Bomber Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⡔⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣤⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠻⣉⡻⢿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣶⠬⣵⡾⠀⠀⠉⠙⠉⠉⢿⣿⡿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣴⣶⣶⣶⣦⣾⣶⣿⣷⣤⣤⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣽⣿⣿⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⣿⣿⣿⣿⣿⣿⣿⣿⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⢿⣿⣿⣿⣿⣿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠰⣿⣿⣿⣧
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣹⣿⣿⣿⡇
⣿⣆⢻⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠻⢿⣿⣿⣿
⣿⣿⣦⠻⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⢠⣾⣿⡟⣻⣄
⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠈⠻⠿⠟⠛⠛⠻⣷⡀
⣿⣿⣿⣿⣷⠎⠛⣿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣿⡿⠟⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣶⣜⢿⡆
⣿⣿⣿⣿⣿⣷⣄⠈⢿⣿⣿⣿⣿⣮⡿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⡙⠛⠿⣎⢿⣆
⣿⣿⣿⣿⣿⣿⣿⣇⠀⠙⢿⣿⣿⣿⣿⣶⣝⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣾⣮⣽⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠙⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣶⠀⠀⠀⠀⢾⣿⣿
⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⣀⡄⠈⠻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⡠⣠⣥⣦⡄⠀⠀⠀⠻⣿⣿⣿⣿⣷⣦⡀⠀⠈⣿⣿
⣿⡟⠋⠙⠁⠀⢀⠀⣰⣾⡿⠁⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢈⢟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⢿⣿⣿⡿⠻⢠⣿⣿⣿
⠁⠀⠀⠀⣠⣴⣥⣾⣿⠏⠀⣶⣦⣄⡀⠀⠈⢻⣿⣿⣿⣿⣿⡿⢂⡰⣡⣾⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠈⠙⠻⠀⠀⠘⣿⢿⣿
⠀⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣷⣦⣀⠈⢻⣿⣿⣿⣵⣿⣷⣿⣿⡟⠁
⣴⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⢠
⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠐⠃⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣮⡛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡾⠋⠀⠻⢿⣿⣿⣿⣦⡈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣦⡀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⡄⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣄⡆⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⠀⠀⢀⠀⠀⣀⣀⡀⠀⠀⠿⠁⠀⠀⠀⣀⢴⣏⣠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠠⠛⠛⣿⣿⠋⢠⣿⠃⠀⠀⠀⠀⣶⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⣀⣄⢀⣠⡄⣀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡂⡤⣼⣷⣾⣾⣿⣿⣌⣃⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠈⠁⣽⢟⡿⣵⣆⣀⡄⠁
⠀⠀⠀⠀⠀⠙⠲⣦⠀⠀⠀⠀⠀⠀⠘⠛⢥⣲⣅⣀⣴⣾⣿⣻⣿⣿⠻⡏⠀⢀⠀⠠⣴⠦⠴⠾⠁
⠀⢀⡀⠀⠀⠀⣀⡈⠀⢀⣀⣤⣀⡒⣤⣠⣀⣠⣄⣭⣉⣹⣿⣿⣽⣿⣿⣷⠶⠶⠲⣩⣄⢀⣀⣄⣠⣀⣀
⠀⠀⠁⠀⠀⠀⠈⠀⢀⠀⠀⠁⠀⠀⠈⠉⠈⠉⠁⠈⠙⠛⢿⣿⡿⠛⠋⠁⠀⡀
⠀⠀⠀⠐⠒⠲⠿⠿⠿⠷⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠒⠀⠁⠁⠲⠂


⣿⡿⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣠⠴⠶⠭⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠙⠻⠉⠙⠳⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠔⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠐⡖⠐⠆⠀⠀⠀⢰
⠀⠀⠰⣶⣿⡦⠀⢲⣶⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠀⣄⣸⣇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠉⠀⠀⠀⠉⣿⠉⠃
