Martian Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⣀⠀⠀⡀⠀⠀⠀⠀⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠒⠉⠁⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠘⠀⠀⠀⢀⢔⠈⡤⠄⠀⠀⣱⡆⠀⠀⠀⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠔⠠⠀⠀⠀⠀⠈⠀⠀⠘⢦⠀⠁⠀⢠⠦⡮⡙
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠈⠀⠁⠀⠀⠀⢼⣄⠂⠈⡙⣢⠋
⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠘⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠉⠉⠄⢄⣀⠀⠂
⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⡄⠠⠀⡘⠀⠀⠁⡀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⣔⡖⠀⠀⠀⠀⠀⠙⠠⡀⠀⠀⠀⠀⠀⠈⠀⠀⠡⣴⣟⣐⣟⣘⣞⣷⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⢴⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠍⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠰⠀⠀⠈⠠⢀⠀⠀⠀⠈⠀⠈⠂⠀⠻⠂⠀⠀⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⠀⠻⠁⣀⠀⠀⣤⣎⠉⠈⠐⢲⣖⠒⠩⣭⠵⠋
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢶⣤⠄⠨⢥⣤⣤⣤⠬⠇⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⢀⡀⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⢀⢀⢀⠠⠊⠓⠂⠒⠀⠋⠑⠴⠤⠤⠤⠤⠤⠀⠀⢀⠠⠄⡀⡀⠀⡀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠠
⠀⠀⠀⠀⠀⠄⠠⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠄⠀⠀⠈⠉⠒⠀⠀⠀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⣠⠴⠒⠦⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⢀⠀⠀⠁⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢁⡀⠀⠀⣠⠀⢄⠀⠉⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠁⠀⠀⣠⠤⠀⢀⣀⢤⢄⠀⢀⠀⠀⠀⣀⡄⠰⠀⠐⠀⣀⣄⠈⠁⠀⡼⠁⠀⠈⠄⠈⠉⠀⠀⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠈⠉⠂⠀⠀⠀⠀⠀⠉⠠⠄⠆⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠊⠉⠉⠉⠉⠑⠒⢲⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⠉⠉⠒⠒⠒⠒⠒⠉⠉⠁⠀⠀⠀⠈⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠙⠛⠲⠶⣒⡒⠲⠦⣤⣤⣀⡀⠀⢀⣀⣀⣀⣀⣀⡀⠠⠤⠤⠤⡴⠶⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠒⠒⠲⠖⢤⣀⣀⣉⣀⣀⣀⣈⠉⠒⠒⠦⠤⠤⠤⠤⢄⡀⣀⠴⠊⣀⡠⠤⠜⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠣⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠢⠤⠤⠤⣀⣀⠤⠔⠂⠉⠀⠀⠀⠀⢈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠈⠉⠒⠤⢄⣀⡀⠀⠀⢀⡀⠀⣀⣀⣀⣀⣀⠠⠤⠤⠒⠒⠒⠒⠒⠒⠐⠒⠚⠉⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣉⡉⠉⠒⠒⠤⢄⣀⣀⠀⠉⠉⠀⠈⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⡠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠀⡠⠤⠤⠤⠭⠍⠁⠠⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠑⠲⢄⠀⠀⠉⠒⠦⠤⢄⣀⣀⣀⡠⠤⠤⠤⠤⠄⠀⠤⠤⠔⠒⠒⠋⠀⣀⣀⣀⣀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠙⠢⢄⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠈⠉⠉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠤⠤⠤⠤⠤⠤⠀⠐⠒⢒⣀⠤⠤⢄⣀⡈⠉⠉⠁⠒⠒⠒⠉⠀⠀⠀⢀⣀⣀⣀⡠⠤⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡤⠤⠤⠔⢒⡢⢭⣭⠵⠦⢤⣬⣉⣉⣒⠪⠭⣁⣒⣒⣒⡒⠶⠶⠖⠚⠛⠋⠉⠉⠉⢉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡒⠢⣘⠧⣀⣣⣤⣀⣀⣀⣀⣭⣝⡠⠽⢀⡠⠤⠤⠴⠒⠒⠒⠒⠒⠒⠒⠒⠒⢂⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣬⣕⣢⠤⢉⣉⣉⣉⣉⡠⠤⠴⢚⣉⠤⠴⠒⠒⠶⠤⠤⢄⣀⣀⣀⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢌⠉⠓⠒⠲⠶⠶⠶⠖⠚⠛⠙⠒⠒⠒⠒⠒⠒⠒⠒⣉⡠⠤⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢆⡈⠉⠉⠉⠉⠉⢁⣒⣒⣒⣒⣒⡂⢐⣒⣋⡡⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠯⠭⢍⣁⣀⣀⣀⠠⠤⠴⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠴⠶⠶⠶⠶⡶⠶⠦⢤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⡏⠀⠉⠙⠳⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⢀⣀⡤⠤⢤⡄⠀⠀⠀⠀⠀⣠⠟⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⢀⣠⠖⠋⠁⠀⠀⠀⡿⠀⠀⢀⡴⠛⠁⠀⠀⣠⠞⠋⢀⣠⠴⠞⢳⡄⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡴⠟⠁⠀⠀⠀⢀⣠⠞⠁⠀⠀⠸⣇⠀⠀⠀⠀⠻⠦⠶⠋⠁⠀⠀⠘⠷⠛⠉⠳⣤⣤⡌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⡴⠋⠀⠀⠀⢀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠈⠉⠙⢦⡀⢀⣠⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣈⣷⡄
⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⢠⡏⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢀⡗⠀⠀⠀⣠⡴⣤⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⣰⠋⣇⠀⠀⠈⠳⣤⡴⠞⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⣰⠋⠀⠈⠳⡴⠖⢦⡀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⣰⠇⠀⠙⠦⠤⠶⠶⣤⠀⠀⠀⠀⠀⡴⠛⠉⠈⢧⣀⣀⣠⡤⠶⠛⠋⠙⡷⠀⠀⢸⡀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠸⣆
⠀⠀⠀⢠⣏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⣧⠴⠒⢦⡀⠉⠉⠀⠀⠀⠀⠀⣼⠃⠀⠀⠈⠳⣤⡴⠋⠀⠀⣠⣄⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⣾⢹⡆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣀⡀⠈⢧⡀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠈⣷⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⣷
⠀⠀⢀⡏⠈⣇⠀⠀⠀⠀⠀⠀⢻⣄⣀⡤⠖⠋⠉⠉⠙⣧⠈⠉⠉⢹⡆⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⡿⠀⣯⠀⠀⢀⡶⡄⠀⠀⠀⢹⡀
⠀⠀⢸⡇⠀⠙⠶⠤⠤⠤⠤⣤⣀⡈⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠳⣄⡀⠀⣿⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡾⠁⠀⠈⠳⢦⡼⠃⣿⠀⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡆⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⠴⠖⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠘⣧⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⢸⡇
⠀⠀⠈⣇⠀⠀⢀⣀⣀⣘⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⢹⡆⠀⢹⡀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⢿⣠⠞⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣤⠞⠀⠀⠀⠉⠛⠒⠛⠋⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠘⣿⠀⠀⠀⢠⡖⠛⠛⠲⢦⣄⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠹⡆⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠹⡆⠀⠀⣼⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⣸⠇⠀⠀⠀⣸⠃⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠹⡄⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡤⠶⠚⠉⠀⠀⠀⣠⠾⠃⠀⠀⠀⡴⠃⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠙⠷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠁⠀⠀⠀⣠⠞⠁⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠉⠉⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⣾⠁⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣀⣬⠷⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣞⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣉⠳⢦⣤⠤⠤⢤⣄⣀⠀⠀⠀⠙⠳⠦⣤⣤⣤⣤⡤⠞⠃⠀⠀⠀⣀⡿⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣄⣀⠀⠀⠉⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠲⠶⠾⠷⠶⠶⠶⠖⠚⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⢿⣿⠿⠿⠟⣳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡟⠿⠿⠿⠿⠟⣳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠉⠻⠿⠻⠟⠻⠟⠛⠋⠁⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⠛⠿⠛⠟⠛⠛⠛⠋⠁⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⣿⠿⣶⣿⣿⣶⣶⣶⣶⣶⣤⣦⣴⣶⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⢶⣶⣥⣶⣶⣶⣶⣤⣤⣤⣤⣶⡾⠿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣀⡀⣙⣛⣛⠋⣿⣯⣙⣋⣩⣭⣭⢴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠈⣛⣋⠉⢹⣯⣉⣉⣉⣭⡤⠴⣺
⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠉⣉⣉⣉⣋⣉⣉⣭⣭⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣀⠀⢉⣉⣉⣉⣉⣉⣉⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠷⠾⠶⠶⠿⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠶⠶⠶⠶⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⢤⣄⠘⠻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁⢀⣴⠞⠛⠛⢷⣌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⢠⡟⢱⣿⣥⠀⢀⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢸⣇⠈⠙⠁⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠐⣿⠉⠋⠉⠛⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠈⠛⠶⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠈⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢣⢀⡴⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠶⣦⡀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢀⣤⣄⢡⠸⠎⢠⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣎⣡⠌⠛⠁⠀⣤⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢶⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⣠⣀⠋⢹⢠⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠁⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⣠⡟⠁
⢣⡈⠷⠸⠇⡼⠁⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⣤⠞⠋
⠀⣿⠀⠀⠛⠂⠛⣳⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠙⢦⣀⣠⠟⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠟⠳⢤⣀⣀⣤⠒⠁⠀⠀⠀⠀⢿⡇
⠀⠀⠀⣽⠁⠀⠀⠀⠀⢀⣠⡴⠛⣿⡇⠀⠀⠀⢰⣄⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠈⠳⠶⠶⠶⠚⠋⠁⠀⠀⣿⡇⠀⠀⠀⠘⢏⠛⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠠⣄⣉⣡⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠻⣷⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠙⠿⣷⣴⣏⣀⡀⠀⢀⣀⣀⣤⣶⠟⠃⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⣸⡟⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠳⢦⣄⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⣹⡇⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠋⢀⣠⡴⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣀⣀⣀⣀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣶⣶⣶⡾⠟⠃
⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠠⢠⠤⡄⠀⣤
⠀⠀⠀⠀⣐⠇⠀⡀⠀⢀⠀⣀
⠀⠀⠀⠀⠉⠀⢠⠟⢈⠉⠀⠈⠑
⠀⠀⠀⠲⡀⢱⠃⠜⠁⠀⢀⡴⠡⢀⠲⠒⠂⠀⠈⠁⠐⠄⡀
⠀⠀⠀⡄⢠⠇⠌⠀⠀⡠⠈⠠⠂⠁⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠤
⠀⠀⢀⡀⡄⠀⠀⢨⠍⠀⠐⠁⠀⠀⡠⢐⣬⡴⣶⣶⣶⣶⣆⡬⡘⠆⠀⠀⠀⠀⠀⠄⠉⠂⠀⠀⠠⠀⠀⡀
⠀⠀⢠⠀⡅⠀⠀⡘⠀⠀⠁⠀⠀⢪⣾⣿⠻⣿⣿⣿⣿⣿⣿⣷⡄⠂⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠖
⠀⠀⠀⠰⡇⠀⢠⡇⠀⢀⠀⠀⢢⣿⣿⣿⠀⠈⠻⣿⣿⣿⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠁
⠀⠀⠀⠀⠀⠐⠁⠠⠀⡎⠀⠀⢸⣿⣿⣿⣧⡀⠀⠈⣿⣿⠃⣸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⢀⣤⠾⡿⢛⢹⣿⣿⣷⣶⣿⣿⣿⣿⠂⠀⠀⣼⣄⠀⠀⣀⠀⢤⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠸⠸⠿⢿⣿⣿⠿⠛⠛⠁⢰⠋⠁⠉⢁⠀⡀⠠⠔⠊⠢⠰⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠒⠂⠁⠀⠀⢂⠀⠀⠀⠀⢐⣲⣾⡷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣁⡀⠀⠀⠉⠀⢸⠃⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠛⠛⠿⡿⠁⠀⠀⠀⡀⢏⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡦⢤⣀⣠⣬⣦⡄⠠⡊⠀⠂⣈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢍⠻⢿⣿⣿⣿⣆⠀⠉⠛⠻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢍⣛⠛⠿⣄⢠⠤⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣮⠀⢱⣶⣁⠠⠄⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⠀⡹⠿⣷⣶⣅⣀⠄⠉⠈⡁⠖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡤⠀⠈⠛⠿⣿⣷⣦⡊⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡙⢿⣿⣿⣶⠀⠈⠁⠈⢻⣿⣿⡄⢀⠠⢪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠙⢿⣿⡇⠀⠀⠀⢸⣿⠬⠤⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠨⠉⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⢤⡄⠘⠻⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⢀⣴⠾⠛⠛⢷⣌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢠⡟⢱⣿⣣⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢸⣇⠈⠛⠉⣀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⣟⠙⠛⠙⠻⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠈⠻⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣧⠀⡠⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⢶⣄⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡇⠠⠾⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣞⢁⡈⠓⠒⠀⣠⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠉⠀⢧⡀⢀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⢀⡀⡞⢳⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⢀⡾⠃
⢏⠙⣧⢠⠞⠰⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⣀⡴⠟
⠈⠷⠀⠀⠶⡧⠶⢆⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⠁
⠀⢹⣄⠀⢀⡔⠐⠋⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⡾⢯⣀⠀⠀⣀⡤⠂⠀⠀⠀⠈⣿⡆
