Candlestick Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠆⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡇
⠀⢠⠉⠒⠒⠒⢾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡁
⠀⢸⠁⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣇
⠀⢶⣠⠄⢀⡀⢁⣍⣡⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠘⠶⠾⠧⠼⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠿⡷⠖
⠀⠠⠀⠐⠀⠒⠀⠀⠠⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⡞⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣸⣧⣄
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠓⡛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢣⠸⡟⠉⠉
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⢠⠀⢸⡀⢀⠀⠌⠛⣿⢺⣦⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⡀⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⡁⠘⣁
⣀⠛⠾⠶⡶⣦⣤⢤⠴⠾⣛⣢⡀⠀⠀⠀⠀⠀⠀⠿⢀⣾⠀⣼⣰⠉⡇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠡⠄⠀⠈
⠛⠮⣍⣉⣓⣲⡒⣚⣛⣿⡿⠟⠃⠀⠀⠀⠀⠀⠈⠀⠈⠽⠀⢿⢭⡔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣀
⠀⠀⠀⠀⠈⠇⢰⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠠⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⡈⠀⠹
⠀⠀⠀⠀⠀⠢⢼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣸⢣⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⠄⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢆⠰⡄
⠀⠀⠀⠀⠀⠈⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⡄
⠀⠀⠀⠀⠀⡀⣹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⢀⣠⡤⢦⠤⢉⢷⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⠀⠀⠀⠀⠀⢠⣮⠚⢯⣼⠸⠴⠯⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠤⣆⠌⠉⣻⣾⢋⣭⣽⡾⠇⠀⠀⠀⠀⠀⠀⢸⣄⣀⡀⠀⣵⣰⣿⣿⡂⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀⢀⣠⣤⣴⣯⣤⣤⣤⣄
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡐⠁⠀⠀⠉⢩⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠾⠷⠶⠟⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠵⠊⡁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠊⣷⠔⠋⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠐⠷⠚⠁⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢠⠀⠀⢸⡇⠀⣀⡇⢸⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠀⠆⢸⡇⢀⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⠀⡇⠀⡇⢸⠆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡇⠇⠳⡼⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢣⡆⠀⠀⠀⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄⠀⠀⠀⠀⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⢠⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣤⣷⣶⣶⣾⢤⣤⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⣿⣿⣟⣛⣉⣉⣉⣉⣉⣉⡉⠉⣳⠀⠀⠀⠀⠀⢀⡴⠋⣁⣤⣤⣤⣌⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡟⡟⠉⠉⠉⠉⠉⠉⠉⠉⣿⡟⠉⠀⠀⠀⠀⠀⡾⢀⡞⠋⠁⠈⠉⢻⣷⡀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢱⡇⠀⠀⠀⠀⠀⠀⠀⠀⢧⢻⡀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣠⡤⡤⠤⠴⠶⣖⣒⣒⣛⣛⣛⣛⣛⣛⣛⣛⣙⣛⣛⣛⣛⣛⣛⣒⣒⣒⠶⠦⠿⠤⠷⣤⣀⠀⠀⣠⠟⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⢙⣿⣿⣿⣏⣉⣉⣡⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⢿⣻⡵⠋⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣯⡽⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢰⠶⠾⠷⠶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣀⣀⡀⠀⠀⣀⣀⣸⣇⣀⣀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⡇⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢸⠀⠀⠀⠀⣿
⢀⣀⣀⣿⣀⣀⠀⠀⢀⣀⣀⣿⣀⣀⡀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢸⣀⣀⣀⣀⣿
⢸⡏⠉⠉⠉⢹⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠉⠉⢹⡏⠉⠉⠀⠀⠈⠉⢹⡏⠉⠉
⢸⡇⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇
⢸⡇⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢸⡇
⢸⡇⠀⠀⠀⢸⠀⠀⠘⠛⠛⣿⠛⠛⠃⠀⠀⠛⠛⢻⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸
⠸⠧⢤⣤⠤⠾⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⣿
⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡑⢢⣷⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⢠⡏⠒⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢻⡆⠀⠀⠀⠀⠀⣰⡣⢌⣇⠀⠀⠀⠀⠀⣼⠇⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡐⠡⢸⡇⠀⠀⠀⠀⠀⣿⠁⠀⢿⡀⠀⠀⠀⠀⣿⢠⠉⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣡⡀⣼⠃⠀⠀⠀⠀⢸⡇⠰⢂⢸⡇⠀⠀⠀⠀⢹⣄⣄⢡⡏
⠀⠀⠀⠀⠀⠀⣀⣀⣈⣙⣟⣁⣀⣀⡀⠀⠀⠈⣇⢁⠀⣸⠃⠀⠀⣀⣀⣀⣙⣿⣋⣀⣀⣀⡀
⠀⠀⠀⠸⠁⠘⠿⠿⠭⠭⠿⠭⠽⠿⠟⠂⠙⠀⠙⠻⡷⠋⠀⠋⠐⠻⠿⠿⠯⠿⠯⠿⠿⠿⠃⠘⠃
