Multi coloured Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⢀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠄⢀⠈⠁⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⡠⠐⠁⢀⠀⠄⠐⠂⠀⠀⠀⠀⠀⠂⠠⠀⡀⠈⠐⠄⠀⠑
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⡀⠈⢀⠀⠊⠀⢀⠠⠀⠀⠒⠀⠀⠐⠂⠀⠄⣀⠀⠑⠠⡀⠈⠢⡀⠐⢄
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠊⠀⠐⠁⢀⠔⠈⠀⡀⠄⠐⠀⠀⠀⠀⠂⠠⢀⠀⠁⠢⡀⠈⠢⡀⠀⢄⠀⠢
⠀⠀⠀⠀⠀⠠⠁⠠⠁⢀⠊⠀⡐⠁⢀⠔⠁⢀⠠⠄⠐⠒⠒⠂⠀⠄⡀⠈⠢⡀⠈⠢⠀⠐⡄⠀⢂⠀⢁
⠀⠀⠀⠀⢀⠁⢀⠁⠀⠆⠀⠌⠀⡠⠁⢀⠔⠁⢀⠠⠀⠀⠂⠀⠠⢀⠈⠢⡀⠈⢂⠀⠡⠀⠐⡀⠀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⡀⠀⣘⠀⣠⠀⠠⠀⢠⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠑⡀⠈⡄⠀⡦⠀⠦⡀⠠⠀⠐⠀⠈
⠀⠀⠀⠀⡆⠀⠃⠔⠀⠀⠀⠁⢆⠀⠄⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠈⢢
⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠘⠀⠀⠀⠀⠀⠘⠁⠐⠆
⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢀⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠒⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠄
⠀⠀⠑⠀⠀⠀⠰⠄⠀⠀⠀⢀⢄⠀⠀⡠⠊⠐⠂⠈⠀⠀⠀⠀⠐⠀⠀⠂⠂⠂⠑⠀⢀⠀⠀⢀⠠⠐⠁⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠂⠁⠀⠈⠁

⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⣿⣿⡿⠛⠛⢿⣿⣿⡄⠀⠀⠀⠀⣀⣠⡾⡵⠊⠉⠱⠯⣷⡄⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⢀⣼⣿⣿⣤⡀⠀⣠⣿⣿⣧⣄⠀⠀⡈⠀⢩⠋⠓⠤⠀⠀⠀⠂⠀⠂⠀⠀⢰⣿⣿⡟⠁⠀⠉⢿⣿⣿⠄
⠀⠀⠀⠢⣐⣄⠀⠀⠀⢀⣆⡔⠁⠀⠀⠘⠛⠛⠛⠛⠃⠀⠛⠛⠛⠛⠛⠀⠀⠈⠈⠈⠁⠈⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠠⠊⢀⠤⠤⢄⠈⢢⠀⠀⠀⠀⠀⢠⡶⣫⡽⣶⡶⢯⣻⣦⣄
⠀⠀⢀⣠⣾⣿⠟⠉⠉⠛⣿⣷⣦⡀⠀⠀⠀⡃⢰⠁⠀⣀⠀⢡⠀⠂⠀⠀⠀⢰⣏⣞⡵⠛⠉⠉⢿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠐⠿⠿⠿⠿⠆⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠰⣼⠦⠋⠀⢱⣎⡔⠀⠀⠀⢠⣾⣿⣿⣿⣶⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥⠤⠤⠤⠤⠬⠕⠀⠀⠀⠀⠙⠛⠛⠛⠉



⠀⠀⠀⢀⡤⠒⣈⠉⢁⡒⠢⡀⠀⠀⠀⠀⠀⢀⡤⠖⣒⣓⣲⠦⣄⠀⠀⠀⠀⠀⠀⣀⡤⠖⣒⣒⠶⢤⡀⠀⠀⠀⠀⠀⢀⡤⢖⣛⣙⣛⠲⣄
⠀⠀⢠⠋⡀⠃⠀⠀⠀⡀⢢⠈⢆⠀⠀⠀⢠⢏⣴⡿⠛⠛⠻⣷⣌⢧⠀⠀⠀⠀⡴⢡⣾⡿⠛⠻⢿⣦⠹⡄⠀⠀⠀⢠⢏⣴⣿⠿⠛⠿⣿⣮⢳⡀
⠀⠀⠌⠰⠀⠀⠀⠀⠀⠈⠀⠀⠸⠀⠀⠀⠟⠸⠟⠀⠀⠀⠀⠘⠿⠘⠇⠀⠀⠸⠃⠿⠏⠀⠀⠀⠈⠿⠇⠹⠀⠀⠀⠾⠸⠿⠃⠀⠀⠀⠹⠿⠊⠇



⠀⠀⠀⢀⡴⣛⣛⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣤⡀
⠀⠀⠀⣾⡾⠛⠻⣷⣌⢻⣆⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠘⣷⣌⢻⣿⣦⡀⠀⠀⠀⠀⠀⢰⣿⠟⣡⣤⣤⣤⣉⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡌⠿⠆⠀⠀⠀⠀⣰⣿⣿⡿⠟⠛⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠸⣿⡆⢿⣿⣿⣦⠀⠀⠀⠀⣿⡇⣾⣿⣿⣿⣿⣿⣆⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⣿⣷⠘⣿⣿⣿⡆⠀⠀⠀⠸⡆⣿⣿⠁⠀⠈⣿⡿⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠛⠀⠀⠀⠋⠘⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⢀⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡿⠿⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⣿⣦⡀⠀⠀⠀⠓⠀⠀⢀⣀⣴⣿⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⠟⣛⣉⠹⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠉⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠉⠛⠛⠛⠋⠉⠉⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠏⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠙⠛⠉⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⡟⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠋⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⠠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀
⣿⣿⣿⣿⣿⠟⠛⠙⡿⠿⠿⠛⠿⣟⠋⠙⠻⣿⣿⣿⣿⠀⠀⠀⠀⠲⠄⠒⠁⠠⠄⠈⠃⠀⠄⠀⠐
⣿⣿⣿⣿⡧⠀⠀⠌⠀⠀⠀⠀⠀⠈⠡⠑⠀⢾⣿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠈
⣿⣿⣿⣿⣷⡀⠰⠀⣤⡄⣶⣷⡄⡀⠀⢆⢰⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣶⣶⡀⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣦⡈⠀⠻⠟⠁⣀⣴⢛⡻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠉⠉⢨⢛⣼⣿⣇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠈⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣤⡦⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣠⠂⡀⠁⠀⠀⠀⠀⢀⠀⠀⠀⣀⣼⠇⠀⡴⠒⣬⠟⠿⣶⣦⡙⠶⠦⠀⠐⢷⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢘⣿⣤⢮⠟⠉⢃⡤⠄⡠⠀⠀⠀⡉⢢⣺⢺⣿⣿⣿⣿⣥⣶⣮⡛⠂⠨⠽⣿⣿⠂⠠⠀⠀⢄⠑⠄⠀⢈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠞⣽⣈⣿⣴⢾⣧⣤⡄⠀⠀⠀⡨⠇⠈⣽⣼⣿⠟⣿⣿⣿⣶⣅⡈⣀⢠⣀⠸⢿⣿⠂⢀⡮⣆⢠⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠉⠀⢠⣆⢠⣙⣿⣿⣢⠘⠩⠶⠂⣀⣤⢠⣄⣤⣿⣿⣋⠇⢰⣿⣿⡿⠋⠁⠀⠄⠀⠈⠉⠉⢻⣷⣁⡴⠊⠉⠈⡀⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠠⠶⢌⡈⢻⣿⣿⣷⡰⠆⢤⢆⣹⣤⣼⣿⣿⣿⡆⠉⣰⣿⡟⠋⣁⣼⣦⣴⢶⣦⣄⣀⠀⢤⣽⣿⡷⣄⠀⠠⠃⠲⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡝⢾⢿⣦⣟⠁⠁⠀⢠⠙⣴⣾⣿⣿⣿⡃⣸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣿⣿⣟⡋⠀⠀⣰⠖⠳
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣍⣻⣌⣾⣿⡏⠀⢀⠰⠀⣰⣿⣿⣿⣿⠋⣱⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠻⠿⣿⣛⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣧⣼⣿⣿⣿⣿⡧⠀⠀⡀⣀⣿⣿⡟⣻⣿⣿⣿⡿⡟⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣻⡶⢠⣿⣿⣿⣧⣸⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣝⡿⣿⡿⢅⠀⠀⢉⣿⡿⣿⡟⢻⣿⣿⣻⣿⣤⣿⣍⣨⣷⣿⣿⣿⣿⣿⣿⣿⣽⣷⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡼⡷⣈⣻⡇⢐⣷⣾⣿⢻⠩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣻⣭⣴⡾⠛⢻⣿⠟⢨⣿⣽⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⣿⢿⣿⣿⠗⣁⣸⡿⡟⠏⠀⢻⣿⣿⣿⣿⣟⠛⠢⣤⣤⣜⠛⠿⠿⠿⠿⠿⠏⠀⠘⢸⣆⡶⣿⡽⠁
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢸⣿⣿⢿⣿⠋⢿⣿⡇⠀⡁⢸⣿⣿⣿⣿⣿⡵⣄⣀⠉⠤⠀⠀⠐⠀⣀⠀⠀⠀⠲⢸⡇⣸⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣟⡄⠘⣣⠼⠋⢁⢘⣿⣿⣿⣿⣿⣷⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠣⣸⣿⣿⠁⡟
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠻⣿⣿⡟⢢⡜⢉⠄⢀⣪⣿⣿⣿⣿⣿⣿⡍⠛⠒⠀⠀⠀⠀⠀⢀⠀⠀⡻⠉⣶⣿⢻⠏⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⣿⡞⠀⠒⢠⣖⠚⣹⣿⣿⣿⣿⣯⠟⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡈⣥⢞⡿⣣⠚⡃⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⣉⣿⠀⠀⠀⠰⠟⢏⠡⣟⣿⣿⣿⣿⡆⠀⠀⠀⠀⠐⠀⠀⠀⣀⣶⢶⣿⣾⠟⠡⠈⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠉⢈⠁⠀⠐⠩⣳⠂⡀⠰⡆⠀⢈⢙⣿⣿⣿⣟⣿⣧⠀⠀⠀⠀⠀⣨⣖⡻⣿⣷⣿⡿⣵⠆⠐⠀⠀⠀⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠀⠰⢿⠛⣀⡚⠋⠀⠘⢫⣝⣿⣿⣿⣟⣹⡀⠀⠀⠀⢀⠙⠈⣅⠠⣿⡏⠙⠁⢀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⡀⣀⠈⢻⣿⣿⣿⣿⣿⣽⣦⣹⣀⣦⠀⣤⣾⡄⠁⠈⣤⡀⠈⡀⠰⠂
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠂⠀⡦⠀⢀⣀⠀⠃⠈⠧⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣷⠄⠁⠊⠁⠀⠀⠀⠠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠒⠂⠂⠀⠀⡀⣈⣠⠤⠦⠀⢤⠌⠉⠉⠁⣺⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣻⣿⣿⡇⠐⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⡉⠀⠀⠀⢰⠒⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⡀⠐⠃
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠼⠆⠉⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⢟⣿⠋⠙⢻⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢀
⠀⠀⠀⠠⢀⡐⠤⣠⠀⠀⠀⠀⠀⠀⠀⠀⣦⣷⣴⣿⣿⣿⣿⣻⣤⣿⣿⡇⠀⢉⠒⢤⡽⣿⣿⡆⠉⠀⠀⠀⢠⡿⡋⠁
⠀⠀⠀⢠⣼⣿⣶⣆⣠⡀⠀⠀⢤⣤⠶⣿⠿⣋⣍⣥⣽⣿⣿⣿⣿⡟⠁⠆⠚⠁⠀⠀⠀⢻⣿⣤⠆⠀⣠⣷⠟⠔⠁⠀⠐
⠀⠀⠀⣨⣿⣿⣿⣷⣾⣿⣿⣧⣾⣷⣶⣷⣾⣿⠿⣿⡿⢿⣿⣿⠏⠀⠀⠈⠉⠃⠀⠀⠒⢿⣛⠛⣀⣼⡏⠡⠀⠀⠀⣤
⠀⠀⠀⣼⣏⣀⣙⡛⠛⠻⠿⠿⢿⣿⡿⠛⣥⠃⣀⣼⣷⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡟⣻⣟⠟⠀⠀⠀⠀⠄
⠀⠀⠐⠻⣿⡿⣿⣿⣷⣄⠶⡦⢸⡟⠱⠾⣣⣾⣿⣿⣿⣿⣿⡏⠁⠈⠀⠂⠀⠀⠒⠀⣾⠟⠳⢶⠿⠀⠀⠃⠀⠈
⠀⠀⠀⠀⠀⢠⣾⡿⣿⣿⣷⣶⣾⣿⣷⣿⣿⡟⠿⣟⠛⠉⠫⢄⡀⠀⠀⠀⠀⠀⠀⢲⡿⢤⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠀⠀⢁⣼⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠂⠀⠈⠁⠐⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡗⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⡀⠘⠳⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⡄⠀⠀⠐⠄⠀⠈⠁⠂⠐⠤⠄⢸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠙⠉⠁⠀⠀⠀⠀⠀⠢⠀⣦⠀⠀⠀⠀⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀
⣿⣿⣿⣿⣿⣿⣿⠟⣺⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠐⠈⠂⠀⠀⠀⠁⠀⡠⠄
⣿⣿⣿⣿⣿⣿⡏⠀⠊⢻⣿⣿⣟⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢄
⣿⣿⣿⣿⣿⣿⣷⡘⢫⣿⡟⣿⣼⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡷⢤⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣏⣹⣹⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠆⠟
⣿⣿⣿⣿⣿⡿⣿⣿⣾⣿⣿⡿⢿⣿⣿⡟⠻⣥⢘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢠⢐⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣵⣿⣦⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠐⠜⠂⠀⠀⠐⠈⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣰⣾⣻⣿⣷⡄⠀⠀⢠⣴⢞⣛⡻⢶⡀⠀⠀⣠⢖⡛⢛⢶⡄⠀⠀⡴⠋⢉⡉⠓⡄⠀⠀⡴⣾⡿⣿⣦⡀
⠀⠀⠀⢸⢿⣯⣎⣹⣿⣿⡀⢠⣿⣿⣿⠭⣿⣮⣿⠀⢰⣗⣵⣻⣳⡵⣿⡀⢸⠁⡾⣩⡙⡆⢸⠀⣸⣿⣡⢶⢮⢿⣷
⠀⠀⠀⠈⠉⠉⠈⠁⠉⠉⠁⠘⠛⠛⠃⠀⠛⠛⠛⠁⠙⠙⠛⠁⠙⠃⠛⠃⠘⠀⠃⠛⠃⠃⠘⠀⠋⠋⠋⠛⠘⠘⠛

