Magnet Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠾⠟⠛⠛⠛⠛⠛⠛⠛⠲⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠚⠛⠛⠓⠲⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠟⠛⠛⠛⠛⠛⠻⢷⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠒⠈⠀⠀⠀⣀⣴⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⢀⣾⣇⣀⡀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻
⠀⣼⠃⠀⠈⠉⠙⠓⠲⣶⡏⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⢀⠀⠒⠀⠀⠀⠀⠀⣰⠃⠠
⣾⣧⣀⠀⠀⠀⠀⠀⣰⠋⢧⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡼⠁⠀⢸
⢻⡆⠉⠙⠲⠤⣤⣴⠁⠀⠈⣇⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⣼
⠈⣷⠀⠀⠀⠀⠀⠹⡄⠀⠀⢸⡀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢰⡟
⠀⠸⣇⠀⠀⠀⠀⠀⢳⠀⠀⠀⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢠⡿⠁
⠀⠀⢻⡄⠀⠀⠀⠀⠈⡇⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⡀⠀⠀⠀⠉⠓⠦⣄⣀⠀⣀⠖⠁⠀⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠈⢷⡀⠀⠀⠀⠀⢹⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠙⠶⣄⠀⠀⠀⠀⠀⣨⢿⠃⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠓⢦⣀⡴⠚⠁⠸⡀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢰⡇⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⣧⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⡀⠀⠀⠀⡇⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⣿⣴⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠾⠟⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠿⢿⣭⡛⠻⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠈⠙⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⣶⡷⠶⠶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⢠⡼⠋⠁⣠⡾⠋⠀⠀⠀⠀⠈⠙⠻⣷⡀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⣧⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡿⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⣷⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣸⣠⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠶⢦⣤⣄⣼⣤⡤⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠴⠶⠟⠛⠛⢻⡅⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠉⡏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠈⡇⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣀⣀⣤⣧⣴⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣤⣤⣄⣀⣿⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⢀⣤⣶⡟⢻⣇⣀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⡇⠀⠀⠀⠀⣿⠻⣷⣴⣿
⠀⠀⠀⠀⠀⠈⢛⣿⠇⣈⣽⡿⠀⠀⣼⢿⣿⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡄⠘⢷⣄⠀⠀⠀⣿⣠⣄⠀⣿⠀⠀⣾⣷⣾⣆
⠀⠀⠀⠀⠀⢠⣾⣷⡾⠋⠁⠀⢀⣼⡟⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠇⠀⣠⡿⠃⠀⠀⠛⠋⠹⣧⢸⡇⠀⢸⣧⣤⡹⣆
⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠸⠿⠻⡿⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢃⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠈⠋⠉⠻⣿⣷⡀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠀⠀⠈⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣵⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣿⡟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠶⠤⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄⡀
⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⢠⠎⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣤⣀⠀⠀⡠⠊⠀⠉⠓⢦⡀
⠀⡞⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡾⢤⡀⠀⠀⡠⠚⡇
⠀⣇⠀⠀⠀⠀⠀⠘⣶⠒⠒⠊⠉⠉⠉⠉⠓⠒⠲⠤⢤⣄⣀⠀⠀⠀⡇⠀⠙⠶⠊⠀⢀⠇
⠀⡙⣄⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠧⣄⡀⠈⠀⢀⡼
⠀⢧⠘⢦⡀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠚⠉
⠀⠘⢆⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠙⠒⠤⣀⡀
⠀⠀⠈⠳⣄⠀⠈⠑⠢⢄⡀⠀⠀⠀⡠⠊⠀⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠘⣍⠓⠊⠭⡁⠀⠐⠒⠒⠒⢢⡄
⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠉⠑⢲⠯⣀⡀⠀⠀⣀⠴⠋⡇⠀⠀⠀⠀⠀⢀⡠⠔⠋⠁⢠⣤⣶⠀⠁⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⢸⠀⠀⠈⠁⡎⠀⠀⢀⡇⠀⠀⢀⣤⠖⡁⣀⠀⠀⣀⣀⣀⠈⠉⠉⠒⠂⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⢦⣀⠀⠀⡇⢀⠴⠋⠀⠀⠀⠀⠓⠐⠐⠀⠒⠒⠒⠒⠀⠘⠋⠓⠶⠶⠶⠶⢒⣚⣓⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠗⠁






⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠛⢿⣄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢿⡇⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⢟⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠈⠳⣄⠀⠀⠀⠀⣠⠖⠋⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠈⠳⣄⡴⠞⠁⠀⢀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠀⠀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢘⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠷⣦⡀⠀⠀⠀⠀⠀⣀⠔
⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠈⠻⣄
⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⣸⣇
⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⣰⢹⣿
⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⣰⠃⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⠀⠀⠀⠀⠀⢀⡼⠃⠀⢨⡿
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠑⢦⣀⠀⢠⡟⠀⠀⢀⡾⠁
⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁⠀⠀⠀⠀⠀⢈⣷⠋⠀⠀⣠⡾⠁
⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⠟⢰⡄⢀⣴⡟⠁
⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⣄⣀⠀⠀⠀⢀⣀⣠⣴⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠈⣧⣾⠏
⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣠⣿⠟
⠀⠀⠀⠀⠀⠈⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣝⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠚⠉⠀⠀⠀⣀⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣬⣉⠛⠛⠓⠲⠶⠶⠶⠶⠖⠚⠛⠉⠁⠀⠀⠀⢀⣠⣴⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣶⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⣤⣶⡾⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⡏⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠛⠛⠛⠛⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣼
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⡟
⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣼⠃
⠀⠀⠀⠀⠀⡟⠙⠛⠛⠒⠒⠲⣿⣄⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢠⡟
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡇⠈⠳⣄⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢀⡾
⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⣸⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠈⠻⣿⣙⠛⠓⠶⠿⢤⣀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠙⠳⢦⣄⡀⠀⠀⢀⡞⠁⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠷⢦⣤⣤⣤⣭⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠈⠙⠳⢦⣞⠁⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⢠⠟⠹⡆⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠳⠦⣤⣀⠀⠀⣠⠋⠀⠀⢷⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⠉⠙⢻⡇⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣀⣷⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠛⠋⠉⠉⠉⠉⠛⠒⠦⢤⣀
⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄
⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⣀⠤⠄⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⡰⠁⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢄⡀⠀⠀⠀⠀⠀⠈⠳⣄
⢠⠃⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠈⠣⡀
⣼⠀⠀⠀⠀⠀⢸⠀⣀⡤⠤⠴⠶⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠙⢆
⡏⠀⠀⠀⠀⠀⠸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠈⢣
⡇⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⢀⣳⡀
⢳⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⢨⠖⠊⠉⠁⠀⢳⡀
⠘⡄⠀⠁⡀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⡆⠈⡄⠀⠀⣀⢤⡇
⠀⠸⡄⠀⠈⢦⡀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⢘⠂⠉⠀⡸⠁
⠀⠀⠙⣄⠀⠀⠑⠀⡀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⡌⠀⠀⣠⠇
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠈⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠓⠊⠉⠁
⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠈⠢⣀⡠⠖⠉⠀⠀⠑⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠓⠠⣀⠀⠀⠀⠀⡀⠽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣸⠀⠀⠀⠁⢲⠖⠉⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⠦⠤⢤⡟⠫⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⢸⠀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡀⢸⡧⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣠⠀⡇⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢆⠀⡴⢲⡀⢸⡛⠫⣉⢹⡄⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠛⠀⠀⢇⠀⠙⢦⡀⢹⠃⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡰⠒⢄⠈⢆⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡸⢠⠤⢄⡑⢌⣆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣟⣁⣀⣀⣉⣓⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠾⠟⠛⠛⠛⠛⠻⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣤⡶⠶⠛⠛⠛⠶⣦⡀⠳⡄⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⢻⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⣰⠋⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⣰⠃⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⢠⠏⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⡞⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⡼⠰
⠀⠀⢠⡟⠀⠀⠀⠀⠀⢸⠃⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⡼⠁⢰
⠀⠀⣸⠇⠀⠒⠒⠒⠒⣿⡀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⡼⠀⠀⣸
⠀⠀⣿⠀⠀⠀⠀⠀⢰⠇⢣⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⢀⡼⠁⠀⠀⣿
⠀⢀⡏⠀⠀⠀⠀⠀⢸⠀⠀⢱⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢄⣀⠀⠀⠀⢀⡞⠀⠀⠀⣸⡟
⠀⢸⡇⠀⠀⠀⠀⠀⠸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠈⠙⠲⣤⠏⠀⠀⠀⢠⡟
⠀⠸⣯⠀⠉⠁⠀⠀⢣⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⡴⢹⡀⠀⠀⣰⡟
⠀⠀⠘⢷⡀⠀⠀⠀⠀⢣⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣃⠀⠀⠀⠀⠀⢀⠞⠀⢸⡅⠀⣰⠏
⠀⠀⠀⠀⠻⣦⣀⣀⣀⠀⢃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠉⠐⠠⣀⡔⠁⠀⠀⠀⠇⣼⠋
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠸⠀⠀⠀⠀⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⡆⠀⢀⣴⠏
⠀⠀⣰⠃⠀⢠⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⢡⣠⡞⠁
⠀⢰⡏⠀⠀⢨⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠋
⢀⡾⠁⠀⠀⣸⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⣰
⠠⠃⠀⠀⠀⡿⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣸⠁⠀⢰⠃⠀⠀⢰
⠀⠀⠀⠀⠜⠁⠀⠀⠸⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⡿⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣁⡀⠀⢀⡴⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠈⠉⢳⣾⠁⣰⠋⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣠⣯⢈⡿⠁⠀⠀⠀⠀⢀⡾⠁⠈⠙⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣰⠃⢈⡟⠀⠀⠀⠀⠀⢀⡞⠳⢤⣀⣠⡏⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣰⠋⢳⡟⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⢈⡿⣆⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢰⠿⣄⡾⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢀⡾⠀⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣾⢦⣸⡇⠀⠀⠀⢠⡞⠁⠀⠀⠀⢀⡞⠁⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠘⢦⣙⣇⢀⣠⠶⠋⠀⠀⠀⠀⢠⡞⠙⣦⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⡴⠋⢳⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢧⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣗⠶⣤⣄⣀⣀⣠⡤⠴⢾⡉⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣧⡀⠙⣦⠀⢀⣀⣷⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⢀⡄⠀⢀⡀⠀⣀⡄⢀⡤⠀⣠⠄⠀⣠⠀⢀⡄⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⢡⠖⠋⢠⠴⠋⢠⠞⠉⠴⠋⠠⠞⠁⠠⠞⠁⠴⠋⠀⠾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡈⠃⠀⠉⠀⠅⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠁⠀⠀⠀⠀⠀⠉⠉⠁⠐⠒⠀⠀⠄⣀⠀⠹⠆⡑⣄⠀⠠⣼⠀⠁⠀⠀⠀⠀⠀⠆⡤
⠀⠀⠀⠀⠀⠀⠀⣰⠡⠀⠀⠀⢀⣠⠰⠒⡰⡲⡦⠠⠄⠀⠀⠀⠀⠀⠂⠌⣁⡐⠦⠬⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠛⡐⠠⠀⠀⠻⣄⣔⠁⢌⡄⠨⡂⠀⠀⠀⠈⠀⠲⠖⠉⡀⠀⣀⣠⠤⢖⣿⠀⣀⠀⢀⠀⡄⠈⠱⠠⣄⠀⣠
⠀⠀⠀⠀⠀⠀⢸⠀⠈⠐⢄⡀⠀⠀⠈⣉⠳⠖⠤⢄⣄⠀⠀⠀⠀⠀⠀⠀⠀⣯⠝⢑⢑⣿⠛⠉⠀⠀⠀⢈⡡⠒⠒⠂⠤⣉⡀⠁⠀⠂⠤⢀
⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠈⡐⠪⢅⡀⣀⣤⠰⠂⣩⠷⠤⣀⠀⠀⢀⠀⠀⡥⠀⠠⣽⠀⠀⠉⠒⠢⠦⠁⡀⠀⠀⠀⠀⠀⠈⠉⠒⡄⠀⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠡⢐⠀⡀⠀⡇⠀⠀⢸⠅⠐⢕⢄⣴⡧⠀⠊⠉⠉⠛⠲⠄⣹⣠⠼⠻⡀⠀⠀⠀⠘⠀⠂⠀⠁⠂⠄⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠀⡃⣄⠀⢸⠠⠀⠓⢱⠉⠒⠄⢀⡀⠀⢀⠠⠔⠊⠁⠀⠚⠷⠂⢥⣀⣀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⣼⣫⣤⠮⠼⢀⠀⠀⠀⠈⡟⠂⠤⣐⠂⠠⢀⠀⠀⠀⠀⠉⠑⠊⠓⠂⠐⠉⠀⠀⠀⠀⠀⣀⠞⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠝⠀⠀⠀⠀⠀⠀⡘⠠⠀⠀⠀⡆⠉⠀⠀⠉⠁⠒⠤⢀⡀⠀⠠⠠⠀⠀⡀⠀⠀⠀⠀⣀⡤⣺⢃⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠐⠀⢀⡆⠑⠢⢄⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠤⠤⠄⠔⢖⠒⠋⡉⣰⠃⠂⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢘⢁⠀⠀⠀⢀⡀⠖⠺⠀⠀⠀⠀⠈⠑⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⡠⠀⠠⡀⠐⠐⠁⣨⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡐⢢⠛⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⣀⡀⠀⠀⠀⠊⠄⠄⠔⢐⢀⣈⠼⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠋⠚⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⢀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠂⠀⠄⠀⢀⠄⢀⠅⡂⠅⠠⠐⠀⠀⠠⠐⠀⠠⢀⠄⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠂⠄⠈⢐⠄⡢⢀⠄⠂⠔⡠⢀⠄⡈⠀⠠⠐⠜⠀⠠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠂⡀⠀⡐⠣⠀⠀⡠⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠤⠁⠀⠈⠂⠀⠀⠑⠀⠀⠀⢂⠀⠔⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⢀⣀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⡀⠀⣀⣤⠴⠚⠋⠁⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠱⣄⠤⠚⠁⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⡇⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑
⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⢀⣰⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠶⣄⡀⠀⠀⠀⠀⠀⢠⠊⠁
⠀⠀⠀⠀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠑⢆
⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠄⠂⠁
⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⣠⠋⠀⣠⠞⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢀⠾⡟⠀⠀⠀⠀⠀⣀
⠀⣾⠁⠀⠀⠀⠀⠀⠀⢰⠃⢀⡴⠁⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⢀⡞⣼⠃⠀⠀⠀⠉
⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⣰⠏⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⢠⡞⣰⡏⠀⢠⠤⠤⠄
⣸⡇⠀⠀⠀⠀⠀⠀⠀⣵⠃⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⢀⡞⣄⣿⣀⠀⡀
⣿⣧⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⢀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⢠⠞⢀⣿⠁⠀⠈⠁
⣿⠸⡆⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⣾⠏⠀⠀⠀⠀⠀⠀⣠⠏⢀⡾⠃
⢸⡄⠘⣄⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠀⠀⠀⠀⢀⡴⠃⢀⡼⠁
⠈⢷⡀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣦⣤⣤⣤⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢠⠏
⠀⠈⢷⡀⠄⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢀⣰⠋
⠀⠀⠈⢷⡄⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠀⢀⡼⠃
⠀⠀⠀⠀⠹⣆⡀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠘⣠⠞⠁
⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠈⠉⠲⠦⣤⣀⣀⣀⣀⣀⣤⠴⠖⠋⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⣤⣤⣄⣀⣀⣀⣤⣤⡴⠖⠋⠁
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠉⠀⠀⢸⡀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡤⠚⢁⡙⢄⠀⢳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢷⠛⠀⣳⣾⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡴⠊⠁⠈⠳⣄⠀⠱⣄
⠀⠀⠀⠀⢀⣠⠴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠳⡄⠈⢳⡀
⠀⠀⠀⢰⠋⠀⠀⢸⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠘⢦⡀⠹⡄
⠀⠀⠀⢸⠀⣠⠴⠚⢢⡀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠱⣄⢹⡀
⠀⠀⠀⠘⢏⠁⠮⠤⡄⠙⢦⡞⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠈⠣⣧
⠀⠀⠀⠀⠈⠳⡀⢊⡠⠖⠉⠙⢄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠘⢯⡀⠀⠀⠀⠀⠳⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠈⠳⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣸⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠳⣄⠀⠙⢦⣀⠀⠀⠀⠀⠀⢀⠴⠁⡴⠃⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠳⢄⡀⠉⠓⠶⠤⠖⠊⠁⣠⠞⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠉⠓⠦⠤⠤⠴⠒⠋⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⠤⣤⣤⣤⠤⠴⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠒⠒⠚⠉⠉⠉⠉⠉⠉⠙⠒⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠊⠉⠀⠀⠀⠈⠉⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢇
⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡄
⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⠤⠔⣇
⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢀⣀⡤⠴⠒⠚⢉⣹⠀⠀⠀⢻
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠙⢿⣄⡀⠀⣀⣀⣸⣤⣅⣀⣀⢸
⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡴⡹⠻⢦⣌⣩⡿⠉⠉⠉⠉
⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣟⠜⠁⠀⠀⣽⣟⠢⣄⡠⠤⠖⠚
⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢻⣀⣠⠤⠾⠛⠊⠙⠺⢕⣦⡀
⠀⠀⠀⠀⠀⠘⡆⠀⢀⡀⠀⢀⣀⡤⢽⡗⠚⠉⠁⣀⣸⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦
⠀⠀⠀⠀⠀⠀⠸⣤⡿⠛⠉⠁⠀⠀⢸⢹⣤⡶⠿⣟⢇⢹⡀
⠀⠀⠀⠀⠀⢀⣴⠿⣕⠢⣀⠀⠀⠀⣘⣘⣄⣀⣀⠘⡌⡎⢇
⠀⠀⠀⠀⠀⠚⠃⠀⢻⡙⠺⢷⣟⡛⠛⠉⠉⢉⣁⣠⠼⢿⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣀⣨⡿⠶⠒⠋⠉⠀⠀⠀⠈⢷

⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⣀
⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⢸⣿⣿⣿⣿⣿⡋⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣦⡀
⢸⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣄
⠀⢻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⢄
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠘⢿⣿⠋⢢⡀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠛⠋⠙⢄⠀⠀⠀⠀⠀⠀⠹⣄⠀⠱⠄⣲⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠁⠑⢄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⠷⠓⠊⠁⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠳⡀⠄⢰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣴⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⡆⠈⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⠙⠢⣜⢏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡦⡀⠀⠀⠀⠀⠀⠀⠘⢷⢦⡀⠀⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣵⡝⢦⠀⠀⠀⠀⠀⠀⢠⡷⠌⠢⣀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢀⣑⣄⠀⠀⠀⠀⠀⠙⢦⠠⡬⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡄⠈⠀⠀⠀⠀⠀⠀⠀⠱⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⠉⠉⠉⠉⠐⠒⠒⠲⢤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢋⢗⢜⠖⠔⠒⠈⠐⠀⠀⠀⠀⠀⠀⠀⠁⠈⠩⢙⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⣷⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡩⢿⣶⡀
⠀⠀⠀⠀⠀⠀⢠⠋⠀⠋⠀⠀⠀⠀⠀⠀⣠⡤⡖⢖⢶⢲⣲⣤⣄⡀⠀⠀⠀⠀⠀⢐⡥⣻⡝⣦
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢠⠾⣱⠷⠛⠋⠉⠉⠉⠙⠛⠻⢷⡄⠀⠀⠀⣠⡺⢊⣿⡫⣧
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⡧⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⢪⡺⢋⣴⡵⣩⣟⢺⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡿⣙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢘⡵⡫⣫⢞⡴⣧⠱⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣟⢼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣨⢊⢖⡵⣫⢚⡷⡱⡇
⠀⠀⠀⠀⠀⢸⢐⠕⡻⡪⢞⢕⢟⣯⠲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢜⠕⡫⣪⢕⣽⠣⡘⡇
⠀⠀⠀⠀⠀⢸⡤⣪⢎⠔⠕⡡⣫⣷⡑⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠗⡣⡪⢞⡵⡫⣾⠣⣹
⠀⠀⠀⠀⠀⠀⣏⠕⡵⡢⢪⢞⠕⣿⣮⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡫⢊⢔⡵⡫⣺⠣⢣⡇
⠀⠀⠀⠀⠀⠀⢹⠛⠛⠛⠛⠛⠛⢻⠳⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠞⠓⠛⠛⠚⡿⢧⣲⠁
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢸⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⡇⠠⡏
⠀⠀⣀⠤⠒⢁⣄⢧⣀⣐⣋⢊⡃⣸⣆⣷⢴⣄⠳⡀⠀⠀⠀⠀⡤⣄⠘⡄⠀⠰⠴⠲⠀⡇⡤⡇
⣠⠔⠛⠁⢰⣷⣤⣿⠙⣍⣭⣝⣻⣻⣇⢟⠋⠁⠙⣅⠀⠀⠀⢸⣴⣿⣔⣿⡷⣖⢶⣿⢿⢽⣞⣓⣀⣬⠓⢄
⠀⠯⣭⡝⣣⡞⣿⣟⢲⣽⠿⢷⡿⣿⣿⡾⢄⡴⢲⣌⠀⠀⠀⡠⢟⡭⠿⡾⢿⣿⢿⣿⢿⣷⣯⣉⡟⣤⠀⠀⠉⡦
⠀⠀⠘⠛⠁⣠⠽⢦⣿⣻⢾⡻⣷⠹⡉⠙⠛⣧⣞⡘⠀⠀⢾⡄⠀⠀⢀⢿⠟⠿⣼⡏⣼⣿⣿⡿⠿⠃⠆⠀⠈⠳⠤⣀
⠀⠀⠀⠀⠆⠛⠋⠉⠁⠙⠛⢣⢻⡶⠇⠀⠀⠀⠉⠀⠀⢰⠟⠠⠖⢴⡷⠃⠀⠷⡟⠙⠋⠙⢯⢣⠀⠀⠀⠀⠀⠀⠀⣒⣭
⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠉⠀⠐⡷⡆⠀⠀⠀⠀⡩⠃⠀⠀⠀⠀⣀⡀⠀⡤⡄⠀⠀⠘⠿⠇⠚⠀⢤⢤⠀⠀⠈⠢
⠀⠀⠀⡜⡴⠁⠀⢀⡠⣄⡠⣔⡮⠆⠀⢹⡘⡤⡀⠀⠀⠁⠀⢰⣖⠢⣕⢾⡷⠀⠳⣞⣦⡀⠀⠠⣶⣾⡿⠿⣿⡇⣀
⠀⡰⢿⣼⡇⠀⠀⢸⢱⣾⠋⠁⠀⠀⠀⢷⣘⡿⠇⠀⠀⠀⠀⠁⠀⠀⠈⢩⢗⣳⣮⠽⣿⣷⣢⡀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠈⠛⠯⠀⠀⠀⠀⠉⡥⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠿⡃⠈⠷⡾⠷⢃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡿⠯⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁
⠀⠀⢀⣤⢠⣀⣀⡀⠀⠀⠉⠀⢀⣀⣀⠤⣖⡆⠀⠀⠀⠀⠀⠀⠀⢠⢤⣔⣪⠜⠂
⠀⢠⡜⠾⠟⠛⠛⠛⠁⠀⠀⠀⡏⢦⡿⢋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⠟⠀⠀⠀⠀⠺⢭⣖⣒⣞⣱⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃
⠀⠀⠀⠀⣀⠔⣢⠔⣊⠔⣊⠤⢊⡠⢒⠤⢚⠤⢊⡤⢒⡠⠒⣡⠔⣋⠔⣢⠖⣠⠔⡡⠔⣡⠔⢁⠔⣪⠔⣩⠖⡡⣂⢔⠄
⠀⠀⠀⠀⠀⠈⠀⠋⠑⠊⠁⠚⠁⠚⠁⠚⠡⠚⠡⠖⠡⠔⠊⠴⢊⡥⠊⡤⠊⠤⠊⠴⠊⠠⠚⠁⠚⠑⠊⠁⠋⠈⠁⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠌⣧⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⡧⠀⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣜⠮⠁⠀⠀⢀⣴⠖⢀⡠⠐⢀⠀⣄⡴⡀⠀⠀⠀⣷⠀⠀⠀⠀⡄⡀⠀⠠⢀⠀⠶⣄⡀⠀⠀⠈⢕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⡁⠐⢁⣄⠀⠀⠄⢉⠈⠀⠁⠀⠀⣿⡀⠖⠀⠉⠀⠓⠀⠀⠀⠈⠢⡈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠛⢦⣌⠡⠘⠁⠡⣀⡄⠆⠒⢙⡂⠀⣿⡓⠃⠓⠬⣤⣀⠎⠀⠐⢏⠦⣠⠏⡈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠔⢁⣀⠀⡙⢦⣐⡤⠃⡡⡔⢀⠧⠌⠃⠀⣿⡗⠣⠽⡒⢠⣉⠒⢤⠃⣠⣞⠁⠀⠈⢄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡌⠞⠀⢈⡢⠙⢷⣾⡔⠉⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠉⠢⠓⣠⡾⢟⠁⠀⠺⢃⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⢑⠞⢡⣂⠄⠙⢿⣦⣀⠄⠂⠀⠀⣿⣿⠐⢠⠀⠀⣠⣾⢯⠁⡈⢖⡁⠀⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢄⡄⠉⠒⠌⢠⣁⠃⠀⠀⠀⠙⢿⣷⣄⠀⠀⣿⣿⠀⠀⣠⣾⡟⠁⠀⠩⣑⡈⢇⠒⠉⠀⡀⠀⠀⢀⡀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⠀⡖⠂⠀⢨⠁⣦⡄⠀⠀⢠⠁⠀⠀⠙⢿⣷⣶⠋⠁⣠⣾⡿⠃⠐⠀⠀⠀⢃⣠⢨⡅⠀⢩⣣⠀⡄⢸⡇
⣉⣽⠿⠆⠀⠀⣀⣀⣀⣿⣠⣤⣤⣬⣥⣴⣾⣶⣶⣷⣶⣾⣿⣿⣿⣿⣄⠀⠙⢿⣠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠈⠈⠀⠋⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⢰⠶⡶
⣉⣻⣶⠆⠀⠀⠀⠀⠀⣶⠀⠀⠠⢤⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠉⣧⡀⠈⠻⣿⣿⣿⣿⡿⠿⢿⣿⢿⡟⠛⠻⠿⠛⠛⢙⡏⠉⠉⠉⠁⠀⠻⠀⠇
⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠠⠀⡒⣃⠈⠨⡆⢢⢥⠀⠀⠈⢆⣠⣿⠿⠁⢀⣴⠻⣿⣧⡄⠀⢀⠐⠀⠀⠀⣆⡌⠸⠅⠁⡰⡒⠀⠃⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠹⡌⢤⢆⠀⢠⣾⠟⠁⡀⠰⣿⣿⠀⠈⠛⢿⣦⡀⠀⠀⢀⢌⡔⠠⠏⠐⠢⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢚⣥⠀⠒⠱⢌⢲⣷⠟⠁⠀⠀⠁⠘⣿⣿⠀⠀⠂⠀⠙⠿⣦⡀⠢⠄⡠⠉⠂⣀⠐⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⢠⠰⢀⠔⣺⠟⣁⠠⣑⠦⢀⠀⠀⣿⣿⠀⠀⠀⢀⡀⢔⡉⠿⣦⡈⠑⢄⠠⣪⠊⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠐⢄⠀⣠⠞⣁⠚⠁⢓⠤⡁⠚⠩⠱⣿⣿⠀⠸⠈⠝⠐⣈⢴⠚⠈⠛⢦⣀⠀⠀⡐⢁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡴⢋⠘⢠⠐⠀⠎⠀⠀⠋⠋⠲⢸⣿⠀⠒⠂⠋⠹⠈⠀⠳⠰⣊⠓⠈⡷⣌⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠛⢷⣄⠑⠀⡀⠀⠸⢱⡄⡠⠀⠂⣸⣿⠀⡀⠁⢠⠄⢶⠰⠄⠀⡀⠄⢉⣠⠾⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡞⡠⡀⠀⠀⠈⠛⠀⠀⠈⠐⠀⠄⢀⡀⠈⠚⣿⠀⠃⠀⢀⡁⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⢀⠤⡙⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣈⣉⣿⢈⣉⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣍⣻⠆
⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⡿⠿⢿⣿⠿⠿⠿⠿⣿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⣤⣶⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡠⠒⠉⣉⠭⠝⠳⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡠⠊⠀⠀⣀⡀⠀⠈⠳⡀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠟⠛⢻⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠰⠁⢀⠔⠛⢢⠀⠑⡀⠀⡇⠈
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⠃⠀⡞⠀⠀⡸⠀⢀⠃⠀⡇
⠀⠀⠀⠀⠀⠁⣼⣿⣿⣿⣿⡟⠀⠀⢰⣿⣿⣿⣿⡿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡸⠁⢀⠎⠀⡸⠀⠀⢠⠃⠀⡘⠀⣸⣁
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠁⠀⢠⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⢀⣜⠀⢠⠃⠀⢀⠏⠀⢰⠁⢠⠇
⠀⠀⠀⠀⢠⠏⠀⣼⣿⣿⠇⠀⠀⣾⣿⣿⣿⣿⡏⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢠⠇⠀⠰⠀⢑⡏⠀⠀⡞⠀⢀⠇⠀⡞⠀⠀⠀⠘
⠀⢰⠀⢀⡏⠀⣰⣿⣿⡟⠀⠀⣼⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡎⠀⢀⠃⠀⡼⠀⠀⡸⠓⠒⡾⣄⡸
⢇⠈⠄⠸⢶⣶⣿⣿⡿⠁⠀⣰⢿⣿⣿⣿⣿⠁⣀⠀⠀⠀⠀⠀⠀⠀⢢⠈⠆⠘⢆⠒⠚⢄⢰⠃⠀⢰⠃⠀⠰⠁⢠⠃⢀
⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⣯⣿⣿⣿⣿⠇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢧⠤⠤⢇⠀⡎⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠶⠶⠲⠶⠶⢶⣶⡶⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠈⢧⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢀⡖⠋⣠⡞⠁⠀⠀⠈⠉⠻⣆⠀⠀⠀⠀⠘⡇⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢠⠏⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣷⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣾⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣀⣀⣧⡤⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠓⠲⠦⣤⣼⡤⠶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⠉⠉⢹⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢀⣀⣸⣦⡴⠇⠀⠀⠀⠀⠀⠀⠀⠘⠷⢦⣤⣄⣀⣸⣡⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⢀⣠⠶⣦⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⣿⣄⣠⡄
⠀⠀⠀⠀⢛⣿⢀⣽⠗⠀⣼⢿⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠘⢷⡄⠀⢸⣧⣌⠹⡇⠀⣶⢶⡆
⠀⠀⠀⣠⣾⠿⠋⠀⠀⣼⣯⡄⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣠⡾⠋⠀⠈⠁⠘⣧⣧⠀⢷⠶⣽⣆
⠀⠀⠘⠛⠁⠀⠀⠀⠀⠈⢸⢇⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠞⠉⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠈⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠂⠉⠉⠉⠉⠐⠒⠒⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⣕⢔⠕⠗⠃⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⢍⡻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⡰⠋⡸⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠛⣷⣄
⠀⠀⠀⠀⠀⠀⡜⠀⠈⠀⠀⠀⠀⠀⢀⡤⡖⣞⣟⣛⣻⣲⣶⣤⡀⠀⠀⠀⠀⠀⢵⣼⣟⢷⡀
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣰⢟⡼⠛⠉⠁⠀⠀⠀⠉⠉⠙⢷⡀⢀⡀⣰⡿⣫⣾⣕⢷
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢠⢏⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⡾⢋⢴⢟⠵⡷⣽⠇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠢⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢖⠕⡱⣫⢞⡟⢌⡇
⠀⠀⠀⠀⠀⡇⢀⢀⢀⠄⡀⣠⡴⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠑⡧⡪⢚⢕⠵⡏⢬⡇
⠀⠀⠀⠀⠀⢃⢐⢕⠅⡨⡪⡫⢿⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡪⣪⢔⠕⡡⣺⠌⢮⠃
⠀⠀⠀⠀⠀⠸⡠⡪⣪⢊⢄⢔⢽⡗⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⣞⢕⡥⡪⣪⣏⢎⡞
⠀⠀⠀⠀⠀⠐⣯⠼⠵⠵⠵⠧⢾⣯⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣓⣵⣧⣮⣮⣾⣇⢪⠃
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡛⠉⣺
⠀⠀⠀⣀⠄⠀⠸⡀⠀⠤⠤⠢⠀⡇⣿⣀⡀⢄⠀⠀⠀⠀⢀⣀⡀⢀⠀⠀⣀⣠⡀⡇⣀⠏
⢀⡠⠿⠀⢰⣏⣱⣟⢟⣓⡒⠶⢾⡟⡿⡖⠋⠲⡃⠀⠀⠀⣼⣰⣧⢼⣦⣤⢤⣤⡶⣳⡿⠧⠀⡐⢤⡀
⠁⣖⣒⡶⣋⢿⣿⡧⣜⣿⣯⣽⣿⣿⣧⣁⣠⢤⡙⠀⠀⠀⡩⣟⣩⣯⠿⣾⣿⣿⣶⣿⣟⡛⡿⡁⠀⠈⠲⣄
⠀⠀⠻⠟⠉⣈⠯⣹⣿⣷⡖⣿⡘⡛⠓⠒⣧⣜⡸⠀⠠⢎⡀⠀⠀⣸⣶⢾⢅⣿⢱⣟⣿⡿⢷⠇⠆⠀⠚⠤⣀
⠀⠀⠀⠀⠜⠓⠚⠋⠉⠒⠻⣸⣧⡷⠀⠀⠈⠉⠁⠀⢴⠏⠠⠄⣴⡝⠁⢸⣼⠛⠋⠙⢯⢧⠀⠀⠀⠀⠀⠀⠐⣭⡒
⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠉⠁⠀⣶⣆⠀⠀⠀⠀⡹⠂⠀⠀⠀⣀⣀⠀⣠⣄⠀⠀⠈⠻⠇⠈⠀⣠⢄⠀⠀⠙⢄
⠀⠀⢀⠜⡜⠀⠀⣀⢤⣠⣤⣢⠆⠀⢸⣜⣦⡀⠀⠀⠀⠀⢶⣦⣬⣽⣿⠆⠘⢯⣦⡀⠀⠀⣖⣶⠿⠿⣾⠄⡀
⠀⡼⣽⣾⠀⠀⠀⡏⣶⡟⠁⠀⠀⠀⠸⣞⠿⠃⠀⠀⠀⠠⠀⠀⠀⠈⠵⣒⣶⠽⡾⢗⡲⣄⠀⠀⠀⠀⠀⠈⠈