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠸⣿⣿⣟⣻⣿⣛⣿⣿⡷⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠰⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠞⠉⢮⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣠⠤⡀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣰⠁⠀⠹⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⠇⠀⠀⠀⠱⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠾⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⡜⠙⡆⠀⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢸⠀⠀⠸⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣧⢀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣇⢸⡇⠀⣇⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣿⣦⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠭⣀⣀⠺⣍⣡⣴⣒⣒⣚⣀⣀⣿⣇⣀⣐⣒⣒⣲⣤⣨⣽⢂⣀⡨⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣶⠖⠲⣶⣶⣶⣶⣶⣶⣶⡶⢶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣄⣠⣿⣴⣶⣼⣤⣴⣦⣷⣤⣴⣾⣤⣥⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣶⣶⣾⣿⣶⣶⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⢿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣄
⠀⠀⠀⠀⠀⣠⣾⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣀
⠀⠀⠀⢀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦
⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀
⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠹⣿⣷
⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠀⠀⠀⠀⠀⠀⢹⣿⣇
⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⣸⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⢿⣿⡄
⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⡖⠺⣅⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠛⠉⠛⠻⠿⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢷⣾⠿⠛⠁⠀⠀⠀⠀⠀⣠⣶⣾⣷⣶⡄⠀⢀⣠⣶⣾⣿⣿⣶⣦⣄⠀⠀⢀⣴⣶⣿⣿⣿⣾⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠉⠈⣻⣿⣤⣿⡿⠛⠉⠀⠈⠉⠻⣿⣷⣶⣿⠿⠋⠁⠀⠈⠙⠻⣿⣷
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿
⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠙⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣤⣤⣿⡿⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟
⠀⠀⠀⠀⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⢀⣠⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣤⣤⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣤⣤⣶⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠘⠀⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠂⠀⠀⠀⠀⠀⢠⣆⡀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠤⠒⠂⠂⠁⠀⠀⡀⠀⠊⡆
⠀⠀⠀⠀⡀⠄⢀⡀⠘⠀⠀⢀⠄⢀⠐⠀⠀⠀⠀⠐⠀⠠⠄⠂⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⡇⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠊⠁⠤⠀⠣⠀⠀⠀⠈⢠⡀⠀⠀⠀⠀⠀⠤⢤⠤⠤⣤⠤⠤⢤⠒⠒⡏⡁⢸⠑⢅⠇⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⣀⠤⣤⢄⠀⠀⠑⠀⣆⠀⢀⠀⠀⠀⠈⡡⠂⢂⡠⠋⢄⣠⠋⠢⠴⠁⠉⠃⠀⠀⠀⠀⠀⢸⠀⠀⢠⡄⠀⠀⠀⠀⣠⡄⠀⠀⡆
⠀⠂⠔⠁⠀⠀⠠⠀⣱⠀⠀⠀⠀⠈⠁⢀⡠⠤⠤⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀⠀⠀⠈⠦⠀⠀⠈⡑⢄⠀⣘⠁⣀⠄⠐⠁
⠀⠀⠮⡁⢀⠠⠀⠈⢡⠱⡀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠁⠒⠀⠀⠀⠀⠀⢀⠀⠀⠠⢄⡀⠀⠀⠀⢠⠀⢸⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠡⢱⠀⠀⡘⠀⠀⠀⣀⠀⣀⢤⣠⡀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠈⢄⠀⠨⡑⢀⠀⠀⢸⠀⠸⠀⠀⢌⠀⡀
⠀⠘⠁⢁⠀⠀⠀⠀⢠⣐⠼⠀⡀⢧⠀⡀⠔⠀⠉⠀⠀⠀⠦⠁⢤⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠦⠀⢠⡃⠀⡀⢣⠀⠸⡛⠁
⠀⠘⠀⠈⠓⠒⠒⢋⠉⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢂⡀⠀⠁⡉⠐⢄⢀⠀⡆⠀⠀⠀⠀⠀⡀⠠⠐⣄⠀⢀⠙⢄
⠀⠀⢀⠀⡤⠄⡀⠀⠀⠀⢀⡾⡀⠀⠀⢢⡀⠀⠀⠀⣀⠜⠀⠀⠀⠀⢀⣧⡁⠀⠄⠁⠀⡠⠊⢰⠀⠀⠀⠀⣔⣃⠸⢒⡤⠤⠃⠀⢇⠘
⠀⠀⢠⡀⠀⢀⡇⠀⠀⡀⠄⠀⠈⡠⠐⠀⢀⡩⠧⡉⠀⠀⠀⠀⣄⠀⠾⠃⠉⠒⠲⠒⠊⠀⠀⢘⠄⠀⠀⢘⠡⠚⠉⠁⠀⡀⠤⠂⢁
⠀⠀⠤⣈⠉⠉⠀⠀⠠⡄⠀⠀⡎⢀⡀⠀⣀⠀⠀⠈⢢⡀⠀⠀⠁⠄⠂⠀⠈⠉⠐⠒⠂⠉⢢⠀⡀⠀⠀⠘⡄⠤⠔⠊⠁⠀⠠⢄⠸⡀
⠀⠀⢀⢀⡉⠁⠀⠁⠠⠀⠀⢰⠀⢰⡈⠉⢽⠀⡠⠖⠀⠓⠀⠀⠀⠐⢀⡈⠱⠂⠲⠀⠄⠀⠄⠀⢨⠀⠈⢂⠈⢄⠀⡂⠀⢪⠦⣤⡡⠇⢰
⠀⠀⠁⠀⠀⠐⡀⠀⠁⠀⠀⢸⠀⠀⣛⣐⢫⠊⠁⠀⠀⠀⢀⠀⠄⠀⢂⠀⠀⠀⠈⠀⠐⠀⠲⠀⠊⠀⠀⠰⠀⠈⠦⣭⢸⠀⡒⣈⠂
⠀⠀⠀⠂⢄⠀⠀⡅⠀⢀⠔⠊⠉⠀⡘⠁⢎⠀⠀⠀⠀⢠⠁⠀⠀⠀⡆⢱⠻⠋⠉⠎⠩⣉⠚⠳⠀⠂⠠⡤⡀⠀⠀⠀⠀⠉⢁⠀⡔
⠀⡀⠀⢈⠀⠈⠁⠀⠀⠸⢄⡄⠀⠀⠀⠢⠄⠁⠴⠄⠄⠰⠤⠤⠤⠎⠴⢏⠀⠁⠀⠈⠀⠁⠒⠒⠁⠀⠀⠀⡔⠀⠀⠀⠀⠀⠈⠈⡀⢀
⠀⢀⡀⠋⠀⠀⡀⠀⠀⠀⠀⢍⡑⠢⠤⢄⣀⡁⠐⠒⠀⠀⠐⠒⠀⠁⠀⠀⠀⠈⠀⠀⠉⠀⠀⣀⡀⠤⢐⠝⠁⡰⠋⠀⠀⠉⠲⠄⠓⠊
⠀⠀⡵⠀⠀⠆⠀⠀⠀⠀⠀⡀⠈⠁⠒⠒⠠⠬⠉⣉⣐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢂⣉⠡⠄⠒⠂⠁⠀⠀⡃⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰⠄⢰⠀⠈⡆⠀⡒⠠⠤⡀⠀⠀⠉⠉⠀⡈⠉⠉⠁⢀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠴⢄⣀⣀⢀⡠⠃⠀⡀
⠀⠀⠀⠀⢆⠀⠲⠀⣀⡄⢀⠂⠀⠀⢳⢠⠨⡄⠀⠈⠐⠤⣀⠐⠋⡠⠐⠂⢔⠀⠀⠀⡆⠲⣄⢀⠀⣠⠀⠀⢄⣀⠀⠀⠀⠈⠉⠀⠤⠊⢸
⠀⠀⠀⡰⡌⠑⠀⠤⠰⡂⠁⠒⢀⡀⠀⠁⡇⠩⡀⠀⠀⠀⠀⡀⡘⠀⠀⠀⠀⠂⠀⠀⢑⡀⢄⠃⡀⠀⢠⠀⠀⠢⢀⠀⠀⠀⠀⠀⠒⠡⠄
⠀⠀⠐⠂⠈⠂⢂⠠⠔⢡⠃⠀⠊⢑⡄⠀⠙⠀⢥⠀⠀⠀⠀⡇⠃⠀⠀⠀⠀⠘⠀⠀⠸⡈⠙⠠⡀⠢⠀⠁⠀⠀⠀⣀⠀⢠⠀⢄⢀
⠀⠈⠀⠀⠣⣀⠂⠀⠀⠀⢂⡠⠋⠀⠀⡀⠂⠠⠈⢆⡀⠀⠀⠁⠆⠀⠀⠀⢀⠃⠀⠌⠁⠡⠀⠀⠘⢆⢁⠀⠠⡀⠀⠑⠀⢈⠄⢄⠐⢄
⠀⠀⠀⠀⠀⠀⡀⢂⢀⡒⡁⠀⠀⢤⠀⠐⡀⠄⠀⠀⠉⠦⣴⡘⣜⠠⠀⠔⠁⠀⣠⠄⠂⠀⠑⠄⢀⣨⠆⠀⠀⠀⠡⠋⠀⠙⢢⠀⠁⠌
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠛⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠁⢀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠺⢧⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠛⠢⢄⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠓⠤⣀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⠇⣇
⠀⠀⠀⠀⠀⠀⠀⠗⢄⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⢰⠎⣧
⠀⠀⠀⠀⠀⠀⠀⠷⢀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢨⡦⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠦⡀⠉⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠄⡈⠑⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠆⠈⠱⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠃⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠀⡌⠳⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⢇
