Mizzle Emojis & Symbols

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠸⡿⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⡿⠿⠿⢿⣿⣿⣿⡿⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⠉⠁⠀⠀⠀⠀⠘⠿⠿⣿⣿⠏⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠈⠙⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠡⢄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠘⠆⠀⠐⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡄⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠩⠿⠻⡅⠠⠀⠀⠀⠀⣉⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠐⣁⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⡷⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⡿⠿⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⡆⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠘⠃⣀⠀⠈⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣩⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⠀⠀⠀⠀⣰⣿⣿⣿⡗⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⠀⠀⠀⣠⣿⣿⠟⠁⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⠋⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⣭⣉⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠈⠀⠀⠀⢀⠀⠀⢄⠄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⣴⣿⣆⣄⢈⠐⣰⣷⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣾⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣷⣁⠠⠀⢀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⡀⠀⠄⣂⣼⣿⣿⣿⣿⡇
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣶⠎⠀⠀⠀⠄⠠⠈⡀⠄⠠⠀⠀⠀⢱⣶⣾⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⡌⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⣴⣾⣶⡄⠀⠈⠀⠂⡁⠀⠀⠀⣴⣾⣷⡌⠆⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷⠀⢀⡐⠂⠄⠂⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢿⠟⠀⠀⠈⠣⠰⣠⣇⠀⠀⠘⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠁⠀⠀⠀⣻⢿⡿⡍⠀⠀⠠⠏⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠃⠀⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠰⣡⣶⣶⣦⣴⣶⣶⡕⡀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡆⢿⣿⣻⣿⣿⣿⣿⠇⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⠿⠿⠿⠟⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠒



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⣿⡄⠀⢀⣤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣼⡷⠀⢾⣻⠀⠀⠀⣰⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠻⠿⠟⠁⠀⠸⠟⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠁⠀⠀⢀⣀⢀⠀⠀⠀⢀⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠳⣄⠁⣤⡀⠀⠀⣠⣿⣿⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠈⠻⣾⣯⠑⠄⠙⢿⣿⣴⢃
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢶⣾⣿⣿⡄⠀⠀⢈⣿⣄⠀⢀⡌⠻⣯⣴⣶⣷⡆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡖⢂⣾⡟⠙⢶⠋⢰⣿⣿⣿⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣆⠀⠀⠀⢸⣿⣿⣿⠏⠀⠀⠈⢇⠘⠿⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠳⣀⠰⣾⡻⣿⣧⣀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢢⣹⣷⣾⠿⢿⣿⣟⣾⣓⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠋⠀⠀⠀⠉⠈⠈⠛⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠸⣏⢡⢄⣀⣀⣀⡆⢀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⠀⢸⠿⠿⠿⠃⠈⠢⡀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢋⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⣟⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⢀⡄⣼⣿⣀⣤⣷⠀⠀⠀⠀⠀⠀⠀⣿⣾⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢿⡇
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢤⠐⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⠀⠀⣀⣀⣀⠀⢀⣀⡀⠀⠀⠀⠀⣠⣶⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣧⡀⠀⢻⣿⣿⣿⣿⡿⠁⠀⠀⣠⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠹⣿⣿⠟⠁⠀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠙⠋⠀⠠⠞⠁
⠀⠀⠀⠀⠀⠠⠤⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢤⣄⣀⠀⠴⠄
⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⡀⢉⣹⣶⣶⣤⣄⣀⣀⣀⣀⣤⣴⣾⠟⠀⠀⠀⠀⠀⢸⣶⣦⣄⣉⣀⣀⣀⣠⣤⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⢀⡠⢄⣠⣴⣟⣉⠉⠹⣯⣍⠛⠿⣿⣽⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠟⣫⣿⠿⠿⠿⡿⠶⣾⣣⠄⡀
⠯⡉⠉⠩⠓⠊⠁⠀⠰⢶⣦⣭⣝⠻⢶⣤⡉⠃⠀⢈⡟⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢰⡏⠀⠴⠟⠛⣋⣠⣤⣽⡿⠾⠑⠢⣄⡀⠀⠒⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡲⢌⠛⢷⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣴⡾⢿⡛⠯⣍⡓⠿⠟⠛⠂⠀⠈⠙⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⣠⣤⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠄⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣄⣀
⣾⣿⠟⠉⣻⣿⠄⠀⠀⢀⣤⣾⡿⠟⠋⠉⠀⠀⠀⠙⢿⣶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣠⣤⣴⡾⠋⠀⠀⠈⠙⠻⣶⣤⡀
⠹⣿⡄⠀⠉⠁⠀⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢿
⠀⠐⠩⣭⣍⠉⠉⠁⠛⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠻⠇⢨
⠀⠀⠀⠈⠛⠻⢶⣦⣤⣀⣈⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠙⠿⣿⣿⡿⠋⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡷⢀⠀⠤⠀⠠⢤⡀⠀⢠⣾
⠀⠀⢀⣴⣿⣿⣿⠂⠉⠉⠉⠋⠙⢿⣿⣶⣦⣤⣤⣤⣴⣶⡿⠋⠀⢀⣿⣿⣦⡀⠢⣝⠻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣂⣉⣀⣀⣀⣀⣤⣤⡌⠀⠉
⠀⢠⣾⣿⣿⣿⣇⡀⠀⠀⠘⠶⣄⡀⠑⠤⣉⡛⠛⠛⣋⡥⠀⣠⣾⣿⣿⣿⣿⣿⣦⡈⠑⠨⢛⡻⠿⢷⣶⣶⣤⡤⠖⢋⡁⠛⠛⠛⣿⣿⡋⠉⠁⢀⡼
⠀⣾⣿⢿⣿⣿⣯⣤⣤⣤⣤⣀⡈⢻⣷⣦⣄⣀⣉⠁⠀⠴⠛⠛⠉⠉⠉⠉⠉⠛⠛⠿⢷⣤⣄⡀⠉⠉⠉⣁⣤⣴⣾⠟⣡⣴⣿⣿⣿⣿⣷⡄⠀⠉
⠀⠉⠀⢸⡿⢿⣿⣿⡿⠿⠛⣻⣿⣦⠙⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣿⣿⣿⡿⣋⣵⣾⣿⣿⣿⡟⠛⠋⠛⠷
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠾⠇⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣤⣄⣀⠀⠀⢀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⣿⣿⣿⣿⣿⠏⢀⣴⣿⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣿⣿⣿⠃⢠⣾⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡀
⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⠿⠿⠿⢿⣿⡿⠿⣿⣿
⣿⣶⣶⣶⣶⣶⣷⣾⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠶⠚⠛⠛⠓⠒⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣩⣝⢻⣄⣔⣀⠤⠐⠒⠉⠉⠉⠉⠙⠻⣶⣬⡙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢷⣟⣿⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠣⡘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠜⣹⡏⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡍⢄⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⢀⡌⡰⠉⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢠⡱⡄
⠀⠀⠀⠀⠀⠀⠀⣔⡛⠂⣛⣶⣇⣸⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠒⢷⡀
⠀⠀⠀⠀⠀⠀⠀⡟⠉⠈⠉⡿⢦⡽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡀⢽⣇
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢰⡇⢰⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⢸⢟
⠀⠀⠀⠀⠀⠀⠸⠐⠂⠀⡸⠃⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡖⢸⢻
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠃⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢻⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⡷⣿⣿⠀⣀⠤⢖⡶⠒⠒⣒⣒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⡞⢰⣟⠳⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⡿⠟⠉⡀⠖⢹⣷⢄⠈⠉⠉⠠⠈⢳⣄
⠀⠀⠀⠀⠀⠠⠀⠀⠀⣿⢸⠇⠀⠀⠀⠉⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠋⠀⠠⠂⠀⠄⠁⠀⠀⠑⣄⠀⡀⠀⠂⠙⢷⡀
⠀⠀⠀⠀⠀⢠⡄⠀⠀⣿⡌⢦⡀⠀⠀⡀⠀⠄⠈⠳⣄⣠⣄⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⢀⡴⣻⠟⠢⡀⢦⡀⠀⠀⠀⢣⡙⣦⠀⠱⡌⢻⣆
⠀⠀⠀⠀⠀⠀⠇⠀⠀⣿⢷⠀⠏⠑⢦⣌⡰⠃⠀⠀⠈⠙⢿⣷⣤⡀⠀⡴⠒⠶⣁⠀⠀⠀⣾⣴⠇⠀⠀⠉⠦⡙⠆⠀⢀⢀⣻⣆⠙⣶⣿⣮⠋⢦⡀
⠀⠀⠀⠀⠀⠀⢹⠀⠀⢙⠀⠁⠸⡄⢸⠋⠟⡷⣤⣀⢰⡀⠀⢻⠿⣿⡾⢁⠶⢦⣌⡑⠒⠚⢱⠇⠀⠀⠀⠀⠀⢙⣄⡹⢿⣿⣿⣿⣧⠀⠉⣭⣤⡁⢳⣄
⠀⠀⠀⠀⠀⠀⠈⡆⠀⢸⡇⠀⠀⠱⢸⠀⠀⠀⢸⡏⠙⢿⡃⠀⠱⣾⠁⠠⣀⡀⠛⠛⠳⡦⣤⡰⢦⣀⡀⣀⣼⣿⣿⣷⣌⠙⣿⡿⣷⡿⣆⠸⣯⣽⡄⠿⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠒⢸⠳⡀⠀⠀⣯⡄⠀⠀⠘⢿⠀⠀⠳⡄⠀⢉⠻⢶⣤⣙⡒⠶⠖⠀⡮⣟⣶⣭⣙⡛⠻⠿⠀⢿⣿⡆⠈⣼⡟⠀⢻⡄⢿⢸⡇⠰⡿⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢈⠀⢱⠀⠀⠘⣧⠀⠀⠀⠀⡄⠀⢀⡯⣙⠹⢦⣠⠛⣿⣿⣷⠶⣤⣙⠺⠷⣿⣿⣿⣷⣤⣀⡈⠛⠋⠀⠿⠵⣤⣀⠀⠸⡬⡇⠐⢀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⢣⠀⠈⢿⡄⠀⠀⠁⢰⠀⢸⣇⠉⠙⢶⣉⠛⠻⢧⡽⢃⣎⣯⣿⠗⢦⣍⣛⠿⠃⢸⣿⢋⢿⢙⡗⣶⠶⣶⠶⠶⣶⢶⢾⠋
⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠀⠀⠀⢃⠀⠘⣷⠀⠀⠀⠘⡇⢨⡙⠣⢄⣀⣨⠛⠓⠦⣤⣈⠛⢯⠀⢉⣿⣫⣿⣳⢀⠖⠻⡟⢸⢰⡟⢩⢠⠿⢀⡆⠛⣼⡌
⠀⠀⠀⠀⠀⠀⡜⠀⠀⢘⠀⠀⠀⠀⢆⠀⠸⣇⠀⠀⠀⠡⣼⢸⠋⠒⢪⣍⡁⠠⠄⣸⣿⢛⠲⢦⣈⠻⢿⣹⢧⣾⠀⡘⣡⡇⢸⣿⡆⣭⢇⠘⣀⢄⣧⠇
⠀⠀⠀⠀⠀⢰⠃⠀⠀⡇⠀⠀⠀⠀⠈⠣⠀⠘⠂⠀⠀⠀⢿⠀⣄⢀⡾⠉⠛⡷⣶⣤⣉⠗⠻⢾⣿⣿⠖⢄⡀⡾⣷⠁⣯⡇⢼⠀⢸⠛⢠⣷⡿⡜⣹
⠀⠀⠀⠀⠀⡼⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠑⣄⠀⢆⠀⠀⠀⢲⣄⣉⡓⠤⢄⣠⣟⣀⣙⣿⣶⢥⣪⠟⡤⠄⢱⠀⠎⡸⢻⠀⣼⠡⣤⠣⡘⠈⢠⠓⢯
⠀⠀⠀⠀⠀⢢⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⣧⡀⠀⠀⢿⣽⣗⠚⠂⠤⢉⣉⡛⠿⠶⣃⣚⠶⡆⠁⣈⣛⠀⠃⠂⠀⠫⠾⠉⠐⠧⠆⢈⣠⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠤⣤⣬⣉⣿⣄⡐⠀⠤⠟⠛⠑⠞⣋⣁⡴⢮⣍⣹⠛⠐⢿⡷⢶⡄⣠⢤⢿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠛⠲⠂⠤⢬⠄⣀⣘⡃⠠⠔⠂⠀⠈⠁⣉⣜⣫⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⣤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⣻⣿⡷⠆⠈⠳⢦⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣠⠾⠋⠐⢾⣿⣟⡃⠁
⠀⠀⠀⠀⠀⠀⠀⡜⣯⣿⡂⠀⡠⠀⠀⠛⠈⠳⡖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡾⠁⠚⠁⠀⢄⡀⢐⣿⢨⡏
⠀⠀⠀⠀⠀⠀⠀⣿⠿⠚⠑⠉⠀⠀⠀⠀⢹⣄⠈⢯⡠⠰⢤⣤⠀⠀⠀⠀⠀⠀⣠⣤⠆⢤⣸⠋⢀⡞⠁⠀⠀⠀⠉⠂⠑⠾⣽
⠀⠀⠀⠀⠀⠀⠀⠡⡧⠀⠀⠀⠤⠤⠀⠢⢬⣯⣿⣂⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⣿⣿⣯⠄⡠⠤⢤⠀⠀⠀⠰⡍
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣍⡳⠦⠢⠘⠛⠙⠛⠿⠋⠀⠀⣰⣀⣰⣆⢢⢴⣠⣆⣀⣶⠀⠀⠙⠿⠟⠋⠹⠃⠐⠢⠖⣋⣽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠉⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⣶⡿⠋⢠⣿⣯⣼⣿⡆⠉⢻⣶⠁⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠀⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣴⡦⣀⠈⠁⠀⠀⠀⠀⢤⡄⡽⢿⣦⠀⣿⣿⣿⣿⡀⢠⡾⢟⣀⡴⠀⠀⠀⠀⠊⠁⢀⢤⣶⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠐⢷⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣇⣿⣿⣿⣿⢅⣿⠁⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⢀⡀⠀⠀⠀⠀⠈⠛⠃⠀⢿⡇⠀⣸⣇⠈⣹⣿⠉⢸⣿⠀⢸⣿⠃⠐⠛⠁⠀⠀⠀⠀⢀⡀⠀⡹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠺⡴⠾⢃⠀⣀⣠⣠⢴⡟⣻⣿⣶⣅⠘⢿⡏⠀⡘⢻⠀⢸⡿⠋⣨⣴⣾⣟⠻⡶⣄⣄⣀⠀⡈⠳⢖⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⣠⣾⡋⠀⠀⠸⡄⠻⣿⡿⢫⣷⠀⣿⡆⡟⢸⠷⣾⠃⣼⣟⢿⣿⡿⢀⡇⠀⠀⠉⣷⣄⡤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⢿⣦⣄⡀⠈⠲⠤⠴⠛⣿⣀⠟⠀⠀⠀⠀⠙⣄⣿⡟⠦⠤⠔⠋⠀⣠⣴⣿⠿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠉⠀⣀⠀⣹⣿⣿⣶⣤⡄⠀⣸⡿⣡⣏⢤⠀⠀⢠⢘⣮⣻⣧⠀⠠⣤⣶⣾⣿⣟⡀⣀⠀⠈⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣺⠙⣿⠋⣛⡻⣿⠿⠋⠰⠛⣹⣿⣿⣄⡀⢀⣠⣼⣿⣯⠛⠦⠉⠿⢿⠟⢛⠉⣻⠋⢵⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠟⡚⠂⠀⠐⡃⠀⠴⠿⣾⡉⠙⠻⢤⠀⠀⣠⠽⠋⢈⣹⡿⠶⠄⢈⠂⠀⠐⠒⡺⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢿⡿⠿⣻⣿⠥⠀⠀⠐⠲⠇⠀⠀⠈⢲⣷⠁⠀⠀⠰⠷⠒⠀⠀⠨⣿⣿⠻⠿⡿⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⠞⢋⣵⠛⡐⢒⣋⠘⣀⢀⡀⣠⣼⣧⣄⣀⡀⢀⡁⢘⡂⣂⠟⢶⣍⠻⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⢿⢧⡞⣿⣷⣟⣶⣾⠿⠛⠟⠙⠋⠙⠟⠻⢷⣶⣿⣷⣿⡳⣬⢿⠗⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠉⠹⠟⠛⢿⡿⢀⣤⠀⠀⠀⠀⣠⡀⠸⡿⠟⠛⠏⠉⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⢂⠒⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠓⢘⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠨⠁
⠀⠀⠀⠀⠀⡠⢺⠀⠐⠀⠀⡆⠀⣶⠀⢬⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣼⡇⣿⡀⣴⣶⣶⠧⡄⠿⢣⣝⣭⢇⠀⠈⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⢸⠙⠋⡅⠀⣼⣿⣿⠀⠇⡰⠋⠈⠋⠉⠓⡄⢀⠄⠈⠀⡻⡀
⠀⠀⠀⠀⠀⡀⠀⢀⣸⣿⣿⡸⣝⣀⠔⠄⢀⠠⠀⠁⢱⠀⣠⠞⠀⠈⠁⠈
⠀⠀⠀⠀⡏⣧⠀⠈⡏⠉⠉⠁⠀⠀⡀⠬⣤⣴⠄⠀⠺⠋⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⡠⠇⠿⠆⠠⠃⠀⠀⠀⠀⢀⠁⠀⠈⠙⢃⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠳⠠⢔⠊⠁⠀⠀⠀⠀⠐⠒⠀⠀⠀⠘
⠀⠀⠀⠀⠀⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠘⡇
⠀⠀⠀⠀⠀⠿⠀⠀⢀⡀⠀⡆⠀⠘⠀⠀⠀⠂⠀⠒⡉⠁⠠⠤⠀⠀⠀⠂⡄
⠀⠀⢀⠀⣿⣷⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢿⢻⡘⡧⠄⠀⠀⣠⣤⡄⠀⠀⠄⠉⠀⠀⢀⠀⠀⠀⡠⠀⢀⡀⡝
⠀⠀⣴⡀⠘⠉⠁⡁⠀⠀⢠⢸⣿⡇⠀⠐⠂⠐⠁⠀⠈⠀⡀⠁
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢨⢺⣏⣷⡄⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠐⠀⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠄⠀⠀⠀⡀⠀⠀⠤⠀⠄⠸⠀⠀⠇⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢀⠀⠀⣄⠀⠀⠀⠀⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢠⠊⠀⢀⡿⢢⠀⠀⡀⠊⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⠋⠀⢀⣾⠃⡸⣀⠎⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠔⠁⠀⣠⡿⢃⠜⣿⠃⠀⡀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣶⡆⠄⠀⠀⠸⢀⣀⣠⣾⠟⠁⢸⡜⢿⣦⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠈⠁⠀⠀⠀⢀⠆⠀⠻⣭⡀⠀⠀⠈⢷⠀⢉⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠉⠀⠀⢰⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢀⣷⠀⠀⠀⠀⠳⡏
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢀⠾⡀⢣⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢊⣴⣶⣿⣶⣶⣿⣶⣿⣾⣶⣤⣄⢀⡠⠷⡀
⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⣠⡆⠴⠆⠈⠉⠒⠒⢀⣀⡀⠀⠒⠆⠀⠉⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠈⢂⠀⢀⣾⣿⣿⣿⣶⣄⢘⠄⠀⡇⢻⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⡄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣂⠀⢀⠌⡐⠀⠀⠀⢦⣿⣿⣿⣿⣿⣿⣏⣈⠄⢠⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⡿⣿⣿⣿⣿⣗⠀⠘⡇
⠀⠀⠀⠀⠨⠀⠀⠀⠀⠁⠀⠁⠁⠀⠒⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠀⠑⢠⡴⠉⠹⣿⣿⡿⠋⠉⠈⠙⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⣧
⠀⠀⠀⠀⠀⠑⢄⡀⣀⠔⠀⠀⠀⠀⠀⡄⠀⠀⣯⠀⠈⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⢀⣿⣿⣿⣷⣁⣿⣿⣿⣿⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⢀⡄⠀⠀⠐⠀⠄⠀⠀⠿⣿⣿⣿⣆⠀⠀⠀⢀⣼⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣯⣿⣿⣿⣋⣄⣼⣁⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡆⠀⠀⠀⠀⢂⠀⠘⠀⣿⣿⣿⣿⣦⣌⣤⣾⣿⣿⣿⡇⠀⠀⠀⠀⠿⠿⠿⠧⠝⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⢠⠁⠀⠉⠻⠿⠿⠿⠟⠛⠛⠛⠻⠟⠁⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠤⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠱⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠁⠀⠀⠀⠀⠀⠀⠀⢤⡤⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠁⠐⢁⡠⠒⠂⠀⠀⠀⠈⠢⣄⠒⡀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⢠⡠⢂⠁⠸⢢⡈⠂⠠⠁⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢎⠄⠀⠁⠀⣀⠆⠈⠛⠃⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⢐⢮⠱⠈⠀⠙⣠⡤⣤⣀⣀⣀⣀⣀⡠⠌⠂
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠀⠀⣀⣤⠶⠛⠁
⢄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡎⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠔⠋⠈⠉⠉⠇⠀⠀⠀⢣
⠀⠀⠀⡀⠀⣄⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠈⡇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠙⣆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡄⡀⢰⠀⡦⢠⢀⡀⡤⢠⣀⡈⠱⡄
⠀⠀⠀⠀⠀⠀⢁⠀⢀⣀⡀⠀⠀⠀⠀⠀⢧⠀⠀⢠⡄⠸⡆⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠇⠓⠚⠃⠂⠐⠛⠃⠃⠛⠈⠄⢠⠇
⠀⠀⠀⠀⠀⠀⠘⢦⡇⠀⠘⣆⠀⠀⠀⠀⠘⣆⠀⠘⢃⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢤⣀⣀⣀⣀⡀⣀⠀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⠛⢧⠀⠀⠀⠀⠛⠒⠄⣀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠛⠤⠄⢀⣒⡖⠀⢠⣤⣾⣿⣅⣤⣶⣾⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⠀⡠⠔⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠈⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⢻⣇⢀⣼⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡍⠀⠀⠠⠄⠀⡇⠀⠀⠀⠀⠀⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠⡀⠀⢨⣻⡆⣠⡈⡙⠻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⣀⣿⣷⣾⣿
⠀⠀⠀⢐⡄⠀⠨⡆⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠋⡃⢁⢀⠏⠁⠂⠀⠀⠀⠒⠀⠒⠒⠒⠒⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀⠀⠀⡤⢊⡼⣿⣽⣯⣿
⠀⠐⠂⠁⠀⠀⠀⢧⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠃⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢘⠀⠀⠀⠉⠒⠁⠐⡋⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠙⠲⠤⠤⠴⠋⢠⠇⠀⣿⠧⢼⣿
⠀⠀⠀⠀⠀⠀⠀⣈⣵⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⢀⡴⠋⠀⠀⣿⣯⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢸⡁⠉⠛⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠙⡏⠉⠀⠀⠀⠀⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠩⠥⠼⢌⡉⠛⠛⠛⠛⣋⡩⠷⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠹⠃⠀⠀⠀⠀⠀⣿⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠙⢆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠤⡀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⡸⠄⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣷⠀⠀⢀⡀⠀⠸⠿⢢⡇⣠⣔⡂⡏⠀⢀⡔⠀⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠲⠂⠀⠀⠆⠉⠂⠈⠉⠝⣉⣨⠟⠀⡀⠀⢤⡌⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠐⠕⠂⣢⠉⠙⠳⠒⡖⡶⠒⠚⠻⡏⠉⠀⠀⠇⠙⠂⠀⣉⠷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⣐⡽⠋⠘⠀⠀⠀⣰⣿⣷⣤⣴⣾⣿⣦⡶⣄⠀⠁⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠤⠖⠠⣀⣠⣵⣶⣿⣿⠋⠙⠛⠛⡛⠀⠈⠓⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⢿⣿⣷⣄⣀⣀⣴⣧⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⣄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣀⣀⢸⠉⢻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠈⠛⠿⢿⡿⠟⠀⣸⣿⣿⡿⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠀⡀⠀⠀⠀⠠⢀⠀⢀⡞⢿⣿⡟⣀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⣦⢌⡂⣄⣼⡼⠀⠀⣼⠝⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣇⢀⣾⣽⡴⠋⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣽⢿⡔⠀⠀⢀⠀⠀⠀⠈⠛⠿⣿⡿⠟⠛⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠶⠖⠛⠛⠉⠉⠉⠒⠒⠲⠤⣀
⠀⠀⠀⠀⠀⠀⣼⣟⣩⡟⢫⣀⠀⣁⡤⠴⠖⠛⠛⠉⠉⠙⠛⠿⣦⢬⡙⠦⡀
⠀⠀⠀⠀⠀⢀⣿⣟⣿⣿⣾⡷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⢢⡘⢢⡀
⠀⠀⠀⠀⢠⠎⠀⢉⡟⣽⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡌⢆⠹⡄
⠀⠀⠀⢠⠃⠀⠀⠈⡘⢻⣵⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠓⡙⣄
⠀⠀⢀⡿⡤⠤⣏⣰⠇⣸⢏⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠉⡸⡄
⠀⠀⢿⠮⠐⠶⢾⣟⠒⡏⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢡⢻⡀
⠀⠀⡇⠀⠀⠀⢸⠉⢻⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣎⣇
⠀⢰⠃⠀⠀⠀⡟⠀⣳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠄⢹⢸
⠀⡜⠀⠁⠂⢠⠃⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣾⢸
⠀⠇⠀⠀⠀⡘⢠⡷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢘⢳⣿⣼
⢸⠀⠀⢀⠀⡇⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢠⡧⣿⣿⠀⣀⠤⠶⡶⠞⠒⢒⣒⡒⠲⣄
⢸⠀⠒⠐⢸⠀⣦⠰⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣗⡿⠟⠉⠀⠖⢩⣯⢥⠀⠉⠉⠉⣠⠙⢦⡀
⢸⠀⠀⠀⢸⠀⣯⠆⠀⠀⠉⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠋⠀⠀⠎⠁⡄⠈⠀⠀⠁⢄⠀⢀⠀⠘⢄⠻⢧⡀
⠸⠀⠀⠐⢸⡇⢣⡀⠀⠀⠀⡄⠠⡈⠙⢷⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⡠⣾⡶⣄⠐⢄⠀⠀⠀⠀⠱⡌⢦⡀⠀⢢⠐⢷⣄
⠀⡆⢀⡨⢸⣟⡄⢻⠲⣤⣀⠣⣠⠆⠀⠀⠉⠻⣿⣷⣄⠀⠀⠀⢀⣤⣠⠖⠀⠀⠀⢀⡼⣱⠏⠀⠈⠳⣌⠳⣄⠀⠀⠀⢘⣦⡙⢦⣤⣷⡌⡯⢦⡀
⠀⢣⠀⠀⡸⠇⠑⠈⣇⠀⣿⢻⣦⣄⠀⠀⠀⡀⠈⢻⣿⣷⣦⣴⠋⣀⣉⠳⢦⣀⣀⡸⢳⠏⠀⠀⠀⠀⠈⠷⡈⠳⣴⣦⣶⣿⣷⡄⠙⠿⠿⠄⠨⠵⡄
⠀⢸⡀⠀⠀⡆⠀⠐⠸⡄⢟⠀⠀⠈⢻⣶⢬⡷⣤⠀⠹⡙⢻⠇⢠⠋⠛⢳⣶⣤⡀⠀⠙⣀⠀⠀⠀⠀⢀⣤⣿⣦⡙⣻⣿⣿⣿⠟⣀⠀⠲⣿⢗⡄⢻⣆
⠀⠀⡇⠀⠄⣿⡀⠀⠀⢳⢸⠀⠀⠀⢸⣷⠀⠙⢧⡀⠀⠸⣿⣀⠘⠲⣄⣀⠀⠐⣙⠓⣶⣌⡳⠦⣄⣤⣾⣿⡿⢿⣿⣍⠙⠿⢻⣾⠋⢷⡀⢿⠎⣷⠸⢻⡆
⠀⠀⡇⠉⠀⡇⢣⠀⠀⠈⣾⡀⠀⠀⢨⡹⡄⠀⠈⢳⢄⣀⣠⠙⠻⣷⣶⣭⣛⠛⠁⠲⢈⠾⢟⣷⣦⣍⡉⠛⠂⠸⣿⣿⡀⠠⣿⡏⠀⠙⡇⢸⣰⣿⠆⠚⠷
⠀⠀⡇⠀⠀⡆⠈⢣⠀⠀⠘⣧⠀⠀⠀⠀⢇⠀⠀⣸⠢⣍⡙⢢⣤⠋⢻⣿⣿⡟⠲⣤⣉⡒⠿⢿⣿⣿⣿⣷⢤⣀⢉⠛⠁⠀⠛⠴⠤⠤⠇⠘⠧⠝⠀⠁⡠
⠀⠀⡇⠀⠀⡇⠀⠈⣆⠀⠐⢻⡄⠀⠀⠀⠸⡄⠀⢿⢸⠀⠙⢶⣉⣙⠛⠶⡤⠇⣼⣐⣿⡿⡓⢦⣄⣙⠛⠋⠀⣾⡋⡨⣏⢹⣷⣶⡖⣺⠛⡶⢶⡾⡿⡟⠁
⠀⢸⠁⠀⠀⡇⠀⠀⠘⣆⠀⠹⣧⠀⠀⠀⡀⢣⠀⣇⠛⠦⢄⡀⢈⠟⠓⠦⣤⣀⠛⠿⣥⡀⢀⣿⣏⣿⢿⠂⡵⠚⢿⡇⡇⢸⠯⢹⠰⢯⢁⣤⢹⢰⢇⠇
⠀⡜⠀⠀⢀⠇⠀⠀⠀⠸⡄⠀⠹⣆⠀⠀⠠⠘⣄⡇⢙⠒⠢⢌⡉⠂⠄⣠⢊⣿⡿⠶⢦⣄⠙⠻⢿⣹⣎⣆⠇⢀⠎⣸⡁⣾⣿⠆⣹⡌⡈⡇⡄⣴⡘
⢠⠃⠀⢀⢸⠀⠀⠀⠀⠀⠘⣄⠀⠙⠄⠀⠀⠂⠹⡇⢸⠀⠀⡾⠛⠷⢶⣤⣌⠙⠳⢾⣦⣼⣟⡶⡦⣉⢈⢹⣦⡞⣸⣛⠀⡟⡘⢸⢿⢀⣦⣼⠸⣍⡟
⡜⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠈⢦⠀⠐⣄⠀⠀⠄⢫⡈⠓⠾⢦⣀⡀⢀⣿⠏⠹⢷⣦⣔⡩⢛⣮⣀⣸⠆⡇⢹⢃⡿⣏⠁⣷⠁⡌⡆⠈⢻⠇⡷⢸⡇
⡇⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣘⣆⠀⠈⠀⢹⠷⣾⢴⣬⣍⠙⠓⠷⢷⣾⣟⣭⠋⣥⡪⡑⠀⠐⢦⠆⢨⣁⠄⠠⣏⡸⠟⢀⡞⠸⠘⠃⢈⡅
⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣦⣄⠀⠉⡑⠾⢷⣤⡀⣉⠑⠒⠴⣦⢍⣙⡶⠆⠘⢋⡠⠶⠦⣤⡄⢀⣀⣀⣈⠉⠀⣀⣈⣷⣦⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠒⠤⢿⣶⣤⣄⣀⡉⠉⠐⠒⠀⠭⠝⣛⣛⠒⠶⠃⠀⢊⣭⢋⡽⣡⣴⠽⣫⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠲⠶⠦⠤⣤⣭⣭⡩⣥⠀⠤⣤⡾⠧⠔⠊⠁
⣶⣶⣶⠶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠂⠛⠁⠈⠈⠙⠈⠙⠀⠉⠁⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠦⣀⠀⠀⠀⠀⠀⠻⣦⣰⡤⠗⠤⠷⣤⡆⣀⡠⠆⠀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢀⡀⠉⠁⠄⠀⠀⠄⠖⠉⠉⡅⠀⢀⠀⠈⠛⣡⢤⢄⣀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⢻⣿⡇⠀⠁⠀⡄⠀⠠⠁⠀⠏⠀⠀⠁⠀⠀⠺⠹⣿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣌⠧⠀⠛⠀⠀⣠⡄⠀⠀⠂⠀⣀⣄⠀⠀⠆⠀⠘⢦⣄⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡔⠀⠀⠀⠤⠦⠌⠈⠁⠠⢀⠀⠀⠛⢀⠀⠀⣀⣤⡀⠀⢢⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠄⠁⠀⠀⢀⠄⠀⠴⠓⢎⠤⡀⠀⠀⠀⡞⠡⠎⠳⠀⡀⠁⢨⡀⠀⠶⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⡄⠀⡎⠀⠐⢤⣄⠘⠀⠁⠀⢀⠀⠀⠀⠃⠀⠈⣁⢨⡇⠉⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⡰⠃⠀⠀⠰⢦⡄⠰⠀⠀⠀⠁⠀⢰⡄⠀⢰⠋⢸⠙⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢸⡆⠀⠳⡆⠀⠸⠀⡈⠁⠀⠀⠐⠀⠞⠁⠀⣮⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⢀⡀⡀⠹⠚⠁⠬⣙⠬⠀⣐⠄⠀⠀⠀⢘⠃⠀⠀⠀⠀⣥⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠴⢀⠂⠀⠀⠀⠀⠁⠹⣀⣤⡄⠀⠉⠲⠊⠁⠀⠀⠀⠀⠹⠆⠀⠀⠀⠀⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡠⠼⣀⠠⠀⠀⠀⠀⠸⢯⡁⠀⠀⣠⠴⣤⣀⠀⠀⠤⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠡⠋⠀⠀⠀⢰⢂⠠⣅⣀⡀⠀⠐⠦⠀⠀⠀⠀⠀⠇⠸⠐⠀⠐⢤⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢠⡎⠀⢨⡈⢰⢋⢿⠁⠰⠤⠴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣜⠀⠀⠀⠀⢺⠅⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⠠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠐⠀⠀⡀⢠⠀⠐⠀⠀⠀⠀⠀⠀⢰⣦⢸⡙⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢡⣀⠐⢧⡄⢰⠀⠀⠀⠀⠀⠀⠀⢻⠈⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠠⣠⢸⡎⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠔⠉⠁


⣿⢿⠿⠿⠿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠙⢿⡿⠋⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⣤⡄⠀⢸⡇⠀⠀⢠⣤⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠈⢿⣿⠏⢀⣼⣧⠀⠹⣿⡿⠁⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠓⠦⠤⠖⢻⣿⣿⡟⠲⠤⠶⠚⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠈⢻⡿⠀⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⣀⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠃⠀⢹⣿⣿⣿⣤⣤⣿⣿⣿⡋⠀⢘⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢉⠹⣦⠀⠉⢉⢻⡏⢹⡟⠉⠉⠀⣴⠋⣉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠡⢙⠡⠙⠀⠀⡘⢸⡇⢸⡇⢣⠀⠀⠋⠌⡋⠌⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠛⠁⠀⢰⠁⣿⠀⠀⣿⠈⡆⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⣿⠀⠀⢿⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠦⠴⠋⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣷⣦⠀⣠⣴⣶⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣼⡿⢟⣛⣯⣭⣭⣽⣛⡱⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠟⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾⣿⣿⣿⣿⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣭⣭⣭⣝⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⢼⣿⣿⢟⣫⣽⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠻⠿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣮⡝⠛⠛⠛⠛⠛⠛⠛⠓
⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⠂⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⠂⠀⠀⠀⠀⢀⣶⣶⣶⣀⣀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣿⣿⣿⣷⣶⡶⠀⠀⢀⣼⣿⣿⣿⣿⣇⣀⣀⡀⠀⠀⠚⠛⢻⣿⡿⠋⠀⠀⣠⣦
⠀⠀⠀⣰⣿⡿⠀⠀⠀⠈⠉⠉⣽⣿⠏⠀⠀⠀⠾⠿⠿⠿⢿⣿⣿⣿⠟⠁⠀⠀⠀⢀⣾⠟⠁⠀⠀⣼⣿⡟
⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢀⡀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢀⣴⣿⡇⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⣼⠟⠁⠀⠀⣠⣾⡀⠀⠀⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣼⠋⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠙⠿⠋




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠊⢸⣷⣶⣦⣤⣤⣄⡶⣞⣷⠸⣷⣜⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡠⣀⠄⠀⠀⠀⢿⣿⡿⣿⢿⠁⡅⡿⢻⡆⢿⣯⢿⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⡅⡊⠊⠀⠀⠀⠀⠀⠛⠀⣡⣼⠀⠀⡆⣼⢣⡘⣿⡷⣀⢺⡏⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠂⣿⠁⠀⡄⣣⢇⣾⡧⢸⣿⠗⢸⡃⡄⠈⡛⠂⠀⡴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠈⠀⠁⠆⢋⠀⣿⡇⠘⡉⠒⠻⠿⢥⡆⠓⡤⠂⠐⢩⡷⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠂⠀⣼⣯⣇⢰⣿⣗⣱⣶⡆⢠⠎⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⢸⢠⡿⢻⡞⢟⡧⡝⠛⠄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠀⣿⣻⡇⡆⢘⠰⠛⠁⠿⠃⠀⠁⣼⠖
⠀⠀⠗⢆⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⣿⠾⠁⠀⠨⡊⠁⠊⠰⠀⠀⠀⠈
⠀⠀⠀⠏⠀⠀⠀⠉⣿⣷⣶⣶⣻⣵⣦⡤⢤⡤⠀⠀⠀⡂⢉⡴⠋⠘⠉⠀⠄⡀⠀⠀⢠⠀⠠⠀⠀⢀
⠀⠀⠀⠐⠀⠀⠀⠀⣿⣿⣿⠫⣾⣿⢃⠀⢈⡄⢀⡠⠎⡔⠈⠀⠀⠀⠄⠎⣠⣜⠳⣷⢸⣄⡄⠀⠀⠂
⠀⠀⠀⢸⠀⠀⠀⠀⠹⠺⢛⡄⢿⢿⡠⠜⠋⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣷⣌⢻⣇⣵⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣗⠋⠈⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠐⡫⠘⠁⢹⡄⢻⣿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠅⠀⢠⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢿⡀⢿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⡁⠀⠁⢃⢘⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠈⠀⠀⣀⠔⠀⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⢀⠔⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣷⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⠿⠿⢻⣿⣿⣿⣟⠛⠛⠛⠻⠿⢿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠋⠉⠀⠀⢀⣾⡿⠉⠻⣿⣦⡀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠉⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧
⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣤⣹⣿⡆
⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣠⣴⣶⣿⣿⠿⠿⠿⣿⣷⣦⠀⠀⠈⢿⣿⠀⠀⣰⣾⡿⠟⠛⠉⠉⠉⠛⠁⣿⣷
⢠⣿⡏⣠⣴⣶⣾⣿⣿⣿⣶⣶⣤⣄⠀⠀⠀⢸⣿⠃⠀⢠⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠸⣿⡇⠀⠈⠉⠀⢀⣀⣀⣀⣀⣀⡀⢹⣿
⣸⣿⠉⠻⠛⠉⠀⠀⠀⠀⠈⠉⠛⠛⠁⠀⠀⢸⣿⠀⠀⠀⠉⣀⣤⣶⣶⣿⣿⡿⢿⣿⣿⣷⣶⣦⣄⠀⣿⣿⠀⣠⣶⣿⡿⠿⠛⠛⠛⠻⠿⣿⣿
⣿⣿⠀⢀⣠⣤⣶⣶⣾⣿⣿⣷⣶⣶⣤⣀⠀⢸⣿⠀⢀⣴⣿⡿⠛⠋⠁⢹⣿⠀⠀⠀⠀⠀⠉⠛⢿⣷⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⣶⣿⠿⠛⠉⠁⠀⠀⠀⠀⠉⠉⠛⢿⣿⣾⣿⣴⣿⡟⠁⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉
⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠟

⠀⠀⠀⠒⠀⠀⠀⠀⠀⡴⠃⠀⠀⡄⠀⠀⠀⢠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠁
⠀⠀⠀⠀⡠⠀⠀⠀⠀⣠⣷⣤⠤⣤⣤⣶⣧⣰⣄⣀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠒⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠔⡀
⠀⠀⢀⣾⡇⢠⠎⠀⠘⠛⠻⠁⠰⢿⣿⢿⣿⣯⠀⠀⠁⠠⠤⠀⣀⠀⠀⠀⠠⣤⡄⠀⠀⢀⠀⠀⠀⣀⠤⠂⠀⠀⠀⠁⠉⠛⡛⠉⠀⠀⠀⢀⠐⠄
⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠿⢟⣿⣶⣶⣶⡾⠋⠈⠉⠠⣄⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠠⠀⠀⠀⠀⠰⡍⠓⠲⠶⠚⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣵⡾⣿⣿⣿⣿⠿⣶⣤⣠⣠⠉⠙⠛⠁⠀⠀⡰⠀⢤⣤⡤⠤⠀⠳⣅⡀⠀⠀⢀⡈⠻⣶⣶⣾⡿⠃
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⠈⠁⠞⠔⠋⠁⠀⠑⢦⣌⣒⣭⣽⣇⠀⠀⢶⣄⣀⣀⣤⣮⣿⠛⣻⣟⣤⣿⣿⡿⠋⠀⣀⡄
⠀⠀⠀⠞⠀⢲⣄⣉⣂⠀⡀⠀⠈⠃⠄⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⣰⣶⢿⣿⠿⢛⣿⣿⣿⣷⡖⣹⣿⣟⡿⠋⠱⠁⠉⢀⣼⠟⢋⡀⠀⠀⠁
⠀⠀⠀⠀⠂⠁⣄⠀⠀⠀⠳⠆⠀⠐⠀⢠⡘⠉⠉⢉⠀⠀⡀⠀⠀⠈⢙⠁⠀⣴⡂⠊⢛⣿⡿⢋⣾⣯⣿⡟⠁⠀⠀⠀⠀⠈⢀⡔⠁⡰⠚⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢰⣆⠀⠰⣄⠀⠉⣓⡈⠁⢀⣌⢷⣤⢤⣶⡽⠂⡴⠛⡁⣰⣼⠟⣴⣿⡿⠟⠋⠀⠀⣴⡅⠀⠀⣰⣯⡀⠊⠀⠀⢀⠞⠁
⠀⠀⠘⣿⣷⣶⣆⣀⡴⠂⠀⠙⠛⠟⣹⣿⣿⣿⣿⣿⣿⣿⣷⣾⢫⡥⠀⠀⢀⢀⣰⣿⣧⡶⣠⢿⡃⠀⣠⣤⡾⢟⡖⠀⠀⢑⣏⠀⠀⠀⠀⠁⣠⠆
⠀⠀⠀⢋⡿⣯⠟⣵⠾⣠⡔⡡⢂⣼⣿⣿⠟⢻⣿⠿⣿⣿⣟⣽⣋⠠⢀⡴⢇⣭⣿⣿⢋⣴⡣⠈⣠⠊⠿⣩⣶⣿⡷⠀⢴⡿⠋⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠋⠀⢀⠞⢃⡿⠋⠀⢰⡾⣻⡿⠂⢠⡔⠂⠀⠀⠁⠭⠨⣻⡆⢈⣴⣿⣿⣿⣡⣿⣿⡿⡿⠛⠀⠘⠛⢻⠟⠂⠠⠍
⠀⠀⠀⠀⠀⣀⡰⠋⠐⠀⠀⠊⠀⠉⠀⠀⠀⢀⣊⠐⢛⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⣚⢞⣁⡀⠀⡐⠀⢠⡜⡁⠈⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠛⡀⠀⢠⡄⠀⠀⠀⠀⠀⣀⣾⣿⣷⣟⣴⣿⣿⣿⣯⣭⣿⣿⠟⣿⣿⣷⣖⣠⣥⣹⠞⡀⠈⠀⠀⠾⠻⠃⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⢀⠚⠿⠿⠁⠀⠀⠀⡠⠊⠁⠁⣰⣿⣿⣿⣿⣷⣽⣯⣼⣿⡿⠃⠾⢿⣿⢯⠿⢿⡿⣿⣿⣅⢠⠄⠀⠈⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠟⢻⣿⣷⣿⡿⣛⢿⣿⣿⣿⡟⣡⡞⣡⡯⠀⠈⠈⠉⠉⢱⣶⣴⣦⣿⣿⣿⣿⣷⣶⣶⣖⠃
⠀⠀⠀⢀⠂⠀⠀⢰⡇⠀⠀⠠⠀⠀⠀⠀⠠⡾⠿⢋⠜⠙⠁⣼⣿⣿⣏⣸⣿⡿⢈⣦⣾⣥⣤⣤⣴⡿⠟⣋⣩⣿⣿⣿⣿⣿⣿⣿⣯⣷⠀⠁
⠀⠀⠀⡤⠊⠀⠀⢼⣇⠀⠈⣆⢠⠀⠀⠀⠀⠀⠜⠃⠀⢀⣾⣾⣿⣿⣿⣿⣿⣧⣿⠛⡁⠾⢿⣿⣫⣵⣾⣿⣿⢟⣿⡛⣩⣷⣧⣍⣙⣷⣶⡄
⠀⠀⠀⠟⠀⠀⠀⣿⣟⠂⢼⡿⣿⡂⠀⠀⢀⡀⠀⠀⠀⢺⣿⣿⣭⣭⣽⣿⣿⡿⣡⠌⠑⠠⠘⠿⢻⣿⣿⣿⣁⣙⣻⣿⣿⣿⡏⠻⣿⣿⣟⣦
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⣸⣿⣿⡇⢰⡄⣾⡆⠀⠀⠰⠃⢾⣿⣿⣿⣿⣟⡿⠈⠁⣀⠄⠀⠀⠀⠀⠀⠸⢿⠿⣿⣿⣿⣦⣼⡰⣿⣿⣷⣿⠁
⠀⠀⠀⡀⠀⠠⢾⣿⣿⢿⣿⢫⣿⣇⣸⣟⣿⣟⠀⠀⣀⢀⣐⣫⣽⣭⣩⣭⣤⣉⠛⢁⣀⣀⡀⠀⠀⠀⢀⡘⡀⡟⠃⠉⠿⢁⠔⠙⠛⠋⣁⣀⣀
⠀⠀⠀⣿⣾⣿⣿⣿⣿⣾⣿⢟⣿⣻⡧⣿⣿⢾⣾⣿⣿⣿⠿⡟⣿⣿⠟⢻⠻⣻⣶⢃⣿⣧⠻⢶⣿⣧⣿⣿⣿⣿⣿⣧⣥⣧⣶⡷⠘⢿⣿⣿⣿⡆
⠀⠀⠀⣉⣍⣵⣾⡿⣧⣌⣵⢿⣿⣟⣡⣿⣿⣷⣙⣉⠁⣤⡤⠄⡀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠉⠉⠉⠉⠙⡇⠁⢹⡇⠉⠉⠀⠀⠈⠛⠛⠛⠁
⠀⠀⠀⡽⠿⠟⠿⡛⠒⠙⠛⠻⠉⠬⠽⠷⠼⠿⣦⣬⣅⡀⠀⠀⠐⠛⠛⠛⠛⠻⠿⠛⠓⠈⠀⠀⠒⠂⠀⠈⠀⣿⡀⢸⡇⠠⠀⢴⣤⡤⠤⢤⡤
⠀⠀⠀⣷⣴⣶⣶⣶⡶⣶⣦⣤⣴⣦⣤⢀⣀⠀⠀⠉⠉⠉⠋⠉⠒⠐⠒⢴⣤⣤⣤⣄⠀⠀⠀⠀⠀⠤⠤⠶⠖⠚⠷⠚⠻⢿⣿⣿⣿⡿⣿⣿⣷
⠀⠀⠀⡻⠓⠚⠉⠋⠀⠀⠈⠁⠐⠒⠛⠛⠛⠛⠻⠿⣶⣶⣶⣤⣶⣶⣾⣿⣿⣿⣿⣿⣷⣽⣿⣾⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠴⠿⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢡⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠤⢀⠔⠉⠐⠄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⡠⠁⠈⠔⡠⢂⠂⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠨⠂⠄⠀⡠⠠⠂⠀⠀⠠⠊⠀⠀⠀⢀⠔⡡⡀⠁⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⣀⠀⠀⠀⠀⢀⢀⠁⠈⠈⠈⠉⡠⠁
⠀⠀⠀⠀⠀⠀⠃⢠⠀⡠⠀⠴⠀⠀⠖⠀⠰⠂⢀⠄⠀⠀⡐⠁⢀⠟⠉⠐⠁⠀⠤⠂⠀⠀⠀⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠠⠂⠠⠀⠰⠀⠀⠃⡔⢀⠊⠀⠀⠠⠮⠄⠀⢲⣂⠀⡰⠂⠀⢈⡀⠀⠚
⠀⠀⠀⠀⠀⠘⠀⠀⠀⡔⠀⢀⠀⢠⠀⠀⡰⠂⠀⠰⠇⠒⠒⠒⠒⠀⠀⠀⠄⠀⠊⠠⠆⠀⠈⡠⠀⠐
⠀⠀⠀⠀⠀⠀⡌⠀⠀⡄⠀⠉⠀⠃⡤⠀⢀⠀⠀⠀⠰⠂⠠⠊⠀⠀⢀⠔⠁⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠐⢀⠀⠰⠁⡄⠀⠀⠊⠀⠸⠁⢀⠔⠁⠀⢀⠔⠁⡰⠀⡀⠀⠊⠀⠀⠈⠀⠊
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠘⠀⠈⠀⠠⠂⠀⠔⠁⠀⠀⠀⠀⢀⠀⠀⠈⠀⣀⠀⠋⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⢠⠇⠀⠀⠄⡠⠂⠀⡀⠈⠀⠀⠀⠋⢀⠀⠀⠈⠁⠀⠜
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⢠⣊⣀⡀⠀⠀⠀⠀⠊⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⡨⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠊⠁⠀⡔⠀⠀⠀⠀⡠⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⠿⠿⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠛⠁⠀⠀⠀⠀⠀⠉⠻⣿⣄⣀⣤⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠋⠁⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢀⣴⣾⠟⠛⠉⠉⠉⠙⠛⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣀⣀
⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠛⠛⠻⢿⣶⣄
⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠁⠀⠀⠀⠀⠀⠀⠈⢻⣷
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏
⠀⠀⠀⠈⠙⠻⠿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠈⠛⠁⠀⠀⠀⠛⠃⠀⠀⠀⠘⠋⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣤⡄⠀⠀⠀⣠⣄⠀⠀⠀⢠⣤⠀⠀⠀⢀⣤⡀⠀⠀⠀⣤⡄
⠀⠀⠀⢀⣾⡟⠀⠀⠀⣼⡿⠁⠀⠀⣰⣿⠃⠀⠀⢠⣿⠏⠀⠀⢀⣾⡟⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠘⠋⠀⠀⠀⠘⠛⠁⠀⠀⠀⠛⠃⠀⠀⠀⠛⠋⠀⠀⠀⠘⠛⠀⠀⠀⠘⠛⠁

⢠⣤⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠⡄⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⠀⠀⠀⢀⣤⡀
⣿⣏⣀⣀⣀⣸⣟⣀⣀⣀⣸⣿⣁⣀⣀⣀⣿⣃⣀⣀⣀⣿⣏⣀⣀⣀⣸⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡇⠰⠄⠠⢠⣤⣴⠶⣶⢠⣆⡈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣌⡇⣠⠀⣠⡟⡟⠀⢰⣟⠘⢻⡄⣸⢿⠤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢏⣰⠋⣨⠀⣠⠄⠀⠀⠂⣰⡙⡶⢾⠋⡿⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⡾⢃⡞⢡⣴⡏⠀⢘⣿⡌⢹⣇⠙⡈⢳⡐⢚⠛⢛⠳⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡿⠁⠀⠀⠘⠛⠋⠀⠀⠀⠈⢿⠀⢹⣧⢿⢠⠁⠀⠀⠀⠁⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣧⣿⠉⡂⠂⠀⠀⠃⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⢸⡇⠀⠀⠀⠀⠀⢠⡟⣩⣄⡳⠙⢽⡀⠂⠀⠀⠀⠀⠀⠠⡀⠀⠈⠳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣅⠀⠀⠀⠀⠀⣾⠏⠨⠩⡅⠀⢸⣷⠄⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡆⡸⠀⠀⠀⠀⣼⡏⢙⡄⢁⡀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢡⡠⠞⢸⠏⠁⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠁⠀⠀⠀⠄⡞⠁⢀⣈⣀⣄⣤⡿⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⢀⠀⠀⠀⠀⠃⣠⡾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣊⡀⠘⠻⠆⠚⠀⠀⢀⠅⠻⡀⢻⣿⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢻⠃⠀⠀⠀⠀⣿⣦⡏⠀⠀⢳⡈⣿⡀⢆⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢠⣦⣶⡀⠀⠿⣼⠁⠀⠀⠀⡇⢻⠀⠈⢣⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣛⣛⣋⣴⣷⠋⠀⠀⠀⠀⢳⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠙⠁⠁⠀⠀⠀⠀⠀⠀⠃⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⢤⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⡀⠐⠈⠉⠛⠓⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢰⣿⡆⠀⠀⠀⢂⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢨⠀⣾⣷⠀⠀⠀⠂⠀⠀⠀⠀⠈⠳⡄
⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⡄
⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠀⡘⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠁⠢⣀⠀⠀⠈⠀⠀⠀⠀⠀⠸⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⣀⣀⣴⣶⡿⠳⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠈⠁⠚⠲⠦⣄⠀⠀⠀⠀⠘⠋⠉⠉⠙⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⠠⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠛⠛⢿⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠆⠀⠀⠈⠙⠦⠆⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠈⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⠃
⠀⠀⠀⠀⠀⠀⡰⠊⠐⣆⠀⠀⠀⠀⡆⠀⠀⡎
⠀⠀⠀⠀⠀⢀⠉⠀⠀⡎⠀⠀⠀⠸⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠈⡃⠀⡀⢦⣀⡀⣠⡃⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠁⠀⠀⡜
⣀⣀⣀⣀⣀⣀⣀⣀⣉⣒⣤⣤⣤⣄⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣆⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣠⡆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⣿⠄⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⣈⡟⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠘⣿⡀⠻⣿⣦⡀⠀⠀⢀⣀⣤⣀⡤⠠⠴⠛⠁⣈⣽⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠸⣿⠀⠀⠉⠉⠀⠠⣚⣿⣿⣿⣿⣿⣄⡀⠰⠟⠁⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡌⠀⠀⠀⠀⠀⠀⢔⣺⣿⣿⣿⣿⡽⣒⠀⠀⡜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣞⡝⠀⠀⢈⠴⣛⣿⣿⣿⣿⡿⠆⠐⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠛⠀⠀⢰⣄⠘⣱⡶⢶⣮⡙⢁⣸⣦⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⣿⣿⠀⠘⠀⠀⠉⠛⠛⠋⠈⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢀⣿⡟⢠⠆⣤⣄⡀⠀⢠⢠⢠⠀⠀⣠⡘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⡇⢸⠀⠻⠿⠷⠀⠈⡿⡾⡄⠀⠿⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⢸⣿⣿⡌⠳⢄⡀⠀⠀⠀⠁⠃⠁⠀⠀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣿⡇⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣠⠀⠙⠓⠶⢤⣤⣤⣤⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣷⣄⡀⠀⠀⠀⢀⣀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠛⠒⠋⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠉⠉⠉⠙⠶⠖⠋⠉⠉⠙⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣀⡀⣀⣀⡀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣐⡢⠀⠀⠀⠀⠀⠈⠏⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡖⠁⠀⠀⠀⠀⠀⠀⠀⠚⠓⠒⠭⠶⠖⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡯⠤⢀⣀⠀⢀⣀⣀⣠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣔⣰⡠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠒⠋⠉⠀⠀⠉⠳⣞⣡⣖⣠⠖⠳⢴⣠⢖⣰⣦⠾⠛⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣰⠃⠈⠁⠀⢀⡤⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢰⠃⠀⠀⢀⡴⢋⠗⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠰⠿⠶⢞⡶⠂⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢠⡯⠴⠒⡾⠃⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣠⠖⠉⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⢞⡵⢋⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢠⣾⠗⠉⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀
⣟⣛⣻⣛⣟⣟⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣟⣻⣛

⢳⣄⠀⠀⠀⢰⣄⠀⠀⠀⠀⡄⠀⠣⠾⠃⠀⢸⡧⡄⠀⠈⣿⣼⣷⠀⠀⢻⡈⣳⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⢶⣄⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⢀
⠈⢿⣳⡄⠀⠀⠻⠄⠀⣀⠀⠙⠀⠀⠀⠀⠀⠈⢧⣿⡆⠀⠈⠉⠁⠀⠀⠈⠻⣯⡿⠀⠀⠀⠀⠀⠘⣟⣆⠀⠸⣟⢧⠀⠀⠀⠸⡟⣦⠀⠀⣦⡈⠀⠰⣦⡀
⣄⠈⠉⠁⠀⢄⠀⠀⠀⣿⢦⡀⠀⠀⢸⡷⣄⠀⠈⠛⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠙⠋⠀⠀⢿⣾⠇⠀⠀⠀⢿⣼⠁⠀⠘⣿⡆⠀⢡⢝
⢾⣆⠀⠀⠀⠈⠁⠀⠀⢿⡨⢻⡄⠀⠈⣷⢹⣦⡀⠀⠀⠀⠀⠀⢹⡷⣄⠀⠀⠀⣄⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢧
⠛⠃⠀⠀⠀⠘⣷⣄⠀⠈⠿⣾⠇⠀⠀⠹⣮⣿⠇⠀⠰⣄⠀⠀⠈⣇⣿⣧⠀⠀⢸⡷⣄⡀⠀⠀⢿⡳⣄⠀⠀⠀⠀⠀⠀⣟⣦⠀⠀⠀⠀⠰⣄⠀⠀⠀⠈
⠀⠀⠀⣦⡀⠀⢻⢻⣆⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⡟⣧⡀⠀⠙⠿⠟⠀⠀⠈⣿⣼⣷⠀⠀⠘⢧⣿⠆⠀⡷⣄⠀⠀⢧⣸⡇⠀⢀⡀⠀⠙
⠀⠀⠀⠘⠛⠀⠈⠛⠃⠀⠀⠀⠀⠀⢿⡦⠀⠀⠀⠀⠀⠳⣿⠇⠀⢤⠀⠀⠀⡀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢻⠸⣷⠀⠀⠉⠀⠀⠈⣿⢦⡀⠀⠀⢷⣤
⣱⣄⠀⠀⠀⠀⠀⢀⡀⠀⠀⢲⣄⠀⠀⠀⠀⢰⣄⠀⠀⠀⡀⠀⠀⠈⠳⠀⠀⢿⣦⡀⠀⠀⢦⡀⠀⠀⠀⢠⡀⠈⢷⠿⠀⠀⢸⢦⡀⠀⠸⣧⣿⡄⠀⠀⣷
⣿⣿⠀⠀⠀⠀⠀⠀⣟⢦⠀⠈⣿⢳⡀⠀⠀⠈⣟⢧⡀⠀⢸⣦⡀⠀⢠⣄⠀⠘⣿⣻⣆⠀⠘⢿⠀⢠⣄⠀⠓⠀⠀⠀⠀⠀⠸⣏⣷⡀⠀⠙⠛⠃⠀⠀⠘
⠀⠀⠀⠘⠦⠀⢤⡀⠈⠛⠀⠀⢹⣷⡇⠀⠀⠀⢹⣮⠇⠀⠀⢿⣻⡆⠘⡏⠳⣄⠈⠙⠋⠀⢀⠀⠀⠘⣯⠳⣄⠀⠀⢸⢦⡀⠀⠙⠛⠁⠀⠀⠀⡀
⢠⡀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠉⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⢹⣀⢘⣆⠀⠀⠀⠀⠁⠀⠀⢻⡄⢻⡆⠀⢸⡇⢿⣦⠀⠀⠀⠀⠀⠀⣿⢦⡀
⠀⣿⣦⡀⠀⠀⠀⣷⡙⢻⡄⠀⠀⠀⠀⠀⣟⢦⡀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠻⠿⠏⠀⠀⠀⢸⣦⡀⠀⠈⠻⣼⡗⠀⠀⠻⣼⣿⠀⠀⢰⡀⠀⠀⠸⣇⣿⣆
⠀⢿⣈⢻⣆⠀⠀⠸⣿⣶⡿⠀⢿⢦⡀⠀⢿⣩⣧⠀⠀⢤⡀⠘⠂⠀⠀⠀⠀⠀⠀⠰⣆⡀⠀⣏⣿⡄⠀⠀⠀⠀⢠⡀⠀⠈⠁⠀⠀⢸⠹⣆⠀⠀⠻⢿⠟
⠀⠈⠿⡿⠇⠀⠀⠀⠉⠉⠁⠀⢸⡌⢷⡀⠀⠉⠁⠀⠀⢸⡟⣦⡀⠀⠀⣦⡀⠀⠀⠀⠛⠇⠀⠘⠟⠁⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠘⢷⣿⠂
⢦⣄⠀⠀⠀⢰⡀⠀⠀⠀⠠⡀⠀⢣⣿⠇⠀⢰⣦⡀⠀⠘⣷⣼⣷⠀⠀⢇⠙⣦⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣦⡄⠀⠈⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⣟⣷⡀⠀⠈⢿⡄⠀⡀⠀⠙⠀⠀⠀⠀⠀⠈⣧⢻⡄⠀⠈⠛⠁⠀⠀⠘⣿⣿⡇⠀⢦⡀⠀⠀⠈⡿⣄⠀⢹⣟⢦⠀⠀⠀⢸⡿⣆⠀⠀⣄⠀⠀⠠⣄⡀
⡀⠈⠛⠁⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⢸⣦⡀⠀⠘⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⢿⠄⠀⠀⠙⠛⠀⠀⢿⣾⡇⠀⠀⠀⢿⣽⠂⠀⠸⣷⡄⠀⢣⠙
⣾⡆⠀⠀⠀⠀⠀⠀⠀⣿⣈⢷⡄⠀⠘⣷⢻⣦⠀⠀⠀⠀⠀⠀⢻⣦⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠈⠉⠀⢠⡀⠀⠀⠁⠀⠀⠀⠉⠃⠀⠈⢯
⠿⠇⠀⠀⠀⠐⣦⡀⠀⠘⢿⣼⡇⠀⠀⠹⣌⣿⡇⠀⢠⡄⠀⠀⠈⣇⣿⣧⠀⠀⢸⡶⣄⠀⠀⠀⣿⡻⣦⠀⠀⠀⠀⠀⠈⡿⣄⠀⠀⠀⠀⠰⡄⠀⠀⠀⠈
⠀⠀⠐⣦⡀⠀⢿⢻⣆⠀⠀⠉⠀⠀⡀⠀⠈⠁⠀⠀⢀⡟⣦⠀⠀⠹⣿⡿⠀⠀⠈⣷⣨⣷⠀⠀⠘⣦⣿⠇⠀⡷⣄⠀⠀⣿⣸⡇⠀⠀⣄⠀⠹
⠀⠀⠀⠘⠿⠀⠘⠿⠃⠀⠀⠀⠀⠀⢿⣦⠀⠀⠀⠀⠈⢷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠈⠉⠀⠀⢻⡙⣧⠀⠈⠉⠁⠀⠀⢹⡳⣄⠀⠀⢶⢤
⢳⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⣄⠀⠀⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣦⡀⠀⠀⠀⣦⡀⠀⠀⠀⢀⠀⠘⢶⡿⠀⠀⢰⣄⠀⠀⢸⣧⣽⡇⠀⠈⣧
⣿⣿⠀⠀⠀⠀⠀⠀⣿⣆⠀⠘⣟⢧⡀⠀⠀⠘⡿⣦⠀⠀⢤⡀⠀⠀⣤⡀⠀⠸⣿⣦⠀⠀⠘⣷⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠸⡎⣷⠀⠀⠙⠛⠁⠀⠀⠘
⠈⠁⠀⠱⣄⠀⠀⠀⠙⠚⠀⠀⢹⣯⡇⠀⠀⠀⢻⣜⡇⠀⠘⣟⣆⠀⢸⡙⢦⡀⠙⠛⠀⠀⠀⠀⠀⢠⡿⣄⠀⠀⠀⢰⣤⡀⠀⠙⠿⠃
⠀⢀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢀⠀⠉⠁⢀⡀⠀⠀⠉⠀⠀⠀⠈⠋⠀⠀⢧⠆⣽⡄⠀⠀⠀⡀⠀⠀⠸⣧⠙⣧⠀⠀⢸⡏⢷⣄⠀⠀⠀⠀⠀⠀⣷⣤⡀
⠀⠸⣷⣄⠀⠀⠀⢸⡷⣄⠀⠈⠁⠀⠀⠀⣿⢦⠀⠀⠀⠀⠰⣄⠀⠀⠀⠈⠳⠿⠃⠀⠀⠀⢿⣦⡀⠀⠹⣧⣹⠇⠀⠀⢷⣸⣿⠄⠀⢠⡀⠀⠀⢸⡎⣷⣄
⠀⠀⢿⣎⣷⡄⠀⠈⣧⣿⡇⠀⣷⣄⠀⠀⢿⣘⣇⠀⠀⣀⡀⠘⠆⠀⠀⠀⠀⠀⠀⠰⣄⠀⠘⣷⣽⣆⠀⠈⠉⠀⢀⠀⠀⠉⠁⠀⠀⢸⠻⣄⠀⠀⠻⣿⡿
⠀⠀⠈⠛⠛⠁⠀⠀⠈⠉⠁⠀⢸⠈⣷⡀⠈⠙⠁⠀⠀⢸⡿⣦⠀⠀⢲⣤⡀⠀⠀⠀⠻⠗⠀⠈⠛⠛⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠘⣦⣿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣤⣒⣀⠍⣍⠏⢫⠉⣉⠙⢢⡾⠛⢒⡀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢐⡏⠡⠠⠈⠃⢈⠒⠉⢄⡰⡘⠏⠀⠢⠈⢒⡨⠏⠀⢀⠯⢲⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠮⠃⠁⣃⠀⠁⠀⢠⠊⠑⣀⠀⢐⠀⠥⠀⠤⠀⢰⡧⡀⠀⢹⠂⠀⡠⠝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡀⢻⢀⠆⠀⡀⢇⠋⠈⢠⠌⠀⠁⢢⠔⣬⠙⣨⢥⠘⣮⡀⠎⠐⠖⠐⠀⠄⢉⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⡤⠀⠀⠀⡰⠆⣀⠒⡠⡯⣔⡡⠖⠤⠐⢆⠃⢠⠀⡎⣙⡃⢰⠋⡇⠂⠀⢛⠈⡀⠈⢬⡡⢜⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠠⠀⣄⠁⠂⣺⡑⠺⠁⠓⢩⡄⣒⢒⠲⢍⠂⠰⢡⠧⠉⠉⠁⢽⡘⣀⠉⡤⡈⠠⠈⠠⠴⠀⣡
⠀⠀⠀⠀⠀⠀⡰⠛⢛⢣⡉⢊⡡⠜⠓⠛⠋⠁⣟⠛⠀⠆⠀⠍⢈⠀⠀⢙⡤⠂⠈⠀⠲⠔⢨⡓⠌⠠⠀⠜⢤⠉⠠⠀⠏⠀⠃
⠀⠀⠀⠀⠀⢠⠝⠃⠈⠀⠀⠀⠉⠑⠶⡇⢁⠀⠇⠀⠀⢠⣀⢀⢚⣃⣴⣾⣄⡚⢀⠅⠢⢠⡔⡟⠐⡀⢻⠮⠔⠛⠋⠐⠀⠲⢌⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣈⠗⡤⠗⠊⠈⠁⠀⠀⠰⠀⠀⠈⠉⠘⠀⢴⡑⠳⣪⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡄⠀⠀⠀⢸⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢇⠀⠀⠀⡔⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢬⡦⣤⣞⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁

⣿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠿⠿⠿⠿⠷⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠿⠿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⠉⠉⠉⠉⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⣠⣾⠿⠷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠹⠟⠉⠉⠛⢿⣆
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠛⢷⡄⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠁⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⠿⢟⣿⣶⠀⠀⠀⠀⢀⣤⣤⣤⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⣀⣐⣿⡅⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⣸⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⢻⣦⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣸⡏⠀⠀⠸⣿⣿⣦⣄⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⣷⣿⠃⣀⣤⣄⠀⢀⣿⣿⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠻⣿⡿⠿⠶⠶⠶⠾⠟⠋⠁⠀⠈⠿⠾⠛⢹⡿⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠛⠛⠿⠷⠿⠿⠆⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⢀⣀⡀⢀⣿⠁⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣽⣿⣆⠀⠀⠀⢠⣿⠉⠻⣾⠏⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣸⡏⠀⡀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⢻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣱⣿⡿⣷⣄⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣌⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡆⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⢀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⢸⣿⠃⠀⠀⠙⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⠀⠀⠀⠀⢿⠏⠀⠀⠀⠀⠉⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠒⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⡉⠝⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⢀⠔⠈⠀⢀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠲⠀⠀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⡠⠊
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠃
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⡿⠟⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠋⠁⠀⢹⣿⣿⠟⠉⠀⠀⠀⢳⡄
⠀⠀⠀⠂⠀⠀⠀⠀⡀⠔⠀⠙⠀⠀⢀⠀⠨⠟⠁⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢀⡔⠈⠀⠀⢀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠁⢀⣴⣿⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⢰⠔⠛⠛⢿⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⣹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⣶⠿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠛⠙⢳⣤⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣤⣄⣠⣤⣔⠉⣹⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡿⠿⢻⣿⣁⣤⢚⣯⣉⣿⣿⣿⣿⣿⣏⣉⣿⡦⡄⣹⣏⡟⠛⠛⢛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡀⢀⣀⣿⣿⡶⠚⠛⣏⣭⣼⣷⣿⣷⣷⣬⣍⡟⠛⠳⣮⣻⣷⡄⡀⢈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⠟⠁⣠⣾⣾⠿⠋⠉⠁⣸⡃⠉⠉⠿⢿⣶⣦⡀⠉⢻⣯⣵⣯⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠋⢱⣷⠘⠛⠛⢁⣴⣶⣦⣴⣌⣴⣦⣶⣶⣄⠙⠛⠛⢰⣿⢼⣿⣿⣶⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣟⣀⠠⠈⣧⡀⠀⠸⠛⠙⢛⡛⠛⠙⠙⠛⣛⣉⠙⠻⠀⠀⣠⡇⠻⣿⣉⣙⣿⣧⡄
⠀⠀⠀⠀⠀⠀⡰⣿⣿⢿⣿⣿⠏⠀⢸⣿⡇⠀⢀⠾⠋⠛⣱⣿⠀⢸⣷⡙⠋⠻⢆⣀⠀⣿⣿⠀⠈⢿⣿⣿⠙⣿⣶
⠀⠀⠀⠀⠀⠀⣰⡿⠷⣾⣿⠁⣤⣶⢈⣿⠣⣾⣿⢰⠄⡰⠋⠟⠀⠘⢏⢳⡀⣴⢸⣿⡶⢻⣏⣰⣦⡄⢹⣿⡥⠚⢿⣷⡀
⠀⠀⠀⠀⢠⢾⣿⠄⠲⣾⡇⢸⣿⠏⠻⣛⡱⠮⢹⣿⠂⢿⣿⠃⠀⠀⢺⣿⠁⢻⣿⠻⠶⣙⡿⠋⢿⣿⠠⣿⡶⠂⠀⣽⣧
⠀⠀⠀⠀⣰⣿⠋⠀⢻⣿⡇⢸⣿⠀⠐⠿⢿⣔⠤⢴⣧⠺⠀⠀⠀⠀⠀⠘⢢⣧⠤⢜⣼⠿⠗⠀⢹⣿⠀⣿⣿⠃⠀⢘⣿
⠀⠀⠀⠀⢡⣿⣿⠂⠈⢽⣷⠌⣿⡄⠀⢶⣤⠙⠿⠸⠿⠀⠀⠀⠀⠀⠀⠀⠸⠟⢼⠟⢡⣴⠆⠀⣼⡏⢴⣿⠍⠀⣀⣸⣿
⠀⠀⠀⠀⠀⢻⠁⠀⢠⣾⡿⠀⢿⣷⣦⣀⣙⣷⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢲⣝⣁⣠⣶⣿⠇⠸⣿⣦⠀⠻⣿⣿⠂
⠀⠀⠀⠀⠀⣸⢁⡀⠰⢛⣿⣧⣌⠙⠈⠻⢋⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⠻⠋⠘⢁⣤⣿⣟⠻⠀⢹⡟⢹⡇
⠀⠀⠀⠀⠀⢹⣿⠀⠀⠩⢿⣿⣿⣾⣿⣷⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⣶⣿⣾⣾⢿⡛⠏⠁⠀⢸⣿⡆⠃
⠀⠀⠀⠀⠀⠘⣿⣡⠀⠀⢈⡉⢿⣿⣿⣿⠇⠺⣄⠀⠰⣄⣀⠀⠀⠀⢀⣀⡴⠀⣀⡼⠂⣿⣿⣿⣿⡀⠀⠀⢀⣬⢻⡇
⠀⠀⠀⠀⠀⠰⣿⢻⣧⠀⠀⠀⠈⠝⠛⠉⢈⣲⠤⣈⡀⠈⠛⣿⣿⣿⡟⠋⠁⣈⣡⢴⣊⣟⠷⠀⠈⢣⠀⠀⢼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠁⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣶⠲⠭⠅⠀⠘⢻⠛⠀⠀⠭⠵⢲⡎⠉⠃⠀⠀⠀⠀⢰⣤⣿⡏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢯⣿⡎⡰⠀⠀⠀⠀⠀⠀⠘⠛⠛⠒⠖⠚⠉⠓⠒⠖⠚⠛⠟⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⡇⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠁⠀⠀⠀⠀⠁⠀⠰⠁⠀⠀⠀⠀⠀⡀⠀⣿⡿⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⣦⠀⣀⠀⠀⠀⠀⠀⠈⠱⠖⢲⣠⣴⠒⠶⠋⠀⠀⠀⠀⠀⠀⢀⡇⣄⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⣿⡆⠀⢤⡀⠀⣆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣜⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣷⣷⣿⣄⠙⠐⡄⠀⠀⠀⠀⢀⣀⢀⡧⣼⣧⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢎⠛⢻⣷⣤⢄⣤⣠⣤⣠⣟⣏⣾⣽⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⡗⣿⣿⣿⣯⢿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠋⠉⠁⠀⠈⠉⠙⠿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣤⣤⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠉⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢿⣿⣿⣆
⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆
⠀⠀⠀⣼⣿⣿⠟⠋⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠐⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⢻⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⡟⠁
⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⡿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣴⣷⡆⠀⢀⣤⣤⠀⠀⣠⣤⡀⠀⢀⣀⡀⠀⢀⣤⡀⠀⢀⣤⣄⠀⠀⣿⠁⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣼⣿⡿⠁⠀⣾⣿⡿⠀⢰⣿⣿⠃⢀⣿⣿⡇⢠⣿⣿⠇⢀⣿⣿⡟⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠻⠟⠁⠀⠻⠿⠋⠀⠘⠿⠟⠀⠈⠛⠛⠀⠈⠛⠟⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⢠⣶⣄⠀⠀⣠⣤⡀⢀⣴⣦⠀⠀⣴⣦⡀⠀⣴⣶⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⣿⣿⡟⠀⢰⣿⣿⠃⣼⣿⡿⠀⣼⣿⣿⠃⠠⣿⣿⠃⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠈⠻⠟⠁⠀⠹⠿⠋⠀⠙⠟⠁⠀⠻⠿⠃⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣆⠀⢀⣤⡄⠀⢀⣠⡀⠀⢀⣠⡀⠀⠀⣠⣄⠀⢀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⣾⣿⡟⢀⣾⣿⡏⠀⣾⣿⡗⠀⢰⣿⣿⠂⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠁⠸⣿⣿⠁⢸⣿⣿⠁⠰⣿⣿⠃⠀⢼⣿⡟⠀⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⠟⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⢿⣿⣿⡟⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣴⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣾⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠙⠛⠛⠛⠻⠿⠿⠟⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠾⠿⠿⠿⠿⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⠿⠿⠿⠿⢷⣶⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⣀⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠙⠛⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⢀⣴⡾⠟⠛⠉⠉⠙⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣹⣧⣤⣤⣀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⢀⣴⡿⠛⠋⠉⠉⠛⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠉⠉⠉⠛⠿⣶⣄⠀⣀⣤⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣄
⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠛⠉⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣴⣶⣶⣶⣤⣄⠀⣿⡆
⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠛⢿⣾⡇
⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡃
⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⢿⣦
⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻
⠀⠈⠙⠿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣽⡟⠉⠉⠉⠉⣩⣿⠋⢿⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⢀⣼⣿⣥⣤⣬⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣃⣀⣀⣀⣀⣈⠉⠉⠉⢉⣿⠏⠉⠛⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⠶⠶⠶⠶⢶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⢻⡿⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⢠⣾⣿⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣁⣀⣀⣀⣀⣉⠉⠉⠉⣩⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⣿⡏⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠤⠤⣄⣤⣀⣀⡀
⠀⠀⠀⠀⠀⢶⣏⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠢⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠙⢍⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠉⢦⡀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣉⡑⠲⣄⡀⠀⢰⢛⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠙⢶⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⢛⣷⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠸⡏⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⡇⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⣎⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠺⣛⠒⠒⠲⠤⣄⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣆⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢹⡄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣰⠃⢙⡦⣄⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢷⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⡴⠁⢀⡞⠀⠈⠣⡀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⡞⠁⣠⠿⠤⢤⣀⠀⠙⢦⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡴⠃⠀⠀⠀⠀⠉⠲⢄⣻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠖⠒⢶⠦⠤⢤⣠⣏⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⠉⠑⠦⣄⡀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠤⣍⡲⢼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣞⣀⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⡤⠶⢤⣍⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⠖⣛⣛⣛⠲⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⡛⢺⠇⠈⠁⠀⠀⠀⠈⠁⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⣋⣭⣤⡅⣼⣿⣾⣿⣿⣿⣷⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⢋⡶⠋⠉⠙⠀⠀⠀⠀⠀⠀⢀⣤⠶⠿⠶⢦⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⡼⢋⣴⣾⣶⣿⣿⣿⣿⣿⣿⡿⠟⣋⣤⣉⡛⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣿⣘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠛⢶⡙⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠘⠧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣤⡙⢷⡙⣿⣿⣿
⠀⠀⠀⠀⡾⠋⠉⠉⠛⢀⣀⡀⠚⠛⣛⣛⣂⣀⡀⠀⠀⠀⠀⠀⠗⢸⠇⠀⠀⠀⣿⣿⣿⣿⢋⣴⣾⣶⣬⡿⣿⣿⣭⣭⣥⣭⣽⣿⣿⣿⣿⣿⣿⣿⣼⡇⣿⣿⣿
⠀⠀⠀⠘⣇⠀⠀⣠⣠⣍⣉⣍⣤⡈⠉⣩⣭⣭⣥⣤⣤⡄⠀⠀⣠⡞⠀⠀⠀⠀⣿⣿⣿⣿⠸⣿⣿⠿⠛⠶⠶⠶⠿⢷⣶⠶⠲⠶⠚⠟⠻⢿⣿⣿⡿⢡⣿⣿⣿
⠀⠀⠀⠀⠘⠳⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣌⣙⣛⣛⣛⣛⣛⣛⣛⣙⣋⣛⣙⣛⣋⣛⣋⣉⣥⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⡹⣿⣿⣿⣿⠋⠹⣿⣿⣿⣿⢏⠹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⢸⡇⢸⡇⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⢼⡧⢹⣿⣿⡏⢼⡧⢹⣿⣿⡏⢸⡇⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠉⠳⣦⣠⡴⠶⠖⠲⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠙⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠒⠶⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟
⠀⠀⠀⠀⠀⢀⣠⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣦
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠘⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡞⢳⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠧⠼⠁⠀⠀⢸⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢀⡏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡸⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡤⠃

⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣴⠛⠙⣿⠁⢹⡞⠛⡿⢈⡷⠀⠙⠛⣻⠟⠀⠙⠛⣿⠏⠀⣿⠈⣼⢋⣹⡇⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣿⠀⢸⡆⠀⠀⢸⡇⠀⢀⣼⣋⡀⠀⣠⣾⣁⡀⠀⡟⠀⣿⣋⣁⣠
⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠛⠛⠙⠒⠚⠒⠒⠒⠒⠓⠒⠛⠛⠛⠛⠒⠛⠛⠛⠓⠐⠓⠒⠊⠛⠛⠁⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠺⠂⠀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠊⠀⠀⠀⠀⢱⣀⡀⠀⠐⣸⣷⡆⠀⠀⠀⠀⠀⢤⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠘⣼⣯⠻⠞⠇⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡇⠀⠀⠀⢢⠄⡸⣦⣀⡠⠊⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠠⠀⠀⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠵⡆⠀⣀⠀⠛⠈⠛⣄⠋⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⢃⠘⣇⠀⠀⣠⠞⠁⠀⡀⠀⠀⠀⠀⠀⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⣠⠆⠀⠀⠀⠀⠠⣀⣀⣀⡄⣀⣽⠀⡀⠀⠀⠀⠀⠀⠑⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠐⠃⠀⠠⠂⠁⠠⠆⠉⠙⢿⡟⠙⢿⠰⣟⣧⠟⠋⠛⢆⠠⣀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠓⣲⡆⠛⠿⡄⠀⠁⠀⠐⠀⠘⠁⣔⡻⢶⠘⢧⠈⠁⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠨⠏⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠨⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⢀⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢐⣚⣀⣦⠀⠀⡀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢴⣿⣿⣿⣾⡇⠀⠇⠀⣄⠠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠈⢿⡻⠛⠿⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠢⣠⡔⠐⠶⠷⠶⣫⣿⠏⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡾⣶⣦⣶⣹⣿⣾⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡏⢹⢏⣹⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢁⣁⡀⡑⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠋⠉⠉⠙⠓⢦⡀⠀⠀⠀⣠⠴⠶⠶⢤⡀⣠⠴⠚⠛⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠖⠚⠁⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠈⠙⠋⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠲⣄⡀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⣸⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⡄
⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠒⠚⠛⠉
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃
⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⢀⠀⠀⢀⣡⠞⠛⠓⠶⣾⠟⠁⠈⠙⠓⠶⠦⣤⣤⣤⣴⣶⠟⠛⠶⢦⣤⣤⠶⠞⠋
⠀⠀⠀⠀⠀⠙⠳⠶⠤⣤⡤⠶⠾⠛⠁⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠛⠛⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⡠⠂⠀⠴⠗⢚⡽⠃⠀⠀⠀⠀⠀⠀⠀⠠⣠⡾⠃⠀⠀⣠⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢀⠜⠁⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⠴⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠁⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣥⡤⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣀⠀⠀⠀⠀⠀⠀⠘⣩⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠖⠚⣹⠏⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⣰⠃⠀⠀⠀⣠⠾⠋⠀⠀⠀⢀⡔⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⣰⠃⠀⠀⣠⠾⠁⠀⠀⠀⠀⡠⠊⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠁⠀⠀⣰⣿⠋⠻⢿⣷⣄⠈⠉⠛⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠙⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⣿⡇⠀⣀⣀⣠⣤⣤⣀⣹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣿⠿⢿⣿⣶⣶⣦⣤⣀⠀⠀⣿⣧⣴⣾⣿⠟⠛⠛⠛⠻⢿⣷⣤⣿⣿⡿⠛⠛⠋⠙⠛⠛⠿⠿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣶⣿⡿⠋⣿⣿⠀⠀⠀⠀⠀⠀⠉⠻⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣀⠀⠀⠀⠀⢀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣶⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣀⣀⣀⠀⡀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⡀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣯⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣯⣤⣴⣤⣤⣤⣦⣶⣤⣽⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣏⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣹⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⢩⣭⣭⡍⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠛⠛⠑⠉

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



⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠯⢼⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⢬

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣉⠀⡏⠙⢦⢸⠈⢻⠉⢰⢳⠀⢸⣙⠆⣶⠀⢰⣏⡁⠀⢰⣋⠀⠙⡏⠁⣏⣻⢠⠞⠙⢦⢸⣠⠋⢸⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣀⡐⣇⣠⠞⢸⠀⣸⢀⡟⠉⣇⣸⣈⡇⣿⣀⣘⣇⣀⠀⢀⣨⡇⢀⡇⢀⡇⢹⡘⢧⣠⠞⣸⠉⢦⣸⣀⡀
⣿⣿⡿⠛⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡿⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠈⢿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁




⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣦⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠛⠿⣍⠉⠙⠛⠓⠶⢤⣍⡉⠉⠉⠉⠉⠛⠛⠓⠒⠶⠦⠤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⢡⡇⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⡞⠁⠀⢸⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠏⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣰⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⢀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⢠⠏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⣠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠛⠋⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣀⣠⣴⠖⠋⠁
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣀⣀⡼⠷⠶⠚⠋⠉⢧⠘⣇
⠀⠀⠀⠀⢾⣁⣀⣀⣀⣀⣀⣠⡼⠻⠴⠶⠖⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⣇⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣽

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣬⡁⣠⣤⠈⢷⣣⡀
⡆⠠⡀⠀⠀⠈⠀⠀⠀⠁⠀⠀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢈⣿⡳⣜⢿⣎⢻⣷⣔⠽⢿⣄⢠
⠈⠢⣀⡐⠒⣋⠀⠀⠀⠀⠀⠀⢈⠐⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣶⣯⠛⡛⢎⢢⡹⣷⣝⢿⣯⣂⠻⣧
⠀⠀⠀⠈⠉⠀⠀⣤⡤⢤⠖⠀⠈⠑⠀⠀⠀⢀⠀⠀⠀⠀⣠⡀⢴⣶⣷⣝⡿⠋⠙⠳⠘⠀⠑⠙⠊⠉⠀⠙⠁
⠀⠀⠀⠐⠒⠒⠚⠁⠀⠀⠉⠓⠀⠀⢀⣀⣤⣼⣿⣶⠲⣿⣿⣿⣦⡹⠿⠻⠃⠀⠀⠀⣀⡀
⠀⣀⢀⠀⠀⢀⣀⡀⠀⠀⢀⣤⡰⣾⣷⡙⢿⣿⣿⣿⣷⡌⠣⠉⠈⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⣿⣿⣍⢿⣿⣿⣿⣿⣧⡻⣿⣮⣿⣿⡦⠻⣿⣿⣇⡈⠒⠐⠠⠤⠔⠀⠀⠐⠒⠈⠀⢀⠀⠀⣤⣀⠰⣝⢷⣗⠄
⠀⠀⠈⢿⣿⣦⠻⠟⠹⣿⣿⣿⣮⣿⣿⣿⣆⢲⣾⣿⣿⣿⣿⣿⡻⣷⣿⣿⣶⣦⡺⣿⣿⣟⢦⡻⣿⣷⡳⠌⠢⡉⠳
⠀⠀⠈⢲⣝⢿⣷⣿⣧⡹⣿⣿⣿⣷⣝⢿⣿⣷⡙⢿⣿⣿⣿⣿⣿⣮⡿⣿⣿⣿⡛⣈⣿⣿⣷⣕⢮⢿⣿⣦⡢⠈
⠀⠠⡙⣝⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣷⣿⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣮⡻⣛⣿⣿⣯⣷⣝⠿⡿⡄
⠀⡝⢮⠺⣿⣿⣿⣿⣿⣏⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄⢭⣝⣛⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣷⡝⠞
⠀⠈⣿⣿⣟⢿⣿⣿⣿⣿⣷⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣼⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⡿⣦
⠀⠠⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⢆⣻⣿⣿⣿⣿⣿⣿⣿⣄⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⠿⢯⡘⠌⠢
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⡿⠟⡛⢮⢠⣧⠳⡀
⠀⠐⢠⡎⡙⡟⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡛⢯⡻⢷⢰⡆⣿⠀⣸⣿⣀⡈
⠀⠀⢐⢯⣿⢰⣿⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⣿⣿⣿⣷⣿⣿⣿⡿⣿⣿⡏⣤⠁⡆⣼⣿⣿⢃⣼⣿⡇⠙
⠀⠀⠂⣼⣿⣵⣿⣏⠷⠈⠻⠿⠟⠍⠛⠟⠗⠙⠛⠉⠊⢛⠋⠛⣛⠛⠻⠿⠮⠙⠐⣿⢘⣷⣸⣿⣿⣿⣿⣿⣷⡄
⢠⣾⣷⣿⣿⣿⣿⣿⣶⣶⣦⣤⣾⣿⣶⣦⣶⣿⣷⣦⣔⢻⠿⣿⣿⣿⣷⣶⣶⣦⢸⣿⣿⣿⣿⣿⣾⣧⣿⣿⣿⣶⣦
⠀⠉⠋⠁⠀⢀⣈⣀⣉⣉⣋⣉⣉⣉⡙⠛⠋⠉⠉⠤⣤⠤⠀⠀⢤⣁⠤⠭⢙⣐⣿⣿⣿⣝⣿⣿⣿⣭⣽⢿⣿⣶⣍
⠀⠐⠀⠂⠢⠀⠐⠀⠀⠈⠓⠐⠒⠶⠒⠀⠀⠀⠃⠙⠛⠉⠛⠋⠁⠀⣀⣠⣬⣴⠼⠗⠒⠛⠛⠛⠛⠋⠛⠻⠿⠛⠫
⠀⠮⠙⠛⠻⠿⠿⠛⠛⠛⠛⠛⠓⠒⠒⠛⣀⡘⢛⣡⣛⠛⣻⡓⠁⠀⠀⠀⣀⣀⣠⣤⣤⡶⡶⠶⢶⠿⠛⢿⣶⠦⣜
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣠⣄⣒⣟⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣟⣛⣋⣉⣉⣉⣁⣀⣀⣀⣠⣀⣀⣀⣀⣈⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠒⠛⢋⠝⠉⠙⠳⡒⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⠯⠋⠁⠀⠀⠀⡠⠋⠀⠀⠀⠀⠘⢆⠀⠉⠛⢗⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⡫⠚⠁⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠉⠪⡑⢄
⠀⠀⠀⠀⠀⢀⡔⢡⠎⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢦⠑⢄
⠀⠀⠀⠀⣠⣎⡔⠁⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠱⡄⠳⡀
⠀⠀⠀⢰⢣⡜⢄⡠⠤⡀⢀⡀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⡏⠱⡄
⠀⠀⠀⢨⠎⢡⠀⠴⢂⢈⣁⡘⠤⠔⡛⠲⣀⡠⠔⠢⢄⢀⡠⠤⢄⠀⣀⠼⡦⣀⠖⠑⠒⢁⡉⢁⠸⡌⠘
⠀⠀⠀⠘⠠⠤⠤⠤⢉⡀⠈⢰⠄⢢⠳⠆⣤⠰⠆⠰⢀⡌⠲⠠⠆⣩⠠⠆⡧⠄⡄⠊⠁⠇⠀⠈⠁⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⢄⡸⢀⣀⣋⣀⣀⣀⣈⢋⣀⣀⣀⠛⠀⠀⠇⢀⡤⠔⠊⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⢤⣴⣶⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠛⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠁⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡷⠂
⠀⠀⠀⠀⠹⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢮⣿⣿⣿⣿⣶⣄⣀⣀⣀⣀⣤⣤⣤⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣗⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⠿⠛⠟⠋⠉⠉⠙⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟⠛⠛⢿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠁⠀⠀⠀⠀⠐⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣶⣶⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠙⣿⣿⣿⡟⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⣀⣀⠀⣀⣀⢠⣴⣾⣿⣿⣿⣿⣷⣦⠀⣀⣀⣀⣤⣴⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣟⣰⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡍⣿⢿⠿⢿⣿⡏⣸⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣾⣶⣶⣴⣶⣶⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠛⠋⠉⠉⠁⠉⠉⠙⠛⠿⠿


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⣞⠃⠀⠀⠀⠀⠉⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠕⠁⢀⣀⣈⣳⡄⠀⠀⠀⠀⠈⡻⣶⡄⠀⠀⣀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡭⢹⡟⢸⡏⠀⠀⢀⠙⠯⠤⠀⠀⠀⢀⡀⠘⠳⢽⣿⡎⣾⡟⠟⡹⢦⡀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⢠⣄⣀⡠⠋⠾⣿⡀⠘⣧⠀⢀⣼⠓⠢⠈⠓⠒⠚⢻⣄⢠⣾⣷⡝⠇⣿⢹⡶⣶⣦⣭⣭⠍⠁
⠀⠀⠀⠀⠀⠀⠛⠉⠉⠁⠀⠀⡿⡏⣧⢹⣷⡿⠃⠀⠀⠀⠀⠀⠀⡀⠻⠌⠻⣿⣧⣴⡿⣸⠁⠛⠛⢋⠥⠄⣾⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠒⠉⠒⠊⣰⠇⣼⠃⠋⠀⡠⢰⠀⠀⠀⠀⠀⣸⣟⡶⠄⠈⠙⢿⡄⢿⣦⣀⡤⠎⣠⡙⢸⣷
⠀⠀⠀⠀⠀⢰⣸⢠⠑⠚⠉⠚⠁⠾⢱⠶⢶⡼⢁⢸⡀⠀⠀⠀⠀⣱⢋⡔⣡⠾⠿⡆⣿⡸⠋⠀⢀⢼⣿⡇⣼⣿
⠀⠀⠀⠀⠀⠸⣿⣼⡎⣺⣧⠆⣿⠀⠘⠰⣅⡇⢸⢠⠇⠀⠀⢤⡄⡏⣼⢰⢋⡴⠇⠀⠃⠀⠀⢀⣧⢣⣿⡇⡿⠟
⠀⠀⠀⠀⠀⠀⠈⠙⠳⠹⣿⣦⡻⣄⠀⢶⢤⡋⠈⡟⠀⠀⠀⢸⢧⢳⢹⣸⠈⢶⠒⣰⠁⢰⢦⣾⣿⡄⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣆⣸⡔⣆⠘⠁⠀⠀⠀⠈⠎⠀⠈⠋⣰⡋⡰⢿⣦⣜⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣧⢘⣃⠀⠀⠀⠀⣀⡀⠀⡆⢀⢫⠆⠀⠘⠿⠟⠛⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⡻⣷⡘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣰⠆⠀⠀⢀⡀⠀⢸⡆⣷⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠹⠀⠀⠀⠈⠩⠛⢾⡗⢻⡟⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢇⠀⠀⠀⣀⣀⡙⣆⠁⡿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡠⣼⡄⠀⠀⠀⢭⡻⠏⠀⡇⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠟⠂⠀⢀⢈⡟⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠃⠀⠀⠈⠻⢳⡦⣀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣴⠂⠀⠀⠀⠉⠀⢀⣿⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣸⡀⠀⠀⠀⠐⢚⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⡈⠓⠒⠒⠚⠉⠭⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠀⠀⠀⣰⣀⡴⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢹⣏⣛⣛⣙⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