Earth Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠀⣾⠟⠉⠑⠂⠀⠠⣴⣿⣷⣦⣤⣤⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣛⣽⣿⡇⠀⠀⠀⠀⠀⠐⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠟⠈⠁⠀⠀⠀⠀⠀⢰⣾⣟⣛⡿⢿⣯⣽⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣶⣴⣯⣽⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢠⠟⠋⣽⣆⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡀
⠀⠀⠀⠀⠸⠺⣇⣈⣭⣩⡇⠀⠀⠀⠀⠀⠈⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠹⡟⠃
⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⢣⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣿⣷⠀⠀⠀⠀⣠⣤⣤⣤⣤⣶⣾⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠾⠿⠿⠿⠿⠿⠟⠛⠋⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⡢⠄⠉⡁⠀⠀⠀⢀⠉⢀⠰⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢦⠁⡠⠐⠅⠀⡀⠔⠁⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⡄⠊⠴⠔⠐⣡⢠⠀⠀⢀⠔⢈⠉⠈⡦⠊⠐⠃⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⡔⢁⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠫⣀⡟⢃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠓⠲⠒⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠀⠈⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⢦⡇⠀⠀⣀⡀⠀⠀⠀⣀⠀⠀⠈⢨⠱⡀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⣀⠔⠊⠉⠀⠉⢆⢀⠾⡖⠋⠀⠀⠈⠢⣸⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠸⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠐⠊⠉⠀⢀⠀⠐⢉⡀⠑⠊⢈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢐⢰
⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠉⠈⠁⢊⣆⠀⠀⠈⢯⡡⢬⠉⠑⢆⠀⡠⠈
⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⠀⠀⠀⠀⢀⠆⠀⠀⠇⠰⡀
⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⣄⠠⠖⠁⠀⠀⠀⠈⠱⢰
⠀⠀⠇⠀⠡⠀⠀⠀⠀⠀⠡⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⠆⠇⠀⠀⠀⠀⠄
⠀⠀⠀⡄⠀⢰⠀⠀⠀⠀⠀⠅⠒⠄⠠⠄⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠀⠀⠀⠀⠀⠈⢠⠃
⠀⠀⠀⠱⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠐⣌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⣨⢁⠒⡁⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠐⠄⡀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⡠⠊⠁⡣⠀⠁⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⣈⠀⠀⠀⠀⠀⠀⠀⠁⢄⡀⣀⠤⠒⠁⠀⠀⢀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠤⠀⣀⣀⡀⠀⠀⣀⣀⠠⠤⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢋⣹⣿⣿⣿⡿⠿⠟⢿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⣀⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⡟⠿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⣨⣤⣶⡄⠀⠀⠀⠀⠀⠀⣤⣤⣶⣶⣦⣄⡀⠀⠀⠀⠹⢿⡦⢻⣿⣿⣿⣟⢳⡄
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠤⣿⣿⣿⣿⣷⡀⠠⣤⡀⠀⠘⠿⠙⢿⣿⣿⣿⣿⡆⣠⣤⠀⠀⢦⣄⣻⣿⣿⣟⠣⣿⣆
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣽⣧⣴⣺⣷⣦⡀⠉⢻⣿⣿⠀⠙⠁⠀⠀⠘⠯⠛⣿⣿⡇⢠⣽⣿⣆
⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⣼⣿⠆⠈⠿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣼⣿⣿⣿⡄
⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣷
⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼
⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⡿⠉⠉⠋⠉⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣇⠀⢀⡀⠀⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣇⣀⡀⠀⠉⠁⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⠀⢀⣠⣤⣤⣤⣤⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡿⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡞⢫⡌⣿⣿⡿⠁⠈⠀⠀⠀⠈⠉⠓⢲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠈⢸⣿⣷⣾⡟⠆⢻⡿⠃⠀⠀⠐⠆⠀⠈⠙⢄⠀⠛⡙⠿⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦⣿⣿⣿⣿⠿⠂⠀⠃⠀⠀⠀⠀⠀⢀⣀⡆⠀⣠⣤⣿⣶⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⣇⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠁⠐⠂⠆⠀⠀⠀⠀⠀⠀⠤⠀⣾⣿⡿⠋⠉⡟⡬⢿⡿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣾⣿⣷⣽⡀⣈⣀⡄⣠⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⣿⣿⡟⠉⠉⠀⠛⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠿⣧⣤⣶⣈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠙⣿⡁⢀⣄⣀⡀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣟⡛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⣿⣿⣿⣿⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢐⠀⠀⠀⠀⠀⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⡿⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠉⠀⠐⢸⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⢁⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⢻⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⠂⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠁⠀⠀⠻⠳⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠈⠒⠴⢦⣾⣄⠀⠠⠄⠀⢀⣤⣶⣶⣾⣶⣶⣶⣞⡁⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⠿⢿⣿⣷⣶⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢻⡟⠻⢵⣶⣮⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠛⢉⣥⣴⡾⢟⣴⣿⣏⣀⣴⣶⣿⣯⣿⣿⣿⠟⠁⣴⡀⠘⠋⠉⠁⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠈⠹⠋⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣟⣏⡻⠋⠚⠋⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⣠⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⢀⣤⡤⡄⢀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠚⠛⠉⢿⡿⢿⢶⡦⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢰⠀⢰⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠳⠶⣤⣤⣠
⠀⠀⠀⠀⠀⠀⢸⣦⣬⣁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣯⠁⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣰⣿⣃⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣰⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠛⠛⠋⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣯⢡⡴⣶⣤⠞⠛⠋⠉⠛⢳⡄⠀⠀⢀⣤⡴⠟⠛⠛⠷⣤⡀
⠀⠀⠀⠀⠀⢀⣴⠟⠁⠸⠧⠴⢬⣩⣽⡛⣦⡀⠀⠀⠈⢷⠀⠀⠘⠷⠶⠶⣦⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⡟⠀⢀⡤⠟⠀⢀⣤⣤⣤⠶⠟⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠳⠤⠟⠀⠀⠀⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⢰⡇⠀⠀⢀⣠⣤⣤⣀⣀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣉⣛⡛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⣼⠛⢶⡀⢸⠁⣠⣤⣈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣤⣾⠁⠀⠉⠛⣯⠉⢿⣄⠀⠀⣴⠲⣄⠀⠀⠀⣧
⠀⣿⠀⠸⣧⣿⣀⣉⡙⠛⠃⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠸⠿⠶⣦⣻⣤⣤⡿⠀⠈⣿⠀⢀⣿
⠀⣿⠀⣰⠟⠀⠀⠈⠙⠦⣤⡀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢻⠇⠀⠻⡴⠋⡿
⠀⢿⠀⣿⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⠈⠛⠛⠉⠛⢷⡄⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢠⡇
⠀⢸⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣶⠛⠀⠀⣠⠖⠒⢺⠇
⠀⠀⢻⡙⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⢿⣤⡄⢼⡋⠀⢠⡿
⠀⠀⠈⢷⡀⠀⠙⢳⡄⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣼⣿⡇⣸⡃⣠⡿⠁
⠀⠀⠀⠀⠳⣄⠀⠀⣿⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡟⢹⠟⠁⢉⡽⠋
⠀⠀⠀⠀⠀⠈⠳⣄⠹⣆⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡴⠟⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣳⣾⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⣀⣠⣤⣤⣤⣤⡤⣤⣬⣍⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠐⡿⠛⡟⠉⠏⢀⡀⠬⠷⣌⡉⣫⣹⢿⣿⣷⡒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡄⠀⠀⠀⠀⠀⠀⠁⠛⢿⣧⠀⠀⠀⠈⣿⣿⠛⣿⣿⣿⡝⣷⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⣀⣤⣴⠃⣨⡿⠀⠀⠀⣸⡿⣻⣿⣿⠟⠙⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡿⠋⠀⠀⠀⠀⠀⢿⡿⠁⢹⣤⣿⣇⣠⣴⣾⣯⣾⠁⣉⡸⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣷⠏⠀⠀⠀⠀⣴⡀⠀⠈⠁⠀⠈⢸⣿⡿⠉⠙⠛⠋⠚⢓⢿⣧⣤⢀⣾⠆⠀⠀⠀⠀⠀⣠⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠋⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⢰⠖⢙⣿⡗⠺⠇⠠⣤⣤⡎⣠⠹⠟⠈⠁⠀⡠⠃⢠⢆⡀⠈⢧⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⢠⡞⠀⢀⠀⠀⠀⠀⠀⠀⣡⣶⣷⡶⠞⠛⠋⠃⢀⠀⠀⠸⣿⣿⣿⡅⠀⠂⠀⠀⠄⠀⠘⠟⠋⠀⠀⠁⠀⠀⡀⡀
⠀⠀⠀⠀⠀⣤⠀⢀⣾⣇⠀⠀⣀⡀⠀⠀⣠⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠶⠀⠀⢘⣿⡟⠛⢀⣴⣿⣾⣕⣆⣰⣤⣴⡆⠀⠀⢦⡾⣧
⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⠁⢰⣿⣟⣹⡆⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⣿⣷⡤⠐⠛⠋⠉⣿⣿⡟⠛⠛⠡⡀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣄⠺⠋⣿⣭⣛⠿⢿⣿⣗⣀⠀⠀⠀⠀⠀⠀⠀⠋⠁⣾⣿⠟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⢢⡀⠀⣾
⠀⠀⠀⠀⠀⠘⠀⠛⠻⣿⣿⣷⡄⢹⡟⢿⣤⣄⣻⣶⣾⡄⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠞⣿
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑⠘⣿⣧⣘⠳⠛⠻⠿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⢀⣟⠀⢆
⠀⠀⠀⠀⠀⠀⢙⠀⠀⠐⠦⢈⢻⣷⠇⠀⢀⣀⢈⡙⠿⣿⡁⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣼⠃⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠈⣦⣢⡀⠀⠘⣿⠃⡤⠒⠃⠈⠀⠁⠀⠈⢹⡄⠀⠀⠀⠈⠁⠈⣿⡧⠀⠀⠀⣀⣠⣤⣀⡄⣶⣷⡟⠉⠣⠀⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢈⠡⡈⠢⡄⠈⣧⠀⠀⠀⠀⠀⠀⠀⠠⠄⠘⠲⢤⣔⣦⣦⠀⠀⠀⠻⠷⢿⣿⣿⣿⣿⠇⠋⣬⠀⠀⠀⠀⣛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠐⠿⣦⡀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠛⣧⣤⣄⠀⠀⠀⠀⠈⣽⢿⣿⣿⢸⣥⠀⠀⢸⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠢⠀⠀⠈⢳⡄⢹⡿⢶⡄⠀⠀⠀⠀⠀⣴⣾⣿⠋⠁⠀⠴⠂⠀⠈⠠⡜⣿⠏⠀⠙⠂⣠⢿⠁⡘⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡂⠀⠠⣌⣇⢾⠀⠈⢱⠿⠂⣀⣄⣤⣿⡿⠃⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡇⠀⢀⡼⠋⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⢈⣿⣼⠀⠀⠀⢁⣠⣿⣿⡟⠀⠀⠀⠀⢀⡠⠴⠒⠚⠋⠉⣻⣿⣡⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠳⢌⣿⣦⠀⢰⣾⣿⣿⣷⣦⣴⣊⣅⣀⣠⣄⣘⡁⢀⣦⣴⡿⠛⠙⠋⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠻⢾⣿⣿⣿⠿⠟⠛⠋⠉⠋⠉⠉⡉⠛⠙⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠂⠈⠉⠀⠠⢤⠔⡉⠉⠐⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠼⠃⠀⠐⠁⠀⠀⡆⣄⣶⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠴⠀⠀⢀⠔⡌⣡⠦⠂⠉⠈⠋⠀⠀⠀⠀⠀⠀⢩⡄⠀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⢀⡄⢠⣯⣔⣐⠽⠚⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢸⡌⢂
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⢚⣞⠄⠾⠁⠊⠉⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣠⠉⠀⠀⠀⠀⠀⠀⠀⠠⡡⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⢀⡞⢁⡀⠀⠀⠀⠀⢀⣤⣠⠀⢀⢄⠦⠠⠆⠀⠀⠁⠀⠀⠀⠀⠡⠀⠀⠀⠀⠐⠱⡀
⠀⠀⠀⠀⠀⠀⠌⠀⠀⢠⢊⡯⠚⠉⢷⣗⢆⣀⣰⣈⣉⣑⠆⠈⢂⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⠀⢣
⠀⠀⠀⠀⠀⠐⠀⠁⠀⡸⠭⠄⠐⡄⠀⠋⢸⠏⢯⣴⣤⠄⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡋⠈⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠼⠀⠀⠀⠀⠑⢄⣠⠤⡀⠀⡀⡸⠀⠀⠀⠀⣀⢀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠐⠉⠣⣄⢈⠀⡅
⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣶⣄⠀⠀⠀⠂⣉⣋⠗⢉⠉⠈⠻⠴⡄⠀⢀⠀⠀⠀⠘⡊⢁
⠀⠀⠀⠀⠀⠠⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⢷⣀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠙⢏⠈⠀⠀⠀⠀⠘⠚⡆
⠀⠀⠀⠀⠀⠰⠈⢧⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠹⣧⡀⢀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠀⠀⠉⢳⠁