⠀⠀⠀⢠⣾⢽⣿⣗⣄⠀⠀⠀⠀⣴⣾⣷⣦⠀⠀⠀⢀⢎⣅⣨⡕⡄⠀⠀⠀⢀⣤⠶⠶⣤⡀
⠀⠀⠀⣿⣷⠉⠈⣻⣿⡄⠀⠀⢸⣿⡷⢾⣿⡆⠀⠀⠆⣿⡟⢻⣿⡐⠀⠀⢀⣾⣵⣫⣙⢮⣷
⠀⠀⠘⠿⠿⠁⠈⠛⠛⠃⠀⠀⠛⠛⠇⠸⠿⠇⠀⠠⠝⣿⠁⠸⣿⠑⡆⠀⢸⡿⣿⡏⣿⢸⢿⠆⠀⠀⠀⢠⡶
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠉⠃⠃⠛⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠀⠈⠀⠁⠉⠂⢄
⠀⠀⠀⠀⠀⠀⠀⡼⢁⣀⣄⣀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⢸⣵⣋⠀⠀⠈⠙⠚⠋⠉⠙⠢⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣊⠀⠀⠀⠁⠀⠀⠀⠐⠢⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⢀⣀⡀⠀⣤⣤⣤⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⠈⠂⢀⣀⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⠁⠘⠿⠛⠸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⠐⠁⠘⠿⠋⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣄⣁⣡⣽⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⢤⣤⣀⣀⣀⣴⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡟⠈⠉⢉⡍⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡟⠀⠀⠀⡀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠛⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠐⠒⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠐⣶⢶⠂⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠄⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠃⠘⠦⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠂⠀⠠⠂

⣿⠛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⠀⠛⠛⠛⠛⠛⠋⠃⠛⠛⠃⠘⠘⠚⠟⠛⠋⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣟⣷⣖
⣿⠀⢰⠀⠠⠄⡄⠀⣆⠀⠄⠤⠦⡠⠤⡄⠀⠀⠀⠈⠀⠦⢠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⣾⢿⣿⣻⣝⢋⣛⣿⣮⣧
⣿⠀⠀⡄⢀⡀⠀⠀⠀⢀⢀⠀⢀⢀⠀⠀⠀⢀⣀⠀⠀⠚⠈⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠨⠃⠀⠀⠀⠀⠟⣹⣼⣏⠜⡶⠀⠍⢸⣿⢿⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣀⠀⢦⡄⠀⢐⡀⠀⡁⠀⠀⠠⠄⢳⢻⣿⣿⣦⠤⠤⠶⢿⣿⣸⠃
⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢐⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂⠀⡀⠀⠈⠂⠠⠈⠳⣙⢿⣧⡞⠠⢘⣿⠟⠁
⣿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠄⠀⠂⠀⠀⠀⠈⠓⠾⠷⠶⠖
⣿⠀⠂⠀⠸⢠⠔⢒⣜⡁⠀⠆⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠑⠁
⣿⠀⠀⠀⠀⠀⠑⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀
⣿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠀⠀⠀⠠⠀⠁⠉⠈⠈⠰⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠄⠀⠀⠀⡸⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠀⠀⠀⢸⡉⠁⠰⡄⠀⠀⠀⠀⠀⠐
⣿⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠐⠀⠀⠞⠀⠠⠤⠄⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⡜⠇⣻⠉⡋⠈⠁
⣿⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠈⢀⡀⠀⠀⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠑⠚⠀⠤⠀⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢰
⣿⠀⠀⠀⠀⣀⣀⡠⠤⠤⣄⣀⢀⡀⠈⠀⠀⠀⠀⠘⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠁⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣠⣴⣾⣿⡿⠁⠀⠀⠀⠀⠸⢧⣿⠔⢶⢀⡀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠁⠒
⣿⣿⣿⣿⣿⡇⠀⠀⡄⠀⠀⠀⣾⡝⡡⢜⡾⢣⠴⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⡇⠀⠀⢖⠃⠀⠀⣻⠘⣧⣀⣁⡏⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡈⠁
⣿⣿⣿⣿⣿⠉⢀⣀⠀⠀⡀⠀⠈⢢⠠⢑⡨⠦⢤⣀⡀⢀⠀⠀⠀⠸⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡑⢆⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣷⡀⠉⡀⠰⢢⢈⠄⢤⡞⡼⠁⠀⠀⠀⠈⠙⡦⢵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠄⠀⠀⠁⠈⠀⠀⡀⠀⢀⠀⢀
⣿⣿⣿⣿⣿⣷⣤⣀⠀⡀⣁⡴⢋⢸⠧⠤⠒⢢⡔⠢⢀⡇⠀⣿⠀⡀⠀⠄⠈⠅⠀⠞⠀⠀⠨⠀⣀⡀⠀⡐⠢⠀⠀⠀⠀⠀⠂⠀⠨⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣏⠀⠁⠀⢎⣵⣏⣾⠀⠀⠙⠁⡙⠈⢸⠁⢠⠇⠈⠁⠀⠂⠈⢀⠀⠀⠀⡀⠓⠀⠀⠈⠀⠀⠈⠀⠀⠠⠀⠀⠀⠒⠂
⣿⣿⣿⣿⣿⣿⣿⣆⢀⡀⣹⢿⡦⣿⠀⠀⠈⠁⠃⠀⠸⠀⠘⡃⠀⠀⠀⡹⠁⠡⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠂
⣿⣿⣿⣿⣿⣿⣿⣏⣈⣿⣷⡾⢻⡻⠤⢤⠀⠀⠀⢠⡼⠀⢸⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠃⠀⠀⢘⠀⢦⠄⣏⡇⠀⡾⠀⠀⠀⠀⠀⠤⠄⠈⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⡖⢦⣦⠾⡇⠀⠁⠀⠀⠀⠀⠀⠂⠐⢀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⣴⣾⣷⣦⣀⡀⠤⡷⠏⠀⠓⠒⠤⢠⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠐⢄⢀⠠⠄⡷⠁⠈⠂⠂⠤⡰⠉⠀⠉⠆
⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠁⠀⠀⠈⠉⠀⠀⠀⠀⠈⠻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠈⠀⠀⠀⠁⠙⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠈⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠗⠐⠀⠐⠂⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠻⠒⠀⠀⠐⠀⠹⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⢠⣴⣦⣄⠀⢸⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡠⡆⠀⡠⠖⠤⠄⠀⢡⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠁⠀⠀⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠍⠅⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠀⠈⠒⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⣿⡟⡉⣿⠟⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠿⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢀⣴⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣿⣿⣿⣿⣷⠶⢶⣿⣶⡶⠶⠚⠛⣿⣿⣿⣿⣶⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣄⣠⣶⣷⣶⣼⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢹
⠀⢸⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸
⠀⢸⣿⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸
⠀⢸⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸
⠀⢸⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡏⠙⠛⠛⠉⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⣾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣷⣾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡿⣾⣷⣾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣷⣾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⢼
⠙⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠙⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠉⠉⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠙⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⣞⣥⣬⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⣦⡍⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣥⣬⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣫⣤⡍⣧
⠀⠀⠀⠀⠀⠻⠿⠿⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠷⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠷⠾

⢙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⡉⢙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠉⢙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡉⢙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋
⣳⡐⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⣡⣣⣟⣳⡔⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⣧⣷⣟⣳⡄⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⣥⣳⣟⣳⡄⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⣥⢳
⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⠟⢿⠿⠿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⠟⢿⠏⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿

⠀⠀⠀⠀⠀⣴⢩⣙⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣭⡑⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢩⣙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣩⡑⣆
⠀⠀⠀⠀⠀⣾⣿⣿⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣷⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣷⣧⣾

⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⣔⢈⢳⡀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣔⣦⣔⢈⢳⡀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢔⣦⣔⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢔⣦⣄⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣔
⣾⡇⣸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣶⣾⣷⣾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡷⣾⡇⢨⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡷⣾⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼
⠙⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠙⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠙⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢞⣭⣬⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⣤⡍⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣥⣬⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⣤⣍⢧
⠀⠀⠀⠀⠀⠿⠿⠻⠮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠷⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠷⠿

⢙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡉⢙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡉⢙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⡉⢙⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋
⣳⡔⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⢡⣳⣟⣳⡔⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⣥⣱⣞⣳⡄⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⣃⣱⣟⣳⡄⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⣥⢳
⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⠿⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⠿⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⠿⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⡿⠽

⠀⠀⠀⠀⠀⡴⢫⣙⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣍⡛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⢯⣙⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣍⡛⣆
⠀⠀⠀⠀⠀⣿⣿⢿⡦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣷⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣷⣧⣾

⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⣄⢎⢳⡀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢔⣥⣔⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣔⣥⣔⠌⢳⡀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣔⣥⣔⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣔

⠀⠀⠀⠀⠀⠀⠀⢰⡏⣼⠃⠀⠀⠀⠀⢹⡆⣿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣾⠁⠀⠀⠀⠀⢹⡆⣿
⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛
⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢠⠖⠑⠳⢄⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢠⠖⠓⠳⣄⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸
⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⢤⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠔⢤⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀
⡄⢃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡎⣠⡄⢃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡎
⠁⠘⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠟⠻⢦⣄⠀⠀⠀⠀⠀⠘⠀⠀⠘⠁⠘⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠿⠿⢶⣄⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣡⡶⠛⠷⣦⡙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣡⡶⠟⠷⣦⡙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡿⢰⠏⠀⠈⠀⠈⢿⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣰⠏⠀⠀⠀⠈⢿⡈⣷
⢤⣄⠀⠀⠀⠀⠀⠘⠃⠛⠀⠀⠀⠀⠀⠘⠃⠛⠂⠀⠀⠀⢀⣤⠴⢤⣄⠀⠀⠀⠀⠀⠘⠃⠛⠀⠀⠀⠀⠀⠘⠃⠚⠀⠀⠀⠀⢀⣤
⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟
⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢀⢄⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠐⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠛⠒⠊⠻⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢣
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘
⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠙⡄⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡐⠉⠙⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡐
⠇⢰⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⢸⠀⠃⢸⠇⢰⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⢸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣉⣭⣭⡙⢳⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⣉⣭⣬⡙⢷⣄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⡾⠋⠁⠉⠻⣦⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢃⣾⠋⠀⢉⠻⣦⠹⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢰⠀⠀⠀⢰⠂⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠸⡆⠀⠈⣀⣀⠀⠘⠁⠀⠀⠛⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⢀⡤⠒⠊⠉⠉⠁⠀⠀⠉⠁⠒⠤⣀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠉⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠚⠁⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠙⠃⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇⠀⠀⠀⢰⣆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠀⠸⡄⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠃⠀⠀⠀⡞⠀⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⠀⠻⣄⠀⠀⠀⢀⠀⠡⠶⣧⠄⢠⠀⠀⠤⠄⠀⠀⠀⠀⢀⡞⢀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠈⠲⣤⠊⠀⠀⠀⠀⠀⠑⢃⠀⠀⣀⠀⠀⠀⢀⡴⠋⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠐⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠁⢲⠉⠀⠀⠙⠂
⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣜⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠉⠉⠉⢀⡀⠀⠀⠀⣀⠉⠉⠉⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠄⠊⠑⠠⠀⣀⣀⠠⠚
⠀⠀⠀⠀⠀⠃⠰⠀⠀⠀⠀⠀⠀⠀⠑⠈⠉⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠃⠀⠀⠀⠀⠐⠦⠤⠆⠀⠀⠀⠀⠐⠤⠴⠂⠀⠀⠀⠀⠜
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣂⣀⣀⣀⣁⣀⣠⣠⣤⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⣊⣉⣉⣉⣉⣉⣉⠑⠒⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⣉⠤⣒⠩⠭⠔⠒⠒⠒⠒⠢⠤⢍⣉⠒⠦⢄⡉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⢀⡴⣫⢔⠭⣒⠭⣐⡲⠭⠭⠭⠬⠭⠭⢍⣒⠢⠤⣉⠒⢄⡉⠲⢄⠈⠢⡀
⠀⠀⠀⠀⠀⡠⢫⣾⢟⣵⣮⣳⣽⡲⠮⣭⣟⣻⡭⠭⢕⣒⠤⣍⠒⢌⡑⢦⡈⠢⡀⠑⣄⠈⢦
⠀⠀⠀⠀⡰⣁⡁⣁⢿⣵⣿⠿⠛⠉⠁⠀⠀⠀⠀⠉⠑⠢⢍⠢⣝⠢⡙⢦⡙⢆⠘⢆⠈⢂⠀⢡
⠀⠀⠀⢰⣱⣟⣾⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⠳⡘⢆⠱⡀⢣⠈⢇⠈⢇⠀⢣
⠀⠀⢀⣇⣿⣿⠿⠿⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠱⣈⣆⣱⠀⡧⠞⠛⠉⠒⠺⡆
⠀⡴⠉⠀⠉⠀⠀⠀⠀⠹⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠋⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⡆
⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢
⢱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠈⠣⠀⠠⡀⠀⣀⠀⢀⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠴⢄⠀⠀⢀⣀⠀⠀⣠⠖⠚⠁
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣾⣿⣿⣷⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠉⠈⠉⠉⠉⠉⠁⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⣀⠠⠐⠂⠀⠉⠀⠉⠉⠁⠐⠂⠄⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⠔⠊⠀⠀⠀⠀⠁⠈⠉⠉⠉⠈⠀⠂⠄⡀⠁⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⠔⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢈⠁⠂⠀⠀⠁⠀⠀⠁⡀⠘⢆
⠀⠀⠀⠀⠀⠀⢀⠂⠠⠀⡠⠂⠠⠊⡠⠔⠈⠁⠀⠀⠤⠤⠀⠀⠈⠁⠠⠀⠑⢄⠈⢀⠈⢄⠈⢆
⠀⠀⠀⠀⠀⠀⡎⣀⠁⠀⠠⠂⡠⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠑⡀⠱⠀⠆⠈
⠀⠀⠀⢀⠔⠁⠀⠀⠸⠔⠋⠉⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢂⡰⠄⠥⠘⡤⠓⠠⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠊⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢤⡀⠀⠀⠀⠀⡠⠂⠤⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⢀⣠⡤⠴⠒⠒⠛⠛⠛⠛⠛⠒⠒⠶⠤⣄⡀⠀⠀⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⣠⠴⠚⠉⠀⢀⣀⣤⠤⠴⠶⠶⠶⠦⠤⣤⣀⡀⠀⠉⠙⠦⣄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣀⠴⠋⠀⢀⡠⠖⠋⠉⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠉⠛⠢⣄⡀⠀⠙⢦⡀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⠞⠁⠀⣠⠖⠋⠀⠀⣀⠤⠖⠋⠉⠉⠀⠀⠀⠉⠉⠙⠲⢤⣀⠀⠀⠙⢦⡀⠀⠙⣆⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⡰⠋⠀⢠⠞⠁⠀⢀⡴⠊⠁⢀⣀⡤⠴⠒⠒⠒⠒⠒⠦⢤⣀⠀⠈⠳⣄⠀⠀⠙⣆⠀⠈⢧⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡼⠁⠀⣰⠋⠀⠀⣠⠋⠀⣠⠔⠋⠀⢀⣀⡤⠤⠤⠤⢤⣀⠀⠈⠙⢦⡀⠈⢣⡀⠀⠈⢦⠀⠈⢧⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣼⠁⠀⣰⠃⠀⠀⡼⠁⢀⡜⠁⠀⡠⠚⠉⠀⣀⣀⣀⣀⡀⠈⠙⠦⡀⠀⠙⣆⠀⢳⡀⠀⠈⣆⠀⠘⡆⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⡟⠀⢠⠇⠀⢰⠇⠀⠀⣼⠁⢀⠎⠀⢠⠞⠀⢀⡴⠋⠉⠀⠀⠀⠉⠲⡄⠀⠙⣆⠀⠘⣆⠀⢷⠀⠀⢸⡄⠀⢻⠀⠀⢧
⠀⠀⠀⠀⠀⠀⢸⢁⣠⠼⠶⠒⣚⡲⠦⣴⠇⠀⡞⠀⢀⡏⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠘⡆⠀⢸⡄⠘⣆⣠⠴⠗⠒⠾⠦⣄⣸⡄
⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀⠀⠀⠀⠈⠓⠈⠳⣼⠷⠶⢼⡁⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢀⡽⠶⠤⣧⠞⠉⠺⠋⠈⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠲⠒⢦⠀⠀⢹⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡏⠀⠀⠴⠳⠖⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡖⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠈⠳⠶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⠞⠁
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡤⠤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⢤⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠙⠶⠤⠤⠶⠒⢦⣀⣀⢀⣀⡭⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢭⣀⣀⣀⣀⡴⠒⠦⠤⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⣿⡿⠀⠀⠀⢸⣯⣽⣿⠀⠀⠀⠀⠀⢹⣿⣿⠇⠀⠀⠀⣇⣿⡿⠀⠀⠀⢸⣯⣽⣿⠀⠀⠀⠀⠀⢹⣿⣿⠇
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠸⠿⠇⠀⠀⠀⠀⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠸⠿⠇
⠉⠀⠀⠈⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠉⠀⠀⠈⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣧⡄⠀⠀⠀⠀⠿⠷⠾⠿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣧⡆⠀⠀⠀⠀⠿⠷⠾⠷
⣰⡿⢿⡆⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣰⡿⢿⡆⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⡀
⠿⠛⠻⠗⠀⠀⠀⠀⠈⠿⠧⠀⠀⠈⢀⠀⠀⠀⣦⡀⠀⠀⠿⠻⠻⠇⠀⠀⠀⠀⠀⢿⡧⠀⠀⠈⢀⠀⠀⠀⣦⡀
⠀⠀⠀⠀⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⣿⡗⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡇
⠀⠀⠀⣿⡧⡄⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠻⣿⠁⠀⠀⠀⠀⠀⣿⡧⡄⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠻⣿⠁
⠀⠀⠀⢻⣷⠃⠀⠀⠀⣿⣭⣿⡇⠀⠀⠀⠀⠀⠋⠀⢀⠀⠀⠀⠀⢻⣷⠃⠀⠀⠀⣿⣭⣿⡇⠀⠀⠀⠀⠀⠛⠀⢀
⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡈
⣶⣄⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⣶⣿⡆⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⣾⣿⡇
⣿⡿⠀⠀⠀⢸⣯⣽⣿⠀⠀⠀⠀⠀⢹⣿⣿⠇⠀⠀⠀⡇⣿⡿⠀⠀⠀⢸⣯⣽⣿⠀⠀⠀⠀⠀⢹⣿⣿⠇
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠸⠿⠇⠀⠀⠀⠀⠙⣿⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠸⠿⠇
⠉⠀⠀⠈⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠉⠀⠀⠈⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣧⡆⠀⠀⠀⠀⠿⠷⠾⠿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣧⡆⠀⠀⠀⠀⠿⠷⠾⠷
⣰⡿⢿⡆⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣰⡿⢿⡆⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⡀
⠟⠛⠛⠗⠀⠀⠀⠀⠈⢿⡧⠀⠀⠈⢀⠀⠀⠀⣦⡀⠀⠀⠿⠛⠻⠇⠀⠀⠀⠀⠈⢿⡇⠀⠀⠈⢀⠀⠀⠀⣦⡀
⠀⠀⠀⠀⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡇
⠀⠀⠀⣿⡧⡄⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠻⣿⠁⠀⠀⠀⠀⠀⣿⡧⡄⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠻⣿⠁
⠀⠀⠀⢻⣷⠃⠀⠀⠀⣿⣭⣿⡇⠀⠀⠀⠀⠀⠋⠀⢀⠀⠀⠀⠀⢻⣷⠃⠀⠀⠀⣿⣭⣿⡇⠀⠀⠀⠀⠀⠋⠀⢀
⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡈
⣶⣄⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⣶⣿⡆⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⣾⣿⡆

⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠉⠉⠉⠐⠢⢄⠀⠀⠀⠀⢸
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠑⢄⠀⠀⢸
⠀⠀⣰⣿⣿⣿⡿⠟⠛⠛⠛⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⡔⠉⠀⠀⠀⠀⠑⢄⠀⠀⠈⠆⠀⢸
⠀⠰⠟⠛⢿⡏⠀⠀⠀⠀⠀⠀⠈⠿⠛⠛⠛⠂⢄⠀⠀⠀⡠⠥⠒⠢⣜⠀⠀⠀⠀⠀⠀⢀⠄⠖⠒⠖⠚⠢⣸
⢎⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡸⠀⠀⠰⡁⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣼⣁⣤⣸⣿⣿⣴⣿⣧⣶⣶⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠿⠻⠛⠛⠛⠛⠛⠛⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠐⣂⠀⢊⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⡿⠾⠿⠿⠻⠿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⡿⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⣿⡿⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⣿⠟⡓⠀⠀⢀⠀⠩⣿⣟⣛⣿⣶⣤⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⣿⡅⠀⠠⢤⣿⠹⡿⢳⣶⡦⢀⡀⠀⠀⠀⢠⢸⠀⠀⣿⣿⠁⠀⠀⠒⠒⢿⣿⣏⡹⠿⠟⠙⠶⣿⣿⡃⢳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⡄⠀⠀⠀⠁⠀⠀⠀⠘⠛⠎⠙⠀⠀⠀⢈⠘⡀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⡜⠀⠻⡿⢵⡏⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⣦⠸⣷⣤⣤⠠⠄⠀⢘⣻⣖⠀⠀⠀⠀⠀⠀⢐⡌⢡⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣒⣥⣤⣀⠀⠀⠈⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠸⣦⣿⣿⣿⣵⣴⣶⡛⠛⠈⡄⠀⠀⠀⠀⠀⠢⠕⣼⡆⠀⣿⣿⣷⣶⣤⠴⣰⡦⠂⠀⠈⢉⣹⣫⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠹⣿⣿⣿⣿⣿⣄⣙⡗⠀⠀⠀⠀⠀⠀⠀⢨⢅⡗⣿⣤⣽⣿⣿⣿⣾⡇⣺⢁⣤⣤⣾⣿⣿⡏⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡌⢿⣿⣿⣿⣿⣿⣿⡌⠀⠀⠀⠀⠀⠀⢈⣿⣑⠸⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠿⣧⣤⣄⠉⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⣤⣀⡀⠀⠈⣿⣮⢻⣿⣿⡟⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠘⢻⣿⠆⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡄⠀⠘⢿⣧⢹⣿⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠃⢻⡄⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢿⣿⣦⠙⢿⣿⣿⣿⣿⣿⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⢹⡀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠈⠈⣿⣿⣖⡈⢿⣿⣿⣿⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠘⠿⠿⠗⠀⠀⠀⠀⠀⠀⠻⣿⣥⠀⠀⠀⠩⢿⣿⣧⠌⢿⣿⡇⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠰⣿⡆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠓⢂⠄⠀⠀⠉⠙⡙⣷⠘⢿⣇⠀⢸⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠿⠛⠛⣉⣉⣉⣉⣉⣉⡙⠛⠻⠿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡉⠛⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⣡⣴⣿⣿⠿⠛⢉⣁⣤⣤⣤⣤⣤⣤⣄⣉⠙⠻⢿⣿⣷⣤⡉⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⢠⣾⣿⡿⠋⣡⣴⣾⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣶⣤⡈⠻⣿⣿⣦⡈⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⣴⣿⡿⠋⣠⣾⣿⣿⠟⢋⣁⣤⣴⣶⣶⣶⣤⣄⣉⠛⠿⣿⣿⣦⡈⠻⣿⣷⡄⠹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⣼⣿⡿⢁⣼⣿⣿⠋⣠⣶⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣷⣦⡈⠻⣿⣿⣆⠙⣿⣿⡄⢹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⢸⣿⡿⠁⣾⣿⡿⢁⣼⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣄⠙⣿⣿⡆⠸⣿⣿⡀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⡇⢸⣿⣿⠁⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆⢸⣿⣿⡀⢿⣿⡇⠸⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠐⠟⠛⢀⡉⠛⠃⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠀⠛⢉⡁⠘⠻⠿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠛⠃⣤⣾⣿⣿⣿⣿⣷⣄⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣠⣶⣿⣿⣿⣿⣷⣤⡀⠛⠛
⠀⠀⠀⣠⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠈⠃⠀⠈⢉⢉⢿⣷⡦⢵⣄⠀⢑⣌⣆⠸⢢⠔⢎⠂⠀⠀⣀⠀⠃⠀⢀⠆⠘⡄⠀⡟⢷⠀⢇⠘⣧⡤⠚⠛⠲⢤⡀⠀⠁⠢⣼⣀⠀⠙⠀⠀⠈⣉⠹
⠔⢁⠟⠰⢋⡵⢹⣿⣵⡑⣇⡰⠁⠈⢻⡁⢇⠀⢸⠂⠀⠴⠁⢄⠈⠀⠈⠢⡀⢱⠀⢻⠀⠀⠸⣤⢿⠧⡀⠈⠁⣠⠛⢯⡁⠐⢺⣏⡠⠂⡰⠃⠞⣰⠞
⠈⠁⠀⢠⠟⡄⢠⣿⡌⢷⠈⡇⠀⡀⠀⢳⠀⢑⠿⠆⠀⠐⠦⢄⠣⣴⠇⠀⠹⡘⡆⢸⠀⠀⣰⠟⠚⢆⠐⠀⣰⠃⠀⠀⠈⠉⠉⢻⠀⠉⠀⠀⡼⢣⠁
⣦⣄⠀⠈⠀⡄⣾⢿⡄⢲⠀⢳⠀⠈⠓⢌⡟⠃⠂⠴⠀⢢⠀⠀⣉⠿⢤⠤⡀⠹⣜⡼⡄⠀⣿⠀⢀⠔⠉⠁⠀⠀⠈⠢⠀⠀⠀⣹⣶⡤⡀⠀⠁⢨⢰
⡟⠀⠱⡀⠀⠀⠁⢿⠘⠇⠀⠀⠧⠀⡀⢨⡇⠀⠀⠀⢀⠎⢠⠏⠀⡠⠊⠀⡿⠀⠈⢷⠇⠀⣿⡾⠃⡠⠄⠀⠒⠐⢀⠀⠀⠀⢀⠟⢸⢇⠈⠄⠀⠀⠘
⠁⠀⠀⠑⡀⠀⢀⡈⠧⠤⠤⡜⡇⠘⢁⢸⡗⡄⢠⠊⠁⢀⡞⡠⠊⠀⢀⣴⠃⡀⠤⣀⠀⠀⢹⠀⠀⠁⠀⠀⣀⠢⠈⠀⢀⡀⢸⣀⠌⠀⠂⠈⢂
⠰⠀⠀⠀⡇⠴⠁⢰⠀⡠⠒⠁⡞⠀⠓⢸⠇⠀⡇⠀⢀⡞⡔⢁⡤⠖⣭⡧⢤⡓⢄⠀⠁⠀⠁⠀⠀⠰⣉⣀⠀⣀⠀⠀⡆⠳⡈⠁⢀⠆⠀⠀⠸⠠⠆
⣀⠸⢨⢠⠷⡄⠃⠈⡌⠁⠀⡰⠙⠠⡀⢸⠀⡜⠀⠀⡜⠰⢁⡞⢰⠛⡇⠈⡆⠑⢊⣴⠖⠛⠛⠓⠶⠤⣤⣀⡠⠝⠀⡇⢁⢸⠙⠴⢅⡀⠅⡄⡾⢦
⠈⢧⢢⣸⡞⢣⢠⠀⡇⠺⠤⠄⠤⡀⡇⢈⠞⠀⠀⣼⣴⠥⠞⢠⠇⢸⠃⠀⡇⢀⡾⠁⠀⠀⠀⣷⡀⠀⢠⡄⠀⠀⠐⢀⠘⢿⡁⠀⠀⠹⣔⡇⣷⠛⡄
⠀⠈⢿⣿⡇⠘⡄⠀⠇⢠⠄⠒⠊⠀⠓⠁⠀⠀⠘⠋⠀⠀⠀⠸⡀⢸⠀⢰⠃⢸⠃⠀⠀⠀⠀⢷⢡⡠⡻⡉⠀⠀⠀⠅⠑⢾⣧⠁⠀⠀⠹⣿⣿⠀⢣
⠀⠀⣸⢿⡤⢂⠽⠶⠀⠈⠀⠒⠒⠒⠒⠒⠂⠀⠒⠒⠢⡄⠀⠀⢳⣼⢠⠋⠀⢸⡇⢠⠆⠀⠀⠈⠛⠷⠑⠁⢀⡴⡞⢀⠀⣀⢹⡆⢀⠀⢀⡿⣧⠔⡨
⠉⠙⡋⡸⠂⠈⢺⡌⡀⠀⡜⠉⠒⢤⠀⢠⠊⠉⠉⡍⠉⠁⡜⠆⢸⣿⠃⣙⣳⣦⣿⣿⡀⠐⠂⠀⡀⢀⣐⣤⣿⠀⠁⠘⠀⠀⠀⠛⠋⠉⠛⢁⠗⠁⠱
⠀⠀⢠⠄⠢⠀⠀⡿⡇⠀⡇⠻⣦⣤⠳⠣⠤⣀⠀⠈⠈⢄⣧⢸⠈⠛⠀⠉⠁⡀⢽⣷⡬⣤⣄⠀⠑⢄⣃⢸⢣⡄⢠⠂⠀⠀⣀⠀⠁⠀⠀⡤⠐⠄
⠀⠀⠘⢄⠀⡇⠀⡇⠀⠀⢳⣰⡿⣅⠀⠉⠀⡸⠷⣖⠒⠂⣽⣏⡠⠆⡽⢠⠞⣹⢞⣿⣽⡄⣯⢡⠊⠉⠻⡋⢊⠁⠈⡇⠀⣡⠊⢄⠀⠀⠀⠣⡀⢸
⢦⣴⠀⠀⢣⠸⡀⣿⠀⠀⣼⡗⠸⡌⠂⠀⡸⠁⠀⠈⠉⠐⠛⡗⠒⠊⠀⢀⡾⠣⠀⣼⡎⢻⡜⢺⠀⠀⠀⠹⡀⠑⡴⠧⠤⠤⠤⢄⠱⣰⡆⠀⠸⡄⡇
⢺⣿⣤⣀⠀⢣⣡⢸⠀⢠⡇⡇⢀⠔⠂⠉⠁⠀⠘⠄⠀⠀⠀⣻⣦⣀⠀⠘⠁⡠⢸⡿⣏⠲⡀⠸⡀⠈⠓⢄⣳⠛⠀⣠⠔⠠⠀⠀⢑⣿⣧⣤⡀⠘⣌
⠁⡠⠃⠈⡇⠀⠹⣿⠀⠀⣧⡷⠁⡀⠤⠀⠀⠀⠀⠂⠀⡄⢰⠃⠿⡄⠡⡀⠀⠃⠋⢣⡍⠇⠁⠀⢳⠀⢀⠀⣿⠀⠀⠀⠀⡰⠀⡖⠉⢀⠜⠀⢹⠀⠈
⠊⠀⢀⡼⢁⠀⢀⠀⠀⠀⡏⠀⠈⠃⠒⠒⠀⡄⢸⠀⠀⡆⢨⢀⠇⠈⠈⠑⡀⠀⠀⠈⢣⣀⠤⣄⢏⠐⠃⠘⣿⢄⠀⠔⠁⠀⣸⢁⠔⠁⠀⣠⠟
⡠⠔⣻⠅⣘⠠⡀⠈⠒⠒⠁⠀⠀⢔⠈⠉⣁⡀⢸⠠⠈⢧⠸⠁⠀⠀⠀⡀⡀⡠⠊⠸⠀⣀⠤⠋⢸⠀⠜⠈⡟⠀⡜⠀⠀⣰⢣⠃⣀⠤⢚⡭⢀⡃⢄
⡰⢾⠉⠱⡈⠒⢃⣤⠖⠚⠒⠲⠤⣤⣀⣀⣠⠏⢈⠀⡇⢸⠣⢴⣀⠀⠀⠀⡿⡄⠀⠀⡇⠑⠒⢒⡜⠠⡀⢠⠇⢠⠃⠀⣰⢃⠇⣸⢁⡶⡏⠉⢆⠙⠚
⠃⢸⠀⠀⡇⢠⡞⠁⠀⠀⢰⣆⠀⠀⣨⡁⠀⠀⠘⠀⠹⣟⠀⡀⠈⢷⣡⡆⣷⢻⠀⠀⡇⠰⠌⠡⠤⡀⢸⠘⡠⠃⠀⢠⣃⣊⠴⠁⡞⠀⡇⠀⣸⠀⣼
⠀⣾⠀⣸⠁⣼⠁⠀⠀⠀⠘⣏⠆⡰⡟⡇⠀⠀⠈⠎⠲⣽⣄⠁⠀⠈⢿⣿⡇⠈⣆⠀⡇⢀⠤⠄⠒⠁⠸⠊⠀⠀⠀⠛⠉⠀⠀⠰⡇⢸⠇⢀⡇⢀⡏
⡆⡇⣠⠃⠀⢻⡀⣠⠆⠀⠀⠙⠾⣷⠔⠁⢀⡴⠾⡀⠀⢈⣹⡀⠀⠀⢨⣯⣧⠄⣸⢦⠃⠈⠒⠒⠂⠀⠀⠒⠒⠒⠐⠂⢤⡀⠀⠀⢹⣸⢀⡜⠀⠸⣇
⢿⣿⠁⠛⢶⣼⣷⣏⡀⠤⠀⠀⢀⣈⣠⣰⡟⠠⠀⠈⠀⠀⠀⢻⠉⠓⠟⢹⠇⠉⢡⣄⡄⠀⣰⠒⠢⢄⡀⢀⡔⠀⠀⡔⠂⠁⡐⢂⠸⣿⡏⠘⢳⣦⣿
⠘⠇⠈⠁⠀⠘⣿⣯⣤⣠⡀⠀⠣⡘⡄⢹⢁⠄⡈⠄⠀⠀⠀⠀⠀⡀⠀⡄⠰⡀⠀⡿⣶⠀⡏⠹⣆⡀⠵⠾⢤⣀⠀⠈⠈⢄⣰⠈⠄⠻⠀⠉⠐⠐⢻
⡠⠂⡴⢠⠞⣹⢾⣿⣳⠨⡏⢰⠊⠙⢟⠂⡎⠂⢸⠄⠐⣠⠋⡀⠐⠀⠘⢄⠀⢣⠀⢿⠈⠀⢸⣀⣿⣇⠀⠘⠂⢈⠷⣆⠀⠠⢽⡟⣀⠔⢠⠆⡴⢋⡶
⠐⠊⠀⢀⡾⡑⠈⣿⡙⣷⠙⡇⠀⠀⠈⢣⠈⠢⣶⡀⠀⠤⣀⡈⢆⣰⡇⠀⢳⡸⡄⢸⠀⠀⢨⡿⠬⡄⠁⠀⢰⠋⠀⠈⠑⠒⠚⢿⠥⠒⠁⠀⣰⠏⠈
⣄⡀⠀⠘⠀⡣⣼⢿⡑⢬⠀⢣⠀⠙⠦⡈⡶⠆⠠⢀⠀⢄⠀⠈⠲⣿⣀⣀⠀⢣⡱⡸⡀⠀⡿⠀⢀⡨⠐⠂⠉⠀⠐⢄⠀⠀⠀⢸⣤⣀⠀⠀⠃⢘⢢
⣿⠈⢂⠀⠀⠁⠋⣞⠹⡎⠀⠈⣆⠀⠀⢘⡇⠀⠀⠀⠀⡘⢀⡖⠉⢀⠜⠈⣷⠀⠙⣧⡇⠀⣿⣴⠊⢀⡀⠀⠠⠤⠀⠀⠀⠀⠀⡟⢹⡏⠑⡀⠀⠈⠘
⠃⠁⠁⠢⠀⠀⠀⠘⣇⣀⣀⡐⡎⠰⠃⢝⡧⡀⢀⠔⠉⠀⡼⢀⠔⠁⠀⣠⠏⡀⣀⠈⠀⠀⢿⠁⠀⠃⠀⠀⠀⢄⠘⠐⠀⠀⢸⠀⡘⠀⠂⠐⠄
⢀⠀⠀⠀⡇⣠⠊⢣⠀⢀⡤⠃⡕⠀⠬⢺⡇⠁⡎⠀⠀⡼⣡⠃⣀⡠⢚⣏⣀⠄⡀⠉⠂⠀⠊⠀⠀⢠⠒⠀⠈⠁⠀⠀⡄⢧⠘⠋⠀⡄⠀⠀⢸⢀⡔
⠀⢐⠰⢠⣏⡀⠂⠸⡐⠃⠀⢠⠧⢄⠀⢸⠀⡰⠁⠀⡸⢡⠃⡼⢡⡶⡏⠱⡌⠣⠜⣠⡤⠶⠶⠦⣤⣀⣈⠉⢀⡿⠀⡆⠃⢠⠳⣠⡂⠀⠀⡄⣼⣁
⠙⣆⢜⢸⡼⢃⠀⠀⡇⢔⣂⣁⣀⠀⡇⠘⡴⠃⠀⢰⣃⣂⡼⢁⠎⢠⠇⠀⡇⠀⣼⠋⠀⠀⠀⣦⠀⠀⢉⡉⠁⠀⢠⠀⠸⡞⠂⠀⠉⢳⡠⡃⣧⠿⡀
⠀⠘⣿⣿⡇⠸⡈⠀⡇⢀⡀⠤⠜⠁⠧⠊⠀⠀⠠⠟⠉⠀⠀⢸⠀⢸⠀⢠⠇⢰⡇⠀⠀⠀⠀⣏⢃⢀⢺⠓⠀⠀⠀⡎⠢⣼⣧⠃⠀⠀⢻⣿⣿⠀⢇
⠀⠀⢸⣿⣀⠄⣳⣴⠀⠘⠀⠤⠤⠤⠤⠤⠄⠀⠠⠤⢄⠀⠀⠀⡇⣸⢀⡞⠀⢸⡆⢀⡄⠀⠀⠘⠶⣧⠇⠃⠀⡠⡴⡀⠀⠈⢻⡆⠀⠀⠀⣿⣏⡠⢘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠶⠶⢦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠉⢀⣀⣠⣤⣤⡴⠶⠶⠶⠶⢦⣤⣤⣄⣀⡀⠉⠙⠻⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠁⣀⣤⡶⠟⠛⠉⠁⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠈⠉⠛⠻⢶⣤⣀⠈⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⣠⣴⠟⠋⠁⣀⣤⡶⠾⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠷⢦⣤⣀⠈⠙⠻⣦⣄⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣤⠾⠋⠀⣠⡴⠟⠋⠁⠀⣀⣤⣤⡶⠶⠶⠶⠶⠶⠶⢶⣤⣤⣀⠀⠈⠙⠻⢦⣄⠀⠙⠷⣤⡀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⣠⡟⠁⢀⣴⠟⠉⠀⣀⣤⠶⠛⠉⠁⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠙⠻⣦⡀⠈⢿⣄⠀⠙⣧⡀
⠀⠀⠀⠀⠀⢠⡾⠁⢀⡾⠋⠀⣴⠟⠁⠀⣠⡾⠋⠁⠀⣀⣤⡶⠾⠛⠛⠉⠉⠉⠉⠛⠛⠷⢶⣤⣀⠀⠈⠙⢷⣄⠀⠈⠻⣦⠀⠙⢷⡀⠈⢷⡄
⠀⠀⠀⠀⢠⡟⠁⢠⡿⠁⢀⡾⠃⠀⣠⡾⠋⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀⠀⠙⢷⣄⠀⠘⢷⡀⠈⢿⡄⠈⢻⡄
⠀⠀⠀⢠⡿⠁⢠⡿⠀⢠⡿⠁⠀⣴⠏⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠹⣦⠀⠈⢿⡄⠈⢿⡄⠈⢿⡄
⠀⠀⠀⣾⠃⢀⣿⢁⣠⣿⣁⠀⣼⠃⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠘⣧⠀⠈⢿⡀⠈⣿⡀⠘⣷
⠀⠀⢰⡏⠀⣸⡿⠛⠉⠉⠙⠻⣧⡀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠸⣇⣠⡼⠷⠶⢾⣇⠀⢹⡆
⢀⣴⠾⠛⠛⠛⠀⠀⠀⠀⠀⠀⠘⠷⠾⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣠⣤⣿⠋⠀⠀⠀⠀⠙⠷⠾⢷⣄
⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢿⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⣶⣤⣀⣠⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠿⣦⣀⠀⣀⣴⣄⡀⠀⠀⣠⡟
⠀⠈⠻⢶⣤⣤⡴⠟⠛⠷⠶⠶⠾⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠈⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠚⠉⠉⠉⠉⠉⠉⠙⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⣀⠤⠒⠒⠒⠒⠒⠠⢄⡀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢀⠜⠁⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠣⡀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢠⠎⠀⠀⠀⡠⠖⠉⠁⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⢱⡀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⠏⠀⠀⣠⠊⠀⠀⢀⣀⠠⢄⣀⡀⠀⠀⠈⢆⠀⠀⠀⢣⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡜⠀⠀⢰⠁⠀⢀⡞⠁⠀⠀⠀⠀⠉⠲⡄⠀⠈⣆⠀⠀⠈⡆⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢠⠃⠀⠀⡇⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠘⡄⠀⠀⢣⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⠀⠀⢠⠁⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢣⠀⠀⢸⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⡮⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠈⡆⠀⠀⡇⠀⠸⡇
⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠉⠑⢇⡠⠒⠉⠉⠲⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⣧⢀⠤⠳⢤⡀⡇⣀⠤⠤⣀
⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠈⠁⠀⠀⠒⠀⠈⠓⠉⠐⢄⠀⠀⠀⠀⠀⡠⠖⠉⠉⠉⠻⠎⠀⠀⠀⠙⠋⠀⠠⠀⡀⠱⡀
⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠂⢀⠆⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠀⠀⡸
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠎⠀⠀⠀⠀⢈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠳⡄
⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠑⠒⠒⠲⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠤⠤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠤⣀⣀⣀⡴⠃⠈⠒⡤⠤⠒⠉⠀⠀⠀⠀⠀⠀⠙⠢⠄⢀⢤⠔⠉⠦⣀⡀⣀⠴⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⡇⠀⠀⣀⣇
⠀⠀⠀⠀⠀⠀⠀⡞⠁⠙⡆⠀⢸⠀⠀⡞⠉⠉⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠘⣆⠀⠀⡇⠀⢸⠁⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠙⠢⠚⠁⠀⢸⡀⠀⠘⢦⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢀⠎⠀⠀⡇⠀⠈⠓⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠘⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡖⠙⠋⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠴⠶⠦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⠒⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⣀⣀⣄⣤⡚⠉⠁⠀⠀⠀⠈⠉⣳⡤⢤⣄⣀⣤⣤⣄⡹⡄
⠀⠀⠀⠀⠀⣠⠔⠛⠉⠛⠲⠞⠉⠀⠀⠀⠉⢲⡀⠀⠀⠀⢀⡞⠁⠀⠀⠈⠁⠀⠀⠀⠙⣿⡄
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠤⣄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠈⢳⣀⡞⠀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⢀⡴⠃⠀⠀⠀⣶⠶⣄⠀⠀⠀⣀⡀⠀⠀⠀⢠⢿⡀⠀⠱⠄⣀⠀⠀⠀⠀⠀⠁⣀⣀⡀⠀⠀⠀⢧⡀
⠀⠀⡞⠀⠀⠀⠀⠀⠀⠠⣈⡀⠀⠈⠉⠛⠃⠀⠀⣏⣰⠃⠀⠀⠀⢠⣴⠶⡄⠀⠀⠚⠉⠉⠁⠀⠀⠀⠀⣷
⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡞⣏⠀⠀⠀⠀⠈⠀⠀⠀⠠⡔⡶⠀⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠈⠳⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⠤⠤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠚⠉⠙⠛⠚⠛⠉⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢊⣉⣉⠑⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⢈⠤⠀⠀⠌⠐⠄⠱
⠀⠀⠀⠀⢀⡤⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠔⠀⠀⠢⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣮⡉⠛⠉⠄⠂
⠀⠀⢀⡴⢋⡴⢛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡾⣬⠄
⠀⠀⡞⢠⠏⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋
⠀⠀⠃⠛⠘⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢐⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠐⠀⡀⠀⠀⠀⠀⢀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⢸
⠀⣰⣿⣿⣷⣶⣦⠀⠀⠀⠘
⠚⠛⠛⠛⠛⠛⠛⠃⣠⣶⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⠿⠿⠟