⠀⠀⠀⠀⠀⠀⠀⣮⣇⣰⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠛⠛⠛⠀⠀⠀⣀⣀⣿⣏⣀⠁⠘⠛⠒⠠⠄⠀⣄⣀⣄⣠⣿⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⡋⠉⠁⠀⠰⠂⠂⣾⠦⢄⡀⠀⠙⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣹⣦⣀⣀⣀⣀⡀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣌⡢⣄⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠛⠉⠉⠉⠉⠛⢻⣿⣦⣤⣀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠉⠙⠻⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣒⣶⣶⣶⣶⣀⣶⣆⣰⣶⣶⣶⣿⣿⣿⣿
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⢤⣤⣤⣠⣤⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠈⠓⠚⠛⠉⠉⠁⠉⠛⠋⠰⠦⢄⣠⣶⣶⣖⣀⣀⣀⣀⣠⣬⣷⣶⣤⣤⣶⣶⣶⣶⣶⣧⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣾⢿⣷⣯⣭⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⠛⠛⣋⡛⠾⢧⣿⣿⣿⣿⠟⠓⠒⠶⠶⠤⢤⣤⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣛⣛⣻⣿⣿⣿⣿⣟⣚⣲⡀⠠⢤⣤⣀⣀⣀⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⢳⣾⣿⣿⣿⣿⣿⠿⠛⠉⢠⠍⣭⣴⣿⠏⠉⠉⠉⠛⠛⠛⠛⠛⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠘⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠒⠒⠒⠒⢺⣶⣶⣿⣿⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠁⠀⠦⠼⠆⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠈⠀⠀⠈⠉⠉⠉⠁⠀⠀⠒⠈⠁⠚⠂⠀⠀⠘⠻⠷⠶⠾⢂⣼⣶⣶⣾⣿⣷⣶⣶⣶⣶⣿⣷⣾⣷⣷⣶⠿⠿⠿⠿⢷⣶⣶⡶⠂⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⠀⠀⣀⣀⣀⠐⠒⠛⠛⠛⠛⠛⠛⠻⠿⠛⠻⠹⠿⠭⢭⣿⣿⠷⠶⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣶⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⣀⣹⣅⣼⣤⣿⣼⣇⣸⣇⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣿⣿⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇
⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⣿⡟⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣿⣿⣷⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣴⠀⣿⡀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣾⠀⠀⣀
⠀⠀⢀⣀⣠⣤⣶⣿⣾⣿⣷⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣿⣷⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣿⣆⣀⣿⣇⣀⣿⡀⣄
⠶⠿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⣿⡟⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⠏⣹⡏⠛⠛⠛⢉⣿⠉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⣀⣀⣀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣄⠀⣀⣤⣤⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣿⣤⣀⠀⢀⣀⣠⣤⣤⣤⣤⣴⣼⣿⣧⣶⣤⣤⣤⣤⣤⣀
⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠃⠀⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠋⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⡿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⠻⠿⠿⣿⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣶⣶⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣀⡀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⣀⣤⣶⣿⣿⣿⡿⠿⠡⣤⣌⠉⠙⠛⠻⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠾⠿⠷⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠛⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠙⠛⢿⠟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠬⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡉⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠙⠻⢿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣽⣽⣭⣭⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠰⠶⢾⣷⣶⣶⣤⣤⣤⣄⣀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠉⠙⠛⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣶⣶⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠉⠙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⢠⣤⣤⣸⣿⣿⣿⣿⣿⣦⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠻⠿⠻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠻⣿⣿⣿⡟⠉⠉⠉⠀⠀⠀⠀⠀⠠⠤⠙⠂⠀⣻⣿⣿⣿⣿⡿⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠢⠄⠀⢸⣿⣿⣿⣿⣿⣷⣶⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣀⡀⠀⠀⠈⢹⣿⣿⣿⠇⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠁⣀⠀⠉⠀⠀⠀⢸⣿⣿⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠀⠈⠃⠀⠀⠀⠀⠘⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠃⢀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠀⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⢀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠈⠲⠀⠈⠀⠀⠙
⠀⠀⠀⠀⠀⢄⡀⠀⢠⡀⠀⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠆⠀⣠⣤⣤⣤⡴⠄⠀⠀⠄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⣷⣶⡄⠙⢻⣿⠏⠀⠀⠀⠀⢀⠈⢀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣞⣿⣿⣶⠀⠈⠈⠀⠀⠀⠀⣠⣧⠀⣻⠃⠀⠀⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣶⣿⣆⣮⡳⣦⣄⣶⣾⣿⣿⣿⡟⠃⠠⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⣿⣿⣿⠀⠀⣇⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠹⣿⣿⠄⠀⣽⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡶⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⣿⠁⠀⣸⠃⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⣰⠃⠀⢠⣯⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠉⠀⠀⠀⢠⡟⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠳⡄⠀⠀⢠⣤⣴⠶⠿⠿⠶⢶⡦⣤⣤⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡀⠙⢦⡐⢿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡄⠀⠙⠲⣼⣇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢿⣿⣦⣀⠀⠀⠉⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠛⠛⣿⣿⣿⣷⣤⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⣶⠆⠀⠠⠴⠤⠤⠠⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠛⠋⠉⠉⠀⠀⠀⠀⣶⠂⠀⠀⠀⠀⠈⣿⡆
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠄⠠⠄⠀⠤⠤⠄⠀⠀⠀⠀⢤⡴⠶⠾⠗⢶⣿⠙⠋⠁⢀⣠⣤⣀⣠⣍⣬⡀
⠀⠀⠀⠈⠙⠂⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⢸⣿⣿⡋⠉⣉⣁⣀⣠⡽⣀⣦⠆
⠀⠀⠀⠋⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⠤⠤⠤⠶⠖⠆⣼⠟⠉⠉⠁⠐⣾⣿⡿⠿⣿⣿⣿⣛⣛⠁⠁⠀⠘⠃⠀⡀
⠀⠈⠁⠒⠐⠛⠉⠉⠉⠉⠛⠻⠿⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡛⠂⠀⠀⠀⠉⠉⠉⠛⠛⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣠⣤⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⣀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠠⣴⣶⣤⣄⣀⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠟⠛⠿⣿⣿⣿⣿⣯⠉⠉⠁⠀⠀⠀⠀⠭⣥⡄⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⠄⠀⠀⠀⢠⠤⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠶⠿⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⢿⣿⣿⣿⣿⣿⣶

⠀⢰⡦⠁⠀⠀⡀⢀⡀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢰⡟⠁⢀⣼⣶⠀⠰⠂⠀⠀⠀⣴⣶⡿⣿⣿⣿⣿⣿⡻⠿⠿⠛⣿⣿⣿
⣿⣶⣵⠗⠀⠀⠁⢺⣿⢧⡠⡄⣀⠀⠀⣻⣿⣿⣀⡀⣀⣈⣻⣦⣄⣐⣶⡀⣄⢘⣏⡀⠀⠉⢠⣿⣿⣿⣤⣤⣶⣶⣦⣠⣯⡟⠁⠘⢻⢿⣿⣿⣷⣤⣶⣿⣿⣿⣿
⠽⠋⠁⠰⣶⠦⠴⠾⠿⣿⣿⡿⠿⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣆⣸⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣭⣿⣿
