Prokaryote Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⣅⠤⠠⠤⣀⠠⠀⠀⣉⣁⠀⠀⠀⠀⢀⢀⢀⣠⠀⠀⡀⢀⠒⡆⠀⠀⠐⠐⠴⠚⢲⠛⠃⡦⠤⠀⠀⠀⠦⠖⠐⠂⠀⠐⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠉⠁⣀⣀⣀⠈⠤⠤⢁⡀⠠⠴⠔⠲⠛⠀⠀⠀⠀⠀⠀⠈⠀⠀⠇⠁⢉⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠅⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠆⠀⠀⠀⠀⠈⠀⠀⠂⠀⡈⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣤⡶⠶⠾⠛⠛⠛⠻⣶⣄⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠃⠀⠠⠀⠈⠀⠀⠀⠰⠀⠰⠀⠀⢁⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠋⠁⠀⠀⢀⠤⣤⣄⠀⠀⠙⣷⣆
⠀⠀⠀⠀⠀⠀⠀⡀⡁⠀⠀⠀⠀⠀⠀⣅⡠⠆⠘⠀⠀⠀⠀⠀⢂⠀⠀⠠⠀⠀⠀⠀⠀⢀⣾⠏⠀⠰⡀⠀⠀⠀⠉⡂⠙⠗⠀⠀⠈⠻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⡙⡜⠱⠂⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠰⠆⠀⠈⡂⡐⠄⠀⡀⠀⠀⢁⣀⠀⠀⢹⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠒⠀⠐⠀⢃⣯⠁⠀⠈⡀⠀⠀⠂⠀⠀⠀⠀⠀⣻⢀⡥⣶⣆⡥⢙⡋⢂⡄⠀⠀⢠⡏⠀⠀⠀⠀⡿⣦⣀⠈⠁
⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⢀⠀⡈⠑⠀⡀⠈⣒⣬⣭⠗⠠⠀⠀⠁⠀⠠⠤⠀⠀⠀⠀⠀⣿⡄⠀⡀⢂⠂⠑⢀⠎⠲⠄⠀⣀⠀⠀⠀⠀⠀⠀⢌⡹⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⡰⠊⢀⠀⠀⣀⠱⡋⠿⣥⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡙⡀⠀⡂⠀⠄⢛⠨⠡⠔⠀⠀⠲⠀⠀⠀⠀⣼⢹⡗⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠜⢦⠀⠠⠀⠀⢠⠚⠁⠀⢀⡀⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⢦⡙⠃⠃⠎⠀⠀⠀⢀⠀⠀⠤⠀⠀⠀⠙⠋⠐⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠰⠋⢲⡀⠀⠐⢀⡄⢀⠐⠲⣤⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡟⠦⢤⣄⣃⠀⠀⣠⠇⠐⠀⠀⠂⠀⠙⣄⡴⣿⠃
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠃⠀⠀⠈⠙⠣⠔⠓⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠙⠶⠀⢼⣍⣁⣹⡀⢉⡉⢉⢈⣉⠭⠕⠛⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠁⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣇⠀⢨⠀⠈⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠁⠀⠀⠀⠀⠣⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠊⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⠀⠑⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠠⠀⠀⠀⢀

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠢⡄⠀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡤⠒⠒⢤⡈⠢⣀⠠⠚⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⠀⣠⠊⡠⠊⠀⠀⠀⠀⠈⠒⠤⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠢⡀⠀⠀⠀⢀⢨⠀⠀⠀⡠⠔⠒⢉⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠠⠐⢄⠀⢀⠀⢱⢰⣀⣤⣤⡇⣮⡀⡰⠋⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠆⠀⠀⠠⢀⢣⣤⠔⠺⣼⠁⠀⠀⠙⠯⠙⢃⡀⠼⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⠀⠀⢈⠮⣒⢤⡶⠛⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣴⠐⠢⠤⠌⢩⡁⠐⢦⠀⠀⠀⠀⠀⠀⠀⠔⢒⣒⡲
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⣤⢆⣡⠞⠋⢤⠅⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⠳⡀⠱⡀⠀⠀⠀⠀⡜⢠⠋
⠀⠀⠀⠀⠀⠀⢣⡄⡀⠠⢀⡼⠘⢅⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⡖⣴⠁⠄⠀⠀⠀⠀⠀⠀⠘⢦⡑⢄⠀⢀⡜⢠⠃
⠀⠀⠀⠀⠀⠀⠀⡨⡎⢶⠋⠀⠀⠉⢀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢨⣒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠭⣁⡠⠊
⠀⠀⠀⠀⠀⢀⠄⣰⠛⠢⠟⠀⠀⠀⠂⠄⡐⠒⠂⠀⠀⠀⠀⠀⢀⣄⠀⣠⠞⡀⠀⠀⠇⡀
⠀⠈⠅⠁⠀⣄⣠⠁⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣝⠣⠄⠀⠀⠀⠀⢰
⠀⠑⠀⠀⠘⠲⡖⠒⠁⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⣏⢲⠋⠡⠈⠉⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠨⠰⠋⡇⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⢄⣀⡴⠛⠁⢆⠇
⠶⠦⠀⠀⠀⠲⣙⠟⣹⣀⣤⣄⡀⣀⣶⢲⡤⠞⡘⠅⠂⠀⠀⠈⠪⠦⡀
⠀⠀⠀⠀⠀⠀⢉⠎⠈⡉⢹⢸⠉⠉⢡⢸⠂⠀⠈⠀⠐⢦⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⠀⠀⠀⠀⠑⠄⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠒⠂⠀⠂⠒⠀⠂⠒⠂⠒⠂⠀⠒⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠉⠀⠀⠩⠄⠀⠥⠉⠥⠉⠀⠬⠈⠡⠤⠭⠁⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⡀⢤⠀⠀⠀⠠⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠀⠘⠔⢂⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉⠁⠈⠀⠨⠵⠌⠠⠄⠩⠤⠍⠠⠬⠄⠡⠈⠭⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣀⡄⠧⠤⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⡄⢀⠀⠀⣀⣀⣀⡀⠀⠀⡀⣀⡠⠀⢀⡀⢀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠖⡀⠸⢤⠀⠐⠌⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠒⠒⠀⠂⠐⠒⠀⠒⠒⠂⠒⠐⠂
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢰⠁⡄⠀⠁⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⢀⡀⠀⣀⢀⣀⠀⢀⠀⠀⣀⣀⣀⡀⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠚⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠂⡐⠲⠶⠶⢄⠐⠄⠤⠁⠀⠠⠄⠀⠠⠴⠤⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⡔⢇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠈⠀⡈⠀⠁⠉⠁⠈⠀⠉⠀⠉⠀⠁⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠎⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠈⠥⠁⠌⠡⠄⠩⠠⠉⠉⠉⠈⠁⠀⠀⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⡄⢄⠡⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⣤⣄⣀⣄⡀⠠⠤⠀⠠⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠁⠐⠚⠀⡄⠠⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠂⠀⢐⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠔⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠩⠍⠉⢡⠀⠨⠍⢭⠡⠄⠄
⠀⠀⠀⠀⠀⠠⠤⠲⠖⠀⠓⠀⠀⠐⣛⠂⡀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⣀⣀⠂⢀⡀⢂⣀⡒⢀⣀⢀
⠀⠀⠀⠀⠀⣘⡂⣒⣀⡀⢁⠀⡀⠀⢩⣉⡉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⠤⠴⠠⠄⢠⠤⠰⠠⠀⠆⠠⠄⠀⠢⠂⠠⠤⠐⠠⠄⠤



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠐⡀⢣⣀⣇⣠⣠⣃⣔⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢂⢰⠀⡄⢢⣈⣆⣣⣸⣤⠷⠾⠶⠛⠛⢛⡋⣭⠉⠀⠀⠉⠙⢾⡔⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣆⣰⣀⣱⣬⡦⠾⠾⠛⠛⠋⠉⡉⢁⡀⡐⠂⡄⠀⠀⠲⠀⠠⠄⠀⠀⠀⢸⠃⠀⢻⡶⠶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡈⣢⠞⡋⠉⠉⠶⠀⠀⠤⠭⣶⠤⣀⡀⡁⠀⢀⠀⠐⣀⠈⠀⠰⠀⣐⠂⠀⠀⠤⠀⠐⠂⢸⠯⠁⠀⠉⢿⡄
⠀⠀⠀⠀⠀⠀⠐⠢⣼⠃⣀⢙⡀⠀⠀⠀⠀⠈⠒⣄⠙⠉⡑⢨⠀⠨⠀⠀⠀⠀⠀⠀⠀⠁⠴⠀⠠⠄⠀⠩⣢⡿⠕⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⣒⣿⠀⠉⠨⠄⠀⢀⠀⠀⠲⡔⠻⠞⠁⢡⠎⠀⠄⣀⢡⠃⠀⠀⠀⠁⠈⣁⣈⣡⣤⣴⠾⡛⠌⠁⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠠⠔⢻⣆⢞⢡⠀⠓⣈⠁⠀⠀⠄⠀⠈⠁⠀⢀⣉⣀⣤⣤⠤⡶⡖⠞⢻⠉⡏⠹⠈⠀⢃⣁⣤⣤⣶⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠐⢁⠜⡷⣤⣤⣤⣬⣤⡬⣴⢶⠖⡞⢟⠛⡏⠋⠈⠆⠘⠀⠁⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠎⠘⠘⠀⠃⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠲⣄⡀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣦⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣛⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡸⠃⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠃⣀⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠿⡋⠀⠈⠁⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠾⠿⠁⠀⠈⠀⢠⡀⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠧⠀⠀⣀⠀⢀⣶⠀⠹⣿⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⣠⡾⠛⠻⢿⣯⠀⣴⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢾⡏⠀⠀⣠⣾⣿⣧⣬⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠃⢸⡇⠀⠰⣿⣟⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣸⡇⠀⢀⣾⣙⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠀⣾⣏⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠓⠲⠛⠿⠿⠿⣿⣿⣀⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣤⣀⣴⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢰⣿⡿⠗⠀⢠⡾⠉⠀⠈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⢸⡇⢠⣶⠄⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠈⠛⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⢀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣷⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠏⠀⠀⠰⠂⠀⠀⠁⠀⠰⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣩⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⡀⠀⢀⡄⠀⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⠀⠋⠁⠀⠈⠁⢀⣾⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠃⠀⠀⠀⢀⣴⣶⡞⢿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣥⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡁⠸⠿⠀⠀⣿⠃⠈⠀⠀⢹⣿⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠉⢱⣦⠀⢶⣶⣄⠀⢾⡇⢠⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠃⢀⠁⠀⠀⠀⠙⣦⣄⣶⡿⠻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⣀⣾⣶⡀⠙⢋⣠⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠒⠀⠸⢿⣿⣿⣷⣶⠟⢻⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⠀⠀⠀⠈⠉⣻⣿⣤⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣶⠄⠻⠛⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣦⣽⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡶⠀⢠⣿⡿⠉⠁⢈⣹⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣀⠴⣶⡟⠁⢰⣿⣏⠀⠀⠀⢿⡏⢹⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣼⣿⣦⠟⠁⠀⠈⣿⣿⠀⠀⠀⢀⣴⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠻⣿⣦⣤⣤⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠆⠀⢀⡀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠉⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠋⠀⠀⠀⣈⡁⠀⠀⠀⠉⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠠⣶⡆⠀⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠰⠛⠃⡀⠀⠠⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⢀⡀⠀⠀⡇⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠙⠃⢀⡄⠀⣴⡿⠃
⢀⣾⣿⠇⠀⠀⣼⠛⠀⠀⠀⠀⠀⠀⢀⡄⠀⠚⢠⣀⠀⠀⠀⠀⠿⠆⠀⠻⡿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣤⣾⡟⠀⠉
⠿⠿⠃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡠⠋⠀⣀⣀⠀⠹⡇⢀⣄⠀⠀⠀⣴⣶⠄⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏
⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠻⣿⠆⠀⢠⣾⠛⢁⣀⣴⣿⣷⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷
⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣸⣿⠀⠻⠿⠁⣸⣿⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡅
⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠈⢀⣄⠀⠀⠀⢀⣴⣿⡟⠐⠒⢶⣾⡿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁
⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣶⣿⣟⠛⣷⣤⠄⢈⣿⣷⣼⣿⣿⣿
⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠦⠀⠀⠉⠀⠀⠙⠉⠰⣿⣧⠀⠘⣿⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⢸⣿⣤⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣈⣁⣠⠟⣻⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⢻⣤⠀⠀⢠⠄⠀⠀⠀⠠⠀⠈⠉⢻⣿⣶⣿⣿⣿⡿⠿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠻⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠉⣿⣷⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠘⢻⣷⣤⣄⠉⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣈⡉⠰⣾⣏⠙⠛⣾⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⢀⣤⡼⠛⠃⠀⢿⣏⣰⡶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⠀⣴⣶⡄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣦⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠏⠀⠈⠙⢿⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢾⣿⠆⠈⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣄⠀⠀⣤⣤⠀⠀⠀⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠋⠁⠀⠀⠀⣀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠉⠻⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣾⣶⣶⣶⣾⣿⣿⣶⣆⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢀⣿⣤⡤⣄⣠⣼⠇⠸⠶⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣶⠾⠛⠉⠉⠀⠘⠋⡿⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⣰⣽⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢺⡌⡆⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢈⡿⠃⠀⠀⠀⠀⠙⠛⠀⠀⠀⢀⠀⠀⡾⡙⠃⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡲⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡇⡦⠠⢤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡁⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠿⠶⠤⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⡽⡆⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠠⣴⡄⠀⣸⣎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⢀⡀⣘⠌⠀⠀⠀⠀⠀⠐⣿⡟⠃⠀⠀⠀⠀⠀⠁⢸⣹⡟⠁⠀⠀⠘⠛⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠏⠀⠀⠀⠀⠀⢀⡾⢋⠁⠀⠀⠀⠀⠘⠑⢢⡾⠿⠳⠦⠀⠀⠀⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣠⣴⠞⠄⠀⠀⠀⠀⠀⣾⠻⡔⠡⠄⠀⠀⠀⠀⠀⣠⢟⡵⠀⠀⠀⠀⠀⠀⠉⠉⠁⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢯⠁⠀⠀⠀⠀⠀⣀⠈⠃⠀⠀⠀⠀⠀⠀⠀⣘⢍⠋⠉⠛⠓⠀⠀⠲⠶⠶⣶⡆⠰⡦⠀⣶⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣾⢃⠆⠀⠀⠀⠀⠀⣼⣋⠀⠀⠀⠀⣤⠀⠀⠀⠘⣿⢋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⢈⠿⡟⠁⠀⠀⠁⠀⠀⣯⠙⠗⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠉⠀⠀⣀⣀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣶⣶⣉⠀⠀⠀⠀⠀⠀⣶⢿⠙⠂⠀⠀⠀⠀⠀⢀⣴⠿⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠘⠳⡄⢀⡸⡑⠝⠀⠀⠀⠀⠀⠀⣄⣅⠁⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠑
⠀⠀⠀⠀⣦⢠⣀⣈⣿⣯⠛⠀⠀⠀⠀⠀⣶⣿⠷⡏⠀⠀⠀⠀⠀⢠⣼⡏⠁⠙⢦
⠀⠀⠀⠀⠀⠉⢰⣿⡿⠃⠀⠀⠀⠀⠀⠻⣿⡾⠃⠀⠀⠀⠀⠀⣰⣿⠙⢦
⠀⠀⠀⠀⠀⣀⣶⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠁⠀⠈
⠀⠀⠀⠘⠛⠟⣿⠶⡖⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡛⠻⣆
⠀⠀⠀⠀⠀⠀⣿⣷⣇⠀⠀⠀⠐⠿⠷⠄⠀⠀⠀⢀⣴⢿⣇
⠀⠀⠀⠀⢀⣤⡿⣯⠷⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡱⠁⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⢋⣶⣤⣀⣀⣀⡀⣤⡾⢋⡾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢠⡇⣼⠓⠷⣯⣭⣩⣧⣿⠞⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡙⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⠕
⠀⠀⠀⠀⠀⠀⠀⣸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣎⣀⣠⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢹⡌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠖⠈⠀⠀⠀⠈⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⢿⡀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣧⠀⠨⣿⡿⠿⣷⢾⣿⠴⡷⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠙⠾⣿⣦⣄⣀⣀⣀⡀⠀⢀⣀⣀⣤⡾⠟⠁
⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠭⠭⠭⢯⣭⣿⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⠛⠛⠻⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠁⠀⡀⠾⠀⠀⠰⠀⠙⠃⠀⠰⢀⡤⠀⠀⠖⠀⠉⠁⠶⠀⠀⢦⡈⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⠊⡇
⠀⠀⠀⠀⠀⣿⣿⣿⡟⢀⠀⠈⠁⢠⠂⡄⠠⡠⠀⢀⡐⠲⡈⣤⢶⠖⢢⡀⠀⢠⠀⡀⠘⠃⠀⣈⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘⠀⡃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣷⠈⠓⠖⠀⠓⠄⠁⠚⠻⠴⠓⠙⠤⠘⠊⠂⠰⠱⠛⠴⠺⠐⠀⠀⠀⠀⢉⣿⣿⣿⡏⠓⡄⠀⠀⠀⡇⠀⡃⠀⠀⠂⢰
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⡀⠀⠀⢀⣤⠴⠀⠠⣤⠀⠆⠀⠛⠡⠆⠀⠀⠠⠆⠀⠀⠂⠨⠀⢀⣾⣿⣿⡿⠁⠀⠐⡀⠀⢀⠁⠀⡇⠀⡈⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⡿⠁⠀⠀⠀⢃⠀⡈⠀⠀⢃⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆⠀⠀⠀⡠⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠠⡀⠀⠠⠀⢂⣁⠶⠒⠲⢤⡀⠄⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠐⠈⠀⡴⠋⠰⠀⠀⠀⠀⠙⢦⣈⠔⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⡒⠬⢻⠆⠀⠀⠁⠀⠀⠀⠀⠀⠻⢆⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠄⡈⣿⠸⡄⠀⢴⠆⢺⣿⣷⣶⢄⠀⠀⠓⣄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⢽⣇⢱⡀⠀⠀⠻⣿⣿⣿⣿⣖⣀⠀⠈⠳⡀⠁⢠⠔⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⢀⣿⣧⣱⣄⠀⠈⡘⣿⣿⣿⣿⣷⣷⡆⠀⠘⢣⡀⠂⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⡀⠘⠿⣷⡜⢦⠰⠛⡱⠿⣿⣿⣿⣿⣿⣦⣤⠀⠙⢦⡀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠂⠤⠀⠚⠭⣿⣦⠱⣜⠵⠶⠻⣿⣿⣿⣿⣿⣿⠟⣄⣦⣱⣖⠈⠤
⠀⠀⠀⠀⠀⠀⠠⡪⠒⠈⢝⣻⡇⣸⣦⠀⠀⠉⠹⣿⣿⣿⣿⣯⣽⠟⢳⡘⣆⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠁⣀⣰⣿⡿⢀⠀⠀⠀⠚⠻⣿⣿⣿⣿⡧⠀⠁⠘⣇⠀⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠿⡗⣮⠃⠰⣄⠀⠀⠀⠛⣿⠏⠀⠀⠀⠀⢹⠉⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣷⣷⣌⠳⣤⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⠒⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠠⢫⣿⣿⣥⣁⠒⠤⢤⠤⠤⠿⣯⣿⡓⠦⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠎⠋⠘⡿⣿⣿⣶⣶⣶⣿⠟⠛⠉⠉⢏⠙⣎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡈⠀⠉⠁⠈⠀⠀⠀⠀⠀⠘⠦⣬⠿⠶⣶⢶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣏⣧⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⢻⡄⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣖⠚⢶⣤⢤⡒⢦⣠⢤⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠓⠓⠾⠛⠛⠈⠃⠸
⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⠿⠿⠿⠿⠿⠿⢷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠋⠉⢁⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡆
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⢻⣷
⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⢸⣿
⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠘⣿⣆⠀⣀⣠⣤⣤⣤⣼⣿⣤⣄⣀⡀⠀⠀⣼⡿⠁⠀⠀⠀⠀⣿⣇
⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠟⠛⠉⠉⠉⠉⠉⠉⠙⠛⠿⣷⣾⣿⠁⠀⠀⠀⠀⠀⠈⠉
⠀⢠⣿⣏⡀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣾⡟⠛⠿⣷⣦⣤⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⠀⠀⠀⠀⠀⠀⠈⢻⣷⣀⣀⣤⣤⣶⣿⣿⡄
⢸⣿⠁⠀⠀⠀⠉⣽⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠋⠉⠁⠀⠘⠋
⣼⡏⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⣀⡀
⣿⡇⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣹⣿⣄
⣿⣇⠀⠀⣀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣀⣀⣠⣤⣾⠟⠋⠉
⣿⡿⠿⠿⠟⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⣶⣦⡀
⢹⣷⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⢘⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄
⠘⣿⡄⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠹⣿⣄⣀⣀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⢻⣷⠀⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠈⠙⠛⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠈⢻⣇⠀⢀⣴⡿⠟⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠙⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠈⢿⣶⡿⠋⠀⠀⠀⠈⠻⢿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣤⣀⣀⡀⠀⠀⣀⣴⡿⠁
⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⢿⣶⣶⣶⣶⣾⠿⠿⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⢀⣠⣴⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⢀⣈⣻⣷⣦⣤⣶⡾⠿⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡄⠀⠀⣴⣶⣿⣿⣿⣧⣄⠐⠐⠂⠐⠤⠄⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⣀⢼⡇⠀⠀⡜⣿⣟⣼⡽⣿⣿⣿⣿⣿⣿⣷⠀⢀⣀⣠⣤⣴⣿⣿⠂⠀⣤⣴⢤
⠀⠀⠀⠀⠀⠀⠈⠦⣌⠁⠐⣶⣷⣾⣯⣗⣚⣟⣿⣿⣿⡿⠋⠶⣿⣿⣿⣿⣟⣿⡿⠀⣶⣬⣭⢄
⠀⠀⠀⠀⠀⠀⠱⡤⢀⡈⠀⠶⠙⣿⣿⡿⠿⠿⠛⢉⡉⠀⠀⠈⠻⠷⣶⣿⡿⡿⠋⠛⣋⣡⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠙⣠⠟⠋⡀⠠⠤⣄⣀⣀⣀⢀⠈⠉⠉⠀⠀⠀⠀⠀⢀⠀⣰⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢤⣑⠤⠁⠂⠀⠉⠉⠉⠁⠀⠀⠉⠉⠀⠘⢀⣼⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢁⣀⡀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⢀⠀⡀⢀⡀⡀⠀⢀⠀⣀⠀⠀⢀⠀⠀⡀⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠌⠸⠃⠐⠑⠈⠃⠘⠀⠢⠁⠀⠀⠃⠤⠀⠣⠀⠇⠘⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⢋⡉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⡀⢀⢀⠀⡀⢀⡀⡀⠀⣀⢀⣀⢀⠀⣀⠀⢀⡀⡀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠹⠿⠻⠼⠻⠧⠼⠳⠼⠏⠹⠹⠤⠃⠧⠸⠿⠤⠀⠧⠸⠧⠾⠤⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠉⠁⠀⠉⣡⣀⣀⣀⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠐⠀⠀⠀⠱⠀⠀⠐⠂⠀⢀⣠⣶⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⠿⠶⠶⢴⣦⣦⡤⠶⠿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡯⠒⢀⡀⠡⠒⢀⣦⣄⣀⣃⣰⣆⣾⣿⠈⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠢⠰⢆⠀⠛⠿⠿⠿⠿⠿⡿⠟⢿⢿⠇⣸⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣤⣄⣀⣀⣀⣐⣀⣀⣂⣈⣴⢏⣴⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠋⠉⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢠⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⡴⠀⠀⠐⠖⠠⠀⠀⠀⡄⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣴⣶⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⡤⠀⠀⢿⡇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠄
⠤⠄⠀⠀⢠⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⡤⠤⠤⣰⠰⠂⠀⠀⠀⠀⠀⠀⠀⠠⣂⡆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠉⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠠⢘⠀⠀⢴⡆⠀⠀⠀⢠⡾⠃⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠐⠓⠀⠀⢡
⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⢠⠄⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⣀⠠⢄
⡤⠄⠂⡀⠀⠈⠓⡀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠌⡑⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⢤⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠋⠀⠀⡀⠀⠀⠆⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠄⠁⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠉⠀⢏⠈⠐⠊⠁⢈⠂⠀⠀⠀⠈⠲⠐⠊⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⢀⡀⡀⠀⠀⠀⠅⡀⢀⠠⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢠⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠆⠐⠊⠀⢁⠐⠁⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠐⠀⠀⠁⠀⠀⣠⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠢⡀⠀⠀⢨⠀⠀⠀⠀⠠⠂⠰⠀⠀⡀⠀⠀⠨⠙⠀⠀⠘⠠⠰⠊⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠊⠁⠀⠀⡀⠀⠄⠀⠀⠰⡿
⠛⠳⠢⣄⠀⠀⢈⠆⠀⠀⡆⡀⠐⠈⠐⠈⠀⠀⢀⠃⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠁⡀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠈⠀⢙⡀⠀⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡄⠐⡇⠀⠀⡮
⠀⠀⠀⣸⠁⠀⠁⠀⠀⠀⠀⠌⠀⠑⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠁⠆⠀⠧⡈
⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠠⠁⠀⠈⠁⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠰⠀⠀⠈
⠀⠀⠀⢀⠀⠀⡀⠀⠒⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠐⠀⠀⠀⠀⠀⠀⢿⣆⠀⢴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠈⠀⢈⠀⠀⠀⠀⠐⠢⢀⠀⠘⢿⣷⣄⠀⠀⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠈⢻⣆⠀⠀⢀⠀⠀⠀⠦⠈⠁⠈⠁⢠⠀⢠⠚⠁⠀⠀⠁
⠀⠀⠘⠁⠀⠈⠦⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠗⠀⠀⠈⠟⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢀⠀⢴
⠀⠀⢠⠀⠠⡄⠀⠠⠀⠀⠀⠀⠀⠈⠀⢀⡀⢿⣿⣦⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⢀⡀⠀⠄
⠀⢠⠚⠀⢀⡄⢀⡀⠐⠀⠀⠀⠀⠀⠀⣼⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⢀⠀⠄⠀⠀⠐
⠀⠈⠀⠀⠇⢤⣌⠁⠀⠈⠀⠀⠀⠴⢀⠏⠀⠀⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⢀⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⡀⠈⠐⠡⠁
⠀⠀⠀⠀⢀⠀⠆⠀⡀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠴⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠐⠃⠀⠗⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠶

⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⢀⡠⠋⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢀⡠⠑
⠊⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⠀⠇⠀⠚⠛⠋⠀⠀⡠⠋⠀⠀⠐⠁⠀⠀⠂⠀⠀⠀⠀⠀⡀⠠⠛⠛⠁⠀⢀
⠀⠀⠀⡀⠘⢏⠀⠀⠀⠂⠀⠀⠀⠈⠩⠂⠠⠐⠀⠁⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠄⠀⠀⠀⠐⠱⠂⠠⠐⠀⠁
⠀⠀⠀⠐⡀⠘⢶⣼⡆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠙⣦⣼⠄
⢀⠀⠀⠀⠈⠢⣄⣀⣯⣢⠃⠀⡠⠐⠒⠁⠈⠀⠀⠀⠠⡀⠀⠀⠀⠐⠦⣄⣰⢷⡢⠀⠀⠠⠐⠐⠉⠁
⠀⠑⢄⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⣠⠤⠈⠐⠐⠀⢀⠈⠢⡀⠀⠀⠀⠀⠉⠈⠀⠀⠈⠀⠀⣤⠤⠀⠂⠂
⢍⢦⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠠⣕⠄⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⣶⠟⠂⢹⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠒⠶⢤⣴⣾⠿⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠉⠒⠦⣤
⣀⣤⡽⠋⠀⠀⡀⠄⠠⠤⣤⣀⠀⠁⠠⡀⠀⠀⠀⠀⢀⣀⣄⡷⠃⠀⠀⠀⠀⠄⠤⣤⣀
⠛⠉⠀⠀⠀⠈⠀⠀⠀⣤⡐⠸⡇⠀⠀⠀⠉⠐⠒⠒⠚⠋⠉⠀⢀⠔⠀⠀⠀⠠⣤⡀⢹⡆⠀⠀⠀⠉⠒⠒⠒
⠀⠀⠀⡈⠀⠀⠀⠀⢠⠿⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡰⠣⠀⢸⠇
⠀⠀⠀⠁⢀⣶⡦⠖⠁⠀⢠⠎⠀⠀⠠⠀⠀⠠⡀⠀⠀⠀⠀⠠⠀⣠⣷⡴⠂⠀⠀⡠⠋⠀⢀⠄⠀⠀⠄
⠀⠀⠀⢔⣤⠀⠀⡀⠠⠂⠁⠀⠀⠈⠀⢴⠀⠀⠈⢂⠀⠀⠀⠀⢄⡀⠁⢀⠀⠄⠊⠀⠀⠀⠂⠀⡴⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⣆⣀⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⣄⣀⡀⠈
⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠐⢄⡈⠛⢻⣀⡀⠀⠀⢀⠀⠤⠄⠀⠀⠀⢀⠀⠀⠀⠀⠑⢄⠈⠛⣇⣐
⠀⠐⠁⠀⢀⠀⠄⠄⠀⠀⠀⠢⡀⠀⠀⠀⠉⠛⠛⠓⠁⠀⠀⠁⠀⠀⠄⠄⠠⠀⠀⠑⢀⠀⠀⠀⠀⠙⠓⠛⠊
⠀⠆⠀⠐⢯⠀⠀⠀⠀⠈⠓⣄⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠁⠀⠀⠀⠈⠲⣄⠱⠄
⠀⠠⠀⠀⠈⠑⠤⣀⣀⣀⣈⣦⡇⠨⡆⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠈⠓⢤⣀⣀⣀⣸⣬⡆⢸⡀
⠀⠀⠑⠄⠀⠀⠀⠀⠉⠉⠛⠉⡠⣲⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠛⠁⣠⡾⠀⠀⠀⠀⠀⢀
⠙⢶⠀⠀⠀⠐⠠⢄⣀⣰⡶⠷⠛⠁⠀⡠⠀⠀⠀⢀⡉⠹⣦⠀⠀⠁⠂⠤⢄⣀⣠⡾⠟⠋⠀⠀⠀⠂⠀⠀⣈
⣂⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣹⣓⣀⣹⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠉⠂⠀⠘⣇⢀⣌⢘⠠⠆⠀⠁⠸⠀⡀⠸⡄⠿⡾⠓⠀⢀⡴⡶⣶⡻⠃⠐⢿⠆⠀⠀⠀⠓⢀⠇⢀⠈⠉⢇⣤⠉⠙⢶⡞⠃⠠⠂⢨⡮⠨⡅⠀⠀⠉⠁⣠⣡⡀
⣌⠒⠂⠈⢡⠷⡄⢠⡄⠘⡁⠀⠄⢠⡀⠈⠀⠩⠐⠀⠁⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠊⠀⠀⠹⠤⢦⡼⠓⠄⢀⠢⠂⠛⠃⠀⠀⣠⠐⢾⠙⣏
⠤⣱⢄⡄⢄⠐⢱⣤⣁⣠⠢⠀⠐⠚⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠠⣀⡡⠀⠄⣴⠅⠠⣌⡰⠁
⠒⢯⡜⢔⠀⠁⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠆⢀⢘⠇⠀⠀⠂
⡤⢄⠙⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⡄⡄⣠⠄⢠⢤⢀⡤⣄⢀⠤⡀⡠⢄⢀⠤⠀⢠⡀⢠⡀⡀⡄⣠⠄⣄⠀⣠⢠⠄⠀⠀⠀⠀⠀⠀⠈⠉⣀⠤⠔⢦⣀
⠧⠜⠀⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠸⠱⠊⠄⠇⢧⡄⠸⠻⠸⢄⠼⠻⣤⠌⠜⠢⠰⣄⠦⠟⠳⠸⠑⠇⠇⢉⠗⠏⠖⠱⢨⡷⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⣶⢾⠏
⠀⠀⢐⡠⠒⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀
⠠⢴⠏⠀⡀⠔⠟⠁⠀⣄⠀⡦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢖⡚⠺⡄⠘⠃⠁
⠀⠘⠛⠋⣥⠎⠀⠀⠀⢸⠇⠛⠛⣧⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢔⠿⢧⠄⠀⠐⠝⣁⡁⠷⠂⢆
⣠⠎⠀⠊⢀⠄⠠⠀⠙⠋⡠⠲⠒⠉⡦⡄⠈⣄⡠⠉⣀⠀⠀⢠⠖⡬⠀⠀⠀⠀⣇⡀⢤⠧⢀⣀⡄⠀⠰⢎⠙⠄⠜⢸⡶⠀⣄⡤⠂⡂⣯⡆⠀⠁⠴⡂⢿⠆⡕
⣷⣦⣤⣤⣷⣶⣾⣧⣤⣼⣧⣤⣴⣾⣶⣤⣤⣤⣷⣮⣤⣼⣦⣬⣿⣧⣤⣤⣤⣾⣷⣴⣦⣴⣿⣧⣤⣴⣷⣴⣧⣤⣴⣾⣧⣼⣧⣤⣴⣷⣿⣤⣤⣤⣬⣴⣶⣾⣦
⣿⣿⣇⣀⣈⣀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡄⠠⠀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⡓⠃⡠⠀⠀⠈⠑⢄⢈⡀⠀⠀⠀⢄
⠀⠀⢀⡀⠀⠀⠀⢠⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⢄
⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠢⠄⠀⠀⠀⠀⠲⡀⠀⠆⠀⠀⠀⠀⢁⡀⠀⠀⣀⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⠂⠀⠀⢂⣀⠀⠀⠀⠐⠀⡀⠠⠶⠶⠶⢦⠄⠂⠀⠀⠀⠀⠠⠀⠀⠸⣁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠈⠀⠀⠿⠿⠇⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠉
⠀⠀⣠⠂⠀⠀⡀⠠⠀⠀⠀⠀⢠⡀⠰⡀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠠⡦⠀⠀⠀⠀⠈⠀⠀⢰⢀⠀⠀⠀⠀⠀⠑⠀⠠⡀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠉⠀⠀⠠
⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⢀⣄⠀⠀⠁⠠⡀⠉⢂⠘⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠠⡀⠄⠀⢀⠄⠀⠈⠁⠘⡆⠀⢶⣤⣄⠀⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⢀⡀⠀⢇⣀⡸⠀⠄⠀⡇⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⡤⠦⡄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠟⠁⠀⠐⠘⡆
⠀⠀⠀⠀⢠⠀⠱⠴⠃⠀⠀⠀⠀⠀⠀⠀⠐⠷⣤⡀⠀⠘⣇⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠛⠃⠀⠈⠒⠆⠔⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠄
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠹⠤⣠⠖⠀⠀⠀⠀⠀⠀⠶⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠂⠀⠀⠀⣀⡀⠀⠀⡠⠀⠀⠀⢀
⠀⠀⠀⠀⠰⠄⠀⠀⡀⠀⠀⠈⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⣠⠊⡠⠒⠂⣉⡁⠀⠀⠀⠉⣤
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠑⠊⠀⠀⠀⠈⠉⠙⠒⠲⠤⡄
⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⡶⠉⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠛⣠⣤⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⡔⠁⠇⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣰⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣂⠀⠀⠃⠀⠀⠙⠛⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠨⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⢁⣄⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉
⠀⠈⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣠⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠁⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⡼⠀⠀⠀⠈⠀⠐⠂⠀⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠐⡸⡀⠀⠀⠈⠉⠀⠀⠀⠃⠧⣛⡫⡰⠀⣠⠁⡃⠸⠃⠀⠀⠀⠠⠜⢢⡑⠊⠐⡸⡀⠀⠀⠈⠉⠀⠀⠀⠃⢣⣛⡫⡸⠀⣠⠁⠇⠺⠃⠀⠀⠀⠠⠜⢢⡑
⠀⡁⡉⢶⠀⠀⠀⠀⠀⢀⣧⡠⠤⠞⠁⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⡇⠈⡉⡈⢶⠀⠀⠀⠀⠀⢀⣧⡤⠤⠞⠁⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⢨⣶⣎⠀⡯⠄⠀⠀⣠⠟⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠜⡡⡠⡍⢦⠀⠀⣉⡏⢨⣶⣎⠀⠧⠄⠀⠀⣠⠟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠞⡡⡀⡍⢦⠀⠀⣉
⢤⣉⡡⢜⠑⠂⠀⠀⡏⠀⠀⡔⢉⡠⠤⣉⠆⠀⠀⠘⣌⢜⢋⠆⢃⠀⠀⠁⡱⢤⣉⡡⢜⠁⠂⠀⠀⡏⠀⠀⡔⢉⠠⠤⣉⡆⠀⠀⠘⡄⢜⢛⠆⣸⠀⠀⠁
⠃⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠊⠁⠀⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠚⠁
⠀⠀⠀⢤⢀⠀⠄⠀⠀⠀⠀⣀⡤⠦⠦⣌⡠⢀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⡀⠀⠀⠀⢤⢀⠀⠄⠀⠀⠀⠀⣀⡤⠦⠦⣌⡠⢀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡄
⢂⠀⠀⢢⡏⢙⡦⠄⠀⠀⠠⢜⣶⣕⣢⠀⢉⣧⠀⠀⠀⢜⢀⣹⡆⠀⠀⠳⡌⢢⠀⠀⢢⡏⢹⡦⠄⠀⠀⠠⠜⣶⣗⣢⠀⢉⣧⠄⠀⠀⢜⢀⣙⡆⠀⠀⠳
⠤⠀⠀⠀⠹⠙⠈⠃⢀⠀⠀⠀⠊⠝⡦⣶⡿⠻⣦⠀⠀⠈⠑⠉⠀⠀⠀⠀⠘⠦⠂⠀⠀⠹⠙⠈⠃⠀⠀⠀⠀⠊⠕⡶⣶⡿⠻⣦⠀⠀⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠠⡀⢨⠀⠀⠀⠀⠀⠁⠁⠈⠀⢹⢆⠀⠀⠀⠀⡄⠂⢂⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢸⠀⠀⠀⠀⠀⠁⠀⠈⠀⢛⢆⠀⠀⠀⢀⡤⠂⢢
⢀⠂⡄⠀⠀⠀⠤⣱⠼⢤⡎⡠⠔⠁⢠⠠⡀⠀⠀⠑⠓⠀⢀⠎⠀⢀⡟⠀⠀⢀⠒⡄⠀⠀⠀⠤⣱⠼⢤⡎⡠⠔⠁⢀⠠⡀⠀⠀⠑⠓⠀⢀⠎⠀⢀⡟
⡎⡸⠀⠀⠁⠀⣰⢱⣶⡆⢸⡖⠊⠀⠀⢧⠰⡀⠀⠀⠀⠀⡌⠀⢠⠎⠀⠀⠀⡌⡼⠀⠀⠁⠀⣰⢱⣷⡆⢸⠖⠊⠀⠀⢧⠐⡀⠀⠀⠀⠀⡜⠀⢰⠎
⠷⠃⠀⠀⢀⡡⠘⡦⣄⣨⡶⢍⡁⠀⠀⠸⣄⡇⠀⢀⣀⣼⡀⣤⠂⠀⠀⠀⠀⠧⠃⠀⠀⢀⡡⠘⡦⣄⣠⡶⢍⡁⠀⠀⠸⣀⡇⠀⢀⣠⣼⡀⣠⠂
⠀⡀⠀⠈⠁⠀⠜⠀⠂⢃⠘⠀⠈⠂⠀⠀⠉⠀⠶⠡⢊⢊⠍⡅⠀⠀⠰⡀⡐⠀⣀⠀⠈⠁⠀⠞⠀⠆⢡⠘⠀⠈⠂⠀⠀⠉⠀⡶⢡⢊⢊⠍⠁⠀⠀⠰⡀
⡛⡥⠆⠀⠀⡠⢤⡀⠀⠘⠀⢀⣀⣀⡀⠀⠀⢀⠔⣡⢃⠃⡰⠀⠈⢱⢊⣅⠭⡛⡥⠆⠀⠀⠠⢤⡀⠀⠘⠀⢀⣀⣀⡀⠀⠀⢀⠔⠡⢋⠁⡰⠁⠈⢱⢊⢍
⢃⢙⠉⠀⠀⠢⠾⠁⠀⠀⡔⡽⣷⡖⠸⠀⢀⠇⠔⣡⡎⠐⠃⠀⠁⢹⡘⢝⡣⢃⢻⠉⠀⠀⠢⠶⠃⠀⠀⡔⡑⣷⡶⢱⠀⠀⠆⠔⣡⡎⠐⠃⠀⠁⢹⡘⢟
⠠⠎⠦⣀⠀⠀⠀⠀⠀⠀⡄⠉⠒⣪⠎⠀⠚⢠⠃⠈⠀⠀⠀⠀⠈⠀⠜⠲⡄⠠⠮⠦⣀⠀⠀⠀⠀⠀⠀⡄⠉⠒⣊⠎⠀⠚⢠⠂⠈⠀⠀⠀⠀⠈⠁⠜⠢
⠠⣂⡢⠙⡄⠂⠀⠀⠀⣴⠟⠊⠉⠁⠀⠀⠐⠃⠀⠀⣠⠄⠀⠤⡀⠀⠀⠤⡆⠠⣂⡢⠙⡄⠀⠀⠀⠀⣴⠟⠋⠋⠁⠀⠀⠐⠃⠀⠀⣠⠄⠀⠤⡀⠀⠀⠤
⠘⠿⠑⢠⢏⡁⠀⠀⡾⠁⠀⢀⠤⠄⠀⠤⡀⠀⠀⢠⠁⢪⣦⡃⡙⠄⠀⠖⢆⠘⠿⠗⢠⠍⣁⠀⠀⡾⠁⠀⢀⠤⠀⠀⠤⡀⠀⠀⢠⠁⢪⣦⠃⡹⠀⠀⠖
⡝⠒⢊⠱⠀⠀⠀⠀⠃⠀⠀⠣⠘⠈⠉⠓⠃⠀⠀⠀⠣⢑⣐⣡⠜⠀⠀⠀⠊⡙⠒⢂⠱⠀⠀⠀⠀⠃⠀⠀⠣⠚⠊⠉⠓⠁⠀⠀⠀⠣⢑⣐⣁⠞
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⡀⠠
⡀⠀⠀⡙⡼⣴⣁⠀⠀⠀⠀⢲⡋⢍⡉⠓⠮⡔⠀⠀⠀⢠⠒⢢⡀⠀⠀⢆⠢⡀⠀⠀⡙⡼⣤⡁⠀⠀⠀⠀⢲⣋⣍⡉⠓⠪⡔⠀⠀⠀⢠⠒⢦⡀⠀⠀⣇
⠘⡀⠀⠘⢧⢴⠣⡅⠀⠀⠈⠐⡻⢗⢛⣄⣴⣿⡁⠀⠀⠱⢄⠾⠃⠀⠀⠈⢣⠘⡀⠀⠘⢧⢼⠣⡅⠀⠀⠈⠐⡻⢗⢛⣤⣴⣿⡁⠀⠀⠱⢴⠶⠃⠀⠀⠈
⠉⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠁⡏⠟⠫⠈⠿⡀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠁⠏⠟⠫⠈⡿⡀⠀⠀⠀⠀⢀⡀⡀
⠀⡀⠀⠀⠀⠀⡈⢆⢸⠀⡠⠀⢀⠄⠀⠀⠀⠀⠐⢕⣄⠀⠀⡰⠋⠀⣴⠀⠀⠀⣀⠀⠀⠀⠀⡈⢆⢘⠀⡀⠀⢀⠄⠀⠀⠀⠀⠘⢕⣄⠀⠀⡰⠋⠀⣴
⠰⢠⠃⠀⠄⠀⢉⢞⣍⡙⢣⡊⡥⠀⠸⡌⢂⠀⠀⠀⠀⠀⠰⠁⠀⣠⠃⠀⠀⠰⢠⠃⠠⠄⡀⢙⢞⣍⡑⢣⣂⡥⠀⠘⡍⢂⠀⠀⠀⠀⠀⢰⠁⢀⡰⠃
⡇⡎⠀⠀⠀⠄⢺⡘⠛⠃⣘⠧⠄⠀⠀⢸⠀⡆⠀⠀⠀⢠⠃⠀⡘⠁⠀⠀⠀⡇⡎⠀⠀⠀⠄⢺⡘⠛⠃⣨⠧⠄⠀⠀⢹⠀⡆⠀⠀⠀⢠⠃⠀⡸⠁
⠉⠀⠀⠠⠔⠊⣠⠋⡓⠞⢫⠑⠢⡄⠀⠈⠧⠃⣀⠔⡪⡻⠮⠟⠀⠀⢀⠀⢀⠉⠀⠀⠠⠔⠊⣠⠋⡓⡞⢣⠑⠢⡀⠀⠈⠶⠃⣀⠔⡺⡻⠮⠟⠀⠀⢀
⣤⠆⡀⠀⠀⠀⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢋⠌⡘⡔⢁⠅⠠⢄⡠⠆⠢⣤⠆⡀⠀⠀⠀⠁⠀⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⢉⠌⡴⠕⢁⠆⠠⢄⡨⠆
⡆⢯⠥⠀⠀⡊⣹⠆⠀⠀⢀⢴⣖⢒⢢⠀⠀⡔⢁⠞⡰⢀⡎⠀⠄⢼⢰⣷⡌⡆⣯⠥⠀⠀⡉⣙⠆⠀⠀⢀⢴⣖⣒⢆⠀⠀⡔⢁⠎⡰⢀⡎⠀⠄⢼⢰⣷