⠀⠀⠉⣿⠉⠀⠀⠀⠀⠀⢀⣠⠶⣿⠇⠀⠀⠀⢸⡀⠉⠉⣩⡟⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠹⢦⣄⣀⣤⡤⠶⠛⠁⠀⣿⠀⠀⠀⠀⠸⡿⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡘⠒⠛⡁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠈⠻⣷⣄⣀⡴⠂⠀⠀⠀⠀⠀⠀⣀⣴⠟⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠈⢻⣿⢷⣶⣶⣶⣶⣶⡶⠿⠛⠁⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⣇⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⠀⠈⠙⢷⡄⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⣀⣠⣤⡾⠇⠀⢈⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⢀⣴⠟⠋⠉⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣶⣶⡶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⣀⠀⠀⢀⣀⣼⡗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠒⣦⠀⠀⠀⠰⣏⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⢤⡴⠚⠁⠀⠀⠀⠀⠈⢳⡶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣀⡤⣦⣤⣄⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⢨⠞⣉⡑⢆⠉⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⣠⠶⣸⣄⠛⣃⣞⡠⣄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢰⢋⣄⡉⣿⠋⣴⡌⢎⠁⠸⡇⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠚⠳⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠼⢦⣉⡠⠛⢦⣈⣠⠏⠀⢸⡇⢠⡶⡄⣿⢸⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣼⣁⣀⣀⣀⣀⣀⣈⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠲⣇⡀⠀⠀⠀⡀⠀⠀⢀⡾⠁⠀⢳⡸⠾⠸⠏⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣡⡽⠛⠉⠉⣀⣠⡴⠟⠁⣴⠒⠲⠟⠃⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠤⢄⠀⠀⡠⣀⠀⠀⣀⣀⠀⠀⢀⢀⠀⠀⡤⢄⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⠋⠻⡍⠁⠀⠀⠀⠉⠉⠹⣄⠀⢀⡼
⠀⣀⡤⢔⣒⣛⣉⡹⠁⠘⠤⠌⠀⠸⣄⡼⠀⠀⣅⣀⠇⠀⢧⣀⠇⠀⠢⠔⠀⢯⣉⣉⣓⡒⠤⣄⡀⠀⠀⠀⣰⠃⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠈⢹⠉
⡞⡱⠊⠁⡠⠔⠊⠑⠲⠤⠤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠴⠾⠧⢤⣀⠉⠓⠦⡙⣆⣤⣾⠃⠀⠀⠀⠀⠈⢯⠓⠦⣄⣀⣀⡤⠞
⠙⠧⣄⣞⠀⠀⠀⠀⠀⠀⡴⠁⣠⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⡏⠉⠹⡄⠀⠀⠀⠀⠀⠈⠳⣄⠀⣹⠟⣱⠃⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠉⠙⠓⢶⠦⠤⣼⣄⣀⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⣹⣀⣀⣀⣀⣀⣤⡤⢿⣿⠋⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⡽⠋⠉⠁⠀⢀⣾⠃⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⢀⡀⣠⠋⠓⠶⣤⣄⣀⡀⠀⠀⠀⢲⠀⠀⠀⠀⣀⣠⡤⠞⠋⠹⣆⣠⣄⠀⣼⠃⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⢰⡋⢙⡇⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⢻⡗⠛⠛⠛⠉⠁⠀⠀⠀⠀⢾⡀⣸⣇⡏⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⢳⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢉⡷⠀⠀⠀⠀⠀⠀⠀⢮⠄⠀⣠⡄⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⢰⠁⠱⣈⡆⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⢳⡶⠦⢤⣤⣤⣤⡤⠴⢶⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣧⡀⠀⠀⠀⠀⠀⢀⣼⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠋⠉⠉⠉⠉⠙⢷⡀⠀⢠⡾⠉⠉⠉⠉⠉⠙⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠞⠁⠀⠈⠳⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⠽

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⠀⠀⠀⠶⠜⣁⣤⠴⠋⠀⠀⠀⣰⣿⡿⠃⢸⠔⢠
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠶⠀⣾⣿⣿⠁⠀⠠⠀⠀⠻⡄⠀⠀⢠⣾⣿⡿⠇⡀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢻⣿⣿⡎⠁⠀⣤⠀⠂⣿⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠄⠀⠄⠐⠐⢸⣿⣿⠃⠀⠐⠁⠀⣰⠏⣰⣿⣿⡟⢛⡟⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⣴⣦⡼⠃⢀⣿⣿⣿⡗⠈⠃⢄⣀⣄⡀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⡏⠰⠀⣿⠀⠀⢠⣿⣿⣿⡏⠀⠀⠀⠀⡘⡃⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠒⠀⢀⠀⠀⢸⣿⣇⠀⣰⠇⠀⠀⢸⣿⣿⣿⣶⠒⠀⠀⢸⢣⠀⢠⣤⣤⣾⣿⣷
⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⡆⢿⡄⠀⠀⠈⢿⣿⣿⣿⣶⣤⡅⠀⠀⠀⠈⢻⡘⣿⣿⣿⣇⡀⠁
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠳⣄⠀⠀⠀⠉⠻⢿⣿⣿⣇⠈⠳⠀⠀⠀⣷⠈⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⢻⣿⣿⣿⠀⢸⡀⠀⠀⠀⠀⣸⣿⣿⡷⢦⠁⠀⠀⠀⡿⠀⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⣿⠆⢈⡇⠀⠀⠀⠀⢻⣿⣿⣯⠰⣀⡀⠀⠈⣧⠀⣠⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⡿⠀⢀⡾⠁⠀⠀⢀⣠⣼⣿⣿⠿⠃⠀⠈⠀⠀⠘⡎⣿⣿⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡰⠾⢿⣿⣭⣽⣿⣭⣭⣭⣾⡿⠳⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢟⣅⡀⠐⠒⠂⠀⠲⠒⠚⠁⢀⣌⠻⣿⣿⣿⣿⣿
⠀⠀⠀⢀⡞⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⢣⡀⠀⠀⠀⢸⣿⣿⣿⡿⢡⣿⣿⣷⣶⣶⣶⣾⣶⣶⣶⣿⣿⣿⣷⡜⣿⣿⣿⣿
⠀⠀⠀⣼⣅⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣇⠀⠀⠀⢸⣿⣿⣿⠃⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢸⣿⣿⣿
⠀⠀⠀⣿⠿⠿⣿⣷⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⠟⣿⠀⠀⠀⢸⣿⣿⣿⠀⣠⣀⡀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⢀⣤⠄⣿⣿⣿
⠀⠀⠀⢿⣄⣀⣈⣙⣫⣉⡩⣽⣯⣍⣉⣉⣭⣤⠴⣚⡟⠀⠀⠀⢸⣿⣿⣿⡀⠻⢿⡿⠶⠶⠶⣖⠂⠐⠲⠶⠶⢚⣛⣋⠥⢰⣿⣿⣿
⠀⠀⠀⠘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣧⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢁⢀⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢷⡈⠉⢉⣉⣛⡛⠛⣉⣙⣋⣉⣩⠞⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣝⢿⣵⣦⣤⣤⣤⣴⣶⡶⠶⢶⠿⣫⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠳⠶⣯⣿⣭⣭⣽⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣭⣛⠐⠂⠒⠒⠒⢀⣋⣥⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢰⠀⠀⢨⠀⢀⡍⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣇⠈⡆⠃⠈⠤⠨⣅⢠⠀⢠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢹⡀⠸⡀⣈⠀⢨⣇⡰⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠲⣄⣀⣽⠀⠀⠘⡇⠀⠑⡠⠋⢡⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡤⠏⠀⠈⢧⡀⠀⢻⠀⡔⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣩⣷⣾⣿⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠄⠠⡄⢂⣀⡥⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⣠⣄⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣤⡀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡲⠮⠒⠁
⠀⠀⠀⢀⣀⡤⠴⠖⠒⢛⡟⠐⡅⣠⠃⠀⡎⠈⢱⠀⠀⡎⠉⢱⠀⠀⢾⠁⢙⠄⠀⢠⡀⡸⠀⠹⡖⠲⠶⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⢐⠀⠤⡀
⢀⡴⠛⣉⡤⠖⠒⠒⠒⣿⣀⠀⠈⠁⠀⠀⠈⠚⠁⠀⠀⠙⠒⠋⠀⠀⠈⠙⠉⠀⠀⠀⠈⠀⠀⠀⢹⡶⣒⡒⠒⠢⢍⡓⢦⡀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠂⠆⠊
⣿⣰⠋⠁⠀⣠⡴⠚⠋⠉⠉⠙⠛⠲⢶⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⣤⠒⢶⡒⠋⠙⠢⡎⠀⠀⠑⢤⡂⠀⠙⣄⡟⠒⢲⡆⣤⣀⠀⠀⠀⠀⠀⠦⠁
⠹⣧⣀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠙⣆⠀⡠⠋⡉⣙⡋⠢⣳⡤⠖⠋⠀⠀⠸⠇⠂⡘⢄⡀⠀⠀⢀⠄
⠀⠀⠙⠻⠷⣤⣤⣀⣀⣀⡀⠀⠀⣟⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣀⣀⣼⣤⡀⠉⢽⡏⣽⠀⠃⠀⠀⠀⠀⠁⠀⠈⠉⠉⢹⡇⠈⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣏⠙⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⢣⣀⠠⠀⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣈⡁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⢿⣁⠍⠹⣍⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢹⠉⠉