⠀⠀⠀⠀⠀⠀⢃⠈⢿⣢⡀⣀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⢋⡉⡄⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⠉⠷⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠁⠀⠀⠈⡠⠄⠂⠀⠒⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡸⣀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⣈⠆⠀⠀⠔⠁⠀⠀⠁⢀⠠⠒⠁⠠⠒⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⠢⡀⠈⢿⣶⣂⠀⠀⠀⣄⠛⠀⢠⡁⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⡄⠈⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡀⠀⣿⣹⠀⠀⠀⠈⠀⢦⠈⢢⠀⠀⠤⡀⠀⠀⠀⠀⠀⠠⢊⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣌⡳⣎⣤⠀⠀⠀⠀⡴⠊⠀⣧⠀⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠶⣶⣼⣃⣈⣀⣈⣀⠤⠤⠖⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠛⠛⣛⠟⠁⣿⣿⡿⠿⠃⠀⠉⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⡇⠀⠻⠟⠁⠺⠇⠀⠀⠀⠀⠀⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠀⢸⣿⣿⣿⣦⡀
⠀⠀⠀⡴⣿⣿⠋⠁⠀⠈⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣷⡀
⠀⠀⡜⠸⣿⣧⣀⡀⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠈⠟⠿⣿⣿⡄
⠀⡸⠁⠀⠈⢹⣿⠁⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⣤⡈⠉⢷⡀
⢀⠇⠀⠀⠀⠀⢹⡀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢣⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿
⠸⡀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿
⠀⢇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇
⠀⠘⡆⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡟
⠀⠀⠘⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡟
⠀⠀⠀⠈⢦⡀⠀⠀⢸⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠑⢄⠀⠘⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠑⢤⡹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⣼⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⣼⣧⣴⡄⠀⠀⣠⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⣿⣿⣿⣿⣷⠀⠘⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠉⠀⠘⢿⣿⣷⣦⣤⣌⠻⠿⠿⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⡇⠀⠀⠀⠉⢻⣧⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⣶⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⠋⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠋⠉⠁⠀⡀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠁⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣏⢁⣤⣤⣤⣤⣠⡶⠛⠛⠛⠉⠙⠛⢷⣄⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠛⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⢀⣾⠏⠀⠙⠦⡿⠱⣯⣤⣄⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢰⣿⣋⣁⣀⣀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠈⠛⠛⠛⠛⢷⡶⠿⢶⣆⠹⣦⣀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠈⠉⠛⠛⠛⠻⣷⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢠⡟⠀⠀⢀⣠⡾⠋⠀⠀⣀⣀⣀⣀⣤⣶⡿⠏⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠸⣧⡀⢀⡿⠁⠀⠀⠀⢸⣿⡛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠶⠶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⣼⣧⣀⠀⠀⠀⣴⡿⠛⠛⠛⠷⢶⣤⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⣦⣄⣻⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⢀⣿⠉⢻⣷⠀⢸⣿⠀⣠⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⡟⠀⠀⠀⠀⠉⠻⣷⡀⠉⣿⣆⠀⠀⠀⢰⡟⠛⣷⡀⠀⠀⠀⠀⣿⡀
⠀⢸⡿⠀⠀⣿⣄⢸⡿⠀⠙⠛⠻⢯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠉⠁⠀⠀⠀⠀⠀⣾⣿⣤⣤⣈⢻⣇⡀⠀⢸⡷⠀⠈⠙⣷⠀⠀⠀⢹⡇
⠀⢸⡇⠀⠀⠘⣿⡘⠳⠞⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠛⢿⣿⣛⣿⣯⣥⡀⠀⠐⣿⠀⣠⣴⣾⠇
⠀⢸⡇⠀⢀⣾⠟⠀⠀⠀⠀⠀⠘⠻⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣽⠃⠀⠀⠹⠷⠟⠀⣿
⠀⠸⣧⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠛⠻⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⠀⠀⠀⠀⣀⣀⣀⣸⡏
⠀⠀⢹⣇⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⢠⡾⠋⠉⠉⣽⡇
⠀⠀⠀⢿⡌⠻⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⣄⠀⣴⡟⠁⠀⠀⣰⡿
⠀⠀⠀⠈⢿⡀⠀⠉⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⢙⣷⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠉⢿⡆⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⠀⣼⣇⣀⣴⡿⠁
⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⢸⣿⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡿⠋⣿⡷⠋⠀⠉⣩⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠈⣿⡀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⡀⠀⣠⣾⠃⠀⠈⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡘⢿⣦⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠾⠋⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣍⠻⣮⡛⢶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⡶⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⠶⣶⠶⢶⡶⠶⠶⠶⢶⡶⠶⢶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣎⡛⣻⢿⢿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣽⣿⡟⠛⠛⠋⣹⣿⡜⣿⣝⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣒⣫⣿⣿⣿⣿⣦⣰⣿⣯⣭⠀⠀⠙⠛⠁⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡟⠛⠛⠀⠀⠀⠀⠀⠀⠈⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⡿⠋⠀⠈⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣿⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣷⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣷⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⠀⠀⠀⠘⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠁⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⡀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⢶⣤⣤⣿⣧⠤⠴⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠀⠐⠒⠒⠒⠂⠐⠒⠐⠂⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠋⡡⠔⠋⠁⠈⣹⠀⠀⠀⠀⠒⠒⠀⢠⡞⠁⠈⠁⠐⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢟⠆⢀⠔⠋⠑⠀⣀⠤⠊⠀⠀⠀⠀⣀⡀⠀⠀⠀⠧⢄⠢⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⡤⠚⠰⡧⠒⠒⢫⠄⢢⠀⠀⠀⢠⠖⠉⠈⠉⠹⣦⠞⠉⠚⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢠⠤⠜⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠰⣃⠀⣞⠧⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⡼⠅⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⣘⡛⣋⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠙⣄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠱⢼⠇⢀⡀⢀⣤⡀⠀⠀⠀⢀⣄⡀⠀⠀⠀⢰⠈⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⢀⠴⠊⠉⠁⠀⠑⢆⠀⢠⢮⠒⠚⠀⠀⠀⠘⠢⡀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⣜⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠍⠥⠴⠒⠠⡄⠀⠀⠨⠗⠊⠈⠣⠤⠊⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⡀
⠀⠀⢠⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠀⠘⠒⠄⡀⡴⠶⠤⢀⣀⡀⢇⠀⠀⠀⠀⢰⠦⡄⠀⣄⠤⣄⠀⠀⠀⠰⠘⡇
⠀⠀⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⡆⢇⠀⠀⠀⠀⠳⠴⠊⢓⠀⠈⠙⣄⠀⡼⠀⡇
⠀⠀⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⢳⡀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠘⠆⠰⡄
⠀⠀⢠⠀⠷⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡑⢆⠀⢀⣠⠞⠁⠀⠀⠀⠀⠑⢂⡇⡆
⠀⠀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠀⠘⢄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⡛⠥⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠇⠀⠈⢀⠀⠀⠀⠀⠀⠰⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠⠃⠊⠀⠀⠀⠀⠀⢠⠃⡘
⠀⠀⠀⠸⡄⠀⠀⡧⠀⠀⠀⠀⠀⠐⠦⡙⠒⠂⠀⠒⠂⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠹⡀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠎
⠀⠀⠀⠀⠀⠱⡌⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠘⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⠤⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢇⡘⠁⡌⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⣎⡤⠊⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢀⡠⠚⠀⠀⠀⠀⠀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠋⠉⠀⠀⠀⣀⠠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠂⠤⠤⠤⠤⠤⠤⠤⠤⠔⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠉⠁⠀⠀⠀⠀⠼⣏⣿⠿⠖⣲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠀⠀⠀⢠⣤⡘⡛⢁⠀⠰⠜⠛⠁⢶⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⣤⣶⣤⣀⣤⣤⡐⠿⠿⠃⣡⠠⠾⢷⣄⠀⠀⠘⣿⣿⣿⣿⣿⡇⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⠖⠀⣀⣿⣇⠀⠀⣻⣿⣿⣿⣿⠁⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⣵⣾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⢁⣤⣈⠛⠁⠀⠀⢿⣿⠋⠉⠁⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⡼⠐⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⣨⣿⣷⣶⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣟⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠈⢙⡇
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣿⣿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣟⣁⡉⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠋⠉⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⣀⡀⠀⠀⠸⣿⠁⠀⢀⣀⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣤⡰⠔⡒⣮⡍⠙⣯⡼⣮⣶⡦⠆⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠉⠛⠋⠁⠈⠁⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡡⠖⠲⠶⢶⣄⠀⠀⣀⡀⣠⠤⡬⢤
⠀⠀⠀⠀⠀⠀⠀⣀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠅⠀⠁⠀⠈⠀⠍⠍⣬⠉⡑⢶⠔⠊⠐⠑⣄
⠀⠀⠀⠀⠀⣠⣾⣸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⠀⠐⠀⠀⠀⠀⠀⡀⠘⠂⠙⠒⣈⣁⡋⣟⠉⢁⣄
⠀⠀⠀⢀⠐⢿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⠏⠀⣀⠀⠀⠐⠀⠓⠄⠀⠉⢂⠀⠋⠁⠉⠃⠀⠀⠀⠈
⠀⠀⠀⣤⠖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠛⡲⣄⠈⢀⠀⠂⠀⠀⠉⠀⠀⠠⠀⡄⡁⠀⠀⠀⠂⠀⠰⢶⡝
⠀⠀⠖⠠⠆⣛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢠⣞⠜⠋⠠⠀⠐⠐⢋⠈⠀⢘⠃⠠⠀⠀⠀⠀⡂⠀⡁⠁⡀⠠⠀⠰⡾⣳⢒
⠀⢠⣔⠛⠀⠀⡰⣍⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡷⡞⠀⠀⣈⠓⣒⣠⠀⠄⢁⠀⢁⣀⡀⠀⠀⠀⠀⠁⠐⠂⠀⡀⢀⠀⠀⠈⡋⠩
⢠⠞⢉⣉⣁⣨⠞⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡣⠤⢄⡊⡳⠓⠁⡄⢩⣁⢀⡱⠙⣁⠇⢼⠠⠞⠠⢀⠀⠀⠃⠀⠐⡀⠁
⢠⢤⡭⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⡵⠋⠀⣈⢳⡼⠲⣄⡀⠠⢤⠠⠀⠀⣄⢎⡁⠰⠇⠈⡑⠁⠴⠀⠒⠀⢄
⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡶⡿⠞⠻⠛⡛⠻⣦⣤⣍⣳⢀⣄⠒⢁⠸⣟⠧⢼⡆⠰⠃⠀⠀⢠⡄⠘⡫⡃⠈
⠀⣳⢀⡀⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠉⠀⠀⠀⠀⠌⠀⠠⠀⢀⠃⠸⣝⣆⠀⢰⡆⠘⢀⠀⠙⢷⡀⣀⡦⢠⠼⢻⠇⣦⢆
⠻⠯⣯⣼⠤⢶⡆⠂⣤⡀⠀⠀⠀⠀⠀⣼⢹⡄⣀⣠⣃⣄⡄⠁⠀⠰⠀⠀⢆⡐⠊⣯⡳⡼⢷⣚⠉⠀⠀⠀⠉⢢⣿⠃⠀⠻⣸⡇
⠀⢠⣯⡚⢺⠃⡏⡛⣻⢦⣤⡀⠀⠀⠀⠻⡈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣫⠼⠁⠀⠀⠀⠀⠘⣿⠀⠀⠀⠻⣿⡀
⠀⠀⠙⣟⠢⠠⡅⡏⣛⣚⠴⢽⡄⠀⠀⠀⠙⠲⣴⡤⣤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⣠
⠀⠀⢀⡷⠊⣀⢌⢣⠱⣻⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣍⠁⣻⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠠⠂
⠀⠀⠘⢧⢁⣹⢠⢈⡧⢜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠠⢄⡠⠀⠖⣶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠘⣇⠙⠿⠾⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠂⠼⠔⠟⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠘⡀⢀⠘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠀⠍⠀⢠⡽⢁⡤⠄
⠀⠀⠀⠀⠀⠀⠻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣶⠟⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⠤⣤⣴⣶⣶⡤⣤⣀⣀⣁⠀⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡠⣴⢶⡶⠶⢶⣟⣿⣿⣿⣿⣗⣲⣐⠐⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⢿⡽⠯⠾⠧⢷⡂⢀⣀⣩⣯⣣⢿⣿⠟⠉⠛⢿⡿⢛⢤⣌⠑⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠛⠃⠉⠘⠿⢋⣶⠦⡀⠙⣿⠷⣻⡄⠀⠐⡩⡢⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠁⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⡘⣿⢵⣚⠁⠠⣉⢞⡡⡷⠀⠑⠌⠉⠀⢶⣀
⠀⠀⠀⠀⠀⢀⢴⠋⡤⢾⣲⠀⠀⠀⠀⢒⣈⠡⠄⠀⠀⠀⠀⠀⣜⢕⠙⡡⡢⣲⠉⠙⢷⢷⣟⡟⣫⡽⡆⠀⠠⠤⡶⡚⠛⢢⡀
⠀⠀⠀⠀⠠⡡⢪⢔⡫⢐⠬⡆⠀⠀⠩⠄⠒⠀⠈⠁⠀⠀⠀⠀⠈⠲⢜⣨⣪⡇⠀⠀⠘⠋⢹⣯⣻⡯⢕⣢⡼⠛⠜⡀⠫⡱⠑⢄
⠀⠀⠀⡐⠘⡁⢜⢕⡪⠔⡓⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣏⠇⠀⠀⠀⠀⠀⠈⠳⡥⢞⠫⡐⠄⠀⡁⠄⢀⠠⠀⠈⢢