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣻⠭⠥⠒⠒⠒⠒⠒⠠⠤⠤⣍⣙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⠕⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⢤⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⡫⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡙⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢏⠞⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠒⠒⠦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢯⠎⠀⠀⠀⠀⠀⡠⠊⠀⡠⠚⠉⠒⢄⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⣿⣿⣿⣿
⣿⣿⣿⣿⢯⠋⠀⠀⠀⠠⠀⡜⠀⠀⢸⠀⠀⠀⠀⢨⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡀⢠⢀⠀⠸⠸⣿⣿⣿
⣿⣿⣿⢏⡎⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠦⣀⣀⡤⠊⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡇⢻⣿⣿
⣿⣿⡟⡸⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢸⣿⣿
⣿⣿⠃⡇⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⢉⠀⡄⠀⢹⢸⣿⣿
⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⢸⢸⣿⣿
⣿⣿⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⣿⣿
⣿⣿⣧⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣼⣿⣿
⣿⣿⣿⣆⢣⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠜⠑⢀⠀⡐⠀⠀⠀⠀⠀⠒⠀⠀⠀⢂⡎⢰⣿⣿⣿
⣿⣿⣿⣿⣆⢣⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣧⡳⣄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣎⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡰⠃⣠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡓⢄⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣀⣼⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣋⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣍⣑⣒⠒⠂⠀⢀⣒⣒⣭⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⢠⠀⡀⠀⠀⠀⡠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠁⠀⠀⠀⠀⠀⢂⠀⠨⣀⠀⠀⠀⠁⠂⠀⠀⠀⠈⠀⠁⠀⠀⠰⠊⠁⠉⢡⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⢠⠀⠌⠀⠂
⠀⡁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠠⠤⠀⠂⠀⠀⠐⠈⠀⠀⠘⣀⠀⠀⠔⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠂⢀⡀⠁
⠀⠀⠘⠀⡄⠐⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠒⠀⠐⢄⠀⠂⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⡀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠄⠁⠈⠂⠀⡃
⠀⠀⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠈⠈⠀⠀⠉⠀⢀⢀⠤⠞⠀⠀⠀⠠⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⣀⣀⣤⣤⣴⣤⣄⡀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠘⠀⠄⠀⠀⠀⣠⣾⠟⠛⠫⠛⡛⡛⢉⣙⡻⢯⡀⠙⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠔⠐⠢⠀⠈⠀⢠⣿⠘⢸⡄⡄⣌⣳⣜⣈⣯⣩⣼⠿⡿⡏⠉⣿
⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠁⠒⠂⢀⠁⠀⠸⡿⠶⢾⠛⠻⡏⣭⣭⡩⡇⠒⢓⡐⢠⡀⢰⣽⠄
⠀⡠⠂⠀⠢⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠻⣌⠌⠂⢦⣀⣝⣉⣷⣹⣌⢉⣣⣠⣥⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠐⠀⠄⠀⠀⠀⠈⠙⠛⠛⠋⠉⠉⠙⠉⠋⠛⠛⠛⠉⠁⠀⠀⢀
⠀⠀⠁⠀⠁⢀⠀⠀⠀⠀⠀⢍⢈⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠⠱⠃⠚⠁⠀⠀⠀⠄
⠀⡊⠀⠀⠌⠀⠀⠀⢀⠀⠂⢀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠊⠀⡀⠀⠀⠐⠠⠛⠁⢀⡀⡀⠀⢀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠂⠀⠀⠀⠀⠈⠀⠀⠐⠰⠖⢲⢸⡣⢈⠄⠂
⠀⠈⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠘⠁⠁
⠀⢀⠂⢐⠈⠀⢃⠂⠀⠐⢈⠄⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡠⠐⠁⠀⢀⠃⠀⠀⠀⠊⠐⠆⠀⠀⠀⠀⠀⠀⠄
⠀⠠⠢⠀⠀⠀⠀⢄⠀⣀⢂⠐⠀⡜⡠⠐⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⠀⠄⠐
⠀⠈⠀⠡⠠⠐⠀⠊⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣒⣭⣙⣫⠅⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡰⠁⠻⡅⠙⡷⠈⢣⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠒⣒⢢⣀⠀⠀⠀⠀⣇⡇⠀⠀⢘⣴⠁⠀⢸⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⡈⢄⡁⡈⢃⠰⠠⠈⢱⠀⠀⠀⠱⣜⠢⣠⠼⢋⠣⣤⢊⡜
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⠀⠀⣳⠁⡢⠂⠉⠐⢄⣧⠀⠀⠀⠈⠢⠬⣀⣀⡤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⣰⣿⣠⠃⠀⠀⠀⣾⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣗⣿⢫⣃⢌⢀⣀⣄⡴⣳⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠵⣒⣚⣛⣯⠭⠚⠁⠀⣀⠄⠐⠋⢡⠀⠉⠉⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢲⡤⠤⠒⠒⢢⢤⠲⠈⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡔⠁⠀⠀⠀⠀⠠⣻⡟⢎⠐⠃⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡀⣇⠀⠀⠀⠀⡴⠊⣀⣼⣼⡎⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠁⡌⣉⠓⡈⢏⠔⠋⠀⠀⠈⣉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣈⠒⠆⠎⠀⠀⠀⠀⢈⡟⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⡀⠂⢄⡀⠀⠀⣠⠞⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠭⠭⠭⠒⠋⠁


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

⠀⠀⠀⣠⣶⣤⡄⠀⠀⠀⢀⣶⣾⢺⡷⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠠⣾⣿⣷⡄⠀⠀⠀⠀⠰⠀⢰⠀⠀⠀⠀⢀⣴⣲⡶⣤
⠀⠀⠐⣇⠙⠃⡧⠀⠀⠀⠀⠴⣷⠚⣿⠅⠀⠀⠀⠰⣯⢯⡧⠀⠀⠀⠀⠀⠩⣍⣉⠀⠀⠀⠀⣴⠚⠛⠛⣿⠀⠀⠀⢈⣭⣭⣭⣭
⠀⠀⠀⠉⠋⠋⠀⠀⠀⠀⠀⠈⠹⠛⠛⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⣸⣿⡧⠀⠀⠀⢀⣴⣿⣷⣦⠀⠀⠀⢸⣿⣶⡿⠿⠶⠀⠀⠀⣠⣴⣶⡶⢦⠀⠀⠀⢻⣶⠶⣶⠶⠉⠀⠀⢀⡦⣵⠟⡂⠄
⠀⠀⠠⣾⣿⡿⠃⠀⠀⠀⠸⣇⠛⠛⣺⠁⠀⠀⠈⣽⣿⠷⠟⠃⠀⠀⠐⣇⣩⣁⣰⡞⠁⠀⠀⢸⣧⣻⣼⡀⠀⠀⠀⣰⣿⠽⠻⠿⠆
⠀⠀⠀⠿⠿⠃⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠠⠟⠁⠀⠈⠱⠆⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⢀⣶⡿⢻⣆⠀⠀⠀⢀⡴⣴⠚⠃⠀⠀⠀⠀⣸⡇⠀⠀⠀⢾⣿⠷⠂⠀⠀⠀⢸⡏⠉⠀⠀⠀⢦⣴⣿⣄⡆⠀⠀⠶⢳⠾⣅
⠀⠀⠘⣏⠀⢀⡿⠀⠀⣀⡤⠛⠋⠀⠀⢠⣤⣤⣴⡿⠀⠀⢐⣲⣾⣿⣷⣾⠀⠀⢠⡟⠁⠀⠀⠀⠐⢲⣿⣿⡷⠂⠀⠀⠀⠈⢧⠁
⠀⠀⠀⠈⠩⠉⠀⠀⠀⠻⠿⠀⠀⠀⠀⠘⠻⠛⠋⠀⠀⠀⠀⠀⠙⠻⠏⠉⠁⠀⠈⠻⠦⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⠟⠿⠿⢿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠉⠛⢿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⣍⡻⣿⡿⢸⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠈⠙⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣭⣴⣿⡿⢛⣛⣿⠿⠿⣿⣿⣿⣿⣶⣄⣀⠀⠀⢨⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣶⣿⣿⡏⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⣫⣥⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⢸⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣷⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠠⠀⠈⢿⣿⣿⣷⠀⠀⠙⣿⣿⣿⣿⡙⣿⣿⣿⠿⠿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠛⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⣻⣿⣿⣦⣀⣠⣿⣿⣿⡿⢃⢿⣯⣴⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠈⠀⠸⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠈⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⣿⣿⣿⣿⣿⣯⠀⠀⢀⣿⣿⠟⠉⡉⠙⠻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠿⢿⣿⡀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡇⠂⠀⢿⣿⣷⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡀⢀⣹⣿⣿⣷⣾⡀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣷⣤⣤⣶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⣀⣾⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣠⠠⠠⠄⡤⠀⠀⠀⠀⣀⢀⠀⣀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠁⠈⠀⠉⠀⣊⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣤⠍⠝⡺⠁⠀⡀⠀⠀⠀⢠⣀⣀⡤⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠰⠀⠧⠁⠰⠄⣰⢤⠰⠄⠀⠀⠀⠀⢀⣀⡆⠈⢰⢦⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠐⠣⠶⢤⡧⡘⠅⢈⠀⠀⠀⠀⠀⢀⠀⠔⠀⠼⠃
⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠁⠀⠀⠀⠀⠘⠀⠐⠒⠂⠈⠆⠀⠀⠙
⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡀⠀⠉⢁⠀⢀⣐⢶⡮⠁⠲⢄⠈⠁⠀⠀⠔⠁⢀⡄⠄
⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤⢶⢆⣀⠀⢤⠤⠀⠤⠶⡤⣀⢤⡤⢤⣦⠤⠀⠂⠐⠸⠀⠁⠀⢉⣨⠤⠤⠤⢀⠄
⠀⠀⠀⠀⠂⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⣀⠤⡄⠀⠀⠀⠀⠂⠈⠉⠀⠀⠁⣀⠀⡀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⢀⠤⠀⠄⡄⠀⢒⣀⣸⣫⢼⣉⠃⢈⠀⠀⡠⠎⠀⢥⢀⡤⠤⣄⢀⠉⡅⠏⠑⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⠡⠇⠒⠀⠀⠀⠀⠌⢨⣿⣿⡟⣳⣀⡭⢾⠑⠙⣨⠀⢸⡤⠁⠒⢉⠘⠁⠂⢨⡷⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠌⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⢤⡖⢤⠀⠁⠀⠀⠁⠘⠿⠿⠿⠟⠃⣱⣄⡀⣀⠂⠀⠰⠚⠁⠉⠀⠈⠃⢚⠠⣔⣰⢦
⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⡄⠜⠃⠈⠁⡜⠛⠉⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠐⠂⠀⠉⠀⠀⠰⠮⠀⠀⠀⠐⠺⠻⠄⠤⠤⠤⢰⡖⠰⠴⠶⠖⠋⠀⠀⠑⠅⠸⠧⠶⢦⠄⠐⠠⠴⠝⠖
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣏⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⠷⢦⣤⣤⠴⠶⠾⠟⠛⠻⠏⠉⠙⠛⠛⠳⠶⣦⣤⣤⡤⠖⠚⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⢸⡇⡄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡇⡃⠀⠀⢤⡀⠀⠀⠀⠙⠿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣷⠁⠀⡆⠀⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢹⡐⠀⢻⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡄⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣠⠎⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣠⣤⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡴⠋⠉⠉⠙⠛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⢋⣉⣉⣤⣤⣤⣤⣉⣉⡙⠛⠿⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⣁⣤⣶⠿⠟⠛⠋⠉⠉⠉⠉⠙⠛⠻⠿⣶⣤⣈⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢁⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠉⠻⢷⣦⡈⠻⣷⣄
⠀⠀⠀⠀⠀⢀⣴⡟⢁⣴⡿⠋⠀⣿⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠹⣧⠀⠀⠀⠀⠙⢿⣦⡈⢻⣧⡀
⠀⠀⠀⠀⢀⣾⠏⢠⣾⠏⠀⠀⢀⣿⣿⣷⠶⠓⣠⣤⣤⣄⠀⠀⠹⣦⣼⠋⠀⢀⣤⣤⣤⡀⠙⣿⡄⠹⣷⡀
⠀⠀⠀⠀⣾⡏⢠⣿⠃⠀⠀⢀⡿⣹⡏⠀⠀⠀⢻⣆⣀⣹⢷⣴⠾⠋⠙⠷⣦⡾⣃⣀⣼⠇⠀⠘⣿⡄⢹⣷
⠀⠀⠀⣸⡿⢀⣿⠇⠀⠀⠀⣼⢷⡟⠀⠀⠀⠀⠀⠉⠋⠙⣷⠀⢈⣀⠲⠂⠀⣾⠋⠉⠁⠀⠀⠀⠸⣿⡀⢿⣇
⠀⠀⠀⣿⡇⢸⡿⠀⠀⠀⢰⣏⣾⠃⠀⠀⠀⠀⠀⣀⣤⣤⡿⠀⣏⣍⣳⠀⠀⣿⣤⣤⡀⠀⠀⠀⠀⢿⡇⢸⣿
⠀⠀⢀⣿⠀⣿⡇⠀⠀⠀⣾⢛⡟⠀⠀⠀⠀⠀⣼⠏⠀⣱⡟⠻⢾⡍⣥⡶⠛⢷⣍⠈⢹⡆⠀⠀⠀⢸⣿⠀⣿⡀
⠀⠀⠈⣿⠀⣿⡇⠀⠀⠀⣿⣾⡇⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⣸⠇⢻⣄⠀⠀⠙⠛⠛⠁⠀⠀⠀⢸⡿⠀⣿
⠀⠀⠀⣿⡇⢸⣷⠀⠀⠀⢻⡌⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⣿
⠀⠀⠀⢹⣷⠈⣿⡆⠀⠀⢸⡟⢿⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⣾⡏
⠀⠀⠀⠀⢿⣇⠘⣿⡄⠀⠀⣿⣼⡇⠀⠀⠀⠐⣶⣼⡷⢦⣤⣤⠶⠾⠛⠛⠛⢷⣴⡟⠀⠀⠀⢠⣿⠃⣸⡿
⠀⠀⠀⠀⠈⢿⣆⠘⢿⣆⠀⢸⡇⣿⠀⠀⢘⣻⡏⢀⠰⠖⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⠃⠀⣰⡿⠃⣰⡿⠁
⠀⠀⠀⠀⠀⠈⠻⣧⡈⠻⣷⣌⠛⠛⠀⠀⠉⣹⣷⣬⣀⡐⠀⠀⣀⣀⣠⣴⠾⠋⠀⠀⣠⣾⠟⢁⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡈⠻⢷⣦⣀⠀⠀⠉⠰⠟⢹⠟⠛⠛⠉⠉⠁⠀⠀⣀⣴⡾⠟⢁⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡉⠛⠿⣶⣦⣤⣄⣀⣀⣀⣀⣠⣤⣴⣶⠿⠛⢉⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣌⣉⣉⠛⠛⠛⠛⣉⣉⣡⣤⣶⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⠿⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⡺⠭⠉⠀⠈⠉⠉⠒⠚⠭⢗⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠕⠊⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠫⣓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⠁⠀⠀⢀⢤⠀⠀⠀⠀⠂⠤⣀⠀⠀⠀⠀⠀⠈⢪⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⠁⠀⠀⠀⢠⠗⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠱⡱⡀
⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠱⣱⡀
⠀⠀⠀⠀⠀⢀⢞⠔⠁⢠⠔⠉⠉⡐⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⢣⢳
⠀⠀⠀⠀⢀⠃⠂⠀⠀⠁⡀⢨⠌⠐⠀⠀⠘⢷⣄⡀⠀⠀⠀⢀⢔⠐⠁⠀⠀⠀⠈⠉⠆⠀⠀⠀⢣⢧
⠀⠀⠀⠀⢸⠸⠀⠀⢸⠀⠈⠤⡀⠄⠀⠀⠀⠀⠙⠻⠧⠤⠖⠚⠁⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠀⠘⡸⡄
⠀⠀⠀⠀⠀⢧⢇⠀⠈⢆⠉⠂⠤⠐⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠀⠀⠀⡠⠤⠤⠤⠀⠀⠀⠀⠀⢃⢇
⠀⠀⠀⠀⠀⠈⢏⢆⠀⠈⠓⠤⠤⠔⠀⠀⠀⠀⡠⠐⠈⠀⢀⠴⠃⠀⠔⠁⠀⢀⡠⠔⠀⢀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠈⢮⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠔⠒⠉⠀⠀⠀⣄⣀⠤⠊⠁⠀⠀⠠⡠⡙⡆⠀⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠐⠁⣆⢀⠀⡘⠀⡐⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣝⢄⠀⠀⠀⠀⠠⠀⠈⠢⠀⠀⠁⠀⠁⠀⠀⠀⠀⠆⡐⠀⠂⠀⡠⢁⠔⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣗⢄⠀⠀⠐⠄⠀⠁⠀⠀⠈⠒⠚⠀⠀⠈⠪⢄⣀⠠⠄⣊⠔⡡⠎
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠳⢵⡢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⣒⡨⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⢤⣤⣆⣤⣶⠤⠭⠵⠒⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁

⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠳⣀⢀⡞⠁⠐⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠒⢷
⠀⣠⣎⠉⠑⠦⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡠⠋⠀⠁⠀⠀⠀⠀⠀⠀⠁⠦⢴⠀⠀⠀⣀⣀⡤⠴⠿⣇
⢴⠉⠉⠲⣄⠀⠈⠐⢄⡀⠀⢀⠔⠁⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠘⡶⠚⠋⠉⢀⣀⠤⠴⠛
⠀⠙⠢⡀⠀⠙⢦⣄⢀⡸⠂⠻⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠐⠒⠉
⠀⠀⠀⠀⠐⠄⡀⠈⠟⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠄⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⣭⣀⣀⣀⣤⠔⠛⠁
⣿⣟⣉⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠄⠠⠠⠤⠠⠄⠤⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠤⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡄⠘⠛⠃⠀⠈⠀⠀⠀⢀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡩⠀⠀⠀⢌⠰⣋⣀⠀⠀⠘⠀⠀⠀⠀⡟⣱⡄⣀⣀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠁⠂⠀⠀⠈⠀⠀⠀⠈⠉⣈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠀⠀⠀⠄⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠝⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⢠⡙⢧⠻⠁⠀⠀⠀⠀⠉⠉⢀⡀⠀⠀⠀⠀⠀⣾⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠂⠀⠀⠀⠀⠀⠀⣠⣦⠿⠗⠀⠀⢰⣷⣄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠉⠁⢀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠐⣒⣀⣀⣠⠀⠄⠀⠨⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠹⠏⡆⠠⠞⠉⡉⠁⠀⠈⠐⠄⢠⡄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠉⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢐⣆⣙⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣅⠀⢀⠀⠀⠀⠨⢨⡃⠀⠀⠀⡂⠢⠄⠠⠼⠄⠀⢠⠭⠴⠀⠀⠄⠀⠀⠠⠠⠤⠤⠤⠠⠄⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠒⠠⠀⠀⠠⠲⢂⣁⣃⠄⠀⠀⢡⠀⢰⡎⠗⡆⠀⠀⢠⣤⡄
⠂⠀⠤⠀⡄⠠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⡀⠀⠀⣠⣄⠘⠊⠈⠀⠀⠀⢋⠀⠸⠇⡆⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠈⠁⠉⠈⠀⠁⠈
⠀⠀⠠⠤⠠⠀⠠⠠⠠⠀⠀⠀⠂⠀⠀⠀⠠⠇⡀⣇⡇⠀⠰⢧⣽⠇⠀⠀⡀⠈⢵⠂⠀⣤⠸⠁⢠⡤⡄
⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠁⣄⢙⠌⠁⠀⠀⠀⢬⡁⠀⢀⡄⠀⠰⠅⠀⠀⠈⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⡈⠃⠐⠒⠢⢄⣀⠚⡄⢀⣰⠌⠡⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠
⠀⠀⠰⠀⠠⠀⠀⠰⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⣤⡄⠀⢘⠷⠬⠗⡀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠺⣧⠀⠀⠉⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠈⠀⠉⠉⠉⠉⠉⢀⢒⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⢆⠀⠄⠄⠀⠤⠤⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⢘⠮⢠⠠⠀⠤⠄⠠⠀⡄⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⠒⣶⡶⠂⠄⡀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠁⠀⠈⠐⠒⠒⠠⡴⠋⡴⢠⠳⣈⡄⣤⠦⡜⠳⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢁⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢋⠃⠚⠀⢋⡗⢱⠋⣥⠖⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠉⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠒⠢⠵⠒⢣⡨⢰⠘⡆⢣⣤⢫⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠦⡀⢒⠠⢤⣈⠗⢟⠀⠚⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠓⣤⠏⠊⣜⢀⡉⢠⠏⢡⣷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠨⠂⠤⢁⡈⣇⣈⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠁⠀⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠄⠀⠀⠈⠔⠠⠀⠀⠀⠀⠀⠀⠀⢃⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⡸⠜⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠐⠦⡂⠄⢠⡄⠠⠀⣄⠠⢠⠀⢀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠄⢀⣀⡀⣀⣀⣠⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣁⣐⣂⣤⣤⣴⣚⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠿⢶
⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⠀⠀⠀⠀⣦⣯⣥⣯⣥⣯⣥⣶⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⣾⢀⣀⡘⠃⣹⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⡏⣧⡌⣧⡆⢽⡏⣿⠀⠀⠀⠀⠀⢿⣿⣿⠆⠀⠀⠀⠀⠙⢮⣙⣁⡴⣋⠀⠀⠀⠀⠀⠀⠀⠐⠀⣤
⠀⠀⠀⢴⡧⣤⢤⡤⣤⠀⠀⠀⠀⠀⣇⣙⣃⣙⣃⣘⣃⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠁⠉⠈⠁⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉


⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⣢⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹
⠀⠀⠀⠀⠋⢽⣿⣯⠢⠄⠀⠀⠀⠀⠀⠄⢸⣿⣿⣿⠀⠀⠀⠀⠀⢀⣶⢿⣏⣿⣯⠀⠀⠀⠀⠀⠀⠀⢸⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠸⡀
⠀⠀⠀⠀⣴⠿⠿⢇⠀⠑⠀⠀⠀⠀⠀⠈⠌⢿⣿⠃⠀⠀⠀⠀⠀⠀⢿⣟⣾⣻⣾⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣶⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠛⠁


⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡰⠊⠉⢀⣭⠑⢆⠀⠀⠀⠀⢀⠔⣉⣁⡄⠉⠲⡄⠀⠀⠀⠀⡴⢫⠉⠀⠉⠓⣄⠀⠀⠀⠀⠀⢳⣝⢫⡆⠀⠀⠀⠀⠀⠀⢀⣾⣏⣀⣤⡀
⠀⠀⢸⢡⣶⡄⠘⠛⠁⠈⡆⠀⠀⠀⡞⠰⣿⣿⣷⡖⠀⢹⠀⠀⠀⢸⠀⠈⢦⢢⡴⠉⠸⡄⠀⠀⠀⠀⡀⠬⠍⢳⠀⠀⠀⠀⠀⠀⠘⠛⠉⢉⡟
⠀⠀⠘⣆⠉⠁⢴⣿⡷⣰⠃⠀⠀⠀⠹⡀⠛⠙⣿⡿⢂⡞⠀⠀⠀⠘⣄⠀⢸⡋⠀⠀⡸⠀⠀⠀⠀⠀⢑⡬⢅⡀⠀⠀⠀⠀⠀⠀⠴⣦⣴⠟⠁
⠀⠀⠀⠈⠓⠦⠤⠵⠚⠁⠀⠀⠀⠀⠀⠉⠲⠤⠤⠖⠋⠀⠀⠀⠀⠀⠈⠓⠤⠭⠔⠊⠀⠀⠀⠀⠀⠀⠚⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠶⠿⠷⠄

⠀⡁⠈⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠘⠀⢠⡀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡇⠈⠀⠀⡀⠀⠀⠀⠀⠀⠉⣽⠋⢉⣉⠓⡂⠄
⠀⠀⠀⠀⠀⠀⠀⠈⣦⣄⠀⡀⠠⠤⠀⠤⠽⢦⡄⠀⠀⠀⠀⠉⠀⡀⠀⢿⢀⡉⠤⠴⠀⠊⠀⠀⠀⣰⠇⠠⡀⠀⠀⠸⡆
⠀⠀⠀⠀⡠⠶⠁⠀⠀⢀⠔⠒⠂⠀⠐⠂⢀⣈⡽⠧⢀⠀⠠⠤⠤⠔⠀⢿⠀⠤⠀⢬⢠⡀⠀⠀⢠⣇⠀⠀⠈⠢⡀⠀⠹⡀
⠀⠀⠀⠀⡇⠒⠢⠀⡐⠁⡠⠊⠀⢀⠀⠀⠈⠀⠀⠀⠀⡠⠴⡓⠢⠀⠠⣼⣎⣀⡈⢁⣰⣀⠀⣠⡇⠸⡄⠀⠀⠀⢀⢴⢦⣥⣄⣀⣀
⠀⠀⠀⠀⢰⡀⠀⠀⢃⠰⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠰⢡⡆⠠⠃⠀⣠⠞⠉⠀⠀⠉⢣⡂⢱⠙⡤⡀⢣⠀⠀⠀⠸⠀⠀⠁⠀⠀⠉⠉⠉⠉⠓⠒⠐
⠀⠀⠀⠀⢸⠇⠀⠀⠈⠀⠂⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣾⡏⠀⠀⣠⣬⠀⠀⣷⢸⠀⡆⡢⠈⠀⠀⢀⠐
⠀⠀⠀⠀⠘⠀⠀⠀⠀⢂⠀⠀⠀⠀⠈⠑⠂⠀⠀⠂⡰⠂⠀⠈⢠⣿⡇⠀⢘⠀⠀⡷⢠⡏⢀⠀⠁⠀⠁⠀⠀⢀⢶⠲⣄
⠀⠀⠀⠀⡆⠀⠀⠀⠀⢸⠀⡾⠀⠀⠀⣀⣀⠀⠀⢀⠇⠀⠀⠀⠡⢹⣷⠀⠈⠓⠉⣰⠋⡄⠸⠄⠄⠂⠀⠀⠀⠘⠈⢦⡘⣧⣤⣀⡀
⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⠀⠇⠀⠀⢨⢹⠀⢢⠀⠸⠀⠀⠀⠀⠀⠀⢉⠓⠦⠤⠔⠙⠈⠂⠀⠀⠉⠀⠀⠀⠀⠀⢀⣈⠛⢈⠉⠁⠉⠉⠉⠛⠒⠒⠒⠤⠄
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠘⠀⠚⠛⣠⡌⠃⢶⣀⠆⠀⠇⠀⠀⠀⠀⠀⠀⠈⠁⠢⢄⣀⠀⠀⠀⢀⣔⢲⠀⠀⢀⠞⠈⠙⢶⠈⡄
⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡄⣠⠀⠅⢀⣠⡄⢀⠀⢀⠀⣄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⡀⢨⣇⢊⡃⢀⠀⠀⠀⡈⠀⢷⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⡄⡈⠀⠀⠀⠴⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠘⠀⠉⠛⠁⢸⢀⠀⠰⣦⠷⡞⠛⠓⠒⠲⠦⠤⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠣⡀⠀⠀⢰⠀⢯⡀⠀⡈⢠⠀⢄⠁⣬⠘⡇⠀⠀⠀⢿⠀⠀⠀⠀⣀⣀⡀⠒⠈⠀⣁⣘⣀⢀⠻⠗⠠⠤⠆⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠢⡀⣈⠀⠀⠡⠶⠃⣄⡆⠾⠂⠁⠀⠀⠀⠠⠀⢾⠒⢁⠀⠀⠀⠈⠩⠭⠉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⣄⠀⠁⠀⠒⠿⠒⠀⠐⣀⠀⠀⠐⠂⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠦⠀⠒⡲⠶⣲⠒⡳⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠺⣻⡤⠉⣁⠀⠠⠬⠏⡘⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⡉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⡥⠗⠀⡀⣀⣀⢀⣀⡀⢀⡖⠀⠀⠠⠄⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⡿⠛⠛⠻⣿⣿⣷⡄⠀⠀⠀⠀⢀⠀⠂⣖⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢐⠀⠀⠀⠐⠻⣿⣷⣤⣤⣴⣿⣿⡿⠇⡇⠀⠀⢦⠁⠀⠀⠘⢀⢙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⠀⠀⠀⠀⡀⠈⠋⠉⠙⠉⠙⠋⢀⠼⠃⠀⠀⠀⢀⣧⡄⠄⠀⠀⢁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠓⠀⠀⠀⠈⠀⠀⠀⠀⡂⠀⣠⠂⢀⡠⠖⢀⠷⢦⡄⡈⠂
⠀⠀⠀⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠁⠲⣏⠁⠈⡀⠀⡈⡑⠈⠉⠆
⠀⠀⠀⠰⠀⠀⠀⢀⠀⠀⠁⢄⠀⢷⡀⠀⠀⠠⢔⡇⠀⠠⠀⠀⠀⠀⠠⠀⠀⠈⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠪⢁⡀⠀⠀⠊⠁⡀⠄⠈⠀⠄⠁⠄
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠐⠶⣄⠀⠀⠀⠀⠀⣀
⠠⣤⣄⣙⣲⣄⡘⠛⠲⠦⣄⠀⠁⠀⠐⢀⠤⠀⠀⢀⡀
⠀⠀⠉⠻⢿⣻⣿⣿⣿⣶⣾⣷⣤⣤⣤⣼⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠈⠙⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣽⣷⣤⡀⠀⠀⠀⠈⠀⣀⣐⣀⣀⣀⠐⠂⠀⢹⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣭⣿⣧⣤⣬⣽⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⢰⡖⣒⡶⠚⡁⠀⠀⠉⠉⠛⢿⡛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⡛⠋⠉⢻⣏⣹⣿⣿⣯⣭⣭⠛⠛⢻⠟⠓⢲⣶⣯⣿⡟⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡆
⠀⠀⠀⠀⠰⠀⠰⣽⣿⣧⣿⣉⣿⢻⣛⣛⣲⢲⣿⠷⠶⠾⢯⠭⣭⣻⢷⣤⣀⣉⠀⢶⣄⢒⣬⣉⡻⠟⠻⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣧⡄⠀⠙⠿⣿⣿⣿⣶⡛⠛⠻⢿⣿⣿⣿⣷⣀⣀⡉⠉⠀⠀⠛⠈⠍⠉⠙⣛⣋⡻⣿⢿⣇⣀⡈⠉⠁⠀⠀⠌⠹⡉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠿⠿⠤⢤⣤⣤⣝⣿⣿⣿⣻⡦⠉⠉⠈⠀⠉⠉⠢⣭⣭⡛⢷⠆⠤⠤⢤⠄⠻⡀⠈⠉⠘⠃⠀⠈⠹⡋⠒⠒⠂⠀⠈⠒⢄
⢀⡐⢉⠞⣡⠞⡡⢜⣿⣇⣘⣿⣿⣿⡿⠻⡗⠀⠀⠛⠒⠂⠀⠀⠘⣿⡢⣤⣄⣀⣤⣄⣬⣠⣧⠈⣾⣤⣀⣴⣤⣤⣀⣀⠀⠐⠀⠀⠀⠀⠁
⢸⣿⣷⣎⡐⠉⠶⣁⠞⡡⠟⡹⢿⣏⣛⣛⡛⠒⢦⣀⠄⠀⠀⠀⠤⢿⡇⡔⠀⡄⠀⠈⠁⠹⡇⠄⠠⠈⠃⢸⣾⣯⣽⣦⣉⠱⡓⠒⠂⢀⠇
⢸⣿⣿⣿⣿⣷⣴⢡⠚⠠⢋⠴⣛⠟⣻⢟⡳⢖⡶⢶⠶⣦⠤⣄⠤⣄⣀⣀⣀⣀⠀⠤⠶⢦⣤⡿⣧⡼⢤⣬⣇⣈⡛⣿⣿⣷⣬⡐⠒⠁
⢸⣿⣿⣿⣿⣿⣿⣿⣾⣤⣁⠊⠱⠋⠴⢉⠾⠡⠎⡱⠎⠰⢋⠴⢋⠤⢒⠭⠓⣏⡯⡛⣟⡲⡶⣖⣦⣼⣿⣍⣀⣀⠉⠉⣿⠿⣿⠧⠀⡀
⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣤⣴⣤⣦⣤⣦⣤⣤⣴⣤⣼⣄⣤⣀⣄⣀⡐⠈⠀⠑⡈⠭⠲⡪⡴⣫⠕⢟⡻⣻⠿⡶⢶⣤⣤⡄
⠣⢎⡝⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣆⣠⡁⢀⠊⠠⠊⠵⢞⠡⠚⡔⣣⠎⡽⢺⢰⠀⠂
⠀⠀⠙⠃⢎⡜⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣧⣴⣤⣤⣀⡄⢀⡀⣈⠀⡁⢀⣀⣦⣆
⠀⠀⠀⠀⠀⠀⠚⢴⢉⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠠⣁⠛⠙⠛⠛⠋⠛⠛⠟⠛⠛⠙⠋⠛⠛⠟⠻⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠚⠠⠀⠄⠀⠙⠛⠻⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠐⠀⠜⠀⢱⠈⠹⠛⠿⠿⠛⠿⢟⠿⢟⠿⠟⠹⠛⢠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠛⠀⠘⠀⠐⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⠟⠿⠿⢿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠉⠛⢿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⣍⡻⣿⡿⢸⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠈⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣭⣴⣿⡿⢛⣛⣿⠿⠿⣿⣿⣿⣿⣶⣄⣀⠀⠀⢨⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣶⣿⣿⡏⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⣫⣥⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⢸⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣷⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠠⠀⠈⢿⣿⣿⣷⠀⠀⠙⣿⣿⣿⣿⡙⣿⣿⣿⠿⠿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠛⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⣻⣿⣿⣦⣀⣠⣿⣿⣿⡿⢃⢿⣯⣴⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠈⠀⠸⣿⣿⣿⣿⣿⣿⣧⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠈⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣯⠀⠀⢀⣿⣿⠟⠉⡉⠙⠻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠿⢿⣿⡀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡇⠂⠀⣿⣿⣷⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡀⢀⣹⣿⣿⣷⣶⡀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣷⣤⣤⣶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⣀⣼⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢀⠀⣀⠂⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠙⢿⢟⡉⠀⠀⠐⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠈⡀⠀⠀⠀⠀⠉⠉⣦⠈⢜⣠⢴⠾⠃⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠒⠀⠀⠀⠀⠐⣌⣩⣾⣿⠶⡗⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠘⠟⣻⡔⡈⠉⡀⢐⠅⣟⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⠀⣸⡂⣿⣽⠒⠀⠀⢀⡄⠈⢉⡀⠀⠀⠀⠀⡀⠀⠀⠸⡿⢧⠀⠂⣪⠴⢶⣿⠋⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡂⢻⡇⠀⠀⠁⡤⠀⠀⠀⢤⠀⠁⠀⠀⠰⡤⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠃⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠈⠊⠀⢸
⠀⠀⠀⣶⡄⠀⠈⠁⠀⠄⠀⣴⣭⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡟⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢀⣀⣀⣔⣦
⠀⠀⠀⣿⣷⠀⠀⠀⠀⢡⣴⠟⠋⠏⠀⠀⠀⠟⢀⡀⡀⠀⠀⠀⣎⠈⠛⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣿⣿⡿
⠀⠀⠀⣿⣿⠀⠀⠀⢠⣿⠉⠀⠀⠀⠀⠀⠐⠀⠹⠗⠁⠀⠀⠐⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡄⠀⠀⡆⠀⠀⠐⠀⣰⠁⠉⣹⣄
⠀⠀⠀⣿⣿⡄⠀⠀⠈⠳⠦⠞⠁⠀⠈⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⣾⣿⣆⠀⠀⢉⣱⣄⡾⣱⠋
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢀⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⡏⠀⠀⠰⣛⡻⢰⡇⢀
⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠰⠆⢙⠋⠀⣀⣤⣈⣧⣤⣤⣄⣠⠇⠀⣾⣶⡣⠀⣼
⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢹⡆⢀⡔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠹⢄⣸⣛⡀⠛⠻⣿⡿⢿⠇⠀⠨⣿⣿⣧⣰⠃
⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⢣⡞⠀⠶⠔⢓⡀⠀⠀⠀⠀⠀⠀⠀⢤⠁⠀⠀⡀⠈⠋⠃⠨⣤⣁⣤⣬⣷⣷⣾⣿⣿⣿⡿⢼⣦
⠀⠀⠀⠚⣿⣿⣿⣿⣷⣰⣄⠀⣠⣦⣾⡄⠀⣸⣿⡿⡇⢀⡀⣀⣿⠇⠀⠀⠀⢀⣰⣾⣶⡄⢀⡀⠀⡴⠀⠀⠀⠀⢻⡟⠛⠛⢿⠿⡿⠟⠛⢋⡡⠲⠋
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⣡⠍⠄⠀⣿⣿⠁⣁⠘⠛⢛⣿⣯⢀⠀⡔⡍⠁⠀⠙⠇⠀⣣⡖⠃⠀⠀⠀⠀⣾⡇⠀⠀⢴⣦⡄⠙⠒⠁⠠⠂⠀⣀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠟⢻⣆⣸⡟⣿⡇⠀⣸⣿⠿⠋⠉⠈⠈⢻⣿⠀⠀⠀⠀⡀⢸⣿⣷⣿⣶⣦⠀⠀⣿⣧⡰⣶⡼⠷⠀⠀⠀⠀⣴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠛⣭⣿⣿⣿⠻⠟⣾⣿⣯⣤⡿⠀⠉⠙⣿⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⣄⡇⠀⡀⣿⡽⡿⠧⠘⣶⣿⣿⣿⠿⣿⣧⡀⠀⠀⢰⠋⠀⣀⠊
⠀⠀⠀⠀⠀⠀⠀⣻⣿⡟⠉⠀⠀⠀⠙⣿⣿⡇⢠⡀⠀⡿⠀⠀⠀⠀⠀⠸⣿⣿⡿⠟⠋⡇⠀⣿⠿⠀⠱⣤⡤⢋⣉⣛⣀⠀⠻⠙⠧⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⢦⡀⠀⠰⢐⣿⣿⡇⢸⣿⣾⠁⠀⠀⠀⠀⠀⠀⢸⠉⠐⠋⠁⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠷⠀⠋⠉⠓⠲⠶⢶⣶⠾⠟⠋⠀⠂⠀⠀⠀⠚⠛⠛⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⠰⠤⠴⠶⠦⣶⠷⠰⡁⢴⠸⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣤⠴⠖⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠋⠁⠀⠀⠀⢀⣤⡀⠀⠀⣀⡤⢶⠖⣦⢤⣀⠀⠀⠀⠙⠿⢶⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⣀⠀⠀⠀⠀⣀⣰⠋⠀⢻⠀⠸⣇⢣⠘⣄⢻⡜⣃⠿⣆⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠈⢸⠩⡏⣹⠗⣤⡀⠙⣧⠀⠀⢸⠀⠀⠈⠙⠓⠿⠼⠧⠿⠴⠋⣀⠀⠀⠀⠘⢿⡇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠕⠀⠀⠀⠈⢿⣁⡷⢸⣁⡿⣄⠙⢦⣤⡞⠀⢠⡞⠉⠙⣦⠀⠀⠀⣠⣼⠋⠀⠀⣤⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢀⡀⠀⠀⠀⠀⠙⠲⣟⣸⠲⢿⠀⠀⠀⠀⠀⠈⠣⣤⡴⠋⠀⠀⢸⣿⡟⠀⠀⢠⠋⠀⣀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢁⡞⠉⠉⣧⠀⠀⠶⣄⢀⣀⡉⠛⠋⠘⠷⠀⠀⠀⠀⠀⠀⠀⡤⠒⡄⠸⡉⠇⠀⠀⣌⣰⢦⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠈⠳⢤⠴⠋⠀⡠⢤⣊⠽⢼⣃⠡⣟⣒⣳⡭⣀⣢⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⡐⡼⡹⡧⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢄⡀⠀⠀⠀⠘⡳⢼⡯⡿⠗⣁⣬⣥⣥⣬⣈⠢⢕⡆⠀⠀⠀⠀⠙⠛⠀⢀⣀⣮⣿⣾⣽⠃⢸⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣔⡴⠡⠾⡀⠀⠀⠐⢶⢏⢌⡴⠋⠁⠀⠀⣀⣤⣌⠙⢦⡀⠀⠀⠀⠀⠀⠀⢠⡗⣲⡿⠟⡹⠁⢨⡟
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⣿⣿⡗⠉⠀⠀⠀⠀⠑⠊⡾⠁⠀⠀⠀⢰⣏⠀⣸⡇⠈⣷⠀⠀⠀⠛⠇⠀⠙⠉⠑⠒⠈⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⡗⢃⡴⠲⣄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠛⠛⠉⠻⢿⡆⠀⠀⠀⠀⣠⠖⠲⡄⠀⠀⢤⡞⢁
⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⢸⣋⡒⣋⣧⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⣾⠀⠀⠀⢠⢾⣉⣣⣙⡇⠀⢠⡟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠸⣭⡼⢉⡼⡇⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⣩⡿⠁⠀⠀⢰⡛⠦⠰⢤⡽⠣⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⢳⡴⠂⡴⢻⠀⢀⠀⠀⠈⠛⠶⠶⠶⠖⠛⡙⢶⠄⠀⠀⣿⢹⣂⡳⢞⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⢠⡟⠻⠵⠏⠀⠀⠤⢊⡐⠠⠌⠀⠒⠬⢀⠀⣀⣀⠀⠀⠈⠉⠉⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣆⡀⠀⠀⠀⠀⠀⣤⠟⠟⠒⡀⠐⠩⠀⢠⡞⠉⠉⢳⠀⠀⠠⣲⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠴⢯⣄⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⠶⠶⠶⠶⣾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠀⠀⠀⠀⡀⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡗⠋⠁⠀⠀⠀⠉⠏⠿⠋⠀⠀⢀⡄⢀⠄⠀⠐⢩⡅⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠬⠁⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠘⠣⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⡢⠊⠑⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠤⠀⠀⠀⠀⠀⠰⣇⡛⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⠀⠀⠀⡿⠽⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠾⠁⠈⠀⠀⠠⠀⠀⠀⠀⠀⠿⣿⣳⡄⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⡅⠀⠀⣠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠉⠀⠀⠀⠀⠀⡆⠀⣨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠗⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠘⠀⠀⠀⠸⠀⡀⠀⠀⢀⠀⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⢠⠀⡄⠀⠀⠀⠙⠠⠄⠀⠀⠂⠄⠒⠈⠁⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢸⠁⠀⠀⠀⠔⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠄⠁⠀⠀⠐⠷⠜⣿⡧⠾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠈⠀⣐⢀⠏⠀⠐⣴⠀⠴⠁⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⠀⠀⣰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠠⠄⠐⠡⠀⠀⢀⠂⠈⠈⠀⠒⢚⡟⢧⠀⠀⠀⠀⠀⠀⡠⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⢢⢀⠘⠲⠼⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⠜⠀⠀⠂⢀⠔⠁⡙⢱⣿⠀⠠⠀⠀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⢀⡐⢸⣿⠆⣄⣠⣶⡄
⠀⠀⠀⡀⠀⢄⡠⢄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⠀⢀⠔⠁⠀⠈⢉⣸⡗⠀⠠⠀⠠⠌⠀⠀⠀⠃⠀⠀⠀⠀⠼⠋⢯⣅⠊⠁⠀⠜⠛⠋⠙⠂
⠀⠀⠀⠀⢀⣴⡗⠀⡀⠀⠀⠀⠦⠙⠃⠀⠀⠀⠈⠠⠔⠀⠀⠠⠁⠀⢠⠙⠁⠀⠀⠀⢠⠀⠀⠀⣘⠂⠀⠀⠀⠀⠀⠀⠀⠚⠑
⠀⠀⠀⠀⠘⠁⠀⠀⠳⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⣞⠃⠀⠀⠈⠀⠀⠀⠀⠀⢀⠴⠟⠳⣦⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢦⠀⠀⣿⠀⠐⠺⠷⠶⠄⠀⢰⣀⡀⢀⣤⠀⠀⠀⠀⠀⠀⠖⠂⣠⠉⠀⠀⠀⠀⢶⣾⡿⣷⠆⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢤⡀⠐⠂⠓⠚⠓⠒⠀⠈⠝⠃⠈⠋⠀⠀⠀⠀⠀⠀⠆⢠⠇⠀⢀⠀⠀⠀⢺⣿⠆⠀⠸⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⡘⠛⠸⠉⠋⢋⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠿⠋⠀⣴⠄⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⣃⠈⡳⠤⠈⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣐⣿⡟⢤⡇⢀⠀⠤⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶⣾⡟⠉⠀⢺⡀⠉⢀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣼⣿⠟⠉⠀⠀⠀⠀⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⣬⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠛⠉⠛⠐⠂

⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠉⠓⠂⣼⡏⠘⠋⠀⠁⠈⡁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⠀⠔⠀⣀⠀⢁⠈⠁⠈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣤⣐⣮⠁⢸⣚⣿⠴⠒⠀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣄⠙⢦⠐⣃⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣿⣆⣉⣳⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⢿⢧⡼⠿⠶⠆⠀⡠⣄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠆⠀⠀⠐⠤⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠿⠱⢧


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⠉⢉⠉⠉⠉⠉⢉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⣉⡄⠀⠀⠀⠀⠀⠀⠠⠞⠋⠸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠘⠀⠂⠐⠂


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⢠⠐⢴⠖⡄⣇⠔⣄⡔⡄⢢⡴⢢⢸⣠⠲⡤⡖⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠒⠈⠀⠃⠉⠒⠁⠁⠑⠊⠟⠊⠘⠈⠚⠁⠒⠁
⢀⡴⠒⠒⠶⠤⠤⠶⠖⠒⠒⠒⢋⣶⠋
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢸
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⢀⠀⣀⢠⠀⣀⢀⠀⡀⣀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⡟⠒⠒⠒⠒⠒⠒⠒⠂⠸⠁⠇⢇⡼⠨⡠⠸⠸⡨⠹⢄⠇⢅⠆
⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠶⠤⠦⠤⠤⠴⠧⠤⠤⠤⠤⠤⠤⠤⠄⠘⣦⠣⡊⡇⣎⢑⢐⢸⢰⠉⡆⡣⡏⡆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⠉⠀⠉⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⡀⡀⡤⢀⢄⢠⡤⡀⡆⡠⣄⢀⠤⢀⣤⡤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠉⠉⠉⠉⠉⠉⠉⠉⠁⠘⠤⠂⡹⠁⠃⠱⠴⢸⠤⠋⠇⠣⠼⠨⠵⠚⠀⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⢧⣀⣠⣠⠤⠤⠴⠒⠒⠒⠒⠒⠚⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠤⠄⢰⠂⢢⠆⠆⣿⠀⠀⢦⣤⢶⠒⡆⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠔⠒⠒⠒⠒⠒⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡑⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠈⠀⢀⠀⠀⠀⠀⠀⣀⣤⣠⣀⡀⠀⠀⠀⠀⠠⠉⠓⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⣆⣥⣍⠹⢲⣀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠺⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⡑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡙⢆
⠀⠀⠀⠀⠀⢠⠞⡀⠀⠀⠀⠀⠀⠀⠔⠡⠤⠀⠂⣁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢳⡀
⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠡⠀⠐⢂⠐⠀⡁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢳
⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠠⡀⠈⣤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠤⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⢇
⠀⠀⠀⡏⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⡁⡐⢦⣡⢈⣵⣀⢋⢂⡀⢰⢎⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⣀⡜⠅⠉⡬⠹⠘⡀⢅⡈⢼⡀⠐⠄⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆
⠀⠀⢸⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠐⡌⠙⠂⣊⣡⡟⢭⡟⡃⡪⣘⠡⠁⢁⣒⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡇
⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣆⢔⣢⠉⡝⠈⢩⠈⡓⣰⢶⣅⠈⡎⠠⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⡇⠀⠀⠀⢬⠰⠠⡂⠀⠀⠀⠠⠋⠡⠚⢠⢫⠇⢾⢀⠣⢎⣒⣢⡔⠐⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸
⠀⠀⠀⢹⠈⠀⠀⢊⠰⠚⠀⠀⠀⠀⠀⠁⢈⠚⡠⡠⢅⣣⢎⠶⠈⢗⢀⠔⡃⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠄⣂⠊⢋⠀⠎⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠠⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣡⢃⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⢁⠘⠉⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠗⢵⠎⠂⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⡨⢅⠏⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠄⠀⠀⠀⣞⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⠃⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠙⡏⡇⠗⡤⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠈⠥⣅⣸⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣊⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣈⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⣐⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⣀⡀⠂⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⣂⣈⡤⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⣀⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢩⣧⣸⣍⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢿⣠⣋⡠⠞⢀
⠀⠀⠀⠀⠀⠐⠒⠢⣄⠔⠉⢻⣅⢀⡟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⠎⡥⢬⠳⣖⣋⡤⠂⡄
⠀⠀⠀⠀⣀⣀⣀⣴⣁⢀⡤⠊⠈⣻⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⣏⢹⣫⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⡼⣆⠓⠚⡠⢬⡙⠲⣏⣡⠴
⠀⠀⠀⠘⠉⠀⠙⣆⠉⢹⡁⢠⡞⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡯⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢀⡞⢳⢤⡙⠚⢡⠶⡌⢧⠤⠴
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⡟⠁⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⡟⢻⡳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠞⢰⠏⣳⣜⠚⣡⠾⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⠀⠀⣷⠀⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠇⠸⡍⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⡄⠀⠀⣀⣀
⠀⠀⠀⠀⠀⡤⢤⠀⠀⠳⡞⠀⠀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⣇⣀⣸⣇⡼⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠲⢤⣀⣠⠖⠉⠉⢢
⠀⠀⠀⠀⠀⠓⠺⣤⠴⠚⠓⠦⣤⠓⠚⠀⠀⠀⠀⠀⠀⠀⢀⡴⠦⣀⡴⠋⠉⢀⣤⡉⠳⣤⠞⠁⢹⡆⠀⠀⠀⠀⠀⠀⢧⡀⠒⠀⣠⢤⡀⠘⠃⢰⠃
⠀⠀⠀⣠⢤⡀⣰⠃⠰⣄⠸⠆⠘⣆⢀⡤⣄⠀⠀⠀⠀⠀⠈⠓⠒⣾⠁⢀⡀⠹⠤⠇⠀⢸⡖⠒⠚⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠈⠛⠀⢀⡀⠈⠣⢄⡀
⠀⠀⠀⠑⠚⠉⠹⡄⠠⠎⢱⠄⢠⠏⠉⠳⠋⠀⠀⠀⠀⠀⠀⣠⠤⢾⠀⠻⠽⠀⡖⢢⠀⢸⠧⠤⣄⠀⠀⠀⠀⠀⠀⣾⠁⠸⣭⠆⠈⠁⠀⢇⡼⠂⠤⠀⢱
⠀⠀⠀⠀⠀⡤⣤⠛⠲⢤⡤⠖⠛⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡴⠳⣄⡀⠀⠉⣁⣴⠋⠑⠦⠞⠀⠀⠀⠀⠀⠀⠈⠒⠖⠒⢄⠀⢠⠀⠀⣠⠤⠤⠖⠃
⠀⠀⠀⠀⠀⠳⠚⠀⠀⡴⢧⠀⠀⠓⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢹⠉⢉⡇⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠛⠀⠀⠳⠤⠞


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣮⢟⡻⣥⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣀⡁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⠓⠊⠑⠚⢧⢤
⠀⠀⠀⠀⠀⠀⠀⢤⣳⢞⡁⠘⠋⠈⠻⣞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡭⡍⢳⠀⠀⠀⢀⠤⡄⠀⠀⠀⠀⠀⠀⠠⡞⠁⡤⠂⠀⣞⠛⢦⡈⢓⡆
⠀⠀⠀⠀⢀⡐⣬⠟⠁⠻⠏⠸⠿⣠⢞⠳⠀⠀⠀⠀⠀⠀⢠⠞⣩⡉⢦⢳⡘⠦⣼⠾⠁⠀⢀⠞⣰⠃⠀⠀⠀⠀⠀⠀⢯⠁⠀⠀⠠⣄⠈⠱⣄⡱⠀⣹⠂
⠀⠀⠀⠀⠠⠽⣇⠿⠇⠸⡷⣠⡾⡍⠂⠀⠀⠀⠀⠀⠀⠀⠘⢆⡑⣷⠸⣍⣉⡓⠺⠦⠖⢚⣡⠔⠁⠀⠀⠀⠀⠀⠀⠐⢧⠀⣏⣹⠆⠀⠀⢀⣈⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠈⡝⣳⣄⣠⢞⠣⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡙⠒⣋⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠈⠁⠀⡔⠀⠘⠾⠁⢴⠛
⠀⠀⠀⢀⣤⡤⠇⠁⠊⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡦⢤⣀⣄⣠⢤⠏⠉
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁

⣀⣀⣀⠀⡀⢀⢀⠀⠀⠀⡀⡀⢀⠀⡀⣀⣀⠀⣀⡀⢀⣀⡀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀
⣿⣿⣿⣿⣿⡏⠍⠋⢻⣿⠋⢻⠉⠿⢩⡉⣽⡟⢩⣙⠋⠭⡏⢻⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣧⣾⣧⣬⣥⣴⣬⣤⣦⣼⣤⣿⣷⣌⣥⣤⣭⣧⣬⣧⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣀⢀⠠⠤⠄⠐⠒⠒⠊⠉⠉⠁⠀⠀⠈⠉⢉⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡞⠉⠀⠀⢀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⠈⠐⠀⠀⠀⢠⣢⠀⢰⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠠⣝⠆⠀⠀⢸⣿⣆⠀⠀⠀⣂⣬⡦⠈⠙⠤⠒⠂⠄⠀⠀⠀⠀⠀⢸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠆⠉⠀⠀⠀⠀⢻⠿⠀⠀⢈⣍⢋⠔⠁⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⣿⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⠀⢠⠖⠀⠀⠀⠋⠀⠀⠀⠀⡜⣁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡆⢞⠉⠀⠀⠀⠀⠀⠀⠀⠂⢔⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⢼⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡱⢸⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡇⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⢀⠄⠠⡆⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠒⠒⢒⠁⡾⠋⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣧⠠⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣿⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠀⢸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠄⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠅⠀⣴⣜⡀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡞⠀⠀⠱⢘⠣⠁⠀⠀⠛⠋⠀⢊⣉⠆⠀⠀⠀⠀⠠⠹⠀⣸⣿⡇⠀⠀⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠤⠶⠶⠶⠶⠒⠒⠶⠶⠶⠦⠤⠤⣤⣀⣀⠀⠙⠛⠀⠀⢠⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠉⠙⣛⡛⠛⠉⣀⡄

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







⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠤
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠤⠤⠤⠤⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠤⣀
⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠱⣄
⠀⠀⠀⡜⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⡐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⢆
⠀⠀⢰⠃⠀⠄⠀⠀⠀⠒⠠⢽⣷⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⢸⡆⠀⠄⠀⠀⠀⠀⠀⠀⠈⠣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣇
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠋⠀⡏
⠀⠀⠀⠈⢧⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠑⢄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣀⣀⡀⠀⠐⠀⠀⠀⠀⠀⢀⣀⣀⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡙⢦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⢁⣀⣈⣭⣭⣙⣛⣛⣛⣓⠲⠦⢤⣄⣀⣀⣤⢆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⣡⣤⠶⠚⠋⠉⠉⠈⠁⠀⠀⠀⠉⠉⠛⠻⢶⣤⣉⠉⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⢉⣤⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣙⠻⠿⠛⣉⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣡⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣎⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡟⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡌⢧
⠀⠀⠀⠀⠀⠀⢀⣿⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡘⣇
⠀⠀⠀⠀⠀⠀⣼⢃⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢹⡆
⠀⠀⠀⠀⠀⣸⠃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢻⡀
⠀⠀⠀⠀⢰⠇⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⣧
⠀⠀⠀⢀⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡘⣧⡀
⠀⠀⠀⡼⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠛⠦
⠀⠀⢰⢷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⠞⠛
⠀⢠⡟⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠛⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢀⣼⠃
⠰⠛⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢠⣦⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢃⡼⠃
⠛⠻⣦⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣼⠁
⠀⠀⢹⡇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢏⡾⠃
⠀⠀⠀⢿⡘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠸⣿⣿⣛⣿⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⡾⠁
⠀⠀⠀⠘⣧⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠙⠿⠟⠋⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡟
⠀⠀⠀⠀⠸⡆⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣱⠏
⠀⠀⠀⠀⠀⢻⡄⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣼⠋
⠀⠀⠀⠀⠀⠀⢻⡄⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣄⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠶⠟⢡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠙⠷⠶⢤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠶⠖⣛⣛⣉⣩⣭⡤⠶⢦⣼⣇⠀⠀⠀⠄⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃⣴⠞⠓⠲⠶⠶⠶⠶⠶⠖⠒⠚⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠙
⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣴⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⢠⡄⢤⣤⢤⣤⡄⣤⣤⢠⣄⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣿⣇⣾⣿⣿⣿⣇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢸⣿⠀⠀⠀⠀⠀⢠⣤⣤⣤⣬⠀⠀⠤
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⣽⣿⣿⣿⡏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠄⣿⡇⢸⣿⠀⠀⠀⠀⠀⢸⡏⠉⠉⣿⠀⠀⠀⠀⠀⡄⠀⠠
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣗⣿⡿⠀⠀⠀⠀⠀⠀⢰⡆⠈⣿⠀⢻⠇⠘⡟⠀⠀⠀⠀⠀⢸⣿⣶⣶⣿⣠⣾⣿⣷⣄⣿⣿⡧
⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠉⠀⠈⠀⠀⠉⠈⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠉⠉⠉⠁⠈⠉⠁
⠀⠀⠀⠀⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡡
⠀⠀⠀⠀⠀⠀⢠⡿⣟⠽⠋⢹⣿⣿⣿⠟⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣶⡂
⠀⠀⠀⠀⠀⢀⡿⢊⠁⠀⢀⣿⣿⣿⠃⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⢀⡤⠒⠒⣀⠒⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠁⠐⠻⠃
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⡿⠀⠀⠀⠀⠀⠀⣼⣴⣿⣿⣿⣿⣷⣼⡆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣥⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠃⠀⠀⠀⠀⠀⢰⡿⣛⠿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠁
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠸⣇⡁⢰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⡷
⠀⠀⠀⠀⠻⠥⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠈⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣤⢠⣀⡄⣀⣠⢀⡀⡄⡀⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠰⠇⠎⠼⠰⠡⠆⠮⠠⠠⠠⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣴⣶⣿⣶⣦
⠀⠀⠀⣰⣋⡘⣘⣁⢋⡋⣘⢁⢀⢀⠈⠀⠐⠁⠀⠀⢀⡔⠄⠠⠁⠀⠀⠀⠉⠀⠠⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⢰⠆⡴⠰⠤⠆⡶⠴⠠⠀⠄⠤⠠⣀⠁⠀⠀⠀⠈⠁⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠐⢀⠘⠀⠀⠀⢃⠰⠀⠀⣎⠁⠀⠀⠉⠑⠢⠄⠠⠄⠊⠈⠋⠑⢤⠀⠀⢀⡦⢓⠃⠛⢢⠀⠀⠀⠀⡌⠒⠂⠐⠤⢀⠀⠀⠠⢠⡀⣠⢃⠀⠄
⠀⠒⠂⠀⠀⠀⠀⠀⠂⠂⠀⠈⠑⠉⠐⠦⣀⠀⢀⣀⡤⠤⠤⠀⡠⠜⠀⠈⢴⡄⠀⠈⠀⣘⠂⠀⠀⣉⠀⠀⠀⠀⠀⠅⠀⠀⠀⡜⠃⠈⠰
⠀⠰⠐⡄⠀⠀⢀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⢀⠀⠀⡀⠀⠀⠀⠈⠒⠦⠴⠆⠋⠀⠀⠀⠈⡀⠀⠀⠀⢠⠲⠀⠀⠀⠀⠐⣞⠀⠀⠂
⠀⠀⠈⠀⠘⠀⠈⠁⠀⠀⠐⠀⠈⠡⠔⠠⠀⠀⠀⠀⠀⡈⠀⢈⠁⢑⠀⠀⠀⠀⠀⠀⣀⣠⠄⡀⠀⠀⠀⠁⠚⠉⠀⠂⠀⠀⠂⠀⠀⣹⡄
⠀⠀⠀⠠⢄⠀⠀⠁⠀⡀⠀⡂⢀⠄⠀⠁⠀⠂⢀⢀⡀⠉⠅⢀⠀⠀⡀⠀⠀⠖⠀⠐⡂⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠈⠀⡀⠁⠀⢠⠀⠀⠀⠄⠀⠒⠀⠀⠀⠐⠀⠀⠀⠀⠈⣀⠀⠐⠀⠁⠀⠀⠀⠈⠁⠞⠘⠀⠀⢳⣄⡈⠛⠲⢦⣄
⠀⠀⠄⠀⠀⠆⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⡀⣠⠠⠔⠒⠒⠄⠀⠀⠀⢀⠈⣿⠀⠀⠀⠹⡢⠀⠀⠀⠄⠀⢀⠄
⠀⢘⠀⠀⡈⠀⢀⠊⠉⠂⠀⠀⠀⢀⠰⠂⠀⡄⠀⠀⠀⠀⠀⡔⠈⠀⠀⠀⠀⠀⠀⠀⠐⠸⠀⠀⣠⠾⠀⠸⡄⠀⡿⠀⠀⠀⠀⠀⠈⠀⠈⡀
⠀⠈⡦⠂⠀⠀⡄⠀⠀⠎⠀⠀⠀⠀⠀⠀⢂⠈⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⣀⠀⠤⠐⠉⠀⠬⠋⠀⠀⠀⠀⣰⠍⠀⠀⠀⠐⠀⠀⠨⡴
⠀⠀⡁⠀⠀⠀⡀⠀⠀⠁⠀⠀⡀⠀⠀⠄⠈⠁⠀⠀⠂⠀⠄⠀⠉⠑⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠋⠉⡀⠘⠀⠀⡫⡈⠀⠀⠁
⠀⠀⠅⠀⠀⠀⠣⡀⠜⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⣶⣿⡿⢿⣷⣦⡄⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠂⠀⠘⠀⠤⠀⡀⠀⠀⣰⡿⡟⡉⠉⠩⠉⡉⢏⠁⣀⣛⡛⢷⣄⠌⣻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠃⠀⠀⡴⠚⢢⠄⠈⠁⠀⢰⣿⠀⠃⣧⢠⡀⣌⣙⣌⣃⣸⣍⣁⣴⣿⣿⢿⠁⠹⣷⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠀⢀
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠤⠀⠀⠱⠦⠴⠁⠈⠂⠀⢸⣿⣦⣼⡿⠻⣿⠋⣙⣯⡉⣽⠉⠤⠧⠐⢀⡄⠇⣆⣿⡀⠀⠀⡁⠈⠀⠌⠀⠈⠀⠈⠚
⠀⠀⡠⠤⠤⣀⠀⠀⠀⠀⠀⠐⠁⢀⡄⠀⠃⠀⠀⠈⢿⡔⣀⠧⢠⡌⠃⠻⠟⢿⡘⣇⠰⠾⢇⢀⢓⢀⣿⣿⠀⠀⠀⠐⠀⠈⠈⠃⡀⠊⣑⣂⠕
⠀⡜⠀⠀⠀⠈⡆⠀⢀⠀⡠⠀⠀⡄⠀⡀⢀⡀⠀⠀⠀⠹⠮⣤⣦⣿⡶⠷⡶⠿⡷⡿⡶⣶⣾⣿⣿⠿⠛⠁⢀⡀⡠⠤⠀⠀⠀⠒⠂
⠀⠙⣄⣀⣀⡰⠃⠀⠀⠀⠀⠐⠂⡤⠤⡀⢈⡀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⢍⣰⠡⣄⢀⠀⠀⠀⠀⢀
⠀⢀⣀⡀⠀⣀⠤⠠⠤⡀⠋⠀⠈⠧⡄⠞⠀⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠀⠀⠐⣶⣄⡽⠞⠋⠉⠁⠀⠀⠀⠀⠂
⠀⢏⠀⡹⢰⠃⠀⠀⠀⠘⡄⠀⠁⢀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠄⡀⠀⠀⠀⠀⡜⠁⢹⠀⠀⠀⠈⠣⠚⠉⠀⢀⣀⣀⡀⠀⣀⠐⠀⠁
⠀⠀⠁⠀⠘⣄⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⠀⠀⣸⠀⠀⠀⠀⠈⠒⠁⠀⠀⣠⠒⣶⠶⣞⢹⣧⢎⡇⠙⠀⠀⠀⠀⠀⠀⠀⠂⠠
⠀⠘⠀⣀⠀⠈⠑⠒⠊⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠊⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠾⠃⠿⠉⠁⠀⠁⠀⠄⠀⠀⠀⢀⢀⡀
⠀⠀⢀⠀⡄⠒⢀⠆⠤⠤⠋⡄⠐⡀⠀⠀⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⡠⡪⡐⠀⠂⡕⡄
⠀⡐⠂⠔⠒⠒⠓⠐⠊⠈⠀⠂⠲⢅⡆⠀⠀⠀⣠⠤⠲⠐⣆⠀⠀⠀⠀⡠⠄⡀⠀⠀⠀⠀⠆⠀⠀⢐⠺⠀⠀⠀⠑⠐⠀⢐⠉⠀⠀⢀⠈⠀⠈
⠀⡐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⠁⠀⡰⠊⢁⣀⣠⠴⠏⠀⠀⡠⠊⠀⠀⡉⠀⠀⠠⠀⠀⠀⠀⢘⣁⠀⠀⠀⡚⠀⠀⠈⠐⢄⠀⠈⢀⢄⠌
⠀⠑⡊⢂⢆⢀⠀⠤⠀⡐⣈⠄⠡⠌⠀⢸⣠⠞⠉⠀⠀⠀⡔⠊⠁⣀⡀⠴⠊⠀⠀⠀⠤⠀⠀⠀⠀⠀⡹⠐⠒⠘⠀⠀⠀⢀⠀⠀⠀⠐⠂⠁
⠀⠈⠁⠈⠠⠰⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠉⠋⠐
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠐⠂

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠤⠄⠀⢐⣷⣀⢀⣀⠐⠂⠀⠂⠶⠶⠶⠶⣶⣦⣤⡀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠠⠀⠹⣧⠈⠀⠟⣿⢿⠟⢻⡆⠸⣷⣀⡀⢠⣥⠞⠙⣻⡏⣛⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⡸⠻⣆⢤⣤⣤⣤⠟⡀⠀⠀⢀⣟⣒⣾⣡⠞⠋⢸⡗⣾⣇⣠⣶⡛⣿⠛⠉⢻⣿⣯⠠⡀
⠀⠀⠀⠀⠀⣾⣋⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡭⠻⣥⣤⣐⣸⡟⠫⡉⠡⣹⣯⣿⣴⣾⣿⣿⣿⣷⣎⠳⡀
⠀⠀⠀⠀⠀⠉⠡⠀⢀⣀⡀⠀⡀⠀⠠⠀⠀⠀⠆⠈⢉⣤⣄⡄⠉⠉⢿⠀⠀⢸⡉⠟⣛⣻⣿⣻⣿⢛⣿⣿⣷⣼⣾⣦⣄⡀
⠀⠀⢨⡀⠀⠀⠀⣴⠏⠉⠙⣦⠀⠁⠀⠀⠀⠁⠀⠀⠘⠣⠘⠀⠀⠀⣀⢀⣥⡾⠶⢶⣯⠖⣴⠻⣟⣈⡿⣿⣿⡏⢿⣿⣿⣿⣶⡀
⠀⠀⠈⠧⣄⠀⠸⣇⠀⠀⠀⢸⡆⡴⢦⡀⠀⠀⠀⠀⣀⣀⣶⢠⣙⡢⠅⡈⢿⡁⠀⠰⡿⣤⠼⣿⣟⠉⢀⣿⣿⠃⢸⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠿⡦⠐⠿⢾⣄⣀⡾⣽⠁⠈⠳⣄⠀⢠⡞⠉⠛⣟⡛⢿⣍⣇⠆⢈⠳⡶⠶⠛⢷⡀⠠⣯⡀⡟⡹⠁⠀⢾⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠈⠙⠘⢷⣦⣜⡉⠀⢹⣦⣀⣀⡟⠀⠘⠷⢿⣄⢀⣝⣛⣻⣿⠠⣠⠀⠀⠀⠠⠻⣇⣀⡽⡷⠁⠀⠐⠠⠟⠒⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢤⣭⣈⣹⣄⡀⣦⠀⠒⠭⠉⠉⠉⢙⠀⡈⠁⠄⠀⠀⠂⠐⠂⠒⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠲⡎⠱⢠⡔⢤⡔
⣧⠍⠈⠀⠔⢲⣆⡀
⠛⠳⢄⡂⣰⠟
⠀⠀⠞⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⣀⢀⣀⣤⠀⡀⠀⢀⡀⠀⣀⢀⣄⣄⢀⡀⠀⢀⢀⣄⣠⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡿⣄⣿⢸⣧⠤⢸⡇⠀⢸⡇⠀⣿⢸⡧⠄⢸⡿⣆⣸⠀⣠⡟⠁⢠⡛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠃⠈⠟⠘⠇⠀⠘⠷⠦⠈⠳⠾⠃⠸⠷⠦⠸⠃⠈⠛⠐⠿⠶⠀⠟⠁⠙⠇
⠀⠀⠀⡀
⣰⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣢⡀
⠎⢳⣿⢲⡆⣠⠎⠀⠀⠀⠀⠀⠀⠙⠋
⠠⠈⢀⡁⢠⣿⡄⢀⡤
⠠⠄⠈⣀⠉⠉⣘⣡⠄

⡆⠠⡄⠀⠀⠴⣯⡅
⠀⠠⡄⠀⠑⢆⢀⡋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢲⠀⣄⠀⣴⣠⡿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠠⢅⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⣤⣄⣹⡰⢿⡉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⢁⡄⢤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠙⠃⠸⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⡀⣠⣜⠓⠂⠀⠀⠀⠀⠐⠶⢤⣴⢧⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠿⢹⡈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⠗
⠀⠀⠀⠀⠀⠀⠀⠠⢄⣷⣶⠾⣶⣶⠜⠀⠀⠀⠀⠀⠀⠠⣄⠈⢛⠀⢸⠃⢰⡆⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠛⠋⠁⠈⣦⡄
⠐⠾⠇⠀⠀⠀⠀⠀⠙⣹⣧⣤⣿⡛⠳⠆⠀⠀⠀⠀⣤⠀⣘⡶⠾⠛⠛⣟⠿⠃⢴⡎⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠘⠉⡿⠟⢋⠀⠀⠀⠀⠠⣄⣩⠾⠇⠘⢗⠀⠀⠉⠀⠀⠰⠞⠛⣶⡞⠉⠀⣀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⠂⠀⠈⠀⠀⣀⡀⠀⢨⡟⠘⠳⡄⠈⢀⠀⡿⠁⢀⠴⠃⠶⠟⢷⠖⠛⠁
⠀⠀⢀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⢙⣋⠀⢈⡁⠈⠳⠈⠀⠰⠂⢀⣄⠰⠶⠿⢶⡗⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⣨⣄⣠⣃⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡋⠀⡈⣁⢀⡀⠀⠷⠀⡀⠀⠀⡀⠀⠠⣴⡇⠄⠀⠀⠀⠀⠀⠀⠀⣀⢰⡭⢱⡄⠀⠀⠀⠈⠷⠘
⢻⣌⠁⠈⠀⠿⠄⡶⢀⢀⡤⠚⠁⠀⠀⠀⢠⣤⠄⢿⡴⠟⠉⠀⠀⣠⠀⠀⢁⠐⠶⡉⠳⣶⡾⠷⠄⣠⠄⠀⠀⠀⠀⠀⠈⠳⠴⠛
⡀⠙⠀⢀⡔⢀⠘⣧⠈⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⣀⣰⡆⠀⠉⠀⣤⠀⣧⠄⠀⣦⡸⠷⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄
⠀⠲⠀⠈⠀⠀⠀⠀⢤⠿⡞⠁⠀⠀⠀⠀⠀⠀⠚⠋⠀⣘⡿⢅⣠⣜⣇⠀⢀⣼⣀⠴⢾⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢹⠖⠛
⢀⠤⠀⠀⠀⠉⠛⠰⠖⢀⡷⠄⠀⢤⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠿⠉⢻⠛⡛⠙⠇⠀⠀⠻⠖⠀⠀⠀⠀⣿⢀⠤⢤⡄⢻⡁⠀⠀⠀⠀⠀⠘⢋⡰⠖
⠋⠠⠄⠸⡏⠐⣤⠔⠶⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠉⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢴⡟⠁⠀⠀⠷⠀⠀⠐⢷⣆⡀⠀⠀⠀⠈⡷⢠
⡄⠦⠀⣤⠤⠦⡁⢠⠤⡀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠃⢀⠁⠀⠀⠀⠀⠀⣠⠀⠠⢈⣡⡞⠃⠀⠈⠁
⠱⠶⢆⡻⠀⠄⠉⠲⠀⠈⠣⡤⠀⠀⢠⣄⠀⣱⣄⡄⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⠁⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠳
⠇⠀⠘⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣁⢈⡁⠶⠈⠷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⡀⠀⠈⠴
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⠓⠻⡧⠌⣠⠀⠴⠒⢴⣧⣀⠀⠀⠠⠼⠃⠀⠀⠀⠀⠘⣭⠀⠀⠴⠀⠀⠀⠰⠆⠀⠀⠈⠀⠄⡴⠀⠀⠀⠋⠓
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣶⡀⠰⠂⡰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡵⣄⠀⠀⠀⠀⠀⠀⠀⠀⣦⠔⠁⡴⢤⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠉⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠿⢧⠄⠐⡦⠀⣀⠀⢠⠿⠾
⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠠⡬⠁⠐⠈⠁⢡⡄⠀⠀⠀⠀⠀⠀⡀⠀⢠
⣰⢦⡗⢀⣸⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⣧⠸
⠉⠉⠁⠁⠩⠶⠒⢄⣰⠃⠀⠀⠀⠀⠀⣎⣷⠀⠀⠀⠀⠐⢢⡄⠀⣀⢨⡄⠈⠀⠉⠀⠙⣿⠶⣆⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠁⠘⠆
⠀⠀⢌⠁⠀⠀⠈⠙⣃⣢⠀⠀⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠸⠋⢠⡀⠁⠀⠐⡂⠀⠀⠁⠀⠉⣱⣖⠁⠀⠀⠀⠀⠀⠀⣀⡱⠀⠀⠈⠉⣻⡉⢁⡄
⠀⠀⠀⢀⠈⠋⠀⠀⡡⠙⡶⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠛⢀⠀⠀⣠⠁⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡯⣤
⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣷⣶⣶⣦⣤⣶⣤⣴⣶⣶⣶⣶⣾⣶⣤⣶⣶⣶⣶⣶⣶⣶⣴⣾⣷⣶⣷⣶⣿⣶⣶⣶⣶⣶⣦⣤⣴⣶⣶⣶⣦⣶⣿⣦⣶
⣿⣿⣿⠻⠍⠛⠟⠉⠙⠛⢻⡟⠏⣹⡿⢻⠝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠧⢲⣦⢄⠀⠀⢀⣀⣤⣤⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠁⠀⠀⣶⣤⡦⠀⠀⠀⠀⠀⠈⠻⢿⣭⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠶⢶⣒⠋⠉⠁⠉⠻⣦⣀⣀⣈⣐⢶⣄⠀⠈⠙⠻⢿⣤⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⡁⠀⣀⠀⠀⠈⢷⡄⠈⢉⡉⠉⠙⠿⣭⠁⠀⠈⢳⡄⠀⠀⠀⠈⠙⠷⢶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠻⢧⣄⠠⢄⠀⠉⠛⠁⠀⠈⣉⣀⠈⠻⣦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣼⣦⣄⢠⡴⠒⢉⡤⠄⠀⠀⠙⠳⣤⡀⠄⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⡛⠿⢷⣦⣍⡀⠀⠀⠀⣀⣠⣤⡾⠛⠚⠉⠁⠀⠀⠀⠀⠀⣀⣠⣤⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⢛⡩⠥⠞⠛⠀⠀⠀⢀⣻⣿⣧⡾⠟⠛⣩⣽⣏⣹⣦⡔⣀⣤⣤⣴⡶⣾⣛⡩⠭⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢉⠁⠂⠙⠀⠀⢠⣤⣴⣶⠶⢻⣿⣍⠁⠈⠛⠛⠛⣿⣿⣿⣿⣿⠿⣿⣏⣳⠾⣿⣿⣥⣶⣶⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠿⠷⣄⣚⡿⢷⠿⣿⣷⡶⢿⣛⡛⠫⣤⣀⡈⢉⠀⠩⠽⠛⠛⠺⠷⣦⡌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⣀⡂⣠⡀⠀⠠⠞⠚⠛⠓⠾⠻⣷⣯⣍⣛⣻⠿⠿⣶⣬⣭⣄⣀⡀⠀⠀⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣿⣟⣻⠿⠷⠿⢿⣿⣿⣧⣴⣴⣤⣀⣀⣀⠄⠀⠈⠉⠉⠒⠲⠷⠤⢭⣭⡛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣤⣭⣍⣉⣙⣒⠒⠶⠧⠬⣭⣍⣙⣛⣛⠻⠷⡶⢷⣶⣦⣤⣤⣄⣀⠘⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⣿⣶⣶⣶⣯⣭⣭⣍⣉⣙⡓⠒⢲⣤⡈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⠟⠋











⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣶⣶⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠚⠐⠂⠒⠒⠓⠂⠁⠒⠘⠈⠚⠀⠒⠈⠐⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠀⡄⡄⣠⢀⣀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆⢀⠠⡀⢂⣀⣸⣠⣤⡦⠴⠶⠞⡚⣛⠛⠉⠉⠛⢷⡡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⣆⣈⣤⡦⠼⠾⠞⠚⠛⢉⠉⡉⡰⢠⠄⠀⠰⠂⠡⠄⠀⠀⠀⡗⠀⢹⡷⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢌⣶⢟⡉⠉⠰⠀⠠⠤⠷⠶⣄⣄⢄⠀⢀⠀⠂⡄⠁⠀⠂⣠⠂⠀⠰⠄⠀⠒⢸⡯⠅⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠑⣾⠁⡄⠥⠀⠀⠀⠀⡌⢹⣆⣉⢹⢱⠀⠐⠀⡀⠀⠀⠀⢀⢀⡒⢀⠐⠀⠈⣠⢞⡋⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠥⣿⠀⣄⠒⢀⠠⠄⠀⠙⠋⠙⠥⠒⠚⢤⠂⠄⠰⠀⢀⣀⣀⣤⡤⢶⢶⢶⠫⠫⠀⠀⣠⣴⠟
⠀⠀⠀⠀⠀⠀⢉⠜⢷⣀⠂⠀⠰⠆⢠⣀⣃⣀⣠⣤⡤⠶⠶⠒⢛⠻⠙⠙⠘⠀⠃⠈⢈⣤⡶⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠑⠩⢛⠛⠛⡋⠏⠩⠙⠈⠀⠂⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣠⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣖⣒⣒⣶⣴⡴⠿⠭⣭⣕⠂
⠀⠀⠀⠀⢀⢴⣽⠞⠋⠉⠁⠠⠉⠁⢠⡄⢀⣤⢬⡀⠙⣦⠣⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⡛⠉⢙⣓⠒⡚⠛⠉⠉⠉⠛⠲⢤⣀
⠀⠀⠀⢀⢣⠟⠀⠀⣠⡷⠾⠿⢷⣶⣄⠀⡘⢯⡝⢳⡄⠘⡇⠄⠀⠀⠀⠀⠀⢀⡞⠉⠘⠀⠰⢀⣀⣠⢮⠤⣚⣁⡇⠀⡀⠛⡤⠤⣄⠉⠳⣄
⠀⠀⠀⠰⣮⣴⣲⣼⡏⠀⠀⠀⠀⠙⢻⡇⠀⠀⠻⣷⠇⢀⡇⠀⠀⠀⠀⠀⠀⡾⢠⠞⡿⡇⡀⠈⡋⣠⢶⣶⡉⣁⡴⠞⠁⠢⣞⣟⢾⢷⢀⡈⢣
⠀⠀⠀⣰⡇⡭⡻⣻⠅⠀⠀⠀⠀⢀⣼⠇⠄⠘⢀⠐⠀⡼⠀⠀⠀⠀⠀⠀⠀⡇⣜⡝⣌⠈⣻⠠⠯⣾⣿⣿⣷⣷⣿⣥⣆⠀⣾⣿⡈⢦⣇⠀⠈
⠀⠀⠀⣼⠸⠿⢆⡿⠀⠀⠀⢀⡴⠛⣡⡤⠄⣙⢞⡂⢰⢇⠃⠀⠀⠀⠀⠀⢠⡇⠿⠮⣻⣾⡇⠀⣨⢗⡿⢛⣿⣭⣍⡉⠹⣛⣬⣬⣟⣦⢻⡇⢀
⠀⠀⢸⡇⢠⠀⣼⠃⠀⠀⢀⣾⠁⣾⣡⡶⠞⢹⡗⡏⢸⢘⠀⠀⠀⠀⠀⠀⢸⡇⠺⡶⡿⣧⣷⡇⠀⠋⡼⠋⠛⢀⠉⢻⠀⢙⡻⠈⠋⢾⠔⡇⢠
⠀⠀⣾⣀⠀⢸⡇⠀⠀⢠⠞⠁⠺⡥⠋⣀⣈⣳⣯⣟⢸⢸⠀⠀⠀⠀⠀⠀⠈⣇⢸⡤⢡⣣⣶⣿⡿⣿⡷⠰⣿⠇⠐⢹⠣⡍⢁⠠⢄⣾⠋⠀⡾
⠀⢴⠇⠀⠀⣾⠀⠀⠀⢸⡄⠀⠀⣴⢿⠋⠉⢹⡉⢹⢸⡄⠀⠀⠀⠀⠀⠀⠀⠘⣎⠙⢬⡉⣾⣾⡽⢦⣷⣆⠀⢁⣨⢯⢾⣤⡯⠀⠆⠀⠘⢠⡇
⠀⣿⣰⣿⣆⢿⡆⠀⠀⣸⠇⢠⡀⣿⠄⠒⣀⢸⡥⠞⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠹⠃⡃⠯⢫⡏⠂⠉⢙⣹⢛⡝⢛⣾⠁⠂⠞⢳⡎⢸⠁
⠀⢻⠸⣿⢿⣆⠻⢿⡿⣋⡤⣾⡌⢿⡄⠙⠿⣏⣧⡆⣸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠃⠹⠆⠀⢳⣼⠞⣷⠛⡩⠔⠻⢫⠟⣸⠎⢐⡏⣼
⠀⡘⢦⠙⠿⠿⠃⠑⢲⣵⣿⣿⠷⠈⣻⣿⣿⣯⣾⣡⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠠⠈⠀⢀⡈⠛⣀⡥⡞⡶⠃⠸⣯⡀⠉⣰⠇
⠀⠘⠈⠳⣄⠀⠀⠁⠘⢳⣛⣁⣀⠐⠓⠾⣛⣫⢟⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠶⠤⣬⣁⣀⠋⠘⠋⠀⠉⢀⣀⣩⠼⠃
⠀⠀⠀⠐⠬⠛⣛⡛⠿⠭⠭⠿⠭⠭⠉⠉⠭⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠋⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣄⣀⡀⢀⣀⣀⣀⣀⣀⣀⡤⠤⠄⣀⣀
⠀⠀⣠⠴⣶⡾⠾⢿⠿⠚⠚⠛⠛⠓⣛⠛⠛⠛⠛⣛⡉⠉⠛⠓⠒⠒⠾⠷⢴⡆⢀
⢠⣾⡔⣋⣄⣀⠐⢫⡤⠶⢦⣥⡀⢈⣥⣤⠚⣳⢦⣍⢁⣀⡀⢀⡤⣤⣬⣥⡀⠙⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣬⡞⢰⣿⣿⣿⣀⡿⣽⡒⣯⣿⣇⣯⠞⣿⡿⣷⣖⣿⣸⣭⣿⢸⣷⣯⣿⣾⠇⠀⣼⣭⣤⣤⡀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠈⢳⡀
⡏⣇⠈⡻⠿⣿⠿⠿⠉⠹⣿⣿⣶⣫⢾⣿⣷⡟⠙⠟⠟⢓⠛⠿⠿⠋⠁⢉⣁⡴⠃⡰⠀⠀⠸⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠘⣮⠣⣄⣀⡀⠘⠀⠀⠀⠈⠉⠉⠀⣀⣈⣤⣤⠤⠤⠤⠤⣔⣖⣒⡛⢫⠭⠥⠒⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣀⣀⣠
⠀⠀⠙⠲⠬⣭⣍⣉⣉⣭⣭⠭⠽⠿⠟⠛⠋⠉⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠐⣶⢠⢦⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣠⣤⣴⣿⠂⠀⠰⠿⠿⠷⠐
⠀⠀⠀⠀⠀⠀⠈⠉⠓⠚⠓⠊⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠸⠿⠿⠟⠁⠀⠀⠀⠀⠒⠦⠠
⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⡄⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢠⣾⣿⣦⠀⠀⠀⢰⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⡿⠀⠀⠀⠻⣿⣭⣽⣿⡆⠀⠀⠳⢦⡝⠛⣋⡀⠀⠀⢼⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠠⠥⠾⠄⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠚⠛⠉⠁⠀⠀⠀⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⣴⣾⣷⣦⡀⠀⠀⠀⢀⣿⣶⣴⠆⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⠷⠀⠀⠻⠿⠿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠛⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⣠⣤⣾⣷⡄⠀⠀⠀⠀⣠⣤⣶⣶⣄⠀⠀⠀⠀⢰⣿⣿⣷⠀⠈⠂⢠⣶⣦⡜
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⣠⡾⠻⠿⠋⠀⠀⠃⠹⣿⣿⠇⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠁⠀⠀⠀⠀⠙⠛⠋⠉⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠄


⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⠛⠉⠉⠛⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⠿⠿⠀⠀⣠⣤⣦⣠⡇⠀⢧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⣿⣷⣶⡶⠀⠧⠙⢻⣾⣿⢟⠀⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢿⣿⣿⣷⣄⠀⠀⠻⣿⣷⡾⠖⠀⠹⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢀⣻⣿⣿⣿⣿⣦⣤⠀⠉⠁⠘⠃⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠂⡻⣿⣿⣿⣿⣿⣷⣄⡀⢀⡀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣃⠀⠀⣀⢀⠄⠀⠀⠀⠀⡀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⣠⠖⠛⠋⠉⠉⠉⠀⠚⠙⠙⠋⠉⠑⠚⡒⠒⣐⠛⠋⠛⠉⠉⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠋⠁⠐⠓⠒⢦
⢀⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⡃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈
⢐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢤⣴⣦⣄⣀⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣿⣧⣥⣦⣿⠿⣿⣿⣾⣿⡆⢄⠀⠀⠀⠀⠀⢀⡀
⢘⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣰⡿⢿⣾⣿⣉⣽⣿⣷⣿⠛⢻⣾⣿⣷⡄⠱
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣿⣏⣹⣿⣿⣿⣟⡀⣿⣿⣧⣶⣧⣴⣧
⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡿⣿⣿⣿⢻⡿⡽⢿⣿⣿⡏⢙⣿⣿⠅⡀⠀⠀⠀⠀⠀⠠
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣬⣿⣿⣿⣿⣿⣾⣇⣼⣿⣿⣷⡿⠿⠋⠀⠉⠀⠀⠀⠀⠀⠀⠂
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠤⣈⣏⢛⣿⠿⢿⣿⣿⠯⠐⠁
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠉⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈
⢸⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢸⡀⠀⢀⣀⡀⢀⣀⠀⠀⣀⠀⣀⠀⠠⠤⣠⣀⡀⢀⠀⡀⠀⢀⣀⢠⣀⣤⣄⡀⣀⣀⡀⣠⠄⢀⣄⣀⣀⢀⣀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠂⠠⠄⠀⠀⠀⠒⠀⢀⠀⠰⠀⡄⢀⠀⠀⠠⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠁⡈⠠⠄⠀⠀⠀⠀⠉⠀⠀⠀⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⣀⣀⠀⠁⠄
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡾⠻⠺⢶⣶⣶⣶⣍⣑⠢⢄⠀⠀⠀⡀
⠘⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⢠⣾⣿⢿⣿⣇⠀⢠⣾⣿⣯⣿⣿⢿⣷⣄⠉⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣾⣏⢻⣶⣿⡅⢸⣿⣿⡇⢰⣟⣿⣷⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⢿⢀⣿⢹⣿⠛⣿⣡⣿⠸⣿⣿⣤⣿⡿⢻⡿⢽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣶⣿⣀⣿⠟⣿⢷⣌⣿⣿⠉⢀⣼⣯⡾⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠩⠙⢹⣿⣘⣷⣾⠛⠉⠻⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠁⠐⠉⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠑⠀⠀⠀⠀⠀⠀⠰
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⠀⠀⠀⠀⠐⠐⠒
⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠈⠣⠀⠀⠀⠀⡀⡀⠀⠐⢀⡀⠀⠀⠀⢈⡀⠐⡀⢀⣀⣀⣀⣀⣠⣤⠤⠤⠀⠀⠀⠀⠀⢀⡤⣀⠀⠤⠤⠤⠊
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⠄⠀⠤⠠⠄⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠴⠶⠶⠶⠶⠶⠤⢤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠠⠄⢀⠀⠀⠀⢀⣀⠀⠈⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠰⠒⠁⠙⠉⠻⠀⠐⢞⠪⣱⣄⠀⠀⢻⠀⠀⠀⠀⠀⠐⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⡀⠀⠀⠀⠐⢀⠀⣀⡀⠑⢌⠯⣷⡀⢸⡆⠀⠀⠐⠒⡒⠀⠒⠒
⠉⣁⠈⡉⣀⣁⠁⠀⠀⣴⡇⠀⢨⢏⠃⠀⠀⠀⠀⠀⡔⢩⠹⣠⡀⠣⠹⠄⢸⠀⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⠃⠈⠀⠀⠀⠀⠀⠂⠑⠀⢐⣟⣿⣆⠀⠀⢸⠀⠀⠀⠬⠌⠡⠄⠠⠌⠥⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡔⢠⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⡿⢋⠀⠀⢸⠐⠀⠀⠤⠀⠠⠄⠤
⠐⠒⠀⠐⠂⠐⠂⠀⠀⠀⡇⠀⠳⠈⠄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠷⠩⠀⠀⣾⠘⠀⠀⠐⠒⠐⠒⠀⠒⠒⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢤⡄⠄⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⣿⣿⢦⣀⠀⠀⣰⣞⣿⣡⡿⡿⢠⠃⠀⡟
⠀⠀⣀⣀⠀⣀⡀⠀⠀⢸⣇⠀⠘⠿⠿⠿⠏⠁⠀⠳⠼⠤⠜⠋⠀⠃⠀⢀⣇⠂⠀⠀⣀⡀⠀⣀⣀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⠀⠀⠀⠠⠄⠀⠤⠤⠤⠤⠄
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠉⠍⣤⡄⠤⠤⣤⣤⣔⡛⠂⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢁⢀⣀⡈

⠀⣉⣈⣁⣉⡀⢀⣀⡀⠀⠀⠀⠀⠀⣤⠞⠁⢀⠄⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢊⠔⠁⠀⠘⠈⠁⡡⠡⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⢀⠀⠀⠀⠀⡸⢀⣀⠈⡇⠀⠀⠀⡆⠀⠀⠨⠀⠉⠡⠤⠁⠤⠤⠭⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⣞⠁⠘⠉⣸⠃⣀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⢯⣍⣉⣥⣴⣟⣠⠀⠃⢠⠀⠠⠄⠤⠀⠄⠀⠤⠤⠤⠄
⠐⠂⠐⠀⠀⠀⠀⠀⠀⠠⡟⡄⠀⠠⢼⣷⣄⠩⢔⠿⠿⠿⠷⠝⠋⠁⠀⡀⢀⠀⠀⠃
⠀⠉⠀⠈⠉⠀⠀⠀⠀⠀⢣⠸⡄⠀⠺⣿⣿⡗⠀⠗⠒⠒⠀⠀⠀⠀⡐⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡘⢦⡀⠉⠉⠁⡀⠀⢀⠀⠀⠂⡀⠈⠀⡇⠀⠀⢈⣁⣉⣁⠈⣁⣈⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠙⠢⠁⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠤⠤⠄⠀⠤⠄⠀⠀⠀⠀⢠⣶⡄⣀⣀⣤⣀⣀⣀⣀⣀⣠⡆
⠀⠀⠀⠀⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠺⠛⠿⠿⠹⠿⠿⠹⠛⠶⠿⠿⠇
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁
⠀⠀⠀⠀⠀⣴⠞⠃⣀⣄⣰⢰⠆⠰⣆⢸⡇⣀⠀⢰⣖⣦⣴⢀⣤⣀⣄⢀⣶⠀⢠⡾⠓⢀⣠⣠⣦⡆
⠀⠀⠀⠀⠀⠙⠲⠂⠙⠟⠙⠚⠃⠀⠙⠟⠀⠿⠂⠘⠋⠁⠘⠚⠿⠛⠋⠃⠻⠀⠈⠳⠖⠈⠻⠋⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⡀⠀⠀⢰⡋⢉⣩⠗⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡠⠖⢾⣇⠀⠀⢀⠁⠘⡓⠠⠤⣾⡆⣉⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠴⠊⠰⡉⢀⢀⠉⣉⢲⡁⣐⣼⡄⢆⡑⣀⣮⠈⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠌⣂⣠⠗⣚⢌⣦⢸⣿⣘⠶⢛⡸⠷⣺⣭⡬⣦⠥⢋⡙⣣⣬⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠱⠧⣤⡄⢡⣊⣛⣮⣿⣿⣿⣧⣼⢽⣾⣾⣇⡛⣍⠒⠑⣋⡹⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠞⣈⠒⢤⡄⣸⣽⢿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⠛⠯⣿⢈⢥⢤⡜⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡏⠑⣿⣫⣿⣿⣿⡏⡖⠀⣦⢻⣿⣿⠿⡁⣇⢀⠘⡷⠷⡏⠉⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⡷⠫⡛⠟⠩⢿⣿⣇⡛⠾⣋⣼⣿⣿⣇⣳⣬⣩⣼⣱⢆⢿⣾⠠⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣡⠰⣇⠀⡼⣸⣤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⡯⣿⠁⣚⣣⡇⣆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠑⢞⡿⢿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⢛⠙⢻⡠⠃⠀⠑⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣉⣦⣽⡼⢛⣛⠿⠿⠿⠿⣹⡅⠷⢴⣸⠥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⣏⠴⠤⡑⡏⢷⠙⣄⡤⡾⠑⢊⠿⠏⣁⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠒⠀⠀⠀⡛⠭⡝⡄⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣿⡿⠿⠿⠿⠿⢿⣿⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠟⠛⠋⠉⣁⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⡈⠙⠛⠿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⢁⣠⣤⣶⣶⣿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⣿⣶⣤⡀⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠇⠀⣠⣶⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣄⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣸⣿⠃⢠⣾⡟⠉⠀⠀⠀⠀⠀⠀⠸⠿⠆⠀⠀⠀⠀⠀⢴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⣿⡏⠀⣿⡟⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⢿⣷⣦⡀⠀⠀⠀⣀⡀⠀⢀⣴⣾⡿⢿⣶⡄⠀⠀⠀⠻⣿⡄⠘⣿⣧
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣧⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠈⠹⣿⣆⠀⠸⠿⠃⠀⣼⣿⠁⠀⠀⣿⣷⠀⠀⠀⠀⠹⣿⡄⠘⣿⣧
⠀⠀⠀⠀⠀⠀⢿⣿⠀⢻⣿⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⢹⣿⡀⠀⠀⣿⡟⠀⠀⠀⠀⠀⢹⣿⡄⠸⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⡄⠸⣿⡇⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⠻⣿⣦⣾⡿⠃⠀⢰⣶⠀⠀⠀⢿⣷⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⣿⣧⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠿⡷⠀⠀⠈⠉⠉⠀⠀⠀⠘⠋⠀⠀⠀⠸⣿⡆⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⢹⣿⠀⠀⠀⠀⠀⠙⢿⣷⣄⣀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⠀⠀⠀⣿⣷⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢸⣿⡄⠀⠀⠀⣀⡀⠀⠉⠛⠛⠛⠉⠀⢠⣤⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣤⡀⠈⠉⠀⠀⠀⢹⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⢀⣴⡿⠟⠋⠉⠀⠀⠀⠉⠻⣿⣦⠀⠀⠀⠀⢸⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⢸⣿⠁⠀⠀⠀⠀⣀⠀⠀⠠⣶⣆⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⢸⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⣾⡿⠀⠀⠀⠀⠸⡿⠃⠀⠀⠈⠁⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣸⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢰⣿⠇⢠⣿⡇⠀⢀⣄⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠈⠉⠀⣾⣿
⠀⠀⠀⠀⠀⠀⣸⣿⠀⢸⣿⠁⠀⠿⠟⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⢰⣿⠆⢠⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡟⠀⣿⡿⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⣾⡿⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⢠⣾⡿⠛⠛⣿⣧⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁⠀⠀⣸⣿⠃⢰⣿⠇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⣸⣿⠀⠀⠀⠀⠙⣿⣦⣀⠀⠀⠀⠀⢀⣀⣤⣴⣿⠟⠁⠀⠀⣰⣿⠃⢠⣿⡟
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣇⠀⠀⠀⠘⣿⣧⡀⢀⣿⡟⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣾⣿⠿⠟⠛⠉⠀⠀⠀⠀⣴⣿⠃⢠⣿⡟
⠀⠀⠀⠀⠀⠀⢿⣷⠀⢻⣿⡀⠀⠀⠀⠈⠻⠿⠿⠟⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⣠⣿⠟
⠀⠀⠀⠀⠀⠀⠘⣿⣇⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⣴⣿⠆⠀⠀⠀⠀⠀⣀⣴⡿⠋⢀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀⠙⠿⣷⣦⣄⣀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠋⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣄⡈⠙⠛⠿⠿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⠿⠛⠁⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣦⣤⣀⣀⡉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⢁⣠⣤⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⣿⣿⣶⣶⣶⣶⣾⣿⠿⠿⠟⠛⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⣿⣿⣿⣿⣠⣄⠹⢃⡘⣀⣁⣆⣾⡁⢖⠀⢄⠸⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⢉⡀⠀⠀⡀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠮⠀⠀⠸⣿⡄⠀⢀⢴⠗⠈⠑⠊⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣀⠀⠀⠀⠉⠁⠀⡺⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠰⠃⠀⠀⠀⠀⠀⠀⠐⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠦⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠐⡠⠜⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⡀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⡀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡇⠀⠄⠫⠂⠀⠹⠟⠀⠀⡄⠀⠀⠀⢀⡄⢰⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠖⠒⠒⠒⠒⠒⠲⠤⠤⠤⢤⣀⣘⡋⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠊⠀⠑⠂⠁⠀⠤⠄⠀⠀⠐⠐⠒⠂⠀⣀⣀⣧⠀⠀⠈⠉⠈⠀⠀⠫⠀⠀⠀⠉⠈⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠈⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢀⠂⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣼⠋⠠⠀⠀⠀⠛⠛⢶⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡪⠑⠂⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠐⠀⢀⣀⡂⠀⠀⠀⢀⡀⠀⠸⡇⠀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠉⠀⢀⠨⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠚⠗⠂⡉⢩⣆⠀⠀⠏⠀⠀⠀⠛⠦⣄
⠀⠀⠀⠀⠀⠀⢀⠀⡠⠂⠀⠀⠠⠞⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⠀⠀⠀⠠⢀⢌⡀⠘⢠⠀⠀⠀⣰⣶⠉⣇
⠀⠀⠀⠀⠀⠀⢢⠀⠀⠈⠰⠊⠁⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡡⣘⠊⠡⠁⠀⠀⠀⠀⠄⠀⠀⠙⠋⢀⡟
⠀⠀⠀⠀⠀⡀⠁⢢⠀⠀⢰⣄⢈⡑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠮⣑⠂⢬⡄⠠⡆⣀⢀⡀⡀⠩⢴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁⠘⡇⠒⠃⠐⠂⠒⠀⠉⠁⠈⠂
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠠⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⣿⣿⣿⣿⡿⣿⣏⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠈⠉⠈⢉⣉⢹⣾⠁⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⣿⣿⣿⣿⡿⣿⡏⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⡶⢸⡟⢸⡟⠀⠀⠀⠀⣿⠉⠉⣿⠀⣀⡀⠀⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠘⠇⠘⠇⠸⠇⠸⠇⡀⠀⠀⠀⠿⠿⠿⠿⠼⠿⠿⠦⠿⠿
⠀⠀⠀⠿⠿⠟⠛⠃⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣴⠄
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⣼⡫⠋⠁⣼⣿⣿⠋⢉⣿⣿⠀⠀⠀⠀⠀⠀⢀⠀⢀⣹⠟⠛⠋⠀⠀⠀⠀⠀⠀⢀⣠⡴⠿⣿
⠀⠀⠀⠀⣸⣷⣶⣶⣶⣿⣿⣇⣀⣾⣿⡏⠀⠀⠀⠀⢠⣮⣴⣶⣶⣬⣳⠀⠀⠀⠀⠀⠀⢠⣶⣿⠋
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣾⣿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠉⠋⠉
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢯⣈⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣟⣀⣀⣗⣀
⠀⠀⠀⠘⠀⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠠⣤⡄⠀⠀⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⠀⠀⠀⠀⣀⣀⣀⣀⣠⢀⢀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⠀⠀⠀⣐⢒⢒⢂⢂⢂⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⣶⣿⣶⡆
⠀⠀⣰⢂⢂⢆⢆⢆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠎⠂⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠟⠛⠻⠃
⠀⠀⠉⠈⠈⠈⠈⠈⠉⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢸⣿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢥⣈⣤⣴⠕⠋⠉⠳⢼⡢⣄
⣶⣴⣶⣀⠀⠀⠀⠉⢻⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⢟⠅⠀⠀⠀⠀⠀⠉⠳⢵⡄⡀
⣿⣿⣿⣿⣦⣴⣦⣤⠈⠉⠻⢗⣄⣰⣄⠰⢄⣠⣾⡿⠫⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⣿⣿⣿⣾⣵⣿⢿⡁⣿⣤⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢷⣦⣀⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠙⢻⣿⣟⣵⣾⠀⠘⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣀⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣴⣯⠟⠙⠻⠏⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣗⣍⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣠⣾⡿⠛⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣴⣿⠟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣷⣦⠀⠀⣀⣀⣰⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⣶⣶⣶⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⠖⠻⣗⣶⣾⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢿⠁⠰⣆⡀⠈⡉⠀⢹⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠉⠉⠀⠀⢳⡬⠛⠉⠠⠘⣧⣧⡀⠀⠀⠀⠀⣠⡄⠀⠀⢠⢦⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠻⡖⢤⡀⢀⣄⡈⠀⢀⠉⣏⠁⠀⠀⠰⣒⡋⡷⠖⠓⠚⣇⣩⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡛⣅⠀⣸⠎⠀⣸⡤⠚⠛⣂⣰⣧⡀⣤⡀⣴⠉⠉⠁⠀⠀⠀⠈⠛⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠟⢦⣤⢀⠄⠛⠀⢀⣴⣧⠎⠀⠀⡱⠙⣯⠀⢀⡤⠜⡇⠀⡼⡂⠀⢬⠶⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠟⠣⢵⡖⠚⠋⠉⠛⠀⠀⠚⠊⡿⠁⣠⣄⡈⠙⠁⠀⠓⠚⠃⢸⡟⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣡⡄⠀⠀⠀⠀⠀⠀⠀⠸⣅⠌⣱⡼⠀⡰⣩⠵⠆⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡤⢼⣢⠉⡼⡳⠦⣄⠀⢠⡄⠀⠀⠀⠘⠷⣍⣄⠄⢙⠁⣠⣰⠻⢥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠸⡏⠀⢊⡁⠙⠀⣀⠀⡑⣷⠎⠧⣀⡀⠀⠀⣴⡫⡸⡋⠉⠉⠉⠸⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠋⠁⣀⡜⢹⠀⢰⠙⢦⡄⠈⡺⣯⠉⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡏⠀⠀⠉⠑⠋⠀⠀⠉⠁⡄⠠⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢈⡽⠀⠾⣁⢒⠄⠀⡔⢒⡦⠀⠀⣤⠿⡲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠘⣤⢠⡈⠚⠀⠀⠷⠁⠀⠃⠀⣿⠳⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠚⣦⣄⠀⣊⣵⢶⡶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢣⡇⠉⠉⠉⡝⡤⠽⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠃⢀⣤⣄⠀⠀⠀⠀⠸⡀
⣤⣤⠀⠀⠀⢀⡤⠊⠁⠀⠀⢀⣶⣿⣿⣿⣿⣶⣷⣿⣶⡄⠀⠀⠀⠀⣠⠞⠁⠀⠀⢿⣿⣿⠇⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠒
⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢿⣿⣿⡿⠃⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠉⠁⣠⣤⡀⠀⠀⢸⡀
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠰⡦⠐⠶⢤⣀⡀⠉⠉⠀⣀⣀⡤⠞⠁⠀⢠⣄⠀⠀⠀⠀⠀⠻⠿⠏⠀⠀⠈⡇
⠀⠀⠀⠀⢷⠀⠀⠀⠀⢠⠖⠒⠶⣄⠀⠀⠈⠙⢦⣀⠀⠉⠀⠀⠀⠀⠀⠀⠙⠳⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠈⢆⠀⠀⢠⡏⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠃⠀⠚⠃⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⢧⠀⠈⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣤⡀⠀⠀⠰⠶⠒⠛⠁⢀⡀⠀⠘⠋⠀⣦⠈⠉⠀⠀⠀⠘⡆
⣀⢄⣠⡤⣀⣄⣄⢳⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⡀⠀⠀⠀⠀⠈⢡⣄⢰⡘⢧⠘⣆⠀⠺⠆⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠻⠿⠟⠛⠛⠋⠉⣡⡴⠞⣋⣉⡁⠀⠀⠀⠀⡀⠀⠈⢷⡙⣎⠳⡌⢳⡄⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣀⠀⠀⠚⣩⣿⣿⣿⣿⣿⣷⣶⣄⢀⡋⠀⠀⠈⢳⡌⢷⡹⣆⠹⡄⠀⠀⠀⣧⠀⠀⠀⠠⣀⣀⣠⣀⡀⣀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡼⠃⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠀⠀⠀⠀⢹⡄⣧⠘⣆⠻⠀⢀⡀⠘⡄⠀⠀⠀⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢸⠃⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⢸⡇⠘⢀⠈⠀⠀⠛⠁⠀⢱⡀
⢠⡄⠄⣠⣤⢤⢠⣠⣤⠀⢸⡀⢸⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠸⠃⠀⠛⠁⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⢷⡀⠀⠀⠺⣝⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⡀⢠⡀⣄⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⠃⠀⢀⡈⠙⠻⠭⠿⠉⠁⠀⠀⠈⣧⢹⡌⡇⠸⡆⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠈⠈⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠙⠦⣤⣤⣤⠄⠀⠲⢤⣤⠟⢠⠇⡿⠀⣇⠀⠀⣸⠁⠀⢀⣴⣾⣿⡷⠀⢨⡇⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡀⠀⠀⠰⣶⠀⠀⠀⢦⡀⠀⣝⠳⢤⣤⠴⠋⢠⡇⢀⡇⠀⢰⠇⠀⠀⠈⢻⣿⡿⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣇⠀⠀⠀⠀⣤⡀⠀⠈⡇⢳⡌⠳⢦⣀⣀⣠⠞⢀⡾⠁⢠⡟⠀⠀⢀⣴⣿⡟⠁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⡙⣦⡀⠀⠀⠈⠀⠀⢠⠇⠀⠙⠳⢤⣬⣩⣤⠴⠛⠀⣠⠟⠀⠀⢰⣿⣿⡿⠁⠀⣠⠋⠀⠀⠀⠀⠀⠀⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠙⠃⣈⡉⠀⢀⣀⣤⠶⠋⠀⠐⢦⡀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠉⠉⠁⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢠⣄

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣀⣀⡀
⠀⠀⠀⠀⣀⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢠⠄⠀⠀⠀⠈⠉⠓⠒⠤⣀
⠀⠀⠀⡔⠁⠂⡀⠀⠀⠀⣀⡀⠀⠁⠀⡀⠁⠀⠘⠘⠀⢀⡀⠀⢠⢲⣲⢦⣤⡄⠉⠳⢄⡀
⠀⠀⢸⠁⡀⠀⠀⢠⢎⣯⣽⣽⣽⡗⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢟⡿⢺⣵⣻⡄⠀⠀⠙⢦⡀
⠀⠀⡇⠀⠀⠀⠀⠈⠺⠿⠇⠿⠿⠚⠁⠀⠄⠀⠀⠀⠀⠠⡔⢠⠀⠀⢑⠫⠿⠽⠎⠀⠀⠀⠀⠑⡄
⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠡⠀⠀⣉⠌⠦⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⢇⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠄⠠⠀⣃⠤⠒⠒⠒⠤⣀⠀⠀⠀⠀⠈⢦
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡈⠀⠘⠀⡜⠁⠀⠀⠀⠀⠀⠈⢫⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠱⡄⠐⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⠄⠘⣉⢸⠀⠀⠀⠀⠀⢀⣤⣄⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⢦⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣨⠂⠄⠀⢸⡀⠀⠀⠀⠀⠈⠛⠋⢁⠇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠑⢄⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣍⠁⠒⠀⠀⠳⡀⠀⠀⠀⠀⢀⣀⠞⠀⠀⠐⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠂⠀⠷⣞⡆⠀⠈⠀⠀⢠⡚⣯⣷⢿⡿⠐⠀⠁⠀⠀⠈⠑⠒⠤⠒⠊⠁⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⣗⢿⣻⡮⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠬⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣀⠤⠴⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠑⠒⠒⠋⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⣚⣉⣉⣀⣀⣀⣀⣀⠈⠉⠙⠒⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢚⣭⠴⠒⠋⠉⠉⠁⠀⡀⠀⠀⠀⠉⠉⠉⠙⠓⠲⠦⢤⣈⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣊⠵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀⡀⠁⠂⠐⠂⠀⠀⡀⠀⠰⠠⠀⠀⠀⠀⠀⠀⠙⣄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⡰⢣⠏⠀⠀⠈⢀⡀⠀⠀⢀⡠⠖⠋⠁⣀⣀⡀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠈⢧⢹⡄
⠀⠀⠀⠀⠀⠀⡰⣣⠋⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⡴⠋⠁⠀⠉⠳⡄⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣧⢳
⠀⠀⠀⠀⠀⣰⢱⠃⠀⠀⠁⠀⢀⠈⢀⡞⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢀⢈⡀⠀⠐⠸⡎⣇
⠀⠀⠀⠀⣰⢣⠇⠀⠀⠤⠀⠀⠀⠀⣸⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⠉⣁⠀⠄⣧⠸⡄
⠀⠀⠀⢰⢃⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠓⠶⠶⠊⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢰⠈⡄⠐⠁⢸⡀⣧
⠀⠀⢀⡏⢸⠁⠀⠈⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⡀⠀⠆⠠⠘⡇⢸
⠀⠀⢸⠃⣿⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠋⠀⢠⠀⠄⠈⡇⢸
⠀⠀⢸⠀⣇⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠈⠁⡌⢁⠈⠀⡇⢸
⠀⠀⢸⠀⣿⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⢄⣀⣀⣀⡤⠴⠚⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⢸⡄⢸⡀⠀⠀⠈⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣼
⠀⠀⠀⣇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠂⠀⠁⢐⠛⠂⠣⠀⠀⠀⢠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠁⡞⢀⡇
⠀⠀⠀⠘⡄⢳⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠠⠬⠀⡀⠀⢀⠟⣂⠀⠈⠢⠄⠀⠀⠁⠀⠀⢀⢀⡀⠀⠀⠀⠀⡀⣸⠁⢸⠁
⠀⠀⠀⠀⠹⡌⢧⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠛⠁⠀⠋⠀⠁⠘⠀⠢⠀⠀⠀⠀⠀⠐⠀⠂⠀⠈⠆⠀⠀⢠⠃⢀⠇
⠀⠀⠀⠀⠀⠹⡌⢧⠀⠀⠀⠀⠈⠀⡀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⣰⠃⢀⡞
⠀⠀⠀⠀⠀⠀⠘⢦⠳⣄⠀⠀⠀⠐⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠤⠀⠀⠀⠀⠂⠘⠀⠀⠀⠀⢀⠄⠀⡰⠃⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠳⣄⠀⠀⠀⠰⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠔⠁⢀⡞⠁⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠳⣄⠀⠈⠀⠁⠀⠀⠀⠐⢄⠢⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⠏⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣌⠳⢤⡀⠀⠀⠀⠀⠀⠀⠲⡀⢂⡀⠀⠀⠀⠀⠰⠀⠀⡄⠀⠀⠀⠀⢀⡠⠞⠁⡠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡙⠳⢤⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣈⠙⠒⠶⠤⣤⣀⣀⣀⡀⢀⣀⣀⣠⠤⠶⢚⣉⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠦⠤⠤⠭⠭⠭⠴⠶⠒⠒⠉⠁

⠀⠀⠀⣀⣤⣤⠤⠤⢤⣤⣤⣤⡤⠤⠤⢤⡤⠤⢤⡤⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⠒⠛⠛⠛⠛⠛⠛⠛⠛⠉⠲⢆
⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢰⡄
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄
⢸⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡀⢠⠀⢀⠀⣀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⣀⢀⣂⣩⣥⣴⣶⣷⡿⢷⣿⣷⣿⣶⣶⣭⣶⣤⣀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣏⣽⣿⠻⣿⡇⣸⡟⠉⣿⣿⣿⠻⣿⣿⣿⣷⡄
⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⣾⣿⠱⢾⡿⠉⢻⣿⠻⠃⠀⣶⠿⣧⡆⢰⣿⣿⡀⣻⣿⣏⣸⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⣼⣷⣤⣾⣿⣤⣦⣰⣿⣶⠛⣷⣼⣿⣿⣿⢿⠟⠛⠋⠀⠠⡀⠉
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⠛⠛⠻⡿⠟⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠏⠁⡀⠀⠀⠀⠀⠀⠁⠀⠠
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢦
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠆
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⡀⠀⠀⣀⠀⢀⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠆⠛⠸⠀⠿⠀⠺⠃⠀⠟⠀⢻⠛⠀⠃⠙⠁⠇⠸⠇⠙⠘⠗⠗⠐⠇⠀⠿⠀⠿⠃⠀⠻⠀⠛⠻⠃⠀⠀⢠
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣇
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⡏⠀⠀⠀⠀⠀⠀⠘⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⢠⠀⠀⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣣⣤⣤⣤⣀⢀⢠⣤⣤⣄⢠⣤⣶⣤⣤⣶⣶⣴⣶⡿⣦⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣶⣿⣿⣿⣿⣿⠿⢿⣿⣷⣿⣿⣿⣿⠉⢹⣿⣿⡁⠈⣿⡇⠀⣿⡇
⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠹⣿⣿⠉⢀⣿⣿⠀⢺⣿⣿⡏⠀⣿⣿⣷⠀⣿⣿⢿⣦⣿⣧⣾⠟⠁⠀⠀⠀⠁
⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣰⣿⣿⣄⣸⣿⣿⣶⣿⡿⣿⣧⣀⣿⣿⣿⣷⣿⣿⣾⡿⣿⣿⡁⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⡿⠿⡿⣿⣿⣷⣿⣿⣿⠿⣿⠿⠟⢉⠛⠻⣿⠿⠛⠁
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠲⠂⠉⠛⠉⠡⠋⠐⠀⠀⠁
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⢸⡇
⢸⡇⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⢦⣤⡄⢠⣤⣤⣤⡄⠀⠐⣀⣀⠘⠀⠀⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠘⠉⠉⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡟
⠀⠀⠙⣦⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠄⣤⣠⣤⣤⣤⣤⣤⣤⡴⠞⠋
⣤⣤⣤⣤⣭⣿⣷⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠉⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠦⣤⠖⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡰⠒⠲⡄⠀⠀⠀⠀⠈⠓⠤⡠⠴⠊⠀⠀⠀⠀⢀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠐⠀⠀⢀⣴⣶⣶⡀⠀⠀⠀⠀⣀⠀⠀⠎⠀⠀⠈⠃⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠀⠀⠀⠀⠸⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠛⠦⡄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⢀⡜⠀⠀⠀⠀⠀⠀⠘⠆⢀⠖⠉⠀⠈⠑⣄⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣸⡧⢾⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠘⡶⠦⣤⣟⢀⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣄⡴⠞⠉⣁⣤⢾⡤⠤⠤⠤⠤⠤⣤⠀⢸⠄⠠⣤⠤⠤⠤⠤⣷⣤⣀⡉⠛⠧⣴⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡾⠋⢀⡴⠛⠉⠀⠈⢧⡀⠀⠀⠀⠀⠀⢠⠞⢇⠀⠀⠀⠀⠀⣰⠇⠀⠈⠙⢶⣄⠈⠻⣏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⢀⡴⠋⠀⢀⠀⠀⠀⠈⠻⢦⣤⣠⣤⠔⠋⠀⠈⠳⣤⣀⣤⡴⠋⠀⠀⠀⣀⠀⠈⠳⣄⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣠⠟⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠙⣦⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⡞⠀⢰⠏⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠘⢧⠀⠹⡄
⠀⠀⠀⠀⠀⠀⣼⠁⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢹⡀⢀
⠀⠀⠀⣠⡤⣤⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣿⣹⡇
⠀⠀⠀⠘⠓⣿⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣇⠀⢻⣉⡀
⠀⠀⠀⠀⠀⡟⠀⢸⠃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⠀⢸⣏⣿
⠀⠀⠀⣠⣤⡇⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⣀⠀⣿⠀⢸⡏⠁
⠀⠀⠈⣧⣈⡇⠀⢸⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠑⣿⠀⠀⡇
⠀⠀⠀⠈⠉⣧⠀⢸⡆⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⢻⡄⠀⢷⠔⠊⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⠇⠀⡼
⠀⠀⠀⠀⠀⠈⢳⡀⠈⢧⡀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣴⠋⠀⣴⣛⡷
⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠙⠶⣄⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⢀⡾⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠈⠉⠛⠶⠶⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠴⠶⠚⠋⠁⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⡦⣤⣀⣀⣀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣀⣀⣀⣤⡤⢶⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠴⠏⠀⠉⠉⠉⠙⠛⠛⣟⢻⡛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⢷⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠐⠂⠀⠀⠐⠀⠐⠐⠀⠀⠀⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠐⠒⢳⣄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠒⡆⠀⣀⢠⡤⠀⠀⠁⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠓⢶⣞⣡⠨⠶⠟⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢢⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⠡⠀⠀⠔⢢⣄⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⢢⠜⣃⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠙⠛⠑⣲⣶⡮⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢽⢞⣯⡉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠐⠦⣄⡀⠐⠏⠀⢀⠀⢁⠀⠂⡀⠀⠐⢩⣮⡙⠓⣄⠀⠱⡆⠀⠶⢲⠋⠁
⠀⠀⣀⠀⣄⠀⠀⣽⣷⣦⣿⣷⣆⠈⠫⡳⣄⠀⠀⠠⡌⣾⡿⠫⡄⠂⠀⠛⠳⣀⠀⠀⢀⠶⢸⣃⠙⡀⠠⠤⡀
⠀⠄⠃⠈⠠⠄⠸⠉⣧⣞⠛⠋⠄⠀⠀⠐⠘⢦⢀⠀⠁⡔⠰⠃⠀⠀⠐⠂⠀⠨⢧⣂⠈⠐⠀⡋⢀⡩⢀⠚⡁
⠀⠂⠸⠂⢁⠀⠀⠀⠓⠓⠀⠀⠀⠀⠀⠀⠀⠲⠊⠀⠠⢁⡔⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡃⢀⠁
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢰⠂⠀⠠⣶⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠤⡢
⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠻⢦⣀⣤⡀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢨⢝⢆⠠⠄⠈⠉⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠻⣦⣛⠘⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠞⣤⠁⣀⡀⠀⠀⢘⠆⠀⠀⠀⢸⠄
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠱⢴⠺⢿⣽⣷⠺⠓⠀⠀⠀⠀⣸
⠀⠀⠀⣢⠤⠄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢀⠀⠀⠀⠈⠒⠒⠏⠁⠀⠀⠀⠀⠀⢈⡏
⠀⠀⠆⠻⢇⠑⢀⠀⠀⠀⠀⢰⣦⡤⢿⣦⠂⠀⠀⠀⠀⠀⠀⠈⢦⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⢂⣴⣦⠘⠁
⠀⠀⠈⠑⠀⠑⠈⠂⠀⠀⠀⠈⠈⣱⣾⣧⣀⣀⣤⣤⣀⠀⠀⠀⠀⠙⠦⠔⡄⠀⠀⠀⢀⣦⣄⣿⣿⣿⡆
⠀⠀⠀⠀⢀⣤⡄⠀⠁⠀⠀⠀⠐⠹⠿⠋⠀⠀⠀⢀⠀⡍⠀⠀⠀⠀⠈⣊⠀⠀⠀⠀⠙⠚⢳⣴⣿
⠀⠀⠀⠀⠀⠻⠁⠀⢰⣦⣅⠀⢠⡀⠀⠀⠉⣦⢐⣺⡹⠁⠀⠀⠀⢴⡟⣋⡍⠉⣉⡽⣇⠈⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣒⡿⠞⠀⠀⢉⣉⠉⡘⠫⣦⡀⠀⠠⣶⠤⠀⠀⠠⣅⣀⣨⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⠊⢀⡀⣀⡀⠀⢰⡶⢤⣙⠩⠁⠙⠓⠒⠐⠶⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠽⠃⠘⠓⠒⠄⠐⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⠀⠠⠤⠄
⠀⠶⠂⠀⠀⠀⠖⠀⡈⠛⠀⢀⣀⣠⣤⠤⣄⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠒⠀⠀⣀⠀⠀⠀⠀⡀
⠶⠖⠀⠀⠀⠀⠀⠀⠀⣰⣶⠉⠉⢈⣙⣤⣿⠀⢸⠿⠋⠉⠉⠉⠉⢶⣦⠀⠀⠀⠉⠀⠀⠀⠛⠉⢠⣴⠆⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠐⢀⣠⠿⠋⠀⠘⣿⣶⣷⡄⣠⡿⢧⡿⠃⣠⠶⠶⠶⠒⣦⣤⡀⠀⠁⠀⠊⠉⢰⡶⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⠛⠙⠛⠋⠁⠀⠀⠀⠀⠀⠉⠙⠿⠛⠛⠛⠀⠀⢿⣦⠀⠀⠀⠈⢉⡟⣷⡄⢀⣤⣤⡀⠀⠛⠁⠀⠒⠂⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣤⡄⠀⣤⣿⠟⢁⣼⠭⠝⠻⢿⣶⣄⠀⠓⡀⠀⠀⠀⠔⠃
⠀⠀⠀⠀⠀⠀⣧⠀⢸⡟⠙⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⢹⣤⡤⠀⠴⠉⠙⣷⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⣿⠀⢠⡇⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣈⣰⠿⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠘⣷⣴⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣡⣴⡦⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⢰⣧⠀⢸⠁
⠀⠀⠀⠀⠀⠀⣀⠀⠰⣿⠻⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠁⣨⡟⠀⠃
⠀⠀⠀⠀⠀⠀⣿⠀⠘⣀⣤⣈⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡂⢉⣃⣤⠂
⠀⠀⠀⠀⠀⠀⣿⠀⠸⣇⣠⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠾⠿⠹⡇
⠀⠀⠀⠀⠀⠀⣿⠀⢠⣅⣠⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦
⠀⠀⠀⠀⠀⠀⣿⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⢤⣤⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢻⠀⣀⣾⣷⣄⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⠀⠈⢹⣿⠀⠀⠃
⠀⠀⠀⠀⠀⠀⣸⠀⢹⣏⠉⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⢾⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠐⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠁⠀⠈⠂
⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣶⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⢶⣄
⠀⠀⠀⠀⠀⠀⢿⠀⠀⢻⣦⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠈⢛⣀⠀⢀⡀⠀⠀⠀⢰⠎⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⠃⠀⠙⣿⠟⠋⠙⠃⠀⠀⠀⢴⡤
⠀⠀⠀⠀⠀⠀⣼⠀⠀⣿⡟⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣴⣲⣶⠀⠁
⠀⠀⠀⠀⠀⠀⢻⠀⠸⣿⡏⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣹⠿⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠸⠀⠰⣏⠁⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣈⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⠉⢹⣧⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠀⠀⠀⠘⣿⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢸⠂⢠⡿⠿⣿⣄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡍⠁⠀⠐⠀⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠸⡇⠀⠈⢛⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠐⠀⠀⠈⣿⡀⠀⠀⢀⡀⠀⠀⠀⡿⠃⣿
⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⣷⡄⠘⢿⣿⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡀⠀⠀⠀⢙⡉⠛⣻⠏⠉⠉⠋⠉⠀⠀⠘⠁⠘⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣧⣴⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡁⠀⠀⣴⡛⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠃⠰⠀⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⡸⠀⠻⠿⠿⢿⣤⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠈⢉⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⣤⣤⣬⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢠⣘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠃⠀⠂⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⣇⡨⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠇⠀⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠘⣿⣧⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠈⠹⡟⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠙⡏⠀⡀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡶⡄⠉⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢿⣦⣶⡄⠁⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢿⣧⡀⣤⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢾⣏⣠⣈⣻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⣿⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⣼⣶⣾⡟⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣥⡴⠛⢻⡿⠀⠀⠚⠛⠐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢸⣿⡿⠁⠀⠈⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠰⠆⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣸⣿⠛⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣋⠀⠠⠀⣿⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢿⡇⠀⠾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⠀⡶⠃⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⢸⠟⠂⣄⠉⢩⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⣶⠆⠉⠂⣈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠻⣿⡃⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠠⠀⠻⢷⣤⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⣿⠖⣿⡇⠀⠈⠁
⠀⠀⠀⠀⠤⠈⠁⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡬⢤⣾⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⣿⣿⣿⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⢀⣤⡝⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣯⡿⠋⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⠿⠛⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⣿⣷⣦⠀⣿⡣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡔⣤⡄⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠘⣿⣡⣶⣿⠗⠀⠀⣈⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⣴⣿⠟⠻⢷⣿⣿⠆⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠙⠿⠟⠋⠀⢀⣼⣿⡿⠋⠉⠉⢻⣶⡄⠀⠰⣾⡟⠃⠀⣧⣀⣽⡿⠂⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠓⣀⠀⠀⠀⠀⠺⣷⣬⣵⣦⣶⡀⢀⣩⡿⠀⠀⢾⣿⣶⣿⣿⣿⠋⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⢀⡀⢈⠙⠛⠛⠛⠛⠛⠋⠀⠀⠀⣀⡸⠿⠿⠈⠙⠃⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠛⠀⠐⠛⠁⠀⠀⠒⠲⠦⠶⠶⠶⠆⠒⠖⠀⠀⠀⠀⠀⠈⠀⠘⠛⠛⠛⠠⠈⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⡿⠟⠻⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠖⠛⠛⠛⠛⠛⠛⠛⠛⠶⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣄
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠓⣀⠀⡖⠀⠌⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⣁⠀⢠⣭⣃⣿⣀⡀⠀⡂⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠠⡿⣝⠀⠉⠻⡀⡄⣻⠍⡫⡄⠀⠚⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣧⣬⡙⠂⠛⣻⣻⠶⣍⠴⣿⢀⠚⠣⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⢭⡀⣾⣫⠹⣅⢪⡍⠋⠆⠴⠂⠤⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠤⠐⢡⣲⠛⡏⣨⡹⠟⣬⡍⠀⠂⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠖⠙⠻⠄⠘⠻⢃⡐⠟⠁⠈⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣥⡀⠐⠀⠀⢈⠵⠐⣃⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⣤⣤⣀⣀⣠⣠⣤⠤⠴⠖⠒⠉
⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⠀⠠⠀⠂⡄⢀⠀⢀⠔⠒⠒⠤⢀⠀⠀⠀⠀⠀⢄⡀⠀⠀⢀⣠⠠⣄⠀⠀⠀⠀⠀⣠⠀⡀⠀⠀⠀⠀⠒⠂⡀
⠀⠈⠀⠀⠀⠈⠤⠄⠘⠂⠄⠤⣀⠀⠀⠈⡀⣀⣀⠀⡸⠀⠀⣌⠀⠀⠀⢃⠀⠀⠘⠀⠀⠀⠀⠄⠀⠀⢀⠇⠱⠄
⠠⠀⡀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠁⠀⠀⠀⠀⠁⠦⠠⠄⡃⠀⠀⠀⣀⠀⠀⢠⠂⠀⠀⠀⠐⢶
⢀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠁⠄⠠⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠤⢀⠀⠀⠈⠁⠉⠁⠂⠀⠐⠀⠀⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠈⠀⢈⠄⡀⡐⠀⡀⠀⢠⣀
⠀⠀⠀⠀⠀⠐⠀⠀⠨⠠⠀⠀⠀⠄⠀⠀⠀⡀⠐⠂⠀⠀⠀⠀⢀⠀⡀⠁⠀⠀⠈⠢⡀⠈⠓⢦⠀⠀⠀⡀
⠀⠁⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠔⠁⠀⠈⠀⠀⠀⠀⠠⠀⢀⡴⠀⠇⠀⠰⠀⠁⠀⠀⠀⠂⠈
⠈⠤⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡀⠤⠐⠁⢠⠞⠀⠀⠈⢀⡗⠀⠀⠀⠀⠀⢀⢠
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠠⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣀⠀⠀⠒⠈⠉⡁⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⣠⣴⣶⠶⡶⣶⠶⠶⣾⣿⡟⠛⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⡀⡀⠁⠠⠀⠀⣾⢹⢡⠀⠈⠰⠎⠦⢰⡶⠎⣻⣮⣼⠟⢿⡆
⠀⠀⢠⠀⠀⠀⠀⡀⠀⠘⣀⠸⠀⠠⠀⢸⣿⣀⣼⠦⣶⠗⢾⡒⢺⠛⣻⡏⠍⡈⠆⣼⡇⠀⠀⠈⠈⠀⠂⠐⠀⠀⠄
⠀⡀⠤⢄⠀⠀⠀⠀⠀⠄⢀⡀⠐⠂⠀⠈⢯⠀⡹⠀⡌⠘⠿⢿⡜⣇⠰⠶⠀⡓⢀⣿⡏⠀⠀⠀⠀⠀⠠⠀⠄⠀⡀
⢐⠀⠀⠀⢱⠀⢀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠓⠧⠶⠿⠾⠷⠾⠿⠿⠶⠶⠿⠿⠟⠋⠀⡀⠀⢢⠀⠀⠐
⠈⠢⠄⠤⠃⠀⠀⠀⡀⠁⡐⠒⡄⠤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⡐⣰⠈⠾⠄
⠀⠀⡄⢠⠊⠉⠁⠢⠀⠤⠈⠂⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢄⠀⠀⠀⠄⢠⠂
⠈⠒⠁⢂⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠔⠁⠑⠀⠀⠀⠘⠠⠜⠀⠀⡠⣤⣠⡔⢶⢰⡖⠢
⠀⠂⡀⠀⠑⠒⠂⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠃⠝⠛⠀⠁
⠀⠠⠠⠔⢀⠀⠀⠆⡡⡀⡂⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢠⠢
⢄⠁⠊⠁⠈⠀⠈⠀⠀⠈⡢⠅⠀⢀⡤⠒⠉⢑⡄⠀⠀⡀⠒⢠⠀⠀⠀⠀⠀⠈⢠⠁⠀⠀⢈⠀⠀⠀⠀⠄⠀⠀⡀
⢂⡀⣀⠀⠀⠀⠀⠀⢀⠈⠐⠀⡰⢃⠤⠒⠂⠈⡀⠠⠂⠀⣀⠜⠀⠀⠈⠀⠀⠀⠀⠂⢠⠀⠔⠀⠀⠀⠈⠀⠄⠀⠂
⠀⠂⠂⡁⡉⠂⠊⠀⠁⠀⠁⠀⠈⠁⠀⠀⠀⠈⠒⠒⠂⠈⠀⠀⠀⠀⠁⠂⠀⠀⠀⠐⠀⠐⠀⠀⠀⠂
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