⠀⠀⠀⠀⠀⠀⢠⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠘
⠀⠀⠀⠀⠀⠀⡃⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠱⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣠⣄⡀⠀⠀⠀⠀⠀⠀⡿⠆⠀⠀⠀⠈⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢻⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠚⢣⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠞⡁⠀⠀⠀⠀⠀⠀⢼⠃⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⣀⡠⠀⠀⠀⡸⢿⣄⠀⠀⠀⠀⠀⠀⠀⣼⡖⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⢀⠂⣘⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠾⠀⠀⠀⠀⠀⠒⠛⡆
⠀⠀⠀⠐⠃⠉⠁⠀⠀⠀⠘⠋⠓⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠐⠚⠋⠛⠓⠀⠀⠀⠀⠉⠉⠁⠀⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠣⣤⢂⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⡜⠲⣲⣧⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠱⣤⠉⡁⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣸⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠀⠀⠀⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠃⠀⢀⣾⣿⣿⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣘⡛⠶⠾⠿⠿⠿⣟⣛⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⠙⠲⢾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢀⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠐⠛⢻⣿⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃⢤⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⣠⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣀⣀⣻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠈⢻⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡣⢄⣄⠀⠤⢲⣿⣿⣿⣿⣿⣾⣗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠤⠾⠿⠾⠿⠿⠿⠿⠛⠛⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⡠⠔⠒⠋⠉⠙⠓⠦⣀⠀⠀⠀⠀⠀⡠⠄⠒⠒⠒⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⠙⠓⢦⣀
⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⡏⠀⠠⣦⠀⠀⠀⠀⠷⠀⠀⢸⠀⢰⠃⠀⠀⠀⣄⠀⢠⡄⠀⠀⠀⠈⡆⠀⢠⠃⢀⣤⡄⠀⠀⠀⠶⠖⠀⠘⡆⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢷
⡇⠀⡄⠀⠀⠀⠀⠀⠀⡲⠀⢸⠀⢸⠀⠀⡀⠀⠉⠀⠈⠀⠀⢴⡁⠀⡇⠀⢸⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⠀⣿⠀⢸⠀⠘⡇⢠⣦⠀⠺⠗⢈⡇⠀⢸
⠹⡀⠈⠢⣄⣀⣀⣠⠔⠁⢀⡞⠀⠘⣆⠈⠣⠴⢄⡴⢄⠴⠒⠚⠁⢠⠃⠀⠘⡄⠈⢿⣭⣧⢼⡤⢿⡾⠋⢀⡏⠀⠈⢧⠀⠙⢦⣀⣀⣀⡤⠞⠀⢠⠟
⠀⠙⠦⣀⠀⠀⠀⠀⣀⡤⠊⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠘⠦⣀⠉⠛⠚⠛⠉⢀⣠⠞⠀⠀⠀⠀⠳⢤⣀⠈⠉⠁⣀⣠⠔⠋
⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⣀⡠⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⢤⣀
⠀⣠⠎⠁⠀⠀⠀⠀⠀⠉⠳⡀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠈⠳⣄
⣰⠁⠀⠀⢀⡀⠀⣀⠀⠀⠀⠹⡄⠀⢰⠋⠀⠀⠀⠀⠀⢀⡀⠀⠀⢹⡀⠀⢀⠎⠀⠀⢀⡀⠀⠄⠀⠀⠀⠹⡄⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⡇⡀⠀⠀⠈⠁⠀⠁⠀⠀⢸⡄⡇⠀⡏⠀⠀⠟⠀⠀⠀⠈⠉⠀⠀⠀⡇⠀⣸⠀⠀⠀⠀⠀⠀⠀⣠⢤⠀⠀⢳⠀⢸⠁⠀⣠⣄⠀⠀⠀⢀⣤⠀⠀⣿
⣇⢹⡀⠀⠀⠀⠀⠀⠀⠀⣸⢡⠇⠀⣇⠀⢤⠤⠤⢒⣒⣒⣊⡟⠁⢰⠇⠀⢸⠀⠀⣠⡔⢞⠉⠉⠉⠙⠦⠀⡼⠀⠸⡄⠀⠈⠁⡠⠤⣄⠈⠉⠀⢀⡏
⠈⢦⡙⠦⣄⣀⣀⣀⣠⠔⣡⠎⠀⠀⠘⣆⠈⠻⢭⣉⣀⠤⠊⠀⣠⠏⠀⠀⠀⠣⡈⠀⠈⠉⠀⠀⠀⠀⢀⡴⠁⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠉⠒⠦⠤⠭⠤⠒⠋⠀⠀⠀⠀⠀⠈⠑⠦⢤⣤⣤⠤⠴⠊⠁⠀⠀⠀⠀⠀⠈⠒⠤⢤⣀⡠⠤⠖⠋⠀⠀⠀⠀⠀⠈⠙⠲⠤⠤⠴⠒⠋
⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⢀⡴⠚⠉⠉⠉⠉⠉⠓⢤⡀⠀⠀⠀⠀⢀⠔⠋⠉⠀⠀⠉⠳⢤⠀⠀⠀⠀⢀⡴⠊⠉⠁⠀⠉⠙⠲⣄⠀⠀⠀⠀⠀⣠⠔⠋⠉⠉⠀⠉⠙⠲⣄⡀
⢠⠏⠀⠀⠀⠀⠀⠀⡀⠀⠀⠱⡄⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢠⠎⠀⠀⠀⠀⠀⢀⠀⠀⠈⣧⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳
⡏⠀⠀⡹⠯⠀⠀⠿⠅⠀⠀⠀⢷⠀⢰⠇⠀⣠⠤⡄⠛⢀⠤⢄⠀⠈⡇⠀⢸⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⢸⡄⠀⢸⠃⠀⠀⠀⠀⠄⠰
⣇⠀⠀⢀⣀⣀⣀⣄⣤⡤⠄⠀⡿⠀⢸⡀⠀⠁⠀⠀⣠⡀⠀⠀⠀⢀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⡄⠀⠤⣤⡤⡴⠶⠒⠒⠋⠁
⠘⢆⠀⠀⠀⠀⠀⠀⠓⠁⢀⡴⠁⠀⠀⢧⠀⠀⠀⠀⠻⠃⠀⠀⢀⡞⠀⠀⠀⢣⡀⠀⠀⡴⠒⠒⠄⠀⢠⠞⠀⠀⠀⢳⡀⠀⠹⣠⠇⠀⠀⠀⠀⢀⡴
⠀⠈⠑⠦⢄⣀⣀⣀⡤⠴⠋⠀⠀⠀⠀⠀⠑⠦⣄⣀⣀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠙⠢⣄⣀⣀⣀⡤⠖⠁⠀⠀⠀⠀⠀⠉⠳⢤⣄⣀⣀⣤⠤⠖⠋

⠀⠀⠠⠀⠠⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⣠⢥⣤⣥⡀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠤⠀⠤
⠀⠀⠐⠒⠚⠀⠀⠀⠀⠀⠠⠊⠂⠀⠀⢐⠒⠚⠀⠀⠀⠜⠋⠁⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃

⠀⡔⠀⣴⢀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠉⠉⠀⠉⠉⠀⠀⠀⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠛
⠀⠀⠠⠀⠠⠀⠀⣁⠀⡀⠀⡀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⣀⡀⠀⠀⢿⠀⠀⠀⠀⠸⠇⠀⠀⣀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠈⠀⠈⢀⠀⠀⣠⠉⣉⠑⡀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠤⢀
⠀⠀⠐⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡂⠀⠀⠀⠻⠃⠻⠃⠀⠀⠐⠃⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀⣒⠀⠀⠀⣐⠀⢀⡂⠀⠀⢄
⠀⠀⠠⠀⠠⠀⠀⠀⠀⡄⠠⡄⠀⠀⠺⣷⠖⢶⡿⠀⠀⠀⠄⠀⠄⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⡄⠀⡄
⠀⠀⠀⠒⠐⠀⠀⠀⠀⠁⠆⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠲⠶⠂
⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠉⡀⠀⠐⡐⠆⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠄⠀⠀⠐⠛⠻⠟⠓⠀⠀⠐⡄⠀⡠⠠