⠀⠀⠀⠀⡠⠄⠒⠒⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⣒⣒⣲⡦⣄
⠀⠀⡐⠁⠠⠔⠈⡉⠉⣑⡢⣝⢆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣫⢞⢽⣚⣷⣒⢭⡲⡵⣄
⠀⠐⠀⠐⠁⠀⠀⠀⠀⠀⠙⢮⣾⡆⠀⠀⠀⠀⠀⠀⣀⡛⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢳⣳⣳⣫⠞⠛⠲⡵⡽⡽⣼
⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠀⠀⠸⠿⡿⠷⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠘⠻⠛⠉⠃⠀⠀⠀⠛⠁⠃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣀⣀⣀⣀⣀⣿⠀⢐⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⠓⡞⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣃⠀⠐⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠉⠉⣿⣿⣿⠿⠿⠟⠛⠉⠉⣀⣠⠉⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⢀⣀⣰⣤⣤⣴⣶⣾⣿⣿⠏⣿⠀⠀⣾⠘⣸⣿⡄
⠀⠀⠀⠀⠀⠀⣧⠀⣠⣇⠀⠦⣇⡀⠁⠰⠤⠄⠒⠦⠝⣿⠿⠟⠛⠛⠿⡋⡁⠐⠿⢄⣡⣿⡄⠞⠀⠈
⠀⠀⠀⠀⠀⢸⡿⠰⠋⠉⡠⠆⢁⠉⠁⠈⠀⠰⠆⠒⠀⢀⠀⠂⠀⣧⠀⠈⠈⠐⢲⡦⡀⠈⠱⠔
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣼⡰⠀⠁⠀⠀⠀⡆⠀⡀⠀⣸⣴⣿⡀⠠⠄⠀⠀⠀⠀⠀⢰
⠀⠸⠀⠄⠀⠀⠀⠀⠀⠰⣶⣶⣶⠀⠀⠋⠀⠲⠸⣿⠘⢋⠄⠉⠉
⠀⠀⠀⠀⠀⠂⠀⠀⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠔⠤⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠

⠀⠀⠀⠀⣠⣾⣻⣿⣷⡄⠀⠀⢠⡴⢞⣛⡻⢦⡀⠀⠀⣠⢖⡛⢛⢶⡄⠀⠀⡴⠋⢉⠉⠓⡄⠀⠀⡴⣺⡿⣿⣦⡀
⠀⠀⠀⢸⢿⣯⣎⣹⣿⣿⠀⢠⣿⣿⣿⠭⣿⣮⣿⠀⢰⡗⡵⣻⣳⡵⣿⡀⢸⠀⡼⣩⡙⡆⢸⠀⣸⣿⣡⢶⢬⢿⣷
⠀⠀⠀⠈⠈⠉⠈⠁⠉⠉⠁⠘⠛⠛⠃⠀⠛⠛⠙⠁⠙⠙⠛⠁⠙⠃⠛⠃⠘⠀⠃⠛⠃⠃⠘⠀⠋⠋⠋⠛⠘⠘⠙

⠀⠀⠀⢠⣾⢽⡿⣗⣄⠀⠀⠀⠀⣴⣾⣷⣦⠀⠀⠀⠀⢎⢅⣨⡑⡄⠀⠀⠀⢀⣤⡶⠶⣤⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣿⣷⠉⠈⣻⣿⡄⠀⠀⢸⣿⡵⢾⣿⡆⠀⠀⠆⣾⡟⢺⣿⡐⠀⠀⢀⣭⣅⣩⣟⢾⣿⠀⠀⡞⣾⡏⢹⣿⣇
⠀⠀⠘⠿⠿⠁⠈⠛⠛⠃⠀⠀⠛⠛⠇⠸⠟⠃⠀⠠⠌⣿⠁⠘⡿⠑⠆⠀⢸⡷⡾⡇⢶⢺⢿⠆⠀⠘⠛⢠⡷⠉⠻
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⠛⠙⠋⠉⠉⠉⠉⠉⠋⠙⠛⠛⠛⠻⠿⠛⠿⠟⠿⠿⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠀⠀⢀⣩⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡎⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠛⢛⡷⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⣠⣄⠀⠀⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢣⣤⣴⣿⣽⣧⣔⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠙⠛⠉⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠇⣡⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⣀⣀⣀⣀⣀⣀⠀⠈⠳⡄⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡜⢠⣆⠀⠀⠀⠀⠀⠀⠰⢶⡾⠋⠉⠉⠉⠉⠙⠛⠒⠄⠉⠀⠀⠀⡠⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣬⠈⣇⠀⠀⠀⢀⠀⠀⠀⠀⠀⢤⣤⣤⣤⠄⠂⠀⠀⡺⠀⠀⠀⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡉⢄⠂⠀⢾⣆⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⣠⣿⠀⣘⣾⣯⡀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡅⠻⣿⣦⡁⠒⢸⣿⣷⣤⣶⣤⣄⣠⣠⣄⢀⣈⣩⣿⢇⣴⡿⠣⣿⣿⣦⣀⣀⠴⠋⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⢹⡷⢈⠈⠻⣿⣧⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⠌⠀⣿⣿⣿⠋⡀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡏⠐⢹⣧⠈⠎⠁⡌⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡉⠊⠀⠀⠀⡏⠙⢣⣸⡄⠾⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⡀⢸⣿⠀⠀⠀⠰⣶⡐⢈⠉⠛⠛⠿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⡿⣄⠀⠋⠀⠀⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠀⢀⢸⣿⠀⠀⠀⠀⠹⣿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢸⣦⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠹⣇⠀⠈⠛⣿⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠇⠀⣯⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⠀⠀⢻⣼⠂⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⠀⠈⢿⡄⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⢰⡄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣦⣤⣤⣤⣤⣤⣶⣿⣿⣿⡟⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠸⣇⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡟⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢻⡄⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠛⣴⠟⠀⠀⠀⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣉⠦⠙⠋⠀⠀⠀⠀⠀⡸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⣷⡄⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⢀⡀⠀⡀⠀⢸⠀⠀⠀⠀⠀⡀⠀⡄⠀⢰⡆⠀⢠⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣸⡇⠀⣿⠀⣸⡆⠀⡇⠀⠀⡇⠀⡇⠀⣸⡇⠀⢸⡇⠀⣿⠀⠀⡀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀
⠀⢸⡄⠆⣿⣧⢀⣿⠀⣿⣿⡄⣿⡤⢸⡇⠀⡇⠀⣿⡇⠀⢸⣇⠀⣿⡇⠠⡇⢸⣦⠀⠀⠀⠀⢀⠀⠀⢀⢰⣼⣿⢈
⡀⢸⣧⡆⣿⣿⢼⣿⡇⣿⣿⡇⣏⣹⢸⣷⣻⣿⠀⣿⣿⡇⣼⣿⡃⣿⣇⣸⡇⣼⣿⠀⠀⣠⠀⢸⠄⡆⢸⢸⣿⣿⢸
⡇⣿⣿⣿⣿⣿⣼⣿⣧⣿⣿⣇⣿⣿⣾⣿⣿⣿⡀⣿⣿⡇⣿⣿⡇⣿⣿⣿⡇⣿⣿⡇⠀⣿⣳⢸⡄⡇⢸⣿⣿⣿⢸
⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣏⣿⣿⣧⢠⣿⣿⢼⣿⣷⣾⣿⣿⣿⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠔⠒⠒⠒⠒⠒⠒⠒⠢⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠠⠐⠂⠀⠉⠀⠀⠀⠉⠁⠀⠂⠠⠀⠈⠓⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠄⠊⠀⠠⠐⠈⠀⠀⠠⠤⠤⠠⠤⠀⠀⠁⠐⠠⢀⠀⠢⢀⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡠⠂⠀⠔⠀⠠⠐⢀⠀⠄⠒⠀⠀⠀⠀⠀⠐⠀⠄⡀⠐⠀⡈⠐⢄⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠊⠀⠀⢀⠔⠁⠄⢈⠠⠀⠀⡀⠠⠤⠤⠠⠄⠀⡀⠀⠀⡀⠂⢀⠐⢄⠀⢀⠀⢄⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡀⠁⠔⠀⠔⠁⠀⡠⠀⠁⠀⠈⣁⠤⠄⠒⠂⠒⠢⠤⢄⡁⠂⢄⠑⢄⠁⠄⠑⠀⠁⡀⠠⠈⢣
⠀⠀⠀⠀⠀⠀⠀⢠⠃⡐⠀⠈⠀⠀⠐⢁⠀⡠⠊⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠑⠄⠀⡈⠀⠐⠄⠠⠀⢧
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⡀⢀⠂⠀⢠⠂⠐⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠡⡀⠀⠐⡀⠄⠀⠀⢃⠈⡄
⠀⠀⠀⠀⠀⠀⢸⣴⢶⠟⠋⠛⠲⠀⠂⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠈⠀⢀⠜⠛⠙⠻⡶⣷⡄
⠀⠀⣀⣀⣰⠶⠾⠄⠀⠀⠀⠀⠀⢘⣶⢶⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣰⡦⣶⡂⠀⠀⠀⠀⠀⠠⠷⠶⣄⣀⣀
⠀⢸⠋⠁⠁⠀⠀⡀⣀⢀⣠⣾⠧⢬⠑⡀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⠊⠥⠾⣷⣄⡀⣀⢀⠀⠀⠈⠉⠙⡇
⠀⠀⡄⡠⠀⠐⠁⠀⢰⡏⠉⠁⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠂⠀⠀⠈⠈⣻⡄⠀⠈⠂⠀⢄⢠
⠀⠀⠘⣧⡀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⢛⠶⡶⢶⣶⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠶⠶⠶⠾⡋⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠙⠛⠻⠛⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠟⠛⠋





