Tige Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢋⡡⠄⠀⠀⠐⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢋⡴⣌⡉⠭⠬⠅⠴⢄⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡰⢣⢀⣸⠿⢂⣀⢲⣝⡰⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⣿⠈⡀⠠⢶⣗⠂⢚⡿⠆⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠈⠀⠐⢠⠰⢀⠐⠘⡒⢃⢠⢀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠺⡐⢦⣄⣀⣀⣴⢖⡪⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⢇⠈⣄⢠⡑⠀⠀⡟⠀⠹⡗⠠⢄⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣰⡿⣦⣀⡜⠂⢇⡀⣀⠋⢀⣩⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣾⠧⡉⠛⢧⣀⠀⠿⠁⣀⡞⢋⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣿⢧⡈⠀⠀⠈⠶⡶⠞⣵⠞⢓⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠘⠳⣄⠀⢀⣀⠀⠞⠁⠐⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢦⣄⣀⠑⠄⠉⠉⢀⣠⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡉⠀⠘⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⣀⠀⠈⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠴⠗⠈⠀⠠


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢀⠠⠀⢤⡤⢶⣦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⢭⠀⠀⡀⠴⣽⠀⠐⠈⡔⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠈⢀⠠⡘⡀⢰⠏⡀⠘⠃⠀⢀⢤⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣉⢠⠸⡇⡤⡈⡀⠀⠀⠤⠀⢉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠐⠦⠴⢀⡄⠀⠀⠀⠀⠀⠈⠃⢀⠊⢀⣦⠀⣀⡤⠀⡁⠀⢀⡉⢁⠂⠴⠂⠀⠨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡦⠀⠁⠀⠀⠀⠀⠁⠺⠂⠀⠀⠀⠀⠀⢸⣃⣩⡿⠠⠀⠐⠻⠁⢆⠈⠉⠁⠔⣊⠓⠀⡀⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⢀⠀⠤⢐⣁⣀⡈⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⠂⢀⠀⠀⠀⠀⠠⣤⡀⠀⢠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠚⠕⢊⣕⢨⡀⢀⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢅⣄⡀⣀⠈⡦⠀⠅⠀⠀⠀⠀⠈⠙⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⣠⣤⣌⠑⢦⠐⠨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠨⠦⢁⠂⠓⠪⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⠑⣂⠠⢄⠀⠨⢭⠱⡬
⠀⠀⠀⠀⠀⠀⠀⡘⠀⣠⠴⠒⠀⡠⠼⣥⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠤⠧⠀⠁⠂⡉⠒⢦⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠉⠅⠒⣡⠂⠻⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡒⠄⢤⠁⠡⣄⠲⠈⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⡀⠀⠐⠒⠉⢘⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣩⠥⢄⠉⣆⠀⡀⠒⠀⠀⠀⠠⢡