⠀⠈⠛⡋⠀⠀⠀⠈⢩⢢⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠼⣋⠀⠻⠾⠗⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⠓⠒⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⢠⢖⣲⣤⣤⣄⠀⠀⠀⢀⡤⣤⣖⣮⠇⠀⠀⠀⠀⠀⠀⠀⣖⣶⡮⠞⠁⠀⢀⣀⠀⠀⢀⡀
⠀⠰⠈⠛⠋⠈⠉⠁⠀⠀⠀⠺⣑⡾⠡⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠛⠁⠀⠀⠀⠘⠒⠲⠥⣯⡼⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⠅
⠀⠀⠀⠀⠀⢀⠀⢀⡠⢀⠀⢀⡀⢀⠀⢀⠀⣀⠀⣀⠀⣀⠀⢀⡀⣀⠀⡀⠀⡀⠀⡠⠀⡠⠀⡠⢀⠄⣀⠀⡀⡀
⠀⠀⠀⠀⠂⠵⢊⠵⢊⠵⢊⠥⢂⠥⣊⠕⣊⠔⢊⠕⢊⡠⢊⡥⢊⠥⢊⠔⢊⠔⣉⠔⣉⠔⣫⠖⡡⢎⡴⠫⠊⠞⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠿⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣁⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠒⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⢀⣴⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠒⠲⡆⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠋⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠙⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⡀⠀⠀⠀⠀⢀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁

⠀⠀⠀⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠓⣁⠫⠀⠀⢠⡷⡆⢸⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⡠⡀
⠀⠀⠀⠧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣹⠀⠀⠀⠑⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠐⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢄⡄⠂⠀⡀⠀⠀⠀⠑⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡀⠀⠀⠀⠀⠀⠀⢶⣾⣵⠆⠀⠀⠀⢰⣾⣧⡆⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⣸⣤⠀⠀⠀⠀⠀⣰⣧⡄
⠟⠠⡀⠀⠀⠀⠀⢨⡿⢿⢠⠤⠂⠀⠈⣿⢿⡅⠂⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠈⠽⢍⠀⠀⠀⠀⠀⡹⠽⡁
⠀⠀⠀⠀⠀⠀⠀⢸⡤⢼⢈⠀⠀⠀⠈⡧⠤⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢿⠀⠀⠀⠀⠀⡧⢿⡇
⡄⣤⣤⣠⠀⠀⠀⢸⡇⢸⢰⠀⠀⠀⠀⡇⠀⠀⡆⠀⠀⠀⠀⠀⢰⠀⢀⢄⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⡇⣾⡇
⠅⢻⠄⢉⢤⠀⠀⢸⠅⠸⠘⠀⠀⠢⢀⡇⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠐⠾⠃⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠃⢹⡇
⠀⠢⠋⠀⠀⠀⠀⠘⣇⠀⠑⠦⣤⡴⠞⠁⡐⠠⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢢⡊⠳⣄⠀⠠⠊⢀⡼⠁
⠂⠀⠀⠀⠀⠀⠀⠁⠊⠳⠦⠠⠀⠄⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⠤⠴⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣢⡴⠶⢤⡠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠳⢠⠀⠸⠀⢀⠄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿

⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠙⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡟⠀⠀⢀⡤⠴
⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠈⠇⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢀⡤⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⢿⣀⣀
⠀⠀⠤⠀⠀⠀⢇⣀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⢤⣄⡀⠀⠀⡴⠢⠤
⠀⠀⡄⠀⠸⡆⠀⠀⠀⡞⠉⡷⠀⠀⠀⢰⠀⢸⠀⠀⠀⠀⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠈⠳⠤⡄⠀⠤
⠀⠀⠹⣄⣠⠟⠀⠃⠀⠀⠐⠃⠀⠀⠀⠈⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⢀⡴
⣀⡀⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⡴⠒⢦⠀⠀⠀⠠⣀⠈⡷⠀⠀⢠⡏⠀⠀⡠⠀⠀⠀⠀⠀⡇⠀⢰⠂⠀⣀
⠀⠣⠀⠀⠀⠀⢧⡀⠙⠀⠀⠀⠀⠒⠀⢣⡀⠀⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⠶⠊⠀⠀⠀⠀⠀⠀⠳⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠂⠀⠀⠀⠀⢀⡴⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠴
⠀⠀⠀⢠⠁⠀⡠⠀⠀⠀⠀⢠⠄⠀⠀⠐⠀⠀⠀⠀⠀⠘⠢⠖⠁⠀⠀⠀⢸⠇⠀⢸⡇⠠⠄⠀⠀⢀⣀⣀⠀⠀⠀⠣⠤
⠀⠀⠄⠀⠉⠉⠀⠀⠀⠀⠁⡏⠀⢀⡏⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠘⠁⠀⠀⠀⠀⣿⠀⠈⠳
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠚⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠐⠋⢙⡆⠀⠀⠀⠀⠀⠀⢀⡖⠒⠦⠀⠀⠀⣸⠃⠀⡴⠀⠀⠀⠀⠄⠀⠀⠀⡀⠐⣄⠀⠀⠀⠀⠀⠀⢰⡟⠉
⠒⠀⠀⠀⠀⠚⠉⠀⠠⠀⠀⠀⠀⠀⠀⠓⠦⠄⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠊⠀⠀⠀⠀⠀⠀⠈⠳⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠐⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⡋⠓⠂⠀⠀⠀⠀⠀⣇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠
⠴⠤⠴⠃⠀⠐⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠈⠀⠀⠈⠉⠀⠠⠄⠀⠀⣠⠶⣄⠀⠀⠀⠸⣤⠼
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠈⠀⡠⠟
⠀⠀⠀⠈⢆⣀⡧⠀⠀⠀⣀⣀⠀⠀⠀⠀⡆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠁
⠀⠀⠀⠀⠀⠁⠀⢀⠀⠸⣇⠈⠑⠀⠀⠀⠣⠤⠃⠀⠀⠀⡤⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢧⣀⣸⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡤⢤⡀
⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣴⣼⡶⠧⡀⠀⠀⠀⡠⠔⠢⣤⡀⠀⠠⠀⣀⣀⡀⠀⠂⠀⠀⢀⠀⠀⠠⡕⠆⡶⠼⢷⣲⣦⡆
⠀⠀⠀⠀⠀⠀⠐⠒⢤⣤⣭⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠅⣨⡥⢌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠚⢿⣿⡀⠀⠀⠀⠀⠀⠀⠐⠒⢠⣢⣦⡤⠀⠀⠀⢠⢀⣢⡌⠁⠴⠒⠈⠀⡀⠀⠀⠀⠀⠀⣸⣿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠔⢂⡽⡿⣻⣽⠙⠚⠘⣅⠀⠤⣀⠀⠩⢉⣉⢉⠛⠃⠈⣉⣉⠠⠴⣂⣥⡦⢋⡵⠃⣰⠛⢟⠛⡏⠹⡀⠙⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⢂⠈⠃⠀⠘⠙⠳⠆⠠⠨⠭⠍⠭⠭⠄⠺⠭⠙⡁⢐⠟⠁⡴⠃⡐⠰⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠃⠘⠂⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂



⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣀⣀⣸⣧⣼⣥⣼⣷⣯⣿⣭⣿⣧⣧⣼⣟⣵⣮⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠂⠁⠀⢴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣆⠤⠂⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⣀
⠀⠀⠀⢀⡠⠴⠚⠋⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⣀⡀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡝⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠽⣶⣄⠀⠈⠛⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠆⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢺⣿⣟⠒⠊⢩⡆
⢀⣤⣶⣾⣿⣿⣿⣿⣿⠀⠀⢸⡇⠀⠀⠒⠦⢄
⢮⣉⠉⠛⠛⠛⠛⠟⠛⠂⠀⠈⠋⠀⠀⠀⠀⣠⡧
⠈⠛⠻⠷⢶⣶⣶⣤⣀⣀⣀⣀⣠⣤⣤⠴⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⡋
⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢸⢀⠞⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⢀
⠆⠴⣡⡏⠀⠀⠀⡀⣁⠀⠀⠀⠀⠀⠀⠀⡄⠀⡁⠀⠀⠐⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠤⡠⡀
⢺⣜⢹⡁⠀⠀⠀⠆⡭⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⢄⡐⢦⢠⠀⠀⢤⠀⠀⡢⠁⠨⠐⠄⠄
⠋⠁⢈⠀⠀⠀⡄⡩⢴⠀⠀⠀⠀⠈⣶⠾⠂⠀⠁⠀⠘⠙⠂⠀⠀⡠⠼⠀⠐⠎⠲⠐⠺⠂
⠀⠀⢰⠀⠀⠀⠃⠤⠞⠀⢀⠀⠀⡸⠿⠃⠀⠀⠀⠀⠀⠀⠈⠥⠐⠖⢤⠀⡄⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠐⠀⠀⢂⠀⠀⠀⠂⢷⠄⠆⠀⠐⠉⠩⠉⠉⠢⠰⡄⠀⠀⠀⠫⠥⡒⠠⠈⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⣀⠀⡇
⠐⠢⠄⣄⢀⣠⡄⠩⢧⣀⡀⠀⠀⠀⠀⠀⠀⠢⢄⡁⠔⠠⠀⢀⣀⣅⠀⠀⡀⠀⠈⢧⡀⠀⠀⡀⠀⠀⠴⠂⡟
⠰⠀⠴⠶⠜⠶⠧⠀⡷⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠠⢐⠀⠤⠀⢀⠀⡉⠖⠀⢀⠇⠀⠀⠰⠀⠀⠐⡁⡇
⠐⠂⠂⢀⠰⡴⠄⠀⣷⠤⠂⠒⠂⠒⠒⠐⠂⠐⠒⠒⠖⠒⡻⢶⣶⣶⠅⣀⣵⠲⣶⣿⣾⣿⠰⡞⠁⠀⢩⡁⡇
⠀⠀⠀⡄⠀⠀⠀⠀⡿⠀⠀⢠⣺⣻⣿⡆⠀⢰⠁⠀⢰⠛⢋⢸⠋⣨⠉⠀⢀⡼⠛⢩⡟⢹⠀⠀⠀⠀⢠⠄⡇
⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⣯⡝⠧⢻⠇⠀⠸⠀⠀⠀⢀⠤⠐⠐⠈⠛⣨⣥⣷⣼⣯⡅⠸⠀⠀⢀⠀⠀⠀⡇
⠉⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠐⠀⠀⠈⠀⠀⠐⠀⠀⣠⡜⠸⠖⠇⠢⣥⠞⠑⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣳⠇⠀⠀⠂⠀⠀⠀⠢⢄⠢⡀