⠀⠘⢗⡂⣚⠇⠀⠀⠀⠀⠀⠂⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠠⣬⣴⣤⣥⠀⠀⢆⠴⠀⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⠀⣀⠂⠀⠀⠐
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡽⠛⠃⠈⢂⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠘⠫⠡⢀⡀⠁⠀⢊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢭⣝⡇⠀⣀⡀⢀⠃⠀⠂⠀⠀⡈⡀⠀⠀⠀⠀⣠⣤⢴⠀⠀⠀⠀⢠⡄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢫⣉⠀⠲⡟⠂⢀⡷⠀⠡⠀⣸⣽⣷⢐⣶⣰⣿⣻⠿⠿⠂⣤⡄⠈⢠⠁⠀⢠⡄⠁⠀⠀⠁⠛
⠀⠀⠀⠀⠀⠀⠀⢀⠞⡹⠋⠐⢺⣟⢰⣦⣽⣤⠌⡤⢤⡤⠈⣿⡟⣿⢻⣭⣿⣷⣿⠀⠀⠀⢸⡆⢸⣷⠀⠀⢸⠀⠀⡆⠀⢀⠁
⠀⠀⢀⡤⣀⠀⠀⢸⣾⣅⢀⣀⣠⣿⠙⠉⢁⠉⣴⣶⣯⡿⣷⠙⠫⠭⠍⠠⢭⣏⠉⠒⠃⠴⠞⠁⡈⠥⠉⠉⠀⠠⠤⠖⠂
⠀⠀⠀⡍⠁⢀⣠⣾⣿⣿⣿⣿⣿⣟⠋⠀⠀⢰⣿⣿⣿⣁⣠⡀⠀⢴⣞⠗⠺⡇⠀⢰⠀⠀⣆⡀⠖⡀⠀⠀⠀⠀⠀⠀⠀⠠⣶
⠀⠀⣀⢀⡄⣸⣿⠏⠙⢿⣿⣿⣿⠿⢚⡳⣄⣀⣈⣩⢽⣿⣿⣿⣆⣿⡇⠀⠂⠐⠀⠸⣧⣤⡉⠀⠀⠀⢠⣆⠀⠀⠀⢀⠀⢘⣨
⠐⣄⣸⡟⠄⠿⣿⠀⠀⠰⣿⡏⣿⣷⣿⣿⣿⠿⡟⠿⠾⢿⣿⣿⡏⣿⣷⡄⠀⢀⣀⣄⠈⠁⠁⠀⠀⠀⡛⣿⡗⠀⠐⠉⠀⠘⠛
⢾⣿⣿⣽⣿⣼⣿⡆⠀⢰⣿⣶⣽⣿⣿⡿⠿⠷⠿⣤⣄⣀⠈⠙⠒⠛⠿⠅⠒⣿⣿⠻⣁⡇⠀⠀⣀⠀⣸⢻⣷⠶⠀⠀⠀⢀⡀
⠈⠻⠿⠻⠿⢻⣿⣧⣠⣾⣿⡟⣿⣷⣤⣤⣤⣤⣤⣤⣿⣯⣿⣤⣤⣄⠶⣀⣽⠙⠋⡉⢛⡉⠀⠀⠈⠀⢿⣻⡏⠉⠂⢉⣼⣿⣿
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠇⠈⢋⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠉⠀⠹⡿⣿⡯⠀⠀⠀⠀⠸⠼⢱⣶⡶⠀⠀⠈⠉
⠀⠂⠀⠂⠀⢋⣽⣾⣿⡏⠉⠀⠀⣾⣿⣿⡟⠋⣻⣿⣿⣯⡿⠀⠀⠀⠀⢰⡦⠀⣴⢶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣾⣿⠟⣿⡇⠀⠀⢸⣿⣿⣿⢷⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠘⡿
⠀⠀⠀⠀⢠⣿⠇⠀⢿⡇⠀⠀⣾⡇⢸⣿⡁⠘⣿⣿⣿⣿⡷⠀⠀⠀⠀⡄⠀⠀⢈⣷⣶⣒⢤⣤⡤
⠀⠀⠀⠀⣼⡟⠀⠂⢹⣷⣀⣀⣘⠃⢸⣈⣑⠒⠂⣄⣿⠟⠒⠿⠷⠶⠼⠄⠀⠀⠼⠿⠿⠟⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⢌⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠤⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠈⢾⡆⠀⠀⠀⠀⠀⠀⢠⠟⠹⡆⠀⠀⠀⠀⠀⠀⣼⠎⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⢄⠸⡇⠀⠀⠀⠀⠀⠀⣿⠎⠑⣿⡀⠀⠀⠀⠀⠀⣿⠀⢤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠆⠈⡄⡇⠀⠀⠀⠀⠀⢸⡏⠀⠀⢹⡇⠀⠀⠀⠀⠀⣿⠘⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣴⣆⡾⠃⠀⠀⠀⠀⠀⢸⡇⡎⠱⠘⡇⠀⠀⠀⠀⠀⠹⣴⣆⣰⠏
⠀⠀⠀⠀⢀⡀⣀⣤⣤⣤⣭⣯⣤⣤⣤⣤⣀⣀⡀⠘⣇⢠⡀⣿⠇⢀⡀⣀⣤⣤⣤⣬⣿⣥⣤⣤⣤⣄⠀⣀
⠀⠀⠀⢰⠁⠒⠛⠚⠳⠶⠶⠿⠶⠶⠞⠒⠓⠒⢹⠀⠈⣻⣗⡋⠀⡏⠐⠚⠚⠛⠲⠲⠟⠶⠲⠚⠛⠛⠒⠈⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠉⠿⣽⣿⣿⣹⣿⣹⣿⣿⣭⠏⠡⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠉⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⣴⣶⡄⠀⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⠀⠸⣿⣿⡀⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⠛⠋⠉⠉⠉⢀⣿⣿⡟⠉⠉⠉⠛⠛⠿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣀⣀⡀⠀⠀⠘⠛⠋⠀⠀⠀⣀⣀⣠⣴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡿⠁⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣀⣠⣶⣺⣗⣿⣷⣿⣶⣿⠚⠁⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣠⣾⣿⡿⠛⠉⠉⠀⠈⠉⠉⠁⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣤⣀
⠀⠀⣀⣴⣾⣿⡿⠟⠛⠉⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠙⠛⠿⣿⣿⣶⣄⡀
⢀⣼⣿⡿⠋⠁⠀⠀⠀⠀⠸⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡿⠀⠀⠀⠀⠀⠉⠻⣿⣿⣄
⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣶⣶⣶⣶⣶⣤⣴⣶⣶⣶⣶⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟
⠀⠀⠙⢿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠙⢿⣿⣷⣭⣉⣛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⢛⣋⣭⣵⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⠿⠟⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠴⠆⠠⣀⠤⠀⠀⠀⠀⠀⠀⣠⣴⠶⠒⠒⠦⢄⡀
⠀⠀⠀⢀⠞⠁⣤⡄⢠⣶⡈⢦⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢾⢁⣀⡖⠂⢛⠍⡀⣽⠒⠀⠀⢀⣾⠋⢀⣤⠀⠀⢠⣆⠈⠲⡀
⠀⠀⠀⢸⡀⠀⠛⢃⡘⠛⠁⢸⠇⠀⠀⠀⡠⠚⢉⠁⠀⠀⠀⠙⢦⠀⠀⠀⢿⠉⣨⠡⠤⠬⢥⡄⢹⡇⠀⠀⣾⠃⠀⠈⣿⠀⠀⠸⠟⠀⠀⠘⣆
⠀⠀⠀⠀⠑⠄⠀⠀⢀⡤⠔⠋⠀⠀⠀⡜⠀⠀⠸⠇⠀⢾⠆⠀⠀⡇⠀⠀⠘⣆⠹⢀⠀⣀⠞⢀⡾⠁⠀⠀⡟⠀⢀⡴⠲⠒⠒⠒⠒⣶⠀⠀⣿
⠀⠀⠀⢀⣀⢠⣠⣴⣾⠁⠀⠀⠀⠀⠀⡇⢠⡀⠀⠀⠀⠀⢀⡄⠀⡁⠀⠀⠀⠈⠙⠒⠛⠓⠊⠁⠀⠀⠀⠀⢻⡀⠈⢇⠀⠀⠀⠀⣰⠏⠀⣰⡟
⠀⠀⠀⡧⠻⠤⠤⠤⠤⠤⠞⡇⠀⠀⠀⠰⡀⠙⠢⠄⠀⠀⠋⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⣀⣀⠀⠀⠙⢦⣄⡑⠲⠶⢚⣁⡤⠚⠋
⠀⠀⠀⠳⠞⠋⠉⠉⠉⠉⠳⠇⠀⠀⠀⠀⠈⠓⠦⠤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⢀⡤⠶⠶⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⢿⣷⣶⣶⣾⣷
⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢱⡄⠀⠀⠀⠀⣿⠈⣙⠛⠛⠋⠁⠘⠿⠿⠿⠋⣿⠇
⠀⠀⡾⠀⠒⠐⠶⠀⠒⠚⠳⠆⠘⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⡼⠃⣄⠀⠀⠀⢹⡀⠙⣦⡀⠀⠀⠀⣠⡆⠀⣰⡟
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠺⣄⠀⠀⠈⠀⣀⠞⢄⠀⠀⠀⠓⠄⠀⠉⠀⠒⠋⠉⣠⡾⠋
⠀⠀⢻⡄⠀⠀⠀⣀⣤⠶⠛⢀⡼⠀⠀⠀⢸⠀⠀⠀⠀⠀⡠⠊⠁⠀⣸⡀⠀⠀⠀⠀⠀⠐⠒⠒⠚⠋⠁
⠀⠀⠀⠙⠲⠤⣤⣀⣤⣤⠶⠋⠀⠀⠀⢠⠈⠓⠶⠀⠀⠀⠀⢀⠴⠊⠁⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⣰⠀⠀⠠⣿⠀⠀⢰⡆⠀⠈⢆
⠀⠀⠀⠀⢀⡴⠚⠉⠁⠀⠈⠉⠲⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⣤⢤⣀⠀⣠⡴⠶⠶⠶⢦⣴⡃⣿⠀⠀⠀⡇⠀⠀⠀⠛⠀⠀⠸⠃⠀⠀⠘
⠀⠀⠀⢀⡞⠀⠰⣷⠀⠸⣿⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣸⠋⠁⠀⠀⠀⠀⠀⠈⠹⣯⡀⠀⠀⡇⠀⢶⡀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⢸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣀⣤⣤⡀⠀⣴⡋⠉⠀⢸⡇⠀⠀⢻⡀⠈⠳⢤⣀⣀⣤⠞⠁⠀⡠
⠀⠀⠀⢸⡄⠐⠏⠳⢄⡞⠉⠦⠾⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠀⠘⠃⠀⠙⠀⣀⠀⢸⡇⠀⠀⠀⠙⠦⣄⣀⡀⠀⠀⣀⡠⠖
⠀⠀⠀⠀⠹⢦⣀⠀⠀⠀⢀⣀⡴⠋⠀⢀⣠⡴⠶⠒⠢⠤⣀⠀⠀⠀⢇⠀⠀⢤⡀⠀⠀⢀⡴⠃⣠⡿⠁⠀⠀⠀⢀⣀⣀⣈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠀⠀⣰⡟⠁⢠⡄⠀⠀⣴⡌⠑⢦⠀⠈⠢⢀⡀⠈⠉⠛⡉⠠⠞⠋⠀⠀⠀⣠⠞⢉⠁⠀⠉⠙⠲⡀
⠀⠀⠀⢀⠔⠒⠒⠒⠢⡀⠀⠀⠀⢠⡟⠀⠀⢸⡟⠀⠀⠿⠇⠀⠀⢳⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣰⠃⠀⠿⠂⠀⡿⠀⠀⠙⡀
⠀⠀⠐⠁⠀⠇⠀⠗⠀⠈⠀⠀⠀⢸⡇⠀⣠⠶⠶⠶⠶⠶⢲⡆⠀⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡠⡤⠠⠆⠤⢠⠀⢀