⠀⠀⡜⠠⡐⠨⡑⢌⠛⢶⡌⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⢤⠤⢤⠤⣏⠐⡉⠤⢒⠡⠐⢈⡠⠔⠀⢰⢆⢡
⠀⡰⠀⠐⠨⠑⡢⠑⡪⢒⣈⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠒⡎⠐⠺⠀⠒⢉⡠⠔⢊⠡⠄⠀⠀⠐⠾⣤⢆
⢀⠁⠀⠉⠒⠂⠤⣁⠊⠲⢷⠀⠀⠀⠀⠐⣩⠔⢀⠠⠐⠀⠀⠀⠐⡂⠅⠀⠀⡀⡎⡉⠍⣒⠌⢒⡡⠔⢊⠥⠒⢈⡠⠄⡂⠁⠠⠀⠀⡇
⠈⠀⠀⠀⠈⠀⠀⠀⠀⠁⠸⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠒⠀⠁⠀⠚⡂⠄⢂⠡⠐⣉⠡⠐⢈⡠⠔⡊⠥⠒⠁⡀⠄⠨⢀⡅⠁⡖
⡆⠀⠀⣀⡀⠩⠄⠐⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⡠⠔⢀⠤⠐⢈⠠⠐⡊⠅⠒⢉⡠⠄⣂⠥⠐⢀⠨⠁⣛⠼⠦
⡇⠀⠠⠄⠒⣀⡈⠅⠂⠀⠀⠀⢦⣆⠀⠀⠀⠀⠀⠠⢠⠤⡂⠒⠄⠣⠀⠄⢂⡨⠄⣂⠩⠔⢂⡁⠤⠒⣈⠥⢒⡉⠄⠂⠀⢐⡀⠅⡀⠀⡀
⡇⠀⠀⢒⡉⠤⠐⣊⠤⡐⠀⡀⠈⢯⠱⡀⠀⠀⢰⠣⢐⠨⣒⠅⡑⡔⠐⢊⠅⠐⢁⠤⠐⢊⡡⠄⢒⡩⠔⢊⡁⠤⠒⢁⢀⠥⠂⠜
⠀⠀⠈⠀⠒⡀⠍⢂⠡⢒⡩⢐⡠⠀⠀⢀⡀⠀⠈⢆⡡⠚⣳⠜⢂⠔⣍⣦⠨⠄⠀⠀⠈⣠⠖⠈⠡⠐⢈⡁⠄⢂⠨⠄⠀⡀⠀⠀⠀⠬⢄
⠨⠀⠀⠀⠠⠔⢈⠤⢂⡡⠒⡡⠐⡠⠀⠀⠈⠒⠄⠤⢀⡀⠢⠻⠕⣉⢔⠹⢊⠕⢋⠔⣊⠔⡩⠀⠀⣈⠥⢒⡉⠤⠂⠀⠀⡂⢸⠀⠰⠛⠉
⠀⢂⠀⠀⠒⣈⠄⠂⣁⠔⢉⠤⢊⠤⢂⠴⢂⡴⠀⠀⠀⠈⠣⡐⣉⡂⣁⠔⠓⠒⠡⠜⠠⡙⠪⢐⠅⡀⠀⠡⠒⠊⠀⠀⠄⢂⠄⠑⣀⠤⢠
⠀⠈⡄⠀⠈⣀⠔⠊⡠⠒⡡⠔⢁⠔⢁⠔⠋⡠⠀⠀⡀⠀⠀⠀⠉⠑⠀⠀⠀⣀⠤⠀⠀⠈⠀⠢⡈⠐⠀⠀⠉⠀⠀⡀⠭⣐⠡⢀⠀⢠⠁
⠀⠀⠰⡀⠀⠠⠒⢁⠤⠊⡠⠞⢁⠔⢁⠴⠊⣀⠔⠁⠀⣈⠔⡀⢀⠜⠀⠔⡪⢒⠉⠀⠀⠀⠀⠀⠐⠆⢄⠀⣀⠀⠀⣒⠩⢐⠪⡐⢠⠃
⠀⠀⠀⠱⡀⠀⠀⣁⠔⠈⡠⠊⡡⠔⢁⠠⠊⡠⠂⠀⠀⠔⡩⠀⢜⠀⠀⠀⡪⠐⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⢇⠠⢐⡈⢐⠜⡠⠃
⠀⠀⠀⠀⠘⢆⠀⠀⠐⢊⠄⠊⡠⠒⣁⠔⡊⠔⢁⠔⠀⠀⢒⡡⠂⡱⡀⠀⠀⠭⠐⠀⠀⠀⢐⠪⠀⠀⠀⠐⠁⢐⡪⠕⡪⢐⠔⠁
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢉⠔⢊⠠⢊⠤⢊⠡⢊⠀⠀⠁⠔⡨⢒⠈⠒⢄⠀⠑⠀⠀⢆⡢⠁⠀⢀⣀⠎⠀⠤⠂⢁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠁⠊⠡⠒⡡⠒⣁⢔⡡⢂⢀⠀⠑⠠⡀⠨⠀⠄⠀⠀⠀⠀⠀⡜⠁⣀⠠⠄⢊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠈⠐⠊⠒⠡⠊⢔⠕⡠⢀⠀⠀⠈⠀⠀⠀⠀⢀⡰⠊⠀⠐⢂⠥⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⡤⠊⠁⣀⠤⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⣈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣶⣶⣿⣿⣿⣷⣾⡿⠿⠗⢠⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣗⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠟⠛⣫⡟⠋⠁⠀⠀⠀⠀⣻⠿⠛⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣏⡉⢹⡟⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠑⠄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⢫⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠈⢢
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡯⢿⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢂
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⢿⣿⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⣿⣿⠀⠀⣙⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⢸⡿⣼⠃⣿⣇⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣟⡀⠙⠦
⠀⠀⠀⠀⢸⠁⠏⠀⢋⠋⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⢠⣦⣀⠀⠀⠀⡆
⠀⠀⠀⠀⢸⠀⠀⠀⢺⢀⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣦⠀⠀⠇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⢆⠛⠻⠀⠲⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁⠀⠀⣀⠘⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠰
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⣴⣿⣧⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⢁⠃
⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢁⠆
⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⢻⡿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠛⠟⠁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠅⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠠⠄⢀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠄⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡄⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⠋⠛⣉⠛⠁⣿⣿⡿⠛⠁⠀⠉⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣤⣾⣿⣿⡇⠀⠙⠋⠀⠛⠃⠀⠀⠀⠀⢰⣿⣶⣄
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣮⡙⠿⣿⣷⣄
⠀⠀⠀⠀⣴⣿⣿⠿⠿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢀⣿⣿⣿⣷⡄
⠀⠀⢀⢾⣿⡟⠁⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⡿⠿⣿⣿⣿⣆
⠀⢀⠎⠘⢿⣷⡶⠀⠀⠒⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣋⣁⣀⣉⠙⠻⢿⣆
⠀⡎⠀⠀⠀⠻⡇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣷⣦⣤⣽⡆
⢰⠁⠀⠀⠀⠀⠻⣤⣤⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⡌⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿
⠈⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏
⠀⠱⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁
⠀⠀⠱⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠱⡄⠀⠀⠀⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠈⢢⡀⠀⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠉⠢⡘⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⢄⣀⣀⡀⠀⠀⣀⣀⣀⠤⠤⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣟⠋⠉⠉⠉⠉⠀⠈⠛⠛⢷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣟⣿⣩⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠛⢿⣿⣿⣦⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡟⠋⡀⣈⣉⡿⠛⠈⣽⣿⣿⣀⠀⠀⠀⠀⠀⠀⡀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣶⡛⠙⠛⢋⣠⣶⣿⣿⣿⡿⠋⠀⣀⠀⠀⠂⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠋⠀⢀⣾⡿⠿⠿⠿⠟⠉⠀⠀⠀⠈⠀⠀⠀⠘⡄⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠚⠋⠉⠽⢡⡝⠁⠀⠀⠈⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⣤⣶⣦⣄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⣹⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠸⢿⣿⠆⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣱⣧⢀⣬⣷⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣿⡿⠿⢿⡟⢿⣿⣿⣿⠏⠙⠃⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠿⠁⠀⠠⠀⠙⠦⢹⡟⢻⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠛⠁
⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣾⣿⣿⣶⠆⠉⠀⠀⠉⠀⠙⠙⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠇
⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣰⣶⣤⣤⣤⣴⣿⣿⣿⣿⣿⣌⠛⢫⣛⠉⠀⠀⠉⠹⣿⣧⠀⠀⠀⠇
⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠙⡿⡄
⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⣿⣿⣿⣿⠟⠁
⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣘⠿⠛⣁⡀
⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡟
⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⡿⠿⠛⠿⣿⡿⠿⠿⠿⠻⢿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⠻⢿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣤⣦⡀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣶⣦⣄⡀⠀⠀⠀⠈⢿⣷⠌⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣿⣿⣿⣿⣧⡀⢠⣤⡀⠀⠐⠿⠙⢿⣿⣿⣿⣿⣦⢀⣤⡀⠀⠰⣄⡸⣿⣿⣿⡿⢺⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣦⣽⣷⣰⡲⣶⣤⡀⠉⢻⣿⣿⡇⠘⠛⠀⠀⠀⠻⠟⢫⣿⣿⠁⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⣸⣿⡦⠈⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣧⣹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣷⣯⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠹⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⣿⣿⣿⣿⠿⠿⠿⠿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣤⣴⡷⠀⠈⠑⠲⠦⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠤⢤⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣄⣀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠿⣿⠟⢯⣥⣶⣦⡉⠁⠀⠉⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠿⠟⠋⣈⣡⣶⠦⣈⣿⣿⠃⢀⣀⣤⣶⡾⢿⣿⣿⣿⣿⡿⠋⡉⠉⠹⡿⠛⠛⠋⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠶⣿⣿⠋⠉⠛⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⢿⣿⣧⣄⣼⡗⠂⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠈⠁⠀⢤⣤⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡧⠝⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢀⣤⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⣠⣴⣔⢦⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠚⠛⠋⠻⣿⡿⢿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣶⣾⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠶⡤⣄⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠹⠟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⢀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣄⠿⠿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣶⣿⠃⣸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣼⣿⣿⣶⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣧⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣀⠀⢀⠼⣿⣄⡠⣾⡷⢄⣰⣿⡗⢄⣀⣀⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣠⠻⣧⡀⠁⠀⡟⢧⡴⠛⠛⢆⠀⣿⠉⠀⢀⣼⣿⢷⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣿⣄⠀⠀⠙⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢱⠇⠈⣼⡟⠇
⠀⠀⠀⠀⠀⣴⣤⡤⠚⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠈⠢⣤⣤⡄
⠀⠀⠀⡀⠀⢀⡟⠻⢦⡄⠀⠀⠀⣀⣀⣀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⠀⣠⣾⠟⢻⠁
⠀⠀⠘⢿⣿⣷⣤⣄⠀⣱⣶⣴⡾⢿⡥⠉⣿⡿⠟⠋⠀⠀⣠⣶⣶⣦⣴⣶⣿⣿⣿⣿⣿⣷⡌⠀⠀⢈⣢⣴⣦
⠀⠀⠀⢈⠂⠉⠳⠄⣾⣿⣿⣅⣰⣷⣆⠀⠉⠀⠀⠀⠠⣦⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠴⠿⠋⠹
⠀⢠⣴⣧⣤⣀⠀⣼⣿⣿⣿⣿⠿⠃⠉⠀⠀⠀⠀⠀⢰⣾⣛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⡀⣉⣤⣠⡀
⠀⠈⠙⠻⠋⢉⢁⣿⡿⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⣶⣶⣾⣿⣿⣿⠿⢿⣿⣿⣿⣿⡇⢉⡽⢿⠟⠉⠁
⠀⢠⣴⣮⣾⠁⠈⠿⣧⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣿⠋⠀⠀⢹⡏⠀⠙⠛⠈⢹⣦⣷⣄⡀
⠀⠀⠈⢣⡙⣦⡀⠀⠀⠉⠒⣾⣶⣦⣄⠀⠀⠀⠀⠀⠛⠛⠛⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠳⢠⠴⢋⠛⠉
⠀⢠⣴⡿⠿⠥⠄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣾⣷⣤⡄
⠀⠀⠀⠑⡄⠀⠀⡀⠀⠀⠀⠙⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠟⠉
⠀⠀⢀⣠⣧⣾⠟⠁⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣳⣤⣰
⠀⠀⠈⠛⠉⢰⠀⢀⣠⡀⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠈⣩⠿⠿⠿
⠀⠀⠀⠀⠀⣼⣶⡿⠋⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⡄
⠀⠀⠀⠀⠀⠈⠁⠉⠑⡀⣠⡾⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣶⡄⢰⠊⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠥⡄⣼⣠⠆⠀⠀⣄⠀⡀⠀⠀⣠⡀⣠⠀⠀⢿⣦⠀⣀⣹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿⣇⢠⡀⣼⣿⣀⡱⣶⡶⣃⣳⣿⠀⡤⠌⣿⣟⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠈⣿⡟⠁⠈⢻⡟⠁⠘⣿⡋⠀⠀⠀⠋
⠀⡀⡀
⠀⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⢒⡲⠂⠈⠉⠁⠐⠒⠂⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠻⠤⠂⡩⠁⢄⠀⠀⠀⠀⠀⠀⠀⠠⠃⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⢩⠃⠀⡔⠈⠀⠀⢀⠀⠀⠀⠀⠲⠂⠀⠀⠱⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⢠⠊⣀⡰⠉⠀⡘⢀⣀⡠⡲⢍⠀⠀⢀⡠⡤⠤⡀⠎⠁⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⢠⠋⠉⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⡄⡗⡌⡪⠜⠈⠉⠀⠀⢀⠒⡄⠀⠀⠀⢣
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠊⡠⣀⣄⡀⢠⢐⡢⠑⡄⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣜⣀⣈⠗⠈⠁⢣⠀⠀⢠⠠⠤⠤⠀⠸
⠀⠀⠀⠀⠰⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠁⠀⠀⠈⠁⠈⠉⠲⠢⡀⠀⠀⢈⠆⠣⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠑⣊⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⠁⠈⢢⠀⠀⠀⠀⠀⠀⢨⡠⢢⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠑⡀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠗⠥⠋⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⠔⠁⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣀⠔⠁⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠤⠄⢀⣀⡀⠀⠤⠄⠐⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡔⠒⢒⣤⣌⠁⠀⠒⠒⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⣩⣫⠿⣫⣶⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⣄⠞⠁⠿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣀⢫⢀⣴⣦⡀⠀⠀⣿⣿⣿⣿⡿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣜⡡⠟⢋⣴⡀⠁⣿⣇⠀⢀⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣶⣶⣦⣄⡀⠀⠀⠠⣤⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠛⣀⠙⠟⠀⠀⠹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⣿⣯⣵⣾⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡁⠀⢸⣿⣧⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠘⡙⠿⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣴⣿⡿⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠛⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡿⠿⣟⠻⣿⣿⠛⠋⢿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣏⣀⣀⠈⠁⠙⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⡟⠉⠉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣶⣴⣶⣶⡾⣿⣿⣿⠻⢿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⠻⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⢿⣿⣷⠗⠀⠀⠹⡇