⠀⠀⠀⠀⠀⠀⢠⡞⠛⢾⡃⠀⠀⠀⠉⠛⠶⠦⣤⣤⣤⣤⣼⣇⣤⣤⣤⣤⠶⠶⠟⠛⠉⠀⠀⢀⠃⠀⢠⠋⠉⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠘⢧⣤⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⡄⠀⠇⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠙⠦⠼⢄⢂⣀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣢⠤⠤⠤⢤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠵⣄⠀⢀⡼⠄⢀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣲⣥⣤⣤⣤⣞⣀⣹⣤⣤⣤⣤⣴⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠙⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠄
⠀⠀⠀⠀⠀⠀⠀⠴⣁⠠⠶⠀⠠⡀⠀⠐⠑
⠀⠀⠀⠀⠀⠀⠀⢀⠻⠠⠆⠙⢠⣸⠒⡾⠓⠶⠶⠦⣤⣄⣀⠀⠀⠀⠴⢖⣒⡒⠒⠒⠒⠲⠦⢤⣄⣀
⡔⢲⣀⣀⣀⡴⠞⠋⠂⣈⣀⢠⠼⣥⠾⠤⣄⡀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⢀⡜⡽⠓⠒⠦⠤⣄⣀⠈⠉⠓⠲⠤⣄⡀
⠈⠁⠀⠈⢷⠀⠀⠀⢀⡇⢀⣾⠀⠀⠉⠲⢬⠹⡄⠀⠀⠀⠀⠀⠀⠹⠘⡟⠻⣮⡀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠤⠤⣍⣳
⠀⠀⠀⠀⠈⢧⡀⢀⠜⠉⢸⢹⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠈⠀⡇⡇⠀⢹⠉⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠘⡜⢆⠀⠀⠀⡠⢃⡏⠀⠀⠀⠀⠀⢀⢰⢣⠃⠀⡸⠀⠀⠀⠈⠙⣷⠔⢤
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⡈⠢⢭⣉⡭⠴⠋⠀⠀⠀⠀⠀⠀⠀⡎⡌⠀⢠⠇⠀⠀⠀⠀⠀⣿⠒⠺⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⢂⢜⡜⠀⢀⠎⠀⠀⠀⠀⠀⢠⡏⠀⢰⣇⣀⣉⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠶⠦⠤⣤⣮⣮⣤⣴⣧⠤⠤⠤⠤⠤⡤⢏⠑⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡸⡀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠴⠷⠷⠶⠤⠤⠤⠤⢤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⢤⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣒⣲⣶⣤⣤⣤⣶⣶⣚⣁⣀⣀
⣿⣿⣉⣩⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡞⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠠⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠈⠀⠈⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⢸⣟⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣶⣄⣠⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⢀⠞⣵⠏⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⢻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠈⠁⠀⢂⠏⠙⠓⠚⠂⠠⣄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠴⣼⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢸⠇⠀⠘⠁⠀⠀⠀⠀⠀⠀⠐⠂⢀⣠⡾⠀⠀⠀⠀⠀⠀⠈⡟⢳⠀⢈⣲⣦⣄⣾⣷⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢼⠟⠆⠁⠀⠀⣄⠀⠀⡉⠰⠁⢸⢓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⢀⢀⠐⢶⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⢁⠀⡄⠀⣤⣶⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠘⣿⣄⡀⠀⠀⠀⠀⠀⢴⣿⠀⠀⠀⠀⠀⠀⠠⠐⢀⣼⣾⡿⠟⠟⠠⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣤⢀⠀⢀⡄⠀⠉⠀⠀⠀⠀⠀⠀⠐⣠⣬⣿⡃⠁⠀⢀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⢿⠷⠿⠃⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡧⠴⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⢱⣦⡞⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠠⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣧⠀⠀⠰⠦⠀⠀⠐⠀⠀⠀⠂⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⣄⡀⠆⠀⠀⠀⣠⣶⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣦⣤⣤⣆⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢳⡀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠓⠞⠀⢳⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠠⠤⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢸
⠀⠀⠀⠀⠀⠖⠲⢄⠘⠄⢇⢀⣀⣀⠀⠀⠀⠀⣸⡤⠿⠒⠒⣶⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢀⠧⡀
⠀⠀⠀⠀⢠⡀⠱⠀⡠⠤⢼⠏⣠⠴⠃⠀⢠⠞⣁⠀⢠⢔⣦⡌⡄⠈⠳⡄⠀⠀⠀⠀⠀⣠⠖⠚⣹⠇⡐⢹⡀
⢀⠤⠒⡖⡀⠈⠉⡆⠀⠀⠀⢀⡇⠀⠀⢰⠃⢨⠋⠁⠙⠋⠘⠋⠀⣤⠄⢿⠀⠀⠀⠀⠀⠹⣄⠉⠙⠻⣀⡞⢡⠀⡀
⠈⠀⠀⠇⢐⡠⡄⠙⠶⢶⡖⠋⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⠀⣾⠀⠀⠀⠀⠀⠀⢸⡷⠤⡤⠞⠉⠁⢫⠉⡆
⠃⠂⠀⠀⣸⢐⠃⠀⠀⠈⢷⡀⠀⠀⠀⠸⡆⢝⣦⡀⠀⠀⠀⢀⡴⠃⣰⡏⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢀⡴⠃⠸⣄⣀⠤⠔⣒⣲
⠘⣄⠀⠉⠁⣸⠀⠀⠀⠀⠀⠙⢦⣄⢀⣠⠽⢦⣉⠉⠛⠒⠋⠁⣀⡴⠋⠉⠓⠦⣄⣀⡴⠋⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⠆⠀⠐⢒⡒
⠀⠈⠑⠒⣾⠁⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠈⠛⠒⠖⠒⠋⠁⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⣼⠋⠲⠶⠶⠒⠒⠒⠢⠟
⠀⠀⠀⠀⠈⠳⣤⣀⣀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⢀⡠⠖⠲⡆
⠀⢀⣀⣀⣀⣀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡉⠀⠀⣸⠃
⠀⢿⡀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠔⠒⠳⣄
⠀⠀⠉⣳⠒⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⡿⢄
⠀⠀⠀⢃⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣷⠀⠈⡐
⠀⠰⡍⠠⠤⣿⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠋⣡⢴⡟⠉⠉
⠀⠀⠀⠀⠀⠸⣧⣄⡉⠛⠶⢦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠴⠖⠛⣉⡤⠖⠋⢡⡟
⠀⠀⠀⠀⠀⠀⠙⢧⡉⠓⠢⠤⣄⣈⣉⡉⠉⠙⠛⠛⠛⠛⠋⠉⣉⣉⣹⣥⡤⠴⠖⠚⠉⠁⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠙⠓⠒⠶⠶⠶⠶⠶⠶⠒⠛⠻⡏⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣼⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢿⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⡀
⠀⠀⠀⣾⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠰⣅⡀⠈⢀⣀⣤⣤⣄⣀⣀⣀⣠⣤⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠖⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣡⠤⠴⠖⠚⠓⠋⠙⠢⡀
⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠤⠄⠨⡁⠘⢯⠭⠉⠩⠭⣲⡄
⠀⠀⠀⠀⠀⡜⠠⠄⠀⡔⠂⠀⢇⠐⠀⠑⠂⣀⣤⠖⠋⠉⠙⠲⢄⣨⢃⠀⠀⠀⠀⠀⠠⠐⠈⡉⠉⠲⡄
⠀⢀⡠⢔⣲⠁⠀⠀⠀⢈⣀⣀⠤⠤⠖⠚⠫⠁⠑⡄⠐⣀⣠⠴⠊⠁⠲⣂⠁⠀⠀⢂⠄⠀⠀⣌⠁⠆⠸
⡔⡝⠈⠔⠉⠉⠉⢹⠋⡏⠀⠀⠀⠀⣀⣀⡤⠧⠒⠛⣹⠋⠉⠁⠀⠀⠀⡄⠀⠀⢸⢁⠀⢔⣎⠋⠂
⠙⠦⠼⠤⠤⣤⠤⠴⠤⠓⠒⠒⠉⠉⠁⠀⠀⢀⣠⠖⠁⡠⠊⠂⠀⠀⠀⠸⣄⠀⠘⣮⡀⣀⠠⢀⠆⠀⡜
⠀⠀⠀⠀⠀⠈⠒⠤⢤⣄⣀⣀⣤⠤⠤⠖⠚⠉⠀⠀⡜⢁⠌⠀⠀⠀⣠⠄⠊⠉⠀⢀⠙⠛⠚⠁⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⣄⡴⠊⠀⠀⠀⠀⠀⡸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⠁⠘⠆⠀⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⡠⠁⠀⠀⠈⠠⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠖⢈⡠⠚
⣶⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣷⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⢀⡴⠒⠋⠋⡿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡟⣲⣤⡀⠀⠀⠀⠀⠀⢀⣴⣚⠯⠛⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⣿⣷⡀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠛⢿⣷⡄⠀⠀⠀⠰⠋⠉⠋⠁⢄⣈⣹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⢹⢿⣿⡆
⠀⠀⢺⠀⠀⡀⠀⢁⣀⠁⣿⣿⡇⠀⠀⠀⠀⠀⠀⢱⡀⡋⢈⣼⣿⡇⠀⠀⠀⣧⣀⣀⠀⠀⢀⣽⣿⣿⣿⠀⠀⠀⠀⢠⣤⣄⣦⣤⣤⣾⣿⣿
⠀⠀⠠⠀⠀⠁⠀⠀⠈⢦⣽⣿⠃⠀⠀⠀⠀⠀⠀⠐⣠⣹⣷⣾⣿⠇⠀⠀⠀⠈⠻⣿⡇⠀⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⡠⠆⣄⣾⣿⢼⣿⡟
⠀⠀⠀⠈⢁⡀⢐⣴⣴⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠒⠸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⢹⣷⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠒⠀⡀⣍⣰⡿⠋