⠀⠀⠀⠐⢄⠀⠀⠠⠆⠀⠀⠀⠀⠘⣧⠀⠸⡀⠀⠀⠀⢀⡼⠃⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢏⣁⣉⣈⣅⣭⠼⢁⠆
⠀⠀⠀⠑⠤⢤⣤⠤⠊⠀⠀⠀⠀⠀⠈⠳⣤⣈⠒⠶⠖⣋⣡⠴⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⣀⣀⣀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⠀⠰⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢀⠜⠀⠀⠀⢰⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠁⠀⣠⠀⠀⠀⠄⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡘⠀⠀⠰⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⡐⠃⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⠁⠀⢰⠁⠀⠀⠀⠰⠀⠀⠀⠘⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠘⠀⢀⠀⠀⢰⠇⠀⠀⠐⠀⠀⠀⠇⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⡄⠀⡀⠀⠁⡀⠀⡆⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠤⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⡀⢠⡇⠀⠀⠃⠀⠁⠀⠀⠀⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠀⠈⡀⠸⠃⠀⡇⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢰⠀⢠⡀⠀⢸⠁⡄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢣⠀⠣⠈⢧⠀⠀⢀⠃⠀⠀⡆⠀⠐⠂⢀⡀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠰⢀⠀⠀⠁⠠⠚⠀⣠⠟⠀⣠⠄⡀⠀⠀⠉⠁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⡀⠀⠀⠀⠀⡶⠀⠐⠊⠁⠀⡀⠁⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠤⠤⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢀⠀⠀⢀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠖⠈⠀⣠⠆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠤⠀⢀⡄⠀⠀⡄⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠜⠀⠀⠀⠈⠁⢨⠀⠄⠘⠛⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⣭⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠁⣄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⣄⣠⠞⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠐⠾⢷⣤⣉⣉⣁⠀⠀⠉⠉⠙⠛⠃⠈⢛⠻⣄⠴⢀⡴⠞⠓⠠⠤⢈⡱⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠂⠀⠰⠒⠶⠋⠉⣭⣁⣤⣤⣄⣠⣤⡤⢤⡄⠈⡄⣙⡦⢉⡤⠄⠚⠓⠒⢤⡑⠀⠆
⠀⠀⠀⠀⠀⠀⢀⡰⠂⠉⢀⣀⣠⡴⠀⠀⠀⠀⠙⠶⠀⠃⠈⠡⠶⠋⠉⠉⠁⠀⠀⠀⠀⠸⡏⠰⠉⠂⢀⠀⠀⠀⠀⠹⠂⠰⡇
⠀⠀⠀⠀⢀⡴⠃⢀⡴⠋⡡⠌⠁⠀⠀⠀⠀⠴⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢀⠚⣦⠀⠀⣤⠄⢀⡀⠀⢄⠀⠀⢸⣤⠃
⠀⠀⠀⠀⡎⠀⡴⠋⢀⠎⠁⠀⠀⠀⠀⠀⢰⠀⠜⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢰⣽⣷⠀⠈⠀⠛⠹⣦⡀⢀⡸⢃⠸⡆
⠀⠀⠀⡆⠀⠶⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⠀⠀⠀⠀⠀⠈⣤⠟⡵⠈⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠳⢄⡀⠈⠓⠤⢄⣀⣀⣀⠀⣀⣠⣼⡿⠋⠀⡶⢀⠤⠔⠛⠁⠁⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠛⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠷⠶⠾⠭⠭⠍⠀⠙⠋⠀⠀⠀⠀⡴⠂⠀⠠⢤⠄⠒⠈⢀
⠀⢠⠀⠃⡀⠀⡆⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠂⢀⡘
⠀⠈⠀⠀⠀⠀⠈⠦⣀⣀⠜⠁⣠⠤⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⣤⠿⠏⠁⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⡞⠁⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠂⠀⢠⣤⠜⠃⠁⠀⣀⡤⠋
⠀⠀⠀⠀⠀⠈⠲⠂⣀⠀⠀⠀⠈⠉⠉⠀⠐⠒⠒⠶⠶⠶⠶⠖⠒⠲⠶⠶⠖⠒⠈⠉⠉⠁⠀⣀⣤⠄⠲⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠤⠶⠶⠤⠶⠶⠦⠄⠀⠀⠀⠀⠀⠠⠶⠤⠀⠘⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠀⠀⣸⣇⠀⠀⠀⠀⠀⢠⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⠀⠀⠸⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⠀⠀⢸⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢸⣿⡇⠀⡇⢸⠀⠀⣶⠀⠀⡼⢦⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢸⠀⢸⣿⡇⠀⠩⠉⠀⠀⣈⠀⠀⡇⢸⠀⠸⣤⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⢧⡼⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢸⣿⡇⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁
⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⣤⣤⣤⣤





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣿⣿⣿⠿⠿⣿⣿⣷⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠙⣿⣦⡀
⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠈⢿⣷⡄
⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠶⠶⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣤⡀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⢻⣿⡄
⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠈⢿⣿⣟⣳⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢻⣿⡀
⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢠⣦⣀⣙⣧⡀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠈⣿⣷
⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⢿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠑⠒⠶⠤⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⢠⣄⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⡟⠿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠈⠂⠈⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⣿⡿
⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣤⣴⣿⣿⡿⢿⣆⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠟⢋⣠⠤⠴⠿⠷⠄⠀⣼⣿⠃
⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠵⠚⣡⠖⠀⠀⠀⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⣰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⣿⣿⣿⣶⣶⣾⣿⣿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠀⠀⠁⠐⠀⢠⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⠉⠀⠠⡬⡁⠀⠈⠃⠀⠀⠀⠀⠀⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣒⡶⢶⠶⠄⡄⠀⠀⠀⠄⠀⡢⢠⠤⡄⣆⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠍⠉⠉⠉⠁⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠚⠂⠀⠁⠀⠀⠤⠀⠀⢀⣀⣀⣀⡄⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠰⠷⠀⠀⣄⣠⡀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢈⠉⠉⠁⡀⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠁⢀⡏⠀⣾⢸⡽⡟⣼⡇⡷⣼⠀⠀⢀⠄⠀⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠃⠀⠀⠀⡀⠀⠀⢸⡇⠀⢹⢸⡄⡇⣿⡇⡇⣿⠀⠀⠀⡇⠀⠀⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠣⠀⠀⠘⣇⠶⢾⣼⢷⣧⢸⡇⡇⣿⠀⠀⠀⠄⠀⠀⠀⠀⠀⠟⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠄⠀⠀⠀⢠⡄⣠⣴⢤⡄⣠⠀⠀⠀⠀⡠⠀⠀⠀⠒⠤⠆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠈⠀⡸⠀⠐⢶⠀⠀⠀⢸⡄⢹⣿⢸⡇⡇⠀⠀⠀⡀⠁⠀⠀⠀⠀⠐⠈⣀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠂⡇⠀⠀⠀⠁⠀⠀⠸⠁⠻⠟⠸⠃⠇⠀⠀⠀⠛⠀⠀⠀⠈⠁⠉⠁
⠀⠀⠀⠀⠈⠀⢀⡀⠀⠀⠨⠄⡇⠀⠀⠀⠀⠀⣆⣀⡀⡶⢂⠀⡀⣀⡀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢁⢀⡀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⡷⠄⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠁
⠀⠀⠀⠀⠀⠐⠛⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠌⠀⠤⠂⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠲⠶⠶⠃⠀⠀⠀⠀⢀⣀⣠⠔⠒⠀⠀⠙⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠂⠤⠀⠀⠀⠐⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀


⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠘⣆⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠉⠇⠉⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⢸⠀⡎⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠸⣀⠇⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⠤⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠙⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠐⠒⠲⠇⠀⠀⠀⠀⠀⢸⡤⢤⣀⣀⣀⠀⠀⠀⢀⡤⠖⠒⠒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⡠⠤⠴⡀⠀⠀⠀⢀⣀⣼⠖⠲⢤⡀⠈⠉⠓⢶⠁⢀⡔⣋⠙⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⠀⠀⠻⣄⠀⠀⠙⠛⠛⠛⠋⠉⠀⠀⠀⣠⠇⠀⠀⠀⢀⠇⡎⢏⠈⠛⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡤⣄⡀⠀⠀⠉⠑⠒⠒⠶⠶⠶⠶⠶⠒⢋⣁⣠⠤⠴⠒⢉⠞⠀⠀⠉⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠬⠍⣙⣓⡒⠒⠒⠶⠶⠶⠶⠚⠋⠉⠀⢀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠁⠁⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡠⠄⠒⠠⢄⠀⠀⠀⠀⠀⣀⠤⠒⠢⢄⡀⠀⠀⠀⠀⢀⠤⠐⠂⠤⡀⠀⠀⠀⠀⢀⡤⠔⠒⠤⣀⠀⠀⠀⠀⠀⡠⠄⠒⠠⢄
⠀⠀⠀⡎⢠⡄⠀⢠⡄⠱⠀⠀⠀⡜⢁⣄⠀⠀⣄⠙⡄⠀⠀⣰⠁⣤⠀⠀⣤⠈⡆⠀⠀⢠⠋⣠⠀⠀⣠⠈⢣⠀⠀⠀⠎⢠⡆⠀⢢⡄⢳
⠀⠀⠀⡄⢀⠀⠀⠀⡀⢀⠃⠀⠀⠇⠀⢀⡀⣀⠀⠀⡇⠀⠀⢠⠀⠀⠀⠀⡠⠀⡟⠀⠀⢸⠀⡤⠤⠤⢤⡄⠸⠀⠀⠘⡀⠀⡠⠤⢀⠀⢰
⠀⠀⠀⠙⠤⣉⠒⣉⡠⠊⠀⠀⠀⠈⠢⣁⡀⣀⡡⠎⠀⠀⠀⠈⠢⣌⡒⢉⡠⠜⠁⠀⠀⠀⠱⢌⡒⢐⣊⠔⠁⠀⠀⠀⠑⢌⣀⠀⣀⠵⠃

⠀⠀⠀⠀⣀⠤⠤⠤⣀⠀⠀⠀⠀⠀⢀⠤⠤⠤⢄⠀⠀⠀⠀⠀⢀⡠⠤⠤⢄⡀⠀⠀⠀⠀⠀⡠⠤⠤⠤⡀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣀
⠀⠀⠀⡜⢁⡀⠀⢀⡀⢳⠀⠀⠀⡰⠁⣆⠀⢀⡆⠱⡀⠀⠀⢰⠃⣀⠀⠀⣀⠙⡄⠀⠀⢠⠊⢀⠀⠀⢀⠈⢆⠀⠀⠀⠎⣠⡄⠀⣠⡌⢣
⠀⠀⠀⡄⠈⠁⠀⠀⠁⢀⠂⠀⠀⡇⠀⠈⣀⡈⠰⠗⡇⠀⠀⢥⠀⠉⠀⠀⢀⠀⡯⠀⠀⢸⠀⠈⡀⢄⡈⠀⢸⠀⠀⠸⡀⢈⣁⣀⣈⡁⢸
⠀⠀⠀⠑⢄⡈⠉⢁⡠⠊⠀⠀⠀⠘⢤⡉⠀⠈⣁⠜⠀⠀⠀⠈⠢⣐⠂⠐⣉⠔⠁⠀⠀⠀⠣⣈⠒⠒⢋⡤⠃⠀⠀⠀⠱⢌⡢⠤⢐⡡⠊
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⢀⡠⠤⢄⡀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢄⡀⠀⠀⠀⠀⠀⢀⡤⠤⢄⡀
⠀⠀⠀⡔⢁⡀⠀⢀⡈⢣⠀⠀⠀⡰⠉⡀⠀⠀⡈⠱⡀⠀⠀⢠⠊⣀⡀⢀⣀⠑⡄⠀⠀⢀⠎⢀⠀⠀⢀⠙⢆⠀⠀⠀⡜⠅⡀⠀⣀⠌⢢
⠀⠀⠀⡁⠈⠁⠀⠈⠁⢀⠆⠀⠀⡇⠀⠁⠀⠀⠁⠀⡇⠀⠀⣟⡆⠀⠀⠀⠀⢐⡻⠀⠀⢸⠀⠘⠀⠀⠈⠀⢸⠀⠀⠸⠀⠀⡡⠤⣉⠀⢨
⠀⠀⠀⠱⣄⠀⠛⠀⣀⠞⠀⠀⠀⠘⢜⠉⠋⠋⢙⠔⠀⠀⠀⠘⢆⡙⠭⠭⢋⡰⠁⠀⠀⠈⠢⡚⠓⠑⠑⡢⠃⠀⠀⠀⠣⣐⢄⣀⠼⣠⠎
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀
⠀⠀⠀⡴⢉⠀⠀⠀⡈⢢⠀⠀⠀⠠⠋⣀⠀⢀⡈⠢⡀⠀⠀⢠⠊⣁⠀⠀⣈⠱⡄⠀⠀⢀⠜⢁⠀⠀⢀⠑⠄⠀⠀⠀⡔⠁⡄⠀⢤⠙⢆
⠀⠀⠀⡁⠈⠁⠀⠈⠋⠀⠆⠀⠀⣇⠶⡈⠀⠈⣱⢆⡇⠀⠀⣈⠀⠉⢠⢠⠤⡀⣷⠀⠀⢸⠀⠉⠀⠀⠉⠀⢸⠀⠀⢰⠀⢈⣁⣀⣈⡁⢸
⠀⠀⠀⠣⡀⠐⠤⠀⢀⠜⠀⠀⠀⠹⣍⠀⠈⠀⢈⡽⠁⠀⠀⠘⢄⠀⠘⠈⠊⡠⠃⠀⠀⠈⢦⡈⠱⡲⠉⣠⠎⠀⠀⠀⠣⡈⠢⠤⠜⢁⠞
⠀⠀⠀⠀⠈⠁⠒⠈⠁⠀⠀⠀⠀⠀⠈⠉⠐⠊⠉⠀⠀⠀⠀⠀⠀⠉⠐⠂⠉⠀⠀⠀⠀⠀⠀⠉⠑⠒⠉⠁⠀⠀⠀⠀⠀⠈⠁⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣧⣭⣴⡇⠐⢿⣿⣴⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣶⡠⣤⠄⠀⣒
⠀⠀⠀⠀⠀⡀⢠⢿⣶⣿⣛⣿⣿⣵⣿⢻⣿⣼⣿⣿⣿⣿⣿⠛⠀⣀⣤⣤⡶⢍⢈⢻⡿⠟⠁⠀⢠⢀⣶⢶⣷⣆⣀⡀
⠀⠀⠀⠠⢀⣵⣴⣿⣯⣏⣩⣿⣿⡷⣾⣉⣿⣿⣿⣿⣿⢿⣿⣶⡶⠯⠈⠉⠁⠀⠀⠀⢠⣄⠀⠀⠀⢘⣻⣿⣿⣿⣷⣶⠢⢄
⠀⠀⢀⣴⣯⣾⣿⣿⠿⣏⣿⣾⣿⡖⢋⣽⣿⣾⣿⣿⣿⣿⣿⣯⣴⡸⠀⠀⠀⠀⢠⡶⠿⠟⢶⣇⣶⣿⣟⣿⣿⢿⣭⣿⣶⣿⡀⠀⠀⠀⠠
⠀⠀⠀⣿⣿⣿⣿⠿⠟⢻⢹⣾⡼⡶⠚⠧⢸⣿⣨⣿⣿⢹⠟⣷⣿⣿⠀⠀⠀⢀⣿⣿⣩⠃⠆⠸⠏⠱⢻⡏⠁⠟⣿⢻⣿⠋
⠀⠀⠀⠙⢻⠟⢿⣶⣷⠈⢿⣿⠊⢻⣿⡦⠻⠿⠍⢏⣀⠸⣀⠟⠻⠏⣠⣄⡀⠀⡿⠿⣼⣶⡄⠀⠀⠀⢸⡇⠐⡾⢿⣦⠉⠀⢠⣤⣄
⠀⠀⢀⣤⣤⣿⣿⣿⡇⠀⢸⡏⠀⠀⣥⠀⠀⠀⢶⣿⣿⠃⠀⣠⣴⣶⣾⣿⣇⣴⣿⣼⣿⣿⠁⠀⠀⠀⢸⣷⠂⣷⣿⣿⣜⣿⣿⣿⢿⡄
⠀⠀⠀⣿⣽⡾⣿⡏⣤⡤⢸⣷⣤⣿⡄⣷⠀⢀⣨⣾⣯⡀⣠⣷⠿⣿⣿⣿⣿⠿⠿⠿⣿⣯⣄⣄⡀⠀⢸⠛⠛⣿⣿⣿⣽⣿⣍⡟⠋⠁
⠀⠀⠀⣩⣄⢢⣴⣧⠉⢿⣸⡇⠀⠘⠀⣠⣿⠿⠿⡿⠿⠟⢻⣁⠀⠐⠛⠛⢛⣶⣂⠈⠈⣿⣿⣿⣿⣦⣼⠀⠀⠹⠱⣟⣯⣿⣯⠙⡄⢀
⠀⠀⠀⢿⣿⡾⢿⠗⠂⠸⢸⡟⠐⣶⠲⣧⣤⠄⣠⣤⣴⣾⣿⣿⣇⢰⣶⣶⡿⣿⣿⠿⠛⡿⣿⣿⣿⣿⣿⣧⠀⠠⢱⣯⣿⣿⣿⣼⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣧⠀⠃⢀⠛⠛⠀⠉⢹⣿⣿⣿⣿⣿⣿⣧⣾⣀⣼⣿⡀⢁⠀⠼⣿⣿⣿⣿⣿⣀⣤⡆⣿⢿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠠⣄⣀⠀⢹⣿⠀⢠⡙⢲⣲⠀⠒⠻⣿⡿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣇⣼⣶⣾⣿⣿⣿⣿⣿⠡⠉⠿⠽⠟⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⣀⢈⡫⠋⠁⢸⣿⢃⣾⣿⠈⢹⡇⢠⣴⣿⣿⣿⣿⣿⣿⣦⡄⠙⠀⡄⠛⠛⠛⠛⠉⠉⠉⠀⠀⠂⠐⠞⠛⡿⣷
⠀⠀⠀⠀⠀⠀⢊⡡⠀⠀⢸⣿⣿⣯⡤⠀⢸⣿⣞⣋⣛⣿⠿⠤⠄⠀⠀⠀⠀⠰⠡⠖⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣰⠇⣥⠄
⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⣸⣇⣀⣀⣘⣳⣦⡀⠈⢿⣍⣀⣀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⣈⣁⡀⠠⠄