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠈⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⡀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡨⠤⠼⠃⠀⠀⠠⠀⠀⠀⠁⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠛⣛⢻⣿⣿⣿⣿⡟⣿⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⠶⣤⠀⠀⠀⠀⣤⠶⣤
⣿⣿⣿⣿⣿⠒⠒⢺⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣭⣭⣭⠀⠀⠀⠀⡍⠛⢩
⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⡇⠀⢸
⣿⣿⣿⣿⣿⡄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⠀⢀⠇⠀⠸
⣿⣿⣿⣿⣿⣷⡀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⡆⠀⠀⡠
⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠃⠐⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠒⠛⠂⠀⠀⠀⠀⡶⠿⢶⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣬⣽⣿⣿⣿⣿⢋⣠⡙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⣇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⡰⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣾⣿⢟⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡀⠀⠀⠐⠰⠜⡐⠀⠀⠠⠚⠃⠀⠀⠀⠀⣠⣞⡡⢪⣾⠭⡁⠠⣀⠈⠁⠀⠀⠀⠀⠀⠒⠒⠦⠄
⠀⠀⠀⠀⠃⡀⡄⠀⠀⢈⠷⠀⢀⣤⡀⡄⠀⠀⠀⢿⢡⢀⣻⠻⣷⣤⣌⣙⣀⠆
⠀⠀⠀⠀⠀⣸⡡⠀⠀⠘⠀⢰⠇⠉⠋⠀⠀⠀⠀⢾⠢⢈⣽⠂⢘⣯⣿⣟⣉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠃⠀⠀⠀⠀⠀⠀⠀⠛⢿⡧⠰⠻⢃⣤⣤⠍⠀⠀⠀⠀⠀⠘⠲⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠋⠀⠀⠀⠀⠀⠀⣀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠠⢂⠀⣂⠀⠀⠀⠀⠘⠷⠓⠁⠀⢠⣰⣩⣶⡶⠋⠁⢲⡆⢰⡔⣖⢒⠂
⠀⠀⠀⠀⠀⠀⠀⠸⢀⡿⠀⠠⠒⠒⠀⠀⠀⠀⢸⣝⣽⠃⠸⢧⣠⣤⡶⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⢡⣿⣆⣼⡟⠩⠍⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠈⠉⠁⠉⢻⠲⠶⠛⠁⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠸⠀⢠⠃⠀⢀⡤⠴
⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠂⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⡤
⠀⠀⠂⠀⠀⠘⢄⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠚
⠀⠀⠀⠀⡀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⢀⠆⠀⠀⠀⠀⠀⠰⠀⠀⠐⠒⠦⡀⠀⢰⠋⠓
⠀⠀⣆⠀⢹⡄⢀⠀⠚⠀⡏⠀⠀⠀⢡⣀⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡤⠃⠀⠈⠉⠂⠀⠘
⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠒⡄⠀⠀⢠⠞⠁⢀⡀⠀⠀⠀⠀⡆⠀⡀
⠙⡆⠀⠀⠀⢸⡉⠑⠄⠀⠀⠀⠄⠘⡅⠀⠣⠀⠀⠀⠁⠒⠁⠀⠀⠘⢤⡴⠋⠀⠀⠀⠀⠘⢄⣠⠇⠀⠘
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⠀⠀⠀⢠⠴⢦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡠
⠀⠀⠀⢐⠁⢀⠀⠀⠀⠀⢠⠀⠀⠀⠂⠀⠀⠀⠀⠈⠢⠒⠀⠀⠀⠀⣿⠀⢠⡇⠠⠄⠀⠀⢀⣀⡀⠀⠀⠸⠤
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⡏⠀⢠⠃⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⣏⠀⠙⠆
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠄⢀⣀
⡀⠀⠀⠀⠉⣀⠽⠀⠀⠀⠀⠀⠀⢰⡉⠑⠂⠀⠀⢸⡁⢠⠏⠀⠀⠀⠐⠀⠀⠀⢄⠈⣆⠀⠀⠀⠀⠀⠀⣏⠁
⠁⠀⠀⠀⠀⠀⠀⠀⢁⡠⣄⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠉⠛
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠠⠜⠀⠀⠀⠀⠀⠀⣠⢄⡀⠀⠀⠀⠀⢰⠀⠀⡆⠀⠀⠀⠀⠀⠀⠐⠂
⢀⣀⣩⠆⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠀⠀⠀⠈⠂⠐⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⡇⢸
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠊⢀⠇⠀⠀⠀⠉⠉
⠀⠀⠀⠠⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠤⠂
⠀⠀⠀⠀⠉⠉⠀⠀⠠⣏⠙⠂⠀⠀⠸⢀⡼⠀⠀⠀⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣸⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⡠⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠪⠁⠀⢀⡀⠈⡁⠈⠀⠀⠉⠉⠈⠁⠅⠀⠤⠤⠡⠀⠉⠁⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠁⡐⢀⡠⢌⡀⠀⠐⠀⠀⠀⠀⣀⡒⠐⠀⠐⠈⠀⠀⠀⠀⠀⠀⡄⠄⡀⠈⠉⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠⢀⠀⠀⠀⠀⠘⠈⠀⠰⠀⠀⠀⠀⠀⠐⠂⠠⠠⠀⠃⠀⠀⠀⠀⢀⠠⠀⠀⠀⠔⠁⠠⠀⠀⠲⡀
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠄⠁⠀⠀⢨⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⢀⣀⠐⠀⠁⠀⠀⡀⠀⡐⠈⢠⠃⠀⠈⠂⠀⠈⠣
⠀⠀⠀⠀⠀⠞⠀⠀⠔⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠠⠀⠁⠀⠀⠃⠀⠙⠀⠋⢡⡐⠂⡀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⡀⠁⠈⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⡀⢂⢂⢂⡐⣂⣁⠀⠂⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢐⠀⠀⠂⠐⠒⠘⡀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠄⠄⠂⠀⠀⠄⠀⠀⠀⠀⠠⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡌⠀⠀⠈⠥⠀⠄⠄⠈⠉⠉⠈⠀⠉⠀⠀⠀⠀⠀⠈⠀⠌⠀⠀⠀⢀⠉⢀⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠁⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⢰⠁⠀⠀⠀⠀⠙⠒⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀
⠀⠀⠀⠆⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⢀⣀⣀⠀⡐⡀⠀⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠈⠈⠉⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠢⠀⠀⡀⠈⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⠀⠐⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⢀⣀⠐⣀⠀⠀⠀⠀⡤⠤⠄

⢀⠀⢀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⡀
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⡟⠠⢾⣿⣿⣿⣿⠷⠈⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣴⣟⡀⠀⠀⠀⠀⣹⣧⡀
⣿⣿⣿⣿⣿⣿⣿⡖⢠⣾⣿⣿⣿⣿⣧⡀⢾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣹⡟⠀⠀⠀⠀⠀⠹⣯⠁
⣿⣿⣿⣿⣿⣿⠟⠓⠛⢿⣿⣿⣿⣿⡟⠓⠚⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣤⣭⣤⠀⠀⠀⠀⠀⣤⣬⣥⡀
⣿⣿⣿⣿⣿⣿⣥⣤⣤⢸⣿⣿⣿⣿⣇⣤⣤⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠿⠿⠻⠀⠀⠀⠀⠀⡿⠛⠻⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⢻⣿⣿⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡁⠀⠀⡀⠀⠀⠀⢀⠇⠀⠀⠃
⣿⣿⣿⣿⣿⣿⣧⢿⣿⣷⣭⡟⣻⣵⣿⣿⢏⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⠢⠤⠔⠊⠀⠀⡜
⣿⣿⣿⣿⣿⣿⣿⣷⣝⡿⢿⡯⣿⡿⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⣀⠀⣀⠤⠊
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡁⠀⠀⠀⠀⣘⣷⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⠰⢿⣿⣿⣿⣿⠆⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣹⡟⠁⠀⠀⠀⠀⠘⣿⡅⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠆⣰⣿⣿⣿⣿⣿⣦⠐⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣭⣤⡄⠀⠀⠀⠀⢠⣬⣥⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⠚⠛⣿⣿⣿⣿⣿⠛⠓⠛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡟⠛⠛⡇⠀⠀⠀⠀⠸⠛⠛⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣠⣤⣄⣿⣿⣿⣿⣿⢠⣤⣤⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠇⠀⠀⢇⠀⠀⠀⠀⡄⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⣿⢿⣿⣿⣿⡿⣸⣿⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⠓⢢⠔⠊⠀⠀⡰⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣎⢿⣿⣷⣽⣛⣯⣿⣿⣿⣣⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⣸⣀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣝⡿⢿⠿⣿⢿⣻⣵⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣟⣿⣻⣻⣛⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣿⣿⣟⣛⣻⣟⣛⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⡿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⢀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡷⠠⠗
⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⢾⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⣴⣶⣦⣀⣚⡉⠙⠛⠙⠉⠋⠻⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠻⠃⣠⣀
⠀⠛⠛⠓⠛⠲⣿⣶⣿⣿⣦⣿⣶⣧⣶⣶⣶⣷⢤⣶⣶⠶⠶⠾⠃
⠀⠀⠿⠀⠀⠀⠈⠉⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣬⣿⣿⡇⠄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢐⡇⠀⣿⣿⡇⠄⣀⣠⣤⣤⣤⣴⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡁⠀⢿⣿⣿⣾⣿⣿⣿⠿⢿⣿⣿⣿⣯⣭⡅
⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠉⠁⠀⠀⢀⣿⣿⣿⣿⣷⠖
⠀⢀⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠋
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣸⣿⣿⠛⣿⣿⠛⣿⣿⣧⠀⠀⠀⠀⠀⢠⠀⠀⣤⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢹⣿⣿⡀⢿⣿⠀⣿⣿⡟⠀⠀⠀⠀⠀⢸⡅⠀⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠻⣿⣷⣤⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣽⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠉⠀⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢇⡀
⠠⢠⠠⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣀⣀⣀⣸⣦
⠀⠀⠃⣢⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠠⠾⢿⣿⣿⢿⡿⠿⠓
⠀⢀⡀⣰⡠⠀⢉⣐⡶⠟⠀⠀⠀⡀⠀⠀⠀⠀⠀⠆⢀
⠲⠈⠥⣦⣼⣲⣩⣉⣔⠶⣎⣡⠄⠀⢀⠀⡀⢀⠀⠀⠈⡔⠀⠘⠂
⠀⠚⠅⠾⡞⠛⢻⣿⣧⠄⣤⡄⠴⢗⣀⠀⠀⠸⢀⢀⠀⢹⠀⠀⠀⠈
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠂⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠔⠀⠀⠀⠀⠀⠀⠀⠐⡀⠂⠀⠐⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠⠂
⠀⠀⠀⠀⠀⠠⠂⠀⣠⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤⢢⠀⣠⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠄⢢⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠁⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠁
⠀⠀⠀⠀⢀⠐⠀⠀⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⡱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⡐⠁
⠄⢴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⡠⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊
⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠈⠀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠁⠜
⠀⠀⠀⠀⠠⠚⠬⠂⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠄⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠔⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠣⠔⠐⠟
⠀⠀⠀⠀⠀⠀⠀⢀⠔⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⢔⠄⠀⠀⠀⠀⠀⠀⠀⢈⠀⡀⠀⡠⢂⠄
⠀⠀⠀⠀⠑⠄⠉⠀⠀⠀⠀⠀⢀⠄⠀⢀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠉⠀⠊⠀⠀⠀⡀⠀⠀⢀⠀⠀⠠⠀⠁⠀⠈⠀⠀⠀⡀
⠁⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠊⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠊⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑
⡀⠊⡑⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⡠⠊⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⠐⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠊⠀⠀⠀⢠⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⢀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⣠⠀⠀⠐⠀⠠⠐⠀⠀⠀⠀⡀⢄⠀⣀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠠⠋⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠁⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠄⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⢡⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠡⠁⠀⠀⠀⠀⠀⠀⠀⠐⡀⠠⠀⠈⠠⠁
⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡂⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡢⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡢⠀⣤⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⢔
⠀⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠄⠁⠀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠠⠐⡅⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡁⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡱⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠁⠀⡶
⠀⠀⠀⠀⠀⠈⠀⠀⡔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⡔⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠢⠀⠀⠀⠌⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⢀
⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠄⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠜⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠌⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡

⡀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡈⠀⢀⣄⡀⠀⠀⢦⠀⠈⠶⣀⠀⢀⠀⠀⣤⠐⣄⢀⣦⢀⢀⡄⠀⣴⢠⣶⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡴⠀⢀⣀
⢁⠘⣻⣿⣡⡄⠀⠈⠙⠁⠀⠛⠃⠉⠛⢶⣄⠀⠀⠹⣤⠙⢷⡀⣦⣀⠈⡆⢹⠈⣿⠀⣾⡏⢸⣟⠈⠁⠈⢀⠀⠰⠆⠀⠁⠈⣼⠃⠀⠀⢀⠰⢃⡰⠆⠈
⠀⠘⠠⠶⠀⠛⠛⠃⢉⣉⡉⠐⠦⣀⡐⠙⠿⣉⣱⣦⡹⠇⠈⠁⠛⠟⠘⠇⠛⠀⢹⣷⡉⣴⣎⠉⢠⡷⠀⠀⠀⠰⣾⠗⣀⠚⠁⠀⠀⢰⠀⠀⣾⢃⡼⢠⡄
⠋⣀⠀⠳⠦⠜⢳⣄⠴⠁⠄⠀⠈⠀⢀⡘⠶⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠁⣼⠿⣩⡀⠀⠐⠀⣀⠞⠁⠀⠈⠁⢀⣰⠇⡀⠛⢀⡴⢀⡁
⠁⢀⣀⠀⠀⣠⣏⠀⠀⠻⠚⠛⢿⣺⡿⠛⠋⠀⠀⠀⠀⠀⢠⡄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠾⠏⢠⡾⠇⠐⠋⠀⠴⠂⠀⠠⠟⠁⢤⠀⠴⠀⠀⣸⣷
⣰⡏⠀⠀⠛⠁⠀⠀⢀⣁⣀⣀⣠⠄⠉⢀⣠⣤⣶⡿⠿⣦⣴⠶⠈⠉⠠⢤⡴⠊⠙⠂⢀⣀⠀⠀⠀⠀⠀⢀⣴⠟⠃⠀⡀⠀⠀⠀⠙⠤⠀⠚⠀⠸⠿⠏⢀
⢈⡿⡏⠀⠀⣠⡀⢈⣡⠛⠋⢠⡄⠀⠄⠀⢠⡴⠋⠀⠘⢋⡄⠀⣤⢀⠀⡀⣀⠀⠀⠃⠀⢤⠀⠀⠀⠀⠀⠻⣁⣠⡴⠆⠈⠳⠄⣠⡄⠘⠁⠤⠒⠂⠀⢘⡋
⠉⠀⡧⠀⠊⠀⠔⠋⡥⠘⠱⠟⠀⢠⠀⠀⣾⠃⢰⠏⠰⠛⠁⢸⠁⢈⠘⠛⠉⠠⣆⡀⠀⠀⣴⠀⠀⠀⠀⠀⠈⠉⣠⡴⠞⠃⣈⡥⠀⠀⠀⠀⠛⠁⣠⠾⡁
⡆⠀⠀⠀⠀⠀⠀⡈⠀⢀⠀⡀⠀⡀⠀⢸⠇⠰⠃⣠⠎⡀⡴⠇⣠⠏⠀⣀⡴⠟⠉⢷⠄⠘⠁⠀⠀⠀⠀⠀⠀⢛⣉⠠⡆⠀⠉⠀⠄⠀⠀⠀⠦⠞⠁⠀⢀
⠀⠸⠀⠀⠀⠀⢰⡇⠀⠀⣆⠀⠀⠃⠀⠀⢀⡤⠘⣡⠆⠀⢀⣜⠻⠟⠁⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⠤⠀⠀⠀⠀⠀⠟⠀⣀⠴⠆⠛⠃
⡀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠛⠀⠂⢰⣦⠀⠸⠁⠞⢁⠄⣠⠋⠁⣀⡴⠀⠀⠠⠂⠙⢃⣠⡆⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢀⣀⠀⢀⠀⠠⠞⢋⠀⢆
⠀⡢⠀⠀⠀⠀⡄⠈⠀⠀⠀⢰⠆⠘⠀⡀⠀⣠⠾⢃⡼⠋⡀⠀⠀⠄⠀⢀⣀⡀⠀⣈⣉⡁⠀⠀⠀⠀⠀⠀⠀⢰⣦⠜⣃⠀⠀⠀⠀⠄⠀⠀⢠⠄⠰⠶⠛
⠂⠰⠄⣀⠀⠀⢀⡀⠐⠄⠀⢸⡀⠠⠀⠁⠀⠁⠀⠛⢁⣠⣀⠠⠀⣀⠁⠈⠀⠀⢀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠘⠁⠀⠀⠀⡀⠚⠛⠃⠀⠄⡀
⠛⣀⡀⠈⠂⠀⠈⠳⡄⠀⠀⠈⣄⠀⠀⠀⠐⠀⠀⠞⠛⣉⠀⠀⡀⠀⠤⠀⠀⠈⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠒⠚⠀⠰⠋⡀⠀⠀⠶⠾⠋
⡄⠈⠻⣤⡀⠀⠀⠀⠘⣦⡀⠀⠛⢠⠀⠀⠄⠀⢠⡔⠛⠁⠐⠀⠀⠀⠄⢀⣤⡤⠤⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⢶⠖⠠⠤⠜⠀⠀⠂⠀⣤⠄⠀⢀⠈⠛⠃
⡁⠀⠶⣍⠁⠈⢦⣀⠀⠈⢳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠾⡟⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠢⠄⠀⣀⠀⠀⢈⡁⠤⠆
⠀⠲⣤⡈⠀⢀⡀⠈⠓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠠⠦⠀⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠓⠠⠂⠀⢠⣀⢀⠈⠀⠀⠂⠀⠁
⠠⣄⠘⠳⣄⡀⠙⠶⡄⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠄⠀⢀⡀⠀⠀⠀⠀⠠⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⣝⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⣦⢄⣀
⢠⣄⡀⠴⠈⠙⠀⠀⠰⢄⡺⢿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣊⠉⠀⠀⠀⠀⠐⢿⣛⠟⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⠂⠘⠓⠀⠈⢁⡤⠄⠀⠀⢀⣡⠄
⠀⠉⠙⠓⠀⠀⠀⠘⠢⣀⠱⡤⠉⠀⠀⠀⠀⠀⠀⠀⠈⣥⣭⣥⠀⠀⠀⠀⠀⠀⣼⢟⡇⠀⠀⠀⠀⠀⠀⠀⣠⣭⡥⠤⠐⠲⠄⠀⠀⠀⢤⣤⡄⡄⢀⡂
⠀⢀⠀⢀⠈⠛⠂⢀⡐⠛⠿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡤⠄⠚⠂⠐⠒⠀⠉⠹⠃⠀⠀⠀⠀⠀⠀⠀⠿⢛⡓⣒⣀⡀⠀⠒⠂⠀⠀⢙⣿⡗⠋⣁⡀