⠀⠀⠀⠀⠀⠀⠀⢠⢂⠀⠀⠏⠐⢊⠅⢂⣉⢀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠭⣉⡷⠗⠛⢱⠄⣀⠀⡄⡘⢦⠂
⠀⠀⠀⠀⠀⠀⠀⢺⡸⠀⠀⢀⢴⠃⠄⠡⠖⣀⢞⡛⠋⠠⡄⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣻⡿⡁⠀⠚⣿⠃⠀⠁⢁⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠜⠁⡢⠊⠀⠀⠀⠀⠉⠀⠀⠐⠠⢠⠀⢠⡀⠀⣀⡤⠆⢀⣤⣶⠀⠀⠀⠀⡤⢦⣝⠳⠈⠄⢊⡀⠀⣄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠞⣋⣁⡀⠀⠀⡀⠀⠀⣄⠀⠀⠈⠀⡀⠈⢰⡿⠏⠀⠀⠴⠆⠀⠀⠀⠀⣴⣦⣼⣈⠷⠋⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠀⠀⠀⠀⠀⠑⠳⠌⠀⠂⠀⠦⡵⢆⠘⢿⣦⡆⠀⠀⠀⣤⠀⢤⣲⡀⠋⣼⠁⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⡀⡀⢠⠂⠀⠃⠀⠀⠂⠀⠃⠀⣨⠁⠀⠈⠁⠀⠀⠀⠛⠃⠘⢿⡕⠦⠁⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠜⠂⠁⠈⠃⠐⠈⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠐⠛⢄⠀⠀⠀⠤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢀⠀⠀⠀⠀⠀⣄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣙⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⠀⣠⡌⠳⣦⠴⡶⣶⣭⣉⣻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠢⠀⠐⣀⣧⣻⠀⠀⠀⠈⣁⠉⠁⠴⠛⡻⢗⢤⣐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡖⣻⣿⣿⡘⢂⡐⠀⢰⣿⡄⠀⠦⠸⡙⠀⡓⠨⠳⡄⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣞⢁⡾⢧⡟⠋⢰⡏⢀⣶⠂⣼⠋⣭⡲⣖⣲⣄⣁⠐⠦⠾⢌⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⢼⠏⠸⡅⣾⠃⢀⣾⠀⣺⡇⢸⡇⢠⡀⢀⣀⣿⠿⠡⠀⠀⢳⣄⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢳⡏⡄⠀⣴⡧⠀⣼⡟⠀⠋⢀⡈⠧⠈⣉⡭⠂⢀⣠⣌⠀⠀⠀⢨⠎⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣿⢧⡆⢾⠇⠐⣿⡇⠀⣶⡜⣷⡤⡾⠋⢐⣽⣿⣿⣿⠋⣿⣿⣿⣆⡾⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠌⡿⠀⣿⡞⠰⣿⣿⡀⠿⣧⠀⠐⣇⣴⡿⣿⣿⣿⣿⣴⠋⠉⡏⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡹⣦⠱⠈⠉⣷⠀⠘⠿⢷⣤⣘⣿⠀⣿⣿⠀⠈⣿⣿⣿⠛⠀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡁⠹⣦⡄⣆⠹⡷⣄⣤⣠⣄⡙⣿⡀⣿⡏⠆⢀⢿⠏⠉⠈⠈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠬⠻⣿⣄⠀⠈⠉⠹⣿⢻⣿⠀⢿⣿⣈⣴⣬⠷⡸⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⠳⣄⣄⠀⢌⠃⢻⣆⠈⠛⠛⡻⠿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⢡⣀⠀⠀⠟⣺⣤⡤⣤⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢑⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⢠⠒⠉⠉⠙⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠉⠉⠒⡄
⠀⠀⠀⢀⡟⠀⢀⣤⣶⣦⣄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⣠⣴⣶⣦⣄⠠⢿⡀
⠀⠀⠀⡼⠀⢰⣾⣿⣿⣿⣿⣷⡄⠐⢄⠀⠀⢀⣀⣀⡤⠤⠬⣭⣯⣻⣿⣛⡥⠤⠤⢤⣄⣀⣀⠀⢀⣠⠊⢠⣾⣿⣿⣿⣿⣿⡆⠀⢧
⠀⠀⠀⢻⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⠈⢛⡙⠛⢀⣤⡶⠶⠶⠲⠶⠔⠶⠶⠖⠶⠶⣶⣤⡀⠛⠛⡻⠁⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⡟
⠀⠀⠀⠀⠡⡸⣿⣿⣿⣿⣿⠏⠉⠁⠔⠛⢀⠔⠉⣠⣤⣶⡾⠿⠿⠏⠹⠟⠻⠷⣶⣤⣄⠙⢦⡀⠛⠢⠈⠉⠹⣿⣿⣿⣿⣿⢇⠌
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⠁⢀⠔⢁⡄⠀⠀⣠⠞⠛⠉⠁⢀⡤⠖⡈⠷⠶⣦⡀⠈⠙⠛⠳⣄⠀⠀⢠⡈⠢⡀⠈⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⡟⠛⠋⣴⠃⢠⠏⠀⠀⠜⠁⣠⠶⠛⣡⢤⣤⠄⠃⠂⢷⣦⣤⣌⠛⠷⣄⠈⠣⠀⠀⢳⡄⠘⣦⡙⠛⢻⣿
⠀⠀⠀⠀⠀⠀⣧⡀⢠⣿⠃⢀⣿⠀⠀⠀⠀⠘⠁⣼⠀⠀⡼⠃⡖⡄⢰⡐⠘⢧⠈⠀⣧⠈⠃⠀⠀⠀⠀⣿⡀⠘⣿⡆⢀⣼
⠀⠀⠀⠀⠀⠀⠛⠀⣼⠁⠀⣿⣿⠆⠠⣦⣶⣶⡀⣿⠀⠸⠛⢀⠃⠃⠀⠁⢈⠋⠇⠀⡿⢀⣶⣶⣴⣄⢸⣿⣧⢠⠘⣷⠀⠟
⠀⠀⠀⠀⠀⠀⠀⣴⡟⢰⡇⠉⢹⣇⢀⣀⣤⣤⣄⠈⠣⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠁⣠⣤⣤⣀⠀⣸⡏⠉⢸⡄⢻⣦
⠀⠀⠀⠀⠀⠀⢰⣿⡇⢸⡧⠀⣾⣏⠉⢻⡙⢿⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢷⡿⢻⡟⢉⣽⣷⠀⣼⡇⢸⣿⡆
⠀⠀⠀⠀⠠⠀⣾⣿⡅⠘⡇⠀⡇⠙⢷⣄⡙⠒⠚⢿⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⡿⠒⠒⢋⣠⡾⠋⢸⠀⢹⠁⢸⣿⣿⠈⠆
⠀⠀⠀⢠⠂⢠⣿⣿⠃⠀⡇⠀⣷⡄⢦⣬⡉⠃⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠃⠀⠙⢩⣥⡔⢠⡟⠀⢼⠀⠘⣿⣿⡀⠰⡀
⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⣧⢰⠈⠳⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⠟⠁⡆⣿⠀⠀⣿⣿⣷
⠀⢠⠎⠀⠠⣿⣿⡟⠀⢠⣿⠘⡀⣶⡈⠐⠐⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣘⢊⢄⢡⡶⢀⠃⣿⠀⠀⢿⣿⣿⠄⠀⠱⠄
⠀⣔⡀⠀⠀⢿⣿⣿⠀⠸⣿⣧⢻⡏⠛⠀⣠⢏⡄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠉⠃⠛⢹⡟⣼⣿⡇⠈⣿⣿⡟⠀⠀⢀⣧
⠰⡿⡄⠀⠀⠘⣿⣿⡅⠀⢿⣿⠀⠉⡀⣴⠃⢈⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄⠀⠀⠘⣦⢠⠋⢀⣿⡿⠁⣸⣿⣿⠃⠀⠀⢀⢿
⢠⣾⠖⠀⠀⠀⢹⣿⣿⣇⠀⠙⢧⣄⠙⢯⣴⡿⠀⠄⠘⣟⠛⠛⠒⠶⠶⠖⠛⠛⣻⣿⠹⠀⢿⣦⣽⡋⣠⡾⠋⢀⣼⣿⣿⡏⠀⠀⠀⢠⣿
⠀⠿⣵⠀⠀⠀⠀⠛⢿⣿⣿⣦⡀⠙⢦⡀⠛⠶⢦⣤⣄⠙⢿⣿⣦⠀⠀⣴⣿⡿⠋⣠⡤⡤⠶⠛⢋⡴⠋⣠⣾⣿⣿⡿⠛⠀⠀⠀⠀⣮⠟
⠀⠀⠡⣤⡀⠀⠀⠀⠈⠉⠛⠙⣿⣷⣦⣽⡷⠶⢴⣤⣤⡀⡀⠈⠛⢶⡶⠛⠁⢀⣀⣤⣤⡦⠶⣾⣯⣴⣿⣿⠛⠛⠉⠁⠀⠀⠀⣠⣤⠉
⠀⠀⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡶⠄⠄⠀⠐⠀⠀⣀⣼⣧⡀⠀⢀⠂⠀⠠⠠⢶⣿⣿⣿⡿⢁⠀⠀⠀⠀⠀⠀⣼⣿⠟
⠀⠀⠀⠀⠈⠿⠆⣴⣄⣀⢠⠀⠀⠀⠀⠛⠛⣿⣶⣶⣦⣤⢴⠞⠙⢿⡟⠙⢳⡦⣤⣴⣿⣾⣿⡿⠟⢡⣤⠿⠀⡀⠀⣀⣦⢰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣀⠀⠀⣠⡀⠀⠻⢿⣿⣿⣇⠀⡷⣤⣬⣤⡴⢾⡀⣸⣿⣿⣿⣿⣃⣴⣌⠁⢀⣀⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠿⠧⠼⠛⠟⠛⠛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠷⠾⠿⠋⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⡿⣿⣿⢿⣿⣿⡿⣿⣿⣽⢻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣭⡓⠈⠉⠋⠋⠰⠟⠙⠁⣺⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠻⠢⠔⠟⠚⠁

⠀⠀⠀⠀⠀⢀⣠⣀⣤⢤⠀⠤⠀⠀⠂⠐⡰⠢⢀⡀⠀⠀⠀⡄⠒⢂⠂⠀⠀⡒⠢⢤⡀
⠀⠀⢂⣴⡞⢿⠈⢛⡋⣄⢠⠄⠀⠀⠀⠠⠆⠀⠁⠀⠀⡀⠈⢠⠀⠈⠈⠀⠈⣴⡤⠃⢺⣆
⠀⠀⠐⠰⠥⢓⣴⢆⢳⡜⣯⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⠐⠀⠳⡄⠀⠀⠀⣟⡿⡀⢛⣿⠄
⠀⢸⣸⡇⠸⢿⣧⣄⣿⢷⣿⡶⠄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣿⢧⡟⠹⢷
⠀⠀⠛⣆⣤⢠⣭⡏⠹⢾⣿⣷⠆⠀⠀⠀⠀⡆⠀⠀⠀⠀⢤⣝⢾⠀⠀⠀⢀⣿⣾⠃⢻⡟
⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠙⣿⣆⡠⠀⠀⠙⠙⢄⣀⠀⠰⣤⣝⠃⠀⠀⢀⢢⣧⣿⣦⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣆⠀⠀⢐⣿⣿⣧⡀⣾⡝⠐⢄⠀⠐⢻⣿⣿⢇⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⣿⡽⢿⡍⠀⠀⠀⠀⠄⢠⠈⣿⠹⠿⣤⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⢾⣿⠋⠀⠀⠀⠀⠀⠀⠐⡿⠋⢃⠘⣯⠲⡟⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠛⢻⡆⠘⠎⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢼⠟⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⡀⢳⡟⠀⠀⠀⠈⠣⡶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠘⣁⣽⠀⠀⠀⠀⠀⡐⢀⣰⡿⠇⣀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠐⠶⠾⠿⠿⠟⠛⠃

⠀⠀⠀⠀⠀⡀⠀⠁⡀⡄
⠀⠀⠀⠀⠈⠀⣀⠈⠀⠀⠇
⠀⠀⠀⠀⢸⠠⡛⢤⡴⡶⠃⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠀⠄⠑⡄⠑⢄⠀⠀⠠⠐⠀⢠⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⢄⠀⠀⠄⠘⣌⠄⠀⠀⠀⠀⠀⠆⢣⣠⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢣⠀⢇⢡⠈⠘⠀⠀⠀⠀⠄⠀⠀⢻⠳⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠈⠻⢾⣦⠘⠂⣧⠘⠐⠀⢸⠀⠀⠀⡈⠀⠷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡞⠰⠀⢻⡄⢱⡿⣠⠃⢀⡀⢓⣶⣄⡆⢈⠰⠀⡌⡃⠀⠰⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠟⠁⠚⠴⠧⠏⠀⠞⠀⠈⠈⠀⠰⡿⠷⣋⢄⣔⠞⢁⠀⠀⢿⣢⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⣛⠫⣤⠚⢯⠆⠀⠈⠙⠷⣤⣬⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡋⠒⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠉⠀⠲⠴⠠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠄⢄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣩⡴⢰⡴⢶⡖⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡴⡤⣸⣦⡍⡰⢮⡀⣾⣯⡄
⠀⠀⠀⠀⠀⠀⠀⡰⣰⡏⣨⣯⣡⣙⣓⣩⠿⠩⠃
⠀⠀⠀⠀⠀⠀⢸⣷⣥⣶⣦⢽⣿⣾⠁
⠀⠀⠀⠀⠀⢰⠛⡟⣩⠞⡹⠛⠳⣿⣦
⠀⠀⠀⠀⠀⢸⢢⣆⡴⢟⣥⠾⢶⣶⣮⣦⡀
⠀⠀⠀⠀⠀⣸⣺⣽⣱⡏⣠⡖⢉⣧⣖⣚⣛⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⡇⢿⡌⡼⡰⡟⣰⢋⡜⣹⢓⣚⣛⣛⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣿⠋
⠀⠀⠀⠀⢠⠇⣜⣧⡇⢁⣧⠃⡏⢸⠏⡼⢩⡷⢶⣒⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⡇
⠀⠀⠀⠀⢸⠠⡁⢴⣇⢠⣿⢸⣵⢾⡼⣧⣶⠳⣸⡽⣟⢉⠗⣬⣟⣓⣦⡀⠀⠀⠀⠀⠀⠹⡛⣳⡀
⠀⠀⠀⠀⡆⠀⢡⠏⠉⠻⣿⣜⣿⣾⡇⡟⣷⣡⣿⣿⠏