⠀⠀⠀⠀⠄⢀⣶⣶⣿⣿⣿⣿⠿⠿⣿⡟⣛⡛⣦⣤⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣠⣴⣤⣴⣶⡶⠟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠈⠛⣗⣖⣙⣿⣷⣶⣚⡛⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣶⡶⣶⣶⣾⣿⣿⣿⣿⡿⠿⠟⣋⣀⣠⣤⣤⠤
⠀⠀⠀⠀⠀⠀⠈⠩⠻⠟⠻⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣷⣿⣿⣿⡉⣉⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠛⠋⠉⠉⠉⠉⠹⣿⣿⣿⠈⢿⣿⣿⣿⣿⡏⠋⠀⠁⣿⡿⠿⠿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠙⠉⠉⠈⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠒⠚⠛⠉⠉⠉⠉⠉⠑⠒⠒⠲⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣤⡀
⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠙⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠨⣿⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣶⣶⡼⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⢸⡧⠠⣤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠒⠀⠀⠀⢻
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡆⠀⠀⢀⢸⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠆⠀⠂⠀⢸⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⠀⠂⢸⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄⠀⠀⠀⢿⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⢀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡓
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡇⠀⠀⠀⠸⢿⡓⢦⠀⠀⠀⠀⠀⠀⢀⢀⣠⠀⠀⠀⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣬⣙⣒⣶⣞⣓⣉⣠⡞⠀⠀⠀⠀⠀⠬⠀⠙⠄⠂⠠⠌
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠀⠁⣬⡂⠀⠀⠀⠈⠀⠀⠁⠀⡁⠄⠁⠀⠀⠈⠐⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⠋⠀⠀⠀⠀⠀⡟⠃⠤⢀⣈⠠⣐⠂⠀⠠⢆⣄⡀⠀⠀⠀⠀⠀⠇
⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠈⠛⣿⢀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⠏⠓⡤⠀⠋⢠
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⣠⣶⡶⣿⣿⠈⠀⠀⠀⠀⠀⢸⡏⠉⡚⠦⠀⠀⠆⠠⠀⠠⢀⣠⢰⣒⠀⠀⠘⠒⠂⠒
⠐⠀⠀⢀⠀⠀⠐⠒⠂⠐⠀⠀⡀⠀⠀⠀⠸⠏⠉⠀⠈⠛⢄⣀⣀⠀⢀⣀⠼⡧⠄⠤⠔⠂⠀⠀⠀⠀⠀⣩⣭⠍⠥
⠠⠀⠀⠉⠀⠂⠀⠠⢄⣀⡈⢿⣿⣦⡀⠀⠀⠈⠛⠿⠯⣵⣬⣞⣫⣭⣛⣫⡭⠓⠓⠈⠉⠀⠀⠀⠀⣠⣾⣿⡿⢻⠟⠲⠂
⠉⠉⠀⠁⠀⠀⠀⠀⠀⠐⠂⢬⣝⣛⢿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⣀⣠⣤⣶⣾⣿⣭⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣉⡻⣿⣿⠿⠿⠶⠶⠶⠶⠶⢶⠿⠿⠟⠟⠻⠛⠛⠋⠛⠛⠁⠀⠀⠀⠁⠠⠄⠄⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠲⠤⣤⣤⠤⠄⠄⣀⣠⣤⣤⡤⠤⣤⠤⡤⢤⣤⠤⠤⠤⠤⠤⠤⠤⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣠⣄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⣦⣤⣀⡀⠀⠒⠆
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⣰⣦⡽⠟⠋⠁⠉⠉⠑⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⠿⠋⠛⢩⡤⣤⠀⠀⠈⠀⠒⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠟⠀⠀⠀⠀⠀⡆⠛⠃⠀⠀⠀⠒⣀⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢐⢂⠰⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠈⠁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡌⠋⠀⠃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢐⣾⣿⠀⠀⠀⠀⠀⠀⢠⠀⢀⡿⠃⠀⠀⠀⢀⣤⣤⣄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⣿⣴⡄⠀⠀⠀⠀⢰⡆⢸⠉⡀⠀⠐⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣟⣿⣿⡇⣲⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⣿⣯⣇⠀⠀⠀⠀⠀⠐⠻⠯⠀⠀⠀⠈⢻⣿⣿⡿⠀⠀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣿⣿⣷⡈⣉⢀⡀⢱⣆⡀⠀⠀⠀⠀⠛⠛⠀⠀⠛⠻⠉⠃⠀⠀⠀⠀⠀⠀⠁⠀⠤⢠⣤⣾⣿⡟⠁⠀⠀⠀⠀⡖⡇
⠀⠀⠀⠀⠀⣱⣒⣾⣛⣭⠙⠛⠛⠻⢽⡕⠿⠁⠠⠞⢻⢛⡟⢃⡤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠿⣧⠴⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠙⣉⠑⠈⢙⣇⢀⣼⠃⠀⡀⠀⣴⠀⣦⣀⠈⠁⣼⡇⠀⢲⣦⠀⠀⣤⡄⢰⡿⢰⡇⠀⡇⠸⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⡀⠀⠠⠀⠙⢻⣦⠈⣿⣶⣥⣤⠾⢿⡶⠉⠓⣿⡏⠀⠀⡿⠁⢰⣾⡿⠀⠀⣡⣿⣿⠗⠈⢿⣇⢰⡇⠛⠀⠀⠐⣾⣄⠀⠀⡄⠸⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢈⡿⣷⣿⣿⣿⣍⣠⠀⢀⡄⣴⡿⠇⠀⣠⠇⠀⣼⣿⣧⡆⢶⠇⡿⠟⠀⠛⢾⡿⠆⠀⠀⠀⠐⠷⣸⣿⣧⠀⡰⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⡀⠀⡎⢠⠁⢿⣿⣿⡟⠉⠠⠂⡞⢃⠀⠀⠀⠀⠀⠀⠀⡉⣿⣟⣧⣀⡇⠀⣀⠀⢤⡀⠆⠀⢾⣿⣷⣾⣿⠿⠉⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⣸⣷⣄⡠⠄⠙⢿⠇⠈⠀⠀⢘⡿⠀⠀⠂⠀⠀⠀⢸⠻⣿⣿⡏⠈⡉⠀⠈⠁⠈⢻⣴⠄⠾⠉⢿⣿⡏⠀⠐⠀⣾⢶⣿⣿
⠀⠀⠀⠀⠀⢠⣡⡄⠈⠗⣀⡄⠀⠀⡀⠆⣰⣿⣿⣆⠀⠀⠀⠀⠀⠙⢤⣿⡿⠀⠀⠀⠀⠀⠙⠂⠈⠁⠀⠀⠀⠈⠻⡆⣠⣶⡄⠀⠀⣽⠟⠀⡀⣀⡆
⠀⠀⠂⠀⠀⠀⢉⣥⠀⠈⢿⡘⠀⠿⠉⣼⣿⣿⣿⡃⠀⠀⠀⠀⠀⠛⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⡋⠀⠈⠀⡀⠐⢸⠆⠘⣧
⠀⠘⠀⠀⠀⠀⠘⠃⠀⠀⢘⣷⡤⡀⠸⠛⠟⢿⢥⣧⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣠⠄⠰⣦⣷⡀⠀⢀⣤⠿⠂⢀⡸⠁⠆
⠀⠀⠀⠀⠀⠀⣤⣀⣬⡄⠀⢿⣿⣟⣴⣧⣦⡿⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⢹⣿⣿⣧⡘⣿⠀⠀⣾⡇
⠀⠀⠀⠀⠀⢺⣿⡏⠈⠃⠀⠈⢿⣿⣿⡟⣽⣷⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⣿⡟⣻⠛⣿⣷⣠⣿⡾⠉⠀⠀⣀
⠀⠀⠀⠠⠀⣿⣿⠁⠀⡀⠀⠀⠀⡿⢧⣍⣼⣿⣿⣿⣿⣿⣄⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢱⣿⣯⢰⣧⣿⣿⣨⠁⢿⡇⠀⠘⢺⣧
⠀⠀⣴⠀⠀⢿⡈⣻⣖⣅⣀⠀⠀⠓⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠙⠋⢀⢾⣮⣿⣿⣿⣷⣙⠁⢸⡇⠈⡏
⠀⠸⠉⣅⢀⣾⣿⣿⣿⡟⠯⠉⣦⠁⠀⡼⠹⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣿⣸⣿⣿⣿⣿⣻⠇⢠
⠀⠀⠀⠈⢾⣿⣿⣿⠃⣧⠀⠀⠈⠀⠘⠀⠀⠀⠘⠛⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⢩⣭⣿⣿⠻⠃⠐⠁
⠀⠀⠀⠀⠸⢯⣿⠏⠀⠈⢧⠀⡄⠠⡄⢠⡄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠟⠉⠀⠛⠁⠁
⠀⠀⠀⠀⠀⠀⠈⠇⠆⠀⠈⠳⠶⡀⠀⠀⠐⠏
⠀⠀⠀⢀
