Hair care Emojis & Symbols

⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠃⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣐⣩⡤⣬⣁⡀⠀⠀⠀⠀⠀⠀⠴⠿⢿⡿⠦⠀⠀⠀⠀⢠⣴⣾⣿⣷⣦⣤⠀⠀⠀⠀⣴⣎⣻⠟⢯⡞⣶⡄
⠀⠀⠂⢄⢰⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠀⠈⢹⠇⠀⠀⠀⠀⠀⢰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠃⠃⠚⠘⠀⠀⠀⠀⣾⣭⡅⠀⠀⣳⠿⡄
⠀⠀⠆⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⣾⡧⠀⠠⣾⣦⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⢤⣄⠀⠀⠀⠀⠈⣷⣫⣿⣿⣻⠕⠁
⠀⠀⠃⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠈⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢄⣀⣀⣀⠀⠀⠀⠀⠀⢀⡐⠑⡄⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢀⣦⢰⠼⡟⢲⡤⠤⠄⠀⠀⠀⠀⢠⡇⠀⠘⣯⠭⠥⠀⠀⠀⠀⠀⢸⠁⠀⢹⡀⠀⠀⠀⠀⠀⠀⠘⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢀⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣾⠯⠿⠥⠀⠀⠀⠀⠀⠹⣦⣤⡾⠅⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢱⢣⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆

⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢠⣆⡀⠀⠀⣴⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠸⣿⣿⡿⠿⠘⠛⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢺⡗⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡧⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠙⠛⠁
⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡅⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠟⠀⠀⠀⠘⡗⠀⠀⠀⣿⠅⠀⠀⠀⠀⢸⡇⢹
⠀⠀⢙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡠⡎⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣷⣿⠀⣤⣤⡄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁

⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣄⡀⠀⠀⠀⠀⢠⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠄
⠀⠀⣸⠋⠻⡀⠀⠀⠀⠀⠀⠀⠀⣾⠛⢰⣿⣿⠋⠉⠉⠀⠀⠀⠀⣺⣷⣾⡏⠉⠉⣿⣷⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣆⠈⠀⠃
⠀⠀⠘⠳⢛⠔⢁⠀⠀⠀⠀⠀⠀⢹⣷⠈⣿⣿⡆⠀⠀⠀⠀⠀⠈⡽⢋⣭⣡⣄⣴⣿⠏⠀⠀⠀⠈⣿⡇⠀⠀⡤⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣤⠿⠛⠃⠀⠀⠀⠀⠀⠀⠈⠳⠐⠈⠆⠀⠀⠀⠀⠀⠸⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⢶⣶⢶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠍⠉⠉⢱⠀⠀⠀⠀⠀⠀⠀⠈⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠘⣌⢦⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣤
⠀⠀⠀⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡜⣿⠇⠀⠀⠀⠀⠀⠀⣬⣥⣤⣤⣤⣬⡄⠀⠀⠀⠀⠈⠢⢅⠊⠍⠒⠄⠀⠀⠀⠀⠀⠀⣸⠉⠉⢹
⠀⠀⠀⡃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠑⠀⠀⠀⠀⠀⠀⠀⠀⢾⣤⣤⣾
⠀⠀⠀⠛⠒⠚⠛⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⢀⠚⠢⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⣾
⠀⠀⠀⠀⠀⠀⠘⢦⣀⡀⠀⢀⡷⣤⣤⣀⠀⠀⠀⠛⠿⠿⠾⣦⣭⣷⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠛⠛⠻⠷⠶⢦⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣠⢟⣴⡤⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠳⠾⣡⣿⠟⠀⠀⠀⠀⠀⠀⣀⣴⡿⠉⠀⠀⠀⠉⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇
⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠄⠀⠀⠄⠀⢻⣿⣿⡇
⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣏⠀⠉⠁⠀⠀⠉⠁⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⣀⠀⣴⣄
⠀⠀⠀⠀⢸⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡄⠀⢀⣀⣀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⢿⣷⣝⣿⣧
⠀⠀⠀⠀⠀⠷⠈⡷⠠⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣄⠀⠛⠋⢀⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠐⡀⢨⠃⠰⠄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣁
⠀⠀⠀⠀⢀⣿⣿⡷⣦⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠙⢻⣿⣿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋
⠀⠀⠀⢀⠾⠁⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢻⠿⡿⠁⠀⠀⠀⠀⠀⠀⠘⠁⠉⠈⠻⠇
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⣴⣿⣿⣦⠀⠀⠀⢀⣾⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⣿⠁⠙⣿⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠙⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠋
⠀⠀⠀⠀⠀⣿⣄⣠⣿⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣧⣹⣿⠀⠀⠀⠀⠀⢀⡤⠋⠁
⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠸⡂⠀⠀⠀⠀⠀⠀⣴⣾⡿⠟⠉⠹⣿⣿⣿⡇⠀⠀⠀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠈⠻⠟⠁

⡶⠶⠶⢶⠶⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⠶⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡁⠃⠀⠀⠀⠀⠀⠕⠒⡄⠀⠀⢀⠀⠀⠁⠀⠀⠀⢀⠀⠁⢂⠀⡐⠃⢀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠘
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠑⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⡇⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤
⠀⠀⠔⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⢀⠂⠀⠀⠄⠀⠀⠀⡀
⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢘⠀⠀⠀⠓
⠀⠀⠀⠀⠀⢀⠀⠠⠂⠠⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⢀⠀⠁⠀⠀⠈⠀⠀⠀⢀⡆⠀⠀⢀⢁⠀⢀⠈⠘⠒⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠤⠔⠀⠂⠁⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠘⡂⠈⠀⠀⣤⡐
⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠐⠀⠈⠀⠈⢀⠀⠀⠀⠀⡷⠆⣄⠴⠂⠀⠀⠈⠓⠐⠂⠀⠀⠁⢿⣆⡁⠀⠀⠆
⠀⠆⠀⠀⠀⠀⢠⣙⠀⠀⠀⠁⠀⠀⠀⠊⡼⠁⢀⣀⢏⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠂⣀⣀⡀⠠⠀⠁⠀⠀⡀⢈
⠀⠀⣀⣀⡀⠀⠀⢲⡆⠀⠀⠀⠀⠀⠠⠋⠁⠀⠠⠤⠈⡅⢠⡄⠀⠀⣄⣀⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠧⠠⠄⠀⠀⢻⡇⠀⢀⢄⠁⠁⠀⠐⠀⠀⢀⠀⠀⠘⠄⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢈⣀⣨⠌⠠⠉
⠀⠀⢀⣀⣀⠀⠀⠘⢳⡀⠈⠟⠃⠀⣀⠀⠀⠀⠀⠐⠒⠀⠸⠃⠀⠀⠀⠀⠀⠀⠾⢍⠠⠈⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠠⠙⠛⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠈⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠃⠀⠀⠀⠀⠀⢀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⡀⠀⠀⠀⢀⠈⠀⡆⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠰⠢⠀⠀⠀⠀⠰⠆⠀⠀⠀⠎⡴⠀⠀⠀⡀⠀⠰⠖⠈⡍⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠲⠰⠃⠀⠀⡶⠁⠀⠠⠀⠀⠃⠀⠀⠐⠗⠀⠀⠀⠀⠠⠀⠀⠀⠄⠆⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⡁⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⡈⠀⠀⡔⠀⠀⠀⢐⠀⠘⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠄⠀⠠⠀⠀⠀⠀⠁⠀⡀⠠
⠀⠀⡀⠄⠀⢀⠄⠀⠁⠀⠁⠀⠐⠀⠀⠀⠀⢀⠀⠠⠀⠂⠄⠀⠀⢈⠅⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈
⠀⢰⡇⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⣖⠁⠀⢦⠀⠀⠀⠀⠀⠀⠐⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠒⣣⡄
⠀⢸⣯⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠃⠠⠀⠀⠀⠀⡇⠰⠋⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣄⠀⠀⢀⠀⠀⠀⠘⡷⠚⠒⠋
⠀⢸⡇⠀⠀⠁⠀⠀⠀⠑⠀⠀⠀⢀⠴⠚⠀⢀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠓⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⠀⠀⠀⠂⠂⠁
⠀⠈⠈⠀⠇⠰⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⣀⣤⡀⠀⠀⠀⡣⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⢠⡀⠀⠀⠀⡄⠒⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢖⠋⠁⠀⠝⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠰⠀⠀⠀⠀⢦⠀⠀⠠⠠⠀⢀⠀⠆⡜⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⡄⠀⠹⠄
⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢘⠆⠢⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠉⠀⢁⠀⠀⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡗⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⡀⢀⠀⠀⢑⢤⣠⡀⠀⠡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠤⠬⠂⠁⠀⠢⠁⠁⠉⢢⠀⠈⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠿⠓⠀⠀⠀⠀⠀⢀⠀⠈⢢⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠈⠀⠀⢠⠀⠀⢀⢠⠐⠨⡀⠀⠀⠁⠀⠀⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠄⠀⠸⠀⠀⠀⡈⢄⡀⠈⢆⠀⠀⠠⡀⠈⠠⢁
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⠀⠀⠀⠀⠀⠀⠀⠁⠚⢁⡈⠀⠀⠀⢄⠠⠀⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃⢺⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠜⣴⠀⠀⠁⠀⠀⠒⠈⠀⠈⠆
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣾⣇⠀⠀⠀⡆⠀⠀⠀⠀⡀⠈⠀⠀⠠⠀⣀⡀⠀⠀⠀⠠
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣿⡜⠀⠀⠀⢀⣀⣐⠀⠀⠀⠀⢰⣆⠁⠠⠀⠒⣀⠀⠀⡄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣦⠀⠀⠀⣿⣿⣽⠀⠀⠀⠰⠀⢀⠀⠀⠀⠀⠈⠀⡼
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⣷⣷⣝⠦⠀⠀⠉⠉⠉⠂⢼⠀⣡⠃⡞⠀⠀⢰⠂⠐⣀⡿⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡔⠀⡀⠀⠀⠀⠀⠀⢸⣴⠏⠀⣶⠀⢠⡀⠐⣧⡈
⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⡒⠀⠀⣼⣬⣁⣀⣉⣀⣈⣁⣵⠀⡆
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣁⣀⣀⠙⠛⠛⠛⠛⠛⠛⠛⠛⡶⠀⠀⠐
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠺⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⠀⡄⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠈⠉⠀⠀⠀⠀⠐⠀⠀⠀⠋
⠀⣀⣉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣶⣶⣶⢶⣶⣾⡿⣷⡶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣟⣿⢼⡇⣿⣧⣻⢷⣽⣿⣿⣳⣽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣭⠞⠉⢿⣿⣾⣽⣿⣻⣿⣶⢻⣷⣿⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢥⡄⠀⠀⠀⢠⡤⣈⡉⢿⣾⣿⣟⢿⣮⡻⢾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⣷⣽⣿⡿⣾⣝⢷⣝⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠒⠊⡸⠀⠘⠦⣀⡠⠔⠁⠈⠓⠊⣿⣽⣿⣟⣿⣟⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠒⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠐⠲⠖⠀⠀⠀⠻⠃⠀⣸⣿⣿⣫⣾⣿⣿⣿⢯⣿⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⣽⣿⣿⣾⣿⣽⣿⣯⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⣠⣿⣷⡆⣴⣿⠋⣿⡟⣿⠟⡿⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⢉⣿⣿⣧⣿⢡⣿⢃⡆⣿⠀⣡⣾⠰⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡴⢋⣵⢶⡍⣿⣸⣃⣶⡄⡟⣤⢹⡏⣴⣿⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡿⣰⢯⣾⣧⣧⡾⢛⠻⢿⡛⣷⡿⢶⣧⣭⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⣿⡇⣿⢽⣿⣿⠋⣴⣿⠇⣾⢡⡶⣠⡞⣩⡍⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡻⣼⣤⣼⣇⠻⠷⠞⣡⡘⠟⡃⡼⢣⡞⣴⡟⢸⢏⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⣿⡿⠛⣿⡾⠟⠶⣾⣿⣟⣿⣷⣶⣿⠸⠿⢃⡰⠟⣫⡾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣿⡇⢈⣴⣾⡟⢠⣾⣷⠈⣷⠏⣹⣷⣿⠿⣷⡾⢿⣽⣿⣯⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⣿⠇⣼⡟⣿⠁⣿⣿⡟⢠⡿⢀⣿⢯⡿⢀⣿⠀⣶⣄⠙⣿⢽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣯⢿⣴⣿⣷⣿⣄⠛⠛⣠⣾⡇⢸⣿⣾⠇⣸⡇⠀⠉⣉⣴⣟⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⣟⠿⣾⡟⣩⣙⣿⠿⠿⢿⣾⣷⣄⣉⣁⡴⣻⠁⣿⡄⢿⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣻⡿⢿⣇⢻⣿⡟⢸⣿⣿⢃⣿⢹⡟⣛⡛⣿⣾⣿⣷⣬⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡛⣿⠆⣿⠇⣶⣾⡟⣸⡟⣿⠃⠿⣿⣿⣻⡾⣻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣶⣾⣿⣘⠻⣿⠃⣿⣿⡿⢸⣿⣿⣟⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣷⣶⣾⣧⣿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠺⣷⡄⠀⠀⠀⠀⠀⠀⠘⠁⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠘⣿⡿⠁
⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⣠⠄⠀⡀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀
⠀⠀⠀⣰⡏⠀⣸⠇⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠰⠶⠆⠀⠰⠶⠀⠀⠀⠀⠀⠀⢠⢁⠊⠀⠀⠀⠀⠀⠠
⠀⠀⠐⠛⠀⢰⡟⠀⠀⠀⠀⠀⠀⠊⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠒⠀⠀⠠⠤⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠨⠁⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳
⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⢀⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢿⣽⡗⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠟⠿⠿⠿⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⢏⡑
⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠢⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠁⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⠀⠀⠦⢄⣀
⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠢⠊⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⠤⠀⡄⠠⠀⢠⠀⡐⡄⠀⡤⠀⠀⠀⠀⠂⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠁⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣇⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⢁⠀⠀⡼⠃⠀⠠⡀⡀⠀⠀⢀⠤⠀⠂⠚⠉⠉⠀⢀⡶⠟⢂⣆⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⡔⣿⠀⠀⠀⠀⢸⡆⠀⠀⠀⠃⠀⠠⢘⠀⠀⠀⢀⡴⠁⠠⠌⢀⠀⠀⠀⠀⠘⣧⣄⣠⣀⣀⠀⡀⢸⡠⠘⣸⡟⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡜⢁⠀⢀⠀⠀⠸⡇⠀⠀⠀⠀⠒⠂⠀⠀⠀⢠⠞⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠡⠀⠙⠚⢋⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⡗⠰⠷⠠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⡇
⠀⠀⠀⠆⠀⠄⢠⡀⡄⠀⠀⠀⠁⠲⢄⢷⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢲⡇
⠀⠀⠘⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⠳⡄⠀⠀⠀⠀⠀⠌⣤⡞⠀⠀⠀⠀⠀⠀⠀⠘⠀⡂⡆⡠⢠⡇⠀⠶⠴⠀⠀⠘⢠⣾⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⠰⠂⠀⠀⠈⠄⢻⡄⠀⠀⠀⠀⠼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠉
⠀⠀⠀⠀⠚⢀⠀⠀⠀⠉⠀⠈⠈⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠑⠢⡀⠀⠀⠀⠀⠀⢀⡀⠤
⠀⠀⠀⠀⠘⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢹⠀⠀⢀⠤⣊⡵⢊⠖⠁
⠀⠀⠀⠀⠀⢀⢠⣜⠉⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠝⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠳⡄⡠⢀⠀⢀⡼⠀⢰⠑⠾⢋⠴⠉
⠀⠀⠀⠀⠀⠹⣧⡍⠻⣆⠈⠳⡄⠀⠀⠀⠀⠀⢠⠔⠁⡀⠀⠘⡠⠘⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢆⣠⡞⠚⠛⠀⠀⠈⠓⠒⠉
⠀⠀⠀⠀⠀⠀⠈⠻⣧⣌⠣⡀⠙⢄⠀⠀⠀⠀⠦⠔⠋⠀⠀⠀⣷⣼⠡⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠁⡀⠀⢀⠀⠀⣦⠈⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣳⣴⡀⠈⢧⠀⠀⠀⠰⠄⠀⡀⠀⠀⠹⣝⠷⣾⣦⣀⣀⡀⠀⠁⠀⠀⠀⠈⠄⢘⠠⠈⣦⣀⡿⣀⣠⣃⣴⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠿⡁⠄⠀⠳⡀⠀⠀⠀⠀⠀⠒⠀⡄⠈⠀⠘⢲⠍⠁⠀⠀⠀⠀⠀⠀⠀⠠⠞⠒⠉⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠅⠀⠐⠀⠶⠀⠆⠀⠀⠙⢦⣣⡀⢳⡄⠀⠀⠀⠀⠀⠈⠖⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⠠⠀⠀⠀⠀⠀⠀⠈⢀⠘⠂⠈⠀⠀⠀⠀⡀⢀⡀⡤⢰
⠀⠀⠀⠀⠀⠀⢀⠀⡐⠀⠐⠙⠂⠀⠀⠀⠙⠒⢿⡀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠈⢀⣀⠇⠀⠀⠀⠀⠀⠀⢈⣧⢀⠀⢀⠄⠑⠐⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠉⠁

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⢰⣿⢩⡅⠀⠀⣶⡄⢠⣶⠀⠀⠀⠀⠀⣗⡶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇
⠀⠀⠀⢸⣿⠩⠅⠀⠀⣿⡀⢸⣿⠀⠀⠀⠀⠀⣟⣜⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟
⠀⠀⠀⢸⣿⠹⠆⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠛⠛⠁
⠀⠀⠀⢸⣿⠹⠀⠀⢈⣿⠂⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠀⡀⠀⠀⠀⠲⠀⢸⣿
⠀⠀⠀⢸⣿⣭⡅⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⢿⣖⣄⡈⠀⠀⠀⠸⠆⠀⣿⣇
⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣅⠀⡈⠀⠀⠀⠀⠀⠇⠀⢹⣿
⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣤⣾⢿
⠀⠀⠀⢸⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡾
⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠸⣧
⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠿⠿⠿⠿⠿⠷⠆⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡏⠣⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣽⣿⠀⢰⣿⣿⣭⡅⠀⠀⠀⢰⣤⣤⣀⣤⣴⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠀⠈⠛⠛⠛⠛⠋⠀⠀⠀⢀⡤⣄⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⡀⠀⠀⠸⣦⠾⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⣠⠞⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠟⠀⠘⠇⠙⡆⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠛⣿⡿⠙⠙⠟⠀⠀⠀⠀⠀⠈⡀⠉⠀⠈⢱⡃⠀⠀⠀⠠⢺⣁⠈⠁⠀⠉⢈⠁
⠀⠀⠀⠀⠀⠀⠰⢾⣷⣤⣤⡄⠀⠀⠀⠀⠀⠀⠁⠀⠛⠀⠘⠇⠀⠀⠀⠀⣾⣿⣦⠐⠒⢠⠏⠀⠀⠀⠠⢤⠐
⠀⠀⠀⠀⠀⠀⢠⣄⠈⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣤⣤⣤⣀
⠀⠀⠀⠀⢠⡿⠿⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⢹⡿⢿⣿⡏
⠀⠀⠀⠀⢸⢀⡀⠀⣹⣿⡇⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠉⠻⠀⠀⠀⠀⠀⠀⣸⢁⡀⠀⣈⠙⣇
⠀⠀⠀⠀⢠⡀⠀⠀⠀⢹⣇⠸⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⣀⠀⢠⣼
⠀⠀⠀⠀⠀⣷⠀⠉⢠⣾⡇⠀⠀⠀⠀⠀⢂⣿⠙⢷⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠛⢷⠀⠉⢠⡿⠟
⠀⠀⠀⠀⠀⠟⠀⠀⠀⠿⡇⠀⠀⠀⠀⠀⠘⣿⣧⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⣾⣿⣆⠀⢰⣿⠀⣿⡿⠿⣷⣆⠀⠀⢠⣶⠿⠿⣷⠄⠀⣼⣿⣧⠀⠀⣿⠿⠿⣷⡄⢾⡿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⢿⣿⠀⣸⣿⣈⣿⡆⢸⣿⠀⣿⣷⣶⣿⠃⠀⠀⢸⣿⠀⠀⢀⠀⣸⣿⣁⣿⣆⠀⣿⣷⣶⡿⠃⢼⡿⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠸⠿⠰⠿⠛⠛⠻⠿⠘⠿⠀⠿⠇⠘⠿⠆⠀⠀⠈⠻⠷⠾⠿⠃⠿⠛⠛⠻⠿⠆⠿⠃⠙⠷⠄⠺⠿⠶⠶




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣌⠛⣠⣤⠀⠀⢀⣀⠀⠛⠛⠉⠉⠉⠉⠙⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣶⠈⠉⠀⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⣀⣀⣠⣴⡿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠻⠛⣀⡘⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⢀⣿⠋⠉⠁⠀⠈⠛⠿⣶⣶⣶⣿⡇⠀⠸⣿⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣿⡇⣠⣄⣴⡆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣿⣦⣴⡄⠀⠰⣿⠀⠀⠀⣿⡇⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⣿⡇⠈⠙⠛⠿⢿⣶⣿⣧⣄⣀⣤⡄
⠀⠀⠀⢀⣀⣠⣼⡿⠿⠛⠋⠉⠁⠐⠿⠇⣀⠺⠿⠀⢹⣧⣀⣠⣤⣴⣿⣿⣶⣤⣤⣴⣾⣿⣧⣤⣄⣀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢷⣦⣤⣤
⠀⠀⢀⣼⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⣠⣾⠿⠛⠋⠉⠁⢸⣿⡀⠉⠉⢉⣿⡇⠈⠉⠙⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣀
⠀⢺⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇
⣀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠉⢻⣧⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⢀⣀⠀⢀⡀⣀⣀⣀⢀⣀⠀⠀⠀⣼⡿
⠀⣾⢿⣦⠀⣴⡿⠛⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠟⠻⢿⣦⡉⠁
⠀⠀⠀⠉⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣰⡿⠛⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠠⣶⠀⢰⣶⣶⣶⣶⣶⡆⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡆⢸⣿
⠀⠀⠀⢰⣾⣿⣷⣶⣾⣿⣷⡆⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡇⠀⣿⡇⢸⣿
⠀⠀⢀⣼⣿⣤⣤⣤⣤⣤⣽⣧⣀⠀⠀⢠⣶⣿⣷⣶⣶⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣦⣤⣦⣴⣶⣤⣴⣿⡇⠀⣿⡇⢸⣿
⢠⣶⠟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠻⣷⣄⣸⣿⣤⣤⣤⣤⣤⣼⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇⠀⣿⡇⢸⣿
⣾⡏⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⢹⣿⠛⠉⢹⣿⠋⢹⣿⠉⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡇⠀⠿⠃⢸⣿
⣿⡇⠀⣴⡿⠋⠉⠻⣷⡄⠀⠀⠀⢸⣿⠀⠀⢰⣿⠀⢸⡿⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡇⠀⣤⡀⢸⣿
⣿⡿⠟⠿⠁⠀⠀⠀⠹⠿⠿⣿⡆⢸⣿⠀⠀⠸⣿⠀⠀⣀⣤⣤⣶⣶⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇⠀⣀⠀⢀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⢀⣴⡿⠛⠉⠁⠀⠀⠈⠙⠻⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣿⡇⠀⣿⡇⢸⣿
⣿⡇⠀⣴⣶⣶⣶⣶⣶⡄⠀⣿⡇⢸⣿⠀⠀⢀⣾⠏⠀⣴⣶⣦⣤⣤⣄⡀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⣰⡿⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡇⠀⣿⡇⢸⣿
⣿⡇⠀⠀⣀⣀⣀⣀⠀⠀⠀⣿⡇⢸⣿⠀⠀⣼⡏⠀⠀⣿⣏⠀⠉⠉⠙⢿⣆⠀⠀⣿⡇⠀⠀⠀⠀⠀⣰⣿⡁⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⡇⠀⣿⡇⢸⣿
⣿⡇⠀⠀⠙⠛⠛⠛⠀⠀⠀⣿⡄⢸⣿⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⣶⣄⣸⣿⠀⠀⢈⠁⠀⠀⠀⠀⣴⡿⠙⠛⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇⠀⣿⡇⢸⣿
⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠇⢸⣿⠀⠀⠸⣷⡀⠀⠈⢻⣷⣤⣬⣿⣿⡇⠀⠀⠛⠃⠀⠀⢀⣾⣿⣧⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇⠀⣿⡇⢸⣿
⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢸⣿⠀⠀⠀⠹⣷⣄⠀⠀⠈⠉⠉⠁⠀⢀⣤⡿⠂⣀⣤⣾⣿⡉⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠇⠀⠉⠀⢸⣿
⣿⣧⣤⣤⠀⠀⣤⠀⢠⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣬⣿⣿⣶⣦⣤⣤⣴⣶⠿⠛⠁⠈⠛⠉⠀⠉⠀⠀⠀⠀⠀⠈⢿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣠⣴⠿⠃
⣶⣾⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶
⣿⣿⣿⠋⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡭⠥⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⠛⠛⠛⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⠶⠶⠶⠶⠶⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⡖⠒⢲⠀⡇⢸⡇⡴⠶⠶⠶⠶⠶⠶⠶⠶⠶⢦⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠧⠤⠼⠀⡇⢸⡇⡗⠚⠓⠚⠒⠓⠚⠓⠚⠂⡟⠀⠀⡼⠤⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⡇⢸⡇⣷⠀⠀⢀⣠⣤⣄⠀⠀⠀⡇⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⡇⢸⡇⢸⠀⠀⡏⠀⠀⠈⢷⠀⢸⠇⡤⠴⠷⠤⠼⠧⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⡇⢸⡇⢸⡄⠀⠳⣄⣀⣠⠏⠀⢸⠀⡇⠀⢀⣀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⡇⢸⡇⠈⡇⠀⠴⠀⠄⠶⠆⠀⣾⠀⡇⡞⢛⣀⡙⢻⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣤⣤⣤⣤⣤⠇⢸⡇⠀⣇⠀⠐⠒⠒⠒⠀⠀⡇⠀⡇⡇⠠⠤⠄⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⡀⠀⢀⠀⠀⠀⢠⡇⠀⡇⣇⠠⠶⠆⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠉⠉⣉⣉⡉⠉⢹⡇⠀⡇⠉⠉⠉⠉⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣈⣉⣉⣉⣉⣁⣀⣸⠇⠀⠸⣖⣒⣓⣒⣛⣒⣾⠃⠀⣇⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡋⠉⠉⠉⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣝⠦⣄⣀⡀⠀⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠤⣍⣉⣉⣩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠂⠀⠀⡾⠀⠀⠀⠀⢀⡤⠖⠋⠉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢸⠃⠀⠀⢀⠔⠁⠀⠀⣠⠞⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢀⡟⠀⠀⢰⣏⣀⣤⠴⠚⣡⠾⣅
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣼⠁⠀⠀⠀⠙⠦⠴⠶⣏⠁⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⡞⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⢰⠇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⡼⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠹⡄
⠀⠀⠀⠀⢰⡧⢤⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠙⢦
⠀⠀⠀⠀⠈⣇⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠔⢊⢧
⠀⠀⠀⠀⠀⢿⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⢻⡆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠇

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

⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢸⡼⣻⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠒⠃⠀⠀⠀⠀⠀⠀⣈⠀⠈⠘⣿⣿⡇⠀⠀⠀⠀⢀⠚⠁⠀⠀⠀⠀⢉⢑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣢⡌⢈⡉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⢻⣿⣿⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠓⠚⠋⢸⣿
⠀⠀⡠⠖⢒⣛⣛⣛⠒⠲⡄⠀⠀⠀⣾⣿⡿⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⡦⢐⣷⡆
⠀⠀⡓⠶⠤⠭⠭⢭⢤⠔⣻⠀⠀⠈⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⡂⠀⠐⠹⠆⠀⠀⠀⠈⠢⡑⢄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠇
⠀⠀⢏⠒⠦⠤⠤⠤⠀⢚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠾⠗⠷⠚⠛⠒⣄⠀⠀⠀⠀⠀⠀⠈⠲⡕⠄⠀⠀⠀⢸⣿⣶⣿⡿
⠀⠀⠀⠁⠒⠀⠂⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠸⡇⢠⠤⠔⠒⢲⡄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠸⡜⢋⢛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⢹⠀⠀⠀⠀⠀⠀⢻⡈⠉⠁⠀⠈⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠄⠄
⠀⠀⠀⠀⠀⠰⡶⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⣀⣰⢶⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠖⠚⠁⠀⠀⠀⠀⠀⠈⠻⣏⣀⡇
⢀⠤⠚⠆⠀⠀⠀⠀⠀⣴⣾⣿⣦⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⢹⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⢠⠑⠁⠀⠈⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠰⡒
⠀⠀⠄⠀⢃⠀⠀⠀⠀⠀⠈⠉⠛⢦⣘⣷⠀⡀⣠⣛⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠰⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣰⢾⣿⣿⣿⣦⠀⠀⠀⠘
⢂⠉⣀⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠛⠛⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠂⠁⠀⠀⠀⠀⠀⠀⠀⢷⣺⣿⣿⣿⡿
⠀⢣⠄⢀⠈⢸⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⠛⠛
⠀⠀⠳⡤⢤⠊⡧⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠙⠒⠋⠁⠀⠀⠀⠀⢀⠀⠰⠷⣶⣶⡶⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠁⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠘⡝⢶⡆⠀⠀⠀⠀⠀⠀⠁⠔⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠊⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠤⠒⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡉⠢⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠑⠒⠀⠉
⠀⢰⠀⠀⠀⠀⠀⠤⢂⠔⠁⠀⠀⠀⠀⠀⠀⠀⣠⠊⡀⢀⠀⠼⠂⣈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡾⠑⠒⠓⠒⠬⣉⠹
⠀⠀⠓⠀⠀⠀⠀⡀⠙⢄⡠⠀⠀⠀⠀⠀⠀⡔⠁⢠⠀⠈⡀⢀⢠⠀⢑⡬⠂⠀⠀⠀⠀⠀⠀⠁⣀⣠⣶⣒⣓⣓⣶⣀
⠀⠀⠀⠀⢀⡴⠛⠷⡤⠊⠀⠀⠀⠀⠀⢠⠎⠠⠀⠀⠠⠄⠀⢠⡤⠒⠁⠀⠀⠀⣀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠢⡀⠀⠒⢀⡤⠚⠁⠀⠀⠀⠀⢀⣸⡍⢆⠀⠀⠀⠘⣿⣿⣉⣉⡉⠛⠛⣿⣿⡇⠀⠀⠀⢠⣤⡴⢦
⠀⠀⠘⢄⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡒⢈⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢧⣠⠏
⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣁⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠰⠍⠉⠉⠋⠙⠭⡆⠀⠀⡠⠤⠤⣤⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡆⠀⠀⣰⠂⠀⠰⠂⠀⠀⠀⠀⠋⠁
⠀⠀⠀⣠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢲⡐⣀⣿⠀⠀⠈⢹⠁⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠄⠁⠀⣠⢀⡀⠀⠀⠈⠀⠁⠁⠀⠀⠀⢸
⠀⢀⡴⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠂⠈⠉⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠀⢠
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠠⠆⠀⠀⠀⢸⠀⠀⠀⠁⠀⠁⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠰⠃⠀⠀⠐⠀⠀⠀⠠⣂⠄⠀⠀⢰⠀⠀⠃⠀⠀⠰⠘⡄⠀⠀⣗⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⡠⠄⠈⠁⠀⠀⠀⠘⠀⠀⡀⠀⠀⠀⠹⠁⠀⠀⠀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠠⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⡀⠀⠀⠀⠀⢀⡠⠒⠉⣠⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄
⠀⠀⠀⠀⠀⡀⠀⠁⠀⠌⠂⠀⠀⠀⣀⠔⠉⢀⡴⠊⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠇⠄⠂
⠀⠀⠀⠄⠈⠀⠠⠀⠀⠀⠀⢀⠤⠊⢀⡠⠞⠁⠀⡠⠔⠋⠀⠀⠀⠀⠀⠀⣀⡠⡠⠁
⠤⠈⠀⡀⠄⠀⠀⠀⠀⡠⠖⠁⣀⠔⠋⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠐⠈⠕⠂⠀⠀⠀⠒⠀⠀⠀⣴⣾⣧
⠘⠁⠀⠀⠀⠀⣀⠔⠊⢀⡤⠚⠁⠀⠀⠂⠀⠀⢀⠔⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠃⠀⠸⣿⣿⡡
⠀⠀⠀⠀⡠⠞⣡⢀⠖⠉⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠰⠋⠁⠀⣠⠺⠁⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⢈⠀⣀⠔⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⣀⡀⡄⠀⣀⠈
⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣤⣤⠤⠔⠒⠈⠉⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⠵⠒⠚⠛⠒⢦⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⣉⣩⣭⣙⡲⡄⢀⢼⡋⠉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⢀⣀⡀⠀⠀⠙⣆⣷⠀⠀⠀⠀⠀⠀⠀⡼⢡⡴⠛⠉⠀⠀⠈⠙⢿⣸⠀⠙⢦⣀⠡⠠⠌⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⡴⠋⠉⠙⢷⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⣷⠋⠀⣠⠖⠛⠛⢳⡄⢸⠏⢧⣄⠀⠈⠙⠲⠦⣤⣤⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣸⠁⠀⠀⠀⢸⠇⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⡏⠀⠀⠀⠀⢳⠞⢠⠏⠈⠛⠶⢤⣄⣀⣀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡼⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣽⡄⠀⠀⠀⠈⣷⠏⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢠⠏⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢠⠏⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣠⠏⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣰⠏⢷
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣠⠏⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣰⠏⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢠⠿⡄⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢠⠏⠀⢻⡀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢠⠏⠀⠀⠈⣧⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢠⡏⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⢀⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢷
⠀⠀⠀⠀⢸⡇⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⢸⡄
⠀⠀⠀⠀⠈⣧⠀⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⢸⡇
⠀⠀⠀⠀⠀⢿⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⢠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⡇
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠁


⣿⣿⠿⠿⡿⢻⠿⢿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡠⠒⠒⠋⠉⠉⠉⢒⠶⣤⡀
⠀⠘⠁⠀⠀⡤⠒⠒⣒⣚⣷⢦⣾⣿⣷⠂⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢰⣦⣄⡀
⠀⠀⠀⢀⡜⢀⠔⠁⠀⡰⠃⠿⠿⠿⠁⠀⣀⠰⣶⣤⠝⣟⡛⠉⠐⠠⠄⣑⠦⡈⠑⠤⡀
⠀⠀⠀⠀⠈⠳⣄⢔⡝⠁⠀⣠⠼⠆⠀⠀⠉⠹⣷⠆⠀⡀⠉⠉⠐⠒⠤⡀⠉⠺⢶⣀⠈⠢⡀
⠀⠀⠀⠀⣀⣀⡴⠋⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠐⠦⣀⠀⠉⠑⠒⢤⡀⠀⠁⠀⠀⠈⠀⠀⠈⠒⢄⡀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣉⠉⠒⠦⠤⠤⠽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠐⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠘⠂⠇⠀⠀⠈⠈⡃⠀⠀⠀⠃⠀⠀⠀⢀⠄⠼⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠤⠀⠄⠂⠀⠀⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣤
⠀⠀⠴⠒⠒⠒⠒⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠉⢱⡆⠀⠀⠀⠀⠀⠄
⠀⠀⡇⢀⠖⠉⠁⠉⠢⡀⢰⠉⠉⡆⡊⠀⠙⠄⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠞⠃⠀⢀⠀⠀⠀⢀
⠀⠀⡇⡌⠀⠀⠀⠀⠀⠱⠈⡲⣒⠁⢙⡶⡊⠀⠀⠀⠀⠀⠀⠀⣀⠀⣃⠀⠀⠠⢀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠛⠄
⠀⠀⡇⠡⡀⠀⠀⠀⠀⡔⢸⠀⠀⡇⣇⠀⢈⠀⠀⠀⠀⠀⠀⠀⡅⠀⠬⠀⠀⢀⣀⣀⡀⠀⠠⠀⠰⠀⠀⠀⠀⠁⠤⠀⠄
⠀⠀⣇⠀⠑⠢⡤⠄⠊⠀⠀⠉⠉⠀⠈⠉⠁⢸⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢀⠀⠤⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢈⠌⡆⠀⠀⠀⡇⠘⠀⠀⠀⠀⠅⡀⠀⠀⠀⠀⡈⠂⠀⠰⠰⠂⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠁⠀⠀⠁⠀⠀⢮⡰⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⡾⢩⠏⢿⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢤⢀⠠⢄⡀
⠀⠀⠀⠆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠄⠀⠀⠀⡅⡆⠀⠹⢍⡘⢹⠀⢀⠔⠛⠋⠲⡄⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡁⠀⠀⢻⡀⢀⢈⡬⢷⡾⠀⢸⠀⠀⠀⠀⡸⠀⠀⠀⠀⡇⠀⢠⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠔⠢⡉⠓⠛⠛⠉⠀⠀⠀⠓⠤⠤⠖⠁⠀⠀⠀⠀⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⢰⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⢢⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠠⢄⠀⠀⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠒⠂⠒⠀⠘⠀⠀⠀⠀⠸⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠔⠀⠀⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⠄⠀⠀⠀⠀⡀⠀⠀⠡⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⠘⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠠⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⣀⢤⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠇⠄⢨⡆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠐⡉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠖⠀⠀⠀⠤⠄⠆
⢀⣀⣀⣀⠀⠀⠀⠀⢀⣀⡀⠘⠄⠇⡸⠀⠀⠀⠀⠀⠀⢀⡀⢠⠄⠀⠀⠀⠀⠠⢘⠀⠀⠀⡛⠠⠀⠀⠀⠀⠀⠀⠄
⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠁⠈⡆⠀⡇⠀⠀⠀⠀⠀⡔⠙⠁⠞⠸⠳⣆⠀⠀⠐⠨⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⠀⠀⠀⡠⠈⠀⡀⠀⠀⠀⠀⢂⡄⠀⢨⣧⣄⢀⢀⡀
⠀⠀⢀⠀⠀⠀⡀⣀⢀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⡰⠊⠉⠂⠈⠫⠤⡈⠃⡄⠘⠦⣅⡀⢦⠗
⠀⠀⠀⠀⠀⠜⠁⠀⠀⠑⡀⠀⢸⠀⢸⠀⠀⢀⠲⡀⠀⠀⠀⠀⠀⠀⠷⡄⢌⢲⠀⢈⢃⡟⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢀⠀⠀⢘⠀⠀⠀⠀⠀⠡⠀⢸⡀⢸⠀⠀⠀⠙⠀⣆⡀⠈⢀⣰⠂⠇⠀⠈⢢⡹⣏⠎⠀⠈⠀⠀⠀⠀⠀⠀⢀⠃⠀⡅
⠀⠀⠀⣤⣽⡀⠀⠀⠀⢀⠗⠀⠸⠇⢸⠀⠀⠀⠀⠑⠮⠁⠀⠀⡠⠈⠀⠀⠀⣠⢉⢈⡢⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⢀⡀⡁⢀⣀⡠⠆⠀⠀⢀⠻⣿⠤⠀⠀⢀⣀⡐⠁⠀⠈⠢⣀⡀⠀⢸⣁⣽⠓⢶⠋⠀⠈⠉⠛⠒⠤⡴⢉⡁⠀⠠
⠀⠀⠀⠂⠀⠀⣸⢀⡀⠤⢀⣀⠈⣧⡠⣃⢾⣶⣁⠀⠁⠸⠈⠀⠀⠀⠀⢦⡴⠁⢐⠖⠚⠑⠂⠄⡤⢀⠀⠀⡀⢀⣀⡈
⠒⠒⠐⠒⠀⣋⣀⡬⠡⠤⠤⠬⠑⢆⠀⠙⠳⡌⠛⡃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠈⣰⡬⠃⠹⡦⠐
⠈⠉⠉⡽⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⠀⠉⢇⠀⠀⠀⠀⠀⠀⡗⣄⢠⡜⠀⠀⠀⠠⠄⠀⠀⠀⢰⠀⠁⠀⠀⢛⡶
⠤⠤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠒⠒⠒⢺⠀⠀⠀⠀⠀⢸⠘⠆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢢⢄⠀⠀⠐⠈
⠀⠐⣀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢗⢀⡀⠠⢼⡀⠀⠈⠀⠀⠸⠀⠐⠢⢄⣀⠀⠀⠀⠀⠀⠀⢰⠤⠀⢀⡠⠃⢀⡀
⠀⢀⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢈⠀⠀⠀⠸⠀⠈⠁⠂⠀⢣⠀⠀⠀⠀⠈⠙⠒⠦⢀⡀⠀⠀⠀⠘⠉
⣀⠀⢦⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠈⠉⠁⠑⠁⠀⣀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣁⣂⠆
⠀⠀⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠀⠀⢠⠀⠀⠀⣾⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠒⠲⡐⠀⠀⢉⡝⢻⠀⠀⠈⠀⢸⠀⠀⠀⡹⠄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢅⠀⠉⡀⢈⣀⣘⠀⢀⣀⠤⡴⠀⠀⠀⡇⠆⠀⠀⠸⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣈⣴⠉⠃⠈⡀⢹⡉⠀⠁⢀⡇⠀⠀⠀⠇⢰⠀⠀⠀⡆
⠶⠒⠒⠚⠛⠉⠁⡠⠒⡄⠀⠀⠧⠎⠀⠈⡆⠀⡀⠀⠀⢰⠂⠘⡇⠀⠀⢱⠀⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⠀⠀⠀⢀⡠⠔⣀⠌⠁⠉⠉⢻⠀⢀⡴⠒⠒⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠙⠚⠛⠛⠑⠋⠀⠸⠧⠠⠄⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣶⣶⣶⣶⣶⡿⢷⣶⣷⣷⣷⣿⣾⣷⣾⣷⣿⣾⣷⣶⣶⣶⣿⣿⣶⣿⣾⣿⣷⣾⣶⣾⣷⣾⢷⡶⢾⠷⢷⣿⡾⢷⣾⠾⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠉⠀⠀⠠⣄⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⣀⠀⠀⠠⠙⠶⡄⠀⠙⠢⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⢄⠀⠈⠁⠈⢧⠀⠀⠀⠀⠹⡀⠀⠀⠘⢏⠉⠉⡇⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⣆⠳⣄⠀⠀⠀⠱⡀⠀⠀⠀⠱⣄⠀⠀⠘⢶⠒⠐⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⣄⠀⢈⣑⢌⠳⡄⠀⠀⠘⢆⠀⠀⠀⠹⣧⡀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⢜⠢⣜⢿⡷⠁⠘⢆⠀⣠⣤⣠⡀⠀⠀⢳⣳⡀⣴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡴⠃⠀⠁⠀⠀⣠⣤⠶⠞⠳⣝⣿⣿⠗⢸⣿⣦⠇⠳⡜⣿⡧
⠀⠀⠀⠀⠀⠀⠀⣀⢀⠔⠋⠀⠀⠀⣠⢶⠿⠋⠁⠆⠀⠀⢈⣈⡥⠄⡈⢿⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣾⠟⠁⠀⠀⠀⡠⡪⠒⠁⠀⠀⢀⣠⠴⠚⠉⣡⠴⠋⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠋
⠀⠀⠀⠀⠀⢠⣴⣶⠀⢀⡴⠋⠀⠀⠀⢀⡠⠚⠉⠀⢀⡴⠟⠁⠐⠀⢀⣠⡤⠶⠒⠛⠉⠉
⠀⠀⠀⠀⠰⡿⠟⠡⢞⣽⣾⡆⠀⣠⠴⠋⠀⢀⡠⠞⠉⠀⠀⢀⡠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⣫⠴⠋⠁⠀⢀⣤⣶⣦⠀⢀⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠯⠵⠚⠉

⠰⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣄⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⣟⣷⣦⣀⣄⣄⠀⣠
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⡉⠙⣿⣿⣿⠋⠀⢻⣿⡿⠋⣽⣿⣿⠘⠀⠙⠻⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣷⣄⠈⠛⠁⠀⠀⠈⣿⠁⣼⣿⣿⣿⢸⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⡋⠉⠉⠉⠳⣄⠐⢾⡴⣼⢣⣾⠋⢛⣿⡟⢸⣷⣦⣀⠀⠀⠈⠛⠿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠃⢨⣄⣵⣿⣿⠰⣿⣿⡇⢸⣻⣿⣿⣷⣦⣄⡀⠀⠀⠉⠻⠿⠃
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠰⢾⣷⣾⡟⣛⣿⠀⠋⠉⡇⢸⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⣤⣛⣿⣿⢡⣀⣧⣰⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⢾⣯⣿⣿⣿⣿⡿⣾⣿⣿⡇⢸⣿⣿⣿⣿⣿⠟⠙⠻⣿⣿⣿⣿⣶
⢤⢠⣔⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠇⠀⣾⠀⠀⠀⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⠟⢉⣾⣷⠀⣼⣿⣽⣿⣿⣿
⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢠⣿⡇⠀⠀⣿⣿⣿⣷⣼⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣡⣴⣿⡿⠥⠴⠿⠿⠿⠿⠿⠿
⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠒⠚⠛⠓⠒⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⣻⠿⣭⢭⣍⣉⡿⣿⡄
⠀⠀⠀⠀⠀⠀⣼⣿⠉⠶⢻⡽⢯⣽⣿⠶⠿⣡⣿⠇
⠀⠀⠀⠀⠀⠀⢹⣿⣛⣛⠛⠛⣋⣉⣤⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠻⣿⣿⡹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡅⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⣻⡶⠶⣍⠻⣷⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⢠⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣍⣻⣷⡤⠜⢧⣹⣿⣛⣿⡿⠿⠿⡿⠿⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⠒⣿⢿⠘⡇⢿⡿⠿⠿⠿⠶⢶⣶⡆⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣜⠛⢁⣟⣿⡇⠀⠀⠀⢀⣾⠏⢁⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠋⠀⠀⠀⠀⣾⣯⣦⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣼⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠌⠉⠭⠵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠏⠉⠔⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠛⠿⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣧⡀⢾⣛⢧⡌⣙⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⡛⢦⣅⣐⡋⠹⠆⠈⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠫⠥⢶⣞⣖⣢⡍⢛⠿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣶⣤⣍⣙⣛⣓⣻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠷⣬⣉⡫⠽⠖⠗⠩⠄⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⣽⡟⠉⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣭⣙⣛⣛⠛⠛⣛⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⠟⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠛⠛⣿⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠟⢋⣡⣤⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣷⣀⣸⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣏⠻⠱⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠭⣭⣭⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⡘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣷⣾⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠐⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣠⣭⣳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⣿⣿⢿⣟⡻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⣴⣿⣿⣟⡷⣮⣛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣼⣻⣿⣿⣯⣛⠶⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⣾⣿⣿⣽⡻⢶⣝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⣾⣿⣿⡿⣯⣝⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠻⣄⠀⠀⠀⠀⠀⠀⢠⠏⢠⣿⣿⣿⣯⣛⠷⣭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠙⣦⠀⠀⠀⠀⣠⠋⣠⣿⣿⣿⣟⢶⣍⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⢷⡀⠀⣰⠃⣰⣿⣿⣿⢾⣝⡳⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⣠⠤⡳⡴⠁⢰⣿⣿⣿⣟⠷⣮⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠽⠃⠙⣆⠀⠻⣿⡷⣭⡛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠈⢷⡒⠒⠿⣶⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢹⡦⠤⣄⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣠⠋⢹⡀⢸⠙⠲⣌⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡰⠃⠀⠀⢣⢸⡄⠀⠈⠳⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡜⠁⠀⠀⠀⠈⣇⢧⠀⠀⠀⠈⢦⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠞⠀⠀⠀⠀⠀⠀⢹⡈⣆⠀⠀⠀⠀⢳⡀⠈⣩⣭⣭⣲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣡⠋⠀⠀⠀⠀⠀⠀⠀⠈⡇⠘⣆⠀⠀⠀⠀⡇⡾⠁⠀⠀⠙⢿⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣈⣓⢤⡀⠀⡇⢧⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣱⠋⠉⠉⠻⣮⣶⣛⣞⢧⡀⠀⠀⢀⡿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠀⠀⠀⠈⣿⣇⠈⠳⢭⣛⣚⣫⣞⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡘⣄⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠈⢣⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣓⠦⠤⢾⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠱⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠠⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⢻⠿⠋⠀⠀⠀⠀⠀⠔⠀⠀⠀⠠⠂⠀⡠⠶⠖⠀⠖⠀⠆⠀⠆⠀⠛⠒⠠⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⣀⣈⠁⠀⢠⠂⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⣀⠀⢐⠀⠀⠁⠀⠀⠄⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠐⠄⣀⠀⠀⠀⠀⠀⠀⠀⡄⢀⢀⡯⠖⠀⠀⢹⠁
⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⢸⠉⠃⠀⠀⠀⠀⠀⠀⠀⠓⠀⢒⠒⠐⠂⠀⠀⠀⠈⠉⠓⠒⠒⠒⠒⠓⠋⠉
⠀⠀⠀⠀⠠⡀⢰⠀⠀⡆⡆⠘⠀⠀⡇⠀⠀⡏⠀⠀⡔⢸⣽⢲⡄⢁⣈⠀⠀⢀⡀⠐⠃⠀⢀⠉⠀⠀⠘⡁⠀⠒⠒⢀⡀
⠀⠀⠀⠀⠀⠁⠈⢀⠟⠛⢻⡁⠀⢠⡇⠄⢠⠃⠀⠸⣚⣚⣗⣰⡇⢀⠀⠀⠀⠈⠀⠀⠀⣰⠛⢿⡄⣴⠀⠀⠀⠀⣄⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⢸⡇⠀⠈⠁⠀⠀⠙⢋⠏⠃⠄⢀⠁⠀⡀⢠⠀⠀⠀⠘⠳⠾⠃⢸⠀⠀⠀⢰⡟⠊⠃⠀⢠
⠀⠀⠀⠀⠄⠀⠀⢸⠀⠀⠀⣿⠀⠘⠓⠀⠀⢸⢠⡖⠀⠸⠀⢰⠀⢸⠀⢀⣇⢀⠀⠀⢰⠛⠉⠀⠀⠁⠀⠀⠀⢸⡇⠀⠀⠈
⠀⠀⠊⠀⠀⠀⠀⠈⠆⠀⢰⠏⣀⠯⠀⠀⠀⠈⢸⡇⠀⠀⠀⢸⠀⠈⠀⠐⠶⢺⡀⢀⡀⠧⠔⠰⠶⠆⠀⠀⠐⠀⡇⠀⣷
⠀⠀⠀⠀⠀⠐⠀⠀⠀⢒⡋⣀⢹⠀⠀⡄⠀⠀⠠⠁⠆⡏⠀⢸⠀⠀⢠⡆⠀⠀⠀⠈⢱⢸⠀⠀⢆⠉⠀⠀⠀⢰⡇⠀⠁
⠀⠀⠛⠒⠋⠁⠀⠀⠀⠸⡝⠹⢸⡀⠀⠳⠀⠀⡄⠀⠀⠁⠴⠞⠀⠤⢹⠀⠘⠌⠀⠀⠈⢘⠀⠀⢸
⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠑⠃⠀⢡⣤⣤⡄⢰⠁⠀⠀⠀⢠⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠇⠀⠀⠀⣀
⠐⠒⠒⠒⠒⠒⠒⠀⠒⠒⠓⠒⢢⣤⣤⣤⡄⢸⠀⠀⠀⠀⠘⡇⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⡄⠀⢀⡃⠀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠘⠀⠀⠂⠀⠀⠏⠀⠀⠀⠀⠀⠋⠀⠀⠄⠀⠃⠀⠀⠳⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⣾⡥⣄⠀⠀⢄⠀⢀⣠⠀⠀⠉⠁⠈⠉⠉⠉⠉⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠁⠀⠀⢦⠀⠀⠱⠂⠀⢀⣀⣀⣨⠀⠀⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠱⠶⠖⠁⠀⠙⠛⠁⠀⢀⣀⠁⠊⡠⠂⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢿⣸⡇⠈⠀⠀⠋⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠉⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢀⣼⡇⠀⠀⠐⠒⠉⡄⠀⠸⣠⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠸⠿⠇⠀⠀⠀⠀⠀⠸⠆⠀⠛⠀⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠸⠯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠚⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠠⠀⠁⠀⠀⠀⠡⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡀⠀⠀⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠚⠛⠃⠀⠀⠀⠈⠀⠀⣀⡜⠁⣀⠆⠀⠀⠀⠀⠀⠘⣄⡀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣠⠆⠘⠀⠀⠀⠀⠀⢄⡀⠀⠌⠀⣶⡄⠀⠀⠀⠀⠀⢀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⣿⣿⢰⣾⡿⣿⡷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠈⠁⠀⠘⠃⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⣠⠄⡠⢔⣶⣶⣤⡀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠁⠋⡴⣫⣿⡿⣿⣿⣦⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⣤⡼⢋⣴⣾⣿⢿⣿⡆⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢈⡴⢉⡜⣿⣵⠏⡴⠚⣿⡇⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠰⣫⠞⠁⠀⠀⠀⠾⢿⡷⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣡⣴⡶⠾⢿⣶⢶⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣾⣯⢤⡄⠀⠀⠠⠛⣿⣧⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⣠⡾⣿⡟⠠⡤⠀⠀⠰⠄⢿⣿⡀⣀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠛⠋⠉⢧⡀⠀⠀⠀⠀⢰⠞⠳⠿⠿⢋⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢠⡒⢤⡀⠀⠈⣵⠀⠘⠛⢠⡜⠀⠀⣠⠖⠉⠹⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢶⠀⠰⠟⠳⣄⠻⡀⠈⠛⠛⠅⢠⡞⠁⠛⠀⠰⢶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⣛⠛⠻⣷⣶⠟⣲⠛⠲⠶⠋⣠⡞⠁⠚⡛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣠⡶⠋⠙⠃⠈⣉⠉⠙⠃⣜⠉⢷⣟⡂⢻⡍⢠⣾⠠⣦⠉⠑⢶⡄
⠀⠀⠀⠀⠀⠸⣿⣆⠘⠃⠀⠀⠉⠀⢠⡄⢹⣆⠂⣙⠛⣂⣤⡿⠋⡀⠀⢠⣤⠀⠻⠄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢈⣿⠇⠀⠀⡶⠀⠀⠈⠀⠀⢻⣄⠛⠉⢉⡄⠀⠈⠁⠀⣀⣀⠀⠀⣤⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣠⠞⠁⠘⠃⠀⠀⠀⠛⠁⠀⠈⠠⠿⣶⣤⡀⣁⣤⠶⠞⠛⠋⠉⢹⠀⣀⠀⢰⡄⢻⡄
⠀⠀⠀⠀⣸⣧⠀⠋⠀⠀⠀⠛⠀⠰⠀⡀⣤⢀⠀⠀⠈⡄⢡⠀⠀⠀⢀⠀⠀⢸⠈⠋⠀⠀⣠⡼⢧⡀
⠀⠀⠀⢸⣿⠃⠰⠄⠀⠛⠀⢴⡄⠂⠲⣍⡄⠠⠀⠀⠀⡇⠸⠀⠀⠀⣨⣥⠂⠘⠷⣄⠓⠐⡏⠀⠀⠙⠷⣄
⠀⠀⢀⠄⠁⠙⢦⠀⠀⣠⡄⠁⠀⠀⣈⣿⠞⠁⠀⠀⠀⠉⠀⠀⠀⠀⠁⠟⢀⣀⣀⠈⠛⠶⢜⣧⣄⣀⡀⠈⠳⣄⠀⠀⠀⠀⠗
⢀⡴⠃⠀⠀⠀⠀⠈⠉⠁⣠⡴⠾⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠗
⣼⠁⠀⠀⠀⢀⣠⡴⠶⠿⣿⣶⡆⠀⣆⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⣠⠔⠛⠃⠀⢠⡍⠻⢶⣤⣀⡀⠀⢀⣿⠂⠀⠀⠦
⠻⣶⣶⡾⠟⣟⠁⠌⠙⠶⠈⣿⡀⠤⠈⠉⠀⠒⠢⢤⣄⣀⣀⣁⡀⠐⠶⣭⣄⡀⠀⠀⠀⠀⠀⠠⠤⠄⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠙⠷⠞⠻⡆⠀⣿⡿⠀⠀⠦⠀⠀⢂⣤⣾⣿⣿⡿⠛⠳⣄⠀⠉⠛⠧⠐⣴⠀⢀⣴⢾⣶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢀⣿⠁⣠⡄⠀⣠⣾⣿⣿⣿⣿⠏⠀⠀⠀⠘⣆⠺⠆⠀⠀⣿⡀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠈⢋⣿⡏⠀⣿⣿⣿⣿⡿⠋⠻⣄⠀⠀⠀⠀⢹⣆⠀⠀⠰⢿⣧⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡿⢀⣇⢰⣾⣿⡀⢰⣿⣿⣿⣿⠁⠀⠀⠘⡆⠀⠀⠀⠀⢿⣆⢀⡄⠀⠉⠣⡈⢣
⠀⠀⠀⠀⠀⠀⣼⣧⣾⣹⣿⣿⡏⠁⣿⣿⣿⣿⡏⢠⡄⠀⠀⡿⠀⠀⠀⠀⠸⣿⡌⠛⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⢠⡟⠇⣼⡇⢹⣿⡇⠀⢸⣿⣿⣿⡇⠀⠁⠀⠀⢷⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠘⠶⠀⠘⣷⡄⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠈⣇⢠⡿⢀⣿⣿⡷⠶⠈⣿⣿⣿⡇⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⢹⣿⣧⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⣿⣿⡇⠘⠃⠀⠀⠘⠃⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⣾⣯⠀⠀⠘⣿⣿⣶⠄⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⣷⡄⠀⠀⢹⣿⡇⠀⠀⣀⠀⠀⠀⢀⡀⠈⢻⣧⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣼⡿⠁⠀⢾⠆⠘⠛⠃⠀⠀⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⢸⣿⡇⠀⠀⠉⠀⠀⠀⠘⠋⠀⠈⣿⡇⠀⠀⣤
⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⢴⡄⠀⣰⣿⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⢸⣿⣷⠀⠶⠀⠀⢸⠆⠀⠀⠀⠘⢿⣿⠀⠀⠁
⠀⠀⠀⠀⣿⣿⠀⠀⠛⠂⠀⠀⠀⢀⡴⠉⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣄⣀⣀⣀⡀⠀⠀⢰⡦⠀⢸⣿
⠀⠀⠀⠀⠸⣿⡀⣠⡄⠀⠰⢀⠴⡏⠀⠀⠈⠛⢻⠀⠀⡟⢻⣿⣿⣿⣿⣿⣷⠀⢡⡈⠙⣇⠀⢈⡇⠈⠳⣄⠀⠀⢸⡿⠀⠂
⠀⠀⠀⠀⠀⠙⢷⣄⠀⢀⣶⡇⠀⠁⠀⠀⠀⠀⢸⡇⢰⠀⠀⠙⠿⠿⠿⠋⠸⣆⠀⢁⢀⡇⠀⣠⠁⠀⠀⢸⣷⠀⣾⠃⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠘⣷⠀⡆⠀⠀⠀⠀⢸⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⢿⡇⢰⠇⠀⠀⠀⠀⠻⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡇⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣈⣵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠃⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡟⠀⠀⠀⠀⠀⢸⣦⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣳⡀

⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣶⣶⣶⣶⣶⣶⣶⡾⣻⡿⠃
⠀⢀⣴⣾⣿⢿⣿⠿⣻⠝⣻⢟⣿⠟⢋⣽⣿⡽⣿⢟⣽⣾⢿⣫⢟⣯⣿⡽⣛⠝⡫⢞⠵⣿⠟⠙⣫⣾⠏
⣠⣾⡷⠿⠖⠛⠷⠚⠕⠋⠕⠋⠀⠚⠋⠘⠁⠈⠀⠉⠁⠀⠈⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⡇⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⣇⠀⠀⠀⠀⠀⠆⠀⠀⠻⠀⠐⡀⠀⠉⠀⠸⠀⠰⠄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⣿⠀⠀⠆⠀⠀⠀⡄⠀⠀⠀⠁⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⢸⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠈⢠⠀⠃⠀⠀⠰⡆⢐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠘⣏
⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢃⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠈⠄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢹⡇⠀⠀⠀⠀⠂⠀⢰⠀⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡈⠆⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⢸⡇⢰⠀⠀⡄⢀⠀⠀⠃⠀⠀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠘⣿⠀⠀⠁⠁⠈⠀⠃⠀⠀⠀⡆⠀⠀⠐⡄⠀⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⣿⠀⡄⠂⠁⠐⠆⢆⢰⠸⡄⠃⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣿
⠀⠀⣿⡇⠀⢆⢲⠀⠀⡄⠈⠀⠁⠀⡄⠀⡀⡄⠃⢦⠀⠠⠀⠀⢻⠀⠀⠸⣤⢀⠀⢰⡄⠀⡃⠘⠈⢠⡆⠀⣿⡄
⠀⠀⢹⣧⠀⠈⠬⠁⠀⠐⠐⡶⠀⠃⠙⣆⣁⠀⠀⠀⠀⠠⠄⠨⠄⠀⠤⠀⢀⣈⣀⣀⣀⣀⣀⣀⣀⣀⢐⣂⡿⠛⢷⣄
⠀⠀⠘⣿⣦⡷⣾⣷⣦⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⣿⡿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣦⠀⠙⣧⡀
⠀⠀⠀⣿⣿⣷⣜⢿⣿⣿⣾⣟⢛⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣤⣄⠊⠻⣦⡀
⠀⠀⠀⣿⢻⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣃⣀⠈⢻⣄
⠀⠀⠀⣿⠀⡿⣿⢿⡿⣦⡻⣿⣿⣍⣻⣷⣶⣾⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣿⣛⣟⣻⣛⣻⣿⣿⣿⣧⠈⠙⢷⡄
⠀⠀⢸⣿⠀⢘⣻⣯⢻⣿⣷⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻⣿⡿⢿⣷⡄⣹⣦⡀
⠀⠀⢸⣿⠀⣌⡛⠙⢇⢻⣮⣿⣷⡝⢿⣿⣿⣿⣭⣽⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠟⠻⠛⠛⢻
⠀⠀⠈⢻⣤⣿⡉⠻⣜⣧⢻⣿⣿⡟⠀⠍⠉⣁⣀⠀⢀⣀⠀⠀⣄⡄⠀⠀⣀⣤⣤⣶⣶⣶⣶⠞⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠹⣿⣿⣆⡵⣜⣷⣿⣿⡇⠀⠚⠉⠁⠀⠈⠉⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⡿⣿⣿⣶⣶⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⢻⣿⡖⡝⣾⣿⣿⣇⣴⣶⠉⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⡿⢿⣿⡙⣿⣷⡸⠿⢻⣷⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠇⠀⠔⢃⣠⣴⣾⣿⣿⣿⣿⣿⡿⣿⣷⢶⣙⢷⣌⣿⣷⣾⣿⣿⣿⡿⣿⣍⣾⣿⣿⣿⡿⠟⠋⠁⠚⠉⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡄⢾⣍⣈⣿⣾⣿⣶⣿⣿⣷⣿⣿⣯⣼⣷⣿⣿⣿⡿⠟⢃⣤⠀⠐⠀⣞⠛⠯⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣟⣭⣶⣶⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣉⣻⣉⣝⢛⣟⢋⣿⢻⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣠⣤⣠⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢻⡿⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⣿⣿⡇⠀⢰⡇
⠀⠀⠀⢸⣷⣶⣶⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠅⠀⠀⠀⣿⣿⣷⠀⠸⠇⠀⠀⠀⠀⢀⣀⡀⡀
⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⣤⣾⠀⠀⣶⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀⢸⣿⡇⡏
⠀⠀⠀⠀⣿⣿⣿⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⡞⠂⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡷⣿⠀⠀⡇⠀⠀⠀⠀⢸⣿⡇⡇
⠀⠀⠀⠀⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⣴⣧⠀⣿⡇⠀⠀⠀⠀⣿⣇⡀⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣷⣿⢰⣾⣷⡆⠀⠀⢀⣘⣿⣧⣇⡀
⠀⠀⠀⠀⢿⣿⣿⠃⡇⠀⠀⠀⠀⠀⣿⣿⠀⣿⡇⠀⠀⠀⢸⣿⡇⡇⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢸⣿⣿⢠⡇⠀⠀⠀⠀⠀⣿⣿⠀⣿⡇⠀⠀⠀⢸⣿⡇⡇⢸⣿⢈⡇⠀⠀⠘⣿⠂⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⠀⠘⣿⣿⣿⣟⡀
⠀⠀⠀⠀⠈⣿⣿⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣠
⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⣀⣤⣄⣀
⠀⠀⠀⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⢹⣶⣾⣿⣿⣿⣿⣷⣶⣶
⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢀⡾⠋⠀⠀⠙⢷⡄⠀⠀⠀⠀⣀⣙⣛⣛⣛⣛⣛⣋⣠⠀⠀⠀⠈⠻⠟⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⣾⠁⠀⠀⠀⠀⠘⣷
⠀⠀⠀⣿⣿⢶⣶⣶⠀⠀⣿⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠉⠉⠉⠉⠋
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢹⡄⠀⠀⠀⢀⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠻⠲⠒⠓⠓⠚
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠙⢶⣤⣾⡷⠏⠀⠀⢀⣤⣤⣤⡄
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠾⠿⢿⣿⣿⣿⠿⠷⠆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⣿⣿⢚⣛⣾⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢀⣈⡇⠀⠀⠀⠀⠀⣾⠉⠙⠻⣿⣿⠟⠋⠉⣷
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠘⡆⠀⠀⠀⢠⣾⣿⣿⣧⡀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠦⣄⣰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⢷⣤⣀⣀⣀⣀⣴⡾⠃
⠀⠀⠀⠿⠿⠛⠛⠛⠁⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠙⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠤⠤⠤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⣀⣀⣀⣀⡐⠂⠄⡀
⠀⠀⠀⠀⠀⠀⡊⠀⠠⠄⠤⢾⣷⣶⣒⡂⠄⠙⣆⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⣀⣀⡼⠀⠀⠀⠀⠀⠀⡀⠀⠰⢮⣝⣀⣐⢧⡽⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠙⢄⠂⠠⠤⠤⠭⠥⠤⠤⢤⡶⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣶⠚⠋⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⠶⣦⣤⣬⣭⣭⣥⣤⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡛⠛⢺⣧⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡂⠠⠬⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢯⡑⣲⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠢⠍⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⡶⠬⢭⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⣁⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠉⠹⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡂⠄⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣍⣓⢲⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⢁⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡑⠈⠽⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣑⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⡁⢲⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢁⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠙⠤⣬⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣑⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡲⠤⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃



⣿⣿⣿⠿⣿⡿⢿⢿⡿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣷⣦⣶⣷⣶⣿⣶⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⣀⡀⠀⢀⣠⢤⡀
⠀⠀⣿⠀⠀⢠⡎⠁⠀⠀⠈⠙⡆⠀⣼⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣀⠀⠀⢸⠀⠀⢸⠀⠀⢹⣿⠀⠀⠀⢸⣿⠀⣼⠁⠀⢳
⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⢠⠃⠀⠘⠿⢿⣿⣿⠿⠿⠛⠛⠛⠛⠙⠉⠀⠀⠀⢸⠀⠀⢸⠀⠀⠸⣿⠀⠀⠀⢸⣿⠀⣏⠀⠀⢸
⠀⠀⣿⠀⠀⠀⢣⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢾⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⢹⡀⢀⡟
⠀⠀⣿⠀⠀⠀⠀⠉⢲⡶⠋⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⠀⠀⠑⣿⠀⠀⠐⢾⣿⠀⠀⢹⡟
⠀⠀⣿⣦⡀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠘⠀⠀⠀⣸⠀⠀⠀⢸⣿⠀⠀⢸⣇
⠀⢰⣿⡆⢹⡄⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠚⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣞⡿⠀⠀⢸⡿
⠀⠸⣿⡇⠀⠁⠀⠀⠘⠃⠀⠀⠀⢀⠀⠀⢆⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁
⠀⠀⣿⡄⠀⠀⠀⢀⡠⠤⠤⢄⡀⠀⠑⢄⠸⣆⠀⠀⠐⠋⠁⠀⣠⣀⣤⡄⠀⠀⠀⠀⠀⠀⠰⣶⣶⣦⣶⣶⡶⠀⠀⣰⡾⠿⢿⣦
⠀⢠⣿⡇⠀⠀⡴⠁⠀⠀⠀⠀⠉⢦⠀⠈⠳⣿⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⢈⣿⡏⠀⠀⠀⠀⣿⣅⠀⢠⣿⠂
⠀⠘⣿⡇⠀⣴⠃⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠈⢷⣦⡀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠛⠿⠛⠁
⠀⠀⣽⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢰⠏⠑⢦⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡳⢦⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⣤⡀
⠀⠀⠛⠀⠀⠀⠫⢗⠤⠤⠤⠴⡺⠏⠀⠀⠀⢀⠼⡀⠀⠀⣍⠈⣢⠀⠀⠀⢻⣻⣿⣿⣿⣿⣷⡄⠀⠀⠀⡇⠀⠀⢸⡀⠀⠀⣿⡇
⠀⠀⢀⡀⠀⠀⠀⠀⣬⣽⣮⣥⠀⠀⠀⠀⠀⢆⢀⡼⠀⠀⠀⠈⠉⠲⠀⠀⠀⠁⠙⠛⢿⡿⣿⣿⠆⠀⢸⣿⣿⣿⣿⡇⠀⠀⣿⡇
⠀⠀⣸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⣤⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⣿⡇
⠀⠀⣿⣿⣧⠀⢠⣤⣤⣤⡄⠀⠀⢰⣷⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠀⠀⣹⣿⣿⣿⣶⢤⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠉
⠀⠀⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⣴⣾⣿⣶⡄⠀⠀⣿⣿⠃⠀⠀⡆⠀⣠⠟⠋⠉⣿⣿⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣇⠀⠀⡇
⠀⠀⣿⣿⣿⠀⠸⣿⣿⣿⠃⠀⣿⣿⣿⣿⡇⠀⠓⣿⡇⠀⠀⢀⡇⠈⠁⠀⠀⢸⣿⣿⡁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⢀⣴⣿⣿⣿⣿⣦⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇
⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⠀⠀⠀⣼⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡷
⠀⠀⣿⣿⡿⠀⠀⢽⣛⣿⠀⠀⣿⣿⣿⣿⡇⠀⠀⡟⠀⠀⠀⣿⣿⡁⠀⠈⢿⣿⣿⣿⣿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⣤⡮⠜⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠠⢿⠏
⠀⠀⠀⠀⠀⠸⠿⢿⣿⡟⠋⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣠⣤⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠚⠙⠓⠶⣤⣄⡀⠀⠀⠀⠀⠀⣇
⢀⣼⣿⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠀⠀⠀⠀⢿
⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠉⢰⠣⠀⠀⠀⠀⠀⠀⡾⠃
⠀⠀⠀⠀⠀⠀⠈⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⢀
⣄⠀⠀⠀⠀⠀⠀⠀⡜⢄⢁⣄⠀⠀⠀⠀⠐⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠻
⠈⠳⢦⡀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢸⣦
⠀⠀⠀⠉⠳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⢀⢴⠏⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣿⣷⠄⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠿⠇⠀⠀⠀⠀⠀⢓⠊⠀⠀⠀⠀⢠⣤⣤⣾⣿⣿⡿⠟⠉⠀⠀⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠐⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢻⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⣆
⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠈⠙⠛⠛⠓⠶⠒⠃⠐⠂⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠈⢀⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢤⢧⣀⣿⠀⠀⠀⠀⠀⠀⠀⢠⠐⢦⣷⣀⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⡼⠀⠈⠉⠂⠀⠀⠀⠀⠀⠀⠘⢦⡼⠇⠈⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣦⣄⠀⠀⠀⠀⢠⣿⣷⣶⣠⡀⠀⠀⠀⠀⠀⣰⣿⣷⡶⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠃⠀⠀⠀⣰⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠁⠀⠀⠀⢴⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠁⠀⠀⠀⠀⠈⠉⠛⢿⡿⠁⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⡀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⠀⠀⠀⠀⠀⠀⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠏
⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢟⠐⠡⠆
⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠃⠀⠀⢀⡔⠱⠀⠀⠀⠀⠀⠀⣠⢘⠂⡀⠀⠨⠗
⠀⠀⠀⠒⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡘⠀⠀⢀⠎⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣰⡄
⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⠃⠀⡠⠃⠊⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠛⠛⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡚⠀⡔⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢈⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠈
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⠃
⣀⣀⣄⣀⣄⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡛⣛⢛⣉⡛⣻⡛⣻⠟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠑⠄⠀⢀⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⡀⠀⢠⠊⠉⠑⡄
⠀⠀⠀⠀⡠⠔⠢⣀⢰⠀⠀⠀⠀⠀⠂⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠐⠀⠈⠀⠀⠀⡆⣠⠄⠢⢄
⠀⠀⠀⠀⣇⠀⠀⠈⢮⢇⠀⠀⢀⢰⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⡆⡀⠀⠀⡸⡵⠁⠀⠀⣨
⠀⡠⠤⣀⠨⠳⡀⠀⠀⡈⢆⠀⠘⠘⠂⠀⠔⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠢⡀⠐⠃⠃⠀⡰⢡⠀⠀⢀⠞⠍⣀⠤⢄
⠸⠀⠀⠀⠑⠄⠑⢄⠀⢡⠈⢆⡴⠀⡀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠁⢄⡐⠁⡌⠀⡤⠊⠠⠊
⠀⠉⠒⢄⣀⡈⠢⡀⠳⣌⠂⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠀⠀⠀⠐⣣⠞⢀⠔⢁⣀⡠⠒⠉
⠀⠀⠀⠀⠀⠈⠑⠚⠂⠀⠀⡠⠒⠒⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠒⠂⢤⠀⠀⠐⠓⠊⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢀⠀⠀⠀⠀⠀⢰⠀⠀⡆⠀⠀⠀⠀⠀⠀⠔⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠀⠀⢘⠀⠀⡃⠀⠀⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡠⠊⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣶⣾⣿⠿⠿⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢀⣠⣶⣾⣿⠿⠿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠀⢹⣿⣇
⠀⠀⣠⣾⣿⠟⠛⠉⠀⠀⠀⠚⠃⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠿⠟⠋⠉⠀⠀⣠⣾⣿⠇
⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⠾⠛⠛⠋⠉⠁⠀⠀⠀⢀⣀⣤⣶⣿⠟⠋
⣾⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⣶⡶⠿⠛⠛⠁⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⡿⠟⠛⠋⠁
⣿⣿⣟⠛⠛⠛⠻⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⢀⣀⣤⣤⡶⠶⠿⠋⠉⠉⢹⣿
⠈⠿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⡾⠿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠈⠉⠉⠙⠋⠉⠉⠉⠉⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠄⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠃⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠁⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⢀⣴⠆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⣾⠋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⢀⠀⠀⠀⢰⣿⠁⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠛⠋⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠀⠀⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⢀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣧⣤⣤⣤
⣿⣿⣿⣿⣿⠿⠛⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⢀⡬⠍⠝⠢⢱⠀⡄⠀⠀⠀⠀⠀⣠⠖⠉⡠⠀⠀⠀⡢⡀
⠀⢠⠖⠚⠒⢁⠔⢠⠀⠀⠀⠀⠀⠀⠀⠀⣰⢳⠎⠉⠁⠀⠈⣞⡁⠀⠀⠀⠀⡼⠁⣠⠊⣠⠴⠊⠀⢱⡘⡄
⠀⢸⠗⠀⡤⢌⡆⠀⡆⠀⡄⠀⠋⡇⠀⠀⡇⠂⠄⠰⠀⠀⠀⡠⡄⠀⠀⠀⢰⡇⢰⠃⡀⠀⠀⠘⠀⠂⡇⢹
⠀⠀⠁⠁⠹⠚⠁⠀⠀⠀⠀⠰⡯⠀⠀⠀⠘⢄⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⡇⢻⠀⠀⠀⠀⠀⠐⠀⡗⢸
⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⡑⠂⠀⠀⠀⠀⢀⠇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢠⢖⣺⡶⠰⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⣉⠭⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠂⡚⠑
⠀⠀⢸⠙⠊⠐⢶⡞⠋⠀⠀⠀⠀⠀⢀⡠⠴⠒⠋⠁⢠⠞⡱⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃
⠀⠀⠈⠑⠈⢝⠉⠀⠀⠆⠠⠀⠀⠐⠁⠀⣀⣠⠤⠖⠃⣼⠁⠆⠀⠆⠀⢄⠀⠀⠀⠀⠀⣀⠀⠀⠊⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠊⠁⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⣸⠂⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠐⠀⠆⠀⠅⣀
⠀⠀⠀⠀⠀⠄⡀⢀⠀⠘⠀⠁⢀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⡀⠀⢀⡱⠀⠀⢀
⠀⠀⠀⠀⠈⢀⠃⡌⠀⠄⠀⠤⣾⠀⠀⠀⠀⠀⠈⢠⠰⢀⠀⠘⡘⠄⠀⠀⠀⠀⠀⠁⠀⢯⠄⠀⠴⠘⢢⠐⠀⡁
⠀⠀⠀⠀⠃⢸⠀⡇⠀⠀⡄⢀⡇⠀⠀⠀⠀⠀⠀⠈⠀⠐⠃⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⣞⠀⠄⠀⠀⢺⠀⠀⠐
⠀⠀⠀⠀⠀⠸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢸⣿⡆⠀⠀⠈⣹⡇⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⡄⠀⢸⡇⠀⡀⠀⢿⣿⠂⠀⣴⣶⣶⣶⣦⣴⣶⣶⣶⡄
⠀⠀⠀⣼⣿⣧⡀⠀⣾⣿⣿⣆⠀⠘⣿⣿⣿⣿⡇⠀⢠⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⣶⠀⠀⡇⠀⢸⡇⢰⡇⠀⢸⡟⠀⠀⡿⠉⠙⡟⠉⠙⡟⠉⠙⡇
⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⠀⠀⢘⣿⡀⠀⠀⠀⠀⠀⢾⣿⠀⠀⣿⡇⠀⣿⠀⠀⡇⠀⢸⡇⢸⡇⠀⢸⡇⠀⠀⠻⠦⠶⠿⠦⠾⠷⠦⠾⠃
⠀⠀⠘⣿⣿⣿⠃⠀⣿⣿⣿⣿⠀⠀⢿⣿⣿⡿⠀⠀⢸⣿⡇⠀⢸⣿⡆⠀⢺⣿⠀⠀⣿⡇⠀⣿⠀⢠⣷⠀⢸⡇⢸⡇⠀⢸⡇⠀⠀⠐⠀⠐⠒⠒⠒⠒
⠀⠀⠀⢻⣿⡿⠀⠀⢿⣿⣿⡟⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⠇⠀⢸⣿⠇⠀⢸⣿⠀⠀⣿⠇⠀⣿⠀⠐⣿⠀⢸⡇⠸⡇⠀⠀⡇⠀⠀⠚⠂⠚⠛⠛⠛⠒⠒⠒⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⣾⣯⡀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⠀⠀⠀⢀⣿⣿⡟⠃⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⣿⡟⡇⠀⠀⢠⣤⡹⢿⠃⠀⢰⣿⣦⣤⣤⣴⣾⣷⣶⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⡄⠀⠀⠀⠀⣬⣬⡉⠀⠀⠀⣿⣿⣿⣿⠿⢿⣿⣿⣿⡇
⠀⠀⢠⣿⣿⡇⠀⠀⠼⠿⠇⠀⠃⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⢸⡇⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣷⠀⠘⢠⣶⣿⣿⣷⣤⠀⠀⣿⣿⣿⣿⣶⣾⣿⣿⣿⡏
⠀⠀⢸⣿⣿⡗⠀⢁⠰⠶⠀⡇⠈⠀⠀⠈⠻⢿⡿⣿⣿⣿⣿⣿⠀⠀⣼⣇⠀⠀⣼⣷⠀⠈⡏⠀⢠⣿⡈⠄⠀⢸⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⠀⢀⣀⣀⣀⡀
⠀⠀⠐⠿⠿⠇⠀⠸⠦⠤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠁⠀⠸⠿⠿⠃⠘⠿⠿⠃⠀⠁⠀⠻⠿⠗⠀⠀⠘⠿⠿⠿⠿⠟⠀⠀⢿⠿⠿⠿⠷⡿⠿⠿⢿⡇
⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⢀⣄⣄⣄⣤⣠⣀⣠⡀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⢹⣟⢸⠠⠀⠆⠀⠀⠀⣿⣿⣧⣤⣼⣿⢿⡃⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣴⡿⢻⡟⡝⠙⢻⣷⡀⠀⠀⠀⠀⣼⣿⣄⠀⠀⠀⠀⠿⠶⠶⠶⠶⠷⠶⠶⠾⠇
⠀⠀⢸⡇⢸⢐⠀⡇⠀⠀⢸⡏⠈⡉⠀⠉⠁⢹⡇⠀⠀⠀⣿⣿⣄⠀⠀⠀⢸⣿⢠⡿⡱⠀⢀⡿⢻⡷⠀⠀⠀⢀⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣄⡀
⠀⠀⢸⡇⢸⢈⠀⡇⠀⠀⠘⡅⠀⠁⠀⠀⠀⢨⡇⠀⠀⡆⢡⣠⡌⢰⠀⠀⠘⣿⣿⡱⠁⢀⣾⣣⣿⡏⠀⠀⢰⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣞⣩⣶⠟⠋⡲
⠀⠀⢸⡇⢸⠘⠀⠇⠀⠀⠀⡟⠈⠉⣿⣿⣿⣿⠁⠀⠀⣇⠈⠉⠀⣾⠀⠀⢀⠈⢻⣿⣶⣾⣿⣿⠋⣀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡿⠛⠁⢀⣤⡇
⠀⠀⠈⠃⠘⠈⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠛⠛⠒⠛⠋⠀⠀⠈⠛⠛⠓⠒⠒⠚⠛⠛⠋⠀⠀⠈⠛⠛⠛⠛⠛⠁⠀⠀⠀⣀⠴⠚⠳⠦⣴⡋⣸⠁
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢷⣦⣄⠀⣀⡴⠛⠁
⠀⠀⢈⣩⠿⠛⠻⢯⣉⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁
⠀⢠⡟⠁⠀⠀⠀⠀⠈⢧⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⢿⢏⣤⡄⠀⠀⠀⢸⣿⣿⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣷⣶⡆
⠀⢾⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣰⠋⢋⣼⣿⣧⡀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠘⣧⡀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣿⣿⣦⣤⣄⣀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠔⠁⠀⠘⣿⣿⣿⠆⠀⠀⣿⣿⣿⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠈⠙⠲⠦⠶⠚⠋⠀⠀⠀⠀⠻⠿⠛⠤⠬⠿⠀⠀⠀⠀⠘⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠿⠿⠿⠃⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡟⡍⣿⠛⠿⠿⠿⠻⠟⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠿⠗⠶⢦⡙⢇⣠⣤⣤⠄⡀⢀⣴⢞⣫⣭⣬⣥⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀⠐⢠⣶⡿⣽⠋⣴⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣦⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠋⣠⣾⣿⣿⣷⠹⣿⣇⣯⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⣼⣿⣿⣿⣿⣿⣷⣌⠻⣾⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⢰⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣽⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⠟⣫⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣏⡄⢸⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠉⠙⠛⠶⠾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢸⡇⠘⣿⣿⣿⣮⣻⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢸⣷⡀⠹⣿⣿⠋⠀⠹⠟⠀⠀⠀⠒⠚⠛⠻⢶⣄⡀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡀⣿⣧⠀⢻⣿⣇⠀⠀⠀⠀⢲⣿⣶⣶⣶⣤⡄⠉⠁⠀⠠⠖⢒⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⢻⣿⡄⢠⢻⣿⣄⡀⠀⠀⠀⠙⠳⡮⣭⠟⠃⠀⢀⣶⣶⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⣿⢿⣿⣿⡇⣼⡞⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣻⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣟⣿⣿⣣⣿⣇⣿⣿⣿⠙⢦⡀⠀⠀⠀⢤⣀⡀⠀⠁⢠⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⣠⢞⣛⣲⠹⡿⢋⣥⡉⢻⣿⡿⣿⣿⠀⠀⠙⣦⡀⠀⠀⠍⠉⣠⣶⣯⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣼⣏⢺⣿⡿⢠⠃⣿⣿⣿⢸⣿⣧⣿⣿⡄⠀⠀⠈⢻⣶⣤⣴⣿⣿⣿⣿⢟⣥⣶⣶⣄
⠀⠀⠀⠀⠀⣿⣿⣦⣭⡤⣋⣾⣿⣿⠏⣼⣿⣿⣿⠋⢧⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡸⠿⣿⡿⣹⠃
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠟⠁⠀⠈⠃⠀⠀⠀⠙⠻⠿⣿⣿⣿⡿⠿⠿⣋⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢠⣤⣀⣤⣀⣤⢠⣤⣤⣤⣤⣄⡄⠀⣤⡀⣄⣄⣤⣄⠀⣤⣤⢀⣄⢠⣠⣤⡀⢀⣤⡀⣤⢠⡄⢀⣤⣀⣄⡄
⠀⠀⠸⠿⠿⠿⠼⠿⠾⢿⠇⠿⠁⠿⠁⠰⠿⠧⠿⠧⠿⠿⠀⠿⠿⠼⠿⠼⠼⠿⠇⠸⠿⠾⠿⠿⠷⠾⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣰⣄⡀⠀⠀⣀⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠝⠉⠀⢰⠿⡛⠃⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢄⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⡴⠠⡄⠀⠀⠐⠃⠀⠀⠀⠀⠅⠀⠀⠀⠋⠀⡀⠂
⠀⠀⠀⠠⠀⠀⠀⠀⠀⡖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠈⠀⢀⠀⠀⢀⠑⠋⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⡄⡀⢀⠀⣠⡀⢀⢤⡀⡀⡀⢀⣄⡀⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣧⡇⣿⡀⢻⡀⠘⢦⢠⣇⠀⢸⢸⢻⡇⠀⠀⠀⠈⢢⠄⠀⢀⣴⡿
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠓⠋⠁⠘⠖⠋⠘⠐⠂⠂⠀⠁⠐⡃⠀⠀⠀⠀⡀⠸⠟⠀⠀⠀⣀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⡀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠈⠈⠀⠀⠁⠀⠀⡀⠀⢄⠀⠉⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠖⠋⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠞⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⡰⠋⡦⠀⢠⡀⡇⠀⠀⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢅⢤⠞⠀⣀⠂⠀⠀⠳⣷⡀⠀⠄⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣆⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠉⠁⣿⡄⠀⠀⠀⡰⡇⠉⠓⢆⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠆⠁⠀⡠⠔⠂
⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠀⠀⠀⠑⠀⠄⡀⣀⣀⠀⠀⠀⠀⠓⠃⠀⠈⠁⢠⡄⠀⠀⠀⠀⠀⠾⠄⢸⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠑⠀⠀⠀⠀⣀⠀⠀⢀⣤⣦⡄⠀⢠⠀⠀⣶⠀⠈⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠈⢩⡥⠀⠸⠀⢀⢛⡀⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠐⠃⠈⠉⠀⠀⠓⠂⠧⠀⠊

⠀⠀⠀⢀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⣯⢺⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠘⣎⢿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠉⠉⠙⡆⠀⠀⠀⠐⠋⢹⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠘⣮⣿⢫⣿⣿⣦⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡃⠀⠀⠀⢸⣷⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠙⢮⡙⢿⣿⣿⣷⣄⠀⠀⠀⢀⣧⣤⣤⣤⣤⣤⣧⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠻⣿⣿⣿⣦⡀⠀⢰⣿⡀⢀⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡜⠁⢺⣿⣿⡄⠘⣛⣣⣬⣭⣭⣭⣭⣄⣀⠀⢸⣿⣿⠀⠀⠀⠀⣠⡾⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⢀⣀⣤⣶⣦⡀⠀⠀⠀⠻⣄⠈⢛⣩⣶⣿⠿⠛⠋⠉⠉⠉⠉⠛⠻⢿⣷⣌⡻⠀⠀⠀⣰⡟⢀⡄⠈⢙⣿⣿⣿⡿⠃⠀⣠⣶⣦⣄⡀
⢾⣧⡤⢿⣿⣿⡟⡆⠀⠀⠀⠈⣱⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⣰⡟⢠⣾⠁⢠⣾⣿⣿⡿⠀⠀⠀⡇⠀⠈⠙⢿⣦
⢺⣿⣷⠀⣿⣿⣷⢹⡄⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣟⣠⣿⠃⢠⣿⣿⣿⡿⠁⠀⠀⡜⣰⡀⠀⠀⠀⢹⠂
⠈⢿⣿⣧⢻⣿⣿⣧⢻⡀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⠟⢤⣿⣿⣿⡿⠁⠀⢀⣼⣿⡟⢡⠆⣠⠎⠁
⠀⠘⣿⣿⣇⢻⣿⣿⣯⢷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢀⣾⣿⣿⡿⠁⠀⣠⣾⡿⠋⣰⣿⡿⠁
⠀⠀⠸⣿⣿⡆⠿⣿⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⣿⣿⠙⠺⣿⣿⡿⢁⣤⡾⠋⠎⢀⡼⣿⡿⠀⠀⠀⢀⣠⡾
⠀⠀⠀⠹⣿⣿⣷⠹⣿⣿⣿⣷⠀⠀⠀⣠⣴⣾⡿⢿⣛⡿⠭⠭⠭⠭⠭⠽⣟⣿⢿⣿⣧⣄⠀⣼⡿⢡⣾⣿⣦⣀⠀⠞⢱⣿⠁⠀⢠⠂⢿⣿⠇
⠀⠀⠀⠀⢻⣿⣿⣆⢻⣿⣿⣿⣧⣴⣿⣿⡯⠗⠋⠁⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠉⠺⢻⣿⣿⣿⢡⣿⣿⠛⣿⣿⣷⣤⣼⣿⠀⣰⠟⣡⣿⡿
⠀⠀⠀⠀⠀⢿⣿⠈⣦⡹⣿⣿⣿⣿⡿⠋⢀⡠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⡀⢹⣿⣿⣿⣿⠧⢄⣿⣿⣿⣿⣿⠃⣴⠃⣴⣿⡟
⠀⠀⠀⠀⠀⠘⣿⣦⠛⠛⣾⣿⣿⠏⢀⠔⠉⠀⠀⢀⣄⣀⢸⣧⣀⡤⢖⣀⠀⠀⠀⠀⠈⢠⣿⣿⣿⣧⢀⣼⣿⣿⣿⣿⠃⠚⢅⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠘⣿⣦⣄⣸⣿⣿⡀⠁⠀⠀⠀⠀⣀⡤⠟⠋⢻⣥⠶⣈⣭⠉⢀⠀⠀⢀⣼⣿⣿⣿⣿⣸⣿⣿⣿⣿⠇⠀⠀⠀⣰⣹
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣟⣻⣿⣧⡳⣄⠀⠀⠐⠿⢥⣭⣶⣒⣻⡧⠞⣋⡤⠖⠁⣀⣴⣿⣿⣿⣿⣿⣏⣝⣻⣿⡿⣵⡆⠀⠀⡴⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠙⣿⣿⣷⣬⡑⣢⣄⣀⣀⠀⠀⠉⠉⣉⣉⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⡿⠛⣽⣽⡇⢀⣼⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠉⠀⠀⠀⠑⢦⡙⠻⢟⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣬⡛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⣉⣠⣽⣿⠟⠀⠀⠀⠀⠀⠀⢰⢸⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣯⣿⣿⣿⣿⣿⣥⣴⣶⣶⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⡜⣼⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⠀⠀⠀⠀⣠⣾⣾⣿⡟⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⢶⣤⣤⣤⣿⣾⣿⡿⢋⣤⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⠾⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣤⣄⣀⣀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⢠⣿⠛⢦⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡀⠀⠀⠈⣿⡀⢸⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢀⣴⣶⣶⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠛⠹⣧⠀⠀⠀⢿⡇⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⣿⡄⠀⠀⢸⣷⠀⢹⠀⠀⠀⢀⣿⣿⡇⠀⠉⢹⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣹⣷⠀⢠⣾⣿⡖⠘⣿⡇⠀⢸⣿⣿⡇⠀⠀⡞⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⣹⠿⢇⠈⣿⣿⣷⠆⢿⣿⠀⢸⣿⣿⠃⠀⢰⠇⠀⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠸⡀⣿⣿⣿⡂⠸⣿⡇⢸⣿⡿⠲⠤⡜⠀⡼⢁⣼⣿⠏⠙⠻⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣷⣾⣿⣿⡇⠀⢸⣇⣿⣿⡇⠀⣾⠃⡼⢡⣾⣿⡟⠀⠀⠀⢈⡿⠛⠋⠉
⠀⠀⠀⠀⠀⣠⣴⣾⠿⠿⠟⠋⠉⠉⠉⠙⠻⣿⣿⣷⡀⠸⣿⣿⣿⡯⢉⣿⡼⣡⣿⣿⣿⣄⡀⠀⢠⠎
⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⠀⣿⣿⣿⠙⢺⡿⣵⣿⣿⣿⣯⣀⣼⣷⠋⠀⠀⢀⠀⠀⢐
⠀⢠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⠁⠀⣼⣿⣿⣿⣿⣟⣵⣿⣿⣷⡶⣶⡆⢸⣷⣴⡟
⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⢹⣿⡀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⡇⣿⡇⢸⠛⠛⡇
⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢰⣿⣿⣿⣷⡼⢤⣤⠧⣄⠠
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣽⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⠀⣸⣿⠀⢸
⢻⣿⣿⣦⣀⡀⠀⠀⢀⣀⣤⣶⢿⣿⣿⡿⠛⠉⠉⢙⣿⣿⣾⣿⣿⣿⣿⣿⣀⢐⣗⣀⣽⠀⢸⣿⣿⣿⣿⠁⣿⣿⠃⢹
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠋⠉⠻⣦⣤⠞⠋⠀⢈⣹⢿⣿⣿⣿⣿⣮⣽⣿⣿⣿⠀⢸⣿⣿⣿⣿⠀⣿⣿⡇⢹
⠀⠀⠉⠛⠛⣻⣿⡿⠋⠉⠉⠻⣦⣴⠞⠋⠉⢙⣷⣶⡞⠉⠀⢀⣉⣿⣿⣿⠫⣭⣿⣯⣿⠀⢸⣿⣿⣿⣿⠀⣿⣿⡇⢸
⠀⠀⠀⠀⢸⣿⣿⣷⣤⣤⠶⠋⠉⠙⣷⣶⠞⠋⠁⢀⣙⣷⣾⣿⣿⣿⡿⢿⠀⢿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⣿⣿⡇⢸
⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣤⠖⠋⠁⠉⣻⣶⣾⣿⣿⣿⣿⠿⠛⠉⠀⢸⡇⢸⣿⣿⣿⠀⠘⠻⠿⠿⠟⠓⠛⠛⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠒⠒⠒⠒⠒⠂⠒⠆⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡠⠄⠀⢀⠠⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⡔⠒⠒⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡚⠀⣀⣀⢘⢲⡀⠐⠀⠀⠀⢰⠒⢢⠤⠄⠀⠀⠠⠄⠀⠀⠀⠀⢃⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢸⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡔⠃⠊⠙⠂⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠘⢀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠂⠘⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⠤⡆⠀⠀⠀⠀⢀
⠀⠀⠀⠖⠲⠖⠒⠒⠒⠂⠒⠂⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡇⠀⡠⠒⠂⠐⠒⢤⠀⠀⡴⠂⠑⢢⠀⠖⠉⠙⢆⢸⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡐⠇
⠀⠀⠀⡇⡘⠀⠀⠀⠀⠀⠀⢱⡀⢣⡀⢀⡼⠀⢦⣀⣀⠎⢸⠀⠀⠀⠀⠂⠀⠀⢸⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⡃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⣠⠤⢤⠄
⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⡇⣠⠆⠠⢄⠀⡴⠒⠢⡄⢸⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠧⠀⠀⠀⠘⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⡇⠱⡀⠀⠀⠀⠀⠀⣰⠁⣇⠀⠀⣸⠀⣄⠀⢀⡄⢸⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠰⠄⠀⠀⠠⠄⠄⠤⠀⠀⠐⠀⠀⠰⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡇⠀⠈⠢⠤⠀⠤⠞⠁⠀⠈⠉⠈⠁⠀⠈⠉⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⡀⠀⢀⣄
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠳⡀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠉⠒⢄⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡼⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠢⢀⣀⣀⣀⣀⡀⠠⠊⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⣅⠼⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠴⠊⢠⠘⠅⠉⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠤⠀⡀⠤⢀
⠀⠀⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠀⠄⡀⠀⠀⠀⠈⠀⠄⠀⠀⠤⠂⠀⠘⡆⠀⢀⡔⠚⠒⠒⠢⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠈⠀⠀⠀⢨⣀⠠⠀⠠⠐⠨⠀⠐⡇⠀⡎⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⢀⡠⠀⠀⠀⠀⠑⢤⡐⣀⢶⠡⡈⠎⠀⠀⠡⡀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⡆
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠔⠉⠑⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠈⠛⠂⠑⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⡇
⠀⠀⠀⠀⡄⠀⠀⠀⡇⠀⢐⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⡇
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡦⠀⠀⠠⠄⠀⢠⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠜⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠢⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠊⠀⠁⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣝⠳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡌⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠘⣿⣆⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⣦⡀⠀⠀⠉⣩⢴⣦⣄⣀⣀⢹⣿⡆⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠈⠛⠘⠋⠁⢸⣿⡇⠀⠀⢸⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⢀⣾⠇⡞⢳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⣠⠿⠁⠊⣠⣿⡇⠉⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡀⠀⠀⠀⠀⢀⣾⠟⠀⣠⠞⠁⠀⣠⣾⠟⠉⠀⢀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⠤⠀⠀⣾⡏⠀⣰⢋⠔⣡⡾⠋⢀⣠⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣿⠁⢰⣇⢎⣼⠋⣠⣴⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⢸⡇⣾⢃⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⢸⣷⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠠⢴⣆⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡀⠀⢈⣿⣿⣇⢀⡀⠀⢿⡆⠈⣹⡆⢀⣴⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠹⣿⣷⡀⢸⣿⣿⣿⣼⡇⠀⠘⣿⡄⠸⡇⠈⠻⢿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠛⠛⠷⠿⠋⠁⠀⢿⣿⣿⣿⡇⠀⠀⠙⢳⡀⠀⡼⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠋⠁⢀⣶⣦⠀⣔⠒⠂⠤⡀⠈⢻⣿⣿⡀⠀⢀⠀⠀⢣⠐⠁⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⢀⣁⠭⠀⠀⠈⢛⠉⠁⠀⢄⠀⠀⠀⠣⠀⡄⠀⠀⣴⣿⣿⡟⠉⢉⣠⣴⠾⠃
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢀⣼⣿⠏⢀⣤⣶⠟⠉⠀⢀⣠⠀⣾⡯⢿⣆⠀⠈⠳⣄⠀⠀⠀⡇⠀⣾⣿⣿⠟⠀⢀⣨⣥⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣿⠿⠃⠀⠀⠑⠁⣀⣤⠾⠛⠉⠀⠘⣿⣋⣿⣆⠀⠀⠹⠇⠀⢀⡇⢰⣿⡿⠋⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢰⡇⠀⢠⡾⠁⠀⠀⠀⢠⣶⣿⠿⠁⠀⠀⠀⠀⠀⠘⣿⣮⣿⡄⠀⠀⠀⠀⢸⡇⠸⠟⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⣠⠋⡅⣰⠏⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⣰⣿⣷⠀⠀⠀⠛⢿⡅⠀⠀⠀⠀⣾⡇⠀⠀⠀⡀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⠁
⠀⠀⢠⠚⢃⡰⠇⠀⢀⣴⡇⠀⢀⣠⣤⣤⣴⣶⣾⣿⣿⣿⣿⡦⠀⠀⠀⠈⢻⣄⠀⠀⠀⣿⣿⠀⠀⠈⡇⠰⠶⠦⠤⠙⠛⠿⠛⠋⢁⡀
⠀⠀⠀⠒⠈⢦⠀⠀⣼⡟⢠⣾⣿⣿⣿⣿⣿⣿⡿⠟⠋⣉⠉⠀⠐⣾⣿⣅⠀⢻⡆⠀⠰⣿⣿⣷⠆⠸⠷⠀⠀⢀⡤⢀⣄⠀⠀⣴⣿⢃⣴⡦
⠀⠀⠀⠀⠀⠈⢀⣼⡟⠀⠸⣿⣿⣿⣿⣿⠟⠋⠀⠀⣼⠟⠁⠀⠀⠻⣶⡟⠀⠀⢉⠄⠀⠀⠈⠃⠀⠀⣀⡴⠞⠉⠀⣸⣿⣆⣼⣿⣵⣿⣏⣴⡖
⠀⠀⠀⠀⣠⠚⣿⣿⠂⠀⠀⠉⠛⠻⣿⣷⡆⠀⠀⢰⠃⠀⠀⣄⡀⠀⠘⣇⠀⠀⠀⠀⠀⠁⣀⢤⣶⠟⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤
⠀⠀⠀⠀⠉⢸⣿⠃⠀⠀⡠⠀⠀⠀⢻⣿⣿⡅⠀⠀⠀⠀⣼⣿⠟⠂⠀⢹⡀⠀⡊⢀⡝⢁⡠⠊⠀⠀⣄⣿⡆⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⣼⣿⠃⠀⣠⠎⠀⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⣼⣿⠋⠀⣠⣀⠈⠇⠀⠀⢸⠉⡹⠁⠀⣤⡀⠘⠿⣿⠘⠻⣿⣿⣿⣿⡿⠛⣁
⠀⠀⠀⢼⣿⠏⢀⣴⠏⠀⢀⣤⡶⠀⠀⠀⠹⣿⠀⠀⣹⡿⠏⠀⣸⣻⠏⠀⠀⠀⠐⠊⠀⣤⠀⠀⢻⣧⠀⠀⢿⡆⠀⠈⠛⠿⠋⢀⣾⡿⢳⠂
⠀⠀⠀⠀⠀⢠⣾⡏⠀⣴⢿⣿⣷⣄⠀⠀⠀⣀⠀⣰⠏⠀⠀⣰⡿⠃⢰⣦⠀⠀⠀⢿⣦⡈⠻⢆⠈⣿⣇⠀⠘⡇⠀⢠⢄⠀⢠⣿⡿⡕
⠀⠀⠀⠀⠰⠿⠻⠁⠈⢻⣾⣅⠀⠉⠑⣠⡾⠋⣰⠋⢠⣀⠀⠋⠀⠀⠅⠀⠐⡀⠀⠀⠻⣷⣄⠀⠀⠸⣿⡄⠀⠇⠀⡄⢨⢀⣿⣿⠎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣦⣤⡀⠉⠀⠐⠁⡀⠈⠉⠙⠒⠄⠀⠈⠄⠂⠑⠀⠀⠀⠈⢻⣷⡀⠀⢻⣷⠀⠀⠀⠣⠃⣼⡿⠧⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⢠⣤⡈⢿⣦⡀⠀⣠⡄⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠙⢿⣦⠀⢻⣧⠀⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠁⣤⣝⢿⣮⣿⣷⣄⣿⣷⠀⠀⠀⢸⣿⣿⡆⠀⢤⡀⠀⠈⠻⣦⡀⢻⡆⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⣬⣻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⣧⠀⠀⠙⢷⣄⡀⠘⢿⣎⡿⡈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣴⡆⢿⣿⣇⠀⠀⠀⠸⡿⣦⡀⠑⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⠟⠁⢰⢿⠀⠘⣿⣿⣆⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠺⠎⠀⠀⠙⠛⠋

⣿⠿⠿⡿⢿⠟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣛⣻⣿⣟⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄⠘⢿⣿⡋⠉⠈⡇⢰⣿⣿⣷⡄⠀⠘⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⣿⠁
⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣆⠀⠀⠘⠛⣷⡀⠸⣿⣷⡀⠀⣷⢸⣿⣿⣿⣇⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⡰⢃⣼⣿⠃
⠀⠑⠤⡀⢀⣠⣴⣄⠀⠀⠀⠀⠹⣉⠀⠀⠀⢸⣿⣧⠀⢿⣿⣷⡀⢹⠀⣿⣿⣿⣿⠀⢸⠀⠀⡿⠀⠀⠀⠀⢠⣮⣀⣿⣿⠃
⠀⠀⠀⠈⢻⣿⣿⣿⣦⡀⠀⠀⠀⢻⣧⢣⠀⠈⡿⣿⣆⠘⣿⢿⣿⣹⡇⢻⣿⣿⣿⡆⢸⠐⠒⡇⠀⠀⠀⣰⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡄⠀⠀⠀⢻⣧⢣⡀⢹⣿⣿⡄⢹⣽⣿⣀⣷⢸⣟⣿⣿⣇⢸⠈⠉⡇⠀⠀⣰⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⣀⣨⣿⣿⣿⣿⣶⣦⣤⣌⣿⣧⢳⡀⢿⣿⣷⠀⢿⣿⣿⣿⡀⣿⣿⣿⣿⡆⠀⢸⡇⠀⣼⣿⣿⣿⣿⠏
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡳⠘⣿⣿⣧⠸⣿⣿⣿⡇⢹⢹⣿⣿⡟⠀⣼⣿⡏⠉⠛⠿⣿⣃
⠀⠀⣴⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣸⡟⠙⡆⢻⣿⣿⣿⠘⡟⣿⣿⡇⢸⣿⣿⣿⣿⣶⣦⣄⡙⠳⣦⡀
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⠀⢹⡈⣿⣿⣿⡄⣧⢿⣿⡇⠀⣿⣿⣿⡿⠟⢿⣿⣿⣶⣄⡙⢦⡀
⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠻⢇⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢧⢹⣿⣿⣇⢸⣸⣿⡇⢰⣿⢿⣷⣍⠀⠀⠉⠛⢿⣿⣿⣦⣽⡄
⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⣠⣔⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⡆⢿⣿⣿⣼⣷⣿⣦⣼⣯⣾⣿⣿⣷⣦⣀⠀⣰⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣅⣀⣠⣴⣿⠾⢋⣽⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⠸⣆⣽⣾⣿⠿⣛⠛⠉⠙⢛⡻⢿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⡃
⢻⣿⣿⣿⣿⣿⣿⣿⣯⢁⣤⣾⣿⣿⣿⣿⣿⣫⣾⣿⣿⣿⡿⣰⣿⡿⣫⣖⣭⡶⠾⠟⠛⠛⠻⢶⣌⠻⣿⣿⣆⠉⠛⠻⠿⠿⠟⠁
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠉⠀⠀⠀⠀⠀⠀⠐⠂⠈⠳⡜⣇⠘⣇
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⡿⠿⠟⠛⠛⢿⣿⣿⣿⠃⠀⠠⠀⠀⠀⠀⠸⠗⠀⠀⠀⢀⢹⣿⡄⣿⡀
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⡁⠀⠤⢤⣤⡀⢸⣿⣿⡏⠀⠰⣦⣶⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠟⠁⠀⠈⠳⣌⣧⣾⣀⣀⣸⣿⣿⣷⡀⠀⢨⠙⠓⠀⠀⠀⠀⠀⠆⠀⠀⣸⣿⢡⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⡏⠀⣤⣀⣀⣤⢀⣀⠈⠓⢦⠜⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢯⣾⣟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⠉⠹⣿⠌⠉⠑⠂⢁⣤⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣤⣤⣤⣤⣤⣶⣾⣿⢟⣫⠶⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⠀⠀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡷⠀⠀⡴⠀⢿⡿⢻⠃⠀⠘⠿⠿⣹⠃⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠺⣿⠟⡅⢀⠞⠀⠀⠀⡴⣡⠊⠀⠀⠀⡴⣣⣴⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠒⠦⡄⠀⣠⠏⠀⠀⣠⢞⡴⠋⠀⠀⠀⠈⠊⠀⠀⠀⢀⡾⠊⠘⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⡌⠘⠁⠀⠀⣴⣡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠄⣇⠀⠀⠀⢿⠀⠀⢀⣼⠟⠁⠒⠀⢀⡴⢁⡀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢹⡀⠀⠀⠘⣇⣠⡾⠃⠀⠀⢀⡴⠋⠀⠈⠁⠀⠀⡀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢷⣠⣾⣷⡜⣏⠀⠀⣠⡾⠋⠀⠀⠀⢀⡤⠊⠈⠙⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠉⠻⣇⠀⠀⠀⠈⠻⠿⣿⣿⠎⠀⠞⠁⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢹⡆⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⣆⠀⠀⠀⠹⣆⠀⢀⣤⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠘⣧⠀⠀⠀⠈⢷⡸⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⢀⡤⢂⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠈⢷⡀⠀⢀⣤⡀⣘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⡴⠋⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⢙⣦⠻⣿⣿⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⠞⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠙⢦⣀⢿⣿⣦⡝⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⣠⡴⠋⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠈⠓⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠛⠉⠁



⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