Kiwi fruit Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠒⠒⠈⠉⠉⠉⠉⠒⠒⠢⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠰⠀⠀⡄⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⢀⠠⡀⠐⢀⠀⢀⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⠠⠠⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⢸
⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠲⠀⠑⠡⠐⢏⠀⢘⠠⠇⢀⠀⠦⠀⠀⠀⠉⠀⠀⠀⠈⡆⢆⣀⡁⠂⠀⢡⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⢀⠎⠀⠀⠀⠂⠀⠀⡑⠦⠐⠉⠔⠁⠀⠀⠀⠀⠀⠀⢠⡄⠀⠄⠉⠁⠀⠀⠀⢸⠾⣺⡻⣿⢺⢝⠨⣂⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⢸⠀⠀⠀⠀⠤⠀⠀⡀⠨⣄⠀⠀⠀⠀⠀⢀⠤⠔⢀⡀⠄⠀⠀⠠⠄⠀⠀⢀⣿⠀⠈⠺⡺⢘⠰⠠⠂⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠞⠀⠀⠀⢀⠄⠀⠠⠆⣨⢤⠓⣀⢐⡉⢪⡸⠐⠆⢀⠁⠘⠂⠀⠀⠀⠀⢀⡾⢹⠀⠀⠀⠈⠰⠘⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⢰⠀⠀⠀⠀⠀⢀⠀⠀⠴⠐⠋⠉⠈⠁⠌⠆⠀⠀⠈⠣⠀⠀⠀⠀⣀⠔⠛⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠔⠁
⠀⠀⠀⢣⡀⠀⠀⠀⠁⠀⠀⡠⠀⢀⠀⠀⡀⠀⠀⠘⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⣸⡃⡎⠐⠀⢄⠠⡐⠄⠢⠑⢀⠁⠊
⠀⠀⠀⠀⠱⣄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⢀⠀⠔⠈⠀⠀⠀⠀⠠⡾⠻⠷⠤⠤⠤⠤⠦⠤⠐⠂⠉
⠀⠀⠀⠀⠀⠙⠯⡒⠲⠤⠤⢀⠠⠤⠄⠂⠒⠂⢉⠁⠀⠀⠀⡀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⢴⣀⣂⣀⡀⠀⠐⠐⠂⠂⠁

⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠠⠠⢤⣀⡀
⠀⠀⠀⠀⢀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⡀
⠀⠀⠀⣠⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣤⢤⣄⣀
⠀⠀⠀⢯⣄⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⡄⠉⠘⣪⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡜⠀⠀⠀⠀⠀⠀⢀⠠⠴⣄⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⢀⣱⡬⠝⠋⠉⢶⡇⢀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠇⠀⠀⠀⠀⠈⣻⡣⣤⠤⢤⣀⡝⡒⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⢀⡀⠀⢀⡀⠤⠐⠊⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠉⠉⠊⡘⠀⠃⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠠⠀⠒⠒⠀⠀⠠⠀⢀⠀⠀⠀⠀⠈⠓⠤⣀⣀⠀⠀⠀⢀⣀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⢀⣀⢐⡀⠠⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⡆⠛⠉⠉⠹⣦⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢳⢦⣤⡀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠽⢛⠓⠞⠃⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄⡀⠀⠀⠀⠀⠀⣠⣀⡤⠴⠋
⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠒⢂⠈⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠋⠉⠉⠉⠉⠉⠛⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠛⠛⠛⠒⠢⢤⣀
⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣿⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢻⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⢄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢣⡀
⣿⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠱⡄
⠸⣇⠀⠀⠀⣏⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠁⠐⡀⠀⠀⠀⠹
⠀⢻⣆⠀⠀⠈⠳⢤⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡀
⠀⠀⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣤⣀⣀⣀⣠
⠀⠀⠀⠀⠀⠈⠛⠿⢶⣦⣤⣤⣤⣤⣤⣤⣴⠶⠞⠛⠉⠁⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⣹⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣶⣶⣶⣶⣶⠶⠿⠛⠋⠉
⣿⣿⣿⣻⣻⣻⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣟⣛⣟⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠒⠀⢀⡀⢀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢄⠀⢀⡀⠠⠀⠀⠈⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠈⠷⡦⣬⣈⣠⡆⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠤⠤⣀⣀
⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⡴⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⢀⠞⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠈⠕⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠈⠀⠀⠈⠉⠐⠒⠒⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠈⠀⠉⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣶⣶⣴⣦⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⠤⢤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠤⢄⡀
⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⢤⡀
⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠱⡀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡢⠒⡄⠀⠀⠀⠀⢳
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⣸⡆
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣶⣿⠇
⠀⠘⣄⢠⠀⠡⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⢃⡾⣥⢹
⠀⠀⠘⣆⠳⡄⠈⠢⡀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠂⠤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡄⡾⢸⡇⣸⣿⣿⡏
⠀⠀⠀⠈⠣⣄⠀⢀⠂⠑⠢⠀⠠⠂⢀⠠⠀⠀⣠⡄⠀⡀⠀⣈⡭⢀⣀⢀⣠⡴⠖⠁⢄⣡⡼⣷⣿⣻⡎
⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠈⠀⡡⠆⠀⠬⣀⣀⠄⠀⡺⠈⠔⡴⠂⢠⣼⣞⠠⣞⡼⡞⡯⢹⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣄⣀⠀⠀⠀⠀⠁⠀⠈⠈⡡⠀⢉⣡⢏⠀⠞⡡⠂⠉⠖⢛⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⢤⣤⣀⣀⣀⠀⢀⣈⣀⣀⣠⡤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠉⠁⠈⠉⠉⠗⠒⠠⢀⡀
⠀⠀⠀⠀⠀⡰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⣀
⠀⠀⠀⠀⡜⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⢄⣀
⠀⠀⠀⠸⣥⡀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀
⠀⠀⠀⢐⠈⠋⠵⢍⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠈⡄⠘⣶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠁⡀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⠀⠀⠀⠀⠀⠀⢀⡄⠶⢌⡯⣹⢆⣠⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠠⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⣦⣳⠓⠋⠀⠀⠙⢿⡆⠦⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠸⡄⠀⠐⠀⠀⠀⠤⣿⣓⣶⠲⡲⢤⠴⠫⠁⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠆⢀⣀⡀⡀⣀⣁⠴⠄⠒⠁⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠈⠀⠚⢈⠁⠈⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⡄⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠚⠃⠠⠤⢀⠀⠀⠀⠀⠀⠀⠁⠂⣄⡀⠀⠀⠀⠀⠈⠙⠒⠶⠶⠤⠤⠶⠶⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣄⡄⣋⡀⠠⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⡮⠘⠋⠉⠙⢻⡤⠄⣤⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣗⣤⣀⡀⠀⠀⠙⢳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠐⠆⢉⡙⣆⡶⣤⣠⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠈⠀⠁⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⢀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠄⣀⠀⠀⠀⠀⠀⠀⡠⣃⡤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠒⠛⠉⠁

⠉⠑⠛⠁⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⢀⢀⣲⡄⠀⡇⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣉⠻⣦⡀
⢦⠤⠤⠤⢐⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡖⠀⠀⠀⠉⠀⢀⠴⠧⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣁⣹⠙
⣦⣠⣷⡾⠏⠁⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣴⣾⠶⡶⠀⠀⠀⠀⠀⢀⠄⡠⠙⠂⠀⠀⢀⠄⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷
⠛⠉⠉⠀⠀⠀⠀⠀⢀⠀⠀⠉⠢⣻⣟⣲⡟⠃⠀⠀⠀⣀⠀⢀⡀⡠⠔⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣀⠀⠀⠈⠂⠀⠀⠀⠀⣠⠖⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⣶⣾⢿⣦⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠈⠂⠈⠙⠲⠦⣤⣤⠤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣴⡟⠀⠀⠀⣨⣶⠾
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⣏⣷⣄⣀⣠⣿⠆⠀⠀⢀⡆⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠉⠉⠚⠿⡒⠋⠁⠀⢠⡞
⠀⠀⠀⠔⠋⠀⠀⠀⢸⠀⠀⢀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⣀⣠⠴⠋
⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠢⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢠⣠⠀⠒⠒⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡰⠀⠉⠄⠀⠐⠆⠀⡀⠁⠀⢀⠀⢂⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠢
⠀⡀⠀⠀⠸⠋⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡤⠲⠃⠁⠉⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠠⠄⠀⠀⢀
⢀⠁⠀⠄⡸⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣠⣀⠤⡼⠁⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠐⠀⠀⡠⠖⠀⢀⠀⠀⠂⠀⠀⢀⡀⠀⠀⠰⠘
⠉⠉⠛⢤⡀⠀⠐⠢⠤⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠁⠀⠀⠀⠀⠀⠀⠐⠒⣄⠀⠀⠀⠀⠀⠀⠡⠉
⠐⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⣀⢠⢠⣤⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠘⢀
⠀⠁⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠼⠀⠀⠀⡴⠀⠀⠀⠀⠀⡀⠀⢀⠄⠋⠁⠀⠼⡇⠀⢠⠈⣿⡄⠀⠀⠀⠀⠀⠀⠉⠢⠄⠠⠴
⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⢳⣄⠀⠤⣀⣰⡇⠀⠀⣕⣦⠦⠀⠰⢣⣀⠀⠀⡴⠗⠀⢀⣼⠐⢻⡿
⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⢢⡙⢿⣿⣿⣿⡇⠀⠰⢿⢫⡀⣀⠀⣉⠛⠻⠜⠀⢀⣴⠯⡄⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠛⠿⢷⡀⠀⠈⠛⠛⠻⣷⡉⠁⠀⢤⡞⢛⡋⢲⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⠀⠀⠀⠉⠁⠀⢀⣼⣶⣣⣼⡿⠟⠁
⠀⠀⠀⣀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠂⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠
⢀⡄⠉⠹⣷⢠⣼⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠀⠀⠀⠰
⠀⠛⢺⣀⠀⠙⠁⠀⠀⢀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣇⠀⠀⠸⡟
⣄⡀⣀⢶⡆⠀⠠⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣟⢦⠀⠐⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⢄⣀⡠⠊⠁⠀⠀⠀⠀⠁⠐⠪⢕⡢⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠑⢄
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⣠⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢰⡿
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⡹⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣦⠤⠤⠤⠤⠔⠚⠉⠀⠀⢀⠜⠉⠑⠢⢤⣀⣀⣀⣀⣀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠤⠤⠤⠤⠐⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠒⠀⠤⢄⡀
⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⢀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠠⠁⠀⠀⠀⣀⣤⡤⣼⣴⣰⣀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⠋⠉⠉⠈⢿⣁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠐⢀⣿⣿⠀⠀⠀⠀⢸⣿⡟⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠰⢻⡿⣤⣄⣀⣰⣾⠻⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⢟⠻⠛⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠤⣶⣠⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣨⠇⠂⠀⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⢀⡼⠃⠉⠀⠔⠁⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠺⠑⠚⠍⠙⠀⠀⠀⢀⣠⠇
⠀⠀⠀⠀⠀⠠⠒⠊⠉⠁⠀⠉⠀⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠠⠐⠂⠀⠀⢀⡦⠋
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠄⠴⠶⠚⠉
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⢸⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⢺⣕⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠝
⠀⠀⠀⠀⠉⠟⠒⡤⣤⡤⠤⠄⠀⠒⠚⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⢶⢾⣷⣶⣿⣿⣿⣿⣶⣶⣶⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠽⠿⣿⣿⣿⣠⣜⣇⣎⣌⣾⣿⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣤⡀
⠀⠀⠀⢀⣠⡤⠤⠶⠦⠤⣤⣀⠀⠘⣦⠀⣀⣤⣴⣞⣋⣉⣭⣍⣙⣦⡀⠀⠀⣰⠊⢡⡶⢷⡶⢈⣷⡄
⠀⢀⣾⠏⠁⠀⠀⠀⠀⠀⠈⣿⣧⠀⠈⠣⡙⠻⣿⣿⣷⣥⣒⠢⢌⠙⢷⠀⢰⡇⠸⢿⣤⢾⢁⣼⣿⣷
⠀⣾⣿⡅⠀⠀⠀⠀⠀⠀⢀⣸⣿⠀⠀⠀⠈⢳⣄⠙⢷⡙⣿⣷⢦⡙⢬⣷⠀⢿⣶⣦⡶⠚⠋⠁⣿⠏
⠀⢹⣿⣷⣤⡀⣀⣀⣤⣴⣾⣿⠏⠀⠀⣀⣀⠎⠈⠱⡄⢻⣾⣜⡆⠙⢦⣿⠀⠀⠙⠳⠦⠤⠴⠞⠋⠀⣤⡀⠈⣆
⠀⠀⠙⠻⣿⣿⣿⣿⣿⠿⠋⠁⣠⣾⣿⠿⣿⣿⣶⡄⢸⠀⠹⣿⣷⢐⣬⡟⠀⠀⠀⠀⠀⠀⠀⣲⣦⣾⠛⠑⢠⣿
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢰⠏⠉⠀⠀⠀⣹⣿⣿⣌⣅⡀⠈⠻⠞⠁⠀⠀⠀⠀⠀⠀⠳⣄⡈⠁⠀⣀⣤⣿⠏
⠀⠀⠀⢀⡤⠶⠦⢤⣄⠀⠀⣾⠁⠀⠀⠀⢀⣿⣿⣿⠿⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁
⠀⠀⣰⠋⠀⠀⣢⡀⠈⢷⡀⢻⣇⠀⠀⢀⣿⠿⠋⠀⠀⠀⠙⢿⣿⣇⠀⠀⠀⣀⡴⠞⠛⠿⢿⣳⣦⡄
⠀⠀⡏⠀⢠⡞⠙⣿⠀⠈⡇⠘⢿⣷⣆⣼⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⣰⣋⠤⠤⠤⠤⢤⣽⣿⣿
⠀⢸⡇⠐⢿⣇⣰⡟⠀⡸⠁⠀⠈⢙⡿⢿⠿⣷⣀⠀⠀⠀⢀⣿⣿⣿⠇⢀⣿⠀⢀⣠⣴⣶⣶⣿⣿⣿⣷⡄
⠀⠀⢳⣀⠈⠙⠉⢀⡼⠁⠀⠀⠀⠀⠃⠈⠀⠘⢿⣷⣶⣶⣾⣿⣿⠏⠀⣸⣿⣛⣭⣥⣾⣿⢿⣿⠃⠘⣿⣿
⠀⠀⠀⠈⠛⠛⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⡿⡟⢳⠀⠰⠿⣭⡄⢀⡼⠟⢋⣾⠏⠀⣺⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠻⠧⠴⣿⠷⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠾⠟⠛⠛⠛⠷⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢰⡄⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢠⡆⠀⠈⠃⠀⠙⢁⣀⢀⣠⡄⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⣤⣜⠇⠀⠀⠁⠀⠀⠙⠁⠘⣉⣀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠠⠶⠶⠄⠉⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⠁⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⢀⣀⠀⣴⡿⠃⠀⠀⣄⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠉⠁⠈⡉⠀⣤⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⢠⡾⠃⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣤⣀⣀⣀⣀⣀⣠⣤⣴⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⠉⠙⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⠟⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠒⠒⠒⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠛⠒⠒⠒⠦⠤⣀
⠀⠀⠀⠀⢠⣿⣿⣶⠀⡀⠁⠄⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢸⣿⠟⠻⣞⣻⣆⠀⠀⠀⠀⠀⣰⣏⢁⡀⠀⠀⠀⠀⠀⠀⠀⣴⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠪⠄
⠀⠀⠀⠀⢹⣿⣄⡀⣹⣿⣟⣄⠀⠀⠀⣸⣟⣶⠀⠀⢐⠤⠀⠀⠀⢠⠲⠀⢹⡂⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢎⠣⠤⠴⢒⠂
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣼⣶⣿⣿⡿⣷⣬⣧⣑⠀⠀⢀⣈⣳⡀⢠⡗⠄⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄⠀⠀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠟⠛⠙⢷⣷⣾⣮⣷⡀⠀⠀⠈⠙⣛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣶⣄⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⠣⡀⠀⠀⠀⠀⠀⠉⠉⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠒⠉⠀⠀⠁⠌⠁⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣼⡋⢆⡀⠀⡀⠀⠀⠀⠀⡀⢀⠀⢠⠉⣦⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐⢦⡄⠤⠤⣆⡜⠁⠀⠀⢀⠀⢻⠏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣄⣌⡗⠀⠓⠆⢃⢀⡔⢥⠚⠒⠙⠢⣹⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣃⣿⣽⣢⣵⣄⣾⡀⠀⠀⢠⣥⣾⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣔⣢⣄⣰⣆⡂⠀⠁⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣞⣗⣤⣲⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣮⣿⣿⣵⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠀⠀⠀⠀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠒⢱⠐⠁⠒⠂⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠧⡀⠀⠀⠀⠀⠀⠀⢀⣿⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡤⠔⠉⠁⠙⢦⡂⠀⠀⠀⢈⡟⢤⣀⡀⡴⠀⡐⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⣑⡆⠀⠾⠘⠀⠀⠀⣄⡀⣠⠰⣿⠂
⠀⠀⠀⠀⠀⡄⠀⠀⠠⡉⢗⡀⣀⢀⠰⠁⠀⠀⠀⠀⣼⡇⠂⠑⠀⠈⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣠⠃⠂⠀⠀⣼⣿⣶⣾⣿⡟
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣀⢾⣿⣅⣀⠀⠀⣀⢠⠤⣌⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⣠⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠙⢷⣦⣄⣀⣀⠀⣀⣀⢠⣔⣲⠟⠋⠛⠛⠛⠿⠓⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⣤⣤⡾⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠂⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠒⠒⠀⠈⠉⠉⠉⠉⠉⠉⠀⠒⠂⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠒⠒⠰⠯⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠲⢄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⢀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠆⠀⡀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠘
⠀⠀⠀⡴⠋⠀⠀⠀⢀⠐⢌⢣⢠⣡⠆⠀⣃⢁⠐⠂⠀⠀⠀⠀⠀⡠⠄⠀⠀⠙⡄⢠⠀⠻⡢⠀⢠⢠
⠀⡠⠊⠀⠀⠀⠀⠠⢌⠢⠀⢠⡂⡸⠂⠀⠒⠙⠀⠒⠀⠋⠂⠀⠂⣠⡄⠀⠀⠀⢸⣀⣴⣶⣴⣜⠠⡶⢄⡀⠀⠀⠠⠀⠀⠀⠈
⣰⠁⠀⠀⠀⠁⠂⠀⠦⢙⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡀⠰⠆⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⡻⡟⠇⡗⡮⡕⠪⠀⠀⠀⠂⠀⠀⠸
⡇⠀⠀⠀⠀⠀⠀⠀⠤⠐⡿⢄⠀⠀⢀⡀⡠⡔⢐⠁⠠⡄⣀⠄⠀⠀⠂⠀⠀⢀⣾⡇⠀⠈⠣⡃⠅⡃⠗⠁⠀⠀⠀⠀⠀⠀⡸
⡇⠀⠀⠀⠠⠒⠀⠰⠚⡠⠶⢎⣡⡄⣥⡈⡦⠑⠘⠇⢀⠂⠈⠃⠀⠀⠀⠀⢀⡾⠫⡇⠀⠀⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⡰⠁
⢳⠀⠀⠀⠀⠀⡠⠄⠈⠘⢁⠃⠈⠀⠀⠡⠘⠂⡀⠀⠀⠓⠀⠀⠀⠀⡠⠒⠋⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⡀⢀⠜
⠀⢣⡀⠀⠀⠀⠀⠀⠀⡠⠂⢀⡄⠀⢀⠀⠀⠀⠙⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⣰⣃⢸⠡⠃⠐⠄⠢⠐⠈⠢⣑⠠⠔⠁
⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⣀⣀⠤⠒⠉⠀⠀⠀⠀⠀⡾⠛⠿⠦⠶⠀⠀⠈⠂⠐⠂⠉⠁
⠀⠀⠀⠐⠮⡑⠒⠤⠤⠤⠤⠤⠤⠔⠒⠒⠉⡁⠀⠀⠀⠀⡀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣠⣄⡠⠀⠀⣐⠀⠲⠮⠑⠂⠁
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠚⠋⠉⠉⠉⠉⠉⠉⠉⠓⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠤⡀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢄
⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠤⠤⢤⣄⣀⣀⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠑⡄
⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠢⣄⣀⣅⠀⠀⢀⡀⣰⠀⠀⠀⠀⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠒⠲⢶⣉⠂⠚⠳⠾⠾⠷⢟⡦⢤⣄⡀⠤⠄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⣠⠤⠒⠺⠔⡀⠀⠀⠀⠀⠀⠉⠲⡱⠖⠄⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠳⣄⠀⠀⠀⠀⠀⠀⠀⠔⠔⠃⡔⠢⣤⣴⣢⣤⣔⣡⠦⡙⠦⠒⠂⠄⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠈⢇⠱⢌⠀⠀⠈⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠈⠙⠲⠤⣄⡀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⣄⣀⣀⣘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠲⠶⠤⠤⠤⠤⠴⠖⠒⠋⡹⠃⠀⠀⠀⠀⢀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠶⠶⠶⠖⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢗⠒⠉⠋⠉⠉⠉⠉⠙⠓⠲⠤⣀
⠀⠀⠀⠀⠀⠀⡄⡠⠔⠉⠁⠀⢂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⡠⠛⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡄
⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡿⡄
⠀⠀⠀⡜⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠸⡽⠇
⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⠇
⠀⠀⠚⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠀⠀⣠⠞⠀⠀⠀⢀⠠⠔⠚⠉⠁⠀⠀⠀⢉⡑⢄
⠀⠀⠀⠀⠀⠑⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⡤⠞⠁⣀⡤⠖⠉⠀⠀⠀⠀⠄⡤⠆⢚⡆⠀⠒⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⢤⣀⣀⢀⢀⡀⣀⣠⣀⣤⠴⠖⠊⢁⡠⠔⠉⠀⠀⠀⡄⠐⠈⠈⠀⠀⠀⠤⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⡠⠒⠁⠀⠀⢠⠐⠘⠁⠀⠀⠀⠀⣀⡰⠎⠁⠀⠀⠀⢀⠜⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠤⠘⠁⠀⠀⠀⠀⡠⡴⠈⠁⠀⠀⠀⠀⡠⠔⠁⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠠⡟⠀⠀⣀⡀⡤⡄⠃⠁⠀⠀⠀⢀⡠⠔⠉⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠒⢁⠀⠉⠋⠘⠈⠁⠀⠠⠈⢀⡠⠔⠊⠁⠐⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⣀⣀⣀⣀⠠⠤⠐⢒⠉⠀⠀⠀⠀⡠⢀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⢤⣀⣀⡀⠀⠀⠀⢀⣠⣠⠶⠟⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⠶⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⢀⣴⠞⠉⠁⠀⠀⠀⠀⠀⠉⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠋⠉⠀⠀⠀⠀⠉⠉⠓⢦⣄
⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢀⡤⠰⠰⢔⡄⠀⡀⠀⠈⠳⡄
⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢸⡀⠀⠀⠈⠈⠓⠠⢀⠀⠀⢻⡄
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⢿⣿⠋⠀⠀⠀⢀⣠⡤⠖⠲⠦⠤⣄⣀⠀⠀⠀⠸⣇⠀⠀⠈⠳⣄⠀⠀⠀⠀⣘⠂⠀⠀⠸⡇
⠀⠸⡇⢀⣀⡀⠀⠀⠀⠀⣠⣾⣿⣟⣯⠟⠁⠀⠀⢀⡴⠋⠁⠀⣄⣀⢀⢀⡀⠉⠑⠲⣄⠀⠙⢷⣀⠀⠈⠐⠁⠃⠜⠃⠇⠀⠀⠀⢸⠃
⠀⠀⢷⣀⢉⣀⣀⣤⣴⣶⣿⣿⡿⠟⠁⠀⠀⠀⠀⡾⠁⠀⣬⠋⠈⠀⠀⠉⠒⢦⠀⠀⠈⢳⡄⠀⠙⠳⣤⣀⣀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠉⠻⠿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢙⢢⣀⠀⠀⠀⠀⢀⠏⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠙⠛⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⡀⠀⠀⠝⠹⠰⠑⠘⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠶⠶⢶⣦⠀⠘⣿⠉⠙⠷⠦⣤⣄⣀⣀⣀⣤⣴⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⣠⡴⠋⠉⠀⠀⢰⡤⠞⢻⡇⠀⠀⠙⢷⣄⠀⢀⠀⠁⠀⠀⢁⣥⡿⠋⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠐⣶⠏⠉⠀⣿⠂
⠀⠀⠀⠀⠀⡼⠃⢀⠀⢐⣧⡞⠋⠁⣲⡟⠀⠀⠀⠀⠀⠈⠙⠻⠷⠶⠶⠟⠛⠉⠀⠀⢀⣀⠠⣤⠀⠀⠀⠀⠀⠀⣘⢥⠂⠀⢀⡏
⠀⠀⠀⠀⣸⠁⠀⣼⡶⠋⠁⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠈⠉⠁⠠⠶⠠⠖⠐⠈⠀⠀⠀⡜
⠀⠀⠀⢠⣃⣴⣾⠋⢁⣠⡤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣤⣀⣠⡤⠤⠒⠉


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣠⠤⠤⠶⠖⠖⠒⠲⠾⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⠙⢆
⠀⠀⠀⠀⢀⡤⠛⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⣀⣀⢀⣀⠀⠀⠈⡇
⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠥⡷⠟⠋⠉⠉⠁⠀⠉⠉⠉⠓⠦⣄⡀
⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠠⠀⡼⢊⠕⡉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠳⢄
⢺⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠺⠈⠃⠘⠀⠀⢀⡞⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠅⡀⠄⠀⠀⠀⠀⠀⠑⢄
⢸⠀⠀⠊⣁⣈⠙⢦⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⢆⡏⢰⡇⠀⠀⠀⠀⠀⡄⢀⡈⠸⡠⢄⣢⠃⠆⣠⢀⠘⠁⠀⠀⡈⠳⡀
⢸⠄⢠⢋⡄⠈⠳⡄⢧⠁⠀⠀⠀⠀⠀⠐⠀⠀⠈⡾⠠⢸⠀⠀⠀⠀⠀⢠⡀⠀⢯⠤⠉⠉⠁⠈⠛⠧⣤⠎⣀⠀⠀⠱⡀⠱⡀
⠘⣇⢸⠸⣄⠀⠀⣿⢸⠀⠀⠀⠀⠀⢀⣀⡀⡤⠀⡇⢱⠸⡆⠇⠀⡀⠀⢀⠀⠈⢉⡖⢄⠀⠀⠀⠀⠀⢓⡦⢁⣀⡀⠀⠃⠀⢱
⠀⠹⣌⠣⣌⣀⣰⠏⡜⠀⠀⠒⠂⠖⠒⠒⠃⠃⠀⡇⠈⠀⢳⠠⠀⠉⠀⠀⣠⠀⠆⠐⠒⠆⡀⣄⣀⡀⣀⢣⠀⠂⠀⠀⠀⠀⡄
⠀⠀⠙⣗⠠⠉⢛⠩⡀⢂⢠⠀⡀⠀⡩⡘⡼⠰⠂⢿⡢⡀⠈⢧⡡⠀⠠⠀⠀⠀⢀⡀⠃⢋⠀⠁⠘⠈⡃⠲⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠳⢤⡑⠊⠐⠀⠁⠈⡙⡙⡁⢉⢁⠄⡀⠸⣏⣣⠄⡀⠳⣔⢄⠀⠀⠀⠀⠀⠁⠈⠐⠈⠀⠘⠁⠀⠈⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣈⣀⣀⣀⣁⣨⣬⠴⠚⠻⡕⠣⠀⠀⠈⠳⢷⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠙⣄⠓⢄⠂⡀⠀⠉⠳⠥⣂⡤⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣒⣒⣀⡀⠀⠈⠙⠛⠲⠦⠤⣤⣤⣤⣤⠤⠶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠬⣀⠠⠠⠄⠖⠒⣀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣒⣒⣥⣬⣴⣶⣦⣾⣗⣚⣋⣁⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠋⠁⠀⠀⠀⠀⠉⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⡀⢄⠀⣠⠆⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⢠⡀⢑⣨⢀⡏⠀⡄⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⣀⠁⢤⠙⠉⠁⠒⠰⡯⠐⠊⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠠⠀⠀⡘⠂⠀⠀⠀⠀⠲⣏⠠⠥⠄⠀⠀⠀⠀⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣀⢀⣭⡁⠀⠀⠀⠀⢁⠒⠀⠒⠂⠀⠀⠀⢀⣿⢺
⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠤⢃⠠⠄⢀⡠⡌⠁⠠⠤⠀⠀⠀⢀⣾⢢⢺
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠈⠁⠀⠉⠞⠘⠈⢥⠀⠳⠀⠀⠀⠀⢀⡾⣻⡤⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠴⠃⠀⠀⠈⠃⠈⠁⠀⠀⠀⠀⣰⡿⠟⣟⣱⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⢛⣳⣾⠳⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡝⡿⣶⣶⢻⠿⢿⣛⠷⢡⣵⣯⣇⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠾⣧⡥⢞⣿⡯⣶⣥⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⣰⠚⢦
⠀⠀⠀⠀⠀⠐⢇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗
⠀⠀⠀⠀⠀⠀⠀⠉⠉⣷⢠⠞⢱⡆⡷⠲⡄⢠⠒⢿⡐⣆⢰⣆⣠⠃⣤⢠⠴⠂⢰⡖⢲⡄
⠀⠀⠀⠀⠀⠀⠘⠲⠶⠃⠘⠶⠊⠛⠻⠀⠷⠸⢤⠾⠇⠘⡷⠈⠿⠀⠰⠛⠦⠄⠸⠇⠀⠿
⠀⠀⡟⠉⠹⠃⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠖⠒⠒⠲⠖⠲⡟
⠀⠀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⠁⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢂⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣾⣿⣿⣿⣿⣆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⣇⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠀⣀⡁⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠙⠁⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠠⠀⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠰⢗⡄⠀⠹⠃
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣉⣠⡀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡄
⠀⠀⡇⠠⠄⠀⠀⠀⠀⠠⠀⠠⣀⣀⣀⣈⡀⠀⠙⠛⠈⢿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⡥⢀⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⡶⠤⠤⠤⠦⠴⠤⠤⠤⠴⠦⠶⠶⠶⠶⠶⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⣇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⡇⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⣷
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧
⠀⠀⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠚⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠉⠙⠲⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⣠⣴⣦⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⢀⣠⣼⡟⠋⠿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣾⡿⠿⠋⠀⠀⠘⠻⢿⣿⣿⣿⣿⣷⠄⠀⠀⠀⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠙⢿⣶⣄⣀⠀⠀⠀⠀⠉⠘⠙⠿⣿⠻⣶⡶⠆⠀⠘⢿⡆
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠐⠟⢻⣿⣴⣀⢀⢀⠀⠀⠀⣤⣴⣶⡿⡄⠀⠀⠀⣸⡧
⠀⠀⠀⠀⠀⠀⠀⠘⣯⠙⢷⡄⠀⠀⠀⠘⢿⣿⠿⣷⠿⡃⣾⣾⣿⡟⢷⣦⠂⠀⠀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⣿⣦⡀⠀⠀⠫⢫⡀⠱⢿⠻⠟⡻⠛⠛⠂⠀⢀⣠⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣄⣀⠉⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣡⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠛⡅
⠀⠀⠀⠀⠀⠀⠀⣀⣴⠒⠉⠀⠒⡞⢀⡗⠒⠢⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣠⡆⠀⣤⣤⣄⠤
⠀⠀⠀⠀⠀⡰⠉⠁⠈⠉⠓⣶⣾⣿⣸⣦⡴⠊⠉⠉⠢⡀⠀⠀⠀⠀⠀⠀⡉⠻⣿⡇⠀⠸⠿⠁⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠟⠉⠉⠉⠛⠳⠀⠀⠀⠀⠃⠀⠀⠀⠀⣴⣿⠿⠃⠀⠀⠈⠀⠀⠀⢻⡝⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⣯⠒⠀⠀⠀⠀⠀⠀⠀⢨⠇⢸⣿
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢽⣯⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢘⣿
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠸⣿⣧⠀⠑⠆⠀⡀⣀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠈⠿⠿⠆⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠹⢭⣤⡻⠀⠀⠀⠀⢠⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⢦⡀⠀⠀⢀⡴⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⡴⠚⠛⠉⠉⠉⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠋⠉⠉⠛⠒⠦⣄⡀
⠀⠀⢀⡼⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⣀⠠⢦⣤⠀⡀⠈⠻⣆
⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠨⡁⠀⠀⠉⠑⢣⠀⠀⠘⡇
⠀⢸⠁⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⠋⠀⠀⢀⣤⠶⠒⠒⠒⠲⠤⣀⠀⠀⠸⣄⠀⠀⠑⢄⢀⢀⡀⣬⠁⠀⠀⡷
⠀⢸⡄⠶⠆⠀⠀⣀⣴⣿⣿⣿⠟⠁⠀⠀⣰⠏⠀⢤⠜⠖⠲⢴⣀⠀⠙⠢⡀⠘⠷⣄⠀⠀⠈⠈⠀⠁⠀⠀⣠⠃
⠀⠀⠓⢶⣶⣶⣿⣿⣿⠿⠋⠁⠀⠀⠀⢠⠏⠀⠘⣧⠀⠀⠀⠀⠈⢲⠂⠀⢸⠀⠀⠈⠙⠒⠶⠤⠤⠤⠤⠚⠁
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠉⠱⢢⠴⠢⠆⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠶⣤⠄⠘⣿⠙⠳⠦⣤⣀⣀⣀⣠⣤⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⣠⠞⠉⢁⠀⣰⡶⢚⡿⠀⠀⠘⠷⣄⣀⠀⠀⠀⢈⣬⡼⠋⠀⠀⠀⠀⠀⠀⠠⠄⠐⣾⠏⠁⢸⡟
⠀⠀⠀⠀⡾⠁⣠⣀⡿⠮⠉⢀⡿⠁⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠁⠀⢀⣤⠔⡲⡆⠀⠀⠀⣀⡠⠗⠁⠀⣸⠁
⠀⠀⠀⡸⢁⣠⠿⠃⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠈⠉⠈⠉⠀⠀⠀⡠⠁
⠀⠀⠐⠓⠛⠿⠖⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⡀⢀⣀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠒⠀⠠⡄⠀⠀⠆⠀⠂⠀⠠⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠁⢠⡄
⠀⠀⠀⠀⠀⠈⡀⠀⠀⣀⠀⠠⠀⠄⠀⠀⠀⠀⣀⠀⠀⠀⠡⠀⠀⠀⠠⠀⡀⠀⠀⡀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⠠⠀⠀⠀⠀⠀⠀⢩⢠⣶⣿⠗⢀⡤⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠐⠀⠀⠛⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢋⡍⠁⠀⠀⠀⠀⠒⠂⠀⠛
⠀⠀⠀⠀⠀⠄⠀⡂⡂⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠰⠀⠀⣀⠀⠀⢀
⠀⠀⠀⡦⠀⠀⡀⢢⠘⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠀⠀⠀⠀⠐⣄⠉⠒⢩⠴⣀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⢀⡠⢀
⠀⠈⠀⠀⠀⠀⠀⠈⠂⠙⢀⠓⢌⡒⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠆⠀⠀⠀⠶⠀⠀⠀⠀⠉⠀⢀⠄⠀⠈⠁⠀⠀⣀⠀⠄
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⢀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⢀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠈⠐⡀
⠀⠀⠀⠀⠀⡀⠀⠀⣄⠀⠀⠀⠀⠀⣤⠀⠀⠁⠀⠀⠀⠁⠀⢀⠈⠁⢀⡀⠁⢂⠀⠀⠀⠀⠐⠀⠀⢀⡀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣀⠄⠀⠈⠁⠀⠀⠀⠀⠘⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠡⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠀⠄⠀⣀⠀⠠⠀⠀⠠⠦⠀⠀⠀⠀⠀⠶⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠃⠀⠀⠀⠉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡄⠀⡀⠂⠀⠀⠶⠀⡀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠉⢀⠀⠂⠈⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠚⠛⠛⡀⠄⠀⠀⠀⠀⠈⠀⠀⢠⡀⠀⠃⠀⠀⠠⠀⠀⠐⠃⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢱⠆⠀⣀⠛⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⣸⠏⢸⡇⠀⢰⠇⣧⠁⣧⣀⣄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠘⠀⠀⠀⠀⠹⡇⠈⢧⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠰⠀⠀⠆



⣿⣿⡿⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠛⠉⠉⠉⠉⠉⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣴⣶⠶⠾⠿⠿⠿⠿⠿⠷⢾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠀⠀⢠⣤⠀⣤⣀⣰⣦⣤⣤⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣤⣤⣤⣶⠿⠟⠛⢉⣉⣉⣤⣬⣍⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⣉⣤⣴⡾⠟⠛⣋⠉⠉⠉⠉⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡾⠛⠉⠀⠰⠷⠀⢛⣁⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣤⣤⣴⣶⠾⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣉⣀⣠⣤⣤⣤⣤⣶⣶⣶⠶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⠛⠉⣉⣉⣉⣉⣀⣤⣤⣤⣤⣴⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠶⠿⠿⠿⠶⠶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⠀⠰⡶⠀⠻⣦⡄⠰⡶⠀⠉⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠿⣶⣦⣤⣤⣈⣁⣀⣀⣠⣤⣴⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⣦⣤⣀⣉⠉⠉⠉⠉⠉⢉⣉⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢉⣹⠿⠛⠻⣿⠟⠛⠿⣿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣀⠀⠈⠉⠀⠿⠀⠙⠃⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⡛⠿⣶⣤⣤⣄⣀⣀⣠⣤⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣄⣉⣉⣉⣩⣭⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⠤⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠳⠀⠚⡦⢰⣀⡃⠤⢯⡣⣼⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽⢨⣽⣓⢯⡐⣈⡇⢰⢐⢠⣬⣚⢡⣟⡾⠣⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢚⡁⠿⣍⠋⣴⠋⢾⣝⣪⣅⡈⡙⢷⡱⡼⢐⢨⣅⠷⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡱⣆⡐⢏⠳⠆⢋⣹⣽⠟⠎⣚⣑⣿⡋⣦⣜⢳⠞⡴⠞⠟⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣤⣴⣰⠙⠋⣛⠚⣷⠞⣿⢙⡄⢯⣹⣨⢟⠛⣯⡙⠒⣏⠿⠈⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠚⠧⢀⣘⠃⡟⠻⣤⢷⢻⣟⠅⣰⣿⡏⢬⣱⠆⢣⣌⣹⣤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⠃⠄⡈⢤⣲⠶⣬⣝⢿⣅⣿⣿⣿⢋⣻⣶⢬⣔⢨⣧⢙⡆⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣴⠤⣙⢠⠉⣼⠳⠍⢳⣝⣿⣿⣿⠟⠯⠸⢗⡉⠴⠎⣟⡵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⠁⡨⣍⠋⣑⡶⠂⢻⣿⣿⡇⠀⠀⠀⡏⠁⠠⠃⢈⡷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠘⠉⠀⠾⠻⠀⠀⣿⣿⡀⠀⠀⠈⠁⠘⠡⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡤⢒⣾⡿⠟⣩⡿⣿⣿⣟⢿⣶⣀⠤⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢉⠔⡒⠋⣁⣴⡾⡏⣴⡏⢿⢻⣦⡉⠛⠛⠿⣿⠯⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⠤⠀⠀⠤⠅⠤⠄⣰⡿⠋⠉⠄⣰⡿⡛⢬⡿⣿⡻⣷⡐⠂⡈⢧⠌⡀⠨⠑⠒⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⣠⠂⠨⠄⢠⣤⠞⠋⢀⡤⠚⣻⣿⠗⠁⠄⢳⣈⣿⡜⢿⣆⠀⠈⠀⠀⠏⠐⠀⠀⠄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⠀⣳⠖⠊⣁⠐⢀⣴⣇⢆⢰⣿⡏⠀⠀⡟⢺⠋⣘⢿⡄⣙⠓⢶⠶⠶⣶⢶⠶⠶⠛⠥⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠈⢉⠍⡇⠀⠀⠄⠐⠉⠀⢹⠀⢸⡏⠻⣶⠶⣇⠈⢳⣹⠘⢝⡲⢤⡈⠁⠀⢸⢀⡗⣆⠈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠀⠁⠠⠁⢀⠌⣀⠰⠞⠋⡩⢀⢸⠳⣴⢏⢳⡬⣿⠢⣿⠒⠸⣤⡀⠙⣷⠀⠘⠎⠀⢻⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠹⠀⡀⠀⢀⡜⢰⢈⣇⢘⣧⠀⠆⡿⠀⠀⠻⢙⠐⢼⠂⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠘⡩⢃⡇⢺⠡⠏⢸⡄⠀⠀⠀⠄⣀⢈⣠⡎⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠈⠀⠘⠁⠀⠈⠆⠀⠀⠈⠀⠀⢈⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠁⠀⠀⠀⠀⠀⠰⠭⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢠⡄⡄⠀⠀⡄⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠑⠧⡻⣧⠁⣘⠁⣐⠃⠜⠃⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠂⠌⡗⢀⣤⡉⣿⣳⢫⠆⣼⠇⡠⠂⠀⠀⠀⠄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠈⠻⠇⠐⣉⠆⡈⠉⢻⡤⠤⣄⠐⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠉⠉⣭⠄⢙⠀⠃⠀⠈⡇⢮⠁⢚⠠⠤⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠠⠍⠒⢴⣡⣤⢷⠀⠀⠀⢦⣀⠾⠷⢀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠡⡤⢀⣬⢡⠳⣤⠇⣶⠬⡷⠑⠪⠄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⡀⠀⠀⠀⠀⠀⢀⠎⡙⠃⠻⢷⣰⠈⠛⢐⠒⠈⠁⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢧⠀⠀⠀⠀⠀⠀⠈⠀⡇⢠⡆⠉⢶⠘⠷⠝⠂⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢧⡀⢀⠀⠀⠀⠀⠘⠀⠈⠁⢉⠰⡐⠆⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡱⣄⠀⢀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡠⠆⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠳⢤⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡉⠓⠦⠤⣤⣤⣤⣤⣤⠤⠤⠖⢋⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⣄⣀⣀⣂⣀⣀⡤⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⡿⠟⠛⠛⠛⠛⠛⠛⠿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡈⡄⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠥⠠⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣤⠀⠄⢸⣿⣧⣤⣴⣶⣾⣾⣿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠤⠂⣤⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⣀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⡄⢰⡄⢠⡇⢀⡞⢠⠆⠀⠀⠀⠈⠹⣿⣦⡀
⠀⠀⠀⠀⠀⢸⣿⡇⢀⠀⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣾⠟⠁⠀⢄⠘⣆⢻⠘⡇⣸⢁⡞⡰⢋⡴⠊⣀⡠⠀⠀⠘⣿⣿⣆
⠀⠀⠀⠀⠀⣿⣿⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⣠⣿⠋⠀⠀⠢⣌⠳⠘⣢⠴⠷⠿⠛⠻⢷⣏⡴⠞⠋⣀⡀⠀⠀⠈⣿⣿⡆
⠀⠀⠀⠀⠀⢸⣿⡀⠀⢂⡄⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠐⠲⠦⢌⣃⡾⠋⠀⠀⠀⠀⠀⠀⢸⣿⢚⣋⣉⣀⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⢰⣿⣇⠀⢯⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠀⣼⡿⠀⠀⠈⣋⣛⣻⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣩⣤⣀⠀⠀⢀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⣰⠀⠆⠻⡤⠁⡄⠀⣄⠀⡤⠀⠀⣿⡇⠀⠈⣉⣉⣡⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠶⠤⣤⡀⠀⠀⣼⡿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠁⢰⡔⠆⡰⢀⠅⡀⠈⠰⠀⠀⠀⣿⡇⠀⠀⢉⣠⡤⠾⣷⣤⡀⠀⠀⠀⠀⠀⡀⢾⢿⡝⠓⠶⠄⠀⠀⣴⡟⣥⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣦⣤⣁⠈⠙⠘⠁⠈⠀⠀⠀⢀⣿⣷⠀⠈⠉⢀⣴⠞⣫⢟⡿⣾⡶⠶⠶⠖⣷⠘⠇⠙⠦⠀⠀⠀⣴⡿⣀⣛⣹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣦⣤⣤⣤⣴⣾⡿⠿⣿⣆⠀⠀⠉⠀⡴⢋⡞⣸⠁⡟⢸⠘⡇⠘⠇⠈⠁⠀⠀⣠⣾⢛⢈⡵⢁⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠋⠉⠀⠀⢹⣿⣷⣀⠀⠈⠁⠈⠀⠁⠈⠁⠈⠀⠁⠀⠀⠀⠀⣠⣾⠟⠃⠦⠬⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⣷⣦⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⠶⠿⣫⠁⠒⠐⡀⣤⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡈⠉⠉⠛⠛⠛⠛⡛⠉⠭⠑⡄⢉⠂⢀⠁⠈⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣄⣀⡀⠰⠀⠑⠀⠈⠐⠁⣀⣡⣤⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣷⡶⠿⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡶⠿⠿⠿⠿⠿⠿⠷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⣠⣴⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⡀
⠀⠀⠀⣰⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄
⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠿⠟⠛⠻⠷⠶⣦⣤⡀
⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠟⠉⠀⢀⣀⡠⢄⡠⣄⢀⠀⠉⠛⢷⣄
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣹⡟⠁⢀⣤⡏⠛⠈⠁⠈⠀⠈⠁⠗⣢⣀⠀⠻⣧
⣿⡆⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢠⡟⠀⠀⡞⠂⠀⠀⠀⢀⣀⣀⠀⠀⡀⠀⢚⣆⠀⢹
⢻⣧⢿⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⣸⡇⠀⢲⡉⠀⠠⢀⠌⠁⠀⠀⠉⢦⠀⡀⠀⢺⡆
⠈⢿⣎⠳⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢿⡇⠀⢪⡄⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠨⡇
⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢸⣇⠀⠸⡤⠀⠀⠀⠣⣀⡀⢀⡠⠊⠀⠀⠀⣽⠆⢀
⠀⠀⠀⠙⠿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠈⢿⡄⠀⠻⣄⡀⠀⠀⠀⠈⠀⠀⠂⠀⠀⣐⡎⠀⣸
⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠷⠶⠶⠿⠿⠟⠻⣷⡀⠀⠈⢿⣄⠀⠙⢲⣠⢀⡀⣀⠀⣁⢠⢄⠗⠃⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠻⢷⣄⡀⠀⠁⠙⠉⠊⠈⠁⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣤⣀⣉⣛⣷⣶⣶⣶⣶⣶⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣺⣿⣿⡿⣟⣷⣄⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣭⣿⠯⢿⣿⣿⡯⢻⣷⣿⣿⢿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠛⠿⣯⣿⣟⠳⣾⣷⣼⣿⣿⣿⣇⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⢞⣫⣿⣿⣛⡷⣞⠿⠋⠁⣉⣀⣉⠻⣧⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⢻⣿⣿⡭⣹⣿⣯⠀⠼⠛⠋⠋⠛⢦⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢰⣿⣷⣚⣻⣿⣿⣂⣴⣤⡀⠠⡀⡀⠀⢠⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⡫⠾⣀⣛⣿⣿⣿⡿⠻⠃⠀⡀⢠⡆⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣠⣾⢇⡽⢋⣽⣿⣿⣶⣧⠿⣭⣾⣿⣿⣛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣿⡴⣹⠿⣿⣿⣿⣿⠀⢸⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣇⢳⡏⣾⣿⣿⣿⣿⠀⣾⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⣿⣿⣿⣿⣿⠀⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣻⣿⣿⣿⣿⣿⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠟⠀⣇⣻⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⡿⠟⠉⠉⢻⣿⠿⣿⢠⡄⠈⠙⠻⣿⣿⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠈⠛⠃⠀⠈⠁⠀⠀⠀⠈⠙⠁

⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠛⠉⠙⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠒⠒⠲⠶⢤⣄⡀
⠀⠀⠀⠀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⢀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢰⠒⠈⠙⠻⢯⣀⠄⠀⠀⠙⣦
⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠘⡆⠀⠀⠀⠀⠈⢡⡀⠀⠀⠹⡆
⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣻⡟⠁⠀⠀⢀⡤⠶⠋⠉⠉⠉⠛⠲⢤⣄⡀⠀⠈⢧⡀⠀⠀⠈⠇⠄⡄⢀⡀⡔⠁⠀⠀⢈⡇
⠀⠘⣆⠠⣶⠄⠀⠀⠀⣀⣶⣿⣿⣿⡿⠋⠀⠀⠀⢠⠟⠁⠠⣤⠧⠖⠰⣤⠄⠀⠀⠙⢦⡄⠈⠻⣦⣀⠀⠈⠀⠁⠁⠈⠁⠀⠀⠀⡼⠁
⠀⠀⠹⢤⣤⣤⣤⣶⣿⣟⣿⡽⠟⠁⠀⠀⠀⠀⢠⡟⠀⠀⢴⡀⠀⠀⠀⠀⠈⠱⣤⠀⠀⢸⡆⠀⠀⠙⠳⠦⣤⣄⣀⣀⣀⣀⠤⠊
⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠨⠓⣤⢄⢀⣀⢀⠠⠑⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⡀⠀⠂⠘⠈⠈⠉⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠛⠛⢋⣽⡗⠀⠈⢿⡄⠀⠉⠛⠲⠶⠶⠶⠶⠶⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠠⣤⡀
⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⡄⢀⣨⡗⠉⣽⠇⠀⠀⠈⠛⢧⣄⣰⡀⢀⠀⣀⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠤⠒⠀⢉⡿⠃⠀⠀⣿⠁
⠀⠀⠀⠀⢠⡟⠁⢰⢀⣨⠿⠏⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠉⠀⠀⢀⣠⠤⢒⢶⠁⠀⠀⠀⠀⢀⠬⠒⠁⠀⢰⠇
⠀⠀⠀⠀⡼⠀⣠⣾⡏⠀⠀⢀⣴⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠒⡋⠘⠉⠀⠀⠀⠀⢀⠏
⠀⠀⠀⣴⣥⣾⣿⣤⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠶⠶⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢀⠀⠓⠚⠛⠲⣤⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣸⣄⣀⢀⣠⡼⠿⠋⠋⠛⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠖⠛⠛⠒⢶⣄⣀⠐⡺⢿⠻⣿⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⡁⢃⠑⣿⡇⠀⠀⠀⠀⠀⣤⡆⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⣾⣷⣷⠟⠀⠀⠀⠀⠐⠁⡄⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣸⣇⣁⣀⣀⣀⣤⣤⣄⢁⠄⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⠋⠉⠉⠛⠛⠶⠤⣼⡇⠹⣥⡀⢀⠀⠀⠒⠂⣿
⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠋⠠⡆⠈⠀⠀⢸⡇
⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣫⢤⡀⠀⠀⣿
⠀⠀⠀⠀⠻⣆⡀⠀⢀⠀⠀⢀⡀⠀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣄⣩⠟⢠⡿
⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⢻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣴⣤⡤⠤⣴⣴⡿⠟⠛⠛⠋⠁

⠄⠂⠈⠉⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠂⠈⠉⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣠⣄⡀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⠁⠀⢀⣠⣄⡀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢠
⢼⣁⠀⠀⢘⡆⠀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠄⠀⡀⠀⠼⣁⠀⠀⢘⡄⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⡀
⠀⠈⠓⠈⠁⠀⠀⣸⡿⠀⠀⠀⠀⢀⡠⠶⠨⠽⠦⣄⠀⠀⠀⠈⠑⠠⢷⠀⠀⠈⠓⠉⠁⠀⠀⡸⣿⠁⠀⠀⠀⢀⡠⠴⠩⠕⠦⣄⠀⠀⠀⠈⠑⠤⢷
⠀⠀⣀⣀⣠⣤⠾⠛⠁⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀⠀⠀⠑⠠⠀⣀⣀⣠⣤⠾⠛⠁⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠜⠀⠂⠠⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠸⠀⠂⠠⢀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⡀⠀⠑⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⡀⠀⠁⠄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⣠⠋⠉⠑⢲⡀⠈⡄⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⣰⠋⠉⠑⢢⡀⠈⡄⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠙⠲⠠⠔⠋⠀⢀⣇⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠙⠲⠠⠔⠋⠀⢀⡇⡠⠔⠁
⣀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠊⠑⠦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠑⠚⠊⠑⠦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠑
⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠄⠀⠈⠉⠉⠐⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠄⠒⠈⠉⠉⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣀⣄⡀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢠⠃⠀⠀⣀⣄⡀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀
⢰⣁⠀⠀⣘⠆⠀⢸⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⡄⠀⢸⣁⠀⠀⣘⡄⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⡄
⠀⠈⠓⠉⠁⠀⠀⣸⣿⠁⠀⠀⠀⢀⡤⠖⠩⠵⠦⣄⠀⠀⠀⠀⠑⠢⢷⠀⠀⠈⠓⠉⠁⠀⠀⣸⡿⠁⠀⠀⠀⢀⡠⠖⠩⠵⠦⣄⠀⠀⠀⠀⠑⠠⢷
⠠⠀⣀⣀⣠⣴⠾⠛⠁⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀⠀⠁⠠⠀⣀⣀⣠⣴⠾⠛⠁⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠘⠀⠂⠀⢄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠜⠀⠂⠠⢀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣸⡷⠀⠀⡠⠋⠉⠙⢢⡀⠈⡄⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⡰⠋⠉⠑⢢⡀⠈⡄⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⢻⣯⠀⠀⠙⠲⠤⠔⠉⠀⢀⣇⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠙⠲⠤⠔⠋⠀⢀⣇⡀⠔⠁
⣀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠑⠐⠊⠑⠦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠑
⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡠⣪⡵⠚⣩⠔⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢟⠕⢋⣵⠞⣻⢦⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣾⡾⠋⣠⡾⠃⣰⠇⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠑⢁⣼⠟⢡⣾⠏⣼⢷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣾⠟⢀⣼⠟⢀⣴⠏⢠⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⣰⡿⠃⣰⡿⠋⣰⡟⣸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⢠⡿⠃⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⢸⣿⣿⣿⢰⡟⢀⣾⣿⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢍⣿⣿⣿
⠀⠀⠀⠙⢾⣁⡼⠟⣘⢧⣀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⢸⣿⣿⣿⣯⡁⡬⢁⣤⢧⡙⢿⣿⣿⣿⣿⣿⣿⡿⢏⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠓⠛⠋⠀⠉⠛⠓⠒⠒⠒⠛⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣭⣭⣭⣭⣵⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠠⠀⠈⠁⣤⣀⣀⠄⠀⡀⠂⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⡠⠔⠂⠈⠱⣦⣨⢐⠅⠀⢀⠀⡀⢀⡞⠁⠀⠀⠀⠀⠀⠠⠆⢐⣊⡀⠰
⠀⠀⠀⠀⠀⢧⣠⣈⠀⠀⣿⠋⠀⠀⢀⠀⢤⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⢢
⠀⠀⠀⠀⠀⢙⡻⠿⠿⡟⠀⠀⠐⠄⢢⣉⢢⡈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣇⠀⠀⢈⠏⡀
⠀⠀⠀⠀⠀⠀⠐⠄⣀⠀⠀⠠⢁⠀⠀⣀⡩⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠓⠖⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠓⣀⠐⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⣡⣬⣖⡩⠥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣀⡴⠊⣰⠀⣰⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠔⢠⠄⡴⠃⠴⠃⣠⠾⠋⠉⠓⠊⠶⠶⠾⠷⠶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠅⠐⠁⠠⠤⠔⠒⠈⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠀⠀⠀⡀⢀⡀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠉⠀⠀⠀⠀⠀⣴⠉⠁⠀⠉⠐⠀⣀⠀⠈⠁⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⣄⠐⠤⠤⠞⠀⡀⠉⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⠛⠶⠶⠲⠞⠇⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⠤⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⡼⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⢰⠁⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠓⠀⠀⠂⠀⠀⠀⡴⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠹⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠐⡌⠑⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⣀⡀⠀⠀⠀⢀⠀⣀⡀⠐⠁
⠀⠀⠀⠈⠠⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⢀⡀⠠⠄⠐⠈⠉
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠚⣩⢔⣒⠆⠀⠀⠀⠀⠀⠀⠀⠰⠭⠆⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠚⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠽⢂⣌⠙⠲⢤⣀
⠀⠀⠀⣰⠾⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠽⠶⣄
⠀⠀⠀⢿⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⠉⠉⠉⠉⢉⣩⣭⣭⣭⣍⡉⠉⠉⢩⠭⠭⢭⣭⡭⠭⠭⣭⣭⡭⠭⠭⣍⠉⠉⠉⣉⢩⣭⣭⣉⡉⠉⠉⠉⠙⡏
⠀⠀⠀⢘⡇⠀⣠⡾⠛⠉⠀⠀⠀⠈⠻⣦⡀⠸⡆⠀⠀⠊⡝⣦⣰⠣⢗⠀⠀⢠⡏⢀⣶⠟⠋⠁⠀⠀⠉⠻⣦⡀⠀⢀⡇
⠀⠀⠀⢸⠀⣰⠏⠀⢀⠀⢄⣢⡀⠀⠀⠈⢻⡄⠻⣆⠀⠀⠐⠙⠀⠂⠀⠀⣠⡟⠑⠛⠁⢀⠀⣦⣶⣴⣀⠀⠈⢿⣆⠘⣧
⠀⠀⠀⠸⣆⡟⠀⠀⡠⣕⡎⠉⠷⣥⠒⠀⠀⢿⠀⠙⠷⣤⣀⡀⢀⣀⣤⡾⠛⢁⣭⠁⢀⡨⣝⣼⠋⢿⣯⠶⠀⠀⢿⡆⡿
⠀⠀⠀⡸⠧⠯⠶⠤⠽⠿⠥⠤⠤⠭⠭⠥⠤⠭⠤⢤⢤⢬⣭⣭⣥⣭⣥⣤⣤⣤⣭⣤⣤⣭⣿⣥⣤⣤⣬⣫⣁⣀⣘⣽⡁
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠒⢶⣛⣿⡆⣦⢄⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⢠⠊⡝⠁⠀⠀⠀⠀⣀⠤⣴⢒⡶⠂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢬⡗⢢⣟⢢⣀⠀⠀⠹⣰⣀⠀⠒⠠⠀⡀⢠⠎⠀⠀⢀⢠⣖⣹⣷⠞⣿⣍⣿⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣭⡿⣏⣳⣄⡔⠉⠁⠀⠀⠀⠀⠉⠛⠄⣠⢰⣧⠞⣻⣥⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠹⢿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⢂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣼⠋⠉⠙⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⢊⠃⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠛⢻⣯⣅⡀⠀⠉⠉⠓⠒⠒⠒⠒⠒⠋⠁⠀⠀⠀⣠⣴⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠈⠻⢢⡀⣀⠀⠈⢉⠉⠉⣀⠄⠀⣀⢀⠘⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠐⠒⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠂⠀⢾⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⢀⣱⠄⠀⠆
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠶⢶⣤⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⠤⠴⠶⠷⠛⠋⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡋⠁⠀⡀⢠⣤⢨⡍⠉⢉⠋⡙⠲⢶⣤⡀⠀⠀⠀⣠⣶⣿⣟⣿⣿⣺⣿⢿⣯⡏⣿⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⢲⣬⠻⣿⣿⡿⣧⣠⡟⣴⣿⢇⣾⢟⣿⣆⣰⣾⣿⣿⡿⣿⣿⣽⣷⣿⣿⣷⣮⣧⣿⠟⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠘⠿⣯⣿⣿⡟⠃⠈⠻⠿⠿⢿⣿⣷⣾⣟⣻⣿⣻⣿⣿⣿⣿⡿⠛⠛⠉⠛⠛⣿⣿⣲⣺⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⠀⠒⠒⢺⣿⣏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣰⣿⣿⣞⠲⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⢸⡾⠟⣻⣿⣶⣤⠀⠀⢀⣠⣿⣿⣿⣿⣾⣿⣟⣻⣿⣿⣿⣿⣷⣠⣶⣿⣿⣿⣿⣭⣿⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣥⡟⣹⣿⣿⣿⣿⣾⣿⣿⣿⢻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣶⣯⣡⣸⣿⠟⣿⣨⣿⣶⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠛⠋⠉⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⢀⠀⠀⠀⡿⠁⣾⠛⣁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣾⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢰⠚⠟⠉⠙⢈⡷⠒⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⢤⠀⠀⠀⢀⠔⠈⠀⠀⠁⠀⠐⠈⠁⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⢀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠓⠋⠷⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣻⡟⣠⡔⣉⡠⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⢠⠏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠉⠀⠀⠉⠉⠑⠿⣿⡗⠒⠒⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⠺⡀⠀⠀⠀⣠⠎⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⣀⣰⠁⠀⢀⡼⠃⠀⠀⠠⠠⠀⠀⠐⠂⠂⠀⡆⠀⠀⠈⢫⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠻⡬⠟⡈⠀⠀⢀⡕⠀⠀⣾⠃⠀⠀⠀⢀⡂⠄⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀⣴⣾⡀⠠⣼⡏⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⠿⠛⠉⠳⣦⣼⡇⠄⠀⠀⠀⠀⠐⡄⢀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠴⡟⠋⢹⣷⡀⠀⠠⠀⠀⠀⠀⢈⠰⢈⠐⡙⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠾⠃⡄⡇⠀⢸⠛⣷⡄⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢋⠀⠰⠀⠁⠀⠁⠀⠈⠉⠓⠤⣀⠈⠀⠀⠀⡀⣀⣠⡴⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠛⠛⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣏⠀⢹⣟⣹⣻⣛⣛⣿⣙⣛⣻⣻⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣟⣻⣟⣿⣿⣟⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⡀⠀⢃⠀⢀⠀⠠⠀⠈⡀⠈⣀⠀⢁⠀⢣⡀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠄⠀⠆⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⡀⠀⠂⠀⢂⠀⢠⠀⠘⡄⠈⣄⠀⢂⠀⢲⡀⠱
⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⢐⠀⠐⠂⠀⠀⠀⠀⠀⠀⠇⠀⠥⠀⠈⠀⠀⠅⠀⠁⠀⠈⠀⠀⠀⠀⠡⠀⠘⠀⠈⢆⠀⢀⠀⠘⡄⠘⢆⠀⢣⡀⠱⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠅⠀⠠⠀⠠⠅⠀⠡⠀⠨⠄⠀⠅⠀⠁⠀⠈⠄⠀⠡⠀⠨⠀⠀⠄⠀⠐⠀⠈⡄⠀⢠⠀⠘⡀⠈⢂⠀⢡⡀⠈
⠀⠀⠀⠀⠄⠀⠘⠁⠀⠀⠀⠠⠀⠀⠅⠀⠨⠀⠀⠅⠀⢨⡄⠈⠇⠀⠠⠀⠀⡄⠀⢠⡀⠈⠀⠀⠀⠀⡀⠀⢀⠀⠀⠘⡄⠀⢂⠀⠐⡀⠀⣂⠀⢑⡀
⠀⢈⠁⠈⠉⠀⠀⠀⠀⠀⠀⢠⣴⡆⠀⠀⠈⠁⠀⠁⠀⣀⣤⡶⢮⠀⠀⠀⠀⢠⣴⣦⣤⠄⣤⣤⣦⣸⣷⣄⠃⠀⡄⠀⠐⡀⠀⣂⠀⠐⡀⠐⣒⠀⠒
⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣠⣤⣠⡀⠀⢸⣾⠿⠁⢘⡃⠀⠀⠀⠨⣿⣿⡟⠈⢿⣿⣿⣿⣿⣿⣧⢠⣧⣆⠀⠐⠀⠀⠂⠀⠰⠀⠀⠢
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣿⣿⣿⠀⠀⢼⠃⠄⠀⠀⠤⠀⠀⠀⠀⢻⣿⣷⠠⢾⣿⣿⣿⣿⣿⣿⡌⢿⣿⡄⠀⠩⠀⠈⠅⠀⠩⠄⠈⠥
⠆⠀⠀⣍⠁⢀⠀⠀⠀⠠⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢨⡷⠀⠀⠀⢉⡀⠀⠀⠀⠀⠻⣿⣷⡟⣽⣿⣿⣿⣿⣿⡗⠨⣿⣿⡄⠀⢀⠀⠐⢂⠀⢒⣀⠐
⣴⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠏⡇⠀⠀⠸⠇⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⢻⣿⣧⡿⣾⣿⠟⠛⠉⠉⠀⢿⢹⣣⠀⠀⠠⠀⠀⠤⠀⠨⠄
⢱⠀⠀⣋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢈⣭⣀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⢹⣿⣧⡻⠁⣶⣗⠀⣀⣠⣷⣜⡀⠀⠀⠀⠀⠀⠐⠂⠀⠒
⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣄⠀⢸⡆⠀⠀⠀⠀⠠⣿⣷⡀⠀⠀⠀⠈⢹⣿⣧⠀⣿⣿⣶⣿⣿⣿⣿⡇⠁⠀⠀⠈⠀⠀⠈⡀
⠐⠀⠀⠖⠀⠂⠀⠀⠀⠀⠀⣀⣤⣤⡘⠿⣿⣿⣿⣄⢸⡇⠀⠀⠀⠀⠀⣿⣿⣷⡀⠀⠀⠀⠈⢿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠠⠀⠀⠠
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣀⣀⣿⣿⣿⣷⡀⠀⠀⠀⠘⣿⣿⠀⠻⣿⣿⣿⣿⡿⠂⢃⠀⠀⠀⠀⣂⣀⣀⣀
⠀⠀⡀⢸⣤⡄⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⢿⠟⠛⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⣿⣇⣁⠽⠿⠿⢋⣡⡆⠀⣲⠀⠀⠘⣿⣿⣿⣿
⡀⠀⠁⢸⣿⡆⠀⠀⠀⠀⠀⠀⣤⣷⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠠⣿⣿⡤⣾⣿⣿⣿⣿⣄⠉⡄⠀⠀⢹⣿⣿⣿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⡇⠀⠀⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠘⢿⡁⠟⣿⣿⣿⣿⣿⣦⣄⡀⠀⠈⢻⣿⣿
⠁⠀⠀⢸⣿⠂⠀⠀⠀⠀⠀⠀⢸⣿⠋⠛⢻⡷⠀⠀⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠰⡿⡆⠉⢻⣿⣿⣿⣿⣿⣧⡀⠀⠈⢿⣿
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠠⢸⣇⠀⢀⣴⣇⠀⠀⠦⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠣⠈⣆⡀⠹⣿⣿⣿⣿⣿⠻⠡⠄⣈⣿
⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⠄⢰⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢠⣸⣻⠸⠋⢿⣿⠟⣡⣤⣤⣾⣿⠿
⠀⠀⠀⢸⡿⠀⠀⠀⠀⢸⡁⠺⡀⠉⠙⠋⠉⠉⠇⠀⠀⠀⠀⠀⣯⣽⣿⣯⣭⣿⣿⣭⣽⣿⠯⠍⠛⠃⠀⠀⠀⣸⡏⢉⣀⣬⡼⠿⠿⠛⠋⠁
⣾⣿⣿⣿⠇⠀⠀⣠⣴⣿⣶⣶⠧⠀⠀⠀⢀⣤⣶⡦⠀⢠⣤⣤⣿⣾⣿⣿⡅⠉⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠛⠿⡛⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⣄⠀⠀⣭⡍⠉⢩⡡⠀⠀⣄⡀⠀⢠⣭⠀⠀⣿⡇⠀⢨⣯⡀⢀⣾⣧⠀⢸⣾⠁⠀⣿⡇⢀⣸
⣶⣿⣿⣶⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⣿⣿⣷⣾⣿⣷⣶⣾⣿⣶⣾⣿⣷⣶⣾⣿⣷⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿
⣉⣿⣿⣃⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠂⠀⢀⣀⢂⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⠊⡀⠀⠀⠁⠠⡤⡀⠈⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠺⣧⣈⠒⠒⠋⢀⡄⠀⠀⠀⠀⠈⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠙⠛⠉⠋⠃⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣠⠤⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⡞⠀⠀⠀⠀⠀⢠⡰⣿⣿⣶⣦⣜⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⣼⠀⠀⠀⠀⠀⠀⠈⠨⠻⢿⢿⣿⣿⣿⣿⣦⣤⠄⠀⠀⠀⠀⠀⢀⡇⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⡄⠉⠻⠟⠟⠉⠉⠃⠀⠀⠀⠀⢀⠞⠀⠀⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠈⢕⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠈⠂⠀⠉⠒⠒⠤⠤⠤⠤⠤⠤⠔⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠒⠀⠄⠀⠐⠀⠒
⠀⠀⠀⠀⠑⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠊⠁
⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⣀⣀⣀⣀⡐⠁⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣠⠶⠛⠉⠉⠉⠉⢩⠞⠉⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡾⠁⠀⠀⢀⠀⣀⣠⢼⣦⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠺⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡴⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠅⠀⠀⠃⠘⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⣱⠁⠀⠀⠀⠀⢱⡀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⢠⠞⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⢺⡄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣷⡿⢽⡀
⠀⠀⠀⠀⣴⠁⠀⢀⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣷⣶⣤⣽⣧⣸⣷⣿⡇
⠀⠀⠀⡘⠁⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣣⣾⣿⣿⠟⣿⠿⣿⣿⣿⣿⣤⣤⣀⡀
⠀⠀⠀⣷⠐⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⢠⣎⣼⣿⡟⠙⡹⢘⠁⠀⠀⠀⢿⣿⣟⣻⢿⣿⠷⣄
⠀⠀⠀⠸⣆⣄⢀⣀⢻⣷⣀⢡⡀⠀⡀⠀⠀⢠⣿⠄⠀⠀⠀⢈⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⠻⡿⠁⠀⠃⠏⠀⠀⠀⠀⡀⠀⠀⠀⠈⠛⠀⠈⡆
⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣿⣼⣷⣀⣴⣿⠃⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡅⠀⠀⣼⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⣭⠟⡿⣿⣯⣽⡯⣽⢻⠟⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⣦⠀⠀⠀⣰⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⠁⠙⠋⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡂⣽⣿⣤⡀⠀⠀⠀⢀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣵⣠⣆⣴⣾⣷⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣿⡿⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡿⠃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⢀⣀⣽⣿⢶⡄⠀⠠⣄⣀⡀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⣀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣡⣶⣶⠟⠉⠀⠄⠀⠸⡇⠀⠀⠙⢿⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢠⠶⣿⠏⠁⠈⠒⣄⣀⠠⠄⠼⢧⡀⠐⠀⠀⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂
⠀⠀⠀⠀⢠⠃⠀⠐⠀⢰⠆⠀⠌⠀⠀⠀⠀⠈⠁⠐⢠⣤⣿⣗⠉⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠐⡿⠃
⠀⠀⠀⠀⠘⣆⣠⣆⠀⠀⠀⠈⠀⠀⠰⠀⢀⠀⢀⠀⠀⡿⠋⠙⢶⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠣⡈⡰⢠⠇
⠀⠀⠀⠀⠀⢸⠟⠻⣦⡄⠴⢧⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠋⠀⠀⣠⡞⢁⡎
⠀⠀⠀⠀⠀⠈⠀⠀⠻⠀⠀⠀⠑⣤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢀⣴⠞⠋⠀⡜
⠀⠀⠀⠀⠀⠀⠐⣄⣸⡇⠀⠂⠀⢨⠀⣀⠀⠀⠃⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣞⡛⠋⠀⢀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠤⣀⣀⣄⠀⠀⢀⣠⣦⣤⠤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠊⠉⠉⠉⠉⠑⠒⢄
⠀⠀⠀⠀⠀⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠷⠤⠀⢄⣀
⠀⠀⠀⢠⣾⣿⠄⠀⠀⠀⠀⠀⠀⠀⡤⠞⠉
⠀⠀⠀⢸⣿⠛⢛⣽⣆⠀⠀⠀⢀⡾⠅⠄⠀⠀⠀⠀⠀⠤⢦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠀⠸⣿⣦⣴⣿⣿⣦⡀⣀⣾⣯⣇⠀⡈⡂⠀⠀⠠⡁⠀⣇⠀⠀⠀⠀⠀⠀⢀⣆⠀⠈⠈⠒⠝⠁
⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⡿⠿⢿⣽⣿⡻⣇⠀⠈⠐⢶⠴⠃⠀⠀⠀⠀⠀⠀⠘⢿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠖⠒⠒⠶⠦⠤⣄⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣏⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⠀⠂⡲⠀⠀⠀⡷
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣜⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⢠⠀⠀⠀⠢⠀⠤⠄⡐⠂⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣔⡇⣀⡓⢀⠀⠄⠔⠀⠀⠀⡖⠀⠀⠀⠀⢸⣦⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⣵⣶⣾⣦⢿⡄⢀⣄⣾⠇⠀⠀⠀⠀⠈⠻⣿⣿⣷⡣⣺⡧⣀⣤⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣷⣿⣶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀⠠⢀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢃⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠢⢄⠀⠀⠀⢠⣇⠀⠀⡠⠈⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⢊⠁⢠⠒⠀⠀⢀⠀⠀⢸⡇
⠀⠀⠀⠀⡀⠀⠀⣐⢇⣀⡀⡠⠂⠀⠀⠀⣼⠃⠉⠀⠁⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠈⠁⡒⠂⠀⢠⣿⣦⣶⡾⠃
⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠂⠀⠀⠀⢠⣘⣿⣄⣀⣀⡤⣴⠊⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠉⠛⠶⢦⢦⣶⡔⠴⠗⠋⠁⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠉⠁

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠀⠤⠄⣀⡀⠂⠀⠀⠀⠀⠀⠀⠐⠪⢕⡢⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠑⢄
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢰⡶
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⡹⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣦⠤⠤⠤⠤⠔⠊⠉⠀⠀⢀⠜⠉⠓⠢⢤⣀⣀⣀⣀⣀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠤⠤⠤⠤⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣿⣿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⢉⡿⣹⠟⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣧⢿⢸⡇⡿⣼⣣⣾⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⡀⣼⣿⣿⣿⣿⣿⣿⣗⢜⢧⣻⣿⡿⣾⢼⡻⣧⢯⡿⣫⡾⢛⣽⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢠⠖⠚⠉⠉⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⠿⣯⣽⣿⣻⣟⢭⠃⠉⠀⠃⠹⠫⢾⣭⢾⣻⣭⠶⢿⣿⣿⣿⣧
⠀⠀⠀⢀⠤⠋⠁⠀⠤⠀⠀⠀⠒⠀⠀⠈⠁⠀⠀⠙⣿⠷⢶⣭⣛⣽⠃⠀⠀⠀⠀⠀⠀⠀⣭⡿⠯⠵⢶⣿⣿⣿⣿⣿⣿
⠀⠀⣴⠊⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠀⠀⠀⠒⠀⠀⠹⣿⣷⣷⡎⣥⢀⡀⠀⠀⠀⠀⠀⠀⠠⣬⣭⣿⣭⣭⣹⣿⣿⣿⣿
⠀⣺⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠄⢘⣿⣿⣬⡿⢶⣭⡄⡀⠀⠀⠀⠀⢀⡨⢿⣲⠶⣾⣯⣭⣿⣿⣿⣿
⠐⡇⠠⠄⠀⠀⠐⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⠹⣿⡻⡇⡆⣆⢶⣸⣧⡲⣮⣙⢷⣬⣽⣿⣿⣿⡟
⢈⡆⠀⠀⣀⠀⠀⠀⠤⠀⠀⠀⠒⠀⠀⠈⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣇⣿⣿⡇⣿⣹⣽⣏⢻⣼⣿⣿⣷⣾⣿⣿⣿⡿⠁
⠀⢾⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣻⡍⣧⢿⣇⢹⣶⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠓⣦⣀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠈⠉⠓⠒⢲⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣶⣾⣿⣿⠿⠻⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⡿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠛⠂⠒⠒⠒⢦⠤⠀⡀
⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⡀
⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⡾⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠉⠉⠉⠉⠉⠙⠓⠦⣄
⠀⠀⠀⢠⠻⢷⠴⡲⢆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤
⠀⠀⠀⠘⡄⠐⠈⢫⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⢣⠀⢸⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⢆⠀⡀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⢠⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⢸⠀⠀⠀⠀⠈⠀⠀⠰⣄⡛⣦⠾⠾⣧⣤⡆⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠁⠾⣶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⢸⠀⠀⠀⠀⠀⠀⠘⣮⣟⠋⠁⠀⠀⠀⠹⡇⣘⠂⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠼⠟⣙⣶⠒⡒⠲⢴⠃⠍⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠄⣀⡀⢀⢀⣈⡠⠦⠐⠋⠁⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠄⠀⠈⠀⠛⢠⠁⠀⠁⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠾⠍⣁⡀⠀⠀⠀⠀⠀⠁⠁⠂⠤⣀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣤⣤⣤⣤⠤⠴⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠄⡀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢆⡰⢓⣮⠶⠿⣤⣅⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢩⣟⠁⠀⠀⠀⠀⠻⣹⣀⠓⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠰⠏⡿⣶⣦⣄⠀⠀⠀⢻⣗⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠈⠁⠀⠜⢹⠜⠛⠦⡞⠟⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠂⠀⠀⣤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⠀⠀⠀⠀⢀⣴⣡⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣀⣰⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⡁⠂⢠⢻⣀⡾⡀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⡴⠋⠁⠀⠀⠀⠀⠉⠓⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡥⠒⠂⢻⠏⠀⠁⠰⢁⠀⠀⠀⣀⣀⣀⡈⣇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣄⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡎⠀⢀⠄⡼⠈⢀⠞⠉⠉⢉⠀⠐⠾⣾⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡆⠃
⠀⠀⠀⠀⠀⠀⢀⣠⡔⠒⠛⠛⠓⠒⠒⠲⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠲⠥⠒⢣⠚⠀⠃⠸⡀⠀⠀⠀⠖⠀⢀⡞⠉⢦⣀⡀⠀⠀⠀⠘⠒⠦⠤⠀⠀⢀
⠀⠀⠀⠀⢠⠞⠡⠠⠤⠐⠤⠤⠀⠤⠄⣀⣀⠀⠀⠈⠉⠓⠒⠶⠦⠤⢤⣀⠀⠉⠀⠀⠀⡠⠃⠀⠀⠀⡀⡠⠟⠄⠀⠰⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠜
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠀⠉⠷⢢⠄⠔⠁⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⡅⠀⠀⢀⡀⠊⠀⠀⠀⠀⢠⡆⠈⠢⠀⠀⠀⠀⠈⣗⠘
⠀⠀⠀⠀⡇⠐⠀⠠⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⡘⠀⠀⠀⠀⡀⡄⠀⠀⡆⠀⠀⠀⢃⠀⡀⠀⠀⡄⠀⠀⠀⢀⠞⠁⠄⠀⠀⢠⣀⠀⠀⠠⠁
⠀⠀⠀⠀⠘⢴⣤⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⢰⠂⠈⠀⠉⢸⣫⣿⣶⣠⡇⠀⠀⠀⠀⠀⠄⢀⠈⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⡈⣩⠖⠈
⠀⠀⠀⠀⠀⠈⠙⢿⡲⣁⡒⠀⠀⣠⣤⣄⣀⣀⣂⣸⡆⣠⠖⠚⠁⠀⠀⠀⠈⠙⢦⠤⠤⠤⢤⣀⠀⠈⠀⠂⠄⠃⠀⠀⠆⠄⠀⣴⣡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⢿⣶⣤⣤⣩⠭⣍⣿⣿⠟⠁⠀⠀⣤⡔⣀⠀⠀⠀⠈⣧⢠⡀⠀⠀⠙⢦⠀⠀⠀⢂⢀⠀⣀⠄⡠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢮⣌⣿⠋⠀⠀⠠⢶⠆⢈⠠⡀⠀⠀⠀⣿⠀⠃⠀⠀⠀⣨⡇⠀⠀⠀⣄⣀⡴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠐⠀⠁⠹⠋⠀⠀⢀⡴⣅⣀⣀⡠⠴⢚⡿⠃⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⢀⣤⢎⣴⡯⠥⠤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣄⣀⡐⡢⠽⠞⠋
⠀⠀⠀⠀⡠⢤⠀⠀⠀⠀⢀⣀⠤⠤⠤⠀⠄⠤⠤⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠤⠖⠒⠒⠂⠀⠒⠲⢤⡀
⠀⠀⠀⠐⣇⢣⡀⠀⣠⠞⠋⠀⢀⣒⣒⣒⠲⣤⠤⠀⢀⡀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⣉⡀⠠⠤⠄⠒⠀⠐⠀⠀⠀⢀⠀⠹⡄
⠀⠀⠀⠀⠈⠲⣌⣽⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠓⠒⡃⠀⠀⠈⠁⠒⠀⠐⠒⠒⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⡠⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠈⡇⢂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠉⠁⠉⠁⠉⠉⡉⠉⠁⢀⣀⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡦⠄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠻⡴⡀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠂⣀⣈⣉⣉⣉⣄⣤⣤⡤⠠⠆⢀⡀⠀⠀⠈⣉⡀⠤⢕⣲⣬⣶⠿⠟⠛⠉⡀⣠⡶⢢⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣧⣤⡀⠠⠄⢀⣀⡀⢄⣠⣄⣀⣀⣒⣒⣒⣂⣀⣠⣬⣭⣥⣤⣤⣬⠿⠖⠒⠋⢭⣉⠀⣀⡀⠤⣔⣺⣷⠾⣋⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠪⢵⣲⣶⣦⣬⣭⠍⣩⣍⡹⠿⠟⢋⣩⣍⣉⡉⠉⠠⠤⠤⠤⠄⠀⠀⣀⣀⠤⠬⠔⣒⣋⡭⠽⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠭⢍⣛⣓⣒⣒⣒⣒⣒⣒⣒⣀⣀⣠⣤⡬⠭⠽⠶⠒⠚⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠏⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣿⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⢻⣧⣤⣤⣄⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⣿⣿⣦⣤⣿⡿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠎⠉⠲⡈⠻⠿⠟⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢩⣭⡠⠄⠀⣨⠀⠀⠀⠀⠀⠀⠐⠀⠠⠤
⠀⠀⠀⠀⠀⠀⣀⠤⠤⣶⠁⠀⠂⠐⠂⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠙⠷⢾⡿⠋⠀⢀⡤⢰⠦⢄
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠳⢄⠀⠀⠀⠀⢀⡞⠀⠀⠀⠈⡆⣠⠆⠐⠢⡀⠀⠂⠄
⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⣼⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⣠⢷⣄⣦⠄⠺⠧⣄⠀⠀⣠⣠⡃⠀⠀⠀⠸⡄
⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣸⠃⠀⢸⡇⠀⠀⠀⠀⠻⣿⠏⢸⡇⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠘⠷⠆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣿⣀⠀⠈⣧⡀⠀⠀⠀⢠⡇⠀⠈⠻⣿⣤⣴⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣷⣶⠟⠛⠷⣶⣾⠿⠁⠀⠀⠀⠈⠙⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⡿⠿⠿⠿⠿⠿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣤⡀
⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄
⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣀⣀⣀⡀
⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠟⠛⠛⠛⠛⠛⠛⠿⢷⣦⣤⡀
⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠋⠀⠀⢀⣀⢠⢤⣀⡤⡀⢀⠀⠀⠙⠻⣶⣄
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣻⡿⠋⠀⢀⣰⠒⠟⠈⠃⠀⡉⠀⠙⠉⠧⢶⠀⠀⠈⢿⣦
⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⢰⡿⠁⠀⣀⣯⠉⠀⠀⠀⠀⠄⠠⠈⠀⡀⠠⠘⢩⣧⡀⠀⢻⣧
⢿⣷⢠⡟⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⣾⡇⠀⢀⠵⠄⠀⠀⠀⢠⠤⠒⠒⠒⠤⡀⠂⡀⠀⢚⣷⠀⠈⣿
⠘⣿⡞⣷⡀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⣿⠁⠀⢈⠦⠀⡀⡀⢰⠃⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⢾⡇⠀⣿
⠀⠹⣿⡌⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡄⠀⢙⡦⠀⠄⠀⠸⡀⠀⠀⠀⠀⠀⢰⠁⠈⠠⠀⣚⡅⠀⣿
⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢿⡇⠀⠘⢦⠄⠀⠈⠀⠱⢄⡀⠀⣀⡠⠃⠀⠀⠂⠠⡽⠂⠀⣿
⠀⠀⠀⠈⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠘⣿⡀⠀⠹⣧⠄⠀⠄⠀⠄⠈⢉⠀⠀⠂⠠⠈⣀⢲⠋⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣶⣶⣶⣤⣴⣶⣶⣶⣾⢿⣷⡀⠀⠀⠹⣷⡀⠀⠙⢿⣴⢀⠁⠐⠀⠀⠀⠀⢀⡀⡦⠼⠉⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⢻⣷⡀⠀⠀⠙⢿⣦⡀⠀⠈⠙⠖⠳⠴⠣⠼⠳⠞⠉⠁⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠙⠿⣶⣤⣀⡀⠀⠀⠀⠀⠀⣀⣀⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣦⣤⣤⣭⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⢖⡢⡒⢅⢖⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⢉⣤⡾⠋⣴⠃⠸⣧⠙⣦⡉⠛⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢀⣴⣿⠋⠀⣼⡟⠀⠀⢿⣧⠈⢻⣦⡀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⢠⣾⣿⠃⠀⢰⣿⠃⠀⠀⢸⣿⣆⠀⠹⣷⡄⠀⠙⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⢠⣿⣿⠃⠀⢀⣿⣿⠀⠀⠀⠈⣿⣿⡀⠀⢻⣿⡄⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⣾⣿⡟⠀⠀⢸⣿⡏⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣷⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⢰⣿⣿⠇⠀⠀⣾⣿⡇⠀⠀⠀⠀⢻⣿⣷⠀⠀⢸⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⡇⠀⠀⣿
⣤⢠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⣿⡀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⡇⠀⠀⣿
⣿⢸⣿⣉⣿⡿⠿⣶⣶⣤⣤⣀⣻⠿⠀⠀⠈⣿⣿⡇⠀⠀⢿⣿⣇⠀⠀⠀⠀⣼⣿⡿⠀⠀⣾⣿⠃⠀⢰⣿
⣿⢸⣿⣿⣿⣷⣾⣿⢿⣿⣿⣿⣿⣿⣿⣶⣶⣭⣽⣓⣀⠀⠸⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⣸⣿⡏⠀⢀⣾⣿
⠹⡏⢿⣿⣩⣿⣿⣤⣾⣿⢿⣿⣿⣿⣿⣿⣿⣏⢙⣿⡛⢿⣿⢢⡆⠀⠀⠀⢀⣿⣿⠁⣰⣿⠟⠀⢀⣾⣿⡟
⠀⢻⣞⢿⣿⣿⠿⣿⣿⣧⣼⣿⡋⣻⣿⣇⣽⣿⣿⣿⣿⣾⢏⡾⣱⣇⠀⠀⢸⣿⠇⣴⡿⠋⢀⣴⣿⡿⠋
⠀⠀⠹⣦⡻⣿⣶⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣷⣤⣿⡿⣣⠟⣁⠹⣿⡀⠀⣿⣯⡾⠋⣀⣴⣿⠿⠋
⠀⠀⠀⠈⠛⢶⣝⡻⢿⣿⣤⣿⣿⣿⣧⣼⣿⠿⣛⣵⠞⠩⠶⣭⣳⣜⣇⣸⣟⣫⠴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢾⣭⣭⣭⣭⠷⠾⠛⠋
⣿⡿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣾⣷⡀⠀⠀⠀⣀⢀⣴⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣷⣧⡸⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠟⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⢏⣁⠘⢿⣿⣿⠻⡇⠀⠈⠟⣿⣿⣿⣾⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⣙⣷⣎⣻⣿⡆⠀⠀⠀⠀⣿⣟⣇⠙⠋⠛⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⢣⡴⠀⠉⠛⣿⣿⣿⣧⠀⠀⠀⠀⣿⢿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⡻⠝⠟⠁⠀⠀⠀⠈⠙⢻⣿⡄⠀⠀⠀⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⡛⢟⣠⡀⠠⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠳⠀⢠⣻⠈⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡄⣠⢏⠀⡀⠀⠀⠀⠀⠀⠀⢠⠈⣻⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣷⣨⠗⢁⡆⠀⠀⠀⠀⢀⠘⢿⣿⣿⠀⢰⣧⣄⠀⢀⠀⣶⣼⣾⡟⣶⣴⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣦⣌⠣⣼⣦⢳⣄⡅⠛⢸⣇⣿⠀⣠⣾⢿⡶⢸⣿⣿⣿⣿⣿⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣇⣻⣿⣿⣿⣿⣷⢿⣧⣿⡿⣇⡸⢿⡿⣿⠀⣿⣼⣆⣷⣼⣷⣿⣿⣿⣿⣿⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⣿⣽⣟⣿⣿⣾⣿⣿⣿⢻⣿⣿⡿⣿⣷⣟⢳⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣹⣿⣿⣿⣿⣿⢿⣿⣽⣿⣯⣿⣿⣯⣶⣿⣸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⢹⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣿⣿⣽⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣧⣿⣿⣯⣿⣿⣿⣾⣿⡋⣿⣽⣋⣿⣬⣿⣹⣿⡜⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⣿⣿⢿⣿⣿⣿⣷⣿⣿⣿⣿⡏⢹⡏⠛⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠘⠭⠛⠳⠿⡛⢥⠋⢹⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⡀⠁⠀⠀⠐⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡄⠀⠀⠀⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠧⠀⠰⠶⠤⠀⠁⠀⠠⢤⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠲⠚⠛⠁⠚⠛⠛⠛⠛⠛⠙⠛⠛⠓⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠃⣤⣲⣭⡌⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠘⢿⣀⠀⠀⠀⣼⡟⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠛⣯⣷⣿⠋⠁⠀⠀⡀⠮⣦⣶⣶⣦⠀⠀⠀⠀⠀⠌⠀⠀⢀⣠⡴⠦⢴⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠋⠻⠛⠻⠋⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠰⡇⠫⠀⠃⠀⠐⢛⡇⢆⢸⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢶⡁⠀⠀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀⠀⠀⠀⣠⣾⡇⠈⠀⠀⠁⠘⠉⣀⣽⠌⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣤⣤⢾⠋⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠺⡉⢸⡇⢀⣀⣠⣶⣾⣿⣿⣿⢀⣨⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠷⢜⠿⣆⣓⣡⣸⡽⣣⣧⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠫⠏⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠙⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀⠀⠀⢀⣤⣾⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣾⣿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣾⣿⣿⣿⣿⣿⣿⡿⢻⠟⢉⣽⠿⠛⣲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠈⠛⢿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠋⠉⠉⠉⠙⠻⣿⣡⡴⠋⣁⣴⢊⣡⡴⠛⡓⠄⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠃⠀⠠⠛⠉⠉⠙⠂⠀⠈⣿⠍⡙⠦⡍⠙⣌⣹⠟⠛⠉⠙⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⢛⠂⠀⠀⢠⣼⣾⣿⣿⡇⠀⠐⠇⠀⠀⠀⢀⠄⠀⢀⣿⡿⠓⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢷⣽⣿⣷⣶⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠂⠀⢀⡀⣿⣿⣿⣏⡠⠤⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠛⠛⠛⠷⣶⣶⣶⣶⣿⣿⣤⣿⣇⣉⣋⣵⣦⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣴⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠛⠓⠒⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⡿⠟⠋

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣉⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⢚⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⡰⠆⠀⠉⠓⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢋⣡⡐⠯⠒⠋⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⡬⡙⠲⢤⣀
⠀⠀⠀⢀⣠⣴⣚⣉⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠈⠙⠲⢤⣀
⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⣷⠶⠶⠶⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣼
⠀⠀⠀⢸⠀⠀⢀⣤⠶⠛⠋⠙⠛⢶⣄⠀⢘⡏⠉⠉⡹⢧⡍⢩⣟⠯⠉⠉⢹⡇⢀⣠⡲⠞⠛⠛⠻⢶⣄⠀⠀⠀⡿
⠀⠀⠀⣼⠁⣰⡟⠁⠀⠀⠀⡀⠀⠀⠘⢷⡄⢻⡄⠀⠀⠁⠻⠛⠀⠁⠀⢠⠿⠡⠾⠋⠀⢠⣀⡄⡀⠀⠙⢷⣄⠀⣇
⠀⠀⠀⢹⢠⡟⠀⠀⣐⢤⡟⢻⡔⣀⠀⠀⢻⠀⠙⢦⣀⠀⠀⠀⠀⣀⣴⡿⠀⠶⠀⠀⠐⢌⠛⢿⣿⣃⡄⠈⢿⡄⣿
⠀⠀⠀⣸⣹⣦⣤⣐⣾⣿⣠⣀⣙⣗⣂⣀⣘⣃⣀⣀⣙⣛⣒⣒⣛⣋⣁⣀⣘⣷⣀⣒⣻⣿⣃⣀⡙⠷⠒⠀⠸⢣⡏
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡠⠤⠐⠒⠋⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠛⠒⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣄
⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣧
⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣥⣶⡿⠟⠛⠛⠛⠛⠛⠓⠒⠾⢧⣄⡀
⠀⠀⣴⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣄⠴⢊⠅⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀
⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣤⣦⢖⡷⠸⠂⠈⢄⡔⢁⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⡀⠀⠀⠉⠳⣄
⠈⣿⠀⡀⠀⡀⠠⢀⡀⠢⣈⠀⠀⠀⡄⢃⠛⠙⠏⠉⠀⠁⠀⢠⢠⡟⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⠰⠀⡐⢰⠀⢃⡄⠈⠀⣀⠀⠀⠈⠳⡀
⠀⣿⠀⠁⠀⣀⣀⣀⠈⠲⡙⡄⠄⠰⠃⠈⠀⠀⠀⠀⠀⡔⣠⢣⡟⠀⡟⠀⠀⠀⠀⠀⠀⠲⠄⣧⣄⠸⣇⣆⣏⣾⣘⠇⡰⢢⠄⠁⠀⠀⠀⡀⠘⢆
⠀⣿⠀⢠⠏⣠⠀⠈⢳⡀⢅⠀⠘⠀⢀⠠⠤⠶⠒⠒⠀⠀⠋⡾⢠⠀⡇⠀⠀⠀⠀⠀⠀⣀⠐⠚⢿⠴⠉⠋⠉⠀⠉⠛⡧⢤⡄⠁⡀⠀⠀⠘⡄⠈⢧
⠀⢻⡆⢸⠸⣇⠀⠀⠀⡗⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⡇⢰⠀⣇⠀⠀⣀⠀⠀⠀⠀⠐⠀⠃⠄⢀⠀⠀⠀⠀⠀⠀⠛⣤⡈⠀⠀⡀⠀⠻⠀⡈⣇
⠀⠈⢷⡘⢧⡙⠃⡠⣠⡏⢸⠀⠀⠠⢀⠄⡀⠠⠠⠤⠐⠁⠨⡇⠈⠀⢸⡄⣇⠘⠗⠀⠀⠁⠀⠀⡀⢀⠤⢤⠀⠀⠀⠀⠀⠀⢣⡀⠠⠈⠑⠀⠀⠀⢳⢸
⠀⠀⠈⢿⣦⣙⡛⠾⡿⠴⠧⣀⠀⠀⠀⠀⠀⠀⠀⠄⡔⢐⠠⣧⣄⠀⠀⢷⡘⡄⠈⢌⠣⢜⠁⠀⠀⠀⠤⠰⠀⠈⠛⠲⠒⡎⢀⡉⠐⠢⢀⡀⠀⠀⢸⠈
⠀⠀⠀⠀⠻⣮⡙⠢⣶⣬⠖⡠⢩⠟⡶⢦⢆⣶⡮⣼⠁⠏⡄⢿⣾⣗⠠⠈⢻⣜⢄⠈⠓⠄⠁⠀⠰⠂⡰⠰⣦⡰⢠⠐⢀⣇⠈⠱⠄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠛⠦⣌⡑⠋⠐⠁⡔⣠⠆⢎⡜⣠⢦⣜⡰⠁⢘⣷⣿⣷⣦⡄⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⣀⠀⢁⢀⡀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠘⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠤⣤⣥⣀⣈⣡⣭⣭⡴⠷⠞⠋⠙⣯⠛⠂⠀⠤⠤⠙⠿⣷⡤⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⢧⡘⠓⠀⢖⡂⠀⠀⠙⠶⣷⣂⠠⣄⡚⠀⠀⣉⣉⣉⡀⠤⠀⠀⠀⠀⢐⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⠀⠑⠼⠂⢒⣂⠀⠁⠈⠹⠿⠿⠦⣤⣀⣀⣤⣄⣀⣀⣤⣤⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣍⠁⠙⠩⣁⣀⣤⠤⠀⢀⣀⣀⠀⠀⠉⠉⠉⢉⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢭⣍⣴⡦⠴⢖⣂⣤⣀⣠⣦⣤⣴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠋⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂⠐⠂⠀⠀⠂⠂⠂⠒⠀⠃⠂⠁⠀⠀⠐⠀⠐⠀⠀⠀⠀⠈⠀⠃⠄⠀⠁⠀⠈⠀⠂