⣿⣿⣿⠟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠉⠉⠙⠛⠛⠙⠛⠋⠉⠉⠛⠛⠛⠿⡿⠿⢿⠉⠛⠛⠛⠉⠉⠛⠛⠛⠻⠟⣛⡛⣟
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣉
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠰⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⢠⠀⠀⠀⣤
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿
⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿
⣿⠇⠀⠀⠀⠐⠀⠀⠒⠀⠀⠀⠀⠀⠀⠠⠑⡆⠠⠌⠔⠣⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉
⣿⠇
⣏⠀⠀⠀⠀⠀⠀⠀⠄
⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠛⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⣿⡀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⣿⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣶⣶⣶⣀⣴⣾⣿⣿

⠀⠄⣢⢾⣿⣿⣷⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠹⣞⣿⠁⠠⣤⣄⠀⠀⠀⠉⢻⣾⡟⠙⢷⡟⢿⡷⣿⠛⣧⡤⣿⣰
⠀⠘⡤⢾⡋⢰⡧⠀⢋⡹⠁⠀⠀⠀⢀⣀⣀⣀⠀⠀⢀⣼⡋⠁⠀⡈⠛⠳⡀⠁⠻⣦⠀⠀⠀⠀⠄⠹⠀⠈⡄⠱⠅⠈⣰⠛⠂⢹⣿
⠀⠀⠀⠘⡇⢹⠁⠀⠘⡇⠠⢀⡴⠊⠁⠀⠀⠀⠈⠑⠺⣇⠀⢾⡃⠀⠀⠀⢹⡄⠐⣋⣛⢤⠀⠀⠈⣶⠀⠀⢀⠀⠈⠳⢝⠀⠀⠸
⠀⠀⠀⠀⣧⢸⠁⠀⠀⠇⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣠⠇⠀⠀⠀⠀⢹⣟⣉⠁⠀⣀⠀⠀⠰⠀⠘⣮⠀⠀⠀⠸⡇⠀⠀⢰
⠀⠀⠀⠀⣹⠀⠀⠀⢰⣤⣤⢶⠀⠀⢀⣴⣿⣿⣿⣷⣶⣄⠀⠘⡟⠀⠀⡠⣶⠼⡷⣍⡛⣆⢹⣷⢶⠀⡇⠉⠘⣇⠴⢦⣴⡇⠀⠀⢸
⠀⣀⣰⠖⠉⡇⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⣿⠟⠉⠩⠄⣹⠇⠀⠘⣀⣠⢠⣧⠄⠀⠜⢠⡴⢄⠀⠈⠛⠓⠀⠀⠁⠀⠘⠶⠇⠀⠀⢸
⠻⠁⠀⠀⢠⠃⢀⣠⡄⠀⠀⠀⠀⠢⡻⡿⠀⠀⠀⢠⡜⠋⠀⠀⠀⡍⠸⠙⣇⠠⡤⠀⢸⣷⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡜⠀⠀⠹⠀⠀⢠⣠⣤⡴⠞⠀⠀⢠⡂⠀⠀⠀⠀⢀⣜⠽⡀⠳⠿⠄⠀⠀⣛⣏⠉⠀⠀⠀⠀⠚⠁⠀⡇⠀⠀⠀⠀⠚⠓
⠀⠀⠀⢠⡗⠀⢤⡶⠞⠛⣹⠉⣠⠀⠀⠀⠀⠀⠁⢘⡶⠀⠀⢻⡆⠸⡧⠶⠀⠷⠤⠴⠏⢉⠈⠁⠢⠀⠀⠁
⠀⠀⠀⡾⣢⣤⠜⠀⠀⢈⡍⢠⣏⡉⢒⠂⡴⠁⣠⠞⠠⠀⠀⠀⠛⣶⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀
⠀⠀⢰⡟⠛⡁⠢⣲⠄⣸⠄⠀⠈⠙⠛⠟⠁⡔⢹⠀⠀⠀⠀⠀⠐⠋⠠⠛⠋⠁⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⠂⠀⠀⠀⠀⠸⡄⠀⠸
⠀⠀⡈⠡⠜⠑⡩⠇⠀⢈⠀⠀⠀⠀⠀⠀⣨⠁⢈⡖⠀⠀⢠⠤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⡇⠐⠒
⠀⢠⠁⠀⠀⡏⠀⠀⠀⠀⠲⣄⣾⡿⣷⡞⠁⢀⣦⡅⠁⠐⠀⡄⠛⣀⡁⡀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠆⠈⣣⠀⠀⠀⠘⠀⠀⠅⠈⠁
⠀⠎⠂⠀⢰⠁⠀⠀⠀⠀⠀⠘⠋⠁⠸⡏⠉⠈⣇⠀⡧⠀⠀⠀⠀⣟⢛⡻⢣⡜⢠⡖⠁⠀⠀⠀⠀⠠⠄⠀⠀⠶⠀⠀⡶⠀⡄
⡜⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠛⠉⠉⠀⠀⠀⡀⠁⠜⠀⠸⡇⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠿
⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠇⠀⠘⠆⠀⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⣧⠀⠀⠂
⠰⢤⣰⡇⢀⡀⠘⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠘⠀⠄⠀⠀⢀⠀⠀⠠⠘⠆⠀⠀⠀⢀⠀⠀⢰⠚⢣⠘⠓⠿
⢼⣿⡩⣦⣼⣇⡀⢒⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣠⡗⡆⠀⠈⠀⠀⠈⠆⠀⠀⠀⣤⡀⣵⠺⡛⠁⢲⡎⠐⡏⢣⣺⡁⢠⢶⡄
⣾⠸⡴⢿⣿⡇⠙⡟⠛⡱⣼⠀⠰⡀⠀⠈⠀⠀⠀⠑⡄⠙⢄⡇⠀⠀⠀⢢⡑⡄⣀⠀⠀⠈⢧⠙⣻⢛⠀⣾⡧⣾⡿⠿⢫⡽⠿⠷⠇
⣯⡰⢷⡼⡿⠴⢷⢿⡖⠁⡁⠀⠀⠡⠀⠀⠀⠀⠀⠀⠈⠀⠈⠿⠀⠀⠀⠀⠑⠕⠘⠂⢀⠀⠘⣦⡟⡛⢛⠹⢷⣄⣿⣶⠈⣧⣾⡇⠐
⡿⣦⣶⣤⣷⢞⣗⢘⡇⣠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢿⢏⣷⢹⣿⡇⡘⣀⢻⣿⣁⠇
⢰⣿⢿⣤⣿⣠⠿⣬⡉⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠈⠁⣼⢹⣓⡟⠛⣢⣏⢐⢰
⣾⠹⣸⢿⣹⣧⡔⠻⢿⢻⡇⠀⠀⠀⠀⠁⠀⠀⠳⣄⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢻⣬⣉⡿⣾⢿⣿⣿⣿
⢻⡈⡇⢈⠟⠹⡗⣶⣅⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣀⢳⣸⣿⠀⠰⠃⡏
⢈⠃⠉⠘⠠⠇⢁⠹⠹⠋⣷⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠢⡀⠀⠀⠀⣠⢠⢤⢀⣀⡀⠀⠘⢟⢿⣿⢹⣿⡏⠀⠀⠀⠁
⠈⠄⣸⢀⡄⠀⠐⠀⠐⠇⣿⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠀⣿⣀⠉⣰⠐⠘⢹⠷⠀⠀⠸⡄⠇⠈⠙⡇⠃
⣦⣶⣿⣾⣷⣤⣶⣴⣿⣼⣾⡇⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⢿⣸⣇⣨⣰⣀⣤⠀⠳⡲⣀⣇⣱⣀⣠⣸⣇
⢛⣟⣿⣿⣿⢿⣿⢷⣿⣿⢿⣿⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢢⠀⠀⠾⡿⣝⢯⡯⠽⣩⢇⡀⠀⢹⣿⣿⣟⣿⢩⡿
⡜⢯⢻⣳⣶⣿⢿⣿⢷⡽⢬⡿⠈⠒⠾⣧⣀⣀⣀⣀⣀⣀⣤⣄⡴⠞⣻⡇⠀⣷⣾⢠⣤⠙⣟⢛⡵⣻⡤⣬⢳⣤⡞⢫⢻⢏⡿⣿⡦
⢴⣶⢿⠿⢿⡻⣣⠟⠠⠛⣸⠃⠀⢀⡴⣹⢫⣏⣽⢋⡏⢹⡇⢹⠁⢺⢠⡇⠀⠀⠿⢚⣧⣐⢫⣹⡎⣳⠌⣾⢓⣫⠀⡼⢭⣙⠜⢋⢫
⡀⢆⠺⡘⢆⠫⡱⢌⣚⠛⠛⣁⣴⠿⡕⣰⢣⣃⡇⡮⣼⣘⣠⣜⣧⣤⣞⠠⣰⣾⢛⠻⡽⡆⢯⢡⢘⠡⠚⢃⣴⣶⣯⠄⣂⣠⠄⠄
⣸⣈⣧⣿⣾⣷⣿⣿⣿⣿⣿⣿⣤⣧⣿⣼⣷⡿⣾⢿⠿⣿⡛⢛⣉⣍⣁⠴⢣⣌⢄⡇⣳⢹⠜⣖⣦⣷⣿⣿⠟⡟⠀⣼⠁⢠⠞⢈⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠌⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠙⠾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢦⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⡤⢈⠇⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⣼⢠⡄⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠀⣿⢸⡇⠁⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⣽⣜⡇⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⠀⢸⡿⠴⠎⠁⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢡⡾⠷⠂⢸⣧⣆⣤⡖⢀⡻⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠫⠼⣽⠾⠜⠛⠉⡨⠋⠩⠁⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣰⠶⡆⠰⠞⢱⡌⡅⠀⠀⢵⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠁⢠⡇⢸⡄⣸⢋⠃⠀⠀⣸⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠸⣇⣸⠃⣧⠀⢀⠀⢀⡏⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡄⠀⠙⠁⠀⣼⢀⡄⠀⢰⡇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡇⠀⠀⠀⠀⣧⠈⠀⠀⢸⣧⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣾⡧⠀⠀⠀⠀⡁⢃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠸⣷⠋⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠊⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠷⣶⣦⣤⣤⣀⣤⠴⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣯⣽⣩⣿⣭⣩⣽⣏⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣥⣭⣿⣯⣿⣿⣯⣭⣭⣭⣭⣽