Boxes Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠙⠲⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⠙⠲⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱
⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⡗⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠀⠀⠀⡇⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⢶⡉⠀⢦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠑⢄⠈⢆⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣄⠀⠀⡰⠁
⠀⠀⠀⠑⢌⢆⠀⠀⠀⠈⠑⠢⢤⡒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡩⠖⠓⠂⠤⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖
⠀⠀⠀⠀⠀⠀⢸⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠑⠲⢄⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖⢻⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢀⡠⠗⠊⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣹⡄⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠛⠒⠒⠲⠤⠤⠤⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢄⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⣄⡀⢸⠀⣀⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⠲⢂⠀⠙⠛⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⣦⣅⣀⣀⣀⡶⠀⠀⠄⠀⠔⠀⠁⠑⡄⠝⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠀⢀⡗⢏⣈⣟⣋⠉⣷⠇⠀⠘⠾⠶⠶⠬⡄⢀⠀⠀⠉⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡈⣼⢹⠉⠈⢆⠀⠀⠀⠀⠀⠀⢉⠔⢰⣦⣤⣄⣀⣄⣀⡀⠀⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢠⠁⠀⢀⠉⠙⠈⠀⠀⡆⠀⠀⠀⠀⠀⠀⠑⠶⠻⢿⠿⠿⠃⠂⡀⠀⠀⠔⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠐⠲⠂⡀⠀⠀⢸⡞⡿⢿⣿⣦⣀⠀⠀⡇⠀⠀⢀⠤⢄⠐⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠄⣂⡴⠁
⠀⠀⠀⠀⠀⠀⡠⠀⠉⠉⠀⠀⠀⠀⠀⠀⣀⡀⠀⠁⠀⡞⣿⢶⢾⣿⣿⣿⢹⣾⠀⠀⠀⠈⣇⠀⠀⠀⠀⢀⣠⡀⠀⠁⠀⠀⠐⠚⠋⠑⢆
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠃⠳⠶⠾⢿⣿⣿⡿⢟⠉⣁⡂⠤⠵⠐⠒⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠠⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢹⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⣤
⠀⠀⠀⠀⠀⠁⠀⠢⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠃⠡⠀⠒⢀⠉⠤⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠉⠙⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿
⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣨⠽⢿⠿⠥⠤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⡀⢀⣀⣀⡠⠤⠤⠴⠒⠒⠚⠉⠉⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣙⣛⣒⠲⠶⠶⠾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠐⠒⠒⠒⠒⠒⠀⠠⠤⠤⠤⠤⠤⠤⠼⢤⣤⣀⣀⡤⠤⠤⠤⠒⠒⠒⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿
⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢻⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿
⣿⣯⣤⣤⣀⣀⣀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢾⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠤⠀⣶⣶⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠐⠒⠒⠒⠒⠲⠤⠤⠞⠀⠀⣿⠀⠀⠀⠀⠈⠒⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠻⣦⡀⠀⠈⣄⠹⡄⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣀⠤⢤⣈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠶⠶⢬⣿⣦⡀⠈⢣⣱⠀⠀⠀⠀⠀⢀⠜⢀⠔⠉⠀⠀⢠⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠠⣄⣈⠉⠛⠶⢤⣨⠤⠶⡦⣄⠔⣃⣔⣁⠠⠤⠤⠴⢥⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠂⠠⠀⣀⠉⠉⠉⠉⠁⢸⣤⠀⢰⡃⠬⡁⠤⠤⠤⠤⠤⠤⢀⠈⢳⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠦⢬⡒⠖⠒⠂⠉⠉⠉⠩⠙⠛⠿⠷⠾⢇⡀⠈⣧⠐⠲⢤⣤⣀⠀⢠⠟⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⣀⡀⠀⠀⠀⠀⠀⠀⠉⢻⠈⣇⠠⠤⠤⠤⢄⣻
⠀⠀⠀⠀⠀⠀⠤⢺⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠉⠉⠐⠒⠠⡔⠊⢹⠀⢸⠲⣤⣀⣀⣠⡟
⠀⠀⠀⠀⢠⢂⣀⣼⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢠⠏⠀⢸⠀⠀⠉⠉⠁⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠎⠀⠀⢸⠀⠀⠂⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡾⢄⡀⡇⠀⠀⠃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣷⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣞⣠⢤⡀⢠⠇⠀⠙⡇⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢳⡼⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡇⠀⠀⠀⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡄⠀⠀⠆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⡇⠀⠀⡇⠀⠀⠘⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡔⠀⢠⠁⠀⠀⡇⠀⠀⢀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠦⣄⡀⡇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⢸⠀⠀⠀⣠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠤⠌⢀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡸⠆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣀⠀⠀⡇⠀⣠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠚⠃⠁
⣿⣟⢻⡟⠿⡿⠻⢟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢴⠖⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⠀⠁⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⣨⣠⣤⣾⠅
⠀⠀⠀⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢋⠐⠂⣀⡀⠀⣀⣀⣀⡀⠠⠤⢿⡴⠋⠙⠉⠉⠀⠀⠀⠀⢀⡠⣴
⠀⠀⠀⢙⠉⠁⠀⠈⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⣇⢸⠀⡏⢀⣀⠤⠠⠄⠒⠂⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⢱
⠀⠀⠀⠐⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠉⠀⠀⢉⡉⠭⠙⠛⠉⣧⠂⡍⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠠⠤⠒⡚⡆⠀⠀⢸⢠⢾
⠀⠀⠀⢠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢨⠉⠀⠀⠀⠀⠀⠀⣿⠇⠅⠀⠀⠀⠀⢢⠉⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠁⣸
⠀⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⡀⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢘⣴⢛
⠀⠀⠀⠤⠠⣤⣠⣤⣤⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡇⠀⠀⠀⠀⢘⠀⠀⠀⠊⠠⠀⠀⠀⠀⡇⢀⡀⣴⡷⡛⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣠⡏⠩⢇⠂⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣠⡴⠶⠚⠋⠁⠀⠀⠀⠈⠀⢄⠀⠸⠀⠀⣀⣀⣀⣠⠤⠴⠾⠓⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠴⠖⠒⠚⠉⠉⠉⡏⠉⠉⠓⠒⠲⠦⠤⢤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣖⡒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⢒⣲⣤⣤⡀
⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠉⠉⠙⠓⠒⠲⠤⠤⣄⣀⣀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⣀⣠⠤⠤⠶⠒⠚⠋⠉⠉⠀⠀⠀⢻⣦⡀
⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⣲⡗⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡙⢦⡀
⠀⠀⠈⠙⠒⠲⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠩⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⠙⠒⠲⠤⢤⣀⣀⠀⠀⠀⠀⠀⡼⠁⠀⡇⢱⡀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠴⠒⠒⠋⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠲⠞⠁⠀⠀⡇⠀⠳⠖⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠧⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠢⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⢤⣀⣀⠀⠀⡇⠀⣀⣀⡤⠴⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉

⡶⠒⢲⡶⣶⣶⣶⠶⣶⢶⡶⢶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠛⠷⣦⣬⣤⣄⣀⣈⠉⠉⠙⠛⠒⠲⠦⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⣶⣟⣭⣉⣁⣠⡤⠶⠚⠋⣉⡠⠤⠔⠛⢋⣉⠽⠛⠓⠲⢶⣦⣤⣤⣀⣹⣭⡽⠿⡦
⠀⠀⠀⣶⠾⠯⢥⣤⣈⣀⣀⠀⠀⠈⠉⠉⠛⠒⠺⠿⠤⢤⣤⣔⣊⣉⣀⣤⠴⠖⠛⠉⢁⣀⡤⠼⠛⠁⠰⠠⡇
⠀⠀⠀⢸⡅⠀⠤⠀⠀⠀⠉⠉⠙⠛⠒⠒⠶⠶⠤⣤⣄⣀⣀⠀⠉⡉⣙⣷⣶⠶⠖⠛⠉⠅⠀⠀⣀⣤⠶⢺⡇
⠀⠀⠀⠀⢳⡶⠶⠤⣤⣤⣄⣀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢻⡏⢁⠀⠀⠀⣀⣤⠴⢒⡫⢽⡇⠀⢸⠃
⠀⠀⠀⠀⠈⡇⠀⠀⢸⡀⠈⠈⢹⠉⡟⠒⡶⠶⠤⣤⣄⣀⣀⡈⠀⢸⡇⢀⣤⡶⠋⠁⠀⠀⠀⢀⣸⡇⠀⢸
⠀⠀⠀⠀⠀⢿⠀⠀⠈⡇⠀⠀⢸⠀⠀⠀⢁⠀⠀⠀⠀⣿⠹⠉⠙⢻⠛⠉⠀⡇⠀⣀⠤⠒⠋⠁⢸⠀⠀⣼
⠀⠀⠀⠀⠀⢸⡆⠀⠀⣷⠀⠀⠘⠀⠀⠀⢸⠀⠄⠀⠀⡟⠀⠀⠀⢸⠀⠀⠀⡟⠉⠀⠀⠀⠁⢀⣸⠀⠀⡿
⠀⠀⠀⠀⠀⠀⣧⠀⠀⢹⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠈⢸⠀⠀⠀⡗⠀⣀⠤⠔⠊⠑⣿⠀⣀⡇
⠀⠀⠀⠀⠀⠀⢹⡄⠆⢸⡆⠀⠀⢃⠀⠀⠈⡆⠀⠀⠀⣿⠀⠀⠀⢸⠁⠀⠀⡗⠉⠀⠀⠄⢀⣠⡿⠞⣋⡇
⠀⠀⠀⠀⠀⠀⢸⡏⠛⠚⠷⢤⣼⣸⠀⠀⠀⢇⠀⠀⠀⣿⠀⠆⠀⢸⠀⠀⠀⡗⢀⣠⠴⠞⠉⠀⢀⡤⠟⠁
⠀⠀⠀⠀⠀⠀⠈⣧⠜⠀⠀⠀⠀⠉⠉⠛⠓⠺⠶⣤⣀⣿⡀⠀⠀⣸⠀⣀⡤⠟⠋⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⢤⣄⣀⠀⠀⠒⠀⠀⠀⠀⠉⠉⠙⠛⣿⠋⡁⠀⠀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⣀⣀⠀⠐⠀⢀⣿⠀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠶⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣶⡶⠶⠶⠶⠾⠛⠛⠛⠛⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣨⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠈⢿⡄⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⡶⠶⠶⠟⠛⢛⣿⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠻⠶⠿⠛⠛⠋⠉⠉⠉⠀⠀⠀⠠⠄⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⠤⠤⠶⢾⢿⣛⠋⠉⠙⠻⢶⣄⡀
⠀⠀⠀⣀⣀⣤⣤⣤⣾⣧⣤⠤⠴⠶⠖⠒⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠓⢦⣀⠀⠀⠉⠛⠷⣦⣀
⠀⠀⠀⠻⣯⡉⠁⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠈⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣀⣀⣽⣶⣤⣴⠶⠶⠟⠋
⠀⠀⠀⠀⠀⠀⢸⣿⠻⣦⡀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⡶⠾⠶⠟⠛⠛⠛⠉⠉⠉⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠈⠙⢷⣤⣤⣤⣤⣦⡿⣶⠾⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⣿⣀⠐⠐⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡘⡇⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⡶⠶⠶⠟⠛⠛⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠂⠀⠀⠀⠀⠀⠄⠰⡄⠀⠀⠀⠀⠀⠀⢀⠔⠁⠐⠂⠤⢄⡀
⠀⠀⠀⠀⠀⢀⠄⢒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠄⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠢⠙⠂⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠨⢆⡠⢐⢕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠗
⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⢐⢀⠸⠠⠒⢊⠟⠒⠂⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⣀⣤⠔⠂⠨⠠⡠⠀⠀⠀⢠⡷⠄⠀⠀⠀⠀⠈⠁⠒⠢⠄⢀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠶⣬⣅⠔⠀⡁⡡⠕⢔⠀⠄⠔⡀⠱⡏⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣨⠽⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠒⠂⠉⠛⠶⣄⣄⢌⢂⠂⠈⠄⠔⢐⡃⠠⠈⠂⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⢦⣊⢎⠈⢨⡇⡐⠀⣑⡤⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢷⡷⠚⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠐⠧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠵⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢂⣀⠔⠃
⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢟⢌⠸⣃⠞⡦⡀⠀⠀⠀⠀⠀⠀⡀⡄⡆⠄⢀⡨⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠑⠢⢄⡒⠠⣠⠔⡡⡋⠐⢕⢄⠀⡧⠊⢊⢜⢦⡀⠀⠀⠀⠀⣁⡠⢔⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡳⡦⡞⢍⠊⠢⠁⠑⠀⡵⡡⡡⠢⠢⢛⢆⣠⠴⢪⣛⠇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⡄⠌⠓⡀⠀⠄⠈⠀⠄⠀⠀⠕⡑⡡⡣⡑⠁⢑⢃⠢⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢔⢀⠱⡌⢂⠁⠁⢨⢈⢈⢈⠈⠜⠐⠌⠌⠈⠄⣂⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠹⣢⡐⠢⢸⡥⡁⠡⠂⠊⣊⠬⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⢾⡄⠤⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠔⡀⢀⠀⠂⠄⡀⠄⡀⠄⡠⠄⢀⠄⠀⠄⡠⢀⠠⢂⠄⡂⢄⡠⢂⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠀⢀⠀⢂⠄⢀⠐⡨⠐⡨⠐⡠⠐⡠⠐⡀⢀⠀⠂⠀⡀⠀⡠⠂⠤⠊⠐⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠈⠛⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⠉⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠀⠀⠙⢳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠉⠀⠀⠑⠠⡀⠀⠀⠈⠂⢄⠀⠀⠀⠀⡀⠔⠊⠁⠀⠀⡀⠔⠊⠁⠀⣉⡛⢦⣄
⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⡀⠀⠀⡈⠖⠊⠁⠀⠀⣀⠄⠂⠁⠀⣀⠤⠒⠉⠀⠈⠓⢬⡙⠶⣄
⠀⠀⠀⣴⡚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⠂⠁⠀⠀⢀⠠⠰⢈⠀⠀⠀⠀⠘⠢⣄⠀⠀⢀⡠⢖⣩⠴⠚⢹⠂
⠀⠀⠀⡏⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⡀⠔⠪⣁⠀⠀⠀⠁⠢⢀⠀⠀⠀⠀⠑⣊⡥⠖⠋⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠈⠙⠦⣄⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠁⢢⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠙⠶⣉⠀⠀⠀⢀⠠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣤⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⠶⠋⠁
⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣇⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⣿⠀⠀⠀⠀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⡯⠀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠒⠊⡟⠑⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠚⠉⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠉⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢄⣀
⠀⠀⠀⠀⠀⡞⠃⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡩⠳⡄
⠀⠀⠀⠀⡸⠀⠀⠀⠈⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⢱
⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⡤⠚⠓⠢⣄⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁
⠀⠀⠀⠀⠀⠈⡷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢸⠸⡄⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠰⢄⡀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⡎⠀⢸⠀⢱⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣀⡜⠀⠀⢸⠀⠀⠳⠴⠊⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⢸⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⢦⠀⠀⠀⠀⢠⠖⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠀⠀⠀⠀⠑⢄⢀⠔⠁⠀⠀⠀⠈⠑⠢⠤⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⡟⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⡀
⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠂⠉⠀⠀⠀⡇⠀⠀⠈⠑⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠑⢄⢀⡠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠣⡀
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⡇⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠉⢲⣗⠉⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠑⠠⣀⠀⠀⢀⠔⠁⡇⠑⣄⠀⠀⣀⠤⠂⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠀⠀⡇⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⣤⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠉⠛⠿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⡇⠀⠰⢊⠥⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⢄⡀⠀⠀⡇⠀⢊⡡⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠇⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⢀⣀⡀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⠛⠛⠛⠛⠛⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠛⢩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⠉⠉⠓⠒⣦⡀
⠀⠀⠀⠀⠀⢰⡿⢭⣁⣀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⡤⠶⠚⠋⠉⡇
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠉⠉⠓⠲⣯⠀⠀⠀⠀⠀⢀⣀⣤⡶⠛⠉⣸⠋⠉⠉⢻⡈⠙⠒⠦⣤⣀⣀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⡷⢤⣄⣀⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠴⠖⠚⠫⣤⠞⠀⠀⢠⠏⠀⠀⠀⠀⢱⡄⠀⠀⠙⣏⠉⠉⠓⠒⠚⠁⠀⠀⠀⠀⣀⣸⠇⠀⢀⣈⡭⢿
⠀⠀⠀⠀⠀⠈⠳⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⢀⡞⠲⠦⣤⠴⠚⠋⢻⡀⠀⠀⠈⢧⡀⠀⠀⠀⣀⣠⠴⠖⢛⣩⡤⠖⠛⠉⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢲⡶⠤⣤⣀⣀⡼⠁⠀⠀⠀⡼⠀⠀⠀⡇⠀⠀⠀⠀⢳⠀⠀⠀⠀⠳⡴⠚⣉⣡⡴⠖⠛⠉⢸⡆⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢨⣟⣀⣤⠀⠀⣼⣁⡀⠀⠀⡇⠀⠀⣀⣠⣼⣧⠀⠀⣤⣀⠹⡏⠉⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⠁⢸⢀⡼⠁⠈⠉⣿⠒⠷⠚⠋⠉⠀⠉⢹⢧⣸⠁⠈⠛⠃⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⢻⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⣀⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄⣸⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⣀⣤⠼⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠤⣿⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣠⠴⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠤⣄⣀⣸⢀⣀⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢀⡶⠚⠒⠦⣄⠀⠙⢦⠀⠀⢀⡴⠋⢀⡤⠖⠛⠉⠙⢦⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠈⠳⡀⠀⢳⣀⡞⠀⣰⠋⠀⠀⠀⠀⠀⢸⠃⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠈⢇⠀⠀⠀⠀⠀⠹⡄⠀⠙⠀⡼⠁⠀⠀⠀⠀⢀⡴⠋⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠈⠳⢤⣀⠀⠀⠀⢹⡀⠀⢰⠇⠀⠀⢀⣠⠖⠋⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠉⠙⠓⠲⠶⠇⠀⠼⠴⠒⠋⠉⠀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⣲⠆⠀⠀⣠⣄⠀⠀⢴⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⢠⣾⠀⠈⣧⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢰⠏⣿⠀⠀⡏⢧⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢠⠏⠀⡟⠀⠀⡇⠈⣇⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⢶⣠⠏⠀⠀⡇⠀⠀⡇⠀⠘⣆⡾⢦⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⡇⠀⠀⡇⠀⠀⠹⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠋⠛⠛⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⡇⠀⠀⡟⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢹⠋⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⠒⠊⠉⡦⠞⠉⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠢⢼⡀⠀⠳⠦⠀⣗⡶⠚⠁⠀⢈⣦⠚⠉⠙⢦
⠀⠀⠀⠀⠀⣴⡒⠒⠋⢹⢀⠀⠀⠀⣀⣙⣧⣦⡀⣰⣿⢽⠇⠀⠀⣼⣧⣖⣲⣦⡜
⠀⠀⠀⠀⠀⢻⣿⣦⠽⠯⣿⣷⢠⢸⣿⣿⣿⣿⢳⡿⣀⣾⡼⠗⠛⠛⠛⢯⣯⡿⠗⠊⠲⡄
⠀⠀⠀⠀⠀⢠⣟⠁⡠⣠⣾⢿⣿⣮⣯⣿⣿⣻⣾⣮⣿⣿⣿⡆⠀⠀⡀⠈⣟⣭⣁⠀⢠⠃
⠀⠀⠀⠀⠀⢸⣯⣳⣮⠇⠈⣛⣓⣛⣛⣉⣿⣿⣿⣿⣿⣿⣵⣡⣼⣖⣥⣾⣿⣿⣿⣞⣁
⢀⡠⠔⠒⠩⠶⢿⣭⣽⠀⣾⢽⠋⠉⠀⠀⢀⣽⣿⢿⣿⣿⡄⠀⠀⢹⣿⠛⠟⠀⢀⣠⢴⢟⡇
⡎⠉⠑⠒⠤⣄⣀⠭⠛⠷⡶⢾⣇⡆⡄⡀⢸⣭⢠⣿⣿⣿⣵⣵⣴⣼⠤⠉⠓⢿⣍⠴⠣⢺⡇
⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣵⡛⠻⠛⠳⠾⠿⠛⠃⠁⣀⣤⡼⣻⡀⠀⠠⠆⠘⡗⠱⢠⣸⡇
⢧⣀⠀⠀⠀⠀⡇⠀⠀⠀⠸⡇⠈⠉⠒⠢⠤⣠⡴⠒⢻⡿⢋⢬⣺⡇⠀⠣⠢⠀⣿⣵⣿⡏
⠀⠹⠛⢶⣦⣤⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢺⡺⣲⢟⢕⠅⣮⣾⡇⢀⡤⠔⢀⡯⡈⢺⡇
⠀⠀⠀⠀⠀⠈⡇⠀⠓⠂⠀⣧⣀⡀⠀⠀⠀⢸⡾⣀⢀⣶⣾⢞⣿⠇⠈⠀⠀⢸⣟⠶⣹
⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠉⠙⠛⠒⢦⣼⢶⣾⣿⢟⣕⣕⣿⠀⠀⠀⠀⠈⣿⢈⣾⡀
⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣗⡹⡾⣫⢺⢝⢕⣿⠀⠐⠒⡁⠀⣷⢋⣾⣿
⠀⣛⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⢅⣾⡫⡣⣢⡗⣿⠀⠀⢇⠄⠀⣯⣿⣿⠒⠂⠀⠀⠈⢁
⠀⣏⡀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣿⣕⢿⣪⡪⡫⣪⣿⠀⠀⠁⢁⣠⣿⡋⢠⠄⠉⠁⠀⡠⠄
⠀⠀⠉⠛⠲⢤⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⢕⢕⢟⢝⢋⣾⣿⢀⣤⡶⠛⠉⠉⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠘⠚⠷⣦⣤⢸⡃⠀⠀⠀⠀⣿⣱⢷⢕⣵⠿⠿⠭⠋⠱⠖⠤⠤⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠛⠶⢤⣀⣿⡥⠟⠉⠩⠥⠄⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⢂⡀⠀⠁⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⢢⡡⠺⣍⠄⠢⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙
⠀⡀⠐⢤⠁⠐⠁⠀⠀⠀⠀⢀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠑⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆

⠀⠀⠀⠠⡠⠀⠠⠀⠀⠀⠀⠀⠴⠰⠄⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠸⡃⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠚⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠂⠘
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢀

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠰⡄⢀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑
⠠⣀⡠⠃⠐⠋⠀⠀⠀⠀⠐⠀⠠⠀⠠⢐⠀⠀⠀⢀⠀⠐⣀⠖⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠊⠤⠖⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡁⣲⠜⡑⡤⠃⠀⠀⠀⠀⠀⡠⠲⠢⠀⠀⠀⠀⠘⠄⠸⠻⠖⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣀⣀⣠⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣰⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣤⣤⣤⣄
⣿⣿⣉⣩⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣾⣷⣦⠈⢻⠟⢿⣛⣻⣭⣽⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣩⣽⣯⣶⣶⣿⣶⣍⠼⣻⣿⣿⣿⣿⢇⠉⢹⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣚⣽⣿⣷⣼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣻⣿⣿⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢰⣶⣿⣿⣿⣿⣿⡱⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⠿⠛⣿⣿⣿⣿⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠧⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣀⣠⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣟⡿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠛⠛⢻⣶⣶⣴⣶⣶⡾⠛⠛⠛⠛⠛⢳⣤⣴⣶⣶⣴⠛⠛⠛⠛⠛⠛⣶⣶⣶⣶⣶⡾⠛⠛⠛⠛⠛⢷⣴⣶⣶⣶⣶⡟⠛
⠀⠀⢈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁
⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⣶⣶⣾⠉⠉⠉⠉⠉⢹⣶⣶⣶⣶⣶⡏⠉⠉⠉⠉⠉⣶⣶⣶⣶⣶⣾⠉⠉⠉⠉⠉⢹⣶⣶⣶⣶⣶⡟⠉⠉⠉⠉⠙⣷⣶
⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠉⠉⢹⣿⣶⣾⣶⣶⣟⠉⠉⠉⠉⠉⢹⣶⣷⣶⣶⣾⠉⠉⠉⠉⠉⠉⣷⣾⣾⣷⣶⡎⠉⠉⠉⠉⠉⢽⣶⣷⣶⣶⣾⡏⠉
⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇
⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣀⣀⣀⠀⡀⣸⣿⣿⣿⣿⣿⣇⢀⡀⣀⣀⢀⣿⣿⣿⣿⣿⣿⡀⣀⠀⣀⠀⣸⣿⣿⣿⣿⣿⣇⠀⣀⠀⢀⢀⣿⣿
⠀⠀⢨⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⣀⣀⣸⠿⠿⠿⠿⠿⢧⣀⣀⣀⣀⣀⡸⠿⠿⠿⠿⠿⣀⣀⣀⣀⣀⣀⠿⠿⠿⠿⠿⢇⣀⣀⣀⣀⣀⡼⠿⠿⠿⠿⠿⣇⣀
⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠿⠿⢿⣤⣤⣤⣤⣤⡼⠿⠿⠿⠿⠿⢧⣤⣤⣤⣤⣤⠿⠿⠿⠿⠿⠿⣤⣤⣤⣤⣤⡼⠿⠿⠿⠿⠿⢧⣤⣤⣤⣤⣤⡿⠿
⠀⠀⠰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇
⠀⠀⢘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⣤⣤⣼⠛⠛⠛⠛⠛⢳⣤⣤⣤⣤⣤⡞⠛⠛⠛⠛⠛⣦⣤⣤⣤⣤⣴⠛⠛⠛⠛⠛⢳⣤⣤⣤⣤⣤⡞⠛⠛⠛⠛⠛⣧⣤
⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿
⣿⣿⠛⢿⠛⠿⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⣀⡀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣧⠀⠀⠀⣰⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⢰⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⡋⠀⠀⢠⡄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⠛⠿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠛⣀⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢸⠁⠀⠀⠀⠀⣿⣿⡁⢸⣿⡇⠀⠙⣿⠇⠀⠀⠀⢸⡏⣿⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⢸⠀⠀⠀⠶⠀⠁⠈⠁⢸⣿⡇⠀⠈⠁⠀⠀⠶⠀⢸⣧⡏⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡟⢿⣦⣀⣀⣤⣾⣿⠟⠃⣀⠀⠘⡶⠒⠒⠶⠦⠤⠤⠤⢼⣿⣧⡄⠀⠀⠠⠤⠤⠤⣾⣿⣇⠀⢀⣾⣷⠚⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⣙⡿⣿⣿⣿⣿⢿⣦⡶⠟⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢠⡄⠀⠀⢠⣿⣿⣿⣧⣼⣿⡧⠞⠁⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠁⠈⠉⢹⡟⠋⠹⣿⣯⡉⠀⠀⠉⢳⠰⡇⠐⠃⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢀⣤⣤⠬⠿⠿⢿⣿⡿⠛⠒⠲⠾⣥⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠇⠀⠀⠀⠀⠸⢈⠁⠀⠀⠀⠀⢠⠀⠀⢸⣿⣿⠀⠀⠀⢸⣿⡿⠀⠄⠀⢸⣿⡇⠀⠀⠄⠀⣿⢿⡇