⠀⠀⠀⠀⠸⡀⠀⠈⠻⢄⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣩⠁⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⠟⢡⡾⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠋⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠁⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⠤⠀⠀⠀⠠⠤⠤⠔⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢢⡖⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⡒⢤⡀⠀⠀⠀⠀⠀⠄⠁⠐⠂⠙⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠁⠌⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠐⡠⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⡈⠁⠠⢀⡜⠤⠃⠀⠀⠀⠀⣠⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢀⢠⡤⠛⢢⠤⠠⡄⠔⠀⡷⠀⠀⠀⠢⢀⣀⠠⢤⠀⠲⡓⠠⠀⠂⠅
⠀⠀⠀⠀⠀⠀⠀⣠⠴⢄⠤⢀⠀⠀⠀⠁⠀⠰⠆⢀⣠⠂⠀⠀⠀⠠⡄⠀⠌⡆⠀⠀⠀⠀⡀⠋⠑⠤⠀⠀⠀⠀⠀⢀⣠⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣤⠀⠀⠀⢡⡔⠛⢄⡤⠀⠀⣛⣁⠀⠀⠀⠀⡬⣅⠲⠀⠀⣄⠀⠀⠀⠴⡋⠉⠈⢃⠈⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⣠⠄⡹⠈⠀⠀⠀⠀⠀⡴⡢⠈⠋⠈⠀⠁⠈⠀⠀⢪⢟⣤⡈⠀⠀⠀⠉⠁⠂⠲⣤⢧⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢠⡘⠁⣨⠖⡀⣀⢠⠆⠀⠈⠠⠀⠀⠀⡀⠐⠁⠈⠀⠀⠙⠢⡀⠀⠀⣶⠐⣆⡀⠹⣃⠐⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠹⢟⡀⠀⠀⠀⠄⠁⠀⠈⠀⠀⠀⡐⠠⠀⠠⠄⠑⣄⣤⠻⢷⡌⠁⠀⡏⠁
⠀⠀⠀⠀⠀⠤⠄⠐⠂⠠⣄⠀⠚⠀⠀⠀⠀⡘⠀⠁⠀⠅⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠈⠆⠀⠀⠀⠀⠀⢓
⠀⠀⠀⠀⠀⠀⠀⠤⢁⠐⢤⠠⠐⠀⠀⠠⣴⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⡀⠀⡠⠖⠠⠀⠀⠀⢀⠀⠘⡄⠀⠠⢀⣀
⠀⠀⠀⢀⢀⡆⠀⠠⠃⠩⡉⠈⠐⠠⠀⠈⠱⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⣦⣀⡌⠠⠓⠄⠼⠠⡔⠀⠐⣸⠛⢂
⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠁⡆⠀⠀⠀⠀⢸⠀⠀⠀⠐⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠴⠊⠉⠱⠘⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡴⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡈⠀⠀⠀⠀⢀⠜⠁⠀⠚⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠆⠀⠠⠀⠄⠠⠞⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠀⡔⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣠⢠⡂⡀⠀⠠⡂⢘⠇⠂⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣴⠂⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠅⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⠒⣦⡤⡐⠐⠀⠀⠀⠀⠀⠀⠒⠙⠎⢡⠂⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀⠀⠀⠀⠀⠀⠈⢙⣙⠉⠀⠀⠀⠀⠀⠀⠄⠃⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠰⠉⠈⢐⠁⠀⠀⡀⡀⠀⢠⠂⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠉⠐⠂⠄⠀⠀⠱⣔⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠑⡀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⢄⡤⠄⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠺⢿⣽⣆⡿⡹⠓⡄⠀⠀⠀⡇⢉⡱⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢰⡋⡲⠛⣥⡺⢗⣿⢀⣔⠭⣺⠕⡪⣒⠭⢙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠛⠁⢠⠞⡺⢗⠭⡫⠕⡩⢔⡥⠚⣡⠚⢳⣆⡝⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⡠⢊⠥⡪⢕⡩⣒⠭⢊⣡⣶⢏⢧⣀⣌⠉⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡆⠀⠀⠀⠀⠀⢠⣫⢕⠭⢊⠵⢊⠥⣚⠕⣳⠿⢞⡬⠕⠃⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠪⢿⡀⠀⣴⣴⠟⡳⢟⠥⢊⠥⢊⠕⣪⡴⢛⣡⡾⠑⡁⢠⡠⡲⡄⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣖⡨⢛⠶⡈⠹⣥⢚⠡⢊⣅⣪⡲⢑⡡⣺⠕⣩⡧⣰⠖⡱⢛⡵⠇⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⢒⡥⢊⣽⡆⠀⠉⠈⠓⢙⡩⢖⠵⡊⢔⠽⡊⢴⠋⠉⠉⠁⠀⢀⠀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⢚⡡⢚⣆⠀⠀⠀⠀⠀⠉⡗⡨⢔⡡⣪⢔⣯⠀⠀⠀⠀⠀⠈⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡥⢂⡡⢊⠵⢲⣄⠀⠀⣸⣊⢔⡡⡪⢗⠕⡩⠛⡹⣆⠀⠀⢀⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⢚⡥⢊⠴⣫⡆⡴⣋⢔⡭⣪⢖⡵⢋⡤⢊⠔⡻⣄⣠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠥⣊⡤⣣⣯⡵⡫⢊⠕⢁⠔⣉⠔⡡⢊⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠛⠎⠴⠥⠴⠡⠾⠡⠞⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⢀⡠⢀⣀⡀⡀⢀⠀⡀⢀⠀⣀⠀⡠⢀⡄⣠⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠀⠁⠉⠀⠀⠁⠈⠀⠁⠀⠁⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢿⣎⡠⣊⠁⠀⠶⣬⡀⠊⠚⣯⣠⠾
⠀⠀⠀⡍⡶⣤⣶⣅⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠳⢶⠂⡙⠢⢌⠂⠱⣎⣏⢳⣇
⠀⠀⠀⠳⣤⠀⠛⠓⠾⢄⡀⠀⠈⠑⢲⣤⡄⠀⠀⠀⠈⠻⣆⠈⢻⡆⢸⡟⠀⣻⡀
⠀⠀⠈⣷⣤⠀⠀⠀⠀⠈⢻⣀⢀⠀⠀⠀⡠⠇⡀⠀⠀⢘⣿⠀⣿⡇⢸⣿⠀⣿⡇
⠀⠀⠀⠿⠿⠛⠓⠒⢦⣤⣼⠉⠀⠀⠑⠒⢷⣦⣽⡄⠀⠘⣿⠀⣿⡇⢸⣷⠀⣿⡇
⠀⠀⠀⠀⡀⠀⠀⠀⡾⠟⠿⣷⠀⠀⠀⢀⣿⠛⠛⣿⠀⢸⣿⠀⣿⡇⢸⢿⠀⣿⡇
⠀⠀⠀⣟⣁⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⢸⠇⠀⠀⣿⡆⠈⣿⠀⣿⡇⢸⣿⠀⢹⡇
⠀⠀⠀⠀⠈⠳⡀⢸⠀⠀⠀⢿⡀⠀⠀⣸⠃⠀⠀⢻⡇⠀⣿⠀⣿⡇⢸⣿⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⡸⠀⠀⠠⢸⡇⠀⢀⡏⠀⠀⠀⠘⣿⡶⠿⢴⣿⣷⣾⣿⣶⣿⣷⣶⡆
⠀⠀⠀⢀⡀⢸⣿⠵⠀⠀⠐⣸⣿⠀⡼⠀⠀⠀⠠⠞⣿⣷⣶⣶⣶⣤⡤⠈⠉⠑⠟⠛⠛⠀⠀⠂
⠀⠀⠀⢸⣇⣸⣿⣦⡀⣤⣤⣿⣿⣷⡕⢀⠀⠀⢀⠀⣹⣿⣇⣿⠿⣿⣻⣶⡶⠓⣶⣦⡴⣼⠒⠃
⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⡿⠿⠿⢷⣴⢶⣶⣿⣾⣿⣿⠻⢶⡆⣿⡿⢭⠅⣾⣯⣽⣾⣿⣤⣤
⠀⠀⠀⣿⣿⡛⠛⣻⡿⠫⠭⠿⠨⠭⠿⠿⠁⣿⡟⠋⠙⠙⠀⣉⣀⣯⣀⣀⣀⠀⢀⠀⣼⣿⠿⠿
⠀⠀⠀⣉⣉⣉⣉⣙⣤⣖⣦⣀⣀⣀⣴⣶⣦⣏⣀⣄⣀⣸⣭⣿⣽⣧⣤⣼⣿⣷⣿⣟⣁⣀⣀⣀
⠀⠀⠀⠿⠿⠭⠽⠤⠤⠤⠤⠤⠽⠿⠷⠿⠥⠼⠷⠿⠶⠤⠤⠶⠤⠤⠴⠴⠽⠷⠤⠤⠽⠷⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⠀⠀⣀⡀⠀⠀⠀⡀⠀⣀⠀⠀⡀⣄⠀⠀⢀⡀
⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠷⠶⣆⡉⣒⡄⠀⠈⠻⢦⣄⣈⠉⠹⣧⡄⠸⡇
⠀⣬⢱⣷⣦⢾⡁⠐⠐⠂⠀⢀⠀⠀⡀⠀⣈⠈⠉⠸⡶⢛⣔⠀⢀⠻⡌⢶⣹⡇⢠⣿
⠀⠻⣆⣄⠈⠛⠢⠶⣤⣀⠀⠀⠈⠒⢠⠀⣈⠃⠀⠀⠀⠀⢹⣧⠀⠰⣿⠀⢹⡟⠀⢻⡆
⠀⣷⣌⣁⠀⠂⠠⠀⠘⢻⣇⡀⡀⠀⠈⠀⠈⢰⡄⠀⠀⠀⠘⣿⡇⢸⢿⠀⡟⣷⠀⠿⣷
⠀⢛⢿⣯⠤⣆⣤⣄⣀⡐⣿⠋⠑⠘⠦⠤⣄⣀⠒⣷⡀⠀⠀⣿⡇⢸⣿⠀⠃⣿⠀⡀⡿
⠀⠀⠁⠀⠀⠀⠀⣽⣿⣷⣿⡀⠀⠀⠀⠀⣬⣿⣿⣿⣧⠀⢠⣽⡇⢠⣽⠁⣆⣿⠀⡒⣇
⠀⠀⠀⢀⠀⠀⠀⠉⠉⠉⣽⡇⠀⠀⠀⠀⢸⠀⠀⢹⣿⠀⠘⢿⡅⠠⣿⠀⣃⣿⠀⡯⡟
⠀⠠⠀⡀⠂⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠐⠙⠀⠀⢸⣿⡄⠀⣿⡄⢸⣿⠀⡇⣿⠀⠅⡇
⠀⠀⠀⠀⢻⡀⠐⠀⠀⠀⠸⣿⠀⠀⠀⡀⡇⠀⠀⠀⣿⣇⠀⣻⡃⢸⣿⠀⣇⣿⠀⢄⡷
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣿⡆⠀⢀⠀⠀⠀⠀⠀⢹⣿⡾⠿⢗⣿⣿⣷⣿⣿⣾⣿⣿⣿⣶⡆
⠀⠀⣀⠀⢸⣿⢰⠀⠀⠀⢆⣼⣧⠀⠀⡀⠀⠀⠀⡠⢺⣿⣷⣴⣶⣶⣤⣤⡄⠋⠋⠳⠿⠛⠛⠛⠂⠒⠐
⠀⠀⣿⡇⣼⣿⣆⠀⣀⣀⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠊⣿⣿⡍⣿⣿⣿⡷⢶⣤⡤⠶⢦⣦⣀⣄⣶⠴⠂
⠀⢶⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣇⣠⣀⣀⣴⣧⣾⣿⣿⣛⣩⣥⢸⣟⡜⠻⠃⢴⡿⣛⣯⣶⣿⣀⣀
⠀⣼⣿⣟⣻⡿⣿⣿⡿⠻⢿⠍⠽⢶⣷⣶⡎⣿⣽⣿⠟⠿⡿⠐⠲⠋⢼⠏⠁⠉⠙⠛⠛⠛⠻⣿⣿⣿⣿
⠀⢿⣿⣿⣤⣴⣾⠛⢉⡉⠉⠀⠉⠉⢉⣉⠁⣿⠟⠀⠀⠀⡠⢤⣴⠶⡾⠓⠒⣦⣶⣂⣤⣄⡾⠛⠋⠉⠉
⠀⣤⣤⣤⠤⡤⠼⠶⠯⠽⠶⠶⠶⠶⠾⠿⠷⠿⣦⠶⡤⠦⠷⠶⠿⠶⠷⠶⠶⠿⣿⡿⠿⠿⠶⡴⠦⢤⣤
⠀⠚⠚⠓⠒⠛⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠒⠛⠛⠛⠒⠒⠒⠛⠒⠒⠒⠒⠚⠒⠓⠒⠒⠒⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣭⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣏⡻⣿⣿⣿⣿⣿⣶⣬⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⡙⢿⣷⢹⣿⣿⣿⡿⠟⣛⣋⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡶⠉⣡⣶⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⣿⣟⣃⣼⣧⣝⣋⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣯⣽⣏⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡛⠿⣩⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⣡⣦⣘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⢛⣩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢟⣿⣿⣿⣿⣿⣯⣍⢻⣿⣿⣿⢫⣙⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢶⣻⣯⣙⣛⣛⣟⣩⣽⣿⢿⠿⣿⣦⠹⣶⣶⣌⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠳⣮⣩⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣼⣿⡿⢿⣟⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⣿⣿⣿⣿⣦⣝⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣬⠻⣿⣿⣿⣿⣿⣿⣷⣶⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⢿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⡿⢃⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⢃⣿⣴⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡜⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⡟⣸⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡹⣿⣿⡿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⡿⢱⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣮⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣞⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⢶⠒⠒⠛⠛⠛⠛⠛⠛⠛⢓⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢞⣋⣁⡠⠤⣄⠉⠙⢦⠀⠀⠀⢀⡤⠖⠻⠭⠼⠃⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠙⠤⢬⡧⡀⠀⠀⢈⡇⠀⠈⠳⣄⣠⠎⠀⠀⠀⠀⠀⠀⠀⠠⢤⡐⢽⢦⡀
⠀⠀⠀⠀⢀⣴⠟⠉⠚⠁⢀⣠⠼⠃⡼⠿⠿⠯⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠃⠙⢦⡀
⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠈⠳⣤⡴⠃⠀⠀⠀⠀⠀⠑⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⣀⣤⣀⡹⣆
⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢰⡇⠈⠿⠉⠚⣧
⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠲⠚⠑⢄⡤⢼⡆
⢠⡿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⣿
⣾⠇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠙⠺⣄⠀⠀⠀⡤⠊⠉⠲⢤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⣠⣄⡀⠀⢸
⣿⠀⠀⠀⠀⠀⠘⡇⠀⠀⢧⣀⣠⢶⠠⣦⣀⠒⠲⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡊⠁⠈⠳⡄⢸
⣿⡀⠀⠀⠀⠀⠀⠙⠓⠦⣄⣀⣀⠈⠃⢢⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣆⠀⠀⠣⣼
⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠮⣖⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠁⠀⠀⢰⣿
⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠈⠙⠒⠒⠛⠓⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠹⣧⡀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠘⢷⡄⠀⠀⠸⠼⠀⠀⠀⠀⠀⠀⠙⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣠⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣦⣤⣀⠀⠀⠀⠀⠀⠙⣷⠀⠀⢀⣤⠶⠋⣠⣤⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠶⠶⢤⣤⣼⣤⣤⣿⣴⡾⠿⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⢀⡤⢴⣶⣶⣶⢦⣄⡤⠖⠛⣛⣛⠲⣄⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡫⢵⣾⠯⠿⢿⣡⠞⠛⢀⠈⠙⢦⠝⠁⠀⠚⠛⠛⠲⠬⠺⠿⣿⣯⣭⣭⣟⠙⠷⡆
⠀⠀⠀⠀⠀⠀⠀⡰⢫⡴⢿⣴⠥⡨⠋⠉⠀⠽⠚⠋⠚⠀⣄⠀⠀⠀⢠⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠈⠻⡅⠀⠿⠷⢶⣄⡀
⠀⠀⠀⠀⠀⢠⢞⢵⠏⠴⢖⡟⠀⠁⠀⡀⠀⠀⢠⠀⠀⠀⢸⠀⠀⠀⢸⠀⢸⡇⠀⢠⠁⠀⢠⠀⢀⠤⡀⠉⠀⠈⠙⠂⢳⠇
⠀⠀⠀⠀⠀⡇⣏⠄⣠⢠⠀⠠⡆⠀⡄⡇⠀⠀⡀⡇⠀⠀⢸⠆⠀⠀⠸⣄⣸⠇⠀⣼⠀⠀⡾⢰⠁⠀⡇⢀⣶⠀⠀⠀⠸⡝⣶⣄
⠀⠀⠀⠀⠀⠑⣼⣧⡌⢀⡀⠀⠘⣎⠀⠙⠄⢀⠇⠹⠐⢲⠤⠁⠁⠀⣠⣺⣁⠀⠀⠀⠀⠀⠃⠸⣀⠔⢁⠞⢸⠀⢀⡔⢠⣿⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠣⣿⣛⠷⢉⠆⠀⠘⠆⠀⠀⠀⠀⠀⠀⢠⠀⢠⡀⢀⠯⠭⠿⠀⣰⣤⣄⠀⠘⠀⠀⠀⠉⠀⢸⡠⠋⢀⣴⣯⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣯⡠⣠⡄⣠⣤⣄⣈⣈⣽⣷⣾⠨⢸⣿⡧⠀⠀⠀⣿⣿⣿⡿⠤⠤⢄⣀⣀⣀⢤⣌⣁⣰⣿⣿⢛⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢽⣿⣿⠇⡾⡿⣏⠀⠀⡿⡟⠀⠘⡿⣇⣀⣀⡀⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣾⣟⠛⠻⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⣿⠀⠀⣳⡇⠀⢀⣿⡇⠀⠀⠀⠿⢿⣤⡅⠀⠀⠈⢹⣿⣿⠋⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢻⣿⣿⢀⠀⣿⡆⠀⠘⣿⡧⠐⠀⠀⠀⠨⠄⠃⠀⠀⠀⣸⡿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠋⠀⣸⣿⠋⠀⢀⣿⠄⠤⠄⢫⣄⡀⡀⠀⠄⠀⠀⠀⠀⠀⠀⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠿⢿⡄⠀⣼⠃⠂⢠⣶⠁⠀⣁⢡⡜⠉⠤⠀⠀⢽⠀⠄⣿⠀⣀⠀⠀⣶⣦⠄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣼⣽⣿⣿⣿⣦⣾⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣾⣿⣿⣵⣼⣶⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉
⠀⠀⢀⢀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠟⠻⣿⣿⣿⣿⣤⣤⣀⣀⣨⣿⣿⣿⣿⡿⠛⠁⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣠⣴⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠻⠿⣿⣷⣄⡀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠟⠋⠤⠀⠤⠀⡀⠀⡀⣀⠀⠀⠀⠀⠀⠉⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡀⠀⠁⢀⣽⡿⠛⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠃⠀⢄⠙⢿⣿⣿⡉⠉⠉⠉⢻⣿
⣿⣿⣿⣧⣠⣴⣿⠟⠀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠙⣿⣧⠀⢀⣶⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠄⠤⡘⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⣿⣿⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠂⠁⢸⣿⡿⢿⣿⣿
⡏⠉⠁⠀⣿⡇⠀⠀⠀⠈⢂⠀⠀⠀⠂⠀⠀⠈⠬⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠙
⣿⣦⣄⣰⣿⡇⠀⠀⠀⠀⠀⢄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⢠⣿⣆⣠⣿⣾
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠖⣜⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠂⠀⠀⣸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠐⠠⢀⡀⠀⠀⠀⠀⠀⢠⠀⢠⣿⣿⠿⣿⣿⣿
⣿⣿⠟⠿⠁⠈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠄⣠⣿⠟⠁⠀⠸⣿⣿
⣿⣿⣤⣀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⣀⣾⣿⣷⣤⣴⣄⣀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣀⣤⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠈⢻⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⡟⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣴⣾⣿⣿⣿⣿⣿⣟⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣶⣧⣀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣀⣀
⠀⠀⠀⠀⠀⢀⣤⠖⢛⣉⠁⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶
⠀⠀⠀⠀⢠⡞⢁⡞⠋⠀⢀⡴⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⣾⠀⢸⡇⠀⠠⡏⠀⠀⠀⠈⠉⠳⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡖⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⢻⡄⠈⠳⣄⠀⠙⢦⠀⠀⠀⠀⣠⠇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠙⡆⠀⠈⢳⠀⢸⡇⠀⢀⡞⠁⠀⠙⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⣼⠁⠀⢀⡞⠀⡼⠀⠀⢾⠀⠀⠀⠠⣄⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⠁
⠀⠀⠀⠀⢰⡇⠀⢀⡞⠀⢸⠃⠀⠀⠈⠳⠄⠀⠀⠈⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢀⡏
⠀⠀⠀⠀⠈⣧⠀⠘⣇⠀⠈⠧⣄⡀⠀⠀⠀⣀⣠⡴⠃⢠⡏⠀⢀⣤⣤⣤⣤⡤⠴⠶⠶⠏⠀⠀⠀⠀⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠘⢦⡀⠈⠳⠦⠀⠀⠙⢦⠀⠀⠉⠀⣀⡴⠏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠦⢤⡄⠀⠈⡇⠀⠀⢸⡇⠀⠀⠀⠀⢸⡷⠶⠶⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣧⠀⠀⠘⢧⡀⠀⠀⠀⢸⣇⣀⣀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠘⠶⣤⣀⣀⠙⠶⠶⠖⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠈⠙⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣤⣀⣀⣀⣀⣠⡤⠶⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢀⣤⣤⡀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠸⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⠀⠀⠀⣿⡀⢈⡿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠈⠛⠋⠁⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣄⡀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⡀⠀⠀⠀⠀⠀⠀⡯⢼⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢋⡴⠞⠀⠀⠀⠀⠀⠀⡵⢼⠀⠤⢤⡀⠀⠀⠀⢀⡾⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⣠⠃⢀⠤⠢⡀⠀⠀⡷⢼⠀⠀⠀⠈⢢⢀⠴⡃
⠀⠀⠀⠉⠀⢸⠬⠐⠲⣀⡀⠀⠀⠀⠀⡅⠀⠀⢙⢶⡢⣉⠉⠁⢲⠀⠀⠼⠋⣄⠁
⠀⠀⠀⠀⠀⠀⠁⠠⣄⠀⠉⢢⣀⠀⢀⡇⠀⣀⣠⣰⣵⠶⠤⠶⣮⣿⠤⢶⡈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡈⣿⡀⢲⣴⣾⣻⣿⣿⠗⠀⠀⠀⠀⠈⠑⢾⣹⡆⠐⠂⡀⣈⡅⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠀⢁⡆⣰⣿⣿⡿⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠀⠡⠿⠦⣄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣀⣴⣿⣿⣿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡐⠂⠤⣶⣓⠄
⠀⠀⠀⠀⠀⠄⣀⡀⢳⠶⣶⣶⣿⣿⠠⠶⣆⣄⣈⡉⠀⠈⠂⠀⠀⠀⠀⠀⣠⡀⢹⣇⡠⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣭⣻⣿⠃⠀⠀⠉⠉⠙⠁⠀⠀⠒⠀⢲⣦⣄⠀⣿⣿⢸⣿⣀⢂⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣧⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⣠⣾⣿⣿⣷⣶⣿⣿⡇⡀⠰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈⠁⠸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠈⣸⣿⣿⣿⣿⣿⣿⡿⢁⠃⠙⡇
⠀⠀⠀⠀⠀⠘⡂⠀⢠⠤⠂⡀⣠⣾⢿⣿⣆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠟⠲⢤⣢⢀
⠀⠀⠀⠀⠐⠃⠠⡆⠀⠀⢀⡽⠋⢀⢦⡽⢻⣧⣀⡀⠀⠀⣼⣁⣾⣿⡿⣿⡷⡠⠦⠀⠉⠑⠤⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠈⠀⠀⠳⢋⠎⠠⠋⡻⠟⡹⣻⠛⠯⣟⢀⠙⡶⡋⠒⠤⡞⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠈⠘⠳⠚⠁⠈⠀⠡⠀⠀⠀⠘⢳⠗⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠛⠿⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠉⠀⠀⣠⠴⠚⠛⠳⡤⠶⠒⠲⣄⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠒⠒⠚⠋⠀⠀⠀⠀⠀⠉⠻⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⢿⣤⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⣠⣾⣿⠯⠖⠚⠳⡄⠀⠀⠀⠀⢩⡟⠁⢀⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠛⢷⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⢀⣠⡿⠒⠒⢶⡀⠈⠻⠶⠟⠉⠉⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢰⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄
⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠓⠀⠀⠀⠀⠀⠘⠷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢸⡇⠀⠀⠀⢶⣶⣤⣀⠀⠀⠀⢀⣀⡀⠀⠀⢻⣷
⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⢀⣤⣾⠿⠿⠿⠟⠀⠀⠀⠀⠘⠿⠿⠿⠿⣶⣄⠘⣧⣀⡀⠀⣀⣿⠈⠙⢷⣄⣰⡟⠙⣇⠀⠀⠘⣿⣇
⢰⣿⠇⠀⠀⠀⣠⣤⣤⡀⢺⡟⠃⠀⠀⠀⠀⠀⠀⠈⠁⣠⠴⠒⠒⠲⢤⡀⠀⢀⠤⠒⠒⠒⢦⣀⠉⠁⠈⠙⠛⠛⠛⠁⠀⠀⠀⠉⠉⠀⠀⠻⢶⣶⠾⢿⣿
⢸⣿⠀⠀⠀⠿⠯⢤⡈⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠙⡴⠁⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣾⣿⣤⣀⣀⣀⣀⠀⣿⢀⣀⠀⠀⢀⣴⡿⠛⠛⠻⣾⡇⠀⣀⣀⢀⣀⣀⣀⣇⡀⣀⣀⣀⣀⡀⠀⢹⠀⣴⠞⠉⠉⠉⠓⠦⣤⣤⠤⠤⣄⡀⠀⠀⠀⠀⠀⣿
⣿⡿⠈⠉⠉⠉⢻⡇⠉⠉⠉⠉⠙⣾⣿⠀⠀⠀⠀⢘⣿⠁⢹⡿⠀⠀⠀⠈⡇⠀⠀⢼⡿⠀⠀⠁⡿⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠹⣿⣀⠀⠀⠠⣂⢽⣦⡀⠀⠀⠀⢀⣴⢻⣄⠀⠀⠀⠀⢀⣼⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢶⡄⠀⣿
⣿⣿⠀⠀⠀⠀⣿⠠⣶⡧⠀⠀⠀⠀⠉⠛⠿⢿⣶⡕⠊⠈⢿⣶⠤⠶⣻⠋⠀⢻⣳⠶⠴⠶⣻⠏⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⢀⣧⠀⣿
⢸⣿⡄⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣦⣀⠀⠙⣷⡋⠁⠀⠀⠀⠉⠛⠒⠋⠁⠀⠀⠈⠻⣦⣤⣤⣤⡀⠀⠀⠀⠀⠚⠋⠀⠀⠀⣸⠇⢠⣿
⠈⣿⣇⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠈⠛⢷⣄⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢻⡄⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣼⣿
⠀⢹⣿⡄⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⢀⡽⠷⠶⠿⠷⠴⠶⠶⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣾⠋⠀⠀⢠⣿⡏
⠀⠀⢻⣿⡄⠀⠀⠀⠀⣿⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣿⡟
⠀⠀⠀⢻⣷⡄⠀⠀⠀⢻⡄⠀⠀⣼⠃⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢰⡟⠀⢠⣿⡟
⠀⠀⠀⠀⠻⣿⣆⠀⠀⠘⣷⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⣤⣴⡿⠁⣰⣿⠟
⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀⠈⠻⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⣀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠚⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠈⠉⠓⣦⢀⣠⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣾⡋⠀⠀⠙⠲⠤⠤⠤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⡿⠟⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠤⠤⠤⠤⠤⢤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⣀⣠⠤⠶⠶⠦⠤⠤⠤⠖⠚⠛⠲⠦⣤⣄⣠⡤⠴⠶⠬⢷⣦⡀
⠀⠀⠀⠀⠀⢀⣴⣏⣀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⣰⠟⠁⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠦⢤⣄⣀⡠⠴⠶⠶⠤⠴⠚⠉⠹⣆
⠀⠀⠀⣼⠋⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⣸⠇⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⢠⡏⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⣾⠁⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢲⠀⠀⠀⡴⢦⠈⣷
⠀⣿⠀⠀⠀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠸⡄⠀⡜⠁⠘⡇⢸
⢸⡿⠀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⣠⠖⠉⠙⡆⠀⠀⠀⠀⢠⠏⠀⠀⠀⠘⠶⠃⠀⢠⠇⢸
⠈⣿⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣹⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸
⠀⢿⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⡿
⠀⠘⣇⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⣸⠃
⠀⠀⠹⡄⠀⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⠏
⠀⠀⠀⠹⣆⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠎⢠⠏
⠀⠀⠀⠀⠙⢧⡸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣰⠏
⠀⠀⠀⠀⠀⠈⠻⢎⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⢀⣠⢤⣤⣤⠤⠤⠖⠊⠉⠉⠛⠛⠋⢙⣶⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢾⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠒⠒⠒⠚⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠶⠶⠶⠶⠤⠤⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠁⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢉⡀⠀⠀⠀⠀⠐⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢠⡄⠐⠂⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⣀⣰⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⢸⣿⣿⠿⣛⠁⠴⠀⠙⠀⢀⣤⣶⣶⣶⠦⢘⣭⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣘⠋⠷⠀⠉⠀⠀⠀⡄⠀⠿⣿⠏⣿⣿⡿⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡜⣹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠠⣾⣏⣁⣠⠀⠉⠀⠀⠀⠀⠀⠀⠘⢻⣤⣶⣶⣾⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣠⠏⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣼⣧⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⣤⣬⡿⠋⠻⣿⣿⣿⣍⣍⣻⣯⠸⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣰⠃⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣽⣿⣿⣿⣙⠋⠀⠀⠀⠀⠀⠀⢙⣯⣶⣶⣄⠀⢙⠛⠛⢛⣿⣿⣷⣾⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢰⠇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⠿⠓⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣛⡿⠿⠿⣿⣿⣆
⠀⠀⠀⢀⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣎⢿⣿⣿⡿⠃⠀⠘⣿⣿⡄
⠀⠀⠀⣸⠁⠀⠀⠈⢻⣿⣿⣿⣿⣿⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠀⠐⢶⠧⡄⠹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣮⣉⣭⠄⠀⠀⠀⠘⢿⣷
⠀⠀⠀⡏⠀⠀⠀⠀⠀⢹⣿⣿⡿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠛⠋⠉⠹⣿⣿⣟⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠈⢻⠿⣷⣿⣿⡿⠛⠛⠛⠁⠉⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣤⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣿⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠘⡇⠀⠀⠐⠦⣶⣼⣇⠈⠻⣿⣿⣧⣀⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡶⣿⣿⣿⠋⢰⣿⠃⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⣇⠀⠀⠀⠀⣸⠏⠻⢦⠀⠀⠉⠉⠙⠿⣿⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠛⠿⠟⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⢻⡀⠀⠀⣈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣏⠀⡀⢀⣶⣿⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠁⠳⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠈⣇⠀⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠸⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⡃⢀⡀⢠⠀⣠⠀⣄⠀⡀⢠⠏