⠀⠀⠀⠠⠄⢤⣀⣀⣀⣀⣠⣭⣭⣉⣉⣐⣻⣷⣶⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠹⢿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡀⠀⠀⠀⠀⠉⠀⠀⠂⠀⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣶⡞⢃⣜⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢈⣀⡶⠷⣶⣶⡶⠦⠤⠀⠀⢀⣩⣍⣉⣙⣻⣟⣻⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢀⣨⡴⠿⠋⠃⠦⠴⠤⠄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⢿⡽⣽⣿⣛⢳⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣦⣤⣀⣀⡀⡀⢀⣀⣼⣷⣞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠒⠸⣧⠀⠈⠙⠿⢛⡋⢡⣍⣿⣿⡼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠉⣁⣭⡿⠾⠛⠛⠃⠸⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣤⣶⣶⣿⣿⣷⣾⡿⠻⣿⣿⠛⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠁⠀⠛⠿⠶⠶⠦⠴⠆⠐⠒⠒⠠⠀⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣿⣿⣿⡿⢿⣿⣿⣿⣯⡀⠀⣀⢹⣄⠀⠉⠉⠀⠀⠀⠀⠀⠤⠭⠉⢙⠛⠛⠛⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⣒⣶⣶⣶⠶⠶⠶⣾⡟⡛⣽⣏⠛⣿⠟⠇⢺⣿⣿⣟⣿⣿⣟⣻⠿⢍⡉⠐⠒⠓⠖⠀⠀⠀⠀⠀⢀⣴⣿⣿⣆⣠
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⣿⣿⣶⣴⣤⣤⣿⣭⣿⣦⣍⣉⣼⣿⣀⠀⠈⠛⠻⠿⠿⠋⠉⠉⣉⣤⣄⣶⣶⣿⣶⣶⡄⠀⢀⣤⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣄⠈⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠿⠿⣿⠿⠿⠿⢿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⡟⠛⠛⠋⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠦⠐⠒⢬⣍⡉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠀⠀⠀⠀⠠⢀⣀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣖⠂⠀⠈⠀⠀⠒⣤⣀⣤⣀⣈⣹⣛⣿⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠲⠄⠀⠀⠁⠉⠁⠈⠸⠟⠿⢳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⠶⣦⠀⠀⠀⠀⠈⠉⠉⠉⠙⠿⠿⠿⠟⠓⠘⠛⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀⠀⠀⠴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢠⣤⣤⣤⣤⣅⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠝⠛⠙⠃⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠁
⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣏⣀⣀
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠈⠉⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭

⠀⠀⠀⠀⠀⢀⢀

⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠈⢻⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾
⠀⠀⠀⢀⣀⣀⣀⣽⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠈⠿⠿⠿⠿⠦⠻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢷⣦⣄⡀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⡴⠶⣶⣶⣾⣻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠉⣿⣿⠿⣿⣿⣿⣿⣿⣭⣽⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⡋⠛⠿⣿⣦⣄⢀⣾⡇
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠻⣿⣿⣿⣿⣿⣿⡉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠙⠻⣿⣿⠁
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠉⠀⢀⣉⣁⣼⡛⠿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡿⣿⡿⠟⠛⠂⠉⠛⢿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣶⣾⣯⣍⠛⠿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠉⠛⠿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣻⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠰⠦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⢳⣝⡌⣦
⠀⠀⠀⠀⣇⠖⠁⠀⢱⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢹⣾⠛⣿⣿⠙⡆
⢀⠀⠸⠓⠈⠀⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⢀⡺⣿⡿⣿⢻⡄⢧
⣎⠥⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇⠃⠀⢿⢸⡇⢸
⠀⠀⠣⠔⠁⠀⠀⠀⠀⢈⠀⠀⢳⣠⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠢⣀⣀⣄⣀⡇⡜⠂⠦⣘⣧⣼
⠀⠀⠀⠀⡀⠀⠀⠐⠦⠘⢄⣀⣻⠍⣁⠠⠾⠤⠤⠤⠀⠀⠀⠀⠀⠤⠤⣀⠘⠤⠔⠉⠉⠀⠘⣷⣧⣀⠴⠉⠁⢸
⠀⠀⠀⠀⠄⠈⢀⣉⡀⠀⠀⠐⠁⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⣿⣿⠀⣧⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢠⠄⠤⢀⣀⣀⣻⣿⠇⡌⠀⠀⡄
⠀⠀⠀⠀⠄⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⡀⠀⠀⠀⣀⠤⠊⠀⠘⠤⠴⠊⠁⠀⠘⡿⠀⠁⠀⢀⠁
⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠒⡂⠉⢐⠂⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢀⠒⠒
