Squash Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣶⣖⢶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠻⣿⠛⠛⣄⠘⠛⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠻⣿⠂⡠⠻⡄⠀⠈⢷⡀⠀⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⣿⠀⠁⠀⠱⠀⠀⠀⠳⡀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢿⠀⠀⠀⠀⠂⠀⠀⠀⢣⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢁⡀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠏⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠁⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣴⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣇⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⠀⠀⠀⢸⡇⢀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠾⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⢲⡄⠀⠘⣧⢸⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⣀⡏⠀⠀⠀⠰⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣿⣷⡀⠀⠹⣿⢳⡌⠀⠀⠀⢠⡀⢠⠀⢀⣿⡿⠀⡤⣤⠖⣉⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆⣷⡿⣿⣿⣦⠄⠠⢸⣷⣿⣠⣾⡿⣡⣾⡿⣯⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠷⠂⠛⠛⠛⠳⠛⠋⠙⠉⠉⠁




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠙⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣼⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢊⡥⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠟⠿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣱⠿⡿⣻⡿⣿⣿⣿⣿⣿⣶⣴⣎⢿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠊⠀⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠘⠀⢸⢇⣿⡏⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡟⢸⣿⢻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⢰⠇⣼⡿⢸⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢘⠀⠀⠀⣾⢀⡀⡁⣈⣻⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢠⣾⠏
⠀⣀⣠⣐⡂⢰⡄⣾⣻⣶⣶⢶⣶⣄⣺⠀⡆⣀⣿⠸⡛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡴⣱⠃⠀⠐
⣬⣤⣼⣿⣟⡿⣿⠿⣯⣶⣿⣿⣿⣿⣿⣿⡟⠉⠻⡀⢱⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⠃⡼⣸⣧⣦⣤⣀
⣿⡿⣫⡿⢫⣿⣧⡘⣿⣿⣿⣿⣿⡿⠉⢀⣠⣶⣶⡟⣿⣌⠁⠺⢿⣿⣿⣿⣿⣿⠟⠀⢠⣼⣿⣶⣼⣿⣿⣿⣿⣿⣿
⠃⠀⠸⠃⠟⠉⠁⢹⡿⢿⣿⣿⣿⡇⣠⡞⠋⣴⡟⢩⣿⡄⠀⢰⣶⣿⣿⣿⣿⠃⠀⠀⠘⢉⣿⣿⣿⣿⣿⣧⣹⣿⣿
⠦⡶⠛⠀⠀⠀⠼⢿⡄⢾⣿⣿⣿⣷⣿⣠⣾⣿⡇⢿⣿⣿⡆⡀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠈⢸⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠾⠀⣿⠀⣾⣿⣿⢳⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⠐⣿⣿⣿⣷⡀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠃⣙⢿⣿⣽⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠋⠛
⠀⠀⠀⠀⠀⠀⠈⠈⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁
⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠳⣄
⠀⠀⠀⠆⠀⠀⢰⠀⠀⢀⠶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⢇⠀⠀⠀⠈⠇⠀⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠑⠀⠘⠀⡰⠋⠀⠀⢠⠀⠀⠀⠀⠀⠀⢇⡀⠀⠢⡜⢹⠀⠀⣰⠀⡄⠀⠀⠀⠀⢰⣦
⢠⣀⣀⡀⠠⣽⣿⣿⡧⠤⠤⠤⢾⠀⠀⠀⠀⠀⢀⠈⠓⠴⠵⠞⠁⠀⣠⡏⡰⠃⠀⠀⢠⣨⡏⠉⡇⢰
⠀⠀⠀⠀⢀⠜⣿⠻⣦⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠱⢦⣄⣀⣀⣤⣶⡿⠟⠀⠀⠀⠀⠏⢹⠃⠀⡀⢸
⠀⠀⠀⡠⠋⠀⢹⠀⠈⠻⣧⡤⠎⠀⠀⠀⠀⣴⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠇⠀⠂
⠀⠀⠉⠀⠀⢀⣸⣄⣀⡠⠊⠀⠀⠀⠀⠀⠠⣿⣴⠀⡠⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠆⣰⠇⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠗⢀⡠⠊⠱⠿⠛⢾⠈⠃⠀⠀⠀⠀⠀⠀⠀⠰⠇⢠⠃⠀⠀⠀⠀⠀⠄⠠⢾
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢐⡇⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⠀⠀⠑⠂⠀⠀⠀⠀⡄
⠀⠀⠀⠉⢳⣄⠀⠀⠀⠀⢸⢢⡟⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠑⣼⣆⡀⠀⢀⡄⠀⣀⡼⠃
⠀⠀⠀⢀⣸⣻⡀⠀⠀⠀⠘⢿⣇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠉⠳⣤⢀⡇⠀⠀⠀⣠⢀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠉⠉⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡤⠂⡀⠐⠒⠒⠊⠗⠀⠀⠀⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠊⡰⠋⠀⠀⢠⠤⡀⠀⠀⠀⠐⠀⠘⣯⠀⠀⠀⠀⠀⠀⣀⣴⠄⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠐⠀⠀⠀⣰⣵⢊⣷⣿⠀⡀⠀⠀⠀⢸⠆⣀⠀⠀⠀⠰⣷⣿⠄⣾⡯⡅
⠈⠳⣄⢰⡀⢀⠀⣀⣠⠟⠀⠀⠀⠸⠀⠀⠲⣿⣯⠟⣿⠏⠀⡀⠀⠀⠀⣼⢀⡏⠀⠀⠀⠲⢩⣏⠀⡿⡍⠋
⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⡡⡀⠀⠈⠫⠟⠻⠀⠀⢀⡄⢀⣴⣿⠎⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣶⣦⣤⣤⣤⣤⣾⣾⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣯⣭⣽⣯⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠀⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢀⣶⣧⠏⠀⠀⠀⠀⠆⠂⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠙⢦⡀⢀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⢐⣈⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢱
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢦⠈⠁⠘⠀⢰⠋⠄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⣀⣼⣶⠇⠒⠀⠀⠀⠀⣀⡤⠤⠀⠀⠀⠀⠀⢀⣠⠴⢖⣺⣟⢶⣭⣧
⠀⠀⢀⣠⠤⠤⠀⠀⠀⠀⠀⢉⠝⠁⠖⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⡴⣋⠀⠞⠋⠡⠝⠻⠶⣾⠇
⠀⠀⠈⠀⠀⠀⠀⠀⠐⡇⠀⠁⠀⠀⢈⡗⣄⢀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠁⢀⡖⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠐⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠔⠋⠠⠼⠇⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣳⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⠀⠀⡀⢸⠀⠀⠀⠀⡠⣄⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡠⠂⠀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣰⠀⡄⠀⠀⠀⢠⠃⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⡾⠁⠀⠚⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢰⠀⠀⠀⠀⢺⡀⢀⣸⠇
⠀⠀⠀⢰⣤⣿⡖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⠊⠀⡴⠃⠀⠁⠀⡰⠁⢀⠀⢀⠀⠀⡎⠀⡎⠀⠀⠀⠀⠈⠻⠿⠋
⠀⠀⢀⠉⡀⠈⢳⡑⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠂⠀⠞⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢸⠇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀
⠀⠀⢨⠀⡇⠰⠀⢧⠉⠘⡄⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡄⠀⠆⠀⠠⠀⠀⠀⠞⠀⠀⡄⠀⣾⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠈⠠⡀
⠀⠀⠘⠀⢸⠀⠀⠈⡆⠀⢳⡀⠀⠀⠀⠀⠀⠀⣷⠀⣼⠃⠀⠀⢀⠀⠀⢀⠄⠀⠀⢰⠇⢀⡟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⡀⠀⡇⠀⠀⠘⡀⠈⢷⡀⠀⠀⠀⠀⠀⠸⡄⣿⠀⠀⢠⡇⠀⢀⡞⠀⠀⢠⡟⠀⣸⠃⠀⡿⠀⠀⠀⠀⠀⠀⡠⠎⠁⠀⠀⡠⠀⠀⠀⢀⢠⠀⡌
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠱⡸⡆⠀⢸⡃⢀⡞⠀⠀⣰⠟⠀⣰⠏⢀⡼⠃⠀⠀⠀⠀⣠⠞⠀⢀⠀⢀⠎⠀⡠⠂⠀⢠⠃⡸⠁
⠀⠀⠀⢠⠀⠀⢧⠀⠀⠠⠀⠀⢄⠨⠑⢄⠀⠀⠀⠀⠘⢦⡸⠌⠁⠚⣁⣴⠞⠃⣠⡾⠋⣠⠞⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⡴⠁⠀⠜⠀⠔⢡⠃⣰⠃
⠀⠀⠀⠀⠆⠀⠈⢆⠀⠀⠀⠀⠈⠓⢤⣀⠑⠤⡀⠀⠀⠀⠉⠂⠄⣀⣉⣀⢀⣈⣡⡴⠚⠁⠀⠀⠀⢠⠞⠁⠂⠀⠀⣠⠊⢀⠔⠁⢀⠊⡰⠃⣰⠃
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⠲⠈⠑⠢⢄⣀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣠⠞⠁⡠⠀⢀⠔⢁⡜⠁⡼⠁
⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠈⠒⢤⣀⠐⠄⡐⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠙⠛⠒⢾⡁⠀⠀⣠⠔⠁⣠⢎⢄⠞
⠀⠀⠀⠀⠀⠀⠡⠀⠁⠀⠠⠀⠀⠘⠀⠀⠈⠛⠶⢤⣐⠢⢄⡈⠑⠟⢦⡀⠀⠀⠀⠀⠀⠀⢰⠁⢀⡀⠀⠀⠀⠹⣄⠀⠁⢀⠜⡵⣱⠋
⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⣕⠲⢌⡐⢤⣀⠹⣆⠀⠀⠀⠀⠀⢧⠀⢄⠓⠈⠤⠀⠀⠙⣦⠔⢫⣴⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡈⠐⠢⢤⣀⣉⠲⣽⣷⢹⡄⠀⠀⠀⠀⠘⡆⠰⠀⠀⠀⡅⠀⠀⢸⠀⣩⠎⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠈⠉⠙⠀⠀⠈⠍⠻⣎⠿⣾⠃⠀⠀⠀⠀⠀⢱⡀⠓⠸⠌⠃⠀⠀⣿⡴⠃⠀⠀⠀⠀⠀⠀⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠶⠤⠤⠤⣤⣤⡤⠦⢄⡽⠃⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⣀⣀⣶⡾⠷⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⡎⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠤⠀⠀⠤⠬⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡏⡠⢤⣸⠀⠀⢀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⡏⠄⠁⠛⠢⡔⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⢸⠁⣀⠠⠤⢸⠀⠀⡠⠋⠉⠀⠀⠀⠈⠁⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⡠⠊⠉⡹⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⡀
⠀⠀⠀⠀⣼⠃⠀⠀⢀⠜⠀⠀⢰⠁⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⢳⡀
⠀⠀⠀⢰⠇⠀⠀⠀⡘⠀⠀⠀⢸⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣠⡴⠞⢱⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⣿⡤⠖⠋⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⡆⠀⠀⠀⡇⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⠶⠚⠋⠁⠀⠀⢀⠐⠄⠀⠸⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⢷⡀⠀⠀⢰⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣦⣤⠤⢤⡤⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡰⠃⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠈⢧⠀⠀⠀⠇⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⠀⠀⡆⠐⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠘⡄⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⡄⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂⠤⠤⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣌⢦⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣄⣀⣀⣀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠲⢤⣄⣀⡀⠈⠀⠀⠀⠀⢀⣁⣀⣠⡤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⡶⣾⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠐⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⠈⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡐⠀⠀⠀⠀⠀⠀⠀⣴⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⢹⠀⠀⠀⠀⠀⠀⠆⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⡟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⣾⣷⡶⣦⡀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠸⡆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠙⠠⣧⣙⠥⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⡔⣿⢲⠄⢀⠉⠁⠐⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣼⢠⡇
⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠗⠺⡁⢀⠏⢁⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⢿⡞
⠀⠀⠀⠀⠀⠀⠸⣯⣑⢤⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠹⣮⡰⠏⠀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢅⡀⠀⠀⠀⠀⠉⠁⠉⠉⠀⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠀⠒⠀⠀⠀⠀⠀⠠⢄⡈⠐⠢⢄⣀⠀⠀⠀⠀⠀⣠⡧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠬⣘⣹⣓⣶⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⣄⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡔⠣⢔⠐⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠂⠐⠀⠀⣇⠰⠁⠀⠀⣀⢞⣀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢢⡀⢀⡀⠀⣦⡍⠀⠀⢀⣰⠏⠁⠀⠀⠀⠗⠞⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣔⠀⠀⠈⠉⠉⠢⢄⠀⠀⢻⠄⠀⣸⢃⠀⠀⠄⢀⣤⠖⠒⠐⠋⠁⠀⠠⠃
⠀⠀⠀⢀⠌⠙⢻⡷⠄⠤⠴⢦⣔⣶⣗⣦⣄⣆⣼⡏⣀⠀⣦⣞⣓⡎⠈⠁⠀⢀⡀⠴⢟⡆⠀⠀⠀⠀⢠⣄⡀
⠀⠀⢀⣼⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣾⣻⣞⣥⣄⠉⠏⠁⠠⠚⠋⠉⣀⣾⡀⠀⠀⡠⢶⣶⡿⠋
⠀⣰⡟⣡⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⣿⣒⢶⠢⠀⢆⠀⣈⢵⣿⣇⢐⠿⠟⠋⠁
⣰⠗⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠦⠼⠿⠷⣿⣾⡿⠁
⣿⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠒⠌⡉⠒⢄⡀
⢿⡗⡀⠀⠄⡀⠀⢀⡖⠀⢀⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠈⠑⣤⣹⣦
⠈⢿⡷⢄⠀⠈⢳⡿⠷⠄⢼⢤⣇⢄⡠⠔⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢻⣾⣿⠋
⠀⠀⠙⢷⣷⣶⠿⢷⡀⠀⠸⢾⣿⢻⣿⣯⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⡁⠀⣀⣤⣬⣽
⠀⠀⠀⠘⢍⠀⠀⠠⢽⣶⡤⠬⠿⣾⣇⠈⠳⣦⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢔⣻⣿⣆⠙⣻⠿⠿⠟
⠀⠀⠀⠀⠈⠲⠌⣷⣿⠃⣄⣀⣠⠤⣬⣽⡦⠟⣿⣷⠶⠶⢦⣤⣦⣄⣀⣀⣀⣀⣀⣐⣖⣲⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⢠⠟⠉⠻⡟⠉⠙⠷⠶⠿⠧⠞⠻⠷⠶⠖⠋⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠙⣲⠴⠒
⣤⣤⣤⣤⣤⣤⣤⣤⣵⣾⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠡⠀⠂⠐⠀⠀⠀⡠⣪⠊⣠⠔⠒⠲⢤⡑⢕⠢⡀⠀⠈⠁⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡱⠁⡜⠀⡴⠒⢂⠀⠹⡆⠑⡕⢄⠀⠢⡀⠃⠀⠀⠀⠀⠀⠤⢄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁⣸⠃⠀⣸⠀⠐⣧⠀⠘⡌⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⢀⣤⠂⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠘⠁⢀⠀⡏⠀⠀⣿⠀⠀⠟⡄⠐⡄⠀⠀⠀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢈⠀⡀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠸⣀⠀⠀⠙⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠄⠀⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠘⣿⠀⠀⠀⡇⠀⠀⠀⢳⡆
⠀⠀⠀⠀⠀⠈⠣⠐⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢹⡆⠀⠀⣧⠀⠀⠀⠘⠀⠒
⠀⠀⠀⠀⠀⠁⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⣀⢸⣧⠤⠘⠉⠀⢀⠠⠀⠀⡀⠘⠂
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠄⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡐⠀⠀⠀⡀⠀⠐⠀⠀⠄⠀⠀⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠃⠘⠻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠚⠀⠀⠀⡀⠈⠂⢀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠄⠔⠀⠀⠀⠀⠠⣼⡂⠀⠀⠀⠀⠀⢀⣄⢀⣄⣤⣄
⠀⠀⠀⠀⠀⠀⠃⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣾⠉⠓⢩⣿⠀⠹⣦⠠⠀⠀⠶⠶⠤⠄⠀⠀⣌⣼⣿⣶⣽⣿⠁
⠀⠀⠀⠀⣀⠜⠛⠩⠗⠀⠀⠀⢀⠀⠀⠀⠀⠀⣤⡴⢋⣷⠀⠀⢸⡈⢿⠀⠈⢸⢇⠀⠀⠈⠻⣧⣤⢗⣫⣛⡿⠛⠋
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣚⠿⢦⣈⠁⠀⠀⠂⠁⠘⠁⠂⢁⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠠⢚⣿⠋⢡⠆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢁⡸⣧⢆⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⢎⢸⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣠⡴⠛⠀⠀⠀⠀⠀⠙⠻⣿⣿⡆⣀⣀⠀⠀⠀⠜
⠀⠀⠀⠀⠈⠒⠛⠒⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠀⠀⠀⠀⠀⢀⣼⢡⣤⠄
⠀⠀⠀⠀⠀⢀⢠⣤⣴⣾⢣⣤⣄⣤⣀⠀⠀⠀⠀⡀⡠⠒⣻⣝⡭⠈⠉⡖⠀⠀⠀⢠⠾⠿⡿⢶⡀⠀⢀⣦⠊⡿⠛⢏⠑⣦⠄
⠀⠀⠀⣀⡐⢩⣿⠋⡹⣿⠟⢉⠻⡝⠫⡑⣦⠀⠈⠈⢡⠀⠀⠀⠰⠀⠀⣓⡇⠀⠀⣿⣤⢠⢀⣰⡇⠀⠀⣟⢰⡇⠀⢸⡀⢸⣀
⠀⠀⢠⣿⠇⣼⠃⣸⠁⢻⡇⠘⡆⠘⡄⠙⣾⡇⠀⢲⡘⡄⢀⠀⢰⡆⢠⣿⠃⠀⢰⣿⡿⢘⢸⣿⠀⠀⠀⢻⡀⡇⠀⢸⡃⢸⠁
⠀⠀⢸⣿⣶⣿⢀⣿⠀⣸⣷⠀⢹⡄⢹⢠⣿⡇⠀⠀⠙⠿⠾⠦⠼⠗⠋⠁⠀⣰⡿⠻⠃⠛⠻⢿⡆⠀⠀⢸⡇⣿⠀⢸⡁⣸⢠
⠀⠀⠘⣿⣿⣿⣾⣧⣾⣿⣿⡇⣾⣯⣿⣿⣿⠁⠀⠀⠀⡤⠒⠂⢤⡀⠀⠀⣸⣿⢁⠂⠀⠄⠀⡆⣧⠀⠀⠈⣷⣿⠀⠸⡇⣿⡀
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠿⠃⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄⢀⡄⢀⣇⣿⠀⠀⠀⣿⣻⠀⢀⡇⣿⠃
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢉⠉⠉⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠘⠀⠀⠸⣿⣿⣇⣸⣃⣼⣿⡿⠁⠀⠀⢻⣿⠀⢨⣧⡟
⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⣠⠀⢀⠀⠈⠉⠛⠻⠿⠟⠋⠁⠀⠀⢀⠀⠙⠓⠛⠋
⠀⠀⠀⣠⡾⣛⠛⠛⢷⣯⡿⠀⠀⡠⠊⢀⣤⣤⠄⡀⠀⠀⠀⠃⠀⡇⠀⢸⡆⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣹⣷⣿⣿⣞⣵⣤⡀
⠀⠀⢰⣯⣞⡁⢀⠀⢹⣿⣷⠀⡘⠀⢠⣿⠟⠁⣸⣿⢀⠀⡀⠀⠀⡇⠀⠸⣯⣵⢫⣴⣂⡤⢰⣤⣀⠀⣸⡭⣿⣟⣿⡗⠦⣶⣳
⠀⠀⢸⣿⣿⣾⣯⣷⣼⣿⣿⠀⢠⠀⠘⠋⣠⣾⡿⢃⠀⡜⠀⡀⠀⢹⡀⠀⠘⠛⠿⠿⢯⣶⣟⣿⣿⡆⢸⡿⢡⠙⡆⠙⢦⡇⠙
⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠃⠀⠀⠣⡀⠀⠉⠁⢀⡡⠊⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣀⣈⣥⣾⡿⠛⠁⠈⠳⣿⠀⢹⠈⠀⠟⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢒⣾⣤⣤⣣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⡀⠈⠘⣿⠐⢹⡎⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠁⠀⢰⢻⠀⠆⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⠀⠀⠀⠀⠇⠀⠀⡟⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡆⠀⠀⠀⠈⠀⠀⠀⠇⠸⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⡄⠀⣀⠤⠔⠒⠒⠒⠒⠢⠤⣀
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠈⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡔⠁⠀⠀⣀⣴⣖⡻⡿⠿⠟⠉⣢⡄⠀⠁⠑⣄
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠉⠀⠀⡠⠺⢽⠟⠊⠉⠀⣀⣤⠾⠙⡽⠀⠀⡠⢸⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠊⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⣟⣉⠁⠁⠀⠉⠀⠀⠀⢐⢿⡇
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡠⠐⢁⡾
⠀⠀⠀⠀⢃⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠒⢈⠡⠀⢠⡟⠁
⠀⠀⠀⠀⠀⢂⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢒⠈⠉⠀⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠻⠷⡀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠤⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠰⣌⠒⠤⠤⠤⠄⠂⠁⠀⡀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠤⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀
⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣶⣶⣴⣶⣶⣶⢚⣿⡻⠟⠻⠻⠟⠛⠛⢻⡿⠋⠀⠀⠑⠄⠀⠀⠀⠀⢀⣠⣤⡤⠤⠤⢀
⠀⠀⠀⠀⠀⠀⣿⣶⣶⣾⣿⣿⢿⠛⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠉⠹⠁⠀⠀⠀⠀⠀⢄⠀⠀⠀⡀⠠⠁⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⢸⣤⣆⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣶⣦⣦⢤⣤⣤⣤⣀⣤⣠⣀⣰⣤⡀⠀⠀⠀⠀⠠⠀⠀⠈⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠓⠛⠿⠿⠿⢿⣿⣿⣿⣷⣦⡀⠀⡠⠊⠀⠀⠀⠈⠻⢿⣷⣄⡀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⢿⠿⢛⠿⠿⠿⠿⠿⠿⢿⣿⣷⣖⣶⣶⣦⡤⢤⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢀⣾⣿⣿⡿⠧⠥⠤⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠚⠻⠿⠿⠿⢿⢿⣿⣿⣷⣶⣶⣲⣶⣶⣦
⠀⠀⠀⠀⠘⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠒⠃⠒⠒⠾⠿⣿⣿⠿⠿⠿⢿⣿⡟
⠀⠀⠀⠀⠀⠙⢿⣿⣷⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⣉⣙⣿⣿⣷⣛⣻⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣾⣶⣴⣤⣄⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⠤⠴⠤⠾⠯⠶⠾⠿⠿⠿⠟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣽⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠿⠿⡟⠿⠛⢛⢶⢄⠀⠀⠀⠀⠀⡸⠁⠀⠈⠙⡆⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⠀⠀⠈⠀⠀⠀⠀⠀⢂⢊⢂⠀⠀⠀⠀⡇⠀⠀⠀⣰⠇⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⡞⡀⠀⠀⢰⡇⠀⠀⠀⣾⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠒⡄⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡅⠇⠀⣠⠿⠃⠀⠀⠀⠃⠀⠀⠡
⠀⠀⠀⠀⠀⠀⣠⣿⣄⡀⠘⡎⠀⢀⠀⠀⠀⠀⠀⠀⢀⣄⡿⠀⡜⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⢠⡎⠁⠀⠈⠳⡀⠙⢿⣎⣄⠐⡀⠀⡀⣴⣼⠿⠁⠀⣧⠀⠀⠀⠀⠀⠀⡸⡇⠀⠀⠀⠀⠀⠴⡀⣽⣦
⠀⠀⠀⠀⣼⡀⠀⠀⠀⠀⢛⣆⠀⠉⠛⠛⠛⠋⠉⠉⣡⠀⠀⠀⠘⠿⣄⣀⣀⣠⣴⠟⠀⠀⠀⡀⠀⠀⢨⣵⡘⢿
⠀⠀⠀⢠⣟⠀⠀⡀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠘⢶⣦⡈⠉
⠀⠀⠀⢸⡄⢆⠀⠀⠀⠈⠀⠀⣿⠀⠀⠀⢠⣤⣤⣲⠠⣦⣿⣁⠤⣀⡄⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠈⠉⠁
⠀⠀⠀⠘⣮⡀⡀⠀⠀⢀⣦⣤⡇⠀⡰⣡⢊⠝⠋⡟⠛⠛⡇⠈⠑⡌⢻⡀⠀⠀⠀⠀⠀⣿⣶⣦⣤⣤⣤⡀
⠀⠀⠀⠀⠈⠻⠿⠶⠷⠿⠛⠉⠀⢰⣷⠇⡌⠀⢸⠁⠀⠀⠀⠀⠀⢱⠀⣿⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠃⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⣧⠀⠈⠀⠀⠀⠀⠀⢀⣸⢆⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣻⡀⡀⢆⠀⠀⠀⣄⣸⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠚⠺⠓⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠑⠦⡔⠁⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢀⠀⠀⠀⠀⠧⠒⡄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠃⠀⠀⢢⠀⠰⡀⠀⡄⢡⠀⠀⠀⡔⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠐⠒⠢⢄⡑⢦⣱⢀⠃⡸⠀⢀⠎⠀⣼⠥⠒⠒⠒⠒⠒⠤⡀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⠀⠀⠈⢑⠿⢇⠔⠁⢠⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⢀⠜⢣⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠀⠈⠉⢀⡠⠊⠱⣠⠃⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⢌⠀⢨⠀⠀⠀⣠⠞⡏⠁⠀⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢀⠏⠀⠀⡇⠀⢀⣀⠠⠤⠤⠤⠤⢈⣁⠁⠀⠀⢰⠁⠀⡇⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠉⠉⠉⠉⠉⠉⣁⠲⠾⡀⠀⢀⡟⠋⠉⠉⠙⠁⠒⠠⢄⡀⠀⠉⠑⠢⢌⠒⠊⠀⠀⠀⠀⣀⣀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⢀⠏⠉⠉⠑⠢⣀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠑⢄⠀⠀⠀⡎⠀⢀⡹⡇
⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠑⡄⠀⠉⠀⠉⠀⢸
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠘⡆⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠘⡄⠀⠀⠉
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡰⠁⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢀⠜⠁⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠘⢦⡀⠀⢀⣀⡀⠤⠤⠼⠤⠤⢄⣀⠀⠀⡴⠁⠀⣀⠔⢁⣠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠛⠁⠉⠁

⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⡤⣀⡀
⠀⢀⡞⠒⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⠀⣼⣿⣦⠀⠀⠀⠀⢀⣠⣩⡄⡀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠖⠻⣼⣠⠅⠀⡀
⠀⠀⣷⡀⡀⢀⣀⣀⡀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠔⠉⠉⠉⠃⠈⠀⠀⠈⠂⠀⠀⠀⠆⠀⠀⠀⠀⠈⢹⡔⡀⠈
⠀⠀⠘⠒⠐⠐⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣼⡷⢁⠂⠠
⠀⠀⠀⠀⠀⠀⠐⢾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⢿⣿⠀⠘⣦⢀⣀⡤⡄⠠⣰⠁⠀⠀⠀⠹⠿⠐⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠵⠄
⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⠀⠀⠀⠀⠀⠀⠐⠀⢠⡇⠀⠸⢿⡆⠀⠈⠛⢯⣿⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡗⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⣠⡄⠉⠀⠀⢨⣿⣿⡤⠤⠄⢀⠀⠀⢄⠀⢸⡁⠀⣀⣸⠇⠀⡀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⠀⠀⠀⠀⠀⠀⠓
⠀⣴⣿⢋⣾⣿⣤⢰⣧⡀⠈⠳⣶⡀⠉⢆⠀⠀⠘⢿⠷⢿⠟⢠⠉⠀⠀⠄⠠⠤⠥⣮⣽⣿⣾⣿⣦⠄⠀⠀⠀⠀⢛⡖⠀⠀⠀⠀⠀⢀⠆
⠀⣿⣿⣿⣷⣿⢯⣿⡿⡁⠀⠀⢻⡗⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⢈⣚⠘⠳⠿⠟⠻⢟⣻⣿⣿⡷⢃⠠⠀⠤⠄⠀⠀⠉⠢⠀⠤⠄⠒⠁
⠀⣿⣿⣿⣷⢿⢹⣿⣧⠄⠀⠀⠘⣿⠖⠀⣠⣄⠒⠖⠒⢘⠟⠋⠀⠈⠙⠛⠛⠛⠛⠛⠋⠉⠁⠐⠁
⠀⠹⣿⣿⣿⣹⣼⣿⣧⢣⠀⠀⠀⣿⣾⡄⠀⠙⢆⣂⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⡀
⠀⠄⠈⠻⣿⣿⣯⣿⣿⣾⡈⣀⠀⣿⡿⢧⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠛⠛⠛⢻⣿⠀⠰⣄⡀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣀⠟⠁
⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠓⠛⠛⠛⠛⠀⠀⠈⠓⠒⠒⠂⠉⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡤⠀⠤⠐⠊⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠚⠋⠉⠘⠓⢖⠀⠀⠘⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⢀⠄⠀⡠⢀⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⡠⠐⠁⠀⠀⡀⠐⠀⣠⢾⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠀⠀⠀⠀⠠⠐⠉⠀⠀⠀⠀⠈⠀⣠⣪⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⣠⠔⠒⠈⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢀⠄⠀⠀⠀⢀⡬⠛⠁
⠀⡠⢊⠔⠊⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⠤⠊⠀⠀⡠⢀⠴⠊
⡰⠁⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠁⠀⣠⠴⡫⠖⠁
⣧⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡠⠔⡫⠕⠉⠀⠀⠀⠀⢀⣠⡤⠤⠤⣄
⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡠⠔⣊⡭⠐⠉⠀⠀⠀⠀⣀⠴⢚⠉⠀⠀⡀⢀⡴⢣
⠀⠑⢤⣄⣈⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢈⡡⠤⠊⠁⠀⠀⠀⠀⠀⣠⠊⣠⣀⠠⠀⢄⣤⠔⠋⢠⠞⣒⠒⠲⠒⠖⠒⠤⠤
⠀⠀⠀⠈⠙⠫⠵⣦⣔⣒⣒⡻⠭⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣁⣀⣀⣀⠼⠖⠋⢀⡠⣞⣁⣀⣁⣀⣠⣁⣀⣤⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣉⣁⣤⠤⠶⠚⠯⣦⣄⡀⠀⠁⠀⠀⠀⣀⣀⣀⠤
⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⠤⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢀⡆⠀⣰⠋⠀⠀⠀⠀⠀⠀⠉⠀⠐⠒⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠉⠐⢾⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⡀⠈⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡐⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠄⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⢝⠀⠀⣀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⢠⡗⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢤⣙⡪⠀⠐⠠⠄⠀⠀⠠⣄⣠⠔⠁⠈⠲⠤⠤⣄⠣⣀⣖
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣥⣦⣴⣶⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣮
⣿⣿⣁⣉⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡬⠥⠴⠶⠶⠶⠶⠶⠶⠶⠶⠤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⠉⢀⣴⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⡀⣀⣴⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⣀⡸⠣⠴⠒⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠉⠛⠻⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠞⣛⠩⠀⠀⣀⣀⣄⣀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠭⠭⠅⠐⠒⠂⠉⠁⠀⠀⠀⢸⠁⠀⠀⠀⠙⡆⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢀⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣠⣴⠟⢁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠾⠟⠛⢉⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠳⡀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣀⣠⠤⣔⠊⠉
⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠙⢦⡙⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠂⢄⠀⠉⠓⢄
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡦⠤⣀⣀⣀⠀⠀⠀⢀⣀⣀⣤⢴⠖⠉⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢳
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⠤⠬⠭⠭⠭⠭⠴⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠀⠀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⠤⣀⣈⠁⠒⠂⠠⠤⠄⠀⠤⠠⠤⠀⠠⠤⠀⠐⠒⠈⢁⣀⣠⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⠟⠿⠁⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠙⢷⠟⢉⣤⡾⠦⣈⣉⣉⣉⣉⣡⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡴⠋⢀⣰⠏⢹⣆⠰⠋⠉⠉⠙⠉⠉⠉⢀⣈⣙⡛⠿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⠃⠀⣿⡇⠀⠀⣀⡴⠶⠶⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠰⠖⠂⣄⡀⠀⠀⠀⠀⠙⢧⣴⡇⠀⠀⢸⣦⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠶⠂⠉⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢠⣤⠘⠋⠀⢀⣠⣤⣤⣤⣤⣤⣄⢠⣤⢠⣤⠀⠀⠀⠀⢀⣄
⠀⣠⣤⡴⠛⢠⣤⡄⠒⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠒⠚⠛⠒⠒⠀⠀⠀⠀⠠⢤⣤⣤⣤
⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢀⡄⠁⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⢿⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠈⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢀⣿⣄⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠿⠁⠈⠳⣄⠀⠀⠀⢠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠚⠛⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⠀⠀⠀⠀⢸⣿⣀⡾⠀⠀⠀⠀⠈⠛⠒⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠘⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⠀⠀⠀⠀⠀⠀⠈⠉⠀⠴⣄⠀⠀⢠⡀⠀⠀⠀⢿⠁⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⣼⡇⠀⠀⠀⠈⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣆⠀⠀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣄⠀⠀⠀⠀⠀⠀⠀⢠⡌⠉⠉⠳⣄⠀⢿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢢⣤⠀⠀⠀⢠⡎⠁⠀⠀⠀⠈⠻⣿⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⠶⠀⣀⡀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣶⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢦⣀⠁⠲⢦⡀⠀⠀⢀⡘⠀⠀⠛⠀⠀⣀⠰⠖⠂⣀⡹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⠻⣆⡀⠸⠃⠀⢶⣀⠰⠂⠁⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⡆⠀⢀⣿⣿⡶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠐⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⣡⡄⠀⢀⡘⠛⠓⣶⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣤⡀⠳⣴⣿⠃⢠⠀⢸⣿⣶⡾⠋⣠⣤⠀⠈⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⠃⣠⠟⢀⣾⠏⠀⢸⡆⠘⡁⠙⢷⣆⠉⢷⣾⠿⣦⣤⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣅⡘⠟⢀⣼⠋⣀⣶⣭⡁⠀⡁⠀⠀⢿⣇⠈⣿⡀⠈⠙⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠃⠀⠈⣁⡾⠻⠈⢹⡇⢰⡇⠀⠀⠀⠙⠀⢻⣷⠀⠀⠹⣿⡻⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⣠⣿⠃⠀⠀⠀⣿⡇⠀⠀⠘⠁⢀⡵⣦⣄⠀⠀⠀⠀⠻⣦⠀⠀⢸⣷⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣴⡿⠁⠀⠀⢠⣾⢿⣧⠀⢰⡆⢠⡿⣷⣞⢿⣷⡀⠀⠀⠀⠉⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠐⠛⣩⣿⠃⠀⠸⠃⠈⠷⣿⡿⣿⡉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢠⡾⠋⠀⠀⢰⡆⢰⡆⢰⡟⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡌⠁⡄⠀⠸⠇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⡇⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⡀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⣇⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⡀⢀⣀⣀⣀⡀⢀⣀⢀⣀⣀⣀⡀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⠛⠛⠛⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣏⠀⢀⡤⠀⢸⣿⠁⣼⡧⠙⠁⢿⡇⠉⠉⠀⠈⡟⢹⣷⠀⣼⠋⠁⠀⢹⠏⢠⡿⠃⠛⠁⠈⠁⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⣀⣠⣶⣿⣿⣶⣿⣷⣿⣶⣾⣷⣾⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣷⣾⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⣀⣤⣤⣤⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣶⣤⣤⣤⣤⣀⡀
⠀⣾⣟⡯⠍⠓⠒⠒⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⣽⣿⣧
⠀⣿⠈⠉⠻⠓⠒⢶⣶⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢴⣶⣶⣶⡶⠟⠛⠉⢸⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⣠⣤⣤⣀⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠟⠋⣉⣉⣉⣙⠻⣷⣄
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣴⠟⠋⠉⠉⠛⣷⡌⢿⣆
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⠃⠀⠀⠀⠀⠀⠘⣿⠸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠃⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿
⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⡟⢸⡿
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢀⣼⡟⢠⡿⠃
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣠⣾⠋⣰⡿⠁
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣠⣴⡾⠋⣡⡾⠋
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠛⠋⣁⣴⡿⠋
⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦⣴⡾⠛⠁
⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⠁
⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠈⠻⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⡾⠟⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣽⣭⣬⣽⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠖⠒⠒⠒⠒⠒⠒⠒⠒⠲⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣚⡭⠵⠖⠒⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠓⠲⠤⣍⣓⠲⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⢀⣀⣠⣤⠤⠤⠶⠒⠒⠒⠒⠒⠒⠶⠤⢤⣄⡀⠀⠉⠛⢦⡙⢦
⠀⠀⠀⠀⠀⢠⡏⡏⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⡀⠀⠀⠀⠉⠙⠲⣄⠀⣿⢸⡆
⠀⠀⠀⠀⠀⢸⣇⢣⡞⠉⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠒⠋⠀⡤⠤⡄⢹⡀⠀⠀⠀⠀⠀⢀⡿⣡⢾⡇⣀⣤⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⢸⡈⠳⣌⡳⢤⣀⡀⠀⠀⠸⡄⠀⠀⢰⠖⠒⠚⠁⠀⢹⢸⡇⠀⢀⣠⡴⢞⣡⠞⣡⠞⠋⠁⠀⣀⣀⣀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠉⠓⠮⣍⣛⠒⠶⠿⠦⢤⣬⣷⣤⣤⣤⠤⠿⠾⠒⢋⣩⡤⠖⠉⠀⠀⣧⣀⡤⠖⠋⠁⠀⠉⠙⣦⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠶⠶⠶⠶⠶⠶⠶⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢧⣄⣀⣀⣀⣀⡤⠞⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣨⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⠈⠉⠉⠁⣀⡠⠔⠋