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡛⣛⣳⣦⡀⠀⠀⠀⠀⠀⠠⠞⠁⡹⢿⣷⣶⡞⢻⣿⠀⠀⠀⠀⠂⠈⠀⠀⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢶⣄
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣩⣽⣷⡀⠀⠀⠀⠀⠀⠀⠊⠐⢁⣼⣿⣿⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣆
⠀⠀⠀⠀⣀⣉⣉⣉⣈⣉⣉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠴⢋⣽⠟⣡⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣿
⠀⠀⠀⠀⠈⠛⠛⠻⠋⠿⢿⣿⠁⠀⠀⠂⠀⠀⠀⠀⠀⠉⣠⣾⣿⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⢰⣿⣿⠏⠀⠀⠀⠀⠀⠀⣀⢠⣶⣶⣶⣿⠏
⠀⠀⠀⠀⠀⠀⣀⣲⣶⡶⠟⠁⠀⠀⢀⠀⠀⠀⢤⣴⣶⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠠⠀⣀⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⡿⡄
⣷⡘⢣⡀⠀⠀⢀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔
⣿⣿⡀⢳⣀⢀⣾⠎⠳⣦⣾⡛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢽
⣿⣿⣿⣷⣬⡙⢻⣷⠀⢹⡟⣻⣾⡒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣴⣦⣀⣀⣿⡷⠿⣿
⣿⣿⣿⣿⡿⠿⠂⠙⢿⣦⣿⣿⣿⣿⡆⠱⡄⢀⣾⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣝⣾⣷⣿⣄⣼⣿⣿⣿⣶⣹
⣿⣿⣿⣿⣶⣶⣦⣴⣤⣽⣿⣭⣿⣿⣧⣤⣾⣿⣿⣧⣡⣤⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⡤⠶⠾⡿⢛⣛⣛⣛⣋⣉⡉⠉⠩⠉⣉⣹
⣿⡯⣴⠋⡉⣀⣤⣭⣿⣿⣿⢿⣏⠙⠓⠢⠤⣤⣠⡖⠛⠉⠁⠉⠋⢩⠍⠆⠂⠈⠀⠀⠀⢀⠔⠛⠋⡩⣽⣿⣿⣿⣿⣿⡗⠄⠀⠉⢼
⣿⣴⣿⣄⡘⠛⠛⠛⠛⠋⠅⠀⠙⠷⠀⠀⠀⠀⠈⠓⢦⡀⠈⠀⠄⠀⠀⠀⠀⠀⠠⠴⣾⣿⣶⣴⣶⣿⣿⠿⠟⡛⢋⡥⠰⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⠿⠛⠚⣛⣡⡛⢂⣀⣀⣀⣀⣀⣀⡀⠀⠀⠙⢦⠀⠈⢀⡤⠖⢀⣰⣶⣾⣿⣿⣟⠻⠿⢿⠟⠛⠋⠀⠀⢀⠀⠠⠖⣹
⣿⠿⠿⠛⠛⠁⡠⠒⠉⠁⠀⠀⣒⡺⣷⣿⣿⣿⣿⣿⣿⡷⣤⢸⡀⠠⣾⣀⠒⠻⠿⠟⠛⠉⠛⠟⠣⠀⣂⣀⡀⠀⠀⠀⢀⣼⣿⠿⢿
⣿⠉⠀⠀⣠⣾⣧⣀⡀⠀⠀⠠⠤⠭⢭⣽⣿⣿⣿⡿⢿⠃⠝⠻⡿⣦⣄⠉⠿⣿⣶⣶⡶⠰⠀⠁⣠⡾⠿⠿⠳⠾⠴⠂⡩⠰⣶⣦⣬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣷⣿⣿⣶⣶⣶⣵⣦⣤⣤⣀⣙⣇⣠⣦⣤⣤⣄⣠⣶⣫⣤⣠⣤⣤⣤⣤⣤⣾⣧⣈⣉⣭⠼
⣿⣿⠿⢿⡿⠿⢿⢿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡔⣖⣒⣶⠶⢤⣄⣲⣄⡀⠀⡀⠀⠀⠈⠀⢀⣤⠒⣟⠀⠉⠳⣶⣄⠀⠀⡀⠀⠀⠀⢀⣠⡤⠤⣤⡀
⠀⠀⠀⠀⠀⣠⣴⣟⣿⣿⣿⣿⣿⣷⣿⣿⣉⠹⣿⡄⠃⣀⡀⠀⢠⡛⠉⠳⣌⠑⢄⠀⠈⠙⢳⡀⠀⠀⠀⢰⠛⠁⡠⠚⢉⣿⣦
⠀⠀⠀⠀⢰⡟⠛⢟⣯⡙⢿⣿⣿⣿⣿⠿⡿⠟⣽⣿⡀⢘⠖⠀⠀⠈⠢⡀⠈⠓⢦⡙⠲⢤⣐⡇⠀⠀⠀⠤⠖⠁⠀⢐⣿⣿⣿
⠀⠀⠀⠀⣴⣏⣼⣿⣿⣧⣌⣭⠙⣿⡛⢉⣿⣶⣿⣿⣷⡛⠀⠀⠁⠀⠀⠈⠢⡀⠀⠈⠑⢢⣬⡇⠀⠀⠀⠀⢶⣤⣶⡭⢒⡽⠃
⠀⠀⠠⣤⠺⠁⣹⣟⣭⣿⣿⡿⣿⣿⣷⠟⢻⢿⣿⣽⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⢶⠟⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠒
⠀⠠⣾⡋⢤⣴⣼⣿⣗⢊⣯⠄⠈⡉⢰⡆⠃⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠶⠚⠁⠀⠐
⠀⠀⠀⠉⠙⠿⢅⠈⣻⣿⣷⣾⣼⣧⣿⣿⣻⠿⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⡛⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢈⣹⣿⣿⣿⠟⠋⠑⠈⠀⠀⠀⠀⠀⠀⠀⣀⠰⡂⠂⡐⢁⣰⣦⣤⡀⠀⠀⠠⣤⣀⣰⣧⣀⣿
⠀⠀⣀⣤⣶⣶⣄⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠓⠂⠀⠀⠠⠔⠀⠒⠛⢛⣦⡀⠀⠱⢼⣃⣀⠴⠃⠤
⠀⠠⣿⠛⠻⠛⠛⠁⠀⠀⠀⢀⣴⡆⡀⢠⣿⣶⣄⠀⠀⠀⠀⠛⠛⠻⣿⠙⠂⠚⠛⠋⠿⢛⠻⠟⣷
⠀⠀⠉⠻⣷⣦⠞⠀⠀⠀⢠⣍⣭⣿⠿⣴⠗⢾⣿⣷⠀⠀⣀⣀⡀⠀⢀⣀⣀⡀⠀⠀⡀⠈⡁⢀⣿⡀⠀⠀⢀⣤⣶⣖⣒⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⡯⣽⡃⣦⣶⠋⠉⣿⡇⠀⢹⣿⣿⣿⣟⣽⣿⣻⣷⣮⣽⠷⠿⣿⣿⠃⠀⢰⡿⠋⢉⣩⣭⣍⣻⣧
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣤⣶⡟⠀⠀⠀⢀⢨⣭⣽⣻⣩⣤⣤⣀⣠⣄⣡⣼⠏⠀⠀⢸⡶⠊⠉⠉⠉⠙⠛⣿
⠀⠀⠀⠀⢰⣿⣯⢳⠀⠀⠀⠀⠀⠠⣼⣿⡿⠿⠋⠀⠀⠀⠀⠀⠹⢤⣤⣭⣉⣉⣩⣩⣭⣿⡿⠋⠀⠀⠀⡘⢿⣿⣿⣿⣿⣭⣿⠟
⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⡛⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠻⠿⠿⠿⣧⣉⡙⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⢤⣤⣤⡀⣀⣀⣐⣤⣤⣖⠀⠀⣠⣿⠼⣿⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠖⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠉⠙⠓⠾⠉⠋⣀⠀⠀⠻⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠹⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠘⠃⠀⠀⠀⠹⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠊⠁⢀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢿⣽⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠗⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠠⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣤⠀⠀⠀⠀⢀⠀⠀⠀⡰⠂⠀⠀⢶⣷⠀⠛⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣷⡚⢳⣶⣮⣤⣀⡀⠁⠀⠀⡀⣻⡇⠀⠀⢾⣿⣿⣿⣆⡀⠀⢀⣤⡀⠀⠀⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⠧⣿⣿⣿⣿⣿⣿⣿⣤⣀⣺⢷⠾⠁⠀⠀⠈⠁⠻⠿⣿⣧⠚⠛⢿⢇⠀⣴⣿⣿⣿⣿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠙⠻⠟⠛⠃⠙⠹⠟⣿⡿⢮⣄⠀⠐⠿⠷⠆⠀⠞⠙⠋⠀⠀⠀⠀⠀⢐⣾⣿⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠂⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣦⣀⠀⠀⠀⠀⠀⠐⡩⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣄⡀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⣿⢟⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣟⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣠⣶⠿⠟⣋⠵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⠃⠛⠶⠽⠾⠟⠋⠊⠚⣙⠬⠦⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉



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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⠀⠀⠀⢀⣌⠙⢢⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢿⣿⣿⣿⣷⡈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠄⠀⠴⡖⣢⠁⠀⠂⠀⠀⠀⠀⢀⠀⠊⠁⠀⠀⠀⠈⠙⡟⢿⣿⣿⡷⢠⠝⣷⡀
⠀⠀⠀⠀⠀⠀⠀⡾⠠⠀⠀⠞⠁⠀⠐⠃⠀⠠⠄⠀⢠⡝⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢉⣱⠁⢠⣽⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⡀⠀⠀⠴⠀⢀⠀⠀⠀⠀⠈⠈⠁⠠⣶⣼⣿⣿⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⣀⣀⣥⣀⠀⠀⠀⠈⢀⡀⠀⢀⡄⠀⠀⠐⢾⣿⣿⣿⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠢⠤⠀⠀⠀⠈⠉⢾⠋⠛⠁⢤⡸⠧⢀⣀⠀⣄⡀⠀⠀⠛⢀⢻⣿⣿⣿⡄
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⣧⡀⣀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠳⠂⠻⠿⠛⣿⣦⣤⠀⠈⢿⣿⣿⣿⡇
⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⡀⢀⣇⠀⠛⠻⣿⠷⣶⣄⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣶⣾⣿⣿⣿⡇
⠀⠀⠀⠀⢺⢳⢤⣄⠀⣠⣠⣽⠀⢻⡇⠀⠀⢠⡄⠹⡿⣿⡿⠟⠻⢶⣤⣤⣤⣤⣀⠀⢠⠀⣤⣾⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠘⣧⠀⠛⢿⢟⣨⣿⠣⠀⠀⠀⠀⠀⠁⠀⢠⣿⠋⠀⠀⠀⠈⠙⢻⣏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠹⣄⠀⠈⠈⠃⠙⡀⠀⡀⠀⠀⠀⠀⠀⠀⠈⣦⣠⠀⡀⠀⠀⠈⣀⣾⠝⠁⣡⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠁⠄⠁⠀⠀⠁⠁⠀⠁⠀⠈⣹⣷⣷⣶⣤⣤⣡⣵⣷⣤⣽⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣤⢤⣄⠀⠀⠀⣀⠀⠄⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡙⠛⣿⠇⠀⠀⠁⠀⢠⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⣾⣄⢠⣾⡴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⠤⠖⠒⠗⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠲⡒⢲⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⡀
⠀⠀⠀⠀⠁⠀⢀⠀⠀⠑⠎⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⠸⢿⣿⣦⠀⠀⠀⠀⢀⡜⠛⠻⠛⢂⠀⠓⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⠟⣿⣿⣧
⠀⠀⢰⡀⠀⠀⠀⠠⠀⠀⠃⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⢂⠀⣴⠀⠂⣿⣿⡇⠀⠀⠀⣸⠀⠀⠀⠀⠀⠑⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠠⣀⡀⡈⣡⣿⣿⣇
⠀⠀⢠⠁⠀⠸⠆⠀⠘⠰⡀⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠘⡃⢒⣤⣚⣿⣿⡇⠀⠀⠀⠸⢿⣿⣦⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠙⣛⠛⢛⣿⡛⣿⣿⡟
⠀⠀⠀⠃⡤⠀⠀⡀⠈⠀⣩⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠐⣶⣿⣿⣿⡟⠀⠀⠀⠀⠀⠠⡹⣿⡀⢠⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣋⠁⠛⢾⠟⢩⣿⡿⠁
⠀⠀⠀⠀⠀⠲⠠⢰⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⣤⣴⡴⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠸⠛⠻⠶⣤⡀⠀⠀⠀⠀⠀⠀⢀⡶⠋⢘⡿⣷⣦⣤⠶⢿⣿⠀⠀⠀⠀⠠⠀⠀⠈⠀⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠔⠡⠞⢁⣽⣿⣧⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢟⣿⠟⢋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢹⣿⣧
⠀⠀⠀⠀⠐⠶⠶⣶⣶⠲⣶⡷⣿⡟⠀⠀⠀⡀⠀⠀⠀⠂⠁⠴⠛⢁⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣱⡟⠁⠀⢀⠀⠀⠀⠀⠀⠀⣀⣄⣴⣿⣿⠋⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠒⠘⠙⠻⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠠⠤⠿⠿⠛⠁⠀⠀⠀⠀⠒⠒⠊⠁⠒⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⠶⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⢰⣿⠛⣿⣦⠀⠀⠀⣿⣿⠉⠙⠛⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⣿⣯⣤⡼⢿⣷⡀⢠⣿⡟⠛⢷⣶⠿⠟⠀⢠⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣦⣀⢹⣿⠸⣿⡆⠸⡿⠁⢀⣀⣀⣛⣃⣘⣛⣁⠀⠈⢿⣧⠀⣠⡈⠻⣦⡀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡙⠻⣿⣿⠀⣉⣥⣶⣾⠿⠿⣿⣛⠛⠛⠛⠛⠿⠿⣿⣶⣧⣄⡙⣷⣀⠈⢻⣦⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠆⣠⣶⡿⠟⠋⠉⠀⠀⠶⠆⠈⠉⠉⠉⠉⢓⣒⣒⣮⠭⠿⠿⣿⣿⡻⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠉⢳⡄⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠑⡄⠀⠀⠰⣞⣛⡆⠀⠀⠀⠀⠀⠀⠀⢀⡉⠉⠉⠀⠀⠀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠈⠒⢤⡀⠀⠉⠀⠀⠀⠀⣀⡀⠀⠀⠈⠁⠀⠀⣤⡤⣤⡀⠀⠀⠀⠻⣿⣄
⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣈⠆⠀⠀⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠘⠧⢤⣄⡽⠀⠀⠀⠀⠹⣿⡆
⠀⠀⠀⠀⠀⣼⣿⠓⠒⠒⠒⠲⠶⠒⠋⠉⣭⡁⠀⠀⠀⠀⠀⢀⣤⡄⠀⠠⣞⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⢰⣿⡏⠉⠑⠒⠢⣄⣀⠀⠀⠀⠈⠁⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣧
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⠉⢳⡀⢠⠖⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⠦⡀⠀⠀⠀⠀⠀⢨⢁⠀⢸⣿
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣻⣄⡀⣀⡼⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠃⠀⠀⠀⠀⠀⠘⠼⠀⢸⣿⡆
⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠛⠉⠈⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣓⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢦⣼⣿
⠀⠀⠀⠀⠀⣿⣧⣄⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣠⠴⠋⠉⣀⠀⠀⠀⠀⠀⢀⣄⠀⡜⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠛⠋⠁⣀⠀⠀⠚⠚⠃⠀⠀⠀⠀⠈⢁⡼⠁⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⢶⠆⠀⠀⠾⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡠⢶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⣠⠴⢚⡲⠂⠙⠋⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠃⠀⠀⠀⠐⠾⠓⠉⠉⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣀⠀⢀⣀⣠⠤⠤⣤⣄⣠⣀⣀⣠⣤⣤⣄⡀⢀⣠⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣾⣿⡿⠟⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣛⣛⣛⣿⣿⣿⣿⣟⣛⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⢠⠶⡄⠀⠀⢀⠀⢀⠀⠀⡀
⠀⠀⠙⠦⣇⡀



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⢛⣉⣉⣉⣉⣉⠉⠛⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⡭⠭⣍⣩⠷⠦⣤⣭⣙⣛⣯⠵⢟⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢣⡾⠥⣤⡤⠏⠈⠙⠓⢛⡷⠀⢀⣠⠞⢉⣭⠽⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣓⣻⣿⣿⣛⠛⠛⠛⠲⢦⣈⠓⠚⠋⣡⡞⢋⣠⠶⠚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⣤⣄⣀⣸⠇⢀⣀⣀⣀⡈⠛⠒⠚⠉⠀⢸⠁⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠳⠶⠶⢟⣻⣭⣉⣀⣈⡽⠃⠀⣴⠋⠉⠛⠀⠀⢀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠺⢿⣶⡄⠈⠉⠁⠀⠀⠀⠛⠶⠶⠒⢚⣋⣉⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣛⣛⣛⣋⣩⣥⠴⠖⣛⣋⠉⠙⠓⠶⠶⠖⠛⣉⣉⣉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣭⠤⠶⠖⠒⣛⣭⣿⣋⣤⠞⠋⠳⣄⢠⣟⠁⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢀⣀⣭⠽⡭⠥⠤⠤⠤⠴⠟⠀⢸⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢤⣞⣋⡉⠉⠛⠓⣲⣻⡽⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⡛⠛⠛⠛⠛⠛⠻⡿⠿⢿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡿⠟⠛⡅⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢉⡟⠿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠿⠋⠁⠀⠀⢠⠃⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡥⠀⣀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠙⠻⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⢧⣀⡀⠀⣀⠴⠃⠰⣶⣮⣿⣷⣶⣶⣶⣾⣿⣿⣷⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣠⣿⣿⡿⠋⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠈⢻⣿⣿⣆
⠀⠀⠀⢀⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣟⠁⢀⣤⣼⡇⠀⢀⣤⢍⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠚⠋⠹⣿⣿⣧
⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⣻⣤⣘⠻⢻⡇⠀⠸⢿⣾⡿⢃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇
⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠂⠤⣀⣼⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣣⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⣼⣿⡿⠳⣄⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠔⠃⠀⠀⠀⠀⠀⡰⠋⣿⣿
⢰⣿⣿⠃⠀⠙⡆⠀⠀⠀⠀⠀⢈⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢿⣿
⣸⣿⡏⠀⠀⠀⠹⡄⠀⠀⠀⠀⠸⡀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⣠⠖⠒⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢸⣿
⣿⣿⡇⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠘⠢⢀⣀⠽⣿⣿⣦⣀⠀⠀⠀⠀⣇⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿
⣿⣿⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡏⠉⠉⠉⣷⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⢹⣿⣧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢧⣀⣀⣠⠟⠀⠀⠀⠀⠀⠀⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠘⣿⣿⡄⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢀⣤⣾⣿⡿⠋⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⣿⣿⡏
⠀⢻⣿⣧⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣄⣀⣀⣀⣠⣤⣴⣾⣿⣿⠟⣁⣹⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⣾⣿⡿
⠀⠀⢻⣿⣧⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡿⢿⣿⣿⣿⣿⡿⠿⠿⢻⡟⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⣀⣞⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣦⣤⣤⣤⣤⣴⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⣠⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⠀⠀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⠿⠿⠛⠋⣀⡠⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣎⡀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣶⣄⡀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⣠⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣷⣾⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣶⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀⣀⣷⣄⣤⣤⣤⣶⣾⣿⣿⡿⠟⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣽⣿⣿⣩⣭⣿⡷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⣿⣭⣙⣿⣉⣩⣴⠷⠢⡀
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠉⠉⠉⠈⠉⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⣼⣦⣴⣤⣤⣤⣤⣤⣀⣀⣀⣀⣤⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⣀⣀⣄⣀⣀⣀⣀⣀⣀⣠⣤⣶
⠀⠀⠀⠀⠀⠀⢿⡁⠉⠻⢿⠟⢻⣿⣛⠟⢛⣛⣛⡥⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠈⠙⠿⠛⠛⣿⡛⠛⠛⣛⣋⡡⢾
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣶⣿⣿⣿⣿⣷⣶⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠉⣉⣉⣙⣉⣉⣭⣭⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣀⠉⢉⣉⣉⣉⣉⣉⢉⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠷⠶⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠶⠶⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡟⠻⠿⢿⡿⠟⠻⠟⣩⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢠⣄⣀⣀⢀⣠⣤⣠⠶⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⠞⠉⠉⢿⣿⡿⢿⡿⠿⢿⠿⠿⠟⠛⠅⠘⢳⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⣡⣾⣶⣀⣀⣀⣁⢁⣀⣈⣀⣀⣠⣤⣿⣷⣌⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣄⡤⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠻⣟⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠈⣿⣿⣿⣿
⠀⠀⠀⢸⣿⠿⠿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷⣶⣿⡿⠟⢻⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⣀⣀⠀⠈⠉⠀⠒⠀⠀⠀⠀⠉⠉⠁⠉⠉⠀⢀⣠⡄⣿⣿⣿⣿
⠀⠀⠀⠘⣿⡀⠀⠀⠙⢛⣛⠛⠛⣛⣿⣙⡛⠛⠉⣛⣉⣉⣥⠾⣿⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⢿⣿⣿⣦⣤⣤⣤⣤⠤⠀⠦⣤⣤⣶⡤⠶⠿⠞⣫⠄⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣿⣶⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⣭⣥⣶⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠐⠒⠚⠉⠀⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣍⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣻⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⢶⣤⣠⣀⣀⡀⠀⠀⡀⢀⣀⠀⠀⣀⣀⣠⠔⣰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠤⣤⣤⣤⣬⣤⣤⣤⡤⢶⣶⠞⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⣘⠿⣿⣛⠛⠛⠛⠛⠛⠛⠛⣛⣛⠏⣡⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣾⣶⣶⣶⣾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣅⣉⡉⠉⠉⠉⢉⣉⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡠⠔⠊⠉⠉⠁⠀⠢⢀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠂⠉⠉⠁⠒⠠⡀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠈⠉⠁⠀⠢⢄⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠉⠉⠁⠐⠠⡀
⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⢠⠊⠀⠀⠀⠄⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠅⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⡈⡃⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡃⠀⠖⠀⠀⠀⠀⠀⠀⠀⠉⠁⡁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠂⠀⠀⠀⠀⢄⠞⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠑⠤⢀⣀⡀⣀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠈⠓⠆⠀⣀⣀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠙⠢⠀⠀⡀⣀⠀⠤⠂⠁⠀⠀⠀⠀⠀⠈⠂⠄⢀⡀⠀⣀⠀⠔⠁


⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⡀⠄⣀⣠⣔⠂
⠀⠀⡠⠔⠊⠁⠀⠀⠈⠁⠢⢀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⡠⣘⡽⢶⡋⢁⠀⡟⡆⠀⢀⠄⠂⠀⠉⠉⠁⠐⠠⡀⠀⠀⠀⠀⠀⠀⡠⠒⠂⠉⠉⠁⠐⠠⡀
⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⡌⠀⠀⡀⢔⡥⠚⠁⠀⠀⠑⣤⢞⠌⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠆⠀⠀⠀⠀⡠⣪⠔⠋⠀⠀⠀⠀⠀⠀⠛⠁⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⡇
⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⡠⣯⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡆
⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⢀⢔⡔⠱⡀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠈⠑⠠⠤⠄⠀⠀⠔⠊⠀⠀⠀⢂⡎⠀⢀⣨⠖⡤⠀⠀⠀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⢀⡀⢀⡀⠠⠔⠁⠀⠀⠀⠀⠀⠈⠒⠄⢀⡀⢀⣀⡀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠙⠫⠉⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠛⢃⠀⠀⠀⠀⠀⠀⠀⠠⣾⣷⠄⠀⠀⠀⠀⠋⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣻⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡸⠁⠀⠀⠀⠀⠉⠀⠀⠀⠐⠻⠿⣿⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠐⠀⠠⢱⠚⠧⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⣿⣫⣿⣿⣇
⠀⠀⠀⠀⠀⣾⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⣠⠇⠀⠀⠀⠀⠀⠙⡾⢏⠀⠠⢤⣀⠠⣶⣤⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠿⠈⠀⠀⠀⠀⠀⠘⠠⠃⢸⢲⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⢾⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠰⠀⣤⣶⣾⢿⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⢹⣷⣀⠀⠀⠀⠀⠀⠺⡿⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⡟⠋⠃⠀⢁⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⡀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴⡿⣇⠀⢀⣠⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠈⢿⣿⡛⠋⢛⠁⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣤⣷⡇⠀⠀⢀⠈⠃⠀⠀⠀⠀⡀⠀⠈⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡀⠀⢈⡁⠀⠀⠀⢀⡀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣤⡀⠀⣐⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣩⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢈⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠂⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠄⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⡈⠀⠀⠐⠀⠀⠐⠀⣀⡤⡀⡀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⠤⠖⠲⠶⡀⠀⠐⠀⠀⠀⢥⠉⡀⠀⢀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⣀⡆⢠⣀⠀⠀⠀⠀⠀⡁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠈⠀⢀⠉⠀⢈⢀⣢⣄⡀⠠⠤⣱⠚⠛⠣⠀⣀⡀⠀⠸⣄⠀⠒⡢⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠁⠀⢄⠁⠶⠐⢦⡴⠂⡐⡁⠀⡰⠊⠤⠢⠀⠀⠀⠄⡄⠁⠤⠀⠐⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠂⠀⠀⡐⠄⠄⠀⠚⠛⠷⠀⠠⢙⡃⠄⢠⡃⠀⠀⠀⠀⠊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠂⠀⠀⠀⠀⠠⠀⠄⠀⠁⡈⠠⠀⢁⠀⡄⢈⠉⠁⠄⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠉⠀⠀⡈⡁⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠠⠂⠀⠀⡁⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠐⠄⠀⠀⣀⠐⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠑⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠠⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⡀⠐⠄⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡤⠤⠤⠤⢤⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠈⠷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⡁⠀⠀⠄⠀⢀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⣀⠀⠀⠀⢀⠀⢀⠈⢧
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠍⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⡇
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣧
⠀⠀⠀⠀⠈⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠂⠢⠀⠀⠀⠀⠀⡀⢙⠆⠠⠄⠀⠆⠀⠁⢀⠀⡟
⠀⠀⠀⠀⠀⣏⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣀⡌⢠⡀⠀⠘⢏⠀⠀⡤⠄⠀⠀⢀⣀⡔⢠⢀⡇
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⢤⠀⠀⠀⠉⠲⡄⣀⣤⡴⠄⢠⢤⠄⠰⠾⠟⢹⠀⠆⢸⠃
⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠹⡛⢻⢦⡛⢢⠀⣄⢐⣤⢀⢀⡏
⠀⠀⠀⠀⠀⠀⠘⣆⣱⠐⠀⠀⠭⣴⡂⣀⢠⣀⡀⠀⠀⠀⢄⠀⠀⠀⢰⡤⡀⢀⠀⡠⢄⠴⢂⡸⢅⣶⡀⣬⡴⠞⢀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠎⣤⠀⠉⡁⠉⣩⡤⢀⡵⠁⠀⠀⠀⠀⠀⠀⣖⡀⠀⠀⠙⠛⠀⣠⡒⠒⠺⠛⢙⡃⢛⠲⢏⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣌⠙⠓⠘⡘⠖⠋⠐⠀⠁⠀⠂⠀⠀⠀⠠⠈⠉⠀⠐⠀⠄⢁⠈⣀⣤⡾⣛⡭⣷⡋⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠂⠀⢀⠀⠀⡀⠀⠠⣀⣸⠃⡀⠤⠉⠀⠄⠀⢘⠈⢸⠟⠉⠘⡻⢓⣦⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⠠⣀⢀⣥⠀⠄⠀⠀⠀⠀⠒⠀⢌⠄⠓⠄⠀⡀⣄⠦⣢⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣽⣷⣪⡄⠀⠐⠀⠆⠂⠂⠁⠂⢀⣄⣠⡿⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠒⠒⠛⠛⠛⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠠⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠁⠀⡀⠀⠀⣀⠤⠖⠊⠉⣙⡶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠠⠀⠈⠉⠀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⣀⡤⠴⠒⠉⢁⣠⠤⠒⠊⠉⠉⠙⠛⠋⠉⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⢠⠟⠒⠉⢀⣰⣋⣀⡠⠴⠒⠉⠁⠀⣀⡄⠀⠒⠀⣀⠀⠀⣀⣤⡴⠚⠹⡄
⠀⠀⠀⠀⠀⢀⡯⠴⠒⠉⠁⠀⠈⠀⠀⠀⣀⡤⣄⠀⣀⡤⠔⠒⠉⣁⡽⠉⠀⠁⠀⠀⣠⠼⡀
⠀⠀⠀⠀⠀⣸⡠⠤⠤⠤⠤⠤⠤⠖⠊⠉⠀⠀⠀⠉⠀⠀⠀⠀⡏⠁⠀⠄⠀⠀⣠⠞⠁⠀⣇
⠀⠀⠀⠀⠀⡏⢀⡀⠀⠀⢀⣀⠤⠖⠊⠀⠀⠀⠀⠀⢀⡤⠴⠚⠀⢀⣠⠤⠒⠋⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡏⠁⢀⠀⠀⠉⠀⡀⠀⠀⠀⠀⠋⢁⣀⠏⠀⠀⠀⡏⢁⣠⠤⠖⠊⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⢹⠀⢀⠤⠖⠊⠉⠀⠀⣀⠤⠒⠊⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⡠⠤⣄⡤⠔⡏
⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠂⠀⡰⠋⠀⠀⠀⠀⢀⡤⠖⠊⠉⠉⠉⠁⠉⠉⣁⡠⠤⠊⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠘⣆⣀⡤⠴⠊⠀⢀⣀⠤⠖⠊⠉⡀⠀⠊⠀⡀⠀⢀⡴⠊⠁⠀⠀⣀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⣀⡎⠀⠀⠀⠈⠉⠀⠀⠀⠈⣀⠴⠋⠀⠀⠐⠚⢉⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡉⢁⣠⠤⠒⠊⠉⠉⠑⠒⠋⠉⠀⢀⡀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⣀⡠⠄⠀⠀⠀⠀⠀⠈⢁⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠚⠛⠉⠉⠹⡏⠛⠓⡶⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⢀⣀⣀⡀⠀⠀⠀⠀⢀⠇⠀⢸⡁⠀⠀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⢀⡤⠚⠉⠀⠀⣿⠀⠀⣠⠖⠉⠀⢀⡴⠃⣀⡤⠖⢦⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣀⠴⠋⠀⠀⢀⣠⠞⠁⠀⠀⠳⣄⣀⠀⠘⠲⠚⠁⠀⠀⠘⠚⠉⠙⠦⢦⠙⢦⡀
⠀⠀⠀⠀⠀⢠⠞⠀⢀⡞⠁⠀⢀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠖⠚⢲⠀⠀⠀⢀⡀⠀⠀⠈⠓⠒⠳⣄
⠀⠀⠀⠀⣰⢻⠀⠀⠸⣄⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣰⠋⠙⢦⣠⢤⡀⠀⠀⠘⣆
⠀⠀⠀⢰⠃⠈⠧⠤⠴⢦⡁⠀⠀⠀⣠⠞⠉⠳⣄⣀⣠⠴⠒⠛⢳⠀⠀⢾⠀⠀⢰⠃⠀⠀⠀⠀⠀⢹⠀⠀⠀⠘⡆
⠀⠀⢀⣯⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠷⠚⠛⢦⠀⠀⠀⠀⠀⢠⠏⠀⠀⠈⠳⠖⠋⠀⣠⠦⡄⠀⢀⡼⠀⠀⠀⠀⢹⡀
⠀⠀⣸⠸⡇⠀⠀⠀⠀⢸⡄⠀⢀⣠⠴⠶⢦⡘⠦⠤⣄⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⡴⠃⠀⣿⢠⡎⠀⠀⣀⠀⠀⠀⣇
⠀⠀⡟⠀⠳⣤⣄⣀⣀⣀⠙⠋⠉⠀⠀⠀⢸⡇⠀⠀⠸⣄⠀⠀⡇⠀⠀⠀⠀⣀⠞⠀⠀⣰⠃⠈⠳⣄⣸⠹⡆⠀⠀⢻
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢙⡆⠀⠀⠀⠀⠀⠳⡀⠀⠀⠈⠉⠋⠁⠀⠀⠀⡞⠁⠀⠀⠀⣇⠀⠀⠀⠀⠀⣸⠃⠀⠀⢸
⠀⠀⣧⠀⠀⠀⠀⢰⡚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣄⣤⡤⠤⠤⣄⠀⢹⡄⠀⠀⠀⢈⡇⠀⠀⠀⡴⠃⠀⠀⠀⣼
⠀⠀⢹⢀⡤⠶⠶⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠳⢤⣤⠤⠞⠀⠀⠀⢸⡃⠀⠀⠀⠀⡏
⠀⠀⠈⣿⠀⠀⠀⡤⠶⠦⢤⡀⠀⠀⠀⠀⢰⠋⠉⠉⠉⠉⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠈⢳⡀⠀⠀⣸⠁
⠀⠀⠀⠸⡄⠀⢸⠁⠀⠀⠀⠉⠓⢦⡀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⣸⠀⠀⠀⡸⠁⠀⢠⠇
⠀⠀⠀⠀⠹⡄⠈⢧⡀⠀⠀⠀⠀⠀⠉⠓⠚⠁⠀⠀⠀⠀⠀⣠⠤⠶⠖⠒⠋⠁⠀⢀⡤⠞⠁⠀⢀⡼⠁⠀⢠⠏
⠀⠀⠀⠀⠀⠘⢦⠀⠙⠒⠶⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⡴⠋⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣀⣹⠄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⢸⢁⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢬⣓⠒⠒⠒⠲⢤⣀⠀⠈⠙⠒⠲⠶⠒⠚⠁⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⢤⣬⣱⣤⣀⣀⣤⡤⠤⠖⠚⠉⠁

⠀⠀⠀⠀⠀⠀⢀⣰⣐⣏⣸⣟⢒⣤⣽⣀⡀⢠⠀⠀⠀⠀⣠⢦⠙⠄⠀⠙⠷⣦⡀⠀⠀⠀⠀⣠⡴⠒⣢⢄⡀
⠀⠀⠀⠀⢰⣶⣯⡿⣿⣿⣿⡿⣿⣿⣤⣸⣿⡌⠄⣄⠀⠐⢅⠀⠑⢤⡐⠀⡀⠈⢑⡀⠀⠀⠐⠃⠀⠈⢁⣼⣿⡄
⠀⠀⠀⠀⣿⢀⣽⣷⡌⠹⠿⢟⡟⠭⣭⣁⣿⣷⡠⠏⠀⠀⠀⠑⢄⠀⠉⠲⠌⠑⠺⡇⠀⠀⠈⡁⠀⣠⠔⠫⣿⠁
⠀⠀⢀⣀⡟⢻⡿⣛⣿⣿⣷⣾⣧⡴⣿⣿⡟⡟⠃⠀⠀⠀⠀⠀⠀⠉⠢⣀⠀⣨⡿⠀⠀⠀⠀⠈⠛⠟⠵⠚⠁
⠀⢠⡼⠃⣀⣘⣿⡏⠙⣋⠈⠛⢋⡄⠈⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠕⠈
⠀⠀⠈⠑⠻⢏⠙⣻⣿⣧⣦⣿⣼⡳⢾⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠛⢲⡄
⠀⠀⠀⠀⠀⠀⠉⠉⢉⠿⠿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⣦⣤⡀⠀⠀⢤⣄⡀⢧⢀⡇
⠀⠀⣤⣆⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣚⣁⣀⡀⠀⣒⣀⡀⣈⣻⣦⠀⠀⠲⠁⠠⠚⠁
⠀⠸⠏⣉⠉⢈⠀⠀⠀⠀⣴⣯⣤⠀⡞⣳⣦⡀⠀⠀⠉⠉⠙⠇⠈⠀⠉⠁⠛⠠⠉⠩⡇⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠙⠛⠃⠀⠀⠀⠶⣶⠿⡏⠛⣉⡿⠿⣷⠀⢰⣶⣦⣤⡤⣤⣶⣄⠠⢤⣤⣤⣾⡧⠀⠀⣤⡾⠿⠷⠦⢵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣼⣦⣾⣿⡀⣠⡏⠀⠈⠋⠙⣛⠿⠿⠓⠛⠛⠉⠉⠉⢻⠇⠀⢸⣋⠀⠐⠛⠿⠶⢿⡆
⠀⠀⠀⠀⢤⣞⠣⠀⠀⠀⠈⠉⣩⣿⣿⡿⠟⠀⠀⠀⠀⠺⣉⣛⣛⣛⢛⣛⣛⣿⡿⠃⠀⠀⠘⣷⣶⣶⣶⣂⣠⡾⠁
⠀⠀⠀⠀⠈⠛⠊⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠛⠛⠛⠉⠀⠀⠀⠀⠀⠈⠛⠻⠿⠟⠋