⠀⠀⠀⠀⠀⠹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣟⣿⣭⡿⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠈⠿⣋⣿⣽⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣯⣴⣆⡸⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⡀⢀⠀⣀⠀⣤⠀⠄⠐⠂⠘⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⣀⠀⠀⣰⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠶⠤⠤⠤⠤⠶⠖⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠚⣉⡀⠀⢄⠠⠔⠠⡀⠀⠀⠀⡀⣀⠀⠀⠀⠀⡀⠈⣐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠃⠁⢀⠂⠀⠀⠀⠐⠄⡀⠁⠀⠈⠀⠀⠀⠁⠀⠐⠂⠀⠀⠀⠉⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠈⠢⣈⠂⠀⠤⡀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠒⠀⠂⢄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠐⠀⢀⠁⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⡠⠒⠀⠀⢀⢃⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⡠⠄⠒⢈⡀⡒⠀⡀⡘⠀⠀⠀⠀⡰⡀⠘⢀⡴⠆⠈⠠⠊⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠣⠠⢂⣁⠀⠐⠄⠀⠀⠀⠀⠀⢸⡵⠌⠤⠄⣁⠂⢀⠰⠖⠊
⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡀⠁⠀⠈⠀⠀⠀⡠⠠⠤⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⢄⠀⠔⠂⠁⠤⠁⠒⠈⠱⣄⠀⠀⠀⠠⠂⢄⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠃⡎⠂⠀⠀⠀⡀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠈⢗⠄⠀⠀⠑⢄⠁⠒⠤⠃⡇
⠀⠀⠀⠀⠀⠀⡇⠇⢀⠀⠀⡘⠁⠒⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⠂⠀⠀⠀⢀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠢⠀⠡⡀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣄⠀⠔⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠁⠁⠀⠀⠈⠐⠂⠀⡀⠀⠀⠀⠀⠑⠄⠀⠂⠢⡀⠀⠀⠀⠀⠀⠀⢀⠠⠃⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠐⠅⠀⠀⠀⠀⡠⠊⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡆⠔⠁⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢣⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⡔⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⠀⠀⠡⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⠈⠂⠄⠁⠀⢰⠀⡠⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠴⢦⠌⠁⠀⢀⡀⣀⡀⣀⡠⠽⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠚⠋⣉⣉⡂⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠁⠀⠀⠀⠀⠀⠀⢀⣛⢙⡃⠀⠔⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠚⠛⠛⡗⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠛⠛⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠰⠤⠤⠤⣾⡀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠙⡏⠙⠉⠉⠉⠉⠋⠉⠋⢹⠁⠀⠀⠀⠙⡋⠙⠉⠙⠉⠉⠉⠉⠉⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠⠀⠀⠀⠀⠀⠁⠀⠙⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠀⠀⠀⠁⠄⠁⠄⠁⡇⠀⠀⠀⠨⠈⠠⠀⠠⠀⠁⠀⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠁⠃⠁⠀⢱⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠅
⠀⠀⠀⠀⢰⠂⠀⠛⠁⠘⠀⠘⠁⠊⠃⠀⠑⠘⠋⠉⠀⠈⠉⠁⠘⠀⠘⠀⠈⠑⠈⠓⠈⠛⠀⢲
⠀⠀⠀⠀⢸⠀⠀⠀⣏⣀⣀⣈⠀⠀⠀⣇⣀⣀⣈⠀⠀⠀⠀⣏⣀⣀⣀⡇⠀⠀⣇⣀⣀⣈⡇⢸
⠀⠀⠀⠀⢸⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⡀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⠀⢸⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢸⠀⠀⠀⢇⣀⣀⣀⠀⠀⠀⣇⣀⣀⡀⠀⠀⠀⠀⢇⣀⣀⣀⠇⠀⠀⣇⣀⣀⣠⠇⢸⣀⣀⣀⣀⣸⡀⠈⠳⡀
⠀⠀⠀⠀⢸⠀⠀⠀⡠⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⡠⠄⠄⠤⡀⢸⠒⠒⠒⠦⠤⣘⡄⠀⢣
⠀⠀⠀⠀⢸⠀⠀⠀⠧⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠃⢸⠆⢀⣤⣶⡄⠈⡇⠀⢸
⠀⠀⠀⠀⠘⠒⠂⠒⠀⠒⠒⠐⠂⠒⠐⠒⠒⠀⠐⠒⠀⠀⠐⠃⠀⠒⠒⠒⠂⠂⠐⠒⠀⠒⠂⠚⢰⠋⠀⠀⠘⠀⠃⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠢⠤⠔⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠦⠈⡁⢉⡒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠄⠲⣤⠀⡀⡤⢈⠕⠂⠠⣠⠞⠉⠉⠳⠀⠈⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⡠⠄⢀⠠⠔⠉⠀⠁⠀⠀⠀⠶⢎⣽⠿⠾⠇⠐⢿⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣬⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣤⠀⠄⠐⠀⠐⠀⠀⠀⣠⢀⡳⢶⠖⠉⠃⠀⣤⣔⡻⠃⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠂⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⡏⠀⠀⣀⠤⠄⠀⠀⠉⢀⣤⣄⣀⣤⡀⠀⠀⢀⠦⠀⠐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠷⠀⠀⠀⠀⠀⣀⠀⡢⢤⣾⣾⠁⠀⠐⠁⠁⠀⠀⠐⢶⣛⣿⡏⠛⠙⠻⠻⣶⢶⡿⡒⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⢀⣀⣠⠖⠾⠞⠁⠀⠀⠈⢹⡀⣠⣆⣴⣶⠶⠤⠿⠺⢾⣛⣩⡗⠂⠀⠐⠄⠀⠀⠀⠀⣠⣀⠀⠁⠤
⠀⠀⠀⠀⠀⠀⢀⣽⣿⣷⣿⣿⣥⡄⠀⠀⠀⠀⠀⢀⣸⣧⣾⣿⣟⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠋⠙⡏⠁⠀⠀⠀⠀⠀⢸⣿⡛⠟⠛⠛⠃⠀⠀⠀⠀⢀⡀⢠⠔⠀⢀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠁⠀⣣⢀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⢀⢉⡁
⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⢉⠘⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠊⠑⠐⠀⠉⠉
⠀⠀⠀⠀⠀⠀⣿⣟⠃⠀⠀⠀⠸⡀⠆⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠆⠀⣸⠎
⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣸⣿⠂⠈⠀⠀⠀⢀⠈⣸⣿⡇
⠀⠀⠀⠀⢰⣿⣿⡇⢦⡀⠀⠀⠀⠀⠄⢰⡀⢀⣿⣿⡀⠒⠀⠀⠀⠈⣁⢸⣿⡇⠀⣀⡀
⠀⠀⠀⠀⣾⣿⡻⠨⠑⠁⠀⠀⠀⠀⠀⣄⢣⣾⣿⣿⣷⡇⠀⠀⠀⠀⢰⣼⣿⡇⠀⣿⡇⠀⣀⣀⡀
⠀⠀⠀⣼⣿⣿⡇⣄⠀⣄⠀⠀⠀⠄⠀⢨⣿⣿⣿⣿⣿⣷⣶⣶⡆⢰⣾⣿⣿⣿⣤⣿⣇⣀⣿⣽⣿⣀⡀
⠀⠀⣰⣿⣿⣿⣿⣿⣷⣿⡓⣄⠀⡐⠠⡎⢿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣟⣾⣿⣿⣿⣿⣿⣽⣿⣿⡇⠀⠀⠀⢀
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣭⠻⢕⠌⠳⢌⠘⠿⠿⡿⣿⣿⣿⣿⣿⣻⣿⣿⣷⣝⣛⣛⣿⣿⣻⠿⢿⣿⣷⣿⡓⠛⠘⢛⣃⣘⡂
⢸⣿⣿⠛⠛⠛⠛⢻⣿⣿⣿⣕⠄⠀⢀⣀⣁⣴⣶⣾⣾⣦⣾⣿⣿⣷⣿⣄⣀⡀⣷⣾⣿⣿⣿⣵⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠃
⠈⠋⠉⠀⠐⠐⠘⠛⠛⠛⠛⠛⠁⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠐⠒⠒⠒⠒⠒⠒⠲⣞⣛⣻⠛⠛⠛⠛⠛⠛⠛⠛⢛⠛⠛⠛⠛⠛⠛⠛⢛⣛⠛⠛⢛⣻⣿⣛⣛⣛⠛⢛⣛⠛⠉⠉⠉⠉⠉
⣴⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣉⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣄⣤⣶⠒⢲⣶⣶⠆⠀⠀⢒⣀⠀⢀⣀⣀⣤⣤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠐⠛⢻⣿⣿⣿⣿⣉⣵⣯⠀⠙⠁⠀⠁⣀⢰⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⠁
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠛⠈⠀⠀⠀⠀⠠⣼⠛⠿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢿⠃⡀
⠀⠀⠀⠀⠀⠹⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣶⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⠇⠈
⠀⠀⠀⠀⠀⠀⠈⠛⠧⣀⣄⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠻⠃⠈⠻⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣤⡀⠀⠀⠈⠁⠘⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠹⠔⠗⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⢃⡆⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠢⠴⠣⠂⠀⠂⠉⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⢆⢀⡔⠊⠀⠀⠀⡠⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠌⢁⠀⠀⠀⢀⠃⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠠⣂⣠⣀⡁⡠⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⡀⡀⠠⣀⡀⠀⢀⡀⢠⢤⠶⢠⠊⡇⠈⠃⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠡⠄⠠⠥⠥⠴⠥⠤⠍⠈⠀⠄⠐⠂⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢘⡳⢅⡴⠒⠀⣰⣶⠖⠲⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⡖⠵⣾⣿⠃⠀⠀⠉⠳⣿⡷⣅⡾⢯⡙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⢊⠌⠀⠶⠈⠁⠀⠀⠀⠀⠀⠀⣸⣿⣁⡀⠓⠤⠬⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣎⠰⢄⡠⣮⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠒⠀⠀⠠⠴⠋⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⢈⡵⠋⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣇⣤⡖⠋⢀⢀⢡⠾⢇
⠀⠀⠀⠀⠀⠀⠀⠈⣼⡿⠉⡉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡠⢱⣼⢶⣻⢥⣠⢾⡆
⠀⠀⠀⠀⠀⠀⠀⡀⣿⡧⠶⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠊⠡⠈⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡀⣻⣇⢀⡀⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠙⠻⣦⡀⢀⠤⠀⠰⢄⣀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢠⣾⠈⠀⠀⠈⠉⢡⡀⢀⣀⡠⠴⠖⠛⠉⠉⣩⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠈⣸⡜⣧⠐⡀⠘⠂⠘⡛⠉⠀⣀⡀⠴⠖⠂⠈⠉⣟⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠁⢣⠘⣷⠐⢂⠀⠀⠈⠳⠭⣀⣠⡬⡴⠶⠂⡹⠃⠀⠀⠀⠀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠹⣆⠀⠑⠀⡀⠀⠀⠀⢳⣤⡼⠞⢻⠋⠀⠀⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢻⡄⠀⠐⠨⢁⠀⠤⣄⠸⣿⣾⣁⡀⢀⠀⢠⣔⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⢿⣖⠀⢉⣉⣀⠿⠿⠿⠏⢭⣽⣿⣗⡒⠒⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡆⠺⢿⣄⣀⠀⠈⠀⠒⠀⠠⠄⠀⠀⠀⢁⣀⡺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠼⣿⢹⣿⡛⠛⠓⠐⠉⠉⠉⣹⣩⡥⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠈⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠐⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠎⠙⠂⢢⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠄⠁⢀⡀⠀⠘⠆⠀⠀⠀⠠⠘⢄⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⠂⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠹⠄⠖⡦⠀⣉⠢⠀⢄⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡺⠁⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⡐⠉⢀⠄⠘⠨⠡⠂⢌⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⢘⡙⢄⠀⠉⠑⠠⠡⠃⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⡐⠀⠀⠀⡀⠀⠂⠀⠈⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡴⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⢤⠔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠬⠀⢀⣀⡀⢠⡀⠀⠀⠠⠤⠄⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢑⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢈⡐⢈⣱⠹⠄⢤⡈⠀⠐⠀⠘⡄⢡
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠀⠀⠀⠀⠢⢀⡠⠙⣀⣱⠀⠀⠀⠁
⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢆⢀⡀
⠀⠀⠀⠀⢰⡀⠀⠄⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠠⠀⠠⢦⠐⠲⢢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡤⡌
⠀⠀⠀⡀⠀⠀⠀⠑⠠⢁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀
⠀⠀⠀⠀⢂⠀⠀⠀⠀⢠⠀⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠘⢀⡀⠂
⠀⠀⠀⠀⠀⠢⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠜⣨⠃
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⠁⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢀⠠⠂⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢐⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠔⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠐⠒

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠄⢠⣧⠎⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⣀⠀⠠⢄⣀
⠀⠀⠀⢠⣄⣤⡾⣆⣾⣟⣉⠳⡖⠉⢁⡄⠀⢾⣠⣄⠀⠰⠤⣄⣉⢳⠉⢱⣮⡙⣮⣷⠀⠀⠀⢀⣀⣀⡴⠖⠲⢦
⠀⠀⠀⠀⠉⠛⠿⠛⠛⠻⣷⣶⣶⠎⣿⣧⣼⣶⡉⢉⠉⠀⠀⢺⣿⣼⡷⠘⢻⢳⣿⢧⠀⠀⣴⠋⠀⠋⢷⠀⡁⢸⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣋⡁⠙⢻⣿⣷⠍⣐⡎⡝⢀⠉⣾⢏⠙⢿⣌⡀⢸⠃⠀⠀⢄⣸⠀⠀⣺⠃⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢶⣿⠋⠽⠿⠿⢉⡙⢯⣿⡿⠿⠏⢙⣻⡇⣹⡇⢂⣾⡀⣇⣿⠀⠀⠀⠀⣿⠀⠀⣿⢀⡟
⠀⠀⠀⠀⠀⢀⣠⠤⣿⡗⠀⡞⠃⢀⣤⣷⣿⣿⣿⣶⣴⣦⠴⣶⠟⠿⠞⠛⠿⡋⠀⣗⣾⣿⠀⠀⠀⠀⣿⠀⢠⡇⢸⠇
⠀⠀⠀⠀⠀⣿⣯⣍⣈⣀⣽⣿⣾⣿⡟⣻⣿⣿⣿⣿⣷⣦⣶⣿⣶⣤⡤⠚⠻⠿⣶⠿⠃⣿⠀⠀⠀⠈⣿⠀⢸⡇⣿
⠀⠀⠀⠀⢀⣙⣋⡀⠀⣀⣯⣽⡁⢈⣻⣉⣋⠀⠙⠿⠦⠽⣿⡟⢓⣨⣶⣞⠕⢀⡴⠖⠶⣿⠀⠀⠀⠀⣿⠀⢸⡇⢿
⠀⠀⠀⠀⢸⡯⢥⡏⠀⢿⠶⢾⠁⠘⣷⠶⡏⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡿⠀⠀⠀⠘⡇⠀⠀⠀⢿⠀⢸⡇⢸
⠀⠀⠀⠀⢸⡇⠀⡇⠀⢸⡆⢸⠀⠀⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢸⡇⠀⠀⠠⢠⡇⠀⠀⠀⢸⡆⠈⠃⢸⡀
⠀⠀⠀⠀⢸⡇⠀⣇⠀⢸⡅⢸⡆⠀⡇⠀⡇⠀⠀⠀⠀⣀⣠⣴⣾⡿⠛⡏⠸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇⠘⡇⠀⡗⠀⣷⢠⣤⣶⣿⠿⠛⠋⠁⠀⠀⡇⢰⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⣼⠀⠀⢸⡀⣸⠀⠀⣷⢠⡇⠀⢹⠀⢹⡟⠁⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣠⡴⠶⠶⠶⠒⠛
⠀⠀⠀⢀⣿⣀⣀⣈⣇⣿⣀⣀⣸⣸⣇⣀⣸⣇⣸⡇⠀⣀⣀⠀⣀⣀⠀⡇⢸⡇⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠈⠜⣻⡇⠀⢿
⠀⠀⣸⣟⣋⣉⣉⣭⣭⣽⣭⣭⣽⣭⣽⣯⣭⣭⣽⣧⠀⢿⣿⠀⣿⡏⠀⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⡇
⠀⠀⠈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⡏⠀⣤⣤⠀⠀⢠⣤⣄⠀⠀⣠⣤⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⡇⠀⣿⣹⠀⠀⢸⣧⣿⠀⠀⣿⣼⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠀⠀⢸⠀⠀⠀⣀⣀⠀⠀⢸⡇⠀⠀⠀⠈⠛⠦⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⢸⠇⠀⣸⠁