⠀⠀⠀⠀⠀⣠⠞⠉⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠻⣍⠛⠋⠉⠉⠁
⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⢸⡷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡏⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⢦⣌⡙⠲⠦⢤⣄⣀⣀⣀⣀⣀⣀⡤⠤⠖⠚⣋⡥⠞⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠤⠤⠤⠤⠤⠤⠴⠶⠒⠋⠉⠀⠀⠀⠀⢀⣠⣾⠟
⠀⠀⠀⠀⠀⠙⠪⣝⡲⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢴⣚⡭⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠺⠭⣍⣓⣒⠲⠦⠤⠤⠤⠤⠤⠤⠤⠴⣖⣒⣻⠭⠷⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⣄⣀⠀⢀⣤⣄⠀⠀⠉⠛⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠋⠉⠀⢠⣿⣿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡀⠀⠀⠀⣩⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠴⠾⠟⠋⠀⠀⠀⠘⣧⠀⠀⠀⢨⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠘⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢻⣿⣿⣿⣿⣸⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⠏⠹⡇⢸⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡜⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⡉⢄⠀⢷⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⠻⣿
⠀⣶⠀⠀⠀⠀⠀⠻⣼⢦⠘⡇⠀⠒⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⣠⣿⣿⣿⣿⣿⣿⣿⡁⠁⠀⠀⢸⣿⣇⠈⠉⢛⣫⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿
⠀⠘⣧⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⠀⠘⣿⣿⣆⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿
⠀⠀⠹⣷⣦⣀⠀⠀⠀⠀⠈⢻⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠋⠉⠀⠉⢻⣿⣿⣿⣿⡆⠀⢿⣿⣿⡆⠀⠈⢿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿
⠀⠀⠀⠹⣿⣿⠁⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠱⢦⣀⣠⣤⠀⠀⠈⠛⠿⣿⣿⣇⡜⡘⣿⣿⣿⡄⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿
⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⣄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠀⠀⠩⠿⢿⣶⣶⡇⠀⠀⠀⠙⢿⡼⣷⢿⣿⣿⡷⠀⠀⠘⣿⣿⣿⣿⡿⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣧⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠈⣿⣹⣤⣿⠿⡥⠃⠀⠀⠸⣿⣿⣿⡇⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣤⣤⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣈⠻⣷⣦⣤⣴⣿⣿⠟⠁⡆⠀⠀⠀⠀⣰⣿⣿⣿⡇⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⠀⠀⠄⠀⠀⠀⠀⢸⣿⣿⣿⣧⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣼⣷⣼⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣿⡇⠀⢰⣾⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣼⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣰⣦⡀⠀⠀⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⡴⠛⠿⣿⣿⣿⣿⣿
⠀⢠⣿⣿⣿⣦⠀⠀⠀⠀⠀⠲⣌⠻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⢻⣿⣿
⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠹⢶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢠⡏⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⠁⠀⡾⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣰⠇⠀⣸⠃⠀⢠⠏⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢠⡟⠀⢰⠇⠀⢠⠏⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠖⣾⠀⢸⠃⠀⡿⠀⢠⡟⠀⢀⡏⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣛⣭⠴⠒⠀⠀⡏⠀⣿⠀⢸⡇⠀⢸⠁⠀⣼⠀⠀⠠⣌⣙⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢾⣿⣶⣞⣋⣥⣤⣿⣤⣿⢠⣼⡇⣤⣼⢠⣤⣿⣀⡀⠒⠦⣭⣛⠆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠈⢉⣠⠟⢑⣶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣍⠓⠂⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⣉⣀⣤⡴⠾⣛⣵⡆⣚⣛⠧⣄⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣝⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢋⣉⣉⣭⣴⡶⠿⣛⣭⠀⠉⠉⠙⣾⡇⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠛⠃⢸⣟⡳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⣉⣉⣥⣴⡶⠿⣛⡅⠈⠑⣂⡴⣻⡣⢠⡏
⠀⠀⠀⠀⠀⢀⣤⠞⣋⡥⢒⡠⠄⠀⠀⢻⣟⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣉⣉⣉⣩⣭⣴⠶⢟⡋⢡⣞⣛⣽⣾⢟⣵⠟⢶⣄
⠀⠀⠀⠀⣰⠟⣡⡞⢡⡞⢉⡴⠊⡀⠀⠈⢿⣟⠒⠄⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⣉⣉⣭⣭⣴⡶⢿⡛⢡⡿⢿⣛⣭⡶⠛⠁⣀⢢⡈⢷⡄
⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⣿⡀⢾⡀⠀⠀⠀⠻⣯⡒⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣭⣥⣤⠴⠶⣞⡛⣱⣿⣿⣿⣿⣿⢿⡌⢳⡈⣆⢳⠈⡇
⠀⠀⠀⠀⠻⣆⠹⣧⣌⠳⢮⣛⠶⣬⣁⠀⠀⠀⠈⠻⣥⣄⣀⠀⠀⠀⠀⠀⠤⠤⠶⢶⣶⣾⣿⣿⣿⣿⣿⢸⣿⡜⣿⢎⡇⢸⠇⡏⢀⡼⠃
⠀⠀⠀⠀⠀⠈⣳⣮⣙⠷⣦⣍⣙⠓⠦⠄⠀⠀⠀⠀⠈⠙⠻⢯⣿⣛⣛⣛⣛⣛⣯⣽⡿⠿⢛⣫⣵⡿⢋⣾⠟⣰⠟⠘⠁⢋⣠⣶⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠨⠽⠿⠶⢮⣭⣙⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠽⠷⠶⠶⠶⣚⣛⣋⣭⡵⠾⠛⢁⣈⣡⣤⣶⣾⣿⣿⠿⠭⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣉⣹⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣛⣉⣉⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣟⣛⣛⣛⣛⠛⠛⠛⠛⠛⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣉⣩⣭⣭⣭⣭⣭⣭⣉⣉⡉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣾⣿⣿⣿⣿⣷⣿⣷⣾⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣾⣿⣿⣿⣗⣿⣯⣟⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⣤⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣀⣠⣤⣶⣶⣤⡀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣉⣙⣻⠿⣿⣿⣿⣿⣿⣿⡿⠿⣋⣁⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡻⢶⣿⣿⣿⣿⣿⡷⢋⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⡇⠹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⡿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠻⠿⣿⠿⠿⡟
⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣉⡉⠉⠉⠉⠉⠉⠉⠉⣭⡍⢉⣭⣉⣭⣧⡽⣿⠛⠿⣯⣥⢭⣉⡉⣉⣉⡉⠉⢉⣽⡯⠉⣿⠉⠉⠉⢉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠈⠛⠁⠀⠀⠻⠈⠁⠀⠠⠜⠛⡩⠰⠟⠃⣠⡴⣇⣀⣈⠛⠉⠓⢠⡉⠛⠿⠥⠀⣀⠀⠀⠀⠙⠗⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡦⠀⠀⠀⣶⠶⠀⠀⠀⠀⢰⣶⠄⢊⡽⠃⠈⣿⠻⣶⡄⠠⣤⣀⡀⡀⠀⠀⠿⠇⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠉⠠⠀⠉⢀⠀⢊⡟⠀⠀⠈⠐⠋⠀⠈⠿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠀⢀⣀⡀⠘⠇⠀⢀⡀⠀⠀⠀⠂⢾⣿⠀⣤⠖⣿⠿⠗⠀⠀⠀⠀⢰⡆⠀⠀⠀⠶⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠛⠋⠀⠀⢠⣶⠈⠀⠀⡄⠀⢹⣄⠠⠤⢠⣤⠀⠈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠼⠀⠀⠸⠃⠀⣀⡏⠱⠆⠼⠿⢆⡀⠀⠀⢿⡇⠀⠀⠀⠶⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠛⠁⠘⠃⠀⠀⢰⡾⠇⠀⠀⡞⢻⠋⢠⡄⠀⠀⠈⠃⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⠀⠰⣾⠇⠘⡄⠉⠁⠀⠸⠿⠂⠀⢀⣀⡀⠈⠁⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠘⠛⠀⠠⡦⠀⠀⠀⡰⠁⠐⠷⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡦⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⠀⠀⢲⡄⠀⠀⠀⠀⠀⣤⠄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢸⡟⠛⠛⠛⠋⢰⡏⢰⠇⣰⢂⠀⣠⡄
⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⢹⠀⠀⠀⢰⠇⡼⢣⡾⢱⡆⢀⣿⢀⡿⢸⢳⡟⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⠈⠀⠸⡷⠊⠀⢸⡇⣼⢁⡟⠘⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠿⠀⠈⣷⣀⡀⠀⠀⠀⠁⠘⠇⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠀⠀⠠⠟⣸⡤⠖⠚⠛⠛⠛⠶⢼⢃⡶⢰⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣯⠁⡀⡆⢸⡆⢰⡆⢀⡿⠃⠛⠛⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⣴⠃⢸⡆⣿⠸⣇⠇⣿⠀⣾⠁⣾⠃⣼⢠⡆⢀⣤⢀⣀
⠀⠀⠀⠀⠀⠀⢠⡆⠁⠲⣄⠀⠘⣇⣿⠀⣼⠀⢿⠘⣇⠰⠏⢸⡇⣾⡃⣼⠃⣼⠋⣹⢻⡏⢰⡇
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⢷⡄⡏⢿⡄⠙⠂⠘⠇⠉⠀⠀⠀⠀⠈⠁⠙⠺⠃⣼⠃⣼⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠘⠓
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⢿⣦⡀⠀⠀⠉⠒⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠀⠀⠈⠉⠻⣶⣄⠀⠀⠀⠀⠁⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢸⣦⣶⣤⠞⠉⠙⠃⠀⠀⠐⠀⠺⢿⣷⣄⠤⠒⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⣿⢻⣷⣤⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢐⣦⣄⠀⠀⠀⠀⠀⠀⢶⣶⣤⣿⣮⣿⣿⣿⣦⡀⠀⠀⡆⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠀⠀⠀⢀⡀⣀⠀⢉⠤⠈⠁⠈⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠘⠀⡀⠀⠀⠄⠨⣿⣨⠶⠆⠂⠀⠀⠀⠀⢸⣿⣦⣅⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠘⢿⠀⡄⠀⢀⡄⠁⠰⣞⣏⡻⠀⠀⠀⡾⠻⠝⢿⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠘⣷⠀⣤⠁⣀⠀⠀⢺⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠐⠆⠀⠀⠰⠏⠀⠀⠄⣸⣆⠀⠘⠏⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠰⣿⣏⠈⠙⠲⣦⢄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠷⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⢀⣀⡀⡿
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠐⢠⣤⡴⠂⠀⠀⣿⠁⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠃⠀⠋⠀⠀⠰⡾⠏
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⡗⢚⠉⢋⡡⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠰⠞⠂
⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣀⣠⣴⣶⣾⣿⣶⣶⡶⠄⠀⠀⠀⣠⠀⠀⠀⡠⠉
⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡠⡄
⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⡠⡜⢄⠉⣇⣀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⡠⠚⠢⢠⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢍⠳⢘⡌⠢⡨⠊⠀⠀⠰⠝⠊⢀⠀⠀⠀⠊⠈⢃⡀⠤⠆⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⡏⡭⡢⡀⠙⠢⠅⢀⡴⢊⠁⠀⠰⠇⠀⠈⠀⠀⠀⠀⣠⡄⠀⠀⢀⠀⠀⠀⠰⡹⠁⠹⠂
⠀⠀⠀⡖⠢⡀⠘⢄⡚⡀⠀⢀⠔⠉⠀⠣⠐⠀⠀⠀⠀⠀⠐⠂⠀⠄⠻⢀⡠⠐⠁⠀⠀⠀⠛⠃⢀
⠀⠀⠀⠘⢄⠑⠄⡄⠀⠀⠘⠀⠀⠀⠀⠀⣠⡾⢑⢄⠀⠈⠐⠁⠀⠐⠂⠁⠀⠎⠐⠀⠀⠀⠀⠀⠃⠁
⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠀⣰⢯⣲⠃⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠞⢛⣼⠃⡐⠀⢀⠀⡰⡡⢀⠀⠀⠀⠀⠛⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠂⠀⠀⠀⠀⠠⡒⠁⠀⠀⠀⠉⢤⡾⠋⢉⠔⠀⠀⠈⢄⣔⢲⠇⠀⠂⠂⠢⡀⢀⠾⠆⠀⠞⢂⠄
⠀⠀⠀⠀⡀⢄⡀⠀⠈⠈⠁⠀⠀⢀⠀⠀⠀⠁⠀⢀⢤⡀⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠁⠀⠀⢀
⠀⠀⡄⠊⡤⠊⠑⡀⠀⠀⠀⠀⠒⠀⠆⠀⠀⠀⠰⡟⠋⡰⠀⠀⠈⢇⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠈⢎⠀⠀⠅⠅⠀⠀⠀⠀⠀⠆⠐⠄⠀⠀⠀⣵⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡁
⠀⠀⠀⣊⡇⠀⠀⠀⠀⢀⠊⠀⠉⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠊⠉⠉⠀⠀⢠⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⠀⠀⣈⠀⠀⠀⠀⠂⠀⠀⠠⠒⢀⠀⠀⠒⠀⠀⠠⡀⠀⠀⠀⡞⠂⠂
⠀⠀⠀⠀⠀⢶⣀⠀⢀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠐⠀⠀⠐⢄⣀⣶⣠⡔⠁⠀⠀⠀⠁⠀⠘
⠀⠀⠀⠀⠄⠄⠌⠍⡒⠀⠀⠀⠀⢀⠴⣗⢄⠀⠀⠀⠀⠀⠀⠀⠌⠍⢿⡇⠀⡃⠀⠀⠀⣀⣀⡀
⠀⠀⢠⢆⠀⢊⠈⠌⠀⠀⠀⠀⣰⡁⠀⠈⡪⠇⠀⠀⠄⠀⠀⠀⡂⠀⢺⣇⣀⡁⠀⠸⠛⠃⠉⢁
⠠⠀⠀⠀⠁⠆⠆⠀⠀⠀⠀⠀⠀⠀⢠⢊⠀⠀⠀⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢆⠄⠀⠘⠃⠀⠀⠂
⠀⠀⠄⠆⠶⠲⠀⠀⠀⢀⠀⠀⠀⠀⠈⠈⠀⠀⠘⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⡀⠀⠀⠀⠀⠀⢨⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄
⠀⢸⢿⣦⡀⠀⠀⠀⢸⠘⢲⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠘⢲⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⢢⠙⢿⣦⠀⠀⠸⠄⢿⡄⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠠⠈⠁⠇
⠀⠀⠀⠱⣤⣙⡇⠀⢸⠁⣟⡇⠀⠀⠀⠀⠀⠀⠀⠇⠂⠀⠄⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⣄⡀⠘⠗⠀⠀⡀
⠀⠀⠀⠀⠀⠸⡇⠀⢸⢰⡦⡇⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠆⠀⠘⠢⠗⠂⢠
⠀⠀⠀⠀⠀⠀⠇⠀⢸⠈⡷⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣧⣿⠘⣆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠳⠀⠀⡀⡘
⠀⠀⠀⢀⡴⠂⠠⠠⠰⣰⠋⠙⠀⠸⡄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡼⢠⡊⢀⢠⣄⣀⡉⠂⠀⠀⠀⠀⠀⠀⠀⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢠⠇⠀⠀⠀⠑⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣵⣾⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⢿⣻⣿⣿⣿⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⣀⡼⣿⣹⣿⣿⡆⠀⠈⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣧⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⣿⣿⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡝⣯⡇⠈⢻⣿⣿⣿⣿⣿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣼⣷⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣱⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⠴⠶⠦⠤⠤⣀⡀
⠀⠀⠀⠀⠀⢀⡄⢀⡤⠖⠋⠉⠀⢀⡠⠴⠒⠚⠛⠛⠛⠒⠀⠉⠛⢦⣄
⠀⠀⣀⢶⡒⠈⡷⠉⠀⢀⠀⠀⠈⠁⠀⠀⣀⣠⠤⠴⠒⠒⠀⢀⣀⣠⠽⢚⡥⣰⠃
⠀⠀⠉⢢⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⡤⠶⠊⠉⠠⠒⣩⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣤⣤⡤⢤⣤⣀
⠀⠀⣰⠃⠄⠀⠀⠀⠀⠐⠂⠤⠤⠤⠤⠤⠤⠐⠒⠉⠀⠀⠀⠀⣠⡴⠞⠁⡌⣇⠀⠀⠀⠀⢀⣀⡠⠔⣉⠤⠒⠉⠀⠀⠀⠀⠀⠀⢉⣲⣄⣀⡴⠋⡙⠛⢶⡄
⠀⢰⠃⡜⠀⢠⠂⠀⠀⠀⠀⡀⢀⣀⣀⣀⣀⣀⣤⣤⠤⠶⠚⠋⠁⠀⠀⠀⢱⣹⠀⠀⣠⠞⠩⠎⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⢿⣀⡠⠀⠹⡄
⠀⡟⢠⡆⠀⡇⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣼⠃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣆⢷⡠⠔⠀⡇
⠀⡇⢸⡇⠀⢀⠄⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⠆⠀⡇⢰⢻⠸⡀⠀⠀⠀⠀⠀⢈⣉⣉⠉⠑⠒⠤⣄⡀⠀⠀⠀⠀⣠⠟⡾⠇⠀⣸⠃
⠀⣧⠀⠇⣠⠋⣠⣤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⡇⢸⠸⢀⠓⢦⣄⣦⠤⣄⣀⠀⠈⠙⠲⢤⡀⠀⠉⠓⠶⠶⠾⣫⠀⡷⠴⠚⠁
⠀⢻⡀⠀⡏⣾⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⠀⠀⣸⠁⠘⣇⣸⠰⠀⠀⣤⠀⠀⠉⠙⢦⡀⠀⢀⠙⣆⠐⠀⠀⠀⠊⠁⡔⡇
⠀⠘⣷⠀⠀⠙⢮⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡼⣰⠃⠀⠀⠈⢿⠀⡄⠀⠈⠀⠀⠀⠀⠀⠃⢸⡍⢱⡈⠀⠀⠀⢀⠄⡼⢡⡇
⠀⠀⠸⣧⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⢞⡵⠃⠀⠀⠀⠀⢸⡘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢬⠼⠁⠀⠀⠂⣡⠞⢁⣾⠁
⠀⠀⠀⠈⠳⣄⡙⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⢉⡴⠋⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⡤⠎⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠒⠉⠀⣠⣿⠋
⠀⠀⠀⠀⠀⠈⠙⠓⠺⠷⠦⢄⣀⡀⠀⠀⠀⠀⢀⣀⣀⡤⠖⠋⠀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠂⠤⠤⠖⣋⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⡄⠈⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠙⠒⠤⣄⡀⠀⠀⣀⣠⣷⣤⠤⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠓⠤⠍⠓⢤⡀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣦⣀⣀⠀⠀⠀⠀⠀⢀⡨⢆⣀⢎⡀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠰⡄⠀⠀⠀⠀⢡⠈⠧⠀⠀⠀⠀⠹⣿⣿⣿⡿⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⠀⡆⠣⢄⡀⠀⠀⠀⠀⠙⠛⠁⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠛⠃⠀⠀⠀⠀⠀⠀⢡⠀⠀⠉⠙⠒⠶⡶⠜⣦⠤⠴⠚⠉⢈⠀⠀⠀⠀⠀⠀⠸⣄⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠊⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠳⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡞⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⠲⡄⠀⠀⢀⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢠⠇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠦⠤⠿⠗⢒⠋⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢑⣠⠀⡀⠀⣀⣠⣼⢰⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⠞⠉⢂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠾⢦⢰⣴⡉⡿⠾⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠃⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⠤⣤⣄⣀⣤⡤⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣄⡤⡀⠀⣏⠋⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢮⠀⢀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠜⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠈⠰⠩⠽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣡⠶⠋⡹⠋⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⣠⠞⠂⠀⣼⠁⢠⠀⠀⠀⢈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠛⠀⠀⣴⢃⣠⡦⠄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠈⠂⠀⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⡤⠚⠀⣠⣦⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢾⠆⠀⠀⠀⠀⠀⠀⠌⠃⠀⠁⠈⠉⢒⡆⠀⠙⣿⠀⡆⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠳⣤⢀⡉⠻⠀⢇⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸⠇⠀⢸⡿⠀⠀⢠⠗⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠱⣤⠦⠈⠢⣀⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠏⣰⡿⠚⠁⠰⠟⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⢀⡤⠃⠀⠀⠉⠻⠆⠐⠶⠚⠾⠃⠀⠀⠶⠀⠀⠒⠛⠉⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠠⡟⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⣦⡀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⢠⠀⠀⠀⠈⠁⠀⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⣧⠀⠀⠶⣦⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⠉⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠀⠀⠀⠀⠀⠀⠐⠒⠲⠚⠀⠀⠀⠀⠀⠀⢀⣤⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢤⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⠀⠘⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠀⠀⠘⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣶⣶⣶⣶⣶⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘






⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣾⣶⣶⣶⣾⣶⣾⣶⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣻⡟⢿⡿⢿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⢠⣤⣿⡏⠀⢠⡤⣶⣋⣷⣰⣶⣄⠀⠀⠀⠀⠀⡄⢀⢀⠀⠀⠀⠀⠀⡰⣗⠠⢤⣄⠀⠀⠀⣤⣶⣶⡾⣴⣶⣿⡶⣾⢻
⠀⠀⠀⠀⠀⠀⠀⣿⡘⢿⣿⣿⣄⢀⣩⣝⣿⣿⡏⣉⣁⣀⠀⠀⠀⠀⠀⠂⢀⠑⠀⢤⡀⠈⢰⣿⢛⣶⣮⣽⡄⢈⡶⢮⣽⣯⣿⠷⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣸⠿⣒⣛⣻⣿⣾⣭⣭⡅⠐⣙⣻⣿⣿⣿⣷⡀⢼⣦⠀⡀⠁⠀⠀⠹⠲⣭⣹⣤⣿⣿⢿⣷⣿⡧⢾⡿⠞⠉⠁⠁⠀⠡
⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⡿⠋⠉⠀⠀⠀⠳⡀⠀⢼⣿⣿⣿⣿⣿⠌⣣⣞⠋⠁⠀⠀⠰⢿⣷⡭⣿⣽⡿⣿⣿⣽⣿⠻⠭⠀⠀⡤⠖⠉
⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⠁⠀⠀⠠⠀⠰⠀⢉⣢⣼⣿⣿⣿⣿⣿⡗⠉⠉⠛⠦⣄⡀⠈⢆⣩⢦⣼⣷⡇⣼⣮⠿⠥⡄⠀⠄⢀⠁
⠀⠀⠀⠀⠀⠀⢹⠟⠿⠟⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⠋⡽⢯⡴⣲⠤⠀⡈⢙⢦⡈⠐⢲⢋⣿⣿⣹⣿⣨⣄⡒⣈⢠⣈⡀⢀⢉⢥⡀
⠀⠀⣀⣄⣀⠀⣖⣀⠀⠀⠀⠀⢀⠀⠀⣸⢿⣿⣿⣿⡟⠻⠿⠀⣾⣾⢳⣿⠿⠁⠰⡼⣆⡙⢦⡀⠙⠟⢿⣿⡿⠛⠍⠉⠀⠀⠀⠀⠀⡴⠋
⠀⠻⣿⣿⣿⣿⣿⣽⠀⠀⠀⠀⠈⠙⡀⢸⣿⣿⠇⡼⠋⠅⠁⠶⡷⢿⠇⣶⠂⠀⡆⠚⠛⠿⣶⣿⣦⡠⢸⡟⢻⡄⠠⠈⠀⠐⠀⢠⠎
⠀⠀⢀⣈⣋⣽⣿⣿⣶⡤⠒⠀⠀⠀⠀⣼⣟⣀⣀⠀⠠⠔⠂⠀⠑⠬⡀⠃⢀⠼⡟⣶⣶⡦⣤⠽⣿⣿⣼⣇⠀⠁⠁⠀⠒⠐⠈⠁
⠀⠠⡿⠽⠏⠀⢸⣿⡯⡉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⢻⠿⠋⠉⠉⠉⠙⠛⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠠⣢⣼⡇⠄⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⣴⣈
⠀⠀⠀⠀⠀⠀⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠂⠠⢄⢠⣴⡿⠊⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠎⠀⢰⠀⢄⡀⠀⠀⠀⢿⡦⢼⣿⣿⣾⣇⡐
⣄⣀⣀⣩⣽⡢⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢚⣷⣾⣿⣿⣍⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣄⠀⠀⠈⠀⠚⣻⣿⣿⣿⡥⠤
⠀⠈⢿⣿⣿⢽⡶⣝⡃⠀⠀⢁⣠⡴⠖⠂⠀⢀⡴⡟⣹⠟⣿⣿⣿⠒⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⢿⣷⢼⡿⠉⢻⠌⠁
⠀⠀⠈⢿⣿⢰⡸⠹⢷⣀⣶⣿⠏⠀⠀⠀⣴⠋⠀⠿⢋⣫⣿⣿⣿⠀⠈⠛⢃⣠⣖⣆⣅⣬⣡⣈⢢⣄⡀⠑⠢⣘⣿⡟⣡⣤⣶⣀⣄⡀
⠀⠀⠀⠈⢿⣯⣿⠀⣠⣿⡿⠁⠀⠀⢠⡞⠁⠀⠀⠃⠈⣹⣿⣿⡟⠀⣠⣾⣻⣿⣻⣿⣎⣽⣷⣿⣿⣿⣷⡄⠀⡘⣻⣿⠃⠀⠉⠛⠉⠁
⠀⠀⠀⠀⠸⠿⣷⣠⣾⢟⡃⠀⠀⣰⡟⠀⠀⠈⠀⡄⢀⣿⣿⣿⠁⠀⠈⢇⢪⡍⣋⣭⡿⢟⢻⣿⣿⣿⣿⣿⡞⠑⣉⣩⢌⠉⢙⣢
⠀⠀⠀⠀⠀⢸⡇⢸⣿⡀⠀⠀⢠⡟⠁⠀⠐⠂⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠉⠫⠤⠶⣘⣿⣧⣿⡿⢹⠿⡙⣿⣿⡴⠶⣶⢿⣽⠻⠆
⠀⠀⠀⠀⠀⢘⣿⣿⡟⠁⠀⢠⡏⠡⠀⣰⠁⠀⠀⣴⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠐⢀⣰⣿⣷⣿⣋⣿⡼⡞⢧⡀⢸⠹⣶⣶⣄⣌⣠⢀
⠀⠀⠀⠀⠀⣼⠇⣼⣷⠀⠀⣿⠀⠀⣴⠅⠀⣴⢰⣿⣿⣿⠁⠀⠀⠀⠀⡠⠉⠁⣠⣴⣫⣿⠣⣏⠚⢿⣪⣷⣿⣸⣮⣼⣿⣿⣿⡿⠿⠉
⠀⠀⠀⠀⠀⣿⠄⣽⣿⡀⢰⡇⠀⣰⠃⠀⠰⣿⣿⣿⡟⠀⠀⠀⠀⠀⢰⠱⠛⣭⣥⣴⡯⡏⠙⣟⣡⣼⣭⣿⠁⠀⠀⢻⣿⢎⣷⣶⡄⠁
⠀⠀⠀⠀⠀⣿⣧⣿⣿⠁⣼⠀⠙⠏⢀⣚⣽⣿⣿⡿⠃⠀⠀⠀⠀⠀⢮⠀⣟⢩⡿⢻⠀⢷⠀⠿⢇⢘⣭⠟⠀⠀⠀⢸⣿⡀⠘⠛
⠀⠀⠀⠀⠀⠹⣿⣿⠏⠀⢺⣴⣻⢢⣤⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⡇⠷⠜⢁⡴⠖⠚⠛⠋⠉⠉⠁⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢸⣿⣟⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣈⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⣳⣦⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣄⣀⣤⣶⠟⠃⠀⢿⣿⣿⣿⢻⠻⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⣿⣿⣿⣇⣷⢹⣿⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⢹⣿⣦⢠⣤⢀⡀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⢠⠦⣠⣶⣦⣤⣤⣤⣵⣦⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣏⣾⣿⣿⣶⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⢠⣀⣴⣿⣿⣿⡿⢉⠀⠀⠀⠰⣦⣤⣄⣀⠀⠀⠉⢩⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣧⣶⣴⣸⣿⣿⣿⣿⣶⣶⣿⣿⣿⡿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⠇⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠
⡄⠀⠀⠀⠀⠀⠀⠀⠉⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣼⣿⣿⣿⣿⣿⣿⡇⣹⡁⢀⣴⡀
⣿⣶⣄⣠⣾⣿⣿⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⠉⠿⣿⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣯⣷⣿⣷⣿⣿⣦⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⣄⣼⡿⣷⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣶⡏⢟⡇⠻⢿⠿⣇⠊⢳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⠋⡿⡿⠿⢶⢷⡌⢀⣼⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠶⠿⡏⠂⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠙⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⡿⠂⠁⠀⠀⢠⡀⣀⢂⠀⠀⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣬⡙⢋⠇
⠀⠀⠀⠀⠀⣠⣶⡿⠿⢫⠙⠿⠶⠒⢂⠐⠛⣄⠻⠿⠻⠁⠀⠀⠠⣆⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂⢦⢢⣦⣼⡇
⠀⠀⠀⢀⣾⣷⣮⡀⣠⣀⡄⣀⠀⣰⣺⣠⣀⢿⠋⠀⠀⠡⠀⠀⠀⠈⠝⠀⠀⣿⡛⠶⣤⠀⠀⠀⣼⣿⣶⣿⣿⡿
⠀⠀⢀⣾⣿⣿⡟⠁⠈⣛⣾⡿⠒⠺⣿⣿⣉⠀⠀⠀⢀⡴⡆⠇⢠⠀⠀⠀⠀⠈⠛⠂⠈⠁⠀⢸⡿⢿⠿⢿⡿⠁
⠀⠀⢸⣿⣿⣟⠂⠀⣼⢿⡿⠁⠀⢠⣿⣿⡇⠀⠀⢀⠊⢠⠇⠀⠠⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⢹
⠀⠀⢸⣾⣿⡏⠀⠀⢻⣸⣄⣼⠯⠛⢱⣶⣬⠀⠀⠈⠀⠁⠀⠀⠄⠈⠒⠦⠄⠀⡀⠀⠀⠀⠀⠀⠒⠃⡠⠂
⠀⠀⠘⣿⡜⡿⠁⠀⠸⣷⡜⣿⡷⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠁
⠀⠀⠀⢿⡷⣘⣴⣦⢀⠀⣤⣿⠃⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠘⠬⢀⡀⣀⢀⡀⠤⠄⠐⠊
⠀⠀⠀⠘⣿⡹⣿⣷⢀⢸⣿⣇⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⢀⠈⢀⠘⣿⣷⡍⢻⣶⣿⡉⠑⠚⠁⠀⠀⢀⣠⠤⠖⠊⠁
⠀⠀⠈⣾⣶⣿⡇⣾⣿⣽⣿⣿⡿⠇
⠀⠀⠀⠙⠝⠟⠿⣿⣦⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣾⣿⣿⣷⣦⡀⠀⠀⣀⣀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡃⠠⣿⣿⡿⠃⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⢀⣷⣄⠀⠀⣶⣿⡇⠀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣑⣾⣉⡍⠀⢠⣄⡀⠀⠘⣿⣇⣼⠀⠀⠀⠈⣿⣿⢀⡀⢿⡟⢠⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⠁⠙⣦⣄⣸⠿⠋⠀⠀⢹⠟⣫⡄⠀⠀⠀⠈⣇⢘⡷⢼⣿⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠉⠀⠀⠀⠀⠈⠛⣇⡀⠀⠀⠀⢸⠛⠟⡀⢀⡰⣀⣤⡟⠁⠀⠘⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣴⡿⢇⠀⠀⠀⠀⣠⡟⠁⣹⡗⠋⠀⢿⣿⣆⠀⠀⠙⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠁⠘⣆⠀⠀⠀⡟⢁⡴⠛⠿⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠀⠀⠀⠈⢆⠀⠀⣷⠞⠀⠀⠀⠀⠀⠀⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠈⢧⣀⡏⠀⠀⠀⣀⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠒⡟⠒⠶⢦⡀⠀⠀⢸⡇⠀⠀⣾⣿⣟⣿⣯⣿⣿⡿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⣬⣧⣟⠀⠀⠙⣦⠀⢸⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⣰⣿⣿⣿⣷⠀⠀⠈⢳⣾⠃⠀⢸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠋⠀⠀⠀⠀⣿⠀⠀⠀⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⣀⣤⡤⢼⡧⠶⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⢦⣿⠀⣰⠞⠛⠁⠈⣧⣾⡀⠀⢀⣨⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣀⡿⠀⠀⢙⣶⣿⣿⡁⠀⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⠇⠀⠀⣿⣿⣿⣿⣿⡆⠹⠿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠶⠶⠶⢶⡿⠂⠀⠘⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⡟⠉⠁
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣿⣇⣀⣀⣀⣀⣸⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⠻⠿⣿⣿⠿⠿⡿⠻⡿⢿⠿⢻⣿⠿⠛⠛⠛⠛⢛⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠺⠟⠀⠀⢴⠄⠀⠀⠀⠘⠃⠀⠀⣿⡆⠀⣾⠱⡶⢴⠿⠃⣸⡏⠱⡾⠇⠀⠀⠙⠋⠀⠀⣤⠀⠀⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⢠⣤⠀⠀⠀⠀⢠⣤⣿⠀⠘⠀⢠⡇⢀⡄⠀⣿⠁⠀⠀⠀⠀⣾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠁⠀⠀⣠⠀⠈⠋⢁⠴⠐⠛⢹⡀⢈⠁⠀⠟⠃⠀⢲⡶⠀⠈⠀⠀⠀⠀⠀⠠⠾⠇
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠶⠀⠀⡀⠀⠉⠀⠀⣴⡿⠀⠐⠁⣰⣿⠧⠀⠀⠀⠀⣄⠀⠀⠀⢰⡄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⠀⠀⠺⠟⠀⠀⢠⣤⠀⠀⠀⠀⠔⠙⠀⠀⠀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⣠⠁⠀⠀⠿⠇⣀⠀⠀⢸⣿⠀⠀⠀⢰⠄⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠛⠁⠘⠃⠀⠀⢠⡾⠆⠀⠀⠈⠟⠃⣠⠀⠀⠀⠙⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢀⣀⠀⠀⢀⣀⡀⠀⠀⠰⣶⠆⠀⠀⠈⠀⠀⠿⠇⠀⠀⣀⣀⠈⠁⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠘⠋⠀⠀⠶⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠂⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠐⠒⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢁⠈⠀⠀⠒⠂⠈⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠒⠂⠀⠈⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠢⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠶⢺⡀⠀⢁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢂⣹⠀⠀⣏⠉⢵⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⢋⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠒⠡⠐⢧⠀⠱⣀⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⣀⡀⠀⡈⡗⢤⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡜⢀⢊⠐⠁⠀⠀⠀⠑⢤⡈⠑⠂⠷⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠴⠊⠉⠀⠀⠀⢀⠻⠲⡐⠄⠑⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠆⠀⠀⠀⠀⠀⠀⠀⡼⠉⠑⠂⠠⠀⢤⡀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠡⠁⠀⠀⠀⠀⠀⣠⠞⠀⠃⠀⢨⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢱⡈⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠙⢒⠉⠀⠀⠒⠀⠀⠀⠀⠀⠀⢀⣁⠤⠖⣒⠼⠶⠶⠦⠤⠶⠚⠁⠀⠀⠀⠠⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠠⠆⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⣠⠴⠶⠒⢉⣡⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⠌⡁⠂⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠉⠀⠀⠔⠊⠁⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⠴⠒⢈⠠⢐⡮⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⣀⠀⠀⠀⠈⠉⠁⠒⠒⠀⠤⠤⠤⠤⠤⠤⠠⠤⠤⠶⠶⠾⠛⠛⠓⠊⠉⠉⠠⠀⠂⢀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠃⠐⠒⠒⠒⠒⠒⠒⠒⠂⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠂⠐⠒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠠⠒⠉⠉⠁⢀⠀⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⡇⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡇⢰⡟⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⡠⠖⠚⠛⠉⠛⠒⢤⣀⡀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣀⢀⡇⣿⣷⣿⣯⣿⣿⣉⣉⣉⣭⣙⣛⣳⢦⡀
⠐⡇⠀⠀⠐⠒⠒⠒⠀⢀⣠⠔⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣹⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⠿⣿⡙⣆
⠀⡟⢤⣄⣀⣀⠤⢶⣾⠟⠉⠀⠀⠀⠀⠀⢠⢾⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾
⠀⢧⣀⣀⣀⣠⠶⠛⠁⠀⠀⠀⠀⠀⢀⠔⣵⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⠞⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡕⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡴⠃⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠞⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠒⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠶⣶⡖⠚⠛⠉⠉⠓⣲⠶⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠙⢦⡀⢀⡤⠞⠣⢄⡀⠀⠀⠈⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⡆⠀⣠⠀⠀⠀⢀⡀⠀⠙⢿⠀⠀⠀⠀⡈⠳⡀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⡰⠀⠀⡇⢠⠃⠀⠀⢠⠎⠀⠀⠀⢸⠂⠀⡀⠀⡆⠀⠘⠢⡀⠀⠀⠀⠀⠹⡄⠀⠀⢀⡤⢤⡀
⠀⢀⣀⣀⣀⠀⢠⠃⠀⠀⡇⠀⠀⢸⡏⠀⠀⡰⠋⠀⠀⠀⢀⡏⠀⠀⢠⢰⠃⠀⠀⠀⣱⣀⣀⣀⣀⠀⢸⣀⠴⠋⠀⠀⠸
⢠⠞⠁⠀⠈⠉⠻⣄⠀⠀⣇⠀⠀⠘⡇⢀⡎⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⠃⠀⣠⠖⠋⠉⠀⠀⠀⠈⠉⢿⠁⠀⠀⡠
⡏⠀⠀⠀⠀⠀⠀⠈⠱⡀⠸⡀⠀⠀⡇⢸⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⡆⣠⠞⠁⠀⠀⠀⡀⠀⠀⠀⠀⢈⡄⠀⡰⠁⡸⢠
⡇⢸⡀⠀⠀⡆⠀⠈⢆⠙⢆⡇⠀⠀⠘⣾⠀⠀⠀⡠⡜⠁⢸⠀⠀⠀⡴⠁⠀⠀⠀⠀⡜⠀⠎⠀⠀⡀⢸⠃⢀⠇⡴⠁⡞
⣇⠀⠱⡀⠀⢸⠀⠀⠘⡆⠈⢻⣀⠀⠀⠸⡀⡠⠊⠘⣇⠀⠀⢃⠀⣸⠁⠀⠀⡔⠀⢸⠀⠸⠀⠀⡴⠀⡞⠀⣼⠞⠀⣸⠁
⢹⡀⠀⠈⠲⢼⡄⠀⠀⣧⠀⠀⢯⠱⡄⠀⡟⠀⠀⠀⢸⡄⠀⠘⡆⡏⠀⢀⠞⠀⠀⠘⡀⣇⡤⠊⠀⡼⠡⣰⠁⠀⣰⠃
⠀⢧⠀⠀⠀⠀⠙⢆⠀⢸⠀⠀⠈⠳⡘⡄⠱⠀⠀⠀⢸⡇⠀⠀⢿⠃⠀⡏⠀⠀⠀⠀⡿⠉⠀⠀⡜⠁⢀⡇⠀⡴⠃
⠀⠈⠳⣄⠀⠀⠀⠈⠳⣼⠀⠀⢀⠀⠙⠺⣦⠱⡀⠀⠀⠳⡄⠀⡞⠀⠀⡇⠀⠀⢀⠞⠀⠀⢀⡞⠀⢀⢞⣠⠞
⠀⠀⠀⠈⠳⣄⠀⠀⠤⣈⣓⣄⣞⠀⠀⠀⠙⣷⡑⡄⠀⠀⢹⣼⠁⠀⠀⣁⣀⣴⣡⠤⠔⢂⡞⢠⢔⠵⠋
⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⠀⠈⠉⠒⠦⢄⣸⡳⢼⣄⠀⣸⠃⠀⢀⡔⠋⠁⠀⠀⠀⢀⣼⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠲⢤⣄⣀⣈⣙⣲⣽⣷⣧⠤⢴⣥⣤⣤⠤⠤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢻⡖⠒⢂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡯⠭⠅⢀⣇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣯⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⡀⠀⢀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⡴⠀⠀⠰⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡎⠀⠀⠀⢀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠠⠀⡘⢡⡷⢤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢤⡄⢖⠀⣠⣴⣶⣶⣿⡿⢷⣼⣿⣿⣿⣿⣻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠷⢂⢹⣧⣤⣬⠍⠉⠉⠁⠉⠉⠉⠁⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠑⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠠⠐⠞⠻⣦⡀⠀⠀⠀⠀⠀⢀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⠷⣤⣍⣓⣶⣶⡤⠴⡋⠁⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣌⠻⣿⣿⣿⣿⣦⣌⣉⣉⣉⣁⡀⠔⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠈⠀⠀⠀⢠⡴⣿⣿⣿⣿⣷⣿⣿⣿⣿⡟⠋⠉⠉⠀⠀⠀⣀⣀⣤⡔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣟⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠈⠉⠁⠀⠈⠁


⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡘⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠛⠒⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠀⠀⠀⣼⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠆⠀⠜⠃⠀⢀⠄⠊⠡⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠚⣷⠁⠀⠀⠀⠀⠀⢀⣄⡠⠴⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⠙⠛⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠋⠀⠀⠀⠀⢁⣀⣴⣶⣶⣶⣐⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠱⣦⣤⣅⡤⠠⠋⠁⠉⠀⠀⠉⠁⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡌⠁⠀⠀⣀⡴⠚⠀⠐⠒⠀⠀⠀⣀⣴⡖⠂⠀⠀⢠⡄⠀⠀⡀⠁⠈⣦
⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣐⢧⡃⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠋
⠀⠀⠀⠀⠀⢘⡇⠀⠀⠴⠁⠀⣼⡿⠆⠀⠀⠀⠀⢘⠉⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⡴
⠀⠀⠀⠀⢀⡜⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠈⠅⠀⠀⣀⣀⠀⠀⣠⠀⠀⠀⠀⠀⡄⢀⣀⣤⠈⠻⣏⡀
⠀⠀⠀⠀⠋⣰⣾⣇⠄⠀⠀⠘⠁⠀⣾⠖⠀⣼⡿⡆⠀⢀⡴⣾⢸⠔⠂⠿⠚⠋⠀⠀⠼⠻⠛⠋⠉⠀⠀⠀⠹⢶⡀
⠀⠀⠀⠀⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⣿⠗⠀⡠⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⡀⠀⠛⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡔⠂⣈⡄⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠏⣠⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣬⣩⠤⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣈⣽⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠐⠐⠂⠈⠑⠚⢿⣿⣿⣯⣙⡁⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢚⣿⣷⣌⠙⡛⠿⠿⠃⠀⠀⠀⠀⠀⠐⠀⠈⠀⢠⣿⣿⣿⣿⣿⣿⡀⠀⠸⠀⠀⠀⠀⠀⠈⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣷⣌⣙⣛⠙⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣮⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⣉⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠈⠻⠉⣻⣿⣿⣿⣧⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢿⣿⣷⢄⠐⠌⠻⠿⣿⣯⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠻⠿⣿⡾⠷⠦⠬⠻⢾⣽⣿⣁⣤⡀⢠⢠⡦⣀⣐⡋⡠⠤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠋⠉⠉⠈⠩⠉⠀⠀⠀⠀⠠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠂⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡈⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠀⠀⠀⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠄⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠐⢄⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠦⣍⣘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⣸⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣠⠔⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⢀⢤⣶⠿⠛⠉⠀⠀⢀⢠⠃
⠀⠀⠀⠈⢇⠀⣈⣉⠐⠠⣀⢮⠢⡐⠄⠀⠀⠀⠀⠀⠙⠓⠲⢦⡴⢒⡵⠟⠁⠀⠀⠀⠀⢄⡴⠃
⠀⠀⠀⠀⠀⠑⠄⡀⠁⠲⣈⣧⠦⠬⠱⡾⣽⡴⡦⡄⣀⣰⣯⣥⣔⣉⡀⡀⠠⢀⡂⠬⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣉⣗⣾⡿⣿⠬⡯⢑⢔⡉⣀⠛⣧⣶⡖⡖⠒⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠤⠠⡿⠿⠹⣞⣛⢯⡉⣯⣽⣿⣘⢣⢻⣯⢏⣿⣾⣤⢀⡠⡀
⠀⠀⠀⠀⠀⠀⠜⠀⢘⢐⣝⡭⠨⣽⢛⠖⢚⣿⣓⠾⠏⠉⠉⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠤⠂⠈⠑⠋⠉⠒⠃⠘⠯⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢩⣟⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠉⣟⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡂⠄
⠀⠀⠀⠀⠀⠀⡰⠋⠀⢰⣿⠟⡤⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⣾⡟⣠⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠞
⠀⠀⠀⠀⠀⡼⡁⠀⣀⢵⣿⡴⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠠⣿⣰⠃⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⠏
⠀⠀⠀⠀⡼⡑⠁⠀⠴⣿⣿⠃⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⣾⣷⠇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏
⠀⠀⠀⣸⢡⠁⡄⢔⣿⣿⢷⠌⢠⠇⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡀⠀⣺⣿⡟⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⡟
⠀⠀⢠⡇⣄⡾⢐⣭⣿⣏⡏⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢰⠃⣨⣿⣟⡙⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣿⣿⣿⡑
⠀⠀⢸⢀⢪⣟⣿⣿⣟⡞⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣛⣸⣿⣽⡱⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⡳
⠀⠀⢸⢸⣾⣵⣛⡽⣾⢡⠎⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⢰⣥⣿⣿⢣⢁⠔⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣾⣿⣿⣿⢣⠁
⠀⠀⢸⣜⣽⣿⣿⣽⠖⠁⢀⣠⠦⣤⢾⣿⣏⢷⡄⠀⠀⣎⣿⣿⣿⣩⠗⠀⠀⣠⠴⣤⣾⣿⣏⢳⡄⠀⠀⠘⣿⣿⣿⣿⡶⠂
⠀⠀⠀⠙⠛⠛⠋⠁⠀⢀⡏⠀⠀⠘⣿⢻⣿⠈⣷⠀⠀⠈⠙⠛⠋⠁⠀⠀⡎⠀⠀⠈⣷⢻⣿⡀⢷⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⢰⠘⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⠀⠀⢸⡷⣟⡇⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠸⣷⢿⡇⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢰⡀⡂⢸⣷⢻⣷⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡀⠀⠀⣿⣹⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⢧⣃⠈⣿⣟⠉⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢧⢀⠀⢹⣿⣿⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣻⣹⠀⣿⢛⡄⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣞⣸⠀⢸⣿⡟⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣠⠀⣿⣿⡟⢀
⠀⠀⠀⠀⠀⣀⡤⢤⣀⠀⠀⠹⣷⣻⠂⣿⢿⢡⡿⠀⠀⠀⠀⣠⠤⣄⡀⠀⠀⠘⣿⢃⠂⢸⣿⢃⡿⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠘⣿⣿⡗⣿⣿⡇⡀
⠀⠀⠀⠀⣞⢡⢷⠲⣮⣦⠀⠀⠹⣧⡜⣷⣿⢿⠃⠀⠀⢠⡞⡁⢆⠢⠽⡄⠀⠀⠙⢧⡜⣹⣿⣾⠃⠀⠀⠀⠴⠱⢿⣿⣷⡄⠀⠀⠘⢿⣿⣿⣿⣿⠁
⠀⠀⠀⢸⣩⠗⣨⡟⡟⡟⡆⠀⠀⠈⠛⠾⠿⠃⠀⠀⠀⣼⣨⠂⠹⠚⢰⢹⠀⠀⠀⠀⠙⠻⠟⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠀⠀⠀⠀⠙⠻⠿⠁
⠀⠀⠀⡟⣼⡫⠜⠁⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢜⠁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿
⠀⠀⠀⣧⢾⡠⢂⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⢋⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⢸
⠀⠀⠀⡷⣞⡴⡆⡀⠐⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣃⡶⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⣧⣯⠿⢷⡷⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⠻⢶⠔⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡆⡠
⠀⠀⠈⣏⠁⢿⣿⣴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠺⢿⣷⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⠁
⠀⠀⠀⠘⠷⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢠⠒⡀⠉⢙⣆⣠⠤⣄⠀⠀⠀⡀⡤⢄⠀⠀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⢠⠶⠚⠐⠃⢰⠋⡞⠁⢠⠸⡄⠀⢀⣠⠔⠃⠀⠀⠁⠄⡀⠀⡡⠀⡠⢂⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⡴⠋⠁⠀⠀⠑
⠀⠀⠀⠀⡜⢀⣪⠉⢠⠟⡜⠁⠈⠃⢀⠁⠀⠀⢀⠀⠀⠀⠠⣤⠀⠀⠀⠀⢸⣅⠁⠀⠀⢀⠀⠀⢀⣴⠟⠀⠀⠀⢸⡁⠀⣀⠀⣀⠀⠀⠠⡄
⠀⠀⠀⢠⠇⠺⠀⢦⠀⣞⠀⢢⠀⠀⣾⠀⠀⡔⡩⠀⠀⠀⠐⠁⠁⠀⠀⢰⠁⠀⠀⢄⠂⠀⠀⢀⡾⠁⢀⠤⡀⠀⠀⠑⠚⠁⠀⠈⢋⠀⠀⠁
⠀⠀⠀⠘⡄⠀⡠⢪⠎⠀⢠⠀⣸⡤⠏⠀⠀⠳⣅⠀⠀⠀⢸⣀⠀⠀⣠⠛⠃⠀⠀⣸⢤⡤⠴⠋⡀⠀⡶⠀⠈⠲⠤⠤⠂⠀⢢⠀⠈⠳⠖
⠀⠀⠀⠀⠀⢤⣁⠈⢀⡎⠁⡸⠁⠀⠀⠰⢩⠆⠀⠉⠓⠒⠚⠋⠀⠀⣇⠀⠀⢀⠔⠁⠀⠀⠠⡏⢦⠀⠘⣄⠀⠀⠀⠀⠀⠰⠋⠀⣀⢄⢀⠂
⠀⠀⠀⡄⢀⠀⠉⠒⠒⠒⠉⠁⡠⠀⠠⢄⠀⠀⠀⠀⣠⡴⠛⢿⡄⠀⠈⠁⠈⢁⠴⠒⠉⠀⠀⠈⠁⠀⠀⠈⠁⠂⠀⠀⠐⠁⠀⠊⠁⠃⠰⠂
⠀⠀⠀⠉⠉⠀⣀⡀⠀⠀⠀⢸⠀⠀⠀⠐⠛⠀⢀⣼⠋⠀⠀⣸⠇⠀⠀⠀⠀⠘⠒⠂⠁⠀⠀⠀⠀⠠⣶⠙⠉⠀⠀⠀⣀⡠⠄
⠀⠀⠀⢠⠔⢿⠁⠂⠰⡆⠀⠘⠎⠀⠀⣠⠞⠀⣼⠃⠀⠀⠀⠉⠀⠀⣠⢔⣶⠀⠀⠀⠀⡼⠁⢀⣀⠀⠀⠀⠀⠀⣰⢏⠁⢀⠀⠄⠈⠀⠱⡄
⠀⠀⢠⢿⡇⠈⠀⠀⠀⢳⠀⠀⠀⠉⠉⠀⠀⠀⠻⠤⠄⠐⠲⣆⢀⣰⠵⢛⠵⣲⢄⣠⣼⠃⡴⠋⣿⠀⠀⢀⠔⠉⠀⠘⣦⠀⠄⠐⠀⠀⠀⢹
⠀⠀⠘⡈⢧⡀⠀⢡⣀⢌⡄⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠣⢠⡿⠞⠋⣿⠡⠏⢸⠁⠘⠁⠀⣰⠣⠐⠋⡀⢀⡸⣆⠀⠀⠀⢊⡴⠃
⠀⠀⠀⠈⠚⠟⢛⣋⠡⠚⠁⠀⠈⠀⠚⠁⠄⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠂⠐⠀⠈⠀⠀⠀⠑⢆⠀⠀⠈⠒⠢⠬⠴⠖⠻⢍⡤⠤⠚⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠁⠀⠲⠀⠀⠘⠦⣤⣤⠶⠋⠁⢀⢤⠀⣠⡀⡄⢠⢤⡄⠀⠙⠓⠁⠀⠾⡀⠀⠀⢀⠀⢀⠔⡄⠀⣀⣀⠀⠓⠁
⠀⠀⢀⠔⠙⠪⠉⠑⣮⠀⠀⡀⠶⡄⡄⠀⢀⠀⠀⢀⠀⠀⠀⠟⠞⠠⠏⠿⠁⠿⠚⢁⣤⡀⠀⠀⠀⠀⠀⠀⠠⢡⠁⠧⠞⠁⠀⣏⠢⠑⢤
⠀⠀⢼⠤⠀⠁⢦⡀⢸⠢⠤⠀⠰⠞⠁⠰⠇⠇⢀⣿⢁⡤⠶⣆⠀⣀⠀⣀⠀⠀⠀⣾⠏⠀⠀⡰⠊⣿⠆⠀⠀⠁⢰⣒⡨⠀⠀⢧⠀⠁⣀⠱⡀
⠀⠀⠘⢷⡀⠄⢀⡨⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⠊⠀⣼⡇⣼⡏⢰⡟⠀⠀⣾⠟⠒⠂⠀⢣⡈⠋⠀⠀⠀⠀⣀⡀⠀⣀⠀⠘⠦⣄⢠⡰⠃
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⡎⠠⠚⠄⢸⠀⠀⠀⣼⠃⠀⢰⡿⠀⢿⠔⠙⠧⠐⠀⢏⠀⠀⠀⢆⣀⡿⠀⠀⠀⣴⠎⠉⠐⠂⠀⠌⡳⠢
⠀⠀⠀⣠⣲⣵⡶⠀⢱⡄⠉⠠⠀⠀⠜⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⣁⣀⡀⡀⠀⢏⡛⡩⠅⠠⢤⠤⠊⠀⡠⠂
⠀⢀⡾⢋⠞⠁⠀⠀⡰⠃⡠⠐⠀⠀⠀⠂⢀⠀⠠⠒⠒⠂⠀⠀⠀⠀⠀⡰⠚⠁⠐⠀⠀⠀⠀⠳⠔⠂⢀⠀⠀⠉⠈⠉⠉⠀⣀⠀⠀⠀⠉
⠀⠈⠛⠁⠀⠤⠖⠋⠀⠀⠃⠠⢤⣤⣀⣤⣤⡇⠀⠀⠁⠁⢠⠞⠉⠣⡀⠙⠋⠁⠀⠄⠀⡐⠀⢀⠀⠰⡷⠀⠀⢀⣤⡖⠨⠯⠈⠉⠿⣷⠢⡀
⠀⠀⠀⠀⡠⠀⢀⡔⠒⢠⣄⡀⠀⠀⠈⠉⠉⠀⢠⣂⡂⢠⡏⠀⠀⠀⢱⠀⠀⠀⠸⡆⠈⠀⠀⢠⠆⠀⠀⠀⣰⢋⠏⠆⠰⢀⣀⠶⢒⠿⢻⣇
⠀⠀⢴⣿⡄⠀⠉⠀⠀⠤⢴⠟⠀⠀⠀⠀⡀⠤⢀⣤⠤⣿⢀⠤⠒⠶⠺⣤⣀⠀⠀⠑⠂⠀⠂⠀⠀⠀⠀⢰⠙⣇⢖⠀⠀⢔⡅⢈⡈⠖⣮⣿
⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢀⣠⠞⠉⠀⠀⢸⣇⠀⠀⠀⠀⡄⠉⣏⢢⡀⠀⢠⢴⡏⠁⢠⠀⠸⢦⣶⡤⣀⠤⠣⢀⣠⢀⣞⣽⡟
⠀⠀⠀⠀⠀⠑⠀⣇⠑⠄⠀⠀⣠⠁⠒⠉⠀⠀⠀⠀⠀⣼⣻⢦⣀⡈⢀⡀⠀⠘⣆⢇⠀⠀⠘⠀⠀⠀⠁⠀⠘⣥⣞⠡⠄⠘⠩⢑⣮⡿⠟
⠀⠀⠀⠀⠢⣀⠀⠈⠂⠀⠀⠀⠓⠒⠒⠂⠦⠴⠶⠷⠚⠁⠈⠙⠪⠭⢭⣭⣑⣊⣩⠜⠀⠑⠚⠂⠄⠂⠀⠀⠀⠈⠘⠋⠣⠍⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣻⠟⣽⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⣟⣿⣿⣿⣝⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣻⣿⣿⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⣮⣽⡷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢿⠿⢫⣼⣯⠗⣯⣼⣽⣿⣿⣟⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡹⠛⠉⢀⣺⠟⣡⣼⣧⣾⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⣏⡰⠒⠉⠁⠀⠠⢜⠁⢀⣿⣶⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⣛⢥⡷⠛⢁⡀⠀⢀⣠⠒⠡⢀⣬⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⣋⣉⣮⠝⠋⠀⠀⣈⠀⣱⠈⠀⠀⣀⣠⣿⣿⣟⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣡⣤⡴⠋⠁⠀⠀⠀⠦⠍⠁⠐⠚⢀⣦⣿⠿⢿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣋⣼⡿⠃⠤⠠⣙⠂⠠⠀⠁⠂⢀⢊⣳⢟⠧⣤⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣧⡆⣰⡀⠅⠁⠀⠘⠀⠏⠀⠈⠐⣛⡾⣻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⡿⣣⣴⠠⡏⣲⣄⠔⠀⠀⢀⣼⣼⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢯⠈⠙⢟⣿⣿⣵⣿⡷⠛⣪⡤⢀⣯⣼⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡆⠀⢩⣿⣿⣿⣿⣞⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠿⣿⣿⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⢷⣦⣄
⠀⠀⢀⣠⣴⡶⢶⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄
⣠⣶⠟⠋⠁⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣀⣈⣙⣿⣦⣀
⠟⠁⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠖⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢷⣦⣀
⢀⣠⠴⣦⢸⡇⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠋⢀⡴⢏⠿⣅⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦
⡉⢣⠀⠀⠑⠬⣩⣏⣠⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⣷⠈⡆⠀⢠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⡿⠤⠷⢤⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⢠⠏⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⢀⡏⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⢸⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢀⣠⣴⡾
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣤⡶⠟⢋⠁
⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢀⣠⣿⣶⠿⠛⠁⠀⠠⠤⣤
⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣦⣶⠾⠟⠋⠁⠀⠀⠀⠀⠁⠘⢦⡀
⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⠢⡀⠏
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣤⣴⣶⠶⢶⣶⠶⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢀⠶⠀⢀
⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠟⠋⠉⠀⠀⠀⠀⢷⠀⢀⣀⣠⠃⠀⠀⣐⡤⠐⠀⢀⠄⠀⢄⠐⠂⠀⠰⠂⠀⡄⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⢀⡠⠈⠉⠈⠋⠲⢢⣁⠀⠀⠀⢈⡀⠀⠀⠆⠀⠁⠀⢁⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⣄⠀⢀⠀⠑⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣼⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⣀⠒⠀⠄⠀⠼⠁⠀⠀⢀⣀⣠⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠒⠛⠛⠛⠉⠉
⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⣿⡇⠈⡄
⣤⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣿⣇⠀⠘⡄
⠉⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠈⢦⡀
⠀⠀⠀⠉⠻⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣤⣤⣤⣀⣀⣀⣀⣀⡀⠈⢻⣷⣄⠀⠀⠈⠑⠢⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠒⠊⠁⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢰⣀⣀⣽⠭⠤⠤⠀⣀⣠⣤⣶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⠶⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⠉⢉⠱⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⣆⢴⣏⣀⣀⣠⣨⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡾⢿⠻⠿⠃⠁⠝⠉⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠛⠻⠟⠁⠀⠀⠀⠀⠑⢐⠀⠀⠀⢀⡈⠳⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⣆⠦⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡗⣤⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣾⢿⣿⡁⠬⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠈⠲⣶⡀⠀⠀⠀⠀⠀⠀⢺⣤⠋⠀⠀⢀⢻⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣦⡝⠁⠀⠀⠀⠸⠘⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇⠀⠀⠀⠀⠀⠢⢹⡄⠀⠀⢀⡤⠃⠀⠀⠀⠀⠀⢀⣾⡄⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠁⠀⠀⠀⠀⠀⠀⠻⢷⡀⠀⠉⠀⠀⢀⠀⠀⠀⠀⣠⠟⠛⢾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⠖⠛⣳⠀⡤⠀⠀⠀⡀⡤⠔⣻⠟⠰⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⣤⠶⠉⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⣀⠀⠀⠀⠀⢀⣀⣤⣾⠃⠀⠠⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⠛⠛⠛⠋⢻⣿⣏⠀⠀⠗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣿⣾⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⡄⠀⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠿⠉⠛⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠏⠁⠀⠀⠀⢸⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⣼⣧⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⡀⢸⣿⠘⣇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢻⣿⡀⣿⠀⠀⠀⠀⠀⠀⢸⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢩⠂⠀⠀⠀⠀⠘⢻⡇⣿⠀⠀⠀⠀⠀⠀⢸⠃⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⡇⠿⠀⠀⠀⠀⠃⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⢿⠟⢻⠿⡿⠟⣿⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢦⠹⡌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⡄⣿⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢰⠃⣿⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢀⠏⣸⠇⠀⢰⢿⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡟⠀⠀⡞⢈⡇⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣾⠁⠀⡼⠁⣼⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣰⠏⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡶⠶⠖⠚⢻⡀⠈⠁⣿⠀⠈⠀⠀⠀⠤⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣋⣥⣤⠴⠶⠶⠒⠈⠻⠦⡘⠙⢧⡘⠛⠳⠶⠶⠤⢤⣀⠉⢻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣥⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠾⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⣀⣼⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⡇⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢹⡇⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠖⢋⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣡⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⠶⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢰⡁
⠀⠀⠀⢀⣀⣤⣶⠾⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀
⠀⢀⣴⡿⠋⠉⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⡶⠶⠖⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡄
⠀⢸⣿⠀⠀⠀⠀⣠⣶⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢤⣄⠀⠀⠀⠀⠀⣹
⠀⠈⢿⣦⡀⠀⠀⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠙⠿⣶⣄⣈⠙⠿⢷⣶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠞⠋⠁⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⣶⣤⣬⣉⣉⡙⠛⠛⠛⠻⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠛⠋⠉⠉⠁⣀⣀⣠⡤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠋⠉⠉⠉⠁

⣦⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣽⣭⣭⣿⣵⣮⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣶⣶⣾⣷⣶⣶⣶⣿

⣟⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⠟⠁⠀⠀⣠⣿⢃⣾⠃⠀⣾⠇⠀⣠⡿⣧⣼⡿⠛⠁⠀⠀⠀⠀⠀⠀⢠⡾⠃⢀⡜⠁⠀⠀⢠⣿⣧⣃⣤⢾⡟⠀⢀⡆
⠛⠁⠀⢀⡴⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⣠⡾⠛⠻⠟⠁⠀⠀⢿⣤⡾⠋⠀⠀⢻⣀⣀⣴⠖⠀⠀⠀⠀⢀⡿⢁⡴⠋⠀⠀⢀⡴⣿⣏⡟⠉⠀⣾⠁⢠⠚⠷⣴
⣀⣀⡴⠞⠀⠀⠀⠀⠀⠀⠸⣿⡀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣾⡷⠋⠀⠀⢀⡴⠋⠀⠻⠛⠀⠀⠀⠿⠖⠁⠀⠀⠸
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄
⠀⠀⠀⢠⡾⠛⣦⠀⢀⣠⣾⠆⠀⠀⠀⠀⠀⣴⡶⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⢀⣿⣿⣰⣿⡶⠿⣿⡏⠀⢀⡄⠀⢠⣾⠋⢠⣾⠇⠀⠀⠀⠀⠀⠀⣠⡟⠁⢀⡼⠁⢀⠄⠀⠀⠀⢴⡆⠀⠀⢀⡀⠀⢀⣴⢿⡆⢠⡀⠀⠀⠀⣠⣿⣿⠁
⠀⣴⣿⣿⢋⣿⠋⠀⣸⣿⠀⢀⣾⡇⢠⣿⣃⣴⠿⠃⠀⠀⠀⠀⠀⢀⣾⡿⠁⣰⠟⠀⣠⢷⣠⡤⠊⣠⠏⠀⠀⠀⣼⠃⣠⣞⡡⠋⠀⢸⠃⠀⠀⣰⣿⡿⠁
⡾⠋⢿⣇⡼⠃⠀⠀⣿⡇⢠⣾⠉⠓⢾⡿⠋⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣡⡞⠁⢠⢾⣏⡠⠀⠀⢠⠏⠀⠀⣠⠎⠻⣴⣿⠋⠀⠀⣠⡟⠀⠀⢠⣿⡿⠁
⠁⠀⠀⠉⠀⠀⠀⠀⠻⢷⠿⠁⠀⠀⠸⣇⣀⣀⣤⡴⠂⠀⠀⢀⣿⣿⠟⠃⢀⡴⠋⠈⠉⠀⠀⠀⣏⠀⢀⡼⠁⠀⠀⢾⣿⣀⣠⣾⠏⠀⠀⢠⣿⡿⠁⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⣿⣟⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠿⠶⠋⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⣼⡿⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⣠⠟⠀⠀⡠⣄⠀⠀⡀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀
⡆⠀⢸⡆⠀⠀⠀⠀⠀⢀⣾⣿⢃⡾⠋⠀⣠⣶⡇⠏⣠⣾⠏⠀⣴⠂⢠⣾⣿⣿⠋⠀⠀⡀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⢠⣿⢻⡆⠀⣠⣿⠃⢀⡀⠀⣠⡿⠋
⠀⠀⣸⠇⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⢀⣴⣿⣏⡟⠋⣹⡟⠀⡴⣿⣤⣿⡿⠋⠁⠀⣠⠎⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣼⡿⣿⣧⣾⣿⠃⠀⣸⡇⢰⣿⣡⣾
⠀⣴⠏⠀⠀⠀⠀⠶⣾⣿⡏⠀⢀⣴⠏⠸⠿⠟⠀⠀⢿⣧⠞⠁⠀⠹⣿⣄⣀⣤⡾⠃⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠛⢹⡏⠀⣰⡟⠙⣿⠟⠋⠁
⡾⠋⠀⠀⠀⠀⠀⠀⣿⣿⣥⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⣠⣿⠛⢿⠟⠀⠀⣿⡇⣴⡿⠁⠀⢿⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠙⠻⠛
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⣠⡖⢶⡄⠀⢀⣴⡷⠀⠀⠀⠀⠀⣠⣾⠟⣶⡀⢠⡏⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⢠⣿⡇⣼⣧⣶⢿⣿⠃⠀⣀⠀⠀⣴⡟⠁⣴⡿⠀⢸⡇⠀⠀⣠⣾⠟⠀⠀⠀⣠⠖⠀⣸⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀
⠁⣶⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⣰⣿⡿⢻⣿⠉⠀⣾⡏⠀⢠⣿⠀⢰⣿⣠⡾⠛⠀⠀⠀⠳⠶⠿⠋⠁⠀⠀⢠⣾⠏⢀⡼⠁⣠⠈⠀⡠⢀⡟⠁⠀⢀⡖⠀⣰⢏
⢠⠇⠀⢠⣿⡿⠃⠀⠀⠀⢠⣾⠟⣿⢃⣾⠃⠀⢰⣿⠃⢠⡿⠉⠳⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢏⣴⠋⢀⣴⠋⡙⠋⢀⡞⠀⠀⣠⢾⣇⣼⡿⠋
⠏⠀⢀⣾⣿⠃⠀⠀⢀⣴⡟⠁⠀⠉⠛⠁⠀⠀⠈⢿⣴⠟⠁⠀⠀⠹⣇⣀⣠⣴⠖⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠁⣴⠋⠘⠛⠀⠀⡼⠀⢀⡴⠁⠀⢸⣿⠀⣀
⠀⠀⣸⣿⠃⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢁⣠⠟⠁⠀⠀⠀⠀⠀⠿⡶⠋⠀⠀⠀⠈⠛⠛⠋
⠀⠀⣿⡏⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠁
⠀⠀⠻⢧⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⣠⣾⠟⠁⢠⣤⣄⠀⠀⣠⣶⠄⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⢷⠀⠀⠀⢀⡀
⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣠⣾⡟⠁⠀⢠⣿⣧⣿⠶⢻⣿⠃⠀⢠⡄⢀⣔⢋⣼⠃⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⣠⠏⠀⠀⢠⡏⡃⠀⠀⣠⡟

⠀⠀⠀⠀⢀⠀⢀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡄⠨⡃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠈⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢐⣀⡠⠂⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠤⠤⠄⣠⢀⣂⠀⠄⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⡀⠄⠀⠀⠀⠀⢀
⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠿⠀⠀⠀⢄⠀⠈⡜⠀⠀⠀⠀⠀⢂⠀⠀⠀⡨⠀⠀⡀⡜⠁⠀⣠⠎
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡄⠄⠀⠀⠀⠐⠂⠀⠀⠞⠁⠀⢀⣼⠇⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠹⣿⠂⠀⠂⢤⡀⠀⠀⠓⠦⡴⠿⠟⠋⠀⠀⠀⠂
⠀⠀⠀⠀⠢⣀⡀⠀⠰⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢀⣀⣤⣤⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⣤⣤⣶⡶⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠈⠉⠁⠀⡊⠐⡀⢸⠀⢱⡀
⠀⠀⠀⠀⠠⠀⠤⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠈⢄⠀⠔⠉⠀⠀⠣⠤⠇⠘⠦⠞⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠠⠤⢄⡀⠀⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠠⠀⠊⠀⠀⠀⠀⠀⠉⠁⠀⠀⠢⠀⠹⡕⣿⢙⢶⣄
⠀⠀⠀⠀⠀⠐⡀⠀⠙⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠐⠀⠅⠰⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠈⠻⣦⣥⣮⠇
⠀⠀⠀⠀⠀⠀⠈⠢⠤⠜⠂⠀⠀⠀⠀⠀⠀⢀⣠⠾⠆⠁⠀⠠⠊⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠐⠀⠀⠀⠀⠁⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠈⠢⠤⠔⠊⠉⡀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠠⠔⠁⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠐⠀⠀⡴⠉⠀⠀⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠐⠄⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠣⠠⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⢀⢃⠌⠀⠀⠀⠀⠑⢤⡀⢀⠀⠀⠀⠡⡀⠀⠀⠀⠀⢰⠀⠈⠂⠤⠤⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⠑⠠⠤⠤⠤⠃⠀⠀⠀⠀⠈⠑⠒⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠏⡭⠆⠈⠁⠁⠢⢄
⠀⠀⠀⠀⠀⠀⠘⠊⠙⠀⠀⠀⠀⠀⢀⠉⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⡂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢕⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠑⢌⠓⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠈⠐⢄⡀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠋⠀⠀⠀⡀⠀⠘⠀⠀⠀⠀⠀⠑⠦⣀⠐⢄⠀⠀⠉⠲⢄⡀⠀⢈⢆⡄
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠡⠀⠀⠄⠀⠁⠀⠀⠲⠜⠀⠀⠀⠀⠀⠈⠑⠢⣍⡒⠤⢀⣀⣹⡿⢋⠞⠃
⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠈⡠⡑⠀⠀⣄⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠨⠁⠀⠀⠀⠀⢀⠈⡜
⠀⠀⠀⠀⠀⠀⠈⠊⠂⠠⠄⠀⠀⠀⡀⢑⡥⠊⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠒⠀⠀⠉⠀⠀⠀⠀⠀⣡⢟⡐⡆⡆⣴⠒⣴⠒⢸⢲⣶⡇⣶⢶⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠉⠉⠈⠁⠈⠁⠈⠘⠉⠁⠁⠋⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠄⠊⠀⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⡿⢿⢶⣦⡀
⠀⠀⠀⠀⡃⡆⠀⠀⠀⠘⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⠃⣸⣟⣿⡇
⠀⠀⠀⠀⠁⠀⠀⠀⠰⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⡾⡦⢹⣷⣿⠇
⠀⠀⠀⠀⠰⠀⠀⠀⡆⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⡇⡇⣿⣿⣿⡀⠀⠀⠀⣀⣀⡀⣀⣀
⠀⠀⠀⣠⠁⠀⠀⠀⢇⢸⣟⣧⠠⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⡞⡼⢱⠇⣿⣿⣿⣷⣀⠔⠊⠀⠀⠀⠀⣾
⠀⠀⢰⠃⠀⢀⠠⠐⠚⠛⡉⠁⠀⠀⠀⠀⢀⣠⣴⡇⠀⠀⠀⡜⡼⢁⣯⠶⢚⣛⢟⡉⠀⠀⠀⠀⢀⣠⣴⡿
⠀⠀⠸⣸⢠⡏⢀⠌⠂⠀⢁⢠⠀⢀⢔⣫⣽⡾⠋⠀⠀⠀⠀⣷⣧⣾⢁⡮⣛⡽⢟⡡⡄⠀⣴⣿⣿⡿⠟⠁
⠀⠀⠀⠙⢿⣇⠀⠀⣀⡦⢔⠑⢀⢎⡾⠛⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⡈⠚⣡⣲⢥⣻⠏⣼⣿⠟⠉
⠀⠀⠀⠀⠀⢣⡁⠂⠀⠉⠀⠔⢁⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⠳⠮⢭⣭⠴⢞⣽⠏
⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠤⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠶⠾⠟⠋

⠀⠠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠙⣙⣛⣶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⠀⠠⠤⠄⠒⠊⠀⠀⠒⠋⠉⠉⠉⠙⢿⣿⠏⢉⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡏⠁
⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠟⣁⣠⢤⣄⣀⠀⢀⡀
⠀⠀⡴⠋⢠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠶⠶⠒⠒⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⢜⣷⡂⡽⠂
⢀⡞⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠉⣼⢷⠁
⢸⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠃
⠘⣙⣷⣄⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⠠⠀⠀⠀⠀⠀⠀⢀⡀⠴⠒⠁
⠀⠐⢏⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠉⠁⠀⠀⢀⣠⡤⠴⠒⠉⠁
⠀⠀⠀⠑⠠⠤⠤⠴⢺⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⣀⡤⢖⣫⡵⠞⠋⠉
⠀⠀⠀⠀⠀⠀⢀⠴⠛⢛⣿⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢊⡡⠖⠋⠁
⠀⠀⠀⠀⠀⠀⢀⣈⡤⢊⡽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠠⠄⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⡄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠐⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋⠀⠀⠀⢀⣴⣶⣄⠀⣀⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣦⣄⠀⠀⠙⠛⠋⠁⣠⣴⣾⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣦⣤⣄⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣠⣤⣴⣦⣤⣄
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⡿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣿⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣀⣀⣹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡟⠋⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠙⢻⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠐
⠀⠀⠀⠀⢀⣀⣀⠌⠀⠀⣀⣀⡀⠉⠙⠛⠿⣿⣿⣿⣟⡁⢄⠀⣾⣷⠀⠀⠀⠀⠀⠀⣾⣷⠀⡠⢊⣻⣿⣿⣿⠿⠟⠋⠉⢀⣀⣀⠀⠀⠡⣀⣀⡀
⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠂⢸⣿⡷⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⢸⣿⡇⠔⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠂

⠋⠂⠀⠀⠀⠀⠀⡵⠃⠀⠀⠀⠺⠉⠉⠉⠀⢠⣄⠀⠀⣠⠏⠀⠘⣏⢂⠀⠀⠚⠊⠁⡔⠀⠀⢰⠏⠀⠀⠈⠓⠦⠕⠀⢩⡁⠀⠀⢯⡄⠀⠉⠋
⠀⣀⠀⠘⣇⠀⠀⠀⢀⣄⣠⠾⠀⠀⢰⣀⢠⡈⢇⠀⠀⠁⠀⠀⠀⠈⠳⠇⠀⠀⠀⠀⠹⣤⠀⠸⠄⠀⠀⠀⠰⡄⠀⠐⣸⠃⠀⠀⣄⠠⣆⡀
⣨⠟⠀⠐⡼⠀⣤⠀⠀⠉⠀⠀⢀⡀⠀⠈⠉⠁⠀⠀⠀⢤⣄⣤⣄⠀⠀⠀⡴⠒⠗⠀⠀⠀⠀⠀⢀⣠⠴⠀⠀⣷⠀⠙⠃⠠⣠⠞⠁⠀⠀⠙⠛
⠀⠀⣀⡀⠀⠀⠈⠳⠶⠀⢀⣀⡼⠃⠀⠀⠀⠛⠶⠶⠒⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠋⡳⣄⠀⠛⠂⢀⡤⣀⠉⠀⣀⠀⠀⢠⡔⠚⠃⢀⡶
⠀⠀⠑⠭⡷⠀⠀⢠⣤⣄⡀⠁⠀⠀⠈⠳⠤⠤⠀⠀⠠⠖⠒⠶⠀⠀⠘⢧⡂⠀⠀⣀⠀⠈⠁⢀⣤⡀⠀⠙⠲⠖⠀⠉⠳⡄⠈⠀⠀⠚⠋⠀⣀
⡳⣄⠀⠀⠀⢠⡀⠀⠁⠒⠋⠀⢠⣄⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⣀⡀⠀⠙⠂⠀⠉⢳⣄⢰⡋⠈⠀⣠⡀⠀⣀⠀⠀⠈⠃⠀⢤⣀⣀⣠⠄⠈
⠈⠉⠀⢀⡀⠘⢦⣀⠀⢰⠀⠀⠀⠈⢳⡀⠚⠒⠚⠉⠀⠀⡽⠀⠈⠋⠍⠳⠀⠸⡲⢤⡀⠉⠀⠀⣴⠆⠈⠉⠉⠉⢠⡀⠀⠀⣀⣠⡀⠀⣄
⠶⠀⠀⢼⠁⠀⠀⠉⢀⣸⢀⡀⠀⠀⠀⠀⣤⣄⣀⠀⠀⠚⠃⢠⢄⠀⠀⠀⣀⣀⠀⠉⣅⠀⠀⢰⡇⠀⠀⠀⢀⡀⠀⢣⠀⠘⠓⠂⠁⢸⡋⢀⣠
⡀⠀⠀⠘⠆⠀⢠⠄⠈⠁⠀⠉⠓⠲⠃⠀⠀⠀⠊⠃⠀⠀⠀⠈⠳⢬⡄⠈⠃⠉⠝⠀⠈⣇⠀⠀⠀⠘⠓⠚⠉⠀⠀⠙⠀⠀⢀⡤⠦⠘⠃⠈⠁
⠍⠀⠀⠀⠰⠵⠋⠀⠀⣰⠆⠀⢀⣀⠀⣠⠖⠋⢀⡀⠀⠚⠛⢒⠄⠀⠀⢹⠀⣠⣄⡀⠀⠋⠀⠶⠚⠻⠆⠀⠐⠒⢤⡀⠀⠰⠍⠀⠀⠀⠀⠀⢀
⠀⠘⢳⡀⠀⠀⢀⠀⢸⠁⠀⢠⢊⡏⠀⠁⢀⠀⠈⠙⣢⠀⠀⢀⡀⠀⠀⠛⠀⠀⠐⠹⠆⠀⠀⠀⠀⠀⠴⢶⣄⠤⠀⠃⢀⢐⡆⠰⢦⣤⣤⠤⠸
⡤⣄⡀⠃⠀⢠⠏⠃⠀⠀⠀⠈⠋⠀⠘⠋⠋⠛⠀⠀⠀⠀⠀⣎⠁⠠⣆⣠⣤⠄⢀⡄⣀⡴⠀⠘⢝⢢⡄⠀⢀⠤⣠⠄⠗⠋⢀⡀⠀⠀⣀
⠈⠈⠉⠠⣄⠈⠁⠀⢀⡴⠚⠃⠀⠀⠀⡶⠀⠀⠸⣆⢀⠀⠀⠿⠀⢀⡀⠀⠀⠀⠀⠉⠁⣠⡄⠀⠀⠈⠀⠀⠛⠋⣁⠀⠀⠀⢠⠇⣠⣠⠞
⠀⢶⠀⠀⢈⢳⡀⠀⠛⢀⡀⠀⠀⠴⠊⠀⠀⣰⠀⢀⣉⠁⣤⠀⢠⡏⠁⠀⠉⢢⡀⠀⠎⠀⠀⠰⠥⠤⠟⠀⢀⡀⠉⢳⣄⠸⠟⢀⡈⠀⠀⡟
⣄⠏⠀⠀⠀⠉⠁⠀⢠⠏⠃⢠⣄⠀⠀⠶⠞⠁⢠⣋⠝⠀⣇⠀⠸⠇⠀⣤⠀⠈⠁⠀⠀⠀⣠⠄⠀⠀⠀⠀⡸⠁⠀⠀⣉⠀⠀⠈⢉⢦⠀⢧
⠀⢀⠀⣤⡶⠵⠃⠀⠘⠂⠀⠀⢈⣧⠀⠀⠤⠤⣬⡀⠀⠀⠉⠀⠀⠀⠀⢻⡀⠰⢦⡀⠉⠉⢁⣄⡦⠝⠀⠛⢁⡀⠀⣀⡟⠀⠀⠀⣀⠉⠁⠀⣤
⡰⢋⠃⠀⠀⠀⠀⠀⣀⠤⠀⢀⡠⢤⠄⠀⠀⠉⠀⠉⢀⡀⠀⢰⠀⢠⢄⠀⠀⠀⠐⠹⠆⠀⠀⠀⢠⠀⠀⢠⠏⠁⠈⠋⠀⠄⡸⠃⠹⡕⠀⢠⢸
⠧⠁⠀⢴⡤⠟⠃⠴⠑⠁⠀⠛⠐⢁⡀⠀⡦⡀⠮⠖⠚⠁⠀⣸⠀⠈⢧⡀⠀⠈⠙⣆⠀⠙⠛⢉⣉⠀⠀⠸⠀⠀⣠⡀⠘⠚⠁⣀⣤⠈⠋⠈⠋
⠀⠀⠀⢠⣀⡀⠀⢀⡀⠀⠀⠀⠀⢸⠁⠀⠙⠯⡄⠀⣦⠀⣀⠁⠀⠀⠈⠁⠀⣶⠈⠺⠀⢀⣠⡄⠉⠙⡆⠀⢄⡴⠋⣀⠀⠀⠴⠅⠀⢠⡄⠄⡀
⣀⣤⠄⠀⠀⠙⣦⠀⠉⠒⠚⠀⠀⠈⠃⠀⠀⠀⠀⡴⠃⠀⠙⠝⣶⠀⠀⠀⣠⠏⠀⠀⠴⠉⠀⢀⣀⠀⠀⠀⠀⠀⠰⡝⢰⡟⡄⠀⠀⠀⠈⠓⠶
⠁⠀⠀⢀⡀⠀⡤⠀⠀⠀⠀⡷⠀⠀⣀⠀⢿⠀⠀⠀⢠⠔⠦⠀⠀⠀⣀⠀⢀⣄⠀⠀⡀⠀⣴⡵⠋⠘⠛⠙⡳⠀⠛⠁⠀⠷⠁⢲⡄⢺⡢⡀
⠀⢠⡞⠙⠃⠀⠙⢦⡄⠀⠴⠃⡠⣠⠏⠀⠘⡄⠀⠀⠟⠈⠀⠀⣤⠴⠁⠀⢠⡌⠉⠉⠁⢀⡀⠀⢀⢴⠄⠀⠀⢀⡤⠲⠂⠀⠀⢠⡇⠀⠳⣴
⣀⠀⠀⠰⢤⠀⠀⢀⡀⣀⡀⠀⠛⠁⠀⠀⢀⡀⠀⣀⣠⠾⠃⠀⠀⠀⠀⠐⣸⠃⢀⠀⠀⢠⡇⠼⠁⠈⠀⣰⠆⠘⠀⠀⠘⢦⡀⠀⢠⡤⠶⡶
⠪⢳⠀⠀⠁⢷⠀⠈⢙⠛⠋⠀⢀⡴⠒⠂⢸⠁⠀⠉⠀⠀⠀⠛⠓⠲⡄⠈⠁⠀⠉⢳⣄⠉⠀⠀⠠⡄⠀⣧⠁⠀⠀⡆⠀⠐⠽⠀⣠⠀⠀⣀
⡄⠀⢴⠒⠲⡦⠀⠀⠈⡇⠀⠀⠋⠀⠀⠀⠈⠧⠀⠉⠓⠴⠆⠀⠀⠀⣠⠚⠦⣤⡄⠀⢀⡀⠀⣠⠞⠀⠀⠀⠀⡤⠎⠀⠀⠀⢠⡴⠋⠀⡼⠁
⢜⡆⠀⠀⣀⣀⡀⠀⠀⠿⠀⣠⢴⠂⢠⣤⠀⣠⡀⢀⣠⢤⠄⠀⢄⠴⠋⢀⡔⠂⠀⠀⠀⡙⣆⠉⠐⠦⣄⣤⠀⢀⡤⡖⠖⠀⠀⠀⠀⠘⠃
⢀⡤⠶⠀⠉⠀⠉⠃⣤⠀⠘⠁⠁⠀⢀⣈⠉⠉⠀⠈⠀⠁⣦⠀⠀⠀⠀⠸⠂⠀⡠⣰⠆⠈⠛⠀⣀⠀⠀⡄⠀⡈⠁⠀⡀⣠⠟⠀⣶⠐⣶⡢⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⣀⢤⢤⡄
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠚⠀⡀
⢀⠀⠊⠈⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠀⢠⠿⠒⠑⡏
⣿⣂⡴⣄⣘⡇⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢇⣀⠀⠠⠂⠀⠀⠘⠀⠈⢉⣀⠀⠀⠀⢀
⠈⠀⠀⠁⠙⠣⠄⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⡌⠁⠀⠀⠀⡀⠀⠀⠀⠀⠈⣩⡵⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⢍⠀⠉⠀⠀⠀⠠⠴⣚⡁⠀⠂⠀⠀⠀⠒⠒⠐⣉⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠘⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⣿⣿⣿⣿⣿⣿⣟⡋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣆⣀⣀⣉⣉⣁⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠀⠀⠿⠷⠄⠀⢀⣤⣀⠀⠀⣴⡆⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠉⠀⠀⠀⠀⠀⠤⣀⠈⠻⠿⠿⠆⢛⠠⠾⠛⣫⣴⡖
⠀⠀⠀⠀⠀⠀⠀⢠⡀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡲⠴⠤⠄⠘⠷⠀⠀⠈⠉⠐⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠁⢀⣛⠂⠀⠀⣀⣀⢀⣀⠺⠿⠷⠂⢀⣴⣾⠆⠀⠀⠀⠙⠲⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡙⢛⢋⣉⣛⠻⠆⠸⣧⠘⠋⢡⣾⠇⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠇⠞⠀⠙⠛⣁⣤⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠻⠆








⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⣀⠀⠀⢠⡅⠐⠀⠉⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠈⠑⢤⠀⠀⠠⢊⠀⠀⠀⠀⠀⠀⠑⢄⢀⡠⣛⡆⢀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⡢⡀⠱⡀⠁⠀⠀⠀⠀⠀⠀⢀⢔⣫⣵⠊⢁⢁⠅⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠁⠀⠀⠀⠀⡀⢔⡬⠒⠉⢁⠸⠀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡥⠚⠁⠀⠀⠀⢐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠈⢆⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢆⠆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⢁⠊
⠀⠀⢀⠄⣒⠃⣿⣶⣤⠄⡪⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠶⠁⠀⠀⠀⠐
⢔⣪⣿⣛⣽⡿⢞⣩⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⡀⢈⠕⠉
⠀⠈⠉⠻⣵⠚⠅⠀⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢑⠠⠂⠁
⠀⠀⠀⠀⢱⠆⣆⠠⠊⠁
⠀⠀⠀⠠⠌⠊
⠀⠀⠀⠀⠀⢠⠀⠀⡠⠠⡀⡠⡢⠀⠀⡰⠂⠀⢀⢄⠀⠀⡀⠀⢀⠐⢀⠀⠀⡀⡀⡀⢀⢀⢀⢀⠀⢀⠀⢄

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣠⣤⣄⣀⣤⣤⣤⣤⣶⡶⣶⠶⡶⣲⡶⠶⠶⣶⣶⠞⠉⠉⠑⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣭⣭⣽⣻⣿⣿⣿⡿⠟⠛⠒⠻⠊⠌⠀⠀⠈⠐⠤⠤⣾⠏⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠜⢉⠟⠉⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣯⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠈⠆⠀⠀⢰⠀⡄⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣷⣛⣻⣷⣿⠶⣷⣶⣶⣾⣿⣆⠀⠀⠀⠀⢀⠅⠀⠀⠀⠻⣽⣧⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠿⠿⠿⢷⣤⣀⡠⠂⠀⠀⠀⠀⠀⠈⠻⢿⣷⣤⣤⡀⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣶⢶⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⠛⢙⠛⡻⠛⠛⠗⠻⠿⠿⠾⢿⣽⣷⣶⣶⡶⢶⣦⢤⣤⡤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠦⠤⠴⠣⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠛⠛⠛⠛⠛⠿⠛⠞⠿⢿⢿⣿⣿⣿⣶⣶⣒⣶⣶⣶⡆
⠀⠀⠀⠀⠀⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠚⠐⠒⠰⠿⠿⣿⣿⡿⠿⠿⠿⣿⣿⠏
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⠶⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⣿⣿⡷⠖⢛⣻⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣶⣶⣦⣤⣠⣄⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣤⣠⣤⣴⣾⣥⣤⣶⣿⣿⣿⠿⠿⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠀⠀⠀⠀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⠃⠀⠀⠀⠀⢠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠠⠆⠉⠈⡈⠉⣁⠉⠀⠀⠀⠀⣼⣿⣿⠿⣽⣶⣶⣶⣮⣉⠙⠁⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠴⠀⠀⠀⠀⢀⠀⢲⣂⣀⣤⣤⣶⠂⠀⡀⠀⠁⠘⠛⣩⠉⠿⣿⣿⡆⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠄⠀⣸⠃⠀⠀⠀⠀⠀⢈⡀⠁⣙⡂⠐⠛⢿⢷⣄⡀⠈⠃⣬⣿⡿⠁⢘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢌⣙⠀⠤⣄⣀⠀⠈⠉⠀⠩⠁⣠⡀⠀⢐⠛⢛⣛⡻⠞⠋⣤⡞⢾⣏⣀⣄⣈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠻⣶⣶⠄⠀⠀⠀⡀⠐⠓⠛⠓⠂⣙⡋⠩⣷⣴⡀⢠⡿⣧⣿⡟⠁⠀⠙⣯⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠁⠀⠀⠉⠄⠈⢸⠏⣿⠇⠀⠀⣠⡿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⠶⠶⠛⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠷⠟⠛⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⣷⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡴⣿⣗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⢀⣶⣿⡿⢟⣳⡄⠈⠉⠛⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢘⣿⣉⣻⣷⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠘⠀⠀⣛⡾⣿⣟⣩⣿⣥⡀⠀⠱⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⢁⣯⣽⡟⠉⣻⠏⣿⣾⣧⣤⣀⣀⠀⣀⢀⠀⣀⣁⣠⣶⣿⣫⢊⡽⣒⣿⣿⣷⠞⠀⠀⠀⢘⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢛⣥⡀⣌⠉⢙⠛⠻⠿⠿⠿⠿⠿⡿⠿⠿⣿⣟⢍⣯⣱⣝⠋⠁⠀⠀⠀⢀⢰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠞⠁⠰⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠉⠉⢁⠀⢀⡮⢶⡋⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠰⠤⠦⠤⠤⠤⣄⣢⣤⣄⣤⡐⠿⠯⠁⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⡆⠀⣴⣶⣶⣾⣷⠀⠀⣠⣤⣶⣾⣿⣿⣷⡀⠀⠀⣠⣶⣶⣶⣄⠀⢠⣶⣶⣦⣀
⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢻⣿⣿⣿⠟⠀⠈⠿⣿⣿⣿⡧
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⢻⠟⠉⠉⠀⠈⠻⠿⠿⠿⠿⢿⣷⡀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⢹⡟⠛⠃
⠀⠀⠀⠀⠈⢿⣿⠿⢿⣿⠟⠁⢀⣀⣠⣄⣀⠀⣠⣶⣶⣶⣤⡀⠀⢀⣶⣤⣄⡀⠀⢀⣤⣶⣶⣶⣦⡀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⣿⣿⣿⣿⣿⡇⠻⣿⣿⣿⣿⡿⠀⣼⣿⣿⣿⣿⠁⣾⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣶⣶⣤⣄⣀⠀⠈⠛⠿⢿⡿⠋⠀⠀⠀⠈⠉⠛⣷⠀⠉⠻⡿⠿⠃⠀⠻⣿⣿⣿⣿⠿⠋⠈⠛⢿⠿⠛⠃
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠆⠀⢀⣩⣄⡀⠀⢀⣀⣤⣤⣤⣀⠀⠀⠁⣀⣤⣤⣀⠀⠽⠟⠁⢠⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠉⠙⠻⣿⡿⣿⡟⢀⣾⣿⣿⣿⡗⢠⣿⣿⣿⣿⣿⣿⣷⠀⣼⣿⣿⣿⣿⣧⠀⠀⢠⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠿⡿⠿⠿⠀⠀⠻⠿⣿⣿⡿⠟⠃⠀⠘⢻⣿⡿⠿⠃⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠈⠁⣤⣶⣶⣦⣤⣤⣄⠁⠀⠀⠈⠙⠛
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣧⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⣶⣶⡄
⠀⠀⠀⠀⠀⠙⠛⢿⡏⠁⠀⠀⠈⢻⣿⠿⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠿⢿⣿⣿⣿⣿⡿⠀⢻⣿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠉⠉⠛⢿⠉⠁⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣯⣏⣶⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣟⣻⣿⣿⣷⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡯⢾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣫⢾⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⣿⣷⡾⣻⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣿⠕⠁⣺⠟⣡⣟⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢞⡫⠍⠉⠀⠂⠜⠁⣼⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢫⣱⠞⠉⡄⠀⡠⠀⠀⢀⣼⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢆⠼⠂⠀⠀⠠⠄⠈⡀⠀⢠⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣰⢏⣼⠟⡁⠀⠆⢀⠀⠀⠀⠄⣤⠞⣉⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣸⣿⣿⢯⡆⡠⠈⠀⠀⠐⠀⠀⠈⠐⣳⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣟⣕⣆⣨⡸⠄⢀⠀⣠⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠸⣄⡈⠻⣿⣿⣾⣥⣶⣥⣼⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣿⣿⣿⣿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⣆⣀⡘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢁⠔⠉⣿⡎⡟⣯⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⠎⠀⠀⡾⡇⠀⠼⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠊⠀⠀⠀⠃⠃⠀⠀⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⢠⠀⠀⡀⠀⢸⠀⠀⠀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡈⠀⠀⠁⠀⡞⠀⠀⢰⡇⢲
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡇⠀⠀⠀⠐⠀⠀⠀⠸⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⡘⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠐⡈⡆⠀⣀⠤⠐⠒⠀⠀⠀⠐⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⡼⠊⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⢀⣠⣴⠞⣫⣿⠭⠟⠙⠢⣀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⢀⠴⣏⣫⠧⠛⠛⠀⢀⣀⣞⠛⣻⠀⠀⠀⠀⣷
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠉⠀⠀⠀⠠⠁⠀⠈⠀⠀⢰⠶⠚⠁⡋⠠⠒⠁⠀⠀⠈⢴⣿
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠄⢀⠤⠂⠉⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⢀⠔⢁⡟
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⠊⠀⣠⡾⠁
⠀⠀⠀⠀⠀⢂⠀⠄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠒⠒⠉⠁⠠⠀⠈⠀⣰⠏
⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⢀⡤⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠹⠚⢢⡀⠀⠀⠀⠀⠀⢀⡠⠐⠁⠀⠀⣀⡀⠠⠤⠀⠀⠂⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢦⡈⠒⠒⠒⠒⠈⠁⠀⡀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠒⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⣿⣀⣤⡄⠀⣤⣄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣨⡴⠟⠉⠀⠀⢀⣀⣿⡿⠟⢃⣠⠇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠨⠿⡇⠈⠻⡉⠁⠀⠉⠈⠉⢳⠋⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⣠⡾⠋⠀⠀⣀⣴⠞⠋⠁⠙⣶⣾⣿⢷⡀
⠀⠀⠀⢀⡀⢀⡔⠋⠁⠀⠰⠿⠴⠆⠟⠀⠀⠀⠀⠠⣿⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠴⠃⣠⠞⠋⠀⢀⣠⠞⠉⠁⠀⠀⠀⢀⡼⠉⢹⡀⠁
⠀⠀⢰⠛⠁⠻⢅⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠸⡇⢺⡇⠀⠀⠀⠀⢀⡔⠀⣠⠞⠃⠀⣀⣴⠟⠁⠀⠀⠀⠀⢀⣴⠟⠁⢀⡼⣨⠁
⠀⠀⢠⠀⠀⠀⠀⣻⠁⠀⠈⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⠇⣾⡆⠀⠀⠀⢠⠊⣠⢞⠅⣀⣤⠟⠋⠀⠀⠀⠀⣀⣴⠞⠋⠀⢀⡴⠋⠀⠁
⠀⠀⠀⠂⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣀⢸⣗⣿⠁⠀⠀⣔⡵⠟⢁⣤⠾⠋⠀⠀⠀⠁⣀⡶⠟⠉⢀⣠⠴⠚⣩⠔
⠀⠀⠀⠀⠘⣷⡀⠈⣷⡀⠀⠀⡆⠀⠀⠀⣿⠀⠀⣱⣿⡿⠃⠀⠀⣶⠟⢂⡴⠛⠁⠀⠀⠀⣀⡴⠟⠁⣀⣤⠶⣿⠁⠐⠉⠀⠀⠀⣀⠀⣀⣀
⢢⣤⣄⠀⠀⠘⣷⣤⣼⣿⡄⢀⡂⠀⠀⠀⣿⣴⢤⡿⠋⠀⠀⠀⢰⡿⣱⡏⠀⠀⡠⠀⣠⡾⣯⣠⢶⡟⠟⠋⠀⠀⠀⠀⢀⡤⢶⡟⢉⡼⢁⣿⠛
⠀⢀⣿⣷⣄⠀⠀⠉⠙⠟⠿⡿⠿⠷⠾⠖⠉⠁⠀⠀⠀⠀⠀⠀⠈⢻⣟⡁⡀⢈⣠⡾⣧⡴⡻⠛⠁⠀⠀⠀⠀⠀⢀⡞⢹⠗⣿⠁⠜⢠⡿⠉⢀
⣾⠿⡉⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢴⣯⡵⠿⠟⠊⠀⠀⠀⠀⠀⠀⠀⢰⠍⣿⡈⠃⣿⠀⢠⠏⠀⠄⢁
⠀⠀⡄⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠚⠢⣶⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⠘⣷⣴⣿⣴⡏⢀⣤⡾⠋
⠀⢀⣀⣀⣀⣰⡇⠀⠀⠀⠀⠀⢠⣾⣀⣰⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣿⣶⣿⣿⣛⠛⣿⣋⠉
⠒⠛⢛⠛⠛⢻⡇⠀⠀⠀⠀⠀⠈⠲⢿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡙⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⠿⣟⡛⣋⡉⢀⠐⣼⣿⡷⠶⠒
⠐⠾⠿⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣌⠉⠛⢿⣿⣷⣦⣙⠻⢿⣦⣀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠳⣿⠿⣿⡿⣿⣿⣿⡿⢦⣀⡁
⣶⣾⣤⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣻⣿⣷⣦⡀⠉⠹⠿⣽⣷⣦⣉⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢁⣼⣯⡇⣿⢻⡻⣎⠑⢍⡛
⣍⣈⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣟⡻⣿⣷⣦⣄⠀⠈⠹⢻⣷⣤⣙⠻⢶⣄⡀⠀⠀⠀⠀⠀⠉⠻⢁⣻⡆⠳⡝⣷⣀⠙
⠛⠁⠀⠀⠀⠀⣀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣿⡿⣿⣿⣦⣄⠀⠉⠛⠍⡷⣦⣍⣻⠿⣦⣄⡀⠀⠀⠀⠈⠙⠑⠾⠷⣌⣿⡤
⠀⠀⠀⢀⡴⢀⡴⠒⠚⠓⠶⠶⣬⣁⠒⠄⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣾⣿⡿⣿⣷⣦⣀⠀⠬⠈⠳⠿⣳⣦⣉⡙⠿⣷⣤⣄⡀
⢠⡴⠦⢾⣷⣿⣤⣤⣤⣤⣄⣀⠀⠈⠛⠿⢾⣇⣀⣄⡀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣻⡿⣿⣷⣄⡀⠠⠒⢈⢷⢿⣿⣷⣦⡉⢻⣿⣆⡀
⠈⠁⢰⣤⣈⣻⠇⠀⠀⠀⠀⠉⠛⠳⠦⣄⣀⠈⠙⠻⠿⣦⣀⡄⢀⣀⠀⠀⠀⠈⠻⣿⣮⣻⢿⣿⣷⣄⠀⠘⠻⣿⣿⣿⣿⣿⣟⢿⣿⣦
⠀⠀⡞⢻⡿⠛⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣤⣽⣛⠓⠶⢾⣧⣀⠀⠀⠈⠻⣿⣷⣹⢿⣿⣿⣦⣄⣈⠙⠿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠂⡀⢧⡀⠀⠈⠛⠛⠶⢤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠷⠿⣷⠀⠀⠀⠈⠹⢿⣿⣾⣿⣿⣿⣿⣿⣶⣮⣽⣿⣿⡿⢿⣷
⠀⠀⠀⠑⡀⡛⠦⣤⣀⡀⠀⠀⠀⠉⠉⠉⠛⠷⠶⣤⣄⣀⠀⠀⠁⠁⠀⠀⠀⢾⡄⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠷⠶⣦⣤⣤⣤⣀⣀⣉⠙⠛⠳⠶⠶⠶⠾⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠤⠄⠠⡄⠀⢈⣉⣉⣙⣛⡲⠶⣶⡾⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣀⣤⡤⠤⢄⡀⣳⡄⠀⢀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠛⠛⠛⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠛⠛⠛⠻⠷⣶⣄⡀
⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄
⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣾⣄
⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣇⣶⣶⡀
⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣿⣿⣷⣿⣯⣥⠄
⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡾⠽⢿⣿⣿⣥⠄
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⣀⣹⣶⣦⣿⣿⣿⣟⡥
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣐⣾⡞⠁⢹⣿⣿⣿⣯⢾⠏
⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣩⠴⢿⣾⠞⣯⢻⣸⣧⣯⣤⠄
⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⢤⣰⣿⢻⣀⣰⣿⣋⠙⣿⣿⢿⣿⡿⠆
⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⢁⣏⣓⣿⣿⣿⣿⠛⢾⡿⠴⣿⠋⣩⠽⣇
⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠳⢾⣍⡿⠛⢿⣽⣿⣌⣿⡛⠙⣧⣾⣷⣤⠈
⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣤⣴⡷⢋⣹⣯⡤⠿⢶⠤⣿⡙⠛⣿⢧⢞⣙⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⡏⣸⣿⡁⡞⢽⠳⡍⢳⣸⡄⢸⡝⢦⢸⣟⣉⠉⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠻⣿⣴⠻⣄⡙⣷⣮⠷⢛⡫⠋⡇⢸⠀⢨⢿⡁⣠⣾⡅⣩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⡏⠙⠒⡾⠻⣄⠈⠫⣭⣭⣟⣋⡤⣾⣴⠋⡰⠋⢀⣿⢁⣀⢻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⡞⢆⢀⡄⣈⠉⢳⣙⣤⣹⣇⠀⢻⡓⠲⠾⠶⠤⠴⠚⢁⡼⠋⢀⣤⠿⣿⠈⣉⣠⣽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠶⣷⣿⣸⣇⣿⢶⣋⣉⠤⢬⡟⠓⣤⣉⣓⣲⣶⡦⠴⠒⠛⢒⣫⢿⣯⣅⠘⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠒⠶⢿⣿⣿⡛⠛⢉⢩⣿⡿⠂⢲⠞⢳⠤⠽⠓⢤⣤⣤⣔⣋⣁⣀⣁⣈⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣉⠛⣹⠿⣿⠗⣺⣿⢻⡇⠀⠉⠀⣀⣠⠴⣾⡉⠉⠗⣨⠏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⣰⠃⢈⡵⢿⣨⡷⠛⢛⣯⠤⠶⠛⠁⠉⠳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡾⠋⠀⠘⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⣆⢤⡀⠀⢀⠞⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⣧⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠶⢤⣄⡐⠿⠷⣤⡏
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢀⣀⣠⡤⠶⠞⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣥⣤⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⣻⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠲⠦⢤⣤⣾⡇⠀⣼⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣶⣶⣤⣀⠀⠀⠀⠀⢰⣿⠁⠸⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢸⣿⠁⠀⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⣿⠟⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢸⣿⠀⠀⠘⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⠷⠿⠿⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠈⠙⠿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣤⡄⠀⠀⣀⠀⠀⠤⠀⢶⣎⣉⠽⢛⡶⠛⠛⣩⡟⠀⣿⡿⠻⣅⠂⢶⣶⡆⠀⠀⠾⠟⠀⠀⣀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠁⠀⠀⠀⠉⢀⡀⠀⠀⠀⠁⠀⠈⠈⠁⠀⢺⠏⠹⣶⣦⣄⡀⠁⠘⠈⠁⠉⠁⣴⡄⠀⠀⠀⠋⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠗⠀⠀⠀⠻⠋⠀⠀⠀⠀⢸⠿⠃⡀⠴⠋⢀⠠⡿⠿⠉⠣⣶⡈⠃⣤⡄⠀⠛⠃⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠿⠀⠀⣠⣌⠀⠀⣈⣡⣾⡧⡄⠀⠀⠀⠀⠠⠛⠁⠀⣀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢠⣤⡄⠈⠁⠀⣠⣤⠀⠀⠀⠀⢛⠛⠋⠀⡉⠟⢻⡁⢀⡀⠀⠀⠸⠆⠀⠀⠀⠙⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠘⠿⢫⠀⢀⡀⠇⠀⠈⡟⠪⣴⣷⡀⡀⠀⠀⣤⣄⠀⠀⠀⢀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⢠⣤⡄⢠⡀⠀⠀⠀⢀⡀⠈⠃⠀⣴⣾⠀⠀⠘⠋⢡⡄⠀⠀⠻⠋⠀⠀⠀⠙⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠐⠟⠃⠀⢀⡲⠉⢹⡰⠖⠀⢀⣀⡀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣤⡄⠀⠀⢠⣤⠀⠀⠀⠀⠿⠃⠀⠸⠁⣀⠀⠘⠛⠁⠀⠀⣤⡄⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠁⠀⠀⠛⠀⠀⠀⠀⠁⠀⠛⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⠰⠶⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠖⣊⣉⠭⡤⠤⢤⠤⠬⢭⣙⡒⠦⣀⠀⠻⠷⣀⣀
⠀⠀⠀⠀⠀⡰⣡⣶⣋⣭⣥⣴⣶⣶⣶⣶⣧⣔⠀⠈⠑⠪⡻⣄⠀⠀⠈⠑⣄⣀⣠⠄⠀⠤⠄⠠⢄
⠀⠀⠀⠀⢀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣺⠗⠀⠀⠀⡹⣏⣹⠦⠤⠚⡁⠀⣀⡴⠂⠈⠀⠠⠊
⡴⢊⡭⠭⣙⣿⣌⠻⢿⣿⣿⣿⣿⣿⣿⣿⢿⡇⢀⣠⠤⣚⣹⡟⠋⢀⠄⣸⣷⣚⡉⠉⠀⠀⣠⣆
⣇⢸⡀⢀⡼⣿⣿⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⣍⣴⣿⣿⣿⢧⣤⡷⢞⣉⠁⠀⠀⠀⣴⣉⣠⣄⣙⡢⢄
⠘⢦⡙⠯⣄⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⣿⣿⠀⣌⢧⡀⠭⠀⢠⢶⡉⠻⠀⠉⠈⠉⠂⢘
⠀⣼⠙⡷⠦⣽⣟⠣⠀⠀⠀⠀⠀⠀⠀⠀⣌⠙⣿⣻⣿⣿⠇⢀⡿⣧⢿⣯⣭⣓⢦⣉⣀⣠⠤⠤⠶⠋⠉
⠀⢿⠠⠂⠀⠀⠙⢦⡀⣠⣄⣀⣄⣠⣀⣦⣿⣼⣿⣿⣿⣿⣶⣄⣠⡿⣻⣧⣩⣿⠟⠁
⠀⠘⢆⠠⠀⠀⠀⠀⠙⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣶⠤⠆⣱⣿⣍⣧⣽⣀⡀
⠀⠀⠈⠓⢤⡀⠀⢀⡀⠀⠀⠈⠙⠛⠿⠟⠿⠿⠟⠛⠉⠉⢀⣠⣾⣿⠛⢽⣿⣭⣿⢿⡆
⠀⠀⠀⠀⠀⠈⠓⠲⠤⣍⣁⣀⣀⣀⢀⣀⣀⣀⣠⣤⣶⣞⣩⣿⣿⣿⢀⡘⠿⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠛⠉⠉⠉⠈⠿⣯⠭⠶⣿⢿⣝⢧⣀⣾⣯⣽⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣎⢿⣼⠏⠳⠬⡅⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠶⠶⠶⣦⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣶⣟⡿⠋⡁⠄⠀⣠⡀⠈⠁⠒⠬⢝⡺⢷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠕⣿⡷⠉⢂⠕⠊⠀⠀⠈⣃⠐⠀⠀⠀⠐⢍⠲⣝⢷⣌⠷⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⡴⣫⠞⠁⣾⠏⡄⡔⠁⠠⠖⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠈⠎⢿⣦⣤⠖⢘
⠀⠀⠀⠀⠀⢀⡞⡴⠁⠀⢸⣼⠘⠨⠀⠀⠀⠁⡀⠀⠀⣴⠄⡀⢁⠀⠀⠀⠀⠀⠀⠘⣼⡇⣠⢾⣧⡀
⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣿⢿⢀⠀⠐⡀⡀⠀⠘⠦⠄⣀⣄⠀⠈⠀⠀⠸⠀⠀⠀⠀⡇⣿⣥⣀⡀⠀⠈⠀⠒⠄
⠀⠀⠀⠀⢰⠃⠁⠀⠀⠀⢻⠸⡈⠌⢆⢳⣕⢄⡀⠀⠀⢈⠃⡴⣋⢔⠵⠁⠀⠀⡸⢸⢹⣿⠟⠻⠉⢗⡶⠦⠤⠃
⠀⠀⠀⠀⢸⠠⠀⠀⠀⠀⠈⣧⠱⡀⠀⠀⠙⠻⢟⣓⠶⣤⡁⣴⡿⠃⠁⠀⢀⠜⡱⢣⣿⠛⠃⠀⠀⠈⣧
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠘⣷⣙⢦⡈⠲⢄⡀⠀⠉⠢⢱⠇⠀⠀⠀⠔⣡⢞⣵⣿⠁⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⢍⡲⠤⣌⣁⣀⣀⣀⣀⣠⠤⢖⣫⠴⣻⠞⠁⠀⠀⠀⠂⠀⠀⡟
⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢂⠈⠻⡷⣍⣙⡒⠲⠾⠭⠶⠶⠒⢛⣉⡴⠞⠁⠀⡀⠠⠀⠌⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠠⡣⡈⠮⡛⠻⠷⠶⠶⠶⠖⠛⠋⠉⠀⠀⠠⠊⠀⢀⠌⠄⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠓⠀⢀⠀⠀⠀⠀⠀⠀⡀⠄⡪⢀⠕⡡⠊⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠈⠂⢅⡀⠀⢀⠀⠈⠀⠀⠀⠂⠉⢀⠁⠊⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⠄⣢⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣗⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣖⣫⠵⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠯⠭⣿⣿⠿⠭⠭⠷⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⢰⣶⠿⠷⣿⣿⣶⣿⣿⡯⠙⡿⠛⠉⠋⠉⠉⣉⣙⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠖⠒⠒⠠⡀
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣥⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣾⣛⣷⣷⢶⣶⣶⣶⣿⣦⡀⠀⠀⠀⠄⠀⠀⠈⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠿⠦⠄⠂⠀⠀⠀⠀⠀⠉⠻⠿⠶⠤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⡿⠿⡿⣿⢽⣟⣳⣶⣖⣲⡤⢤⣀⣀⣀⣀⣀⢀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣉⣀⣀⠀⠐⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠙⠓⠶⠿⠿⠿⠿⠿⡿⢿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⢺⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠲⠚⠻⠿⢿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠻⣿⣿⠶⠶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠙⢛⣻⣿⣷⣛⣛⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠈⠛⠿⢾⣶⣴⣤⣄⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠴⠴⠶⠥⠶⠶⠷⠷⠿⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢁⢠⠂⠀⠰⡁⠀⠀⢀⠀⠀⠀⠀⠆⠀⠀⢀⠀⡀⡐⡐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠀⠃⠀⠃⠈⠈⠀⠀⠈⠘⠀⠁⠋⠀⠀⠁
⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⣶⡄⠀⠀⠠⣶⠀⠀⠀⢠⣶⠀⠀⠀⢠⣦⠀⠀⠀⣴⡆⠀⠀⠀⣶⠀⠀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠃⠀⠀⠀⣿⠀⠀⠀⠸⣿⠀⠀⠀⢸⣿⠀⠀⠀⢻⡇⠀⠀⠀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢸⡿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠘⡇⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⢠⣾⣿⡆⠀⠀⣿⠀⠀⠀⠈⠀⠀⠀⢠⣾⣿⣦⠀⢠⣾⣿⡆⠀⢰⡿⠷⡄⠀⣾⣿⣦⠀⢰⣿⣷⡄
⠀⠀⠀⠀⠀⢸⣸⣧⡇⢰⣄⣀⣠⣤⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠈⣿⣿⡇⠀⣿⣿⣾⡇⠀⢻⣷⡏⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠘⠛⠛⠃⠈⠛⠿⠟⠁⠀⠀⠒⠀⠀⠀⠙⠛⠋⠀⠀⠛⠛⠁⠀⠛⠛⠛⠛⠀⠈⠛⠁⠀⠘⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣻⣿⣿⣆⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣧⠞⠋⠁⢹⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣽⠟⠁⠀⢀⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⣻⡾⠟⠁⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠟⠉⡠⠖⠉⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⠀⠈⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣃⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣤⣿⡷⠛⠉⠉⠀⠈⠑⢰⡖⠛⣁⠒⠂⢄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣤⣠⣀⣴⣿⣿⣿⠃⠀⠀⠈⠀⠄⠀⠈⣿⣿⠈⠄⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠋⠹⠀⠀⠀⠀⠀⠀⠀⡼⢹⣧⣤⣤⡶⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠑⠤⣄⣀⡤⠖⡺⠔⠿⠿⠯⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠤⠠⠀⠒⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠤⠀⠀⠀⠀⠀⠠⠤⠍⡒⣤⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠄⠒⠈⠁⠀⠀⠀⢀⢀⠀⠠⠄⠒⠒⠒⠒⠀⠤⠤⢼⠀⠀⠀⠀⢘
⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢀⡀⠠⠔⠂⠈⠉⢀⠀⠀⠀⠠⠄⠀⠒⠂⠀⠉⠉⠀⠀⠀⠀⠀⠀⠠⠤⢀⠢⠄⠹⠗⠐⠀⠉⠉⠁
⠀⠀⠀⡐⠀⠀⠀⠀⡠⠔⠈⠀⠀⡀⠄⠐⠀⠁⠀⠀⠀⠀⠀⡀⠤⠀⠀⠂⠀⠉⢁⡀⠠⠤⠀⠂⠀⠈⣀⠤⠀⠁
⠀⠀⠀⠀⠀⡀⠔⠁⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠀⡀⠔⠀⢁⡀⠄⠂⠈⣈⠀⠤⠐⠒⠀⠀⠀⠉⠉
⠀⠀⠒⣤⠊⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⡀⠔⠈⠀⢀⠠⠂⠁
⠀⠀⢁⢠⠄⠊⠁⠀⠀⠀⠀⠀⠀⡠⠐⢁⡠⠐⠁⠀⠀⡠⠂⠁
⠀⠀⠈⢆⠀⠀⠀⠀⠀⠠⠔⠒⣁⠄⠂⠁⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠐⠢⢄
⠀⠀⠀⠈⢬⡉⠁⠤⠤⠄⠂⠉⠀⠀⠀⣀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠒⡳⠲⡇⡘⢸
⠀⠀⠀⠀⠀⠁⠒⠂⠀⠀⠀⠠⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡡⠀⠰⠁⠀⠈⣧⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⡜⠀⢠⠁⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠤⠤⠔⠒⠀⠉⢀⠤⠊⠀⠀⠆⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠔⠊⠀⠀⢀⠐⠁⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⡔⠉⠀⠀⣀⠠⠄⠀⠐⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⡸⣄⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁⠀⠀⠀⠀⠀⡠⠊⠁
⠀⠀⠀⠀⡇⠘⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠤⠔⠂⠉⠀⠀⠀⠀⠀⡀⠄⠂⠁
⠀⠀⠀⠀⣆⡔⠉⠉⠒⠒⠒⠒⠒⠀⠀⠒⠒⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠒⠉
⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⠤⠀⠀⣀⣀⡀⠤⠄⠐⠊⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣻⡛⡛⢛⡛⣻⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣠⣿⣄⣀⣩⠶⠛⠉⡠⠴⠶⢿⣷⣦⠤⠒⠉⠀⠀⠀⠀⠀⠀⠈⢢⡀⠈⢑⠪⣐⣌⢦⣄⡀⠀⢀⣀⣴⠿⠷⠖⣲⣶⡿⠶⢷⣕⣄⠹⡟⠉⠐
⠴⠯⢄⡼⠋⠁⠀⠀⠀⠀⣢⢝⣻⡎⠁⠀⠀⠀⢀⣤⠒⠋⠀⠀⠒⢞⣀⠴⠖⠐⠛⠋⢉⣩⠟⠛⠋⠁⠀⠀⠀⣡⠜⠋⠉⠉⠙⠳⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣴⠋⠀⠀⠀⠀⠀⠒⠉⠐⢁⠒⠁⣀⣠⠤⠴⠿⢧⣄⡀⠀⠀⠐⠂⠁⢀⡀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣠⠖⠁
⡞⠁⠀⠀⠀⠀⠀⠀⠀⠔⣊⠵⠛⠋⠁⠀⠀⠀⠀⠀⢮⣿⡂⢌⡓⢿⣰⠋⢿⣶⣤⣧⡀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠏⠁⠀⠲⢶⠋
⣷⡤⠔⠋⠉⠐⠲⣤⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣽⡇⠀⠉⡞⠁⠀⠀⠁⠀⠈⠻⣷⠀⠒⠒⠂⠠⠼⣇⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠳⣶⠶⠦⣤
⡈⠁⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⣀⣀⣤⣪⣿⡿⠃⠄⠙⡇⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠠⣀⠢⣍⠲⡴⢳⠶⣿⣋⣀⠀⠀⠀⠀⠀⠀⠘⠋
⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡤⠒⠂⠉⠀⠀⠀⠀⠈⠢⣄⣤⠬⠧⠄⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⡀⠀⠙⠂⠩⣿⡧⠊⣡⢿⠋⢻⡦⢄⡀⠀⠀⠀⠇
⠈⠳⣄⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠺⡁⠀⠀⠀⠈⠑⠬⣀⠄⣸⣷⠰⠃⠈⠀⢸⡧⡀⠍⠢⣀⡀⣂⣀⣀
⢳⡀⠙⠳⣤⣀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠛⠛⠛⠒⢦⡀⠠⢀⣅⣋⣻⣽⠏⠀⠀⠀⣠⠟⠡⠈⠢⠀⠙⡙⠁
⢸⣧⡶⠛⠁⠀⠀⠀⠐⠖⠒⠛⠳⠶⢶⣶⣶⡿⠿⠖⠚⠛⠛⠻⢿⡄⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⣿⠶⣦⣤⠴⠿⠟⠒⠐⠃⠚⠻⠦⣄⠀⠀⠑⠀⠐
⣼⠃⠙⣄⠀⠀⠀⠀⠀⠀⣀⡵⠖⠋⠩⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⡈⠁⣾⠀⠀⠀⠀⠀⠀⠀⢀⣿⠚⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠁
⡋⠀⠀⠈⢷⡀⠀⠀⠀⡟⠁⠀⠀⠊⠀⠀⢀⠒⠲⢦⡤⣄⣴⡟⠁⠈⠛⠛⢷⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⢀⣠⣼⠛⠛⠳⢦⡀⠀⣀⣠
⠿⣳⢶⢦⡄⠙⠷⠄⠨⠳⣤⡀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠉⠳⣄⠀⢀⠠⠛⢊⠉⢹⠷⣶⣿⡁⠀⠀⠀⠀⠀⠀⠈⠟⠛⠛⢿⠋⠉⠀⠀⠀⠀⠘⣿⠎⢉⠄
⡴⢃⠃⣨⠿⠀⠳⡦⠀⠀⠀⠙⠳⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⠡⡢⠊⡠⠂⢁⢾⣽⢀⢻⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⡾⠀⠀⠀⠀⠀⠀⢸⣟⠀⠠⠊
⠁⣴⡿⡁⠀⠀⠀⠑⢦⣄⡀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⢀⠂⢀⠄⠀⠂⠀⢀⡇⠀⠈⠉⠉⠙⠓⢦⣤⣤⣄⡀⠑⠀⣼⣷⣶⣶⣤⣤⠀⣠⡿⠁
⢸⠃⡀⠀⠑⠄⡁⠀⠀⢉⣻⠷⠒⠒⠒⠀⠒⠂⠓⠦⣤⣀⣤⢴⠃⠀⠂⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡈⠙⣻⠞⠋⠉⠁⢀⢖⡿⠾⠟⠁
⢺⡀⠈⠁⠀⠀⠈⠓⢄⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢤⠶⣬⣑⡄⠀⠀⠀⠠⠀⣠⡾⠋⠉⠀⠀⠀⠢⠀⠀⠀⠀⢸⡷⠚⠁⠀⠀⠀⠠⢂⣞⠁⠀⠀⠀⠂⠀⢀⠔
⠀⢳⡀⠀⢤⣦⡀⠀⢌⠀⠘⢧⡀⠀⠀⠀⠀⠄⡀⢠⡄⠀⠉⠇⡄⠀⠀⢀⣼⠏⠁⠂⢄⠀⠀⠀⠀⠈⠢⣠⡶⠛⠁⠀⠀⠀⠀⠐⣱⠋⠈⢰⣆⣄⣀⣠⠄
⠀⠀⠙⠶⣄⡀⠀⠀⠀⠢⣑⣄⠙⣦⡀⠀⠀⠀⠈⢹⠂⠀⠀⠈⠻⠿⠟⠛⡇⠀⠢⠀⠀⠁⠢⢄⠀⠀⠀⠱⡀⠀⠀⠀⠀⢀⣴⠞⡁⠀⠀⡇⠀⠉⠛⠉⠒⠢⣄
⣦⠀⠀⠀⠈⠙⠳⣦⣌⣣⣬⣹⡷⠽⠿⢶⣄⡀⠀⠆⣦⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢄⠀⠀⡀⢇⠀⠈⢢⣷⠴⠂⠐⠚⠛⠀⠀⡈⠲⠼⠁
⢸⡗⢛⠉⠉⠉⣻⡿⠟⠋⠁⠀⠀⠀⠉⠁⠈⠙⣳⠶⣶⡶⣀⠀⠀⠀⠀⣼⠏⠙⢦⡈⠉⠁⠀⠈⠢⡐⣄⠈⣿⡇⠀⠠⠀⠀⠀⠀⠈⠐⢤⡄
⠟⢱⢶⣄⣠⡛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠈⡐⠀⡎⢲⠠⠄⣴⡟⠀⠀⠀⠙⠳⢦⣄⡀⠶⣎⠺⣧⡘⣇⢀⡠⣄⡀⠤⠀⢘⠀⠈⣿⣦⣀⠀⠀⠀⢀⣠
⠀⢡⠀⠈⠛⠉⠛⠳⢦⡄⠀⠀⠀⠀⢀⠀⡊⠰⠠⠀⠃⠀⣃⡀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⢈⠟⠻⠿⣿⣿⣿⠿⠋⠀⠉⢀⠎⠀⣤⣷⣾⠿⣈⡙⢿⣗⡞⠋⠁
⣀⠄⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⢀⣤⢾⡇⠀⡀⠀⠀⠈⠉⠉⠙⠺⣷⡾⠷⠦⠤⠤⠴⠖⠁⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⡐⢒⣶⣷⡟⢉⣛⠻⠿⢿⡿⠃
⠀⠀⢄⠀⠀⠀⠀⠀⠀⢀⣴⠿⠞⠻⠋⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⣴⢋⠀⠀⠚⠁⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⢀⡴⠛⠛⠋⠀⠀⠀⠀⠙⢢⡢⢌⣻⡿⠛
⠀⠀⠀⠠⡀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⢰⡿⠅⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⠀⠻⣿⡄
⠀⠀⣀⣠⡼⠶⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⣦⡀⠀⠀⠀⠀⠀⠉⠛⠶⣶⡶⢶⣿⣛⣧⠀⠀⠀⣀⡴⠚⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠑⠪⣕⣀⢿⡇
⠛⠋⠉⠉⠀⠄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⠋⣸⣶⠿⠛⠲⣤⣀⣀⣀⣤⣀⣀⣹⡆⠀⠉⠉⠉⢳⡖⠋⠈⠓⠒⠒⣟⡲⠶⠶⠶⢾⣿⣍⡀⠑⠦⢬⣭⣧⣾⡟
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⡤⠤⠤⠤⠊⠁⠀⢹⡀⠀⠀⠀⠀⠈⠉⠉⠠⢍⡣⡍⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⡀⠀⠀⠉⡆⠀⠐⣄⣆⠈⠙⠓⠶⠶⠞⠋⠀⢳
⠉⡿⣿⠀⠀⠀⠀⠀⣄⣵⣼⣦⡀⠀⠀⠀⠀⠀⣀⠽⠶⠆⠠⠤⡀⠀⢄⡀⠀⡁⠘⡄⠀⠀⠀⠀⠀⠈⢳⣄⠐⠚⠂⠀⠑⢌⢀⠀⠺⣿⡄⠀⣀⡠⣤⠶⠖⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⣉⠖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡛⠁⡱⠞⠉⠐⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠚⠆⠀⠀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⡀⠉⠙⠒⠢⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⣀⡤⠠⠐⠀⠀⡀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠈⠉⠑⠒⠂⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⡾⠃⠀⠀⠀⠀⠀⠈⢣⣤⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⠁⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⡀⠀⠀⠀⠀⣹⠁⠀⠁⠀⠀⠀⠀⠀⠀⢀⣈⣳⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠱⣄⠀⠀⢰⠻⠀⠀⠀⠀⠀⠀⢠⠔⠉⠁⠀⠀⠀⠉⠉⠐⠄⡀⠀⠀⠀⠀⠤⠀⡀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⣑⠒⠘⣇⠣⡀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠉⠑⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢦⣈⠐⠠⣄⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠄⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠤⡆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣤⡤⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠑⢄⡀⠀⠀⠀⠀⢀⠠⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠈⠳⢤⣈⠐⠢⠤⠄⠤⠤⠔⡺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠒⠉⠀⠀⣴⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢤⡀⢻⡆⢰⡟⠙⣿⠀⣶⠀⣰⡄⢠⡞⠑⣶⠀⣯⡀⢸⣏⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠁⢘⡿⠸⣇⢼⣟⡐⣿⠀⣿⠁⠾⣇⢼⡇⣰⡈⣷⢸⡟⢠⣿⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⣠⠞⠁⠀⠀⢸⡿⠀⡈⢁⠘⡂⣀⢀⠈⡋⢀⠀⡋⢈⠁⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠼⠀⠓⠂⠃⠛⠛⠀⠃⠘⠃⠃⠀⠂⠛⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⣠⠄⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣼⡏⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢻⣧⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠻⣷⡀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢹⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⡼⠃⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠀⠒⠒⠂⠒⠒⠒⠒⠐⠒⠒⠒⠒⠐⠒⠀⠠⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡖⢉⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⡍⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⣇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠳⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡰⠁⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣃⠤⠊⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣁⣀⣀⠤⠐⠁
⠀⠀⠀⠀⡠⠄⠒⠒⢈⣉⣭⣤⣬⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣧⣤⣤⣤⣉⡁⠒⠒⠠⢄
⠀⠀⠀⠀⠢⢄⣀⠀⠛⠿⠿⣿⣿⣿⣿⣿⣶⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⢀⣀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⢤⡀⠭⠭⠉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠭⠭⢀⡤⠒⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠂⠀⠤⠤⠤⠤⠤⠤⠀⠐⠒⠒⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⡀
⠀⠀⠀⢤⠂⠀⢨⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢰⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠈⠇⠀⠀⠀⠀⣀⠴⠖⠒⠲⢤⡀
⠀⠀⠀⢹⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠸⠀⠀⠀⠀⢰⠃⠀⠀⠰⠂⠀⠙⡄
⠀⠀⠀⡆⠇⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠓⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⡇⠀⠉⢀⡀⠒⢀⢷
⠀⠀⠀⠡⣀⡀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⢀⡌⠀⠀⠀⢀⡤⣀⢹⠀⡀⠀⠑⣄⠁⠈
⠀⠀⠀⠀⠀⠹⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡀⠈⠛⠀⠀⠰⠁⢀⠆⡆
⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢸⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⢧⠀⠠⠀⠁⣀⠜⠣⠀⡇
⠀⠀⠀⠀⠀⠀⢡⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡎⠁⠈⢧⠀⠀⠀⠀⠀⢠⠃⢨⠁⠀⠀⠀⠀⠀⠀⠈⢇⠀⠐⠊⠀⠒⠁⢀⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠈⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⡞⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⣤⠄⠒⠒⠊⢉⣇⡀
⠀⠀⠀⠀⠀⠀⠸⠀⠀⢱⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢠⠀⠀⠀⠀⣸⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢷⡻⡄
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠈⡇⠀⠀⠀⡇⠐⠞⢠⠀⠀⠀⠀⠀⢹⢀⠀⠀⢸⠀⠀⠀⢠⠇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠦⠞⠁⠀⠀⠀⠙⠦⠴⠋⠀⠀⠀⠀⠀⢸⠈⠀⠀⢸⠀⠀⠀⡜⠀⡌⡌⠀⠀⠀⠀⠀⡠⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡇⠀⠀⠀⠇⠀⢱⠁⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠘⣄⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠉⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⡴⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠡⠊
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⢁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠉⠂
⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡸⠀⠀⠀⠀⠀⢘⡞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⢄⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⢀⡞⡇⢹⣗⠄⠀⠀⠀⠀⠀⢀⠊⠀⠀⡀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⣾⠁⣇⢰⠹⠈⠀⠀⠀⠀⠠⠁⠀⠀⠠⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠸⣿⡀⢘⣦⣀⡴⠀⠀⠀⡐⠁⠀⢀⠀⠆⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠯⠴⠋⠀⠀⠀⡐⠀⠀⠀⠊⠐⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⢀⠈
⠀⠀⣠⠔⠉⠁⡰⠉⠉⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢱⠄⠤⠐⠁
⠀⠀⡇⠮⠵⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⡠⠀⠀⠀⠀⠀⡠⠊⢠⠃
⠀⠀⠈⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⣀⣠⡞⠀⣴⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠀⠀⢙⠶⢿⣇⣠⠖⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⢀⠖⠀⠀⠀⠉⠈⠙⢻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠁⠀⡀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠁⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⡠⠴⠚⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⡭⠁⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⡠⣴⠞⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⢠⠔⠁
⠀⠀⠀⠀⠀⢀⠜⣽⡟⠁⠀⠀⣀⠊⠉⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢁⡤⠊⠀⠀⠀⠀⠀⠀⠠⠤⢤⣀
⠀⠀⠀⠀⠀⡜⢰⣿⠁⠀⠀⡴⠀⠀⠀⢀⣠⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⡇⢸⡷⠀⠀⠊⠀⣰⣢⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠐⠄⠁⠀⢀⣤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠁⠈⣀⠀⠀⣷
⠀⠀⠀⠀⠀⢳⣿⡁⠘⣇⢹⣿⡋⣉⠀⠀⢀⣀⣀⣠⣤⡖⠶⠾⠋⠘⠁⠀⠀⣀⢤⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢦⠀⢀⣀⠀⣿
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡓⠛⠛⠛⠛⠋⠉⠉⠉⠁⠈⠀⠀⠀⢀⡤⢶⡋⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⢀⡀⠀⢸⣦⠈⠋⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠙⢶⣾⣻⡖⠥⢶⣀⡄⣂⣀⣀⣴⢶⠧⢴⠮⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠶⠖⠀⠀⠀⠈⠁⠀⢸⠏⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠷⠜⠊⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠐⣄⠀⣠⡶⠀⣰⡄⠙⠋⢀⡘⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠈⠛⠃⠀⠀⠈⠁⠀⠀⢸⡆⠀⠀⠀⠈⠀⠀⣠⡾⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠘⠛⠁⣀⠀⠀⠀⠒⠀⠀⢸⣧⣠⣤⣠⣄⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠘⠋⠀⠭⠆⠀⢀⡼⠋⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣶⣄⣀⠀⢀⣀⣠⡆⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢢⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣧⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠓⠒⢦⣄⠀⠀⠀⣸⠀⢀⣴⣋⡁⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠖⢻⠀⠀⠀⠀⠳⣄⡀⠐⣽⡀⠀⠀⣿⡴⠛⠻⣄⣀⣀⣀⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⢦⡀⠀⠀⡟⢀⠄⢀⡟⠀⠀⠀⠀⠀⠈⠉⠉⠁⠙⢦⣸⠟⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⣇⣀⡤⠟⠷⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣧⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠀⠀⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠉⠁⢻⣌⠉⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠉⠁⠙⢧⡉⠙⢷⣄
⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⢀⡀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠉⠛⣦⠀⠘⣷⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣀⣸⡇⠀⠀⠙⣧
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣤⣬⠃⠀⠀⠀⠈⣧⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣤⣦⡴⠋⠀⠀⠸⡇⠀⠀⠀⢠⡏⠀⠀⠀⠠⡿⢿⣟⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢾⣿⠏⠀⠀⠀⠀⢀⡟⠀⠀⠀⠘⣇⠀⠀⠀⠀⠸⣿⠟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣇⠀⠀⠀⠀⠔⡾⢸⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢻⣄⠀⠀⠀⠐⠟⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢻⣄⠀⠀⠀⠘⡇⠁⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉




⣿⣿⡿⠿⣿⡿⢿⣿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣷⣮⣶⣷⣶⣿⣶⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⣰⡁⢀⣀⣤⣴⣶⣾⣿⣿⠿⠿⠿⣿⣿⣿⢿⣿⣟⣛⣛⣛⠛⠻⣛⡿⠿⣿⣿⣶⣦⣄⡀⠀⠀⠀⡉
⠀⠀⠀⠀⣦⠻⣿⣿⣿⠿⣿⣿⣿⣿⣷⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣷⣬⣉⣙⢻⣿⣷⣆⣴⢁⡼⢀⣠⡔⠂⠉⠀⠲⣄
⠀⠀⠀⠀⢻⡷⢈⣛⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣥⣾⣿⣿⣣⠴⠀⠀⠈⠙⣿⡄
⠀⠀⠀⠀⢈⠁⠀⠀⠁⠀⠉⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⡛⠛⢋⢡⣴⣾⡯⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠈⠼⣿⣿⡯⢸⣿⡿⠟⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⣻⣿⣧⣾⠇⠀⠀⠀⠀⠀⠀⠊⡀⠁
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣷⡏⠀⠀⠀⣀⠤⠚⣡⠜
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣤⡴⠒⢊⣁⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⡞⣿⣿⡿⣛⣉⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠙⠟⠛⠛⠉⠁