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡭⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⠿⠟⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠑⠒⠂
⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠛⠉⠁
⠀⠀⠀⢀⣴⡾⠟⠋⠁
⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣖⣁⣀⣠⡴⠀⡀⠀⡀
⢠⠞⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣠⣤⣶⣶⣶⣿⣿⢿⣿⡟⠛⠛⠻⠿⠿⢿⣿⣿⣷⣶⣧⣤⣶⠕⠊
⠀⠀⠀⠀⠀⠀⢀⣴⣶⠾⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⠿⠁
⠀⠀⠀⠀⠐⢻⡿⠋⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣾⣿⠟⠓⠂
⠀⠀⠀⠀⢰⣿⡁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣴⣿⠯⠅
⠀⠀⠀⠀⠀⠉⠻⢦⣀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠤⣀⡈⠙⠻⠿⠿⠿⠿⠛⣁⡠⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠤⠄⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⡁⠀⠀⠀⡁⠀⠀⠀⠀⠀⢉⠀⠀⠀⠈⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⡠⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠈⢆
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⠀⡀⠀⠔⡀⠀⣀⠤⠒⠂⠉⠉⠉⠐⠂⠤⡀⠀⠈⠢⡀⠄⠠⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠄⠀⠀⠈⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠠⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⢀⣁⣈⣤⠦⣆⡀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⢠⡴⢦⣆⣸⡀
⠀⠀⠀⠀⣠⣴⡋⠉⠀⠀⠀⠑⢆⣄⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⣁⣠⡘⠀⠀⠀⠈⠉⣻⣤⡀
⠀⠠⠛⠙⠁⠀⠀⠀⠀⢠⣶⣔⠋⠈⠉⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠈⣳⢴⣦⡀⠀⠀⠀⠀⠙⠙⢷⡀
⠀⠁⠀⠄⠀⠀⠀⢠⡟⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠙⣯⠀⠀⠀⠀⠄⠀⠁
⠀⠀⢻⣄⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡼⠃⠀⠀⠀⢀⣼⠃
⠀⠀⠀⢻⣄⣀⣀⣀⢀⡹⠷⠾⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠛⠟⠻⣁⢀⣀⣀⣀⣼⠃
⠀⠀⠀⠀⠉⠙⠋⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠛⠉⠁





⣿⣿⣿⣻⣻⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣛⣿⣿⣟⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠟⠛⠉⠁⢀⣀⣀⣀⣀⣀⣀⡀⠉⠉⠛⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⢁⣠⣤⡶⠾⠛⠛⠋⠉⠉⠉⠉⠛⠛⠻⠷⣶⣤⣀⠈⠙⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⣠⡶⠟⠋⢁⣠⣴⡶⠾⠟⠛⠛⠛⠛⠿⠶⢶⣤⣄⡈⠙⠿⣦⣄⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢀⣴⠟⠋⣀⣴⠾⠛⢉⣀⣤⣴⡶⠶⠶⠶⢶⣦⣤⣄⡈⠉⠻⢷⣤⡀⠙⢷⣄⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⣰⡿⠃⣠⡾⠛⢁⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣦⡀⠉⠻⣦⡀⠙⢷⡄⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢁⣼⠏⢀⣼⠟⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠈⢿⣆⠈⢻⣆⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣼⠏⢠⣿⠃⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠹⣧⠀⢻⣇⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠇⣸⡏⢀⣾⠃⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⢹⣧⢀⣿⣦⣽⣧⣤⣀
⠀⠀⠀⠀⠀⠀⢠⣿⡶⠿⠿⠿⣿⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣠⡿⠛⠉⠁⠀⠈⠉⠙⢷⣦
⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⣀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣷⡶⠶⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀
⠀⠀⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣦
⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠙⠿⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡓⠀⣠⣿⣤⣤⣤⣤⣤⣤⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣔⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⡈⡿⠋⠉⠹⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠛⡵⣶⢦⣀⣨⣷⣧⡀⣴⣾⣿⠛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠙⠆⠸⠶⠾⣿⢿⣿⣿⡿⣿⠿⠋⣠⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠉⠁⠀⠀⠀⠐⡿⠟⠃⠀⠀⠀⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣤⠶⠓⠶⣄⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⢻⡟⢀⣛⡟⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣡⣿⣿⣿⡆⠀⠀⠀⣰⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⢰⡉⢛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡧⠀⠀⠀⢠⣾⣏⣉⣉⣽⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠟⠛⠻⣿⣿⣿⣿⣿⣶⠀⠀⠀⢸⣿⣿⣉⣽⠛⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠉⠙⣿⣿⠃⠀⠀⠀⠨⡝⠛⠛⠈⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣶⣦⣄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠿⠋⠷⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣶⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⣉⣤⣶⣾⠿⠿⠿⠿⠿⢿⣶⣶⣤⣉⠛⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⢁⣴⣿⠟⣋⣥⣶⡶⠿⠿⠿⠷⣶⣦⣭⡙⠿⣷⣤⡙⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢃⣴⡿⢋⣴⡾⢛⣭⣶⣶⠿⠿⠿⢿⣶⣮⣝⡻⣷⣌⠻⣿⣆⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢁⣾⡟⣡⣿⢋⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⢿⣮⡻⣷⡌⢿⣧⠘⣿⣿⣄
⠀⠀⠀⠀⠀⣰⠋⠉⠉⠑⢾⠿⣰⡿⢱⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡘⣿⣌⢿⣧⠊⠉⠉⠑⣆
⠀⠀⠀⠀⣠⡇⠀⠀⢀⠇⠀⠀⠈⢧⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠹⠁⠀⠘⣅⠀⠀⠀⠸⣄
⠀⠀⠀⡼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⢧
⠀⠀⠀⢧⠀⠀⠉⠑⠦⠄⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠤⠊⠉⠁⠀⠀⡼
⠀⠀⠀⠀⠑⠲⠶⠶⠶⠶⠶⠶⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠶⠶⠶⠶⠶⠶⠶⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢿⣆⠀⠀⠘⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣿⡆⠀⠀⠛⠁⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠟⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢠⣾⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣦
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⣿⡆
⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠻⠉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠟⠹⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⣸⡟⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⣾⠟⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠛⠇


⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠁⠙⠃⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠛⠃⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠸⠿⠉⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠙⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠛⠃
⠀⠀⠀⣼⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣧
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠐⠒⠒⠒⠒⠀⠠⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡁⠀⠄⠐⠂⢀⡉⠀⠀⠀⠉⣁⠀⠒⠠⠄⠀⡁⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢁⠄⠂⢁⠀⠀⠂⢈⡁⠠⠄⠀⠀⠀⠠⠤⠀⣉⠀⠂⠀⢀⠁⠂⢄⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠊⡠⠐⢈⠠⠐⠀⡁⠠⠄⠒⠂⠀⠀⠀⠀⠐⠂⠠⠀⠀⠐⠠⢈⠐⠠⡈⠢⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⢀⠄⠈⠠⠂⡀⠔⠈⡠⠀⠐⠀⠉⠀⠀⠀⠀⠀⠈⠁⠐⠀⠠⡈⠀⠄⡈⠢⡀⠐⢄⠁⡀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢠⠊⡠⠊⡠⠀⠐⠈⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡈⠀⠄⠠⡀⠠⡈⢢⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠⠁⡔⢀⠎⠠⠂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠢⡈⢄⠐⡄⠣⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⠂⡘⢀⠆⠰⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠑⡀⢂⠘⡀⢂⠐⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡥⠞⠐⠣⠮⣠⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢡⡨⠦⠓⠘⠦⣥
⠀⠀⠀⢠⠊⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⢢
⠀⢀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄
⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠈⠉⠢⢄⣀⣀⣠⡀⠀⠀⠀⠀⣀⠤⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢄⡀⠀⠀⠀⢀⡠⣀⣀⣀⠤⠊⠉

⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⣰⣯⣿⣿⡿⠿⠛⠿⢿⣿⣟⣿⣦
⠀⠀⣼⣿⣿⡷⠋⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧
⠀⠠⠟⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣤⡀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣤⠉⢿⣿⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠁⠀⠘⡿⡟⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣟⣿⢹⡄⠀⠀⠀⠀⢠⠒⠀⠀⠀⠀⠀⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦
⣿⡿⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠋⠁
⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⡄
⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⣿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⠏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣴⣡⣦⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡿⠗⠋⠀⠟⣷⣿⠸⠏⠀⣀⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⢿⠇⠐⠀⡀⣠⣤⡶⡿⠀⢀⡀⠉⠀⠉⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⣹⣧⣾⣷⣾⡟⠋⣹⠿⣁⣤⡄⠘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠘⢡⠿⡞⢿⡟⢁⡀⣠⠀⠈⢯⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⡟⢈⣴⣿⣿⡿⠀⠀⠘⣇⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠌⠠⠋⣤⡾⣿⣿⠛⣷⠀⠀⠀⣿⠘⢇⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡜⠀⡌⠀⡀⢠⣏⣼⣿⡿⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠈⢢
⣠⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⢀⣡⡞⠀⣿⣭⣿⡏⢁⣤⠀⠀⠂⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⣿⡇⢸⣿⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠻⣇⢀⣾⣿⠀⠀⠀⠀⢸⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⢠⠂⠀⣿⡿⠈⠀⢻⣌⣿⣿⠆⠀⠀⠀⠏⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠈⠂⠀⠸⣿⣧⠀⠀⢸⣼⣯⡽⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⣿⠁⠀⡄⢸⣿⣿⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⡠
⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢰⡿⠀⠀⠀⠈⠟⡵⢣⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠈
⣰⡿⠁⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠈⠇⢀⠀⠀⠀⢈⣶⣿⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣠
⠋⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢘⣿⠃⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢨⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⢿⡞⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣴⣿⣎⢿⣿
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠋⣰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⣴⣿⣿⣿⣿⣧⠹
⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⡿⠇⠀⠃⠀⠀⠀⠠⢎⡔⣱⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⢔⡄⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠠⢃⣾⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣰⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣼⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣾⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣴⣿⣿⣿⣶⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣶⣶⣤⣤⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢉⠷⢊⠵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠠⢤⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣆⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠂⢀⠈⢜⣯⠳⢾⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢨⠖⣷⣾⣯⡿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣢⢰⣿⣿⢶⣄⣺⣿⣿⣿⣻⡿⣿⣧⡿⣿⣾⢾⣿⠀⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⡄⣿⣿⣿⣿⣿⣾⠉⣻⣿⣿⣿⣿⣯⣽⣧⣟⡟⢉⣿⢠⡵⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣽⣿⣿⣿⣿⣿⣏⠙⠄⣿⣭⠟⢉⣽⣻⣿⣷⣿⠃⡼⢽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣝⣿⣿⣿⡿⠿⠃⠀⣿⣷⣾⡽⣿⣭⣤⡿⢁⢾⣲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣝⠛⠡⠀⡀⠀⣿⢤⣀⣰⠿⠛⢁⣴⣯⠝⠁
⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠙⠿⣿⡑⠲⠤⣄⣀⣉⣉⡡⢤⣔⣸⣳⠟⠁
⠀⠀⢀⣴⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠈⠑⠒⠰⠴⠿⠶⠿⠛⠋⠉
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢢⠀⠘⠀⠀⠏⢀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢁⠠⠀⠒⠈⠁⠁⠒⠠⢄⠘⠀⡄⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢒⠃⠀⠈⠁⠒⠂⠐⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠓⠀⠀⢣⠎⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠚⠑⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠤⠚
⠀⠀⠀⠀⠀⣀⣉⡁⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣀⣀⡀⠈⠃⡝⠢⠔⠃⠉
⠀⠀⠀⠀⠀⠀⠉⡠⠀⢃⠀⠀⠀⠀⠀⡠⠔⠊⠉⠀⠀⠀⠀⠉⠑⠢⣄
⠀⠀⠀⠀⡤⠒⠊⠑⠉⠐⡧⡀⠀⡴⠋⠀⠀⢀⣀⠤⠤⠤⢄⣀⠀⠀⠀⠑⢄
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠴⣡⢨⠟⠁⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠈⢢⢀⡀⣀
⠀⠀⠀⠀⠑⠢⠀⠔⠐⠋⢠⠏⠀⢀⠎⠀⢀⡤⠒⠉⠉⠉⠓⠢⡀⠀⠸⡄⠀⠀⠇⠀⠀⠉⠐⠊⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⠇⠀⡠⠋⣠⠖⠒⠋⠐⠢⡀⠈⢆⠀⢹⡀⠀⠸⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠘⠀⢠⠃⢠⠃⠀⠀⠀⠀⠀⠘⡀⠘⠀⠀⡇⠀⠀⡇⠀⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠔⠤⠼⠄⠜⠀⠀⠀⠀⠀⠀⠀⢇⣠⢇⣀⢇⣀⡰⠃⠐⠉⠉

⣉⡇⣿⠷⠆⠂⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠠⠠⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⡆⠾⣿⢸
⢙⡇⣿⣶⠄⠀⡈⠢⡈⢀⠀⠄⠁⠬⢀⣀⠤⢒⠈⠅⠀⢀⡀⠀⠉⠁⠀⢐⡀⠀⠌⢑⠂⢄⡀⠀⠀⢰⠀⠀⠀⠀⠀⢈⠆⡇⢴⣾⢀
⠉⠁⠉⠀⠀⠀⡈⢀⠔⠁⠀⠀⢀⠔⡊⠔⢈⠡⠐⢀⠉⠀⠀⠀⠀⠀⠀⠀⠠⢉⠀⠂⠌⡐⠌⡑⢄⡀⠁⢐⠀⠐⠂⡂⠀⡇⠀⠉
⠶⣦⣶⣄⡀⠀⠀⠂⠀⠀⢀⠔⡡⠊⠠⢊⠠⠐⡁⠄⢐⡀⠁⠠⠀⠠⠀⠉⣐⠀⠄⣁⠂⢌⠐⢌⠢⡉⢢⡈⠈⠂⠆⠁⠀⡇⣀⣴⣤
⣶⡟⣿⣋⠁⠀⡀⠀⠀⡔⠡⠊⡐⢁⠔⠁⠔⡁⠐⣈⠥⠐⠂⠁⠀⠀⠁⠒⠢⠍⡀⠠⡁⠢⡑⠠⡑⢌⠢⡑⠄⠃⠀⠆⠀⡇⢙⣿⢻
⡴⠇⡿⠛⠃⠀⠄⢡⠜⡐⢁⠊⡐⢁⠄⡠⢊⠔⠉⡄⠠⠀⢀⡀⠀⢀⠀⠄⠀⣜⢂⠑⢤⡑⠌⠢⡑⢄⠠⠑⡈⢆⠀⠀⠀⡏⠛⢿⠸
⠀⠀⠀⠀⠀⠀⠊⡌⠐⢀⠂⠌⠠⢁⠎⡔⠁⠀⠈⡔⡀⠀⠀⠀⠍⠀⠀⢀⠨⠁⠀⢂⠀⠙⢄⠢⠐⡈⢂⠡⠐⡈⠆⠀⠀⡇
⢉⡇⣿⡶⠄⠀⢰⠠⠁⠀⡘⠀⢁⠂⡌⠀⠀⠀⡐⠀⡠⠀⢀⠊⠀⠀⡠⡑⡠⠤⢄⠡⢂⠀⠈⢆⠡⠐⡀⡄⢃⢀⠘⡀⠀⡇⠶⣾
⠀⠀⠀⠀⠀⠀⡆⣰⠈⠁⠒⠉⠘⢼⡀⠀⠠⠡⢻⢹⢁⢡⠂⠀⠀⡐⠌⠀⠣⠤⠞⠀⠡⢂⠀⢈⠤⠏⠉⠉⠈⠈⠑⠦⡀⡇⠀⠈
⠶⡆⣦⣄⡀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢈⠀⠢⢆⠈⢉⠀⣃⣀⡀⢺⢊⠠⢄⠀⢰⠤⠄⡄⠛⠀⢅⠀⠀⠀⠀⠀⠀⠀⢀⠄⣇⣠⣴⢠
⢾⡇⣿⣉⠀⠀⠡⡀⡠⡀⠀⠠⣀⡠⠁⠀⠀⢸⠀⢨⠀⡇⠀⠁⢸⠨⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠠⠠⠤⣀⠠⠤⠄⠂⠀⡇⢉⣻⢘
⠴⠇⠿⠛⠁⠀⠀⠀⣀⠀⠀⠀⠠⠤⠀⠀⠐⠘⠤⠼⠀⠧⠤⠄⢸⢀⠀⠈⠀⠸⠀⠀⠇⡆⠀⡀⠤⠤⣀⠀⠀⢀⡀⠀⠀⡇⠙⠻⠈
⣀⡀⣀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠠⣀⠄⠀⠀⠁⠀⠀⠒⠂⠀⠀⠸⠸⠀⠀⠓⠒⠀⠀⠀⠁⢈⣈⠀⠀⣀⠀⠀⠀⠀⠈⠉⡇⠀⢀
⣩⣿⣿⡷⠆⠄⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠼⠁⠀⠀⠀⠀⠀⠇⠾⣿⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⢀⠉⠀⠀⠀⠈⢁⠀⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⣁⠄⢂⡁⠄⠐⢀⣀⡀⠐⠀⠄⢁⠂⠄⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡠⠊⠠⢊⠡⠒⡈⠤⠀⠀⠀⠠⠀⠐⠠⢀⠂⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⠌⡠⢂⠔⡡⢂⠅⡂⠬⠀⠀⠀⠈⠀⡂⢅⠢⡑⠄⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠰⢁⠂⡔⠠⢁⢊⠔⠕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⡅⠬⠴⢠⠡⠦⠦⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠄⠠⠠⠠⠄⣀
⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⡿⠿⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠟⠋⠉⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣶⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠋⠁⠀⢀⣠⣤⣶⣿⣿⣿⡿⠿⠟⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠋⠁⠀⣀⣤⣾⣿⣿⠿⠛⠋⠁⠀⠀⢀⣀⣀⣠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⢀⣤⣾⣿⡿⠟⠉⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⢀⣴⣿⣿⠟⠉⠀⢀⣠⣴⣿⣿⡿⠿⠛⠉⠉⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⢀⣴⣿⡿⠋⠁⠀⣠⣴⣿⣿⠿⠋⠁⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⠀⠀⣴⣿⣿⠏⠀⠀⣠⣾⣿⡿⠋⠁⠀⣀⣤⣾⣿⣿⠿⠟⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⢀⣾⣿⡟⠁⠀⣠⣾⣿⡿⠋⠀⢀⣤⣾⣿⡿⠟⠉⠀⠀⢀⣀⣤⣤⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⢠⣿⣿⠏⠀⠀⣴⣿⡿⠋⠀⢀⣴⣿⣿⠟⠉⠀⢀⣠⣴⣾⣿⣿⠿⠿⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠁⠀⣠⣿⣿⠋⠀⢀⣾⣿⡟⠁⠀⣠⣾⣿⠟⠁⠀⢀⣴⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⢀⣤⣿⣿⣿⣶⣶⣾⣿⡟⠀⠀⣴⣿⡿⠃⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣾⣿⠿⠛⠉⠉⠉⠉⠛⠿⣿⣷⣼⣿⡿⠁⠀⣠⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠁⠀⣰⣿⣿⠋
⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠁⠀⠈⠉⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⢰⣿⣿⠃
⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣧⣿⣿⡏
⠀⠀⠀⢀⣼⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⡅
⠀⠀⣴⣿⡿⠋⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⢻⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠃
⠀⠀⠀⠙⠿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣶⣶⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⣿⣻⣯⣽⣷⣶⣶⣶⣶⣭⣬⣍⣙⠛⢿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⢋⣥⣾⣿⠿⠟⠛⠛⠉⠉⠉⠉⠙⠛⠿⢿⣿⣦⣌⡙⠿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣾⣿⡟⣡⣶⣿⠟⠉⢀⣠⣤⣶⣶⣿⣿⣿⣷⣶⣦⣤⣀⠈⠙⢿⣿⣶⡌⣻⣿⣷⡄
⠀⠀⠀⠀⢠⣿⣿⢋⣼⣿⠟⠀⣠⣶⡿⠟⠋⢉⣁⣀⣀⣈⣉⣉⠙⠻⢿⣿⣦⡀⠙⣿⣿⣿⠿⣿⣿⡄
⠀⠀⠀⢠⣿⣿⢣⣾⡿⠃⢠⣾⡟⠁⣠⣶⡿⠿⣛⣛⣛⣛⣛⠿⣿⣶⣄⠉⢿⣿⣄⠈⢻⣿⣷⡘⣿⣿⣆
⠀⠀⠀⣾⣿⢃⣾⡿⠁⣰⣿⠋⣠⣾⢟⣩⣶⣿⠿⠿⠿⠿⣿⣿⣾⣝⢿⣷⣄⠻⣿⣆⠀⠹⣿⣷⠸⣿⣿⡀
⠀⠀⣸⣿⡏⣼⣿⠃⢠⣿⠏⣰⡿⣻⣿⡿⢋⣠⣴⣶⣶⣶⣄⡙⢿⣿⣷⡹⣿⣆⠹⣿⣄⠀⢻⣿⣇⣹⣿⣇
⠀⠀⣿⣿⢰⣿⡇⠀⣿⡟⢰⣿⢱⣿⡟⣠⡿⠋⠉⣀⣈⠉⠻⣿⣆⠹⣿⣧⢻⣿⡀⢻⣿⡀⠘⣿⣿⠽⣿⣿
⠀⢸⣿⡇⣾⣿⠀⣸⣿⠁⣿⡇⣿⡟⢰⡿⠁⢠⠞⣫⣛⢷⡄⠈⣿⣧⢻⣿⡆⢻⡇⠘⣿⣇⠀⢿⣿⡇⢻⣿⡄
⠀⣾⣿⢰⣿⡇⠀⣿⡟⢸⣿⢱⣿⠇⣿⠃⢠⡟⣼⠋⢻⡆⣿⠀⠸⣿⡜⣿⣿⢸⣿⠀⢿⣿⠀⠸⣿⣷⢸⣿⡇
⠀⣿⡏⢸⣿⡇⢸⣿⡇⣼⣿⢸⣿⢸⣿⠀⢸⢳⡏⠀⠘⣿⢸⡇⠀⣿⡇⣿⣿⠘⣿⡆⢸⣿⡇⠀⣿⣿⠈⣿⡇
⠀⣿⡇⣿⣿⠅⢸⣿⡇⣿⣿⣸⣿⢸⡧⠀⣼⢸⡇⠀⠀⣿⢸⡇⠀⣿⣷⢹⣿⡆⣿⡇⢘⣿⣷⠀⣿⣿⡇⣿⡇
⠀⠉⠁⠈⠉⠀⠈⠉⠁⠈⠉⠘⠋⠈⠁⠀⠙⠘⠁⠀⠀⠛⠈⠃⠀⠙⠋⠙⠛⠁⠙⠃⠈⠛⠋⠀⠘⠛⠁⠛⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣙⣻⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⣟⣿⣭⣽⠿⠿⠿⢿⣭⣽⣟⣷⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣟⣽⢾⣻⣽⢷⣟⣻⣿⣿⣿⣿⣛⣷⢿⣽⣻⢾⣝⡷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⣾⣯⢾⣫⡷⣞⣿⣽⠿⠶⠶⠶⠾⠿⣭⣟⡷⣯⣻⢮⣿⢮⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢯⡾⣿⢟⣵⣟⣵⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣽⡷⣝⢷⡿⣮⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣳⣟⡾⣳⢟⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⢷⡿⣞⢷⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢳⣟⡾⣽⢯⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣻⡽⣯⣷⣻⡆
⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⡼⠷⠯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⠿⠾⢯⣷
⠀⠀⠀⠀⠀⠀⠀⡼⠿⠁⠀⠀⠀⠈⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠏⠀⠀⠀⠀⠹⢄⡀
⠀⠀⠀⣠⣤⣊⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣔⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣉⣐⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⠋⠉⣁⣀⣀⣀⣀⣀⣀⣀⣈⠉⠉⠛⠳⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠉⣀⣠⡴⠶⠛⠛⠉⠉⣉⣀⣀⣀⣉⡉⠉⠙⠛⠲⠦⣤⣀⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⣠⡴⠞⠉⢁⣠⡴⠶⠚⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠶⢦⣤⣀⠉⠛⢶⣄⡈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣴⠞⠉⣀⡴⠞⠋⢁⣠⣤⠶⠖⠛⠛⠛⠛⠛⠛⠛⠓⠶⢦⣄⣀⠉⠻⢦⣄⠈⠻⢦⡀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⣴⠟⠁⣠⠞⠋⢀⣴⠞⠋⢁⣠⣤⠶⠶⠚⠛⠛⠛⠓⠶⠶⢤⣄⡈⠉⠳⢦⣀⠉⠳⣦⡀⠙⢦⡀⠙⣦⡀
⠀⠀⠀⠀⠀⢀⡼⠃⢠⡾⠁⢠⡾⠁⢠⡶⠋⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀⠙⢷⣄⠈⠻⣄⠈⢻⣄⠈⢷⡄
⠀⠀⠀⠀⢀⡾⠁⢠⡟⠀⣰⠏⠀⣴⠋⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⢧⡀⠙⣧⠀⠹⣆⠀⢻⡄
⠀⠀⠀⠀⣼⠃⢠⡟⠀⣸⠏⢀⡾⠁⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠈⢻⡄⠘⣧⠀⢹⡆⠈⢷
⠀⠀⠀⢰⡏⠀⣾⠁⢰⡏⠀⣼⠁⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢿⡀⠸⣇⠀⢿⡀⠸⡇
⠀⠀⠀⣸⠁⢠⡏⠀⣾⠀⢰⡇⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠘⡇⠀⣿⠀⢸⡇⠀⣿
⠀⠀⠀⣿⣠⡼⠗⠚⠻⠶⣼⡷⠞⠛⠛⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣧⣴⠿⠛⠛⠛⠻⢷⣄⣻
⢠⡾⠛⠛⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣀
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳
⠈⠻⠦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰
⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⣀⣴⠦⣤⡤⠶⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣀⣀⡴⠶⣤⣄⣀⣤⡴⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠐⠀⠈⠀⠀⠀⠈⠀⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠈⠀⠀⢀⡀⠤⠤⠀⠀⠀⠠⠔⠀⠐⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⢀⠠⠒⠈⠁⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠄⠀⠀⠀⠠⣀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡠⠄⠊⠤⣀⠔⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠢⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀
⠀⠀⡄⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠣⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⠒
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠊⠀⠀⠀⠀⢀⡀⠀⠈⠒
⢀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠆⠀⠀⠀⠀⢒
⡆⠀⠀⠀⠀⠘⠉⠂⠀⠀⠐⠉⠂⠀⠀⠀⠀⢈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠐⠌⠀⠀⡄⠈⠒
⢃⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠃⠀⠀⠀⠀⡀
⠀⠑⢢⡄⠠⢄⠀⠀⠀⠀⢠⡀⠀⠀⠤⢠⠃
⠀⠀⢀⡀⠀⡐⠉⠐⠒⠈⠈⠉⠀⠚⠤⠁
⠀⠀⠀⠀⠀⠂⠀⠀⡄⠀⠈⠁⠀⢤
⠀⠀⠀⠀⠀⢠⠀⠸⡸⠀⠀⡀⠀⠤
⠀⠀⠀⠀⠀⢆⠆⠀⠀⠀⠀⢁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⡴⣶⡏⢻⣿⣿⣿⣿⣷⣲⣤⣀
⠀⠀⠀⠀⣤⣾⣟⣾⣿⠁⡁⠙⣿⣿⣿⣿⣿⣹⣿⡷⣤
⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡾⠷⡀
⠀⢀⣾⣿⣿⡟⣿⣿⣿⡇⠀⠀⠠⢻⣿⣿⣿⣿⣿⠟⣡⡶⢷⡀
⠀⢸⣿⣿⣿⣧⣿⣿⣿⣿⠀⠴⠀⠌⣿⡿⠟⠛⠛⠋
⠀⢸⣿⣿⣿⣿⢛⠿⠟⠻⠇⠈⢻⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠸⠟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣶⢶⢶⢶⠶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⡶⣶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⠄⠀⠀⡀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠐⡀⠀⠀⠀⠀⠀⠐⠁⠀⠄⡈⠤⠒⢀⠩⠀⠀⠀⠀⠉⠁⠒⠀⠈⠀⠀⠄⡀⠁⠀⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡠⢊⠠⢂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠐⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⠋⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢀⠁⠄⠁⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠄⠑⢄⠀⠈⢪⢂
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⠆⠀⠁⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠌⢂⠀⠀⢡⠡⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢊⢣⠐⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⢃⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠌⠆⠀⢐⢠⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⣀⡀⠤⠄⠦⠤⠬⣠⠀⢁⢘⠀⡄⠀⠘⣐⡀⠀⢀⣀⡤⠄
⠀⠀⠀⠀⠀⠀⠓⠀⠄⠔⠘⠀⢀⢀⣀⣀⣀⠄⠀⠁⠈⠀⠀⠀⠀⠐⠀⠘⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠤⠤⠤⠀⡂⡄⠀⠀⠀⠓⠚⠁
⠀⠀⠀⠀⠀⠀⡀⠐⠀⣀⣐⣀⡀⠠⠄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠀⠀⠀⢈⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠆⠀⠀⠁⠀⠀⠀⠈⠉⠉⠒⠢⠤⣄⣀⣀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠈⠀⠀⠀⠠⠀⠄⠄⠄⠀⠠⠀⠠⠀⠠⢄⡀⣀⡀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠤⠄⠀⡀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠁⠐⠤⠠⠂⠀⠀⡀⡀⠀⠀⠀⠉⠉⠐⠐⠂⠠⠀⠤⠄⠤⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡠⠐⠀⠀⠀⠐⣀⡀⠀⠠⠔
⠀⠀⠀⠀⠀⠄⡀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠔⠀⠀⢀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡀⠀⠀⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠊⠀⠀⠀⠀⠐⠀⠀⠀⢀⠠⠊
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⢀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⠑⠤⠀⠀⡀⠀⠂⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠀⡠⠐⠁⠀⠀⠂⠈⠀⠀⠠⠀⠐⠒⠂⠀⠤⠀⠀⠁⠐⠠⡀⠈⠂⠄⠀⠀⠠
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠊⢀⠀⠊⢀⠄⠂⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠐⠠⠀⠑⠀⡀⠑⢄⠀⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠈⠂⠤⠀⠀⠂⠀⠀⡠⠀⢀⠔⠁⡠⠊⢀⠄⢊⠀⠐⠀⡀⠀⠀⠀⠀⠀⡀⠀⠂⠀⡀⠠⡀⠑⢄⠀⠢⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠁⡠⠂⠠⢂⠀⢊⠠⠀⠀⠁⠀⠠⠤⠀⠤⠀⠀⠁⠐⠠⡈⠀⢌⠢⡀⠁⠀⠐⠄⠬⠦⢀
⠀⠀⡀⠄⠀⠒⠀⠊⠀⠀⠀⠀⠀⠀⠠⠴⠀⠔⠁⡠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⡀⠓⠐⠦⠈⠀⠀⠀⠀⠀⠈⠂⠒⠂⠀⠀⡀
⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠎⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠈⢂
⡄⠀⠀⠘⠁⣴⡆⠀⠀⠀⠀⠀⠀⠀⢀⣶⡝⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢩⣶⡄⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠙
⠇⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⢀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⢀
⠐⠄⠀⠀⠀⠀⠀⠀⢹⡟⠞⠿⠀⠀⠀⠀⠀⠀⡤⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠠⠄⠀⠀⠀⠀⠀⢿⠗⠚⡿⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠈⠐⠀⠀⠀⠀⢄⠀⠁⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡀⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⠀⠀⣀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠀⠄⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠄⣀⠀⠀⠤⠂⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠈⠁⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠈
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⣀⣤⣴⠶⠞⠛⠛⠛⠛⠻⠶⢶⣤⣄⡀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣰⡟⠁⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠉⠛⢷⣄⠀⠀⠀⠀⠀⣻⣦⣴⣤⣄⡹⣧
⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⣰⡟⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⢀⣾⠋⠁⠀⠀⣉⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣿⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⠶⠾⠇⠀⠀⠀⢰⡟⠁⠀⠀⠙⣷⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡏⠀⠀⣀⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢀⣤⣶⣦⣄⠘⣷⣀⣀⣴⠆⠉⠉⠹⣧
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣷⡾⠛⠛⠙⠛⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢸⡏⠀⠀⣿⡄⠈⠉⠉⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⣨⣿⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⢻⣷⣄⡀⠀⠁⣀⣴⠟⠀⠀⠀⠀⣠⣤⣤⣤⣾⡿
⠀⠀⠀⠀⠀⠀⢀⣿⣤⣤⣾⡇⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣧⣀⣀⣀⣠⣴⣿⠟⠿⠛⠋
⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⠿⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠛⠉
⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⢀⣴⠶⠷⢶⣄⠀⠈⢻⣦⣀⣀⣠⡾⠃⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⢹⣇⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠙⠃⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠹⣿⣶⣄⡀⠀⠀⠀⣀⣤⡾⠋⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣴⣶⣿⡿⠃
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢀⣠⣼⣿⠛⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠻⣿⣿⣿⣶⣾⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠠⠤⠤⠀⠀⠠⠀⣀
⠀⠀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠤⣀
⠀⠠⠀⣀⠄⠐⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠐⠂⠠⠀⡀⠀⠀⠈⠐⠠⡀
⠀⠀⠀⠐⠄⡠⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠄⢀⡀⠀⠁⠂⠤⡀⠀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠐⠤⡤⠀⠀⠒⠒⠒⠒⠒⠂⠀⠠⠄⡀⠀⠈⠁⠂⢄⡀⠀⠑⠤⡀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠡⢄⠤⠀⠀⠀⠀⠀⠤⠄⣀⠀⠀⠈⠐⠠⢀⠀⠈⠐⢄⠀⠈⠢⡀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠒⠠⡀⠀⠈⠢⢀⠀⠑⠂⠀⠈⠢⡀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⡀⠀⠀⠀⠈⠀⠂⠄⡀⠀⠑⠠⡀⠀⠑⢄⠀⠐⢄⠀⠈⢄⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠉⠐⠢⢄⡀⠈⠑⢄⠀⠈⠢⡀⠀⠠⡀⠀⠡⡀⠀⢂⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠒⠠⢀⠀⠈⠂⢄⠀⠁⢄⠀⠈⢆⠀⠈⠄⠀⠐⡀⠀⢢⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠁⡀⠀⠱⡀⠀⢣⠀⠈⠄⠀⠰⡀⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠈⢄⠀⠐⡀⠀⢃⠀⠈⡄⠀⢡⠀⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠈⠄⠀⠠⠀⠀⡄⠀⢀⠀⠀⠀⠀⢁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠀⠀⡃⠀⠰⠀⠀⡄⠀⠃⠀⠘⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡄⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⢀⠄⠄⠼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠇⠠⣄⡀⢠⠀⠀⠶⠂⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠊⠀⠈⠀⠀⠀⠀⠀⠀⠘⠪⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠄⡀⠀⢀⠀⠀⠀⠀⢠⠂⠒⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠂⠐⠊⠁⠀⠀⠀⠑⠀⠀⠐⠂⠄⡀⣀⡀⠠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠒⠉⠉⠉⠁⠀⠈⠉⠉⠉⠑⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⢁⠠⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡁⠀⠀⠀⠄⡈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⡀⠄⠊⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠁⠂⢄⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠠⠊⢀⠔⠈⢀⠄⠂⢁⡀⠤⠀⠒⠒⠀⠒⠒⠀⠠⠀⡈⠐⠠⢀⠈⠢⢀⠈⠂⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⡠⠊⠀⠀⢁⠄⠊⡠⠐⢈⡠⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠄⡁⠐⠄⡁⠢⡀⠑⢄⠈⠠⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⠄⢀⠔⠁⠔⠁⠄⠈⡠⠂⢁⠠⠐⠈⣁⣀⣠⣄⣤⣀⣈⠁⠂⠠⢀⠑⠄⡈⠢⡈⠢⡀⠁⡀⠑⡀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⠂⢀⠂⠀⠊⡠⠂⡠⠊⡠⠊⢀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⠁⠄⠈⠢⠈⢂⠈⠄⠈⠄⠘⠄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠄⢀⠂⠠⠁⡐⢀⠌⢀⠊⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠑⠄⠑⡀⠣⠈⢂⠈⠄⠈⠄⠸⡀
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠘⣠⣶⣤⡄⡐⠀⡄⢠⠃⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⠄⠘⠀⢃⠈⣆⣴⣤⣤⠀⢣
⠀⠀⠀⠀⠀⠀⠠⣿⠞⠻⠋⠀⠈⠙⠇⡰⢀⠂⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⡀⠀⠈⠦⠋⠁⠈⠙⠟⠻⣶
⠀⠀⢠⣤⣤⡾⠛⠓⠄⠀⠀⠀⠀⠀⣀⣱⠾⠶⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣠⠷⠾⣏⡀⠀⠀⠀⠀⠀⠠⠚⠛⢷⣤⣤⡄
⠀⠀⠟⠁⠀⠀⠀⠀⠀⢀⠀⣀⣾⠷⠦⡌⢂⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⡐⠡⠶⠿⣷⣄⡀⡀⠀⡀⠀⠀⠀⠈⠻⠄
⠀⠀⠄⢀⠄⠒⠒⠁⠀⢠⡟⠉⠁⠀⠀⠀⠂⠑⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠊⠐⠀⠀⠀⠈⠈⣿⡄⠀⠀⠒⠒⠠⡀⠠⠂
⠀⠀⠐⣿⡀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⡃⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢈⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⢀⣷⠂
⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠻⣦⣤⣤⣤⣤⡴⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢶⣤⣤⣤⣤⣶⠟⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠙⢿⣶⣦⣴⣦⣤⡶⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠈⢷⣤⣴⣦⣴⣶⡿⠋