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣯⢽⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠲⣞⣀⣠⡟
⠀⠀⠀⣿⣞⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣄⣀⣠⣧⣾⣄⣀⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠯⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢴⣶⣿⠻⣿⣿⡁⠀⠀⠈⢹⣿⣷⣦⣄⣀⠀⠄⣀⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠛⠋⠀⢛⣍⣿⣷⣽⣿⣻⣦⡀⠀⣹⣿⣿⣿⠿⠉⣭⡘⠉⠉⠉⠉⠩⣬⣥⣼⣿⣿⠷⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⣠⢏⣨⣧⠀⠀⠸⣿⣿⠟⢁⣸⣿⡻⣷⣤⠾⠿⠃⠀⠀⠀⣀⣤⣤⣤⠄⣴⢚⣲⡿⠿⠆
⠀⠀⠀⣀⠴⠇⠀⢀⣤⠦⡈⢻⡷⠿⣿⡋⣿⠟⠁⠀⠀⠈⢘⣟⣀⣠⢜⣻⣿⣤⡙⢲⣶⠷⣶⣶⣿⣿⡿⣿⢳⡊⠛⠛⠛⠁
⠀⠀⠐⠁⠀⠲⠶⠿⠋⠐⠓⠚⠃⢰⢃⣿⠃⠀⠀⠀⠀⣨⢿⣷⣾⣿⣿⣿⣶⣿⠿⣭⣿⣿⣿⣿⣿⣿⣥⡟⢽⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢸⡏⠊⠀⠀⠀⠀⠀⠙⣂⣶⣿⣟⡯⢶⣽⣋⣹⢿⣻⣿⣿⣿⣿⠋⣵⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣽⣇⠀⠨⣴⣾⣷⣄⢺⣿⡿⢯⣶⣯⣭⣕⣺⣿⣿⣿⣿⣿⣿⣿⣤⣬⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡌⡛⣿⣿⣿⣿⣼⣿⣿⣿⣽⣟⣿⣽⣿⣻⣿⣿⣿⣿⣿⣿⡿⢛⣱⣾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣿⢿⣿⣷⣈⠙⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢤⣴⣿⣿⡟⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠭⣟⠳⣼⣿⣿⣿⣿⣷⡉⢿⣿⠿⢿⣿⣿⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⠈⢽⣿⣿⠃⠀⣠⠔⣣⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠷⣈⠛⠝⠛⠿⠿⠷⠌⠿⠆⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣻⣯⣛⠛⠚⠛⠋⠚⢁⣀⣤⡼⠿⠶⠶⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⡶⢶⣶⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣴⣾⣯⣭⣭⣍⣥⣴⡷⠀⠒⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣎⠙⠒⢺⣿⣿⣿⣿⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠿⠟⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡋⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⣤⣤⣤⣭⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣠⠖⠒⢦⡈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠸⡄⠀⠀⢠⠀⠀⠐⠒⠀⣇⠀⠀⢀⡇⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⢸⣁⡇⢠⣄⠀⠀⠀⠇⠀⠀⠀⠁⠀⠀⠈⠇⠀⠀⠀⡠⠈⠓⠒⠋⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠰⠏⠀⠀⠀⣀⣠⡤⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠖⠉⠁⣀⣀⣠⣄⣀⣀⠈⠉⠲⢤⣀
⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⡄⠀⠀⠐⠋⢀⡠⠖⢋⣩⢇⣠⠤⠞⠈⠉⠲⢄⡀⠛⠇⠀⠀⢠⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⢸⢡⡞⡆⡇⠀⠀⠀⣠⢋⡖⠉⠉⠀⠸⠀⠀⠀⠀⢀⣀⣀⠙⣄⠀⠀⠀⢸⢸⢹⡎⡇
⠀⠀⠀⠀⠀⠀⢸⢸⡇⡇⡇⠀⠀⣰⠗⠋⠀⠀⢰⣊⣁⣀⣀⣀⠀⠳⢤⣬⠷⠈⣆⠀⠀⢸⢸⢸⡇⡇
⠀⠀⠀⠀⠀⠀⢸⢸⡇⡇⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡄⠀⠀⢠⢤⣸⠀⠀⢸⢸⢸⡧⡇
⠀⠀⠀⠀⠀⠀⢸⢼⡇⡇⣇⠀⠸⡇⠀⠀⢠⠞⠉⠉⠉⠙⠒⠚⠉⠀⠀⠀⢸⠆⢹⠇⠀⣸⢸⢸⡇⡆
⠀⠀⠀⠀⠀⠀⡞⢸⠃⢳⢸⡄⠀⢧⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⡼⠀⢠⡇⡞⠘⡇⢳
⠀⠀⠀⠀⠀⠀⠱⣌⣓⡋⠘⠀⠀⠈⢧⠀⠀⠑⠦⡄⠀⠀⠀⠀⠀⠀⠀⢀⡏⡴⠁⠀⠀⠣⣍⣛⡁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠈⢳⠀⠀⠀⠀⢀⡸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣄⡀⠉⠓⠦⠤⠬⠧⠤⠴⠚⠉⢀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣤⣀⣀⣤⡤⠴⠚⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠞⠻⠿⢿⣿⣿⠷⢶⢦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠻⢉⢋⢻⡆⠀⠀⠀⠀⠉⠳⣕⣡⣂⣭⠿⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠹⠀⠆⠄⡌⠐⣇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠹⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣴⢿⢀⢃⠂⠌⡌⡜⠐⣰⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡽⢿⣄
⠀⠀⠀⠀⢀⣾⢏⢂⢆⠎⠌⠐⡜⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣦⢼⣶⠟⢻⣦
⠀⠀⠀⠀⣾⢋⠆⣌⠌⡜⠀⡜⡠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢕⠕⣱⠿⣴⣥⢿⡆
⠀⠀⠀⢰⣯⣼⣰⡌⡘⡀⡜⡰⣱⣫⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠾⠚⠁⠀⠀⢀⣨⣿
⠀⠀⠀⢸⡇⠀⠙⢷⣠⡞⠰⢱⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⡙⡡⣿
⠀⠀⠀⠘⣧⠀⠀⠀⠈⠉⠓⠶⣝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⣡⠎⠊⣐⣿
⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠨⡿⠻⠟⡝⠹⢻⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⢸⣯⡾⠃⡠⠞⢡⡿
⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠸⣇⢃⡜⢠⢃⠆⡄⡌⠜⣷⡀⠀⠀⠀⠀⠀⠸⣟⠁⡠⢊⠔⣹⠃
⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠙⢾⡠⢁⠎⡰⡘⣐⣞⡟⠀⠀⠀⠀⠀⠀⠀⢹⡊⢂⢔⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⢳⡎⡐⡝⡔⣌⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⢻⡜⣐⢊⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠸⡧⠏⣼⠇⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢶⣿⣬⣟⣀⣀⣠⣤⡴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⣽⡆⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⢀⣋⣀⣀⣀⠈⠉⠙⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⡴⠛⠉⠉⠉⠉⢉⣭⣙⣿⣿⣿⣿⣿⠁⡛⠳⣦⡀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⡰⠁⠀⣰⠋⡀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⡗⠀⢐⠈⢳⡄⠀⢳⡀
⠀⠀⠀⠀⠀⢰⠃⠀⣸⠃⢂⠐⠊⢐⢀⠀⠀⢀⣾⣿⣿⣿⣿⡟⣛⣸⣿⡀⢀⣆⠹⡆⠀⢳
⠀⠀⠀⠀⠀⡾⠀⢰⣿⠀⠀⣠⣶⣶⣶⣦⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣦⣿⠀⠘⡇
⠀⠀⠀⠀⠀⠇⠀⢸⣿⡇⠀⠻⢿⣿⡿⣿⣿⣾⣿⣿⣿⠟⠩⠀⠀⠀⠈⠈⡉⢿⣿⣿⡇⢀⢷⡤
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡀⠠⠀⠀⠀⠀⢀⠀⣾⣿⣿⡇⠈⠻⠃
⠀⠀⠀⠠⢾⡷⠀⠸⣿⣿⣿⡿⢛⠛⡉⠉⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣼⣿⣿⣿⠁⠀⡞
⠀⠀⠀⠀⠀⣇⠀⠀⢻⣿⣿⣿⣴⡙⠁⠣⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⣹⣿⣿⣿⠏⠀⣸⠁
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠻⣿⣿⣿⡿⠞⠔⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⠋⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠙⢿⣿⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠈⠛⠿⣿⣿⠻⡟⠻⠛⣟⢻⣛⡽⠿⠋⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⠀⠈⠉⠉⠉⠉⢉⠉⠁⠀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠲⠶⠂⠰⢿⡒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢴⠒⣶⣿⣿⡿⠉⠫⠙⠩⢐⠒⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⣾⣿⡟⣥⣼⡃⢹⣿⣿⠁⠀⠀⠡⠀⠀⠑⢤⡀⠄⠹⣿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⡀⢠⣿⣿⣿⣿⣌⠁⠘⣿⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠂⠀⠉⣀⠉⢡⣷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣿⣿⣿⡿⠿⠟⠃⠀⠌⠀⠀⠀⠀⠀⠐⣀⣤⣼⠀⢀⣵⣴⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣤⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⣠⣿⡄⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠈⠁⠀⠀⠦⠠⠀⠀⠀⠀⠀⠀⠨⠄⢠⣿⣿⡿⠋⠉⣝⢮⢻⣿⣿⣿⣿⣿⣿⣄
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⣩⣭⣷⣶⣶⣙⡊⠀⠛⠀⡈⢉⣿⣿⣿⣆
⠀⢀⣾⣿⣿⣿⣿⡿⠿⠛⠛⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣷⣾⣿⣿⣿⣿⣆
⠀⠀⠈⠓⢿⣿⣿⠀⠀⣀⠐⠀⠒⠒⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠃⠉⠻⠷⠾⣿⣤⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢤⢀⣴⣤⣤⣉⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣛⣉⠉⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠇⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠔
⠀⠀⠈⠐⣄⡀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡄⣷⠈
⠀⠀⠀⠀⢁⠀⠀⠀⠐⠂⠤⠀⢀⣈⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⠋⠰⠿
⠀⢀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠂⠀⠀⢀
⠀⠀⢂⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠋⠀⡀⠀⠀⢀⠂
⠀⠀⠈⢦⣀⠀⠁⡀⠀⠀⠀⠡⠀⣸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠀⠀⠔⠀⠀⣠⠇
⠀⠀⠀⠀⠢⡀⠂⠰⢄⠀⠀⠀⠂⢸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠮⠐⠂⡠⠂
⠀⠀⠀⠀⠀⠐⢄⠀⠀⠡⡀⠀⠈⢺⣿⡿⠀⠤⠤⠄⠸⡄⠀⠀⠀⠀⠀⠀⡼⠀⠤⠤⠄⠀⠐⠲⠃⠉⠁⠐⠁⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠈⠂⢀⠀⠻⣿⣄⡀⠀⠀⠀⢁⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠔⠀⢀⠔⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠁⢤⣀⣀⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣠⣈⣠⠤⠅⢀⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⢀⣁⣽⣿⣿⣬⣭⣙⣁⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⡾⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⣴⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠳⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⠀⣠⣦⡄⠀⠀⠀⠀⠀⢀⣿⣄⠀⠀⠀⠀⢀⡄⠰⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚⠋⠀⠀⠀⣞⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠻⣄⣀⣀⣠⠟⠋⠁⠉⠛⠶⠶⠚⢻⡅⠀⠲⣄⣀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠉⣀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⠀⠀⠀⠀⢻⣄⠀⠀⢀⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾⡀⠀⠀⠀⠀⠙⠓⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⠶⠛⠛⠛⠲⣦⡀⠀⢸⡇⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⡜⠁⠀⢾⡛⣿⠆⠀⢻⡄⢸⡇⠀⢠⡤⠤⠤⠤⠤⠤⠤⠤⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠠⡶⢾⣟⣷⢶⡆⠀⣿⠈⣧⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠈⣧⡀⠻⠾⠉⠻⠞⠁⣰⠇⠀⢿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠈⠻⢦⣄⣀⣀⣤⠾⠋⠀⠀⢸⣇⡟⠀⠀⠀⠀⢀⡴⠶⠶⠒⠛⠚⠛⠛⠛⠛⠒⠒⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢿⠇⢠⡤⣤⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⡴⠞⣋⠛⠳⣦⠀⠀⠀⠀⠀⠀⠘⣇⠘⠶⣿⡿⠳⠒⠖⠒⠲⠶⠀⠄⠀⠐⠠⠿⠿⠾⠿⠿⠿⢿⣿⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⣿⠁⡞⠉⠁⠀⠘⣿⣿⠛⠛⠛⠛⠛⠛⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣿⠸⣏⡛⣶⠀⣿⠛⣿⠛⢻⡟⠛⢻⡟⠻⣿⠛⣿⢠⡾⢛⣻⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠶⠄⠀⠀⢰⡋⠀⠀⠀⠀⠀⠀⣿⠀⠈⠙⠋⠀⠈⠳⠿⣤⣼⣧⣤⣼⣧⣴⠷⠞⠁⠀⠙⠉⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢀⡾⢡⡶⠛⢦⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣤⢤⢤⠤⡤⠤⢤⠤⣤⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠹⣄⣀⣬⣉⣷⠀⢻⣦⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⢴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁⠀⠸⣦⣤⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣤⣼⠇

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






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⡾⠟⠀⠀⢸⣟⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⣀⠀⠀⠀⢸⣧⠀⠀⠀⣾⣿⣯⡀⠀⠀⠀⠀⢰⡿⠛⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠷⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠿⣶⠄⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⡀⠀⠀⠛⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠻⣶⡾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⢀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢃⠠⠃⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠂⠄⠁⢡⠈⠀⡀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠘⡆⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⣿⠃
⠀⠀⠀⠶⣦⣄⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠈⠀⠠⠃⠀⢤⡂⡀⢱⠈⢡⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣿⡶⠟
⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠘⣄⠈⠢⠀⠀⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⣤⠀⠀⣀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠉⠀⡄⠀⠀⠐⢂⠈⠁⠀⠀⠀⠀⠀⠀⢠⡶⠷⢶⣄
⠀⠐⣿⣀⣠⡿⠀⠀⢀⠀⡇⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣾⢠⡿
⠀⠀⠈⠛⠋⠁⠀⠀⠀⠉⢅⠸⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠤⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⡆
⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠛⠻⠇
⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⡡⡀
⠀⠀⣿⠸⣿⠙⡷⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠻⢶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠁
⠀⠀⠀⠀⢀⣴⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠸⣿⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⡶⣦
⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡄⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢀⣤⠀⠀⣀⡀⠀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⣴⡿⠻⣶⡀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣴⡾⠃⠀⠀⠙⠛⣿⠛⠃⠀⠀⠀⣿⡀⠀⠀⠀⠹⣧⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⡬⠥⠤⠤⢌⡁⢐⠂⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⣻⣿⡟⢩⠇⠀⠀⣀⠴⠋⠀⠉⠉⠰⣮⣹⣖⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢡⠊⡹⣿⠛⠁⣃⠴⠊⠉⠳⠖⠀⠀⡰⢩⡍⠿⠋⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠘⣉⣀⡬⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⣷⣼⡿⠁⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠠⠔⠒⠚⠉⠃⠀⠀⠀⠀⠀⠀⠀⠙⢷⠛⠁⠀⠀⠀⢀⣠⡀⢰⣄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⣰⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠚⡰⢲⡟⣷⣄⣼⣋⣉⠁⠙⠂⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⠋⠁⠓⠠⠤⠛⠄⠚⡀⠀⠰⣤⣄⣿⡄
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⡸⠘⡇
⠀⠀⠀⠀⠀⠀⢸⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠸⢋⠓⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠐⠒⠊⠑⢲⠀⠀⠀⠀⠀⠀⢠⠂⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠈⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⢠⠁⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣠⢾⣶⢋⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⡢⡀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢀⡴⠁⠛⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣄⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠔⠋⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠂⠐⠂⠒⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⠛⠛⠛⠳⠔⠋⡡⠤⠐⠐⠶⠒⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⠋⠉⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣟⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢮⡂⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⢄⠸⡆⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡙⠒⢠⠶⣅⡀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡠⠄⠁⠀⢀⡆⠀⠀⠀⠀⠪⡉⠉⠁⠀⣾⠇⡟⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠰⡁⠀⣨⠀⢸⠁⠀⠀⠀⠈⡆⠑⡀⠀⠀⠘⣦⠝⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠒⠃⠛⠛⠓⠒⠚⠒⠒⠂⠀⠤⠁⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠐⠁⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠉⣿⠉⠀⠀⠀⠀⢀⡐⠃⢀⣿
⠀⠀⠀⠀⠀⢀⡇⠀⢀⣤⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠸⠀⢀⣴⢪⡀⠀⠀⠀⠈⠉⢀⣼⠛⠉
⠀⠀⠀⠀⠀⠀⠁⠀⣾⣿⠉⢻⣿⠀⠤⠤⠤⠤⠤⠤⠀⣾⣟⠙⣿⡷⠸⠖⠚⠻⠦⠽⣗⣰⡦⠖⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠲⢶⣚⢽⠛⠀⠀⠒⠒⢦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠙⣛⡾⣿⣸⡣⢝⡙⡆⠀⠀⠀⣸⠀⣠⢝⡓⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⣾⡅⡪⠒⢫⣔⡭⢚⣿⢀⣴⡫⢔⡫⢖⡩⢚⡥⠂⣱⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠗⠁⢀⡤⠷⣺⢕⡫⢟⡭⢚⡡⢔⡡⠞⢉⠔⠛⣴⢊⠵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⢓⡩⢒⡥⢚⡥⢒⡭⠒⣉⣤⡚⣏⠀⠀⠓⠊⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡀⠀⠀⠀⠀⠀⠀⢀⡾⢔⡥⣚⠥⢚⡥⠚⣡⠔⣪⣿⣷⣹⠈⢖⣹⠃⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡩⢇⠀⠀⠀⡀⢠⣤⡘⢶⡥⢊⡥⠚⣡⠔⣫⠔⣫⡴⠟⣫⢔⡏⠁⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠐⣹⣄⡀⠸⣿⣝⡩⢘⡩⠞⣡⠔⣉⢔⡫⣰⠟⣋⢔⣪⠏⠉⡔⣰⢦⢫⢹⡄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣊⠔⣋⠝⣆⠀⠫⡖⣉⠔⢋⢔⡪⣶⠕⣊⠴⣪⠗⣡⢜⠶⣼⢟⡵⢋⡵⠝⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡥⢊⡥⠚⣩⣷⠀⠀⠀⠉⠙⢍⣋⡴⢊⠵⣋⠴⡪⠖⡡⢺⠉⠁⠉⠉⠀⠀⣀⠀⡰⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣩⠔⢋⡤⢿⡀⠀⠀⠀⠀⠀⠈⢘⡕⢊⡴⢊⠔⣩⢔⡇⠀⠀⠀⠀⠀⠀⠘⣷⢟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢊⡡⠒⡩⠟⣦⢤⡀⠀⠀⠀⣼⠔⡡⢚⡥⣪⢕⡽⢛⠶⠲⣄⠀⠀⠀⠀⣇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⡴⢋⠴⢊⠤⢊⡽⡄⢀⣴⠗⣋⢔⡫⢚⠕⣡⠖⢁⠀⢋⠙⠃⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣖⣡⠖⣡⠔⣇⢸⡡⢚⡵⣋⠔⡡⠚⢁⠔⢫⡜⣉⢈⣹⣻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⠤⣚⣹⢺⡶⣫⢞⡵⠋⣠⠞⢁⠔⢁⠜⣡⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠓⠫⠤⠾⠥⠴⠇⠒⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⡠⢀⡠⢀⡀⣀⢀⡀⢀⠀⣀⠀⡀⠀⡀⠀⡠⠀⣠⢀⡀⢀⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠉⠀⠉⠈⠁⠉⠈⠁⠈⠁⠉⠀⠈⠀⠈⠀⠈⠁⠈⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⣀⠐⠂⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⣄⣄⢣⣠⠤⠄⠄⠀⠀⠀⢤⡄⠂⢉⡻⢒⣤⠱⠀⠀⠀⠀⠀⠀⠀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⢾⣷⠿⠉⠀⠀⠀⡀⠀⠀⠀⠀⢀⠌⡤⢫⢀⡥⡹⢸⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣜⠳⣴⢏⡪⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠁⢸⠀⠓⠠⢦⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠈⢠⠁⣾⢦⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⣀⠄⢊⣆⠁⡀⠀⠀⠀⠀⠀⠀⡠⠤⣬⣶⣄⠈⠐⢁⠙⠄⠀⠀⠀⠀⢼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠀⠀⠀⢈⠵⣊⢼⡇⣣⠎⠀⠀⠀⠀⠀⠀⢷⣮⣶⡌⠡⡉⠈⣆⡴⣄⡀⠀⠀⠀⣾⠆
⠀⠀⠀⠀⠀⠀⣀⠰⣱⠇⠀⠀⠀⠃⢀⣢⠔⠋⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⢓⠴⢤⠃⠀⠀⠧⠄⡁
⠀⠀⠀⠀⢸⣼⡧⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠰⢃
⠀⠀⠀⠀⠸⣤⡀⡀⣸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠐⣄
⠀⠀⠀⠀⠀⠀⠁⢸⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠈
⠀⠀⠠⠄⠒⠠⠰⠌⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡕
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⡬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⡀⣦⡦⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠠⠀⠠⠀⢳⠉⠀⠀⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⠞⡏⠀⠠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢡⡤⠀⠚⠃⠀⠀⠠⢄⣀⣒⣒⠉⠉⠁⡸⡄⠐⣀⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⡀⢀⠉⠀⠖⠉⠇⠀⠀⡐⠂⠤⠀⣠⡤⠬⣭⣷⠾⠃⢰⠻⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⠿⠶⠜⠁⠀⠰⠋⣉⣀⡀⠠⠿⠶⠄⠱⣖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡰⣠⠔⠠⠉⣀⣸⣷⣶⣶⣶⣶⠀⠀⢨⡄⠐⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡉⢟⠉⠐⡀⢠⣾⡿⠟⠋⠙⠛⠿⠋⠀⠀⢿⣿⣟⠂⠀⠈⠲⢄
⠀⠀⠀⠀⠀⠀⠠⢊⡈⠀⣒⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠄⡰⢀⠠⠿⣿⣧⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠰⠣⠉⠉⠀⠁⠂⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠋⠀⠀⠀⠀⠀⠈⠧⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⢴⡡⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⢀⣸⣿⣿⣿⣿⣿⡤⢹⡀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠈⠉⠉⠀⠀⠀⡅
⠀⠀⢠⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⢸⡀⠀⠀⢰⣿⡏⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠈⡧⡀⠀⠸⣿⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢣⢹⣦⣄⣠⣄⡘⠒⠛⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣄⣈⣉⡸⠁
⠀⠀⠀⠈⡎⢿⣿⠿⠟⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣰⣿⣿⣿⣿⣿⣿⡇⢠⠃
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⣄⣀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢠⠃
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠆⣠⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⠂⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⡐⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣉⣉⣉⡙⣁⠀⢈⠨⠀⡁⠀⠑⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠄⠀⠀⠐⠂⠈⠀⠀⠈⠒⠴⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠒⠚⠛⠋⠉⠉⠉⠉⠙⠛⠓⠲⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⣹⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢞⡿⠶⠒⠺⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠍⠻⣦⠀⣤⡄⠀⠙⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠁⠀⠀⠀⠀⢴⣿⠟⠀⠀⣄⣿⣿⣿⠀⠀⠀⠀⣠⣴⣾⣿⣿⠻⠟⢻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⣴⣿⣶⣿⠉⠛⢦⣴⣿⣿⣿⣿⣇⠀⢀⣾⡟⠋⠉⠻⣿⣶⣶⣾⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⠛⠳⣄
⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠻⢿⣿⣿⡿⠀⠀⠈⠁⠹⣿⣿⣿⣿⣿⣿⣿⡀⠀⣀⣼⣿⣿⣿⣿⣿⣿⠿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡀⠹⣿⡿⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠂⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣥⠄⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠉⠀⣤⣶⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡤⠴⠛⠛⠻⢿⣧⣾⣆⣼⣅⡀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠛⠿⠟⢿⡿⠿⡿
⣿⣿⣿⣆⢤⠀⠀⠀⣰⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⣿⣿⣿⣿⣿⡇⠀⠀⠻⢿⠟⢻⣿⣭⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠻⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠸⢿⡿⠋⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢾⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟
⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢹⡿⠁
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⡿⢁⡾⠁
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣾⣿⣷⠞⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣠⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡟⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣄⠦⠒⡲⢬⡍⠙⣯⡸⣦⣵⣶⠴⠀⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠙⠓⠖⠛⠉⠓⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢉⡤⠰⣤⣤⣄⠀⠀⠀⠀⠀⢀⣀⣐⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠰⠀⠐⠊⢑⢲⠊⣙⠓⠫⣤⣁⠴⠀⠲⠄
⠀⠀⠀⠀⠀⠀⣠⡔⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⠀⠀⡀⠀⠀⠀⠀⠀⠀⠩⢈⢷⡬⠁⠦⠤⢴⠾⠳
⠀⠀⠀⠀⠀⣼⣟⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠠⡀⢰⣀⠐⢀⢤⠀⠀⠤⠞⠆⣗⠈⠂⠀⠟⠂
⠀⠀⠀⠀⢂⣘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡲⣻⣁⠀⠐⠀⠀⢀⠀⠆⠨⠄⠈⠈⠐⠀⠀⠄⠀⠀⠀⠈⠀⠀⢄⡀⡄
⠀⠀⢀⠙⠋⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡼⢿⡤⠀⠋⠖⢀⡄⠄⠤⠀⣀⠀⠀⠀⠀⠘⠀⡃⠂⠄⠀⠀⠠⠀⠀⣋⣿⣅⡀
⠀⠀⠘⣐⡋⠰⠈⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⡞⠏⠀⢠⡐⠤⠌⠈⠐⠤⠈⢠⠌⠀⠓⠀⠀⠀⠀⠄⠐⠒⠀⠂⠀⢂⠀⠙⢧⣏⡥
⠀⢰⣯⣭⣀⠀⡠⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⢻⣁⢀⠠⠄⢋⡭⡶⠁⠢⣀⡄⠀⢤⢤⣄⢆⠀⢀⠀⢀⠀⠁⠂⠠⡀⠄⠀⠀⢰⠀⠰
⢠⠋⣀⡠⣤⠤⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⠒⣒⣪⣡⡝⢉⠄⠢⠐⠤⠄⠤⠃⡁⠌⠂⢯⠐⠋⠐⢀⡄⠀⠁⠂⠀⠡
⠰⢢⠬⠥⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠡⢡⡞⠁⣀⣀⡻⡾⠙⢧⣅⠈⠢⠎⠢⢀⠐⣴⢬⠄⠐⠃⠈⡄⠈⠐⠂⠒⠁⡀⣄
⠐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠶⠷⠛⠙⢛⡋⠛⢷⣤⣤⣙⠆⡠⡐⠂⠀⢻⡝⠦⠼⡇⠰⠏⠈⠀⠀⣶⠢⢙⠍⠁⠈
⠀⢹⢀⣀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠫⠁⠀⠀⠀⠀⠌⠀⡀⠀⠀⠇⠘⢯⢳⡀⠈⣶⠀⠙⣀⠀⠙⢾⡆⢀⣴⠀⡤⠞⡺⢬⣆⢆
⠳⣯⣟⣽⣦⡴⣦⠐⢀⣄⠀⠀⠀⠀⠀⠀⢰⢋⣄⠀⠀⣼⣠⣀⠔⠑⠀⠰⠂⠈⢤⡈⠶⢻⡝⢦⠿⠦⠚⠉⠀⠀⠀⠉⠣⣽⡟⠁⠘⢧⣸⡁
⠀⠀⣿⡼⠦⡾⢸⠓⡖⣾⣄⣤⠀⠀⠈⠀⠸⡁⠁⠈⠉⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠚⣋⠽⠂⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⢿⣷
⠀⠀⠻⡟⠦⡁⣘⢸⠲⠧⢎⣩⢳⡀⠀⠀⠀⠙⢦⣬⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⠀⠉⣀
⠀⠀⠀⣸⠠⠃⠈⠾⡘⢽⢽⡴⠞⠁⠀⠀⠀⠀⠀⠈⠉⠈⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⠰⠒⠓⡼⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⣌⡉⠈⠅
⠀⠀⠀⣯⠖⠰⡏⠑⢱⢈⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⣀⠀⠀⢡⣈⣥⠶⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠁⡈
⠀⠀⠀⠘⣆⠻⣧⣇⡾⣬⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⢉⢻⡄⣡⡾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠧
⠀⠀⠀⠀⠹⡄⠈⠉⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠂⠤⠉⠁⢨⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠑⢠⡆⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⠐⡂⣢⡿⢁⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡽⠋⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⡦⠶⢦⣾⢿⣷⣶⢶⣄⣀⣈⡈⢀⠠⠄⠀⠁