⠂⠘⠣⠀⠀⠔⡐⠀⠙⠢⠄⣀⠙⢃⠐⠂⠀⠀⠀⠀⠀⢨⣤⡶⡶⠒⠂⠐⠂⠐⢚⠻⡇⠀⠀⠀⠀⠀⠀⠀⢠⣤⠅⠈⠉⠁⠀⢠⠀⠀⠛⠋⣫⣤⡟⠈⠁
⠄⠠⠀⠀⠀⠺⠧⠄⠐⠒⠀⢤⣿⣾⣄⠀⠀⠀⠀⠀⠀⠀⣹⣞⣀⡄⠀⠀⠐⠶⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⡷⢂⡀⠤⠗⠚⠋⠉⠙⠿⠠⠍⢡⡀⡛⠂
⠀⠀⠀⢤⣀⠀⠂⠄⠀⠀⠀⠀⠌⠙⣧⠀⠀⠀⠀⠀⠀⠘⠻⠋⣉⣀⣀⣀⢠⣤⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⣀⣶⠌⠁⠀⠀⠀⠀⠀⠀⢠⡤⠄⠉⠉⠁
⠀⠺⠷⢦⣈⠙⠳⠀⠘⠓⠶⠦⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡉⠉⠉⠉⢀⣬⣭⣼⠁⠀⠀⠀⠀⠀⠀⢠⣿⣷⣤⠀⠶⠗⠚⠒⠾⠟⢡⣀⠀⠀⠚⠓⠢
⠉⢳⣤⠤⠈⢥⡴⠦⠀⠀⠐⢶⣮⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⣫⣥⣤⡄⠉⠛⠩⣿⣿⠆⠀⠀⠀⠀⠀⠀⠸⣿⡿⢦⣤⣤⡤⣶⡶⠟⠂⠀⠙⠓⠚⠛⠛
⢀⣈⠉⠒⠐⠒⠒⠀⠀⠤⠄⣀⠀⢈⣉⡄⠀⠀⠀⠀⠀⠀⠀⣽⣿⣯⣅⣀⠲⣴⣬⣿⡄⠀⠀⠀⠀⠀⠀⢰⣿⠗⠒⠀⠤⠤⣤⣤⣄⣺⠒⠾⠒⠀⠘⠓⠛
⣈⣉⡀⢀⣠⣤⠠⣤⠄⠀⢀⡉⠷⠚⣽⡇⠀⠀⠀⠀⠀⠀⠀⣹⣿⡷⢤⣍⣡⣽⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣯⣀⡀⠀⠀⠀⣠⣍⣩⣐⣶⣦⠈⠛⢛⡂
⠉⠉⠉⠉⣉⡉⣤⠤⠀⠀⠀⠀⠠⣏⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣂⣀⣀⣴⣾⣿⡄⠀⠀⠀⠀⠀⠀⢠⣿⠟⢭⠍⠈⠀⢩⡭⠙⠛⣉⠉⠉⠀⠉⣉⡁
⠓⠒⡤⠺⠋⠉⠑⠂⠈⠉⠁⠉⠛⠻⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣍⣉⣽⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠠⡤⡤⠀⠀⠀⣨⣉⡀⣤⣍⠁⢩⡟
⠾⢥⠤⣶⡌⠛⠛⠛⠛⠟⠒⠐⠒⠲⣿⣷⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣛⠛⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⡀⠀⠀⠀⠈⠉⠅⠉⣥⣯⣤⣤⡬⣁
⣦⣴⠆⠈⠓⠀⠀⠒⠲⣶⣾⡶⠶⠾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠹⣿⣿⡀⠀⠉⠿⠿⠾⠳⠶⠤⣤⣤⣤⣄⠀⠐⣁
⡶⠒⠊⡉⠀⢉⣀⢲⣀⣀⣠⣤⣶⣤⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢰⣿⣿⡁⠀⠐⠲⢤⣤⣤⣄⠀⣤⣈⡁⢘⣃⡀⠉
⠀⢀⣈⣡⣴⣏⣩⣿⡿⠛⠋⠀⠈⠉⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⠨⣧⣤⣄⣀⠀⢀⠃⢤⡄⡙⠻⠿⠁⠶
⠿⠿⠋⠱⠿⠛⢯⣍⣥⣤⣶⢄⣤⣤⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⡀⠐⠀⠘⠻⣿⣍⠑⠶⣦⣥⣤⣀⣰⡄
⢠⣶⣶⡶⠀⣀⣴⣟⣉⣴⠶⠾⠟⠛⢉⣿⣿⣧⣤⣀⣤⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⡟⠶⠶⣦⣄⡙⠿⠛⢿⡿⢢⣍⠙⢿⣶
⢒⣮⡿⠒⣚⣿⢿⡿⢋⣡⡤⢀⣤⣶⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⢿⣿⣿⣍⠻⣆⣠⣠⣹⡿⢧⡄⠀⠁⠒⢈⣹⠖⠿
⣿⡇⠀⠚⠉⣡⣼⣷⡟⢉⡶⣧⠟⢁⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⢀⣾⣿⠇⠈⡇⢻⣿⣤⡞⢄⠹⠏⠁⢿⡏⠀⠀⠻⣾⣍⣷⣶
⣯⡜⢠⣴⠟⢻⠿⠃⣴⣾⣶⢋⣤⣛⡷⢉⣿⣹⣟⠀⠟⠈⣿⡷⣘⣿⣿⣏⣉⣉⠉⣁⣤⣤⣿⣿⣿⡇⢰⡇⢰⣿⣿⣿⣦⡉⠿⠀⠀⠻⣧⡄⢢⡉⢻⡉⠛
⢫⣼⣏⠉⣼⡟⣤⡼⠛⣡⣿⣿⣿⠛⣠⣿⣿⣿⡉⢃⢠⣇⠸⣷⣿⣏⠛⢮⡙⠛⠛⠻⣫⣶⡿⠋⣤⠀⣽⣇⣈⣿⣿⡿⣿⣷⡀⢡⣦⠠⣿⡇⠸⡏⠠⣷⡆
⠊⠀⣿⠟⢉⡙⠋⢁⣴⣿⣿⣿⣿⣾⣿⣿⣿⣿⠇⣼⠀⠹⣤⡈⠙⣿⡗⠐⣍⠻⣶⣦⠻⠟⢁⣴⡏⣸⣿⣿⢛⣿⣿⡿⣹⣏⣿⣀⠿⡧⢻⡿⡦⢠⡄⡌⢀
⢴⣿⡄⠺⡟⣹⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠻⢷⡆⢿⣿⣶⠻⣷⣴⣾⣧⣴⣦⣴⢿⣿⠏⣴⣿⡟⢣⣿⣿⢹⡇⠙⢻⡋⡛⣶⣽⢿⡿⢷⠎⣥⠀⣤
⠈⢉⠶⠀⠘⣿⣿⣟⣷⣿⡏⣽⣿⣿⣥⣿⣿⣿⡄⣼⡄⢿⣿⣿⣿⣷⣬⣿⣿⣿⣟⣻⣿⣟⣛⣾⣿⣧⣾⣇⡿⢋⣼⡇⢀⠹⡷⢀⣿⠻⠉⠁⠺⠿⢿⡶⢀
⢠⡙⠂⢠⣾⠿⣿⣿⣯⣿⢀⣿⣿⡿⣿⣿⣿⣿⣷⣼⣿⡜⢿⣿⣿⣷⣿⣤⣾⣿⣿⣿⣾⣿⣿⣋⡀⣩⡿⠛⢠⣾⢻⣷⡿⠘⡷⢸⡏⠀⠀⠀⣀⡶⠀⠃⠈
⢏⣿⡆⢰⣾⣧⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠋⠹⣿⡿⣿⠞⠻⣧⡙⠛⠛⠿⡿⠟⢿⣿⣿⣿⣿⠿⢏⠀⡰⢛⡀⠈⠙⠁⠘⣄⢉⠀⠰⠀⣤⠉⢱
⣼⣿⣶⣷⢿⣿⠀⣹⣽⣷⣿⣾⡿⣿⣿⣿⢷⣴⣄⠙⣧⢘⣍⣣⣈⠹⣾⣟⣾⣧⣤⡿⠆⢠⣿⣶⠶⠶⠾⣷⠞⠙⠀⣴⡄⠇⠀⠀⠀⢀⡀⠀⣀
⡻⣿⣿⣽⣿⠿⡁⠘⠉⠉⣿⣯⣴⣿⣿⣿⡾⢿⣿⠀⢹⣮⡛⠲⣿⠷⣦⣍⠛⠟⠓⠠⣤⠶⠆⣵⠶⠚⠃⢈⠓⠚⢀⡿⣀⠀⠘⠀⣰⣿⠓⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠃⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣇⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⣦⣀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⠙⢷⣄⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠰⠶⢦⣤⡀⠀⠀⠙⣧⡀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠙⢷⣄⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡀⠀⠈⣷⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠻⣦⡀
⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠈⠻⣦⡀
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢷⣄⠀⠀⠀⠀⠀⠈⣻
⣾⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠙⢷⣄⠀⠀⣠⡾⠋
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠙⣷⡾⠋
⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠈⠻⣦⡀⠀⠀⣠⡾⠋⠀⠀⠀⠙⢷⣤⣀⣀⣀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠈⠻⣦⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢶⣶⣤⣤⣴⣶⠞⠛⠁
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣑⣈⠀⠀⠀⠀⠀⣁⡁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠷⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⣤⣤⣾⡿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⡀⠈⠛⠛⠛⠁⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⠑⠀⠀⠀⠀⠀⠈⠃
⣿⣿⣿⣿⣿⣿⡏⠉⣿⣿⣿⣿⣿⠉⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⠀⣿⡷
⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⣿⣷
⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠻⣿⣿⣿⠟⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣧⣀⣀⣀⣼⣿⠇
⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠛⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⣴⣿⡷⠀⣠⣾⣿⠆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠰⣿⣷⣄⠀⢾⣿⣦⡀
⠀⠀⠀⣾⣿⡟⠀⢰⣿⣿⠃⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⡆⠀⢻⣿⣷
⠀⠀⢰⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⠿⠿⠿⢿⣿⠁⠀⠀⠀⠀⢸⣿⣷⠀⠀⣿⣿⡆
⠀⠀⢸⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿⣿⡇
⠀⠀⠀⣿⣿⡆⠀⢹⣿⣧⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣼⣿⡏⠀⢰⣿⣿
⠀⠀⠀⠘⢿⣿⣦⠀⢻⣿⣷⡄⠀⠀⠀⢸⣧⣀⣀⣀⣠⣀⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣠⣿⠃⠀⠀⠀⢠⣾⣿⡟⠀⣴⣿⡿⠃
⠀⠀⠀⠀⠈⠛⠁⠀⠀⠙⠋⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠙⠋⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢀⡀⠀⡠⡠⣤⣤⣤⡤⠤⠤⣤⣤⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐⢲⠄⢀⣀⣠⣤⣍⣬⡦⣽⢫⣧⣤⢭⣩⣿⣿⣿⣿⣶⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⡐⢏⣿⣟⣿⣿⡿⢿⣿⣷⣿⣿⣿⣿⣽⢿⣶⣿⣿⣿⣿⡟
⠀⠀⠀⠀⢀⣀⣀⣤⣴⡏⠻⣦⣹⣷⣻⣭⢽⣧⣗⣦⣿⣻⣔⣚⣼⣛⣟⣻⣿⣻⠿⣿⣠⢤⡀
⠀⠀⠀⣟⢙⢭⡫⣼⣿⠉⣻⣿⣿⣿⣶⢻⡿⠇⠻⠟⠇⠛⠓⠚⠛⠛⠉⠁⠀⢀⣴⢿⢁⡿⢇
⠀⠀⠀⡆⢸⣵⢝⡯⣿⡿⣿⣿⣿⣿⣿⢛⡷⡶⠶⠤⠤⠤⠤⠀⡔⠒⠂⠉⠉⡀⢠⠾⠊⢁⣼⣷⣦⡀
⠀⠀⠀⠷⢸⣹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠊⠉⠀⠀⠀⠒⠲⠚⠛⢒⠆⠉⢁⣀⣤⡴⠾⠿⠟⠛⠋⠉⠁
⠀⠀⠀⣿⢸⢹⣿⣿⣿⣿⣯⡻⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⡶⠶⠖⠚⠛⠛⠉⠁
⠀⠀⠀⡋⢸⣸⣿⣿⣿⣿⣿⣿⣾⣻⠛⠛⠋⠉⠉⠉
⠘⠉⠩⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⡈⠀⠒⠩⣿⣯⣿⣿⣿⣿⣿⣿⣿⡇
⠉⠢⢄⠀⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠢⢄⡩⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠉⠲⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⡄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⢀⣀⣠⣤⡴⣶⣶⣿⣿⣛⣏⣛⢉⣀⢀⣁⠀⠀⠀⠀⠀⠀⠐⠒

⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⣼⡇⠀⠀⠀⢀⣀⣀⣀⣀⣀
⣿⣿⣿⢟⣩⣭⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⣰⣿⣧⣤⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⡞⠿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠿⣿⠀⠀⠀⢨⣿⠏⠀⠀⢸⠿⠿⠿⠿⣿
⣿⣿⣿⡿⣛⡛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸⡏⠀⠀⠀⢸⣷⣶⣶⣶⣿
⣿⣿⣿⡱⣿⣿⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⡿⢶⡶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿
⣿⣿⣿⡱⣿⣿⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣷⣮⣴⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠉⠛⢻⣧⣬⣭⣽⣽⣿⣿⣿⡿
⣿⣿⣾⣷⣶⣶⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢸⣿⣿⣶⣾⣶⣶⣶⠞
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣄⣀⣸⣿⣿⣿⣿⠿⠛⠁
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⡇