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢄⠀⠀⠀⠀⣀⣀⣔⠀⢀⠬⣄⣘⡄⡀
⠀⠀⠀⠀⠀⠇⠄⠀⠀⠀⠀⠑⠦⠀⠀⠻⠇⠱⡀⠈⠂⠀⠸⢷⣼⡄
⠀⠀⠀⠀⠀⡆⢆⣀⣀⠠⠀⠀⠀⠀⠀⠀⠀⢠⣷⠔⠀⠉⠈⠛⠛⠁
⠀⠀⠀⠀⠀⡇⠀⢹⠙⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶
⠀⠀⠀⠀⠀⠃⠄⠨⡄⢀⠠⠀⠠⠄⠀⡔⢒⠀⣇⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢐⠉⢱
⠀⠀⠀⠀⠀⠀⡇⠀⠸⠞⠀⠀⠀⠀⠀⢱⣸⡀⢸⠀⠀⠀⠀⠀⠐⢅⠀⡇⠀⠈⢣⡎
⠀⠀⠀⠀⠀⠀⠇⠀⠐⠄⠀⠀⠀⠀⠀⠉⡏⠀⣸⡀⡀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠲⠤⠤⠤⣤⣤⣤⣐⣒⣾⣋⡉⠿⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⢀⡀⢡⠄⠋⠓⠘⣦⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⣈⣿⡀⠀⢀⣆⢸⣴⣶⣿⠊⠓
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠚⢿⣧⢀⡉⠀⠈⠙⣏⣀⠁
⠀⠀⠀⠀⡀⢀⡀⠀⠀⠠⠀⠈⠛⠷⠁⣜⠻⠃⣶⡀
⠀⠀⠠⣴⣢⠋⡙⠒⠶⢶⣤⣌⠛⠀⠀⠀⠂⠀⠐⡉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⢀⡄
⠀⠀⠀⠀⠁⠀⠛⢠⣄⡆⠉⠿⢳⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣿⣷⣾⣷⣾⣿
⠖⠀⣤⡀⠀⠀⠀⠀⢉⠛⠻⣷⠿⢿⣿⠿⣿⣶⣄⢀⠀⠀⠀⠉⠛⡟⠋⠛⠛⠻⢃⣄⡀⠀⠈⠉⠹⠛⢛⡛⠛⠻⠿⠿⠿
⣼⡓⢛⠸⣷⠶⠤⣀⣉⠃⠀⠀⠄⠘⠻⠛⣙⣿⣿⣿⣟⡒⢢⡄⣤⡀⠀⠀⠀⠀⠀⢿⡃⡀⠀⠀⠀⠀⠈⠁⠒⠀⠐⠀⠘
⢳⠟⠓⠽⠀⠀⣤⣼⣿⣷⣶⣤⣄⠈⠀⠀⠘⢿⣿⣿⣟⠮⢢⡉⣤⠙⠀⡀⠀⠀⠀⠨⢷⡟⠀⠀⠀⠀⠀⢤
⡄⠀⠂⠣⠀⣘⡓⣿⣿⣷⡿⢛⣿⣿⣦⣄⠀⠀⠩⠉⠻⣶⣬⣿⣿⣷⣦⣸⢧⡀⠀⠀⢠⣿⣆⠀⠀⠀⠀⢸
⡜⣷⣦⠈⣧⡀⢞⣫⠟⢹⣾⣿⣿⣿⣿⣯⣷⠤⣀⠀⠀⢹⣿⣿⣿⣿⣷⣧⠸⣿⣄⣀⠀⠛⠋⠀⠁⠀⣠⣤⡄⠀⠀⡀
⡿⢡⣿⣤⢴⣿⣿⣭⣿⡲⣯⠆⣸⣿⢿⣿⣿⣻⣿⣿⣿⣤⣿⣿⣿⣿⣿⡍⢷⣼⣿⣧⣶⣟⣸⣶⣾⣿⡿⠋⠀⠔⣁⢹⢸
⠙⠀⠈⠁⢾⣿⣿⣿⣿⣿⣭⣴⣿⣿⣿⣿⣽⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣟⡅⠙⣛⣯⢿⣛⣻⣽⣴⠇⠀⡀⠘⢃⠎⣠
⠀⠀⠀⠀⠀⠀⠈⣇⠀⢭⣛⠛⢿⡿⠏⠻⠿⠿⡟⠋⢹⣍⣹⡇⠀⡎⠉⣿⣿⡷⣿⡏⠡⢬⣿⣿⣷⣼⡿⠿⠍⠀⢀⡀
⠀⠀⠀⠀⠐⠤⠠⡆⢀⡀⡘⠀⠀⢁⣠⡆⠀⠠⠀⠀⠘⢿⣿⣿⣦⣵⡄⢸⣏⠓⠾⠀⠐⢶⣷⣿⣥⢶⢷⡶⠿⢿⢿⡿⠶
⢀⢸⣶⣯⣶⣴⣉⣧⠘⢣⣴⡖⠀⠈⠉⠠⣁⢠⡜⠉⣛⠻⠶⠿⣿⡴⣾⣶⣿⣼⡃⢸⣤⣤⢥⡀⣠⣴⡟⢻⠀⣻⣼⣷⠐
⠳⡻⣿⣿⣿⢽⣿⣿⣾⢹⣿⣤⣴⣆⣤⣄⡘⠏⠑⣦⠌⠺⠗⢀⣘⠛⠖⢰⣿⣾⣅⣼⣯⣽⣾⣟⣹⣿⣁⣴⡇⢸⡿⣿⣷
⡆⣠⡄⣻⣿⣿⣿⣿⣽⣿⣿⣿⡿⣿⡿⢛⣽⡿⣿⣿⣿⣿⣶⣾⣥⣍⣿⣿⣿⣿⡏⢿⣿⣿⣿⣏⣿⣽⣿⢧⠽⣿⢿⣿⣿
⣿⣭⣿⣿⣿⣿⣿⡿⣿⡷⣵⣶⣿⣿⣿⣻⣯⣿⣆⣛⣻⣿⣿⢿⣿⣿⣩⣿⣟⢛⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣾⣷⣿
⣍⣩⣭⣩⣉⣹⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿
⣿⣿⡟⠙⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠐⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠁⣀⠀⠑⠀⠄⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠱⠛⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠰⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠄⢠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠓⠁⢊⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⢈⠀⢡⣄⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠿⠀⢲⡊⡈⡃⠀⠀⠈⠀⠙⠢⠀⠀⠀⠀⠀⠀⢑⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠈⠤⠍⢀⡀⠔⠁⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⢀⠠⢊⠔⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣽⠜⠁⠀⠀⠈⠁⠁⠁⠀⠀⠀⠀⠐⠂⢑⢀⡀⠄⠂⠁⠐⠁⡞⠛⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⠠⠀⠑⠀⠠⠂⠀⠀⠃⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢁⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡌⢹⠤⠄⣀⠀⡠⠤⠤⠀⠀⠀⠀⠀⠤⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⡈⠑⠤⠖⠀⡇⠀⠂⠀⠇⢭⢽⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠈⠐⠀⠐⠀⠀⠀⡤⠦⡄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⡁⠀⠀⠀⠀⢠⠂⡀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢲⣖⠋⣀⡴⠀⠀⠀⠀⢈⡀⡁⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠙⠐⠀⠘⠓⠈⠐⠒⠲⠶⠲⠷⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⣆⠴⠀⠀⠶⠐⠂⠀⠀⠘⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠠⡀⣀⠔⠒⠒⢂⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣀⠀⠀⠀⣛⢌⣳⣴⣲⣟⡔⠁⠀⠀⠀⢠⠂⡇
⠀⠀⠀⠀⣿⣬⣰⣶⣦⣤⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣧⣤⣴⣉⢶⣠⣤⠏⢸⣿⣿⣿⡿⠶⡄⠀⠀⠀⣾⣠⡷
⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⢿⣾⣶⢼⣿⣉⠉⣙⣽⡶⣶⣤⣤⣿⣿⣿⣿⣿⠙⡻⢻⣌⠀⣿⢛⣿⣿⣿⣶⣝⣻⡖⣶⢿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣷⣾⣯⣭⣿⣟⡿⢟⣷⣶⣤⣶⣾⡇⢀⣿⣿⣻⣿⣿⣿⡿⣷⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿⡿⠿⢷⣿⡯⠤⣤⣌⣡⣈⣙⣻⣿⣿⣿⣿⣿⣿⣿⣣⠏⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣥⠬⣍⣛⣿⣇⣾⣿⣿⣶⣷⣦⣿⣿⣿⣻⣦⣼⣶⡏⠉⠉⠉⠙⠋⠰⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢶⣶⣶⣾⣿⣿⣿⣟⣻⡿⣿⣿⣵⣦⣼⠿⠛⣿⣯⣷⣾⣷⣿⣶⣦⣴⠆⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣷⣬⠩⢿⣾⣿⣿⣿⣿⣿⣷⣶⣻⣩⡥⢶⣠⡀⠙⢿⣿⣿⢻⣿⣿⣿⡻⠀⠄⠀⠀⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠿⠿⢿⡿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣟⠤⢷⠶⣾⡗⡇⢠⣶⡈⠛⠿⢙⢿⣿⣇⣰⣿⣟⢹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣿⣿⣻⣤⣿⣿⣿⢣⣿⣽⣏⣤⣿⣿⣿⣿⣶⣿⣧⣴⣠⠀⣿⡙⠛⠛⣿⣹⠟⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠴⠶⣫⣿⣿⣯⣿⠏⢿⣏⣿⣿⣾⣿⣿⣿⣿⣿⣿⣉⣿⣿⡿⠏⢁⣽⣆⢨⣝⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⣿⣿⣿⡏⢀⡀⣨⣯⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣏⠔⣠⣶⣿⣿⡟⢀⠻⣷⣼⣤⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⢱⣶⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢃⢻⣿⣿⣿⡇⠈⣆⠹⣿⣿⡄⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠃⠹⣿⣮⣛⣿⣿⣿⣯⣩⣿⣿⣿⡁⣿⣿⣿⣿⢿⣦⡉⠀⡀⢿⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡟⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⠀⢙⣫⣴⣇⢨⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣝⣿⣿⣿⣿⡃⢿⣿⣿⣿⡛⠛⠋⣿⣿⣿⣿⡏⠵⢾⣿⣷⣿⠻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣎⠆⢼⣿⣿⠋⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠷⠿⢿⣿⣷⣙⠿⣛⣭⣳⣿⣿⣼⣿⡿⡋⣼⣿⣿⣿⣷⣿⣿⣿⣧⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠃⢀⣘⣛⣿⠿⠿⠿⠷⠿⠶⣿⡇⠉⠙⠹⠿⠿⠿⠿⠿⠿⠿⠿⠻⠗⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠒⠒⠒⠒⠠⠤⢀⡀⢀⠔⠈⠉⠑⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠧⠤⢀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢄
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢏⠀⠈⢦⡀
⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⡘⠀⠀⠀⠙⢦⡀
⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠊⡞⢋⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠒⠈⠉⠀⠀⢀⠎⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠶⠶⠂⠀⠀⢠⠊⡴⠞⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⡆⠀⠀⠀⠀⡜⠁⠀⠙⢦⣀⠊⠀⠀⠀⠀⠀⠀⢀⣤⠀⡠⠃⠀⠰⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⢠⠀⠀⠀⠀⢃⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠘⠿⡖⠁⠀⢢⡀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⢆⠀⠀⠀⠀⠣⣀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠈⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠁⠆
⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⢶⣮⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠰
⠀⠀⠀⠀⠀⣹⠠⡀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢠⠋⠛⠛⠓⠂⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⣀⠔⠉⠀⠑⠠⠓⠂⠠⠤⠬⢦⣄⣠⠄⠰⡁⠀⢀⣀⠤⠆⢁⣀⣀⢀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠠⠤⢼⡤⠤⢷⠀⠀⠒⠒⠒⠒⠒⠒⠀⠀⠀⠉⠉
⡄⠉⠀⠀⣀⡀⠤⠧⠤⠶⠈⠉⠐⠒⠚⠁⠐⠂⢹⠤⡄⠙⠀⠉⠉⠉⡍⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢚⠁
⠀⢩⣀⣼⠀⠀⠀⠀⠀⢀⣀⣀⠠⠄⠒⠢⢀⣩⡟⠊⠀⠀⠀⢀⡀⠀⠗⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠉⠉⠉⠉⠙⣄⡀⡞⠁
⠀⠀⠀⠉⠉⠚⠋⠉⠀⠀⠈⠈⠁⠙⠀⠀⠀⠀⠱⡄⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠘⢆⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠄⣀⣀⡀⠀⠀⠀⣀⣀⡀⠤⠤⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢠⠛⡀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠂⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠌⠀⠀⠀⢣⠀⠀⠀⠀⢠⠀⠀⠀⠘⢄⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⢂⠀⠀⠀⠘⠀⠀⠀⠀⠈⢆⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣀⠠⣙⢶⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡶⣫⠄⣀
⠀⠀⠀⠀⠀⠀⣾⣿⣷⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣾⣿⣧

⢾⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠷⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠰⠶⣶⣦⣬⣙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣚⡛⠻⢾⣽⣷⡄⠀⠀⠀⠀⠀⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣧⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠮⣽⣿⡄⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀⠀⠘⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢷⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⢷⡀
⠘⣧⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣜⣇
⠀⠈⢷⡌⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠙⠷⣝⣧⡀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⠤⠀⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠛

⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⢶⣦⣄⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡹⣆
⣀⣀⡉⢳⡜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⡻⣾⣷⡀
⠀⠈⠙⠢⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣆
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠿⢦⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠈⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡿⢿⡏

⠀⠐⠾⡏⢱⣦⣠⡦⡬⢴⠄⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠉⠀⠤⠀⢀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡀
⠀⠀⠄⠠⠐⠀⠧⠖⠀⠀⠀⠀⠀⠀⠀⠿⢷⢦⣤⣄⡀⠐⠀⠀⠐⡖⠂⢠⠀⢀⢸⠀⠀⢀⣨⠇⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣰⣦⣠⣴⢶⣀⣀⡀⠉⠿⠋⢢⡄⠀⠀⠄⠀⠀⠀⠀⠸⠀⠀⣸⡿⠃⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⡀⠀⢷⡿⣿⡁⠈⠟⢿⣿⣿⡷⣤⣴⣦⠀⠀⠀⠀⠰⠄⠸⠀⠀⠀⠀⠀⠉⠰⠂⠂⠐⠀⠂
⠀⠀⠀⢠⣶⣶⣷⣤⡾⢁⣤⠜⡇⣀⡸⣧⣤⣽⣿⡟⠓⠄⢄⢠⣀⣀⡈⠀⠀⡀⣀⣀⠀⠀⣄⠀⢀⠀⢠⡄⣠
⠀⠀⠒⠀⢙⣯⣔⠒⠛⣧⣤⣴⠙⣿⠛⣾⣿⠟⠀⠠⣄⠷⢦⠞⠀⠋⠁⠀⠈⣿⠁⠸⠙⣄⢉⠁⡍⠿⠙⠉⠛
⠀⠠⣲⠶⢿⣿⣿⠀⢰⣷⣿⣿⣶⣟⠲⢭⠟⠛⠓⢒⡏⠀⢀⠐⢀⣀⠀⠀⣀⠀⣁⢼⠀⠈⠉⠀⠒⠂⠆⠀⠚
⠀⢾⣷⣴⣼⣿⠋⠲⠿⠛⠁⠉⠋⢁⡀⠀⠒⠄⠁⠠⢦⠀⠀⠠⠀⠙⢂⠹⠛⢛⠏⣍⠋⡗⡂⠰⢠⠈⠀⠀⣤
⠀⠀⠀⠈⠁⠀⠀⠀⠀⢤⣀⠚⠗⢀⡀⠀⢀⠁⠄⠲⠤⠀⢠⠀⠀⠡⢈⡱⠄⠠⠂⢣⡄⠘⡁⠀⡾⣤⢄⣾⡿⠂
⠀⠀⠀⠤⠄⣀⠩⠓⠂⣈⡤⠖⢺⡟⠻⢊⣡⣤⣎⣩⣄⠆⠄⠀⠀⠀⠀⠀⢀⠀⠐⠚⡷⠀⠛⠑⣿⠹⠀⠑⠁
⠀⠀⠒⠀⣀⢠⠖⠂⠉⠁⠰⣄⠄⠻⠖⠋⠁⠈⠋⠉⠻⠀⡓⢀⠀⠀⠀⠦⡔⢢⠀⠐⣄⠰⢂⠀⠏
⠀⠀⠀⠁⢉⡀⢀⡀⠀⣊⣴⣿⣠⣾⣛⣦⠀⠀⢶⡖⠀⠈⠉⠡⡀⡔⡙⠑⡜⢁⣠⢀⢨⣤⣴⠒⣴⡄⠦⡲⠇
⠀⠀⠀⢠⡔⠀⠈⣁⡾⠷⠉⢉⢩⠹⡃⠀⠀⠈⠉⠀⢀⠀⠀⢐⣿⡿⠄⠈⠀⢀⡛⢈⣇⠐⠏⡒⠉⠃⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡙⠀⠀⠀⠘⠀⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩
⠀⠀⠀⠀⠀⠀⠠⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢨⢄⣤⡀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢻⠀⠀⣀⠤⠀⠈⠊⠀⠀⠁⠀⠀⢀⡀⢈⠤⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠎⠀⠀⠀⠀⠀⢰⠁⠀⢆⢘⠁⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⡼⢀⠀⠈⡌⠓⠢⠤⢤⠤⠊⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⣄⣸⡀⠈⣶⣆⠘⡀⠀⣴⡁⠀⠠⠠⠄⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠾⡀⠑⣖⢁⠈⡎⠁⠀⠀⠡⡉⠑⠢⠀⠀⠀⠀⠀⠀⠀⢑⡨⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⢄⠜⠈⢈⢁⠔⠁⠀⠀⠀⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀
⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⢄⡒⠀⡴⠂⠀⠀⠀⠀⠙⡌⡆⠀⠀⠀⠀⠠⠤⠀⠠⡀⠀⢀⠀⠀⠀⡀⠀⢠⠦⢼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠀⠀⡀⠀⠀⢀⠀⢸⡜⠫⡀⠀⢀⠊⠀⠀⠀⠀⢀⡟⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢁⡠⠀⡰⠃⣀⠉⠤⣀⣈⡂⠀⠀⠀⠐⣢⡀⢀⠀⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⢁⣠⠚⠁⠘⠉⠐⠒⠧⠤⡍⠀⠀⠀⠈⠀⠈⢉⡶⢃⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢆⢨⣓⠂⠠⡄⣀⡄⠒⠶⠆⢤⠀⠀⡀⠒⠒⠉⢴⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⡨⠈⠲⢰⠃⠒⡇⠀⠃⠀⢸⠤⢬⠭⠃⠀⠀⠠⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠈⠀⠀⠈⠁⠒⠢⠜⠀⢸⠀⣄⠴⠐⠢⠀⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠄⠀⢀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠒⢀⠬⠄⢀⡀⢀⡀⠀⠤⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⢀⣀⣀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⠀⠀⠘⠁⠙⠀⠀⠛⠁⠛⠀⠀⠀⠈⠐⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⡾⠋
⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⡖⠁
⠀⠀⠀⠀⠀⠀⢸⣷⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣰⣆⠀⢠⡏⢀⡇⡀⠀⡠⢀⣶⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⡀⣠⣼⣿⢻⣦
⠀⠀⣴⠄⢹⡥⠾⠆⠈⣧⠚⡀⣸⠞⣿⣅⠀⠁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣴⠜⣻⣿⣏⣹⣿⡿⣫⣿⣷⡀
⠀⠀⠁⢀⡌⠁⢤⢿⡿⣿⠂⠀⢻⣙⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢶⣄⢽⣧⡿⣿⣾⣿⡾⢯⣄⣻⣷
⢰⠀⠀⣼⣃⠀⠂⣴⣶⠟⠀⠴⣤⠛⡶⢯⣿⡃⠀⠀⠀⢠⣤⣄⣀⠀⣦⣽⡏⣻⣋⣿⡯⠉⠛⣾⣳⢙⣿⣿⣇
⣼⡇⠀⢑⠋⠉⣉⡋⣼⠀⢰⣶⠿⠟⢻⣥⣿⠷⣷⡀⠀⣄⣈⡙⢿⠚⠛⠹⠉⣻⣿⣧⣧⡀⠀⠈⣡⣿⣿⣿⣿
⣍⡷⣶⢌⣴⣿⣿⣿⠿⠄⢾⡏⠀⠈⢿⣿⣿⡶⠅⠀⢘⡶⠊⠀⠀⠀⠀⢀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢿⣏⣿⣿⣿⣿⢠⢦⠘⡇⠀⠀⠸⣿⣿⡇⠌⠂⠈⡁⠠⠶⢶⡄⠀⢿⣿⣽⢿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣿⠟⠻⣿⣿⠈⣮⠈⠁⠀⠀⠀⣿⣿⡇⠀⠐⣶⠉⠈⠀⠀⠉⠀⠈⣽⣿⣿⣿⣿⠉⡶⣇⢿⣿⣿⣿⣿
⡿⣿⡗⠀⠀⠀⠙⣯⣿⠋⠀⡇⠀⠀⠀⣿⢻⡇⠀⠀⠙⣿⢠⠀⢙⠶⠗⠎⠀⠹⢿⣽⡏⠘⡇⢸⢸⣿⣿⣿⣿
⢹⣿⣹⣼⠀⢰⣾⣟⣿⡄⠠⡇⠀⠀⣀⣿⠿⢥⣄⠀⠁⠐⠀⢴⠀⠀⠀⢀⣤⣾⣿⣿⠷⠀⡇⣿⠘⣿⡿⢻⡿
⠀⠠⡟⡋⢀⡘⣧⠰⡿⣿⡎⠻⢟⠋⣻⡷⠆⠈⠻⢧⡌⠑⠒⠃⣠⠀⠀⣼⠀⠿⠿⣿⠀⢸⡏⡿⣿⡿⣿⣿⠁
⠀⠀⢶⣃⣿⠗⠋⢼⡇⣏⣿⡄⠈⣷⣶⣄⢁⣀⠀⠀⠙⣷⠇⢠⡏⠀⢠⠏⡤⠴⣶⣷⡄⣿⣶⠦⣾⣇⣿⠃
⠀⠀⠀⢻⣇⣠⣴⣼⣡⠾⡿⠿⣿⣿⡿⠁⠀⠐⠈⠉⠞⢳⠴⠛⠀⢠⡏⠐⠓⠠⢽⣿⣱⣯⣤⡼⣿⡿⠃
⠀⠀⠀⠀⠙⣧⣕⣫⠤⣤⣀⣀⡿⢛⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⣀⡣⡾⠣⢄⡀⢲⣼⠟⠁
⠀⠀⠀⠀⠀⠈⠁⢤⣶⣯⡿⠷⣬⣤⣀⠀⠀⢀⣠⡄⠈⠀⢀⠂⢠⣯⣤⠤⣄⡼⠓⢾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠁⠘⢛⡻⣯⣿⣷⣄⠀⠀⠀⠀⠘⣴⣟⣩⣴⣶⣾⢿⣶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠹⢿⣿⣿⣿⣶⣦⣶⣿⣿⣿⣿⠿⠮⠓⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣬⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠒⠠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠼⠉⣠⠈⠁⠠⠀⠀⠈⢤
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⠉
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠠⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠾⡀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠴⠀⢸⠶⡀⠀⠀⠀⠀⣠⠐⠀⠀⠀⠀⠀⠢⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⢢⠨⠧⠀⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠕⣦
⠀⠀⠀⠀⠀⠀⠀⠠⣄⢠⡄⣤⠀⠘⠉⠤⢦⠃⠀⠀⠀⠀⢀⠩⢄⠀⠀⠀⡠⠐⠁⢀⣁⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠁⢀⠄⠀⠼⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⣀⠑⠘⢭⣁⡖⢐⠉⠉⠀⢰⠠⠤⡄⠈⠀⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠂⠄⠀⡨⠈⠉⠁⢀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠀⠀⠀⢠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⢢⡴⢃⣀⡥⠀⠀⠀⠀⢱⠈⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠚⠩⠤⠭⠧⠀⠐⠦⠤⠬⠼⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠃⠖⠀⠠⣔⡢⠀⠠⠄⠲⠀⠀⠀⠊⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⣀⣉⡩⡉⠒⠒⠒⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠒⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠑⠲⠦⣤⣀⣀⣀⠶⠖⠠⠦⠔⠘⠇⠀⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣿⣷⣶⣶⣶⣤⣤⣤⣄⣙⣦⠤⠀⠀⠀⠀⠀⠀⢀⡠⢞⣩⠞⠋⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠬⣿⣿⣿⣿⡛⠶⠯⣥⣤⣄⣴⡿⠾⣏⣷⡄⠀⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢿⣷⣍⣻⣷⣾⣿⣿⣍⣉⡻⠿⠿⣿⣷⣴⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠮⣾⣿⣿⣿⣷⣶⣭⣽⣒⣶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣀⣀⣀⣀⠴⠤⠄⣀⠠⠀⠀⠀⠀⠀⢄⣀⣀⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