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⠃⠀⠀⠀⠉⢀⣾⣷⣀⣶⣷⣤⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠈⢻⣷⣤⠤⠤⢼⣿⣷⠤⠤⠄⢴⣿⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⣶⠘⠛⠉⠙⣿⡏⠉⢉⠉⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡿⠀⠀⠀⢸⣟⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⡀⠀⢠⠌⣿⠰⡄⠈⠀⣿⣤⠤⠤⢤⠂⠀⢸⣿⡿⠀⠀⠃⠀⢸⣿⠁⢀⡀⢸⣿⡇⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣦⣠⣿⣟⡿⠀⠀⠀⠈⠀⣿⠄⡇⠰⠀⣿⡟⠀⠀⢸⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣟⠻⢷⣘⣿⣿⢉⡿⠀⣸⡇⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠰⠠⢤⣬⠿⡗⠛⠛⠻⢿⣭⠀⠀⡄⠁⠀⢹⡇⡇⠀⠀⣿⡇⠠⠄⢸⢄⣰⣿⣿⡇⠀⡀⢀⠀⠼⠯⠽⢛⣿⠟⠛⠻⣿⣿⡆⢸⡇
⠀⠀⠠⠄⠀⠠⣤⢸⣇⠀⠀⠀⠀⠀⠀⣿⣀⣠⠇⡤⠓⠛⠃⠇⣤⡄⠛⠃⠠⢤⣼⣿⣿⣿⣿⣷⣾⣿⠜⣻⣧⡀⠀⢸⣿⡄⠀⠀⣿⣿⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠉⠑⠲⠒⠾⣿⣿⠉⠻⠀⠃⠀⠀⠀⠀⣿⡇⠀⠆⠀⢀⠛⠛⠛⢛⣿⡟⠙⠛⢻⣿⣾⢶⡄⢸⣿⠀⠀⠀⣿⣻⡆⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⢸⠀⠉⠉⠉⣿⣿⠉⠉⠙⢿⡄⠀⠀⢸⣿⣧⠄⠀⣼⣿⡷⣿⡷⢸⣿⠀⠀⠀⣿⡏⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⡀⠀⠀⣿⡇⠀⠀⠀⠸⡇⠀⠀⠀⣿⡿⠀⠀⠋⢼⡇⣿⡃⢸⣿⠀⠀⠀⣿⣇⡇⢸⡇⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⣤⣤⣆⠀⠀⠀⠀⠀⢿⡇⠀⠂⠀⠀⡇⠀⠀⠀⣿⡏⠀⠀⠀⣾⡇⣿⡇⢸⣿⠀⠀⠀⣿⣿⣧⣾⣷⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⠤⠶⠞⠛⠛⠛⠛⠻⠄⠈⠀⠀⠼⠇⠀⠀⠀⠠⣇⠀⠀⠀⣿⡗⠀⠀⣰⣿⣷⡿⠿⠋⠉⠀⠀⠀⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠤⠶⠖⠒⠛⠳⣄
⠀⠀⠀⠀⢀⣀⣠⡤⠴⠶⠒⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢐⡀⠈⠓⢦⡀
⠀⣰⢾⡋⠉⠁⡠⡠⡠⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠀⠒⠀⠉⠉⠑⢄⡀⠀⠙⢦⡀
⣰⠃⠀⠙⠳⣄⠀⢀⡀⠠⠄⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠙⢦⣀
⠛⢤⡀⠀⠀⠈⠻⣄⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠄⡌⠢⡀⠀⠉⠳⣄
⠀⠀⠑⣦⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⣤⠤⠼⢷⠶⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠹⢦⡀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⠒⠚⠋⠉⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠉⠙⠓⠲⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠙⢦⣀⣤⠤⠶⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠶⠚⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⢀⣠⠞⡏⠙⠲⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⡤⠴⠖⠚⠋⠉⠉⠀⠀⠀⠀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⡷⢤⣄⠀⠀⠈⠙⠓⠦⢤⣀⣀⣤⠤⠶⠖⠒⠛⠉⠉⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠖⠚⠋⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡨⡙⠳⢦⣄⡀⠀⠀⢸⡇⠀⠐⠔⠌⠂⠀⣀⣀⣤⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⡒⡂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠓⠃⠀⠀⠀⠉⠓⠦⣼⣇⣠⡤⠴⠖⠛⠉⠉⠀⠀⢰⢒⠀⠀⠀⡸⠲⠤⡆⠀⠀⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢆⡀⠀⡦⣄⠤⠄⠀⠈⡇⠀⠀⢠⠢⡀⠀⠀⠀⠀⠀⠁⠀⠀⠛⢄⠀⠐⡄⠀⠠⠢⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⡠⠃⠀⠘⣦⠀⠀⡇⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠎⠉⠉⠀⢀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⠀⠹⡼⠁⠀⠀⠀⣿⠀⠀⠀⢠⠠⠎⢆⣀⠀⠀⠰⣉⠆⠀⠀⠀⠀⠀⠀⠧⠜⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⠤⠃⠀⠀⠀⢰⣉⠀⣿⠀⠀⠀⠈⡆⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⣄⡀⠀⠀⠀⠀⢹⠀⠀⠀⠘⠋⠉⠾⠀⠀⠀⣀⣠⡤⠴⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⢸⡄⠀⣀⣀⣠⡤⠴⠒⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠱⢤⡤⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠦⢤⣾⣋⣴⣋⣴⠯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣿⣖⠒⢶⣶⣖⠒⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡇⠈⡦⢤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣌⠻⣿⣦⡙⠻⣿⣦⣴⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣭⠀⠃⠀⡴⣜⠷⠖⠛⡆
⠀⠀⠀⠀⠀⠐⠚⢿⡉⠉⢻⣻⣄⣀⠼⠉⣩⡍⢁⡜⡃⠀⠀⠀⠀⣯⡛⢷⣌⡙⢿⣶⣌⡙⢿⠀⠀⠀⠀⠀⠀⢠⠾⡤⠤⠭⢿⠶⢺⣷⡏⠀⠤⣴⠇
⠀⠀⠀⣀⣈⡘⡛⣀⣏⠁⣠⠛⣧⠙⢿⣂⣌⣴⠻⣤⠃⠀⠀⠀⠀⢿⣿⣦⡙⢿⣦⣉⠻⢿⣿⠀⠀⠀⠀⠀⠀⢸⡬⠯⠤⡼⠃⠠⠿⠀⢳⣄⣀⠞
⠀⠀⠀⡑⠂⢄⠙⠋⠭⠉⢻⣴⠛⢳⣶⢃⣂⡭⢃⡜⠀⠀⠀⠀⠀⢰⣌⠻⣿⣦⣝⠻⣷⣤⣹⠀⠀⠀⠀⠀⠀⢰⡇⠛⠃⠛⢳⠃⠻⢧⡟⢴⠄⠀⠂
⠀⠀⠀⢸⠁⢴⠆⡀⠾⠆⠁⣷⠄⡀⢴⠆⢹⡬⠋⠀⠀⠀⠀⠀⠀⠘⠻⣷⣬⡙⢿⣷⣬⣹⠟⠀⠀⠀⠀⠀⠀⠈⠀⣤⠀⠰⠟⠀⠠⠄⣁⡀
⠀⠀⠀⠈⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠁⠀⠀⠉


⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣴⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣴⣶⡄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⣿⣿⣿⡏⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣇⠀⢀⡀⠀⠀⠀⢼⣿⣿⣶⡴⣾⣿⣿⣧⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⢷⡤⠤⢠⣿⣯⣿⣿⡥⣴⠚⠝⠀⠀⠀⠀⠀⠀⠀⡀⠀⠻⣿⣿⣿⠿⢁⡠⠊⡃⠀⠀⠀⢸⣿⣿⣿⣦⣾⣿⣿⣿⣤⣤⡤⢤⠒⢻
⠀⠀⠀⠀⠀⠀⣦⢄⣀⢸⣟⣿⣁⣉⣥⡤⢶⡇⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠁⠊⠒⠉⣠⡖⡇⠀⠀⠀⠈⠛⠛⣿⣿⣹⣿⣷⣀⣁⣀⣁⠤⢀⡎
⠀⠀⠀⠀⠀⠀⢻⢎⣿⡀⣿⡁⣿⠄⣼⣇⠺⣧⠀⠀⠀⠀⠀⠀⣷⣶⠒⣶⣶⠂⣶⣶⣻⠟⡿⠇⠀⠀⠀⠀⠀⠀⣿⠙⠂⣿⣻⡍⠙⠛⠁⠀⣿⣧
⠀⠀⠀⠀⠀⠀⢸⡏⣿⡎⣻⡡⢾⡦⢼⣏⢺⠏⠀⠀⠀⠀⠀⠀⢉⣹⣿⣇⣸⣿⣏⣹⠟⣿⠗⠁⠀⠀⠀⠀⠀⠀⢸⣶⡀⢿⣿⡷⠀⣤⣦⡀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠁⠛⠢⠿⠅⠻⠟⠚⠃⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠻⠿⠄⠿⠿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠠⠭⠀⠀⠿⠛⠃⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢰⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⡙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠦
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⡿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⡇⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠃⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄
⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⢀⡴⠛⠁
⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡿⢯⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠙⠷⣄⡀
⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄
⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠟
⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⡟⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⣠⡴⠋⠀⢸⡇⠀⠈⠳⢦⡀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠈⠙⠦⣄⠀⣠⠞⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠳⡴⠋⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠀⠀⢸⡇⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀⢘⣇⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⡶⠶⠶⠶⠶⠿⠛⠛⠛⠋⠉⠉⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣬⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠘⣷⡀⠀⢀⣀⣀⣠⣤⣤⣴⠶⠶⠞⠛⠛⠛⢉⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠘⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠐⠂⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣋⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⠤⠤⠴⠶⠶⠒⠒⠛⢻⠻⢭⣀⠀⠈⠙⠳⣦⣄⡀
⠀⠀⢠⣴⡶⠶⠶⠶⣿⡶⠒⠚⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠳⢤⣀⠀⠀⠉⠛⢶⣤⣀
⠀⠀⠀⠙⢷⣤⡀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠈⢙⣻⣦⡀
⠀⠀⠀⠀⠀⠈⢻⣦⣄⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣤⣤⣤⣴⠶⠾⠿⣿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⢸⡇⠙⢷⣤⡀⠀⠀⠈⠙⢦⣄⣀⣀⣤⣤⣴⠶⠶⠶⠟⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠛⠛⠛⠛⠛⠛⢻⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⡶⠶⠶⠟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⣴⠶⠶⠾⠛⠛⠛⠋⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢘⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢨⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⣤⡤⠴⣿⣀⡀
⠀⠀⢀⣀⣀⡤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢨⠀⠑⢄⡀⠀⠠⠤⠤⠀⠠⠀⣿⡞⠁⠉⠀⠀⠀⠀⠀⠀⡠⢴⡇
⠀⠀⠀⠨⠀⠀⠀⠐⠤⠄⠀⠀⠀⢀⠀⠀⠀⡀⣰⣀⣸⣀⡄⠂⢠⡄⠐⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣧⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⠀⠤⠐⠂⠉⠁⢸⡃⠀⠀⠀⠀⠀⡀⣀⠠⠠⠀⠂⠀⠂⠁⠘⠀⠀⠀⡇⠎⡇
⠀⠀⠀⢸⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣸⠏⠐⠀⠀⠀⠀⢑⣀⣀⡀⢀⣀⣀⣐⣀⣠⣂⠀⠀⣇⣀⡇
⠀⠀⠀⢰⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⡆⡀⠀⠀⠀⠀⢀⠀⠉⢁⢸⡿⡿⢿⠿⣿⡿⣧⠀⣿⣿⣧⣤⣄
⠀⠀⠀⠚⠐⠒⠒⠒⠺⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⣾⠧⡆⠀⠀⠀⠀⠐⠒⠒⠖⠲⠒⠒⠒⠒⢲⡖⠾⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠟⠀⠣⠄⡀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠾⠉⠁⠁⠂⠀⠀⠀⠀⠀⠐⠀⢀⣠⣤⣤⢴⡖⠒⠉⠍⠉⠁

⠀⠀⠀⠀⡠⢄⠴⠒⠂⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⢠⠎⠀⣀⡔⢠⠄⢈⡀⠘⠒⠺⠿⠖⠒⠐⠀⠀⢲⡂⠲⣀⡠⠴⠒⠿⠟⣋⡽⠟⢛⣳⠶⠶⢢⡄
⠀⠀⡇⣀⣀⠀⠀⠉⠀⠂⠈⠰⢾⡳⣶⣒⡶⢀⡴⡟⠃⠊⠝⠡⢖⠤⢠⠀⡈⠡⠖⠛⡁⠤⠖⣾⠻⢓⡀
⠀⠀⡇⠉⠙⠁⠴⠾⠖⠐⢀⣀⣀⣀⡀⠈⠀⡾⠋⠇⠁⠀⠀⠀⠀⠀⠁⣀⠐⣶⣯⠱⠄⠀⠀⠸⣈⡅⠃
⠀⠀⠘⡴⢲⡄⠀⠀⠀⠀⠈⠉⠈⠓⠾⠀⢸⡇⠀⠀⠀⠀⠀⡄⠀⠠⠀⠀⢰⡇⣭⠈⡆⠀⣀⣤⣾⠁
⠦⠀⠀⢁⣾⠼⠿⠷⠶⠦⢤⣄⣠⠒⢢⡀⢸⡇⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢨⢓⣺⠼⠒⠉⣙⣯⢾
⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⣰⣨⡿⠮⢿⣿⠀⠀⡄⠀⣀⠀⢰⠀⠀⢰⣿⣧⠶⠚⠛⠉⢀⣸
⠀⠑⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣜⣀⡆⢠⠨⠀⠀⠀⠀⣸⠁⠀⢀⣌⣠⣶⣾⣿⠿⡷
⠀⠀⠀⠀⠀⠉⠐⠂⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠦⠦⣤⣶⣿⣷⣬⣶⠾⠟⠋⠁⢀⠆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠋⡋⠀⠀⠀⠀⠀⣀⣬⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠠⠀⣀⠀⠴⡄⠀⡆⣃⣆⣀⠤⠴⠋⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠓⢍⠀⠀⠑⢶⠒⠒⠤⣤⠎⠁⠀⠀⡨⠝⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣴⠞⠓⠤⣑⠢⢀⠀⠑⢤⡤⠁⠀⢀⠤⣊⠠⠐⠓⣄⡀
⠀⠀⠀⣀⡠⠤⠒⠊⠉⠁⠀⢸⠁⠀⠈⠑⠂⠭⣙⣛⣿⣈⣑⣾⣛⣉⠡⠐⠂⠁⠀⠀⡩⠉⠒⠒⠤⢄⣀
⠀⠀⠀⡏⠉⠒⠢⢤⣀⠀⢀⣀⠬⢒⣂⡤⠝⠛⠭⠑⠋⡹⢌⠙⠊⠉⠛⠫⠍⣛⠪⢍⣀⠀⣀⠤⠒⠊⢹
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢙⡻⠖⠊⠉⠀⠀⠀⢀⡠⠔⠊⠀⠀⠉⠒⠤⡀⠀⠀⠀⠉⠲⣎⡏⠀⠀⠀⠀⢸
⠀⠀⠀⣇⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⣠⠖⠯⢄⣀⠀⠀⠀⠀⢀⣀⠼⠢⡀⠀⠀⠀⠈⠣⡀⠀⠀⠀⣸
⠀⠀⠀⠀⠙⠒⢢⠞⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠈⠉⠒⡖⠊⠁⠀⠀⠀⠙⣄⠀⠀⠀⠀⣼⠤⠒⡋
⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⣠⣋⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣇⣢⡀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢀⠜⠁⠈⡏⠒⠤⢄⡀⠀⠀⠀⡇⠀⠀⢀⡠⠔⠚⡇⠀⠐⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠃⠀⠀⠀⡇⠀⠀⠀⠈⠉⠒⠤⡧⠔⠊⠁⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠘⠢⠤⣀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⢀⡠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠢⢄⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⢀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⣀⣇⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⣿⡫⣟⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⠐⢀⠂⢁⢀⡀⠒⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⣴⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⣠⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣷⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡿⠟⢻⠿⢿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢘⣾⣿⣟⣹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠃⣾⣿⡿⣿⣿⣿⣿⡿⠻⣻⣽⣶⣿⣿⣿⣿⣿⡆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠻⢿⣛⣯⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⡗⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣷⡆⣡⣾⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠣⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⡟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠈⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡩⠻⢿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣧⢸⣿⣿⣿⡿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠿⠋⠙⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠃⣀⠀⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠄⣀⣀⠀⠀⠀⠀⠨⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠈⠀⠈⠂⠉⠊⠉⢁⠀⣀⢀⣀⡀⢀⢀⣠⣤⣤⣤⣀⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⡆⠉⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡠⠚⠉⠓⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢹⠟⠟⠋⠻⢿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠈⠈⠁⠀⢀⡌⠀⠀⠀⠀⠀⠈⡄⠐⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠤⣄⣀⣀⣀⣰⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠒⠒⠒⠒⠒⠒⠒⠒⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠓⠒⠒⠚⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⡠⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣴⣿⡀⢀⡖⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢀⣴⣾⡿⣽⣿⣿⣿⣿⣿⣿⡿⣷⡞⠫⡏⠉⠐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢰⣿⣇⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⠥⠀⡀⠄⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠳⠶⠚⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠀⠀⠠⡿⠿⠿⠟⠛⠋⠉⠉⠀⠀⢀⣀⣤⣴⡖⡀⠀⠀⠀⡄⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣀⣤⣤⣶⣶⣿⣿⣿⣿⠟⢩⣗⠠⠀⢰⣷⠈⢠⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⢠⣀⣿⠀⠀⠋⢀⣤⠀⣀⣍⠴⣍⡛⢿⣿⣿⡿⡟⢿⠿⢿⣿⠛⠍⠀⣼⣿⡀⠒⣸⣿⠀⣤⠆⢀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⢸⣼⡿⠞⠀⢈⠗⠲⣂⠄⢈⡅⠉⢁⡀⠆⣉⡩⠛⠉⠁⢀⠐⠂⡄⠑⠐⠭⣢⡀⡀⢨⠑⠣⠛⠻⢇⠁⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠊⠀⠀⠠⠖⠧⢀⡄⠀⠀⡀⠀⠁⠘⠋⠈⠁⠀⡀⠄⠂⠙⡀⢰⣷⠀⠠⡀⠀⠀⠈⠻⠗⡤⠀⠀⠈⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠡⠔⠃⠀⠀⢀⠂⠠⢸⣇⣾⠀⠈⠁⠀⠀⠀⢠⡆⠈⢀⠀⠂⢠⣇⣸⣿⡀⣀⣀⠄⢀⠅⠀⠁⢠⡀⠀⢀
⠀⠀⡆⠀⠐⠀⠀⠀⠤⣀⣀⠀⢀⣠⣤⡤⣬⣍⠀⠀⠴⠄⠀⣠⡄⣺⣇⢒⠶⠖⠠⡚⠛⠙⠉⠉⢀⠄⠊⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠁⠨⠑⠠⠄⠉⠀⢀⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠐⠆⠨⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠂⠈⠘⢿⣿⣶⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⡰⢠⢤⣄⡄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⣤⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠐⠀⠑⢄⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⣛⣛⣛⠃⠀⠀⠀⡀⠀⠑⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠀⠘⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠟⡣⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠐⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣗⠲⠾⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠁⠀⣠⠢⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡷⠈⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠔⠂⠀⠤⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠈⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⢀⣀⣀⡀⢉⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠓⢤⡀⠀⢠⢃⡞⢉⡽⢻⠀⣠⣞⣑⠦⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠣⢄⡀⠀⠈⠑⢾⣞⠜⢋⡠⠞⠊⠉⠀⠀⠀⠘⢯⡒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⡠⠞⢓⣂⠾⣧⣼⠛⠷⠴⣖⠒⠒⠚⠉⠉⠉⢉⡵⠋⡇
⠀⠀⠀⠀⠀⣠⡊⠀⠀⠀⠀⠀⢣⡾⠋⡠⢊⠟⡇⢣⡀⠀⠈⠙⠢⢄⡀⢀⠔⠋⢀⠜⠁
⠀⠀⠀⠀⠀⠸⡈⠑⠦⣀⠀⢀⡴⠧⣎⣠⣮⢾⠃⠸⡍⠒⢤⣀⠀⢀⠜⡇⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠉⠛⢤⣀⣠⠞⠁⢸⠀⠀⡇⠀⠀⣨⢿⠁⢀⠗⢹⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⡚⠓⢦⣀⠈⠑⠢⢄⡇⣀⡀⢸⣠⠞⠁⢸⠖⠉⠉⢹⠓⢌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠫⡉⠉⠙⠢⣄⡀⠟⠓⢬⠛⠃⣠⠞⠁⠀⠀⠀⢸⠀⠀⠑⢄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠢⣀⠀⠀⠉⠒⢤⣸⣀⠜⠁⠀⠀⠀⠀⠀⢸⡀⠀⢀⣀⣑⣤⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⠬⠥⠤⠤⠖⠒⠒⠒⠋⠉⠉⠉⠁⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠔⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣗⠀⣀⣀⣀⠤⠤⠔⠒⠒⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡾⠛⠛⠻⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠘⣿⣿⡀⠀⠈⠉⠳⣦⡀⠀⠀⠀⠀⠀⢀⣼⠛⣿⣿⠃⠀⠀⠀⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣄⣀⡀⣹⣿⠷⢤⣀⡀⢀⣼⣿⣦⠀⠀⠀⢠⡟⠁⢀⣿⠿⣄⣀⣤⣶⣾⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠉⠉⠉⢛⣻⣧⣀⠀⠀⠙⠻⣿⡿⠉⢷⡀⢠⣿⣷⣴⠋⠀⠀⢸⠿⠛⠋⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢿⣿⣿⣿⡿⠛⠲⢤⣄⣈⢧⡀⠈⢷⡞⢹⡟⣁⡠⢤⣶⣇⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠤⢤⣄⣉⠙⢻⡦⢸⡇⢿⣿⣅⣠⡴⠿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠿⣿⣿⠉⠋⠉⠉⠉⢻⠋⠉⠉⠉⠛⠛⠓⠒⠒⠲⠶⠶⢶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣀⣠⣼⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⡇⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣶⣶⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⣤⣤⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣴⣶⣶⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠿⠿⠿⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠦⣤⣤⣤⣤⡼⠷⠶⠶⠶⠶⠦⠤⣤⣤⣤⣤⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠴⠖⠚⠛⠉⠉⢀⣀⡀⠠⣤⣌⡩⠍⠛⠓⠲⠶⠤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣀⣤⣤⠤⠶⠶⠶⠶⠖⠚⠛⠉⢩⣅⣀⣀⠤⠤⠔⠒⠒⠉⠉⠓⠢⠤⣀⡀⠙⠛⠒⠶⠤⣤⣀⣐⡂⠀⠀⠈⠉⠉⠉⠛⠛⠛⠒⠲⢦⣄
⠀⠀⠀⠀⢿⢿⠛⠫⢭⣉⠓⠒⠒⠒⠛⠻⢿⣯⣀⠀⠉⠲⠤⣀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⠒⠦⠤⣐⡂⠀⠀⠉⢉⣑⣲⠶⠦⠤⠙⠒⢒⣚⣿⢿⣿⡇
⠀⠀⠀⠀⢸⠀⢳⡀⠀⠈⠉⠓⠦⢄⣀⠀⠀⠀⠉⠛⠲⢤⣄⡀⠉⠑⠢⢄⣀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠜⠓⠊⠉⠁⣀⣀⡠⠤⠒⠚⠉⠉⠁⠀⡜⢸⠃
⠀⠀⠀⠀⢸⠃⠀⢱⡤⠤⢤⣐⠀⠀⠈⠉⠓⠦⢄⣀⠀⠀⠀⠉⠓⠢⢄⣀⠬⠽⠖⠒⠋⠉⠉⠀⠀⢀⣀⡤⠶⠚⠋⠉⠀⠀⠀⠈⠀⠤⠀⢀⡞⠀⢸
⠀⠀⠀⠀⢸⡄⠀⠀⡇⠀⠀⠈⠙⠖⠦⣄⣀⠠⠀⠈⠉⠓⠶⢤⣄⣀⠀⠹⡀⠀⢀⣀⣤⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⢀⣀⣀⣤⣤⠞⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣄⡀⠀⠀⠀⠉⠙⢛⣷⣞⠉⠁⠀⠀⠀⢀⣀⣀⠤⠤⢤⠖⠒⠒⠉⠉⢹⠁⠀⠀⢸⡀⠀⠀⣾
⠀⠀⠀⠀⠀⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠛⡶⠤⣤⡴⠋⢸⠀⠑⣤⠴⠒⠋⡏⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⠀⠀⠀⢸⠇⠀⠀⣿
⠀⠀⠀⠀⠀⢹⠀⠃⢸⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣗⠀⠀⠀⡇⠀⠸⡆⠀⠀⠀⠀⠹⠀⠀⠀⠁⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡆⠀⢸⠁⠀⠀⣿
⠀⠀⠀⠀⠀⢸⠀⠀⠈⡆⠀⢡⠀⢠⠀⡄⠈⠀⠀⡟⠀⠀⡀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠄⠀⠀⠀⡇⠀⠈⠀⠀⠀⡄⠀⠀⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠃⡇⠀⠀⡇⠀⠀⡄⠀⣤⠀⠇⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢿
⠀⠀⠀⠀⠀⢸⡇⠤⠀⣧⠀⠀⠀⢸⠀⠀⢰⠀⠀⠇⠀⠀⠀⡇⠀⠀⠇⠀⠀⡇⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠇⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠘⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⢸⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⠀⠀⠀⢀⡔⠛⢄⠀⢸⠀⠄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⡆⢻⠀⠀⠀⠀⡀⠀⢀⠀⠀⡄⠀⠀⠀⡇⠀⢸⠀⠀⠀⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠾⢦⠀⡏⠀⢸⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⣡⠞⠳⢤⣀⠀⡇⠀⠀⠀⠀⣇⣀⠤⠲⡇⠀⢸⠀⠀⢀⡇⠀⣿⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⢛⣧⠤⠾⣄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢹⡔⠁⠀⠀⠀⠈⠙⠳⠤⣀⠀⠀⣿⠈⡇⠰⡾⠄⢸⠀⠀⢸⠇⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⣀⣸⡤⠤⠖⠚⠋⣉⠀⠀⠀⠈⠳⣄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⡀⠄⠀⠀⠀⠀⠉⠒⠾⣄⡉⠛⡇⠀⢸⠀⠀⢸⠀⠀⠈⠀⢀⣀⣤⠷⠖⠚⠉⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢈⣳⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠐⠂⠀⠀⠉⠑⠷⣀⣸⠀⠀⢸⠀⠀⣸⠋⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠡⡀⠀⢸⠀⢰⠃⠀⠀⠀⠀⠤⠔⠂⠀⠀⢀⣀⣤⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀⠀⠀⠀⢳⡀⢸⢀⠇⠀⠀⠀⠀⠀⣀⣤⡴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠱⣸⡏⢀⣠⡤⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⣀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠛⠛⠋⠉⠁⠀⡸⠉⠙⢮⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢣⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠈⣆⠀⠀⠀⢣⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠢⣄⠈⠳⣄⠈⢣⡀⠀⠈⣿⠀⠀⢀⢀⡠⠔⠋⠁⠀⠀⠀⠈⠉⢉⣹⠖⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣢⡤⠤⠤⣀⣀⡈⠑⠦⣌⡑⠀⠙⢦⡀⢸⡷⡆⠉⡙⢄⣀⣀⣀⣤⠤⠤⠒⠊⠉⠀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠯⣭⣉⣀⣀⣀⠀⠀⠀⠉⠉⠓⠒⠩⣵⣶⡤⡟⠒⢇⢸⡄⡈⠌⢧⠀⠀⢀⣁⣀⠀⠀⠀⠀⠀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⢠⡖⠓⠛⠛⠩⠭⠥⠤⢄⣀⠤⠭⠙⠛⠛⣛⣋⠭⠟⠒⠺⠧⠖⠻⢄⡇⢠⠀⢨⡭⣙⣒⠒⠒⠒⠶⣾⠭⠭⠭⠭⠚⠛⠒⢲
⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⡎⠉⠉⠉⠙⠒⠒⠒⠒⡶⠒⢺⠁⠘⠀⢸⠉⠉⢹⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⡆⠀⠸⠀⠀⢸⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⡀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠁⠀⠀⡇⠀⢸⡇⠀⠀⠨⡇⠀⠀⠀⠀⠀⢀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢹⠉⠉⠉⠉⠁⠒⠚⡇⠀⠀⠀⡧⠤⠤⢄⣀⣀⣀⣀⣀⣇⠀⣿⠀⠀⠀⠀⡧⠤⢼⡇⠀⠀⠀⡗⠒⠈⠉⠉⠉⠉⡏
⠀⠀⠀⠀⠀⠀⢀⠜⠁⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⡏⠁⣿⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠐⠛⠒⠒⢻⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⢡⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⢀⡀⠀⢸⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⠊⠁⠈⠑⠚⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠒⠒⠻⠤⣄⣀⠼⠤⠄⣤⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣄⠠⠤⠴⠧⠀⠠⠤⠛⠚⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠚⠉⠛⠒⠶⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠦⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⢦⣄
⠀⠀⠀⠀⠀⣴⢯⣍⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⠉⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠓⠲⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠋⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠤⣤⣀⡀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠟
⠀⠀⠀⠀⠀⠘⡶⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⡶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠉⠁⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠉⡟⠒⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣠⡴⠖⠛⠉⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠉⠉⠛⠒⠶⢤⣄⣀⣇⣀⣤⠴⠚⠋⠉⠀⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠳⠤⣄⣀⣸⠀⠀⠀⠀⠀⠀⠀⠈⡏⠁⠀⠀⠀⠀⠀⠀⠧⠖⠚⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⡤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠤⣤⣇⣤⠴⠚⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣷⣶⣦⣤⣄⣀
⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⡀
⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠛⠻⠛⡛⡛⢉⣋⣈⣙⣛⢛⠛⡛⢛⣙⡛⡛⠛⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠋⠙⡄⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠃⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢃⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠉⠉⠛⠷⢶⣿⣛⣉⣉⣛⣿⡶⠾⠛⠉⠉⠹⣧
⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⣿⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⣿⢶⣦⣤⣄⣀
⠀⢠⣶⠾⠛⠋⠉⠁⠉⠉⣿⠀⠀⠀⠀⠀⠀⣸⣇⣀⣀⣸⣇⠀⠀⠀⠀⠀⠀⣿⠉⠁⠈⠉⠙⠛⠷⣶⡄
⠀⢸⡟⠛⠷⢶⣦⣤⣤⡶⠻⣦⣀⣠⣤⡶⠟⢛⣻⣯⣭⣉⡙⠻⢶⣤⣄⣀⣴⠟⢶⣤⣤⣴⡶⠾⠛⢻⡇
⠀⢸⡇⠀⠀⠀⠀⢨⣿⠛⠛⠿⢿⣯⣶⣚⡋⠉⠀⠀⠀⠀⠉⢙⣓⣶⣽⡿⠿⠛⠛⣿⡇⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡏⠉⠛⠻⠶⣶⣶⠶⠟⠛⠉⢹⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⡇
⠀⠸⠷⣦⣤⣀⣀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇⣀⣀⣤⣴⠾⠇
⠀⠀⠀⢸⡏⠉⠙⠛⠿⣶⣦⣤⣀⣸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣇⣀⣤⣴⣶⠿⠛⠋⠉⢹⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠈⠉⠛⣿⡷⢶⣤⣤⣸⣇⣤⣤⡶⢾⣿⠛⠉⠁⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠉⢹⡏⠉⠀⠀⢸⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⣧⣀⡀⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⠀⠀⢀⣀⣼⡇
⠀⠀⠀⠀⠈⠉⠛⠛⠷⢿⣦⣤⣀⡀⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⢀⣀⣤⣴⡿⠾⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠷⣶⣤⣄⣸⣇⣠⣤⣶⠾⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠈⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡋⠉⠉⠙⢢⡄⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢺⠉⢦⡀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢸⡄⠀⠙⣄⠀⠀⢳⠔⠒⠒⠛⠛⠛⠋⠉⠑⠢⣤⠏⠀⠀⠀⣀⣠⡬⣦⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢷⠚⠉⠉⢦⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢀⣴⠚⠉⠀⠀⠘⣆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠋⠉⠙⣦⡈⢧⡀⠀⠈⢷⡀⠸⡀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡴⠋⠈⢓⣦⡀⠀⠀⢹⡄⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠈⠻⣦⡙⢦⡀⠈⢷⠀⢷⣄⠀⠀⠀⣰⠋⣠⠶⢋⣠⠴⠞⠉⠉⠙⢷⣄⠀⣧⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⣤⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣝⢦⡘⣇⣨⡿⠷⢤⣜⣡⣾⠿⠚⠉⠀⠀⣀⣠⣤⠶⠚⠛⠣⣿⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠘⣎⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⠏⠀⠀⣾⡋⠉⢀⣀⣤⡶⢞⣛⣉⣡⣤⣤⣤⡴⠶⢋⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠞⠩⣯⡀⠀⠀⣏⠉⠙⠛⠛⠛⠋⠉⢉⣉⣀⣠⡤⠤⠶⠚⠋⠁⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⠑⢦⡀⢀⣠⣤⠴⠖⠛⠉⠀⠀⠀⠀⣈⣽⠿⣟⠉⠉⠉⠉⠉⠻⣍⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⠀⠀⠀⠀⠀⠀⢙⡏⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠉⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⣀⡤⠴⠚⠋⠁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⠠⣀⠀⠀⠀⢸⡇⠀⠀⠀⣴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⢀⣈⣿⣦⠤⠒⠉⠁⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠈⠑⢤⡀⢸⡇⠀⠀⢀⡟⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⣦⡴⠞⠋⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠙⣷⣄⠀⢸⡇⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣤⣤⡤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡏⠈⢷⣼⠇⠀⠀⠀⠀⠈⠢⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣠⣿⠴⠖⠚⠋⠉⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠷⣄⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠞⠛⢹⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣸⠀⠀⢀⡿⠀⠀⠑⠢⢄⡀⠀⣿⠀⠀⠀⣀⡠⠴⠚⠉⢹⡇⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡿⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⢦⣷⠖⠚⠉⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⢸⡇⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣼⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⡀⠀⣀⣀⣤⡤⠤⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢦⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣀⣠⣼⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⡿⠀⠀⠀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡇⢀⡴⠋⠁
⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⢉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠄⠀⠀⢀⢀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⠓⢦
⠀⡀⠀⠀⠀⠀⠈⡈⠀⠄⠀⠠⠀⣀⠀⠀⠀⠤⠀⡀⠀⠀⠀⠙⢂⠀⡀⢀⠀⠂⠀⠀⡀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⢸⡇
⠀⠀⣀⡂⠈⠀⡀⢁⠀⠒⠆⠖⠀⠀⠀⠀⠠⠆⠀⠠⠤⠤⢥⣄⡀⢧⣁⢀⠔⠉⢀⣡⠤⡀⠠⠀⠁⠀⠀⠀⠉⠉⠙⠛⠒⠐⠒⠺⠛⠒⠒⠂
⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⡳⠆⠀⠀⠀⠀⠀⡀⠀⠀⠱⢭⠉⠙⠻⣶⠿⠯⣤⣞⠭⠤⠶⠀⠀⠀⠀⠀⠀⡐⠀⢀⠂⠀⠀⠐⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠖⠒⠒⠒⠒⠒⠒⠳⠀⠀⠘⠒⠒⠒⠒⠒⠒⡒⠋⠐⠀⠀⠀⠉⢴⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠰⠀⠀⠀⠊⠀⠅⣀⠐⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⢈⢀⠀⠀⠀⠁⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠠⢄⠀⠐⠂⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠐⠄⠸
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠂⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⢀⡛⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⢀⡐⠁⠠⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠈⠀⠐⠂⠀⠀⢀⡀⠀⡀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠠⡏⠠⡐⠠⠂⠀⠀⠢⠀⠀⠀⠀⠀⠐⠁⠀⠀⢐⠈⠈⢅⠁⠀⠀⠀⠇⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠐⠀⠀⠀⠈⠀⠀⢀⡀⠀⠀⡈⠈⠉⡑⠂⢁⠋⣁⠀⠀⢀⠠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠸⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⠀⡐⠄⠀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠈⢾⡁⣀⠴⠋⠸
⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⠄⠀⢣⣤⠈⣉⡵⠡⠤⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠰⡀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢍⣉⡉⠀⡀
⠀⠀⠀⠀⠀⡀⠠⡔⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⡤⠂⢐⠀⣀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⢁⠀⡀⡁⠀⢈⠏⠺⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢘⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⠢⡈⠳⡄⠀⠘⣿
⠀⠀⠀⠀⠠⠉⠉⢼⡶⠡⠊⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢨⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠘⠦⠘⢆⠀⠻
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠅⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠚⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠄⠒⠒⠀⡞⠃⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⢀⠀⣀⠀⡀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠄⠐⠀⠂⠰⡖⠀⠗⠞⠒⠻⠲⠂⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⣀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠲⠔⠚⡟⠡⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡂⢀⠒⠒⠒⠒⠒⢗⠒⠳⠚⠒⠒⠒⠒⠒⠒⠂⠀⠀⢀⠀⠀⠄⠘⢰⠀⠀⠀⠠⠠⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠀⠀⠀⠀⢮⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠁⠀⠈⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠄⢀⣲⢶⡶⠒⠆⠬⠀⣁⠈⠁⠒⠠⠄⠀⣀
⠀⠀⠀⠀⠀⠀⣀⠀⠄⠐⠀⢉⣀⡤⠔⡖⠋⢉⢃⠈⡇⠀⠀⠀⠀⠀⠀⠉⠁⠐⢠⣤⠄⠈⠁⠰⠦⠄
⢀⡀⠀⠂⠀⢁⣀⡤⠴⠒⡿⢋⠎⠏⣈⠂⢀⡆⢓⡾⡇⠀⠀⠀⠀⠀⡀⠤⠒⠈⠀⠀⠑⡄
⠈⠀⠀⢀⠔⠉⠉⠑⠒⠾⢴⣌⡰⠃⠉⠄⠢⢃⡏⠞⣥⢀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢧⣴⡿⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠃
⠀⠀⠀⠁⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠆⠁
⠀⠀⠀⠀⠀⢸⠉⠛⠒⣤⢤⣀⡀⢀⣼⠟⢽⠇⣹⣄⠀⠀⠀⠀⠀⣀⢤⠖⢫⠏⡸⠃
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⠁⠹⠛⠉⠂⠸⢠⠁⣹⡧⣀⣤⣖⠟⢣⠎⠀⡈⡜⣸⡖⠂⠤⠀⣀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⡶⠁⠙⠉⡔⠡⠀⠎⢀⡊⠄⣰⣽⡆⠀⠉⠥⠤⠀⠐
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡜⠀⠀⢄⡾⢀⠣⠞⣌⣞⣤⡶⠟⣯⠭⠭⠅⠀⠀⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⢸⣉⣄⡴⡛⣢⣯⣤⡶⠛⠉⠩⠭⠭⠭⠤⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⣸⣫⣽⠿⠟⣻⣷⣶⣄⣀⣀⣀⠤⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠑⠀⠀⠘⠀⠀⠀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡶⠵⠮⣴⣀⣄⢠⡠⠀⠀⠤⠀⠀⠀⣠⣤⣤⣄⣀⣳⣤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠊⡠⢂⠔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣃⣖⣡⣊⣄⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⠤⠤⠤⠽⠄
⠀⠀⠀⠀⠀⠀⠀⢸⠖⣡⢞⡡⠊⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣎⡕⣉⡀⣁⣔⢁⠀⢀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣥⠜⡡⢊⠝⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡷⢊⠐⡁⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃
⠀⠀⠀⠀⠀⠀⠀⢸⠟⠉⠛⡩⠋⠉⠉⠉⠉⢉⡉⢩⡭⠍⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠆⡠⢊⡴⠂⢀⡠⠖⠫⣀⠀⢁⣘⡀⠤⠀⢍⠲⡄⠀⠀⠀⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢃⠔⢋⠔⢁⡠⢦⡁⠶⢢⠉⠁⠀⢀⠉⢐⡂⡸⠧⢀⠀⠀⠀⠀⡇⣠⠾⣉⠆
⠀⠀⠀⠀⠀⠀⠀⢘⡁⠖⠡⠬⠅⢀⡠⠔⠁⠀⠀⠀⠠⠁⠀⠀⠉⠒⠄⡀⢌⠲⠄⠀⠟⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⢨⡅⠀⠀⠛⠈⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠴⠃⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠸⡶⠶⠶⠶⢲⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠔⢉⠔⢁⡀⡀⢀⠐⠂⠈⠉⠉⠉⠉⠉⠉⢉⡙⠃⣰⠇⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠠⢧⠴⣤⠮⣤⣞⡝⡩⠛⡸⡫⠋⡴⢋⠀⠀⠉⠉⠁⠈⠁⠀⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢘⡁⠔⣡⠊⡀⢿⡹⢓⠟⢚⠓⠛⠐⠛⠒⠒⠂⠒⠒⠒⠒⠒⠒⠘⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣡⠜⡡⠊⡠⢻⡔⠋⡰⠋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾⠴⠮⠴⠾⣧⠊⡠⢊⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠊⡠⠋⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢡⠞⢀⠔⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣁⡴⢋⡴⠃⠀⠀⠀⠀⠐⣠⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠮⣤⣇⣀⣀⠀⣠⠊⠀⠤⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠄⠀⠀⡇⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠃⠀⡱⠀⠘⢦⣀⣂⣀⡠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠄⠤⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠿⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⡙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠷⣦⡀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠀⠀⠀⠁⣿⡇⠀⠾⣿⡿⠿⢶⣄⠀⠀⠀⠀⠈⠻⣦⣀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠉⠀⠀⠀⢀⣤⡶⠟⠋⠀⠀⠀⢻⡗⠀⠀⢹⡇⠀⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⠂⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⢸⣧⣀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⠆⠀⣀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⠇⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠐⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⣸⣿⣴⣶⡶⠶⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⣀⣀⠀⠀⠤⠤⠍⠛⠛⠻⣷
⠀⠀⢀⣀⣤⡴⠶⠛⠛⠛⠛⠛⠋⢁⢠⣤⡤⠄⠀⠀⠐⠒⠒⠀⠈⠉⠉⠁⠀⠀⠀⢉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⣴⡾⠛⠛⠛⠒⠒⠂⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠛⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⢿⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⢸⡇
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢸⣧
⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⢸⣿
⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠘⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠳⠀⠀⠀⠀⠀⠀⢀⣡⠀⠀⠀⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠈⢆⠀⠀⠀⠀⠈⡄⠀⠀⠀⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠰⡀⠀⠀⢿
⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠡⠀⠀⠀⠀⢡⡄⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⢠⠊⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢡⠀⠀⠀⠀⠱⡀⢸
⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠡⣸
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⢻
⠀⠀⣿⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⢀
⠀⠀⣿⡄⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢸
⠀⠀⣿⡇⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⣸
⠀⠀⢺⣇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣿
⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠸⣿⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁
⠀⠀⠀⣿⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋
⠀⠀⠀⢻⡇⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠟⠋⠁
⠀⠀⠀⢸⣧⣠⣎⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣶⠾⠟⠋
⣤⣤⣤⣤⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡛⠉⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣩⣼⣿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⢿⣆⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢡⣾⠟⠉⠀⠀⠻⣜⢧⠀⠀⢀⣤⠄⠀⠀⢀⣴⡿⠋⠀⠀⢀⣴⡿⡟⠛⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣰⠟⠁⠀⠀⠀⠀⠀⠹⡌⣆⠀⠘⠿⠃⠀⣠⡾⠋⠀⢀⣠⡶⠟⠁⠀⠉⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⠏⣀⣠⣤⣀⡀⠀⠀⠀⢻⡜⡄⠀⠀⣀⣼⣯⣄⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣴⡿⠟⠛⠛⠛⠿⣷⣄⠀⠀⠹⣿⣴⠿⢛⣛⣩⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠸⡿
⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⡶⢷⠘⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⡼⠱⣿⠿⠿⢿⡏⠀⠀⢠⣤⣤⣄⣀⣠⣤⣤⣤⣤⣴⣿⣤⣀
⠀⠀⠀⢸⠿⢿⣿⣿⣯⣤⣤⣬⣿⣶⣤⣤⣄⣀⣀⣀⣀⣀⣤⣿⣧⣷⣶⣶⢶⣾⠟⠃⢰⣶⣿⣿⠿⢿⣿⣿⡟⢛⣛⣛⣋⣁⣬⣿⣿⣷⣶⣶⡄
⠀⠀⠀⣸⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⢛⣿⡿⠛⣫⡿⢻⡿⠟⠉⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠛⢻⠁
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⢀⣼⠏⢠⡟⠁⠀⠀⠀⠀⣌⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⢀⡾⠁⢠⡟⠀⠀⠀⠀⠀⠀⣿⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠸⣿⣿⣶⣶⣶⣦⣤⣤⣤⣄⣰⠟⠀⠀⠀⡼⠁⠀⡾⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢷⣠⣤⣤⣤⣶⣶⣿
⠀⠀⠀⣤⠀⠀⣿⠉⠉⠙⠛⠛⠛⣿⠋⠀⢀⠀⠀⠁⠀⣼⣥⣀⣀⣀⠀⠀⠀⠀⢹⠀⠀⠀⢀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⢻⠋⠉
⠀⠀⠀⠿⠀⠀⡏⠀⠀⠀⠀⠀⣼⢁⣠⣾⠿⠀⠀⠀⢰⠏⠙⠛⠿⠿⣿⣿⣶⣦⣼⣤⣶⣿⣿⠿⢧⠀⠀⠀⣤⡀⠀⠀⢠⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣷⡾⠋⠀⠀⡄⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠋⠉⠁⠀⠀⠸⡀⠀⣼⠋⠻⡄⠀⡾⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢳⡀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠇⢰⠇⠀⠀⢻⣾⠃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠻⠿⢿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣶⣶⣤⣤⣀⣀⠀⣿⠀⠀⣀⣠⣤⣶⣾⣿⣿⠿⠿⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⣿⣿⡿⠿⠟⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠶⡖⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠒⠋⠉⠀⠀⠀⠀⡇⠀⠀⠀⠉⠑⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⣠⠔⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢤⣀
⠀⠀⠀⠀⠀⣸⠁⠁⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠙⡆
⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠈⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⢹
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠤⠚⠓⠤⣀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉
⠀⠀⠀⠀⠀⠈⠱⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⣤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣹
⠀⠀⠀⠀⠀⠀⠀⡇⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣶⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢹⠈⢧⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⢀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⡸⠀⠀⢸⠀⠈⢆⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⡴⠃⠀⠀⢸⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁
⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⠖⠉
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⢸⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠞⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠉⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⠀⠙⣻⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠙⣻⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡋⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣫⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣁⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⠾⠛⠛⣻⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠻⠶⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠁⢀⣀⣠⣤⣼⣿⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣦⣤⣤⣄⣀⡀⠀⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣟⣉⡉⠉⠛⠁⠰⣦⣤⠀⢛⡁⠀⡶⠀⠘⠛⠻⡆⠀⠉⣉⣙⣿⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⡀⠈⠉⠛⠛⠛⢳⠶⠶⣶⠶⢾⣷⠶⠶⠶⠶⠶⠶⠞⠛⠛⠋⠉⠀⣀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⣤⣤⣙⣃⣀⣛⣻⣈⣉⣀⣀⣻⣀⣀⣀⣠⣤⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠋⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⠿⠿⠟⠛⠛⠛⠛⠻⠿⠿⢶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠘⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿⠃
⠀⠀⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇
⠀⣴⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⡛⠛⠛⠛⠛⠛⢛⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⢿⣦
⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠙⠿⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠿⠋
⠀⠀⠀⣸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇
⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠙⢿⣿⡉⠉⠉⠉⠉⠉⣹⣿⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡆
⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠙⠻⢷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡾⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⢿⠉⠀⣻⠏⠛⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣣⣠⣇⣤⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣢⠔⢊⣩⠟⡇⢸⠙⢦⡉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣅⣠⡎⠀⠀⡇⢸⠀⠀⠳⣄⡽⠆
⠀⠀⠀⠀⡰⠶⢍⡔⠛⠛⠋⣷⢺⠛⢿⣇⣀⣀⡇⢸⣀⣀⣀⣹⠁
⠀⠀⠀⡞⠁⠘⣤⣇⠀⠀⠀⣿⡞⠀⢀⣿⠁⠈⡇⢸⠈⠉⢹⡇⠀⣀⣤⣤⠴⢦⡀
⠀⠀⠀⠘⢦⡠⠮⠿⢄⣤⠼⠟⢦⣢⣞⣿⠐⠀⡇⢸⠀⠀⢸⣧⣼⠃⠀⠀⠀⠀⣧⠴⠲⢦⣀
⠀⢠⠴⠖⡾⠁⠀⠀⡼⠳⡄⠀⠈⢯⠉⠉⢻⠂⡇⢸⣤⠞⠋⠰⡂⡆⠀⠀⠉⠀⡿⢠⠃⠀⠉⢷
⠀⢸⡀⢰⡷⠺⡆⣼⠁⠀⢷⠀⠀⠘⣆⡀⣼⡉⡇⢸⠾⡄⠀⠀⠱⣽⠀⠀⠀⠀⣿⠃⠀⠀⢀⡟⠜
⠀⢆⢻⠛⠛⠛⠛⣿⠀⠀⠸⡇⢠⣄⣿⢹⡇⠈⡇⢸⠀⢹⣄⣠⠤⠼⢧⣀⡤⠼⠓⢦⣀⣴⣏⣀⣀⣀⡀
⠀⠀⢸⡆⠀⠀⠀⣿⠀⠀⠀⣷⡏⠈⠛⢸⡉⠀⣧⡟⠉⠉⡽⠁⠀⢠⠞⠁⠑⣄⠀⠀⠹⣆⣀⣀⣀⣀⡇
⠀⠀⠸⡇⠀⡀⠀⣿⠀⠀⠀⡏⠀⠀⠀⢸⠀⠀⡏⢳⡶⢶⡷⠲⣄⡞⠛⠛⠛⠛⣆⢠⢤⣸⡏⠉⢹⠋
⠀⠀⠀⣇⠀⠀⠀⢻⠀⠀⠀⡇⡄⠀⠂⣸⠐⠀⡇⣸⠸⡄⠀⠀⠈⠁⠀⠁⠀⠀⠹⠋⢀⢈⣋⣀⡟
⠀⠀⠀⠹⠤⠤⠤⢿⣤⣤⣤⠷⠶⠶⠖⠛⠛⠛⠓⠛⠛⠛⠛⠛⠛⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⡿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣔⠒⠈⠉⠀⠀⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠢⢤⡒⠉⠉⠢⢄⡀⠀⠀⠀⠀⠈⠒⠤⣀
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠈⠓⠤⣀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠈⠑⠢⢄
⠀⠀⠀⢠⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢴⡊⠁⠉⠢⢄⡀⠀⠀⠀⠀⠉⠒⠤⡀
⠀⠀⠀⢸⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠈⠑⠢⣄
⠀⠀⠀⢸⠀⠀⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢖⡉⠀⠑⠢⢄⡀⠀⠀⠀⠀⣉⡶⡄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⡀⠀⠈⠒⣒⠭⠛⠁⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢜⡡⠔⠊⠁⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⣠⠾⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠘⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠉⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⢸⠀⠀⠀⠀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣸⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠉⠉⡦⡀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠃⠘⣆⠀⢱⡤⠤⠔⠒⠒⠀⢄⡔⠁⠀⣀⣠⡄⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⢆⠘⡏⠉⢣⡀⢃⠀⠀⠀⠀⢠⠊⢀⡴⢏⠁⠀⠸⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠉⠀⠀⠈⠳⢌⡢⡀⢱⠘⣄⠀⠀⡰⢃⡴⣋⠴⠚⠛⢦⡀⢧⠀⢰
⠀⠀⠀⠀⠐⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣦⣧⠟⠓⣾⠶⠛⠉⣀⡤⠴⠒⠋⣙⡾⢀⡜
⠀⠀⠀⠀⠀⠘⡀⠉⠢⣄⠀⠀⠀⠀⠀⢀⣀⡤⠞⣏⡀⢸⡓⠒⠚⠛⠓⣚⣋⣉⠭⠭⠒⠙⢦
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⢤⡤⠒⠊⠉⠀⢀⣠⠴⠛⢫⡀⠀⠈⠙⢭⡁⠀⠀⠀⠀⠀⣀⡠⢵
⠀⠀⠀⠀⠀⠀⠉⡆⢀⠀⠀⢸⠀⠀⢠⠖⠚⠉⠀⠀⠀⠀⠙⢦⡀⠀⠀⣉⣷⣤⠔⠒⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠢⢼⡀⠀⣼⠑⢦⡀⠀⠀⠀⠀⠀⡀⠈⢷⠋⠁⠀⡇⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠟⢦⡿⠀⠀⠈⠂⡀⠄⠂⠁⠀⠀⢸⡄⢀⣠⡧⠤⠒⠊⠉⡏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⢀⡏⠠⢀⠀⠀⡇⠀⠀⠀⣀⠤⢾⠉⠉⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⡾⠀⣸⠁⠀⠀⠉⠢⡧⠔⠒⠉⠀⠀⢸⡄⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⡇⢠⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠸⡇⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣸⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣧⢀⣀⡤⠤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣹⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢸⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠸⠀⡠⠖⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣽⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠊⠀⠁⡀⠀⠀⢠⠀⠀⠀⠀⢀⣠⣤⣤⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠁⠀⠀⠀⠈⡀⠀⠈⢆⠀⠠⡄⠘⠟⠀⢠⠜⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⢠⠀⠠⠄⠀⠀⠀⠀⠀⢀
⠀⠀⠁⠀⠀⡀⡄⠀⠐⠀⠀⠈⠣⡀⠑⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠄⠊⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀
⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢴⡀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠔⢚⣒⣒⠉
⠀⡄⠀⡈⠈⠀⠀⠌⠂⠀⠀⠀⠀⠀⠀⠀⠙⠳⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠓
⠀⠇⠈⠀⠀⠀⠐⠢⡀⡀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠈⠀⢀⡤⣀⠀⠀⠀⠔⢰⣀⠆⠀⠠⠆⣦⠠⠀⠀⢴⣤⠄
⠀⠀⢠⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⡃⠀⠈⡇⠀⠀⠘⢿⣄⠀⠀⠀⠓⡏⣈⠀⠀⢿⣯⡃
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⠒⠊⠁⠀⠀⠐⠈⠘⠁⠀⠀⠓⠟⠚⠀⠀⠲⠷⠃
⠀⠀⡀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠶⢶⣤⣤⡴⠶⠦⠄
⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣿⠀⣷⠀⠀⠀⢀⣼⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠁
⠀⠀⠀⠆⡀⠂⠀⠄⠀⠀⠀⠀⠀⠛⠀⠁⢀⡀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠀⣤⠠⠶⠈⠀⠀⠀⠀⠀⠀⣠⠴⣶⣀⢀⠀⣤⡄⡼⣵⢣⢶⡞⡜⣹⠋⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⢀⠀⠑⠄⠀⠀⠀⠀⠈⠀⠀⠀⢀⢠⣄⠀⠀⠀⠀⠾⠥⣍⢰⢣⡏⣾⠛⣿⠓⠇⠛⢘⣭⠿⠓⠂⠀⠀⠰⠆⠀⠈⠻⡣⠉
⠀⠀⠀⠘⠀⠀⠸⠀⠀⠀⠀⣠⠐⣾⠈⠟⠀⠁⠀⠀⠀⠀⣼⡴⠋⠈⠀⠀⠀⠀⠓⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⣀⢠⣄⠀⠀⠀⠀⠁⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⣾⠀⠟⠈⠁⠀⠀⠀⠀⠀⠸⣽⡽⠀⠀⠀⠀⠀⢀⠀⠸⠅⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣤⠠⣤⠐⠀⠀⠀⠀⠁⠀⢀⠤⠀⠀⠀⠀⠀⢀⡤⠻⢾⣟⡆⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠋
⠀⠀⠀⢠⠀⠀⢠⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠐⢀⠀⠀⠠⣿⡷⣾⡧⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠂⠁⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣰⣾⣿⡿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤
⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣾⣿⡿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⡿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⣿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⣶⣿⣿⠿⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣦⣤⣠⣤⡶⠚⠁⠀⠀⠀⠀⢹⣷⡶⣠⣴⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣯⠙⠿⣿⣀⠀⣲⣥⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⣀⡤⠤⠒⠚⠙⣿⡏⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢟⡦⢤⣀⣀
⠀⠀⠈⠁⠠⠀⠀⠀⠀⠀⠘⢧⣀⣀⣤⣶⣿⣿⡿⠿⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠦⠀⢘⡟⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⢿⣿⣿⣿⣿⠿⠟⠋⠁⠈⠙⠿⢛⡿⣿⣿⣿⣿⣿⣿⣿⣏⠀⡀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⣶⣿⣉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢹⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠈⠁⠐⡖⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⢀⠀⠀⣀⣴⡿⠃
⠀⠀⠀⠙⠳⠦⣤⣤⣠⣀⡀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣷⠄⠀⠀⠀⠀⠈⢸⣿⣿⣿⣷⣠⣴⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠹⠛⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⣀⡀⣿⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣶⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠮⠉⠉⠉⠙⠻⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠰⢪⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⠛⠋⣿⣿⣿⣿⣿⣿⡖⠼⡞⢻⡿⠿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠨⢿⠯⣿⣿⣿⣿⣷⢩⠗⠁⣠⣼⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡉⢰⣖⣢⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠘⠋⢹⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⣾⣿⣿⣿⠄⠰⠀⢹⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠛⠀⣿⣿⣿⣿⠀⠀⠂⠘⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢘⠀⠀⣿⣿⣿⣿⣃⣠⡥⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣰⣸⠠⣀⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣿⣷⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⢀⣀⣤⡴⠶⠞⣛⣛⣩⣭⣭⠭⢽⣛⠲⠦⣄
⠶⠟⢋⣩⣤⠶⠞⣛⣩⣥⠶⠖⣚⣫⡭⠽⢗⣚⣨⡽⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⢀⣀⣀⣤
⠶⠟⢋⣡⡴⠶⠛⣉⣥⡴⠞⢋⣩⡤⠶⢛⣉⣥⠶⢚⣋⣷⡘⢦⡙⢦⡰⣄⠀⠀⣀⣠⠴⠖⣛⣩⣭⣤⣤⣶⣶⣦⣤⣤⣤⣄⣉⡉⠉⠛⠛⠛⠛⠋⣉⣁⣤
⠶⠛⣉⣥⡴⠞⢛⣩⡤⠶⢛⣉⣥⠶⢚⣋⣥⠶⢚⣫⡥⢖⣳⣄⣁⡬⠵⠖⣚⣫⣭⠶⠚⣋⣩⣥⣤⣤⣤⣤⣤⣤⣄⣀⡉⠉⠛⠻⠿⠿⢿⠿⠿⠿⠟⠛⠋
⣚⣫⡭⠴⣒⣫⠭⠴⢖⣛⣭⠥⠶⢛⣫⡥⠶⣚⡭⠶⣚⣩⣥⣶⡖⣒⣛⣋⣩⡥⠶⠚⣋⣉⣥⣤⣤⣤⣤⣤⣄⣉⠉⠛⠻⢿⣶⣦⣤⣄⣀⣠⣤⣤⣤⣴⣶
⣤⣐⣚⣓⣒⣚⣋⣩⣭⡥⠶⠚⣋⣩⠴⢖⣫⠵⢒⣋⣩⣤⣀⠈⠙⢯⣭⠥⠤⠶⠞⢛⣉⣭⣤⡤⢤⣤⣤⣌⣉⠛⠻⢷⣦⣄⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉
⣀⣉⣉⣉⣉⣉⣩⣤⣴⠶⠞⣋⣩⠴⣚⡭⠖⣚⣉⣉⠉⠙⠻⣿⡄⢸⡟⢸⢛⣛⣛⣉⣥⠴⠶⠶⠶⠶⣤⣍⡙⠻⣶⣄⠉⠻⢿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤
⠛⠛⠛⠛⠛⢉⣉⣤⡴⠖⣛⡭⢖⣫⠵⠚⡛⠉⠛⠻⣿⣆⠀⣿⠃⣼⠃⡟⢼⡲⠬⠥⠶⣚⣛⣛⣛⠳⠦⣌⡙⢷⣄⠙⢿⣦⣀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿
⣶⣶⡶⠿⠟⢛⣉⡥⠖⣋⠵⣺⠽⢒⣛⠛⠛⢿⣷⠀⢸⡏⢰⡟⢠⣿⠀⣷⣌⣙⣓⣛⣭⣭⣤⣬⣍⡙⠳⣮⡙⢦⡌⢳⣄⠙⠻⣷⣶⣤⣄⣀⣀⣀
⣀⣤⣤⡶⠞⣋⡥⢖⡯⣶⢽⣒⣋⣉⡙⢻⣦⠀⣿⠀⣿⠁⢸⣇⠈⢿⣦⣤⣭⡭⠵⠶⠶⠶⢶⣤⣉⠛⢷⣄⠙⢦⡙⣦⠙⢷⣄⡈⠙⠛⠿⢿⣿⣿⣿⣿⣿
⢋⣉⣤⠖⣫⢵⣪⣷⡜⠮⠙⠒⠒⠌⢻⢀⡏⢸⡇⠀⣿⡄⠘⢿⣶⣤⡤⠴⠖⣚⣛⣛⣛⠳⠶⣤⣍⠻⣦⡈⢷⣌⢳⣌⢷⣄⠻⣿⣶⣤⣀⣀⠀⠀⠉⠉⠉
⣋⡥⣖⢭⣲⡭⠛⠉⠀⠀⠀⠀⠀⠀⣾⢸⡇⢸⣷⡀⠙⢿⣶⣤⠴⢖⣚⣫⠭⠭⠭⠭⠭⣍⣛⢦⣌⠠⣬⠡⣤⠻⣦⢻⣎⠻⣷⣄⠙⠻⢿⣿⣿⣷⣶⣦⣤
⢵⣾⡷⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣷⡀⠛⠿⠶⠶⠶⣒⡫⠽⣒⣺⠭⠭⠭⠭⢭⣒⡮⢷⡦⢴⢦⡳⣌⠷⡜⢷⡙⢷⡌⠻⣿⣦⣄⠀⠉⠛⠻⠿⢿
⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣈⠛⠷⠶⢒⣚⡭⠕⣚⣭⠵⠖⠛⠋⠉⠉⠛⠒⠮⠭⣝⣓⣛⣚⣚⣓⣩⡢⣙⢦⡙⢶⣄⠙⠻⢿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠭⣙⣛⣭⠭⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠁⠙⠲⢍⡛⢶⣤⣈⠙⠛⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⠙⡻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠒⠒⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⠉⠙⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣬⣷⡀
⠀⠀⢠⠟⠋⠉⠉⠛⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢋⣩⠤⠶⢦⡈⢳⡀
⠀⠀⡟⠀⢰⡏⠉⠉⠛⠲⠦⢤⣍⡓⠦⣄⡀⠀⠀⠀⠀⣀⡤⠶⠿⠷⠶⠦⣄⠀⠀⠀⢀⣠⠴⠚⣉⣤⠴⠚⠉⠀⠀⠀⣠⠇⠀⡇
⠀⠀⢳⣄⠀⠙⠲⠤⣄⣀⣀⣀⣀⣉⣙⣛⡻⣶⣤⣀⢰⡏⠀⠀⠀⠀⠀⠀⢸⣇⣠⣶⣿⢗⡚⣉⣁⣀⣀⣀⣀⣤⠴⠚⣁⣠⣞⣁⣀⣀⣀
⡟⠛⠛⠉⠛⠲⠦⠤⢤⣤⣭⣭⠭⠭⢭⡿⠛⠛⠋⠉⢉⣻⣶⠦⠤⠤⠶⠖⠛⢿⣉⠛⠛⠛⠛⠛⠛⠿⠿⠟⠗⣶⠛⠋⠉⣻⠉⢻⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⠖⠋⠀⢸⡄⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡴⠋⠁⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣿⠀⠀⢀⣿⡀⣸⣀⣀⣀
⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡉⠉⣿⠉⠉⠉⣿⠉⢻⠉⠁
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⣿⠀⠀⠀⣿⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⣿⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣿⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠁⠀⠀⣿⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠀⣿⠀⠀⠀⣿⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠦⣄⠀⠀⢰⢿⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠓⢤⠏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⣸⣀⣠⠤
⢸⡇⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⣇⣀⢀⣀⣀⡀⣸⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⣀⣿⣀⣤⠴⠟⠛⠉⠁

⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⣠⣴⣿⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣴⣶⣤⣤⣤⣤⣤⣀⣀⡀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⠿⢷⣶⣶⣾⣿⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢺⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠉⠉⠹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⡟⠙⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠶⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡏⠈⠁⠉⠉⠉⠉⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠗⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢾⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⣿⣇⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣽⣿⣿⣧⣿⡇⠀⠀⠀⠀⠀⠀⠻⢿⣿⠿⠿⠷⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⣿⣿⣫⣿⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⡇⣿
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣶⣼⣿⣿⣧⣿⣄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⠿⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠿⡟⠁
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣿⠀⠉⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠳⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠈⠉⠉⠍⠉⠉⠉⠉⠉⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠙⠒⠶⠶⠖⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠋⠙⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⢀⣤⣤⣼⡇⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠙⢦⡺⠧⣄⣀⢀⡇⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⢠⡾⣭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⡉⠙⠳⠦⣄⣀⠀⢠⡇⠀⠀⠀⠀⡾⠉⠛⠲⠦⣤⣀⡀
⠀⠀⠀⠘⡇⠀⠈⠙⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣀⠉⠙⠛⠧⣤⣀⠀⢸⣇⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⢤⣄⣀⡀
⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⣤⣉⣙⠛⠿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣧
⠀⠀⠀⠀⣿⠈⠉⠒⠤⣀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⣿
⠀⠀⠀⠀⠉⠙⠲⢤⣄⡀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⣠⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣄⡀⠉⠒⠠⢄⡀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⢀⡠⠊⢁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⠀⠀⠀⢀⡤⠞⠁⠀⠀⢀⠴⠋⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠈⠙⢲⡶⠋⠀⠀⠀⡠⠞⠁⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣀⠈⠉⠒⠤⣀⠀⠀⠀⠀⢸⡇⠀⢀⡤⠊⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠉⠒⠦⢄⣸⣧⠖⠁⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠈⡇⢀⡴⠋
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠷⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⡀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⡠⢛⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⡒⡛⠛⡉⠉⠋⠼⠛⠯⠩⠭⠍⠉⠉⠭⠭⠭⠭⠭⠭⠭⠭⠭⠬⠉⠉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡠⢊⡴⢋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣯⣴⣩⡴⣡⡤⣤⠮⢥⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠦⠾
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢃⡴⢋⠴⢃⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡖⣩⠖⢁⠐⢁⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢩⠛⣩⠟⡹⠛⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡡⢚⡥⠊⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡴⢤⡤⢮⣤⠮⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠠⠤⠶⠖⠂⠺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠠⠂⡠⠊⡀⠀⠀⠀⣀⠤⠐⠂⡐⢒⠁⠀⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣋⠤⢋⡤⠊⡀⠀⠔⢛⠈⠣⢄⣀⠠⠬⠄⢓⡂⠰⠡⢙⡆⠀⠀⠀⠀⠐⠂⡇⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠴⢋⡠⠊⣀⡤⠲⣤⠰⠎⡥⠀⠀⠀⢀⡠⠀⣟⣂⡼⠣⢤⡀⠀⠀⠀⠀⡇⣠⠾⢁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠴⠋⠤⢬⠄⢀⣀⠤⠋⠀⠀⠀⠀⠠⠊⠀⠀⠈⠉⠲⢄⡀⢨⠳⠦⡀⢀⢟⠁⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⠄⢀⠐⠓⡘⠉⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⢄⡴⠁⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⣄⣠⣤⣥⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡤⠀⠀⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠈⡠⠎⡠⠂⠀⠀⢀⢀⣀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡄⢂⣤⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠊⡠⠊⡠⠲⢺⡭⡴⢦⡴⢠⣤⣤⠄⣤⠀⠀⠤⠤⠴⠎⠤⠴⠉⠤⠄⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⠟⣻⠟⣓⠾⣯⣎⣴⢃⡰⣫⠖⣠⠞⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠘⢁⠜⢁⠄⣻⠜⢉⡽⠋⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⠔⢁⠔⢁⡴⢻⡤⠋⣠⠎⢁⠀⠀⠀⠈⠀⠀⠁⠀⠐⠀⠀⠀⠈⠀⠀⡾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠧⠴⠏⠴⠾⣧⠜⢁⡔⢉⡔⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠘⠃⠀⢣⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠉⡰⠋⣠⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠞⢁⡔⠁⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡴⠋⣠⠞⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡴⠁⡴⠋⡀⠀⠀⠀⠀⠀⡠⠚⠃⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠾⠦⠤⠤⠤⠠⡞⠀⠈⠓⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠲⢄⠀⠸⡄⠀⠀⠀⠀⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠛⠀⠘⠆⠀⠹⢦⣀⣂⣀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠀⠀⢀⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠥⣀⢀⣀⡠⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠾⠛⠋⠉⠁⣿⡇⠉⠉⠛⠻⠶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⣷⡀
⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠉⠛⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠋⠁⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣄⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣤⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⣿⡇⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠈⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣿⡟⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⢻⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣿⡇⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠛⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣿⡇⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠈⠙⠻⢦⣄⡀⠀⠀⢀⡿⠁⠀⠀⣿⡇⠀⠀⠹⣆⠀⠀⠀⣀⣤⠾⠛⠉⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣾⠃⠀⠀⠀⣿⡇⠀⠀⠀⢻⣦⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⠀⠀⠀⣿⡇⠀⠀⢀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣿⣧⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡒⠒⠋⠉⠓⢦⣀⣠⣤⣀⣀⠀⠀⢀⡴⠋⠉⠉⠙⠓⠒⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠉⠢⣄⠀⠀⠀⠈⠢⡀⠀⠉⠉⡳⠋⠀⠀⠀⠀⢀⡴⠋⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⢶⣶⠛⠙⠲⢄⣈⠑⠤⣀⠀⠀⠈⢦⣠⡜⠁⠀⠀⣀⡤⠖⣁⡠⠔⠊⢑⢢⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠛⠉⠁⠀⡰⠋⠉⠉⠙⠒⠦⣌⣉⠓⠺⠿⢶⣶⠖⠛⢲⣶⠶⠾⠗⠒⣉⡥⠴⠒⠋⠉⠁⠈⢻⠓⠲⠦⣤⣀⣀
⠀⠀⠀⠀⢰⠾⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢀⣀⣀⣀⣀⡀⣀⣭⣵⠶⢖⣻⠦⡄⠾⣛⠲⠶⣮⡭⠤⠤⢄⣀⣀⣀⠠⠴⠋⠀⠀⠀⠀⠀⢉⣉⠷⡆
⠀⠀⠀⠀⢹⠀⠀⠈⠙⠒⠦⢤⣀⡀⠀⣀⡤⠴⠚⣉⣡⡤⠶⠒⠉⠁⠖⠚⠉⠀⡴⠓⣄⠀⠉⠁⠀⠈⠉⠒⠦⢄⣉⠓⠲⢤⣀⠀⣀⡤⠴⠚⠉⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢙⡟⣳⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠙⠲⠤⣀⠀⠀⠀⠀⠀⠀⠉⠳⢴⠚⢻⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠑⣾⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠺⣄⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠱⣄⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⢀⣠⡟
⠀⠀⠀⠀⠀⠀⡟⠙⠲⢤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠈⠉⠓⢶⠖⠋⠉⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⢀⣎⣠⠴⠚⢻
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⣄⠀⠀⠀⢀⡜⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢱⡀⠀⠀⠀⠀⢀⡴⠳⢤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣸⡤⠞⢣⡀⣠⢾⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⣄⠀⠀⣠⠎⠀⠀⠀⡏⠉⠛⠲⢤⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣠⠴⠞⠋⢹⠀⠀⠀⠙⠁⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢣⡼⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠑⠲⠤⣀⣸⣇⣠⠴⠚⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠛⠦⢄⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣬⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣸⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣀⡀⠀⠀⢸⠀⠀⢀⣠⡴⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣼⡴⠖⠋⠁



⣀⣀⣀⢀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⢀⠕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠁⠢⣤⢄⡀⠀⠈⡄⣀⣸⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣘⣗⢌⣆⠀⡇⡴⡿⢿⣷⠖⠢⠌⠳⡄
⠀⠀⠀⠀⠀⠀⢀⢩⠐⠒⢻⣀⠀⠀⠀⣠⡿⢸⣿⣾⠿⢼⣾⣤⡶⠊⢹⠦⠤⠄⢨⡇
⡤⠤⠤⠤⠤⠤⠼⠶⠴⠶⠶⠿⠟⠲⠶⠿⠿⢷⠟⠷⠶⠾⠻⠛⠿⠲⡟⠿⠿⠿⠾⠤⠦⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⡇⠀⠀⠀⠀⠀⠀⢰⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⢸⠏⠉⠉⠉⠉⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣶⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⢠⣶⡄⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⠏⠙⣿⣄⣀⡀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠰⣶⣄⠘⡿⢃⣴⣶⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠙⢻⣆⢠⡿⠋⢙⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡶⠛⠛⠛⠒⣾⣿⠴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣤⣤⣭⣍⠁⠚⣋⡁
⠀⢸⣿⣿⣿⣿⣿⡟⠋⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣇⣀⣿⣀⣀⣀⣀⣀⣿⣿⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠿⠿⠿⠿⠿⠀⠸⠿⠿⠿⠇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠈⠀⠀⠀⠀⠀⠀⠘⢂⠀⠀⠀⠀⠀⠀⡠⠊⠀⠁⠒⠠⠤⣀⡀
⠀⠀⠀⠀⠀⢠⠂⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠗⢢⡄⠨⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠎
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠘⠐⠉⠠⡋⠉⠁⠒⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⡀⠄⠒⡎⡁⠀⠀⡀⠅⠀⠀⡰⡏⡂⠀⠀⠀⠀⠀⠀⠈⠐⠂⠤⣀⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠑⠦⣜⡁⠐⡐⠉⠀⠀⢂⠀⢄⢜⡇⠱⢄⠀⠀⠀⠀⠀⠀⠀⣈⠵⠒⠉⠢
⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠉⠓⠪⢤⣂⠀⠠⠂⠂⠨⡇⠄⠔⠀⠀⠀⡀⠄⠒⠉⠀⠀⠀⠀⠀⡕⢄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢥⣅⣐⣇⣪⠮⠚⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⢏⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡄
⠀⠀⠀⠀⠉⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠫⢸⠍⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢀⡀⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢄⡀⢀⡀⠀⢀⠄⡴⠋⠀⡪⠂⡆⠀⡹⡦⡀⠀⠀⠀⠀⠰⠨⢘⣠⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠑⢦⣌⣡⠞⠅⠀⠄⠨⠀⢏⢊⢈⢌⢝⢦⡀⢀⣠⠰⢾⠉⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠐⢐⠅⠣⠀⠀⠀⠑⠀⡁⠁⠀⡂⡡⠢⠛⡃⡡⢱⢁⡒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⣑⢅⢠⡘⢆⠀⠂⠐⠔⠐⠐⠔⠐⠁⠀⠀⢄⠠⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⢹⢄⠀⢄⢰⣂⠢⢂⠊⠌⢀⡂⠬⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣤⣐⡀⠥⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠠⠀⠄⡠⠀⠀⢀⠀⢀⠀⢀⠠⠀⠄⡀⠀⠠⠀⠄⡠⢀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠅⡀⠀⠀⠄⡨⠀⠁⢂⠅⠊⠄⡈⠄⡈⠄⠀⢀⠀⠀⠁⠈⢀⠁⠂⠔⠈⠐⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⠈⢛⠂⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠄⠀⠀⠀⠀⠂⠈⠀⠁⠀⠀⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠰⠂⠈⠀⢰⠖⠐⠀⠀⠰⠋⠁⠀⣀⡈⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢⠀⢀⠀⢈⠁⠀⠀⠀⠀⠀⠄⠰⠀⠁⠈⢀⠐⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠘⠀⠀⠀⠀⠀⠀⠈⢄⠀⠖⠀⠁⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠅⠘⡀⠀⠀⠀⠀⠀⠀⠠⠳⠶⠂⠁⠀⠀⠀⡠⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡈⠂⣄⣱⡄⠀⠀⠀⠀⡠⠁⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣂⠑⠲⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠄⠀⠋⣈⠀⠁⠈⠰⣤⠴⠊⠀⠀⠀⠀⠀⠀⢶⠂⠐⢄⠀⠀⢀⣈⠐⡤⠀⠐⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠙⠁⢨⠡⠄⠄⠰⠲⠀⠢⠂⡀⠁⠉⠀⠀⠀⢀⠀⠀⠀⠀⢠⢀⠁⠀⢢⠊⠈⠁⠀⠉⢁⠀⠂⠐⢂⣀
⠀⠀⠀⠀⠀⠰⠒⠀⡄⢙⠁⠀⠀⠀⠀⠰⠄⠁⢂⡐⠶⠀⠀⠀⠀⠸⠀⠠⠀⠀⠈⡀⠈⠁⠆⠀⠀⠀⠀⠀⠈⢠⡀⠲⡦⠁
⠀⠀⠀⠀⠀⠀⢦⠀⠠⢀⠀⠀⠀⠀⠀⠀⣐⠒⠀⠟⠀⠀⠐⠀⠠⠀⠀⠃⠀⠀⠀⠙⢀⡅⢰⠀⠀⠀⠀⠀⠀⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠰⠖⠈⣄⠀⠀⠀⠀⡀⠉⠉⠀⠀⠀⣀⠀⢧⡰⡄⠀⠀⠀⠀⠀⠀⠈⠁⠶⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠏⠢⣤⡤⠂⠀⠂⠰⠢⢉⡱⡉⢰⣭⢤⠙⣝⠒⡢⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠂⠠⢀⡉⠁⠔⢈⠳⡩⠦⢠⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⢀⡠⠤⡚⡖⠣⡄⣋⠃⠀⠀⠈⢀⢆⣋⢈⡏⠓⠀⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⡉⠀⠤⢘⣀⠵⠺⢀⡳⠁⠀⠀⠀⠀⠘⢥⠌⠒⠂⣋⡁⠄⠀⢨⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀⠓⠠⠄⢀⡀⢠⠇⠀⠀⠐⠀⢠⠀⢸⠂⢘⠁⡅⠀⠈⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠠⠤⣀⠀⠈⠀⠠⡆⠀⠐⠠⠄⠀⠀⢸⠀⢈⡀⠇⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠀⠉⠂⢤⡠⠤⠤⠐⠉⠈⠀⠀⠈⠁⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠄⠑⠄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⣠⡤⠤⠤⢤⣤⣤⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣰⢀⡒⣎⠜⣁⠦⣤
⠀⠀⠀⠀⠀⣿⡂⠀⠀⢸⣿⣇⣀⡀⠀⣿⠀⠀⠀⠀⠀⢠⡿⠿⠿⠚⣿⣶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⡿⠿⠿⢿⣿⡾⢷⣦⣌⣔⠁⡸
⠀⠀⠀⠀⠀⣿⡿⠿⠿⢿⣿⡿⠿⠛⠛⣿⡀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣿⣿⣀⣀⣀⣀⡶⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⢸⣿⡇⠀⠀⠉⢹⡇⣘⠋
⠀⠀⠀⠀⠠⣿⣀⣀⣀⣸⣿⣇⣀⣀⣀⣿⠂⠆⠀⠀⠀⢠⡿⠿⠿⠛⣿⣷⡿⠿⠿⠿⡇⠀⠀⠀⠀⠀⠐⣶⣿⠿⠿⠿⢿⡿⠛⠿⠿⢿⢿⡇⢉
⠀⠀⠀⠀⠈⠿⣿⣿⠿⣿⡏⢛⠛⠛⠛⠿⡡⢘⠂⠀⠀⠸⣇⣀⣀⣀⣿⣿⣀⣀⣀⣀⡿⠀⠀⠀⠀⠀⠐⣯⡵⠀⢀⡠⠸⡄⠀⠀⠀⠀⢠⠀⡶
⠀⠀⠀⠀⢠⣾⣿⣿⠿⠛⠀⠀⠀⠀⠠⠄⠳⡇⠀⠀⠀⢀⡿⠛⠛⠛⣿⣿⠿⠿⠿⠿⡇⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠘⠓⠀⠀⠀⠀⠀⣟⣰⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣿⣿⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⣿⣾⠟⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣿⣷⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢠⣾⠋⠁⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⢰⡟⠛⠋⠙⣿⣿⠛⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠤⠀⢀⣴⣿⣅⡀⣸⠏
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢒⡒⠛⠙⠀⠀⠀⠀⠀⠸⠧⠤⠤⠤⠿⠿⠤⠤⠤⠼⢇⣤⡴⠓⢄⠀⠀⠀⠁⠀⠀⢀⣼⣿⡟⠙⠻⣿⡏
⠀⠀⠀⠀⠀⣇⡀⠀⢀⡀⣀⣐⠤⢩⡿⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣿⠟⠁⣠⠼⠃⠀⠀⠢⠀⢴⣋⣾⡟⠀⣠⣰⠏⠘
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡶⣾⣿⠏⠙⢾⣻⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢤⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣿⡇⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⠞⠁

⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⡤⠤⠶⠶⠶⠖⠛⠛⠳⢦⣄⡀
⠶⠿⠿⢿⣭⣍⣉⣉⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠴⠶⠶⠶⠖⠛⢻⠿⣶⡶⢤⣤⣀⡀
⠀⠀⠀⠀⢀⣠⡽⠟⢿⣍⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⠙⢶⣄⠈⠙⠷⣄⡀
⠀⠀⢠⣶⠋⢡⢀⣯⡄⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⢦⣄⠈⠙⠷⣤⡀
⠀⠀⠀⠈⠳⣄⡈⠈⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡀⠀⠀⠀⠀⠙⢦⡀⠘⣡⡿⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⡤⠶⠾⢷⡶⢤⣤⣬⣽⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⣦⡀⠀⠀⠀⠀⣹⣶⠶⠶⠶⠖⠚⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⡆⡴⠂⢻⡄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡄⡏⠻⣦⡀⣠⠞⠋⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠞⠐⠁⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡁⠻⠀⠈⠛⠁⠀⠀⣿⠸⣇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⢤⡴⠶⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⢀⠀⣿⠀⠙⠓⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠰⡜⡆⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠖⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡰⢋⠄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡼⠇