠀⠈⣿⣿⡟⡛⣷⣦⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿
⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢼⣡⣾⣽⡆⠀⠀⠀⠀⠀⠀⢸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⠁
⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢶⣿⣿⣿⣶⣄⠀⠀⠀⠀⢸⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠈⠁
⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣤⡀⠀⣾⣿⣿⣿⣿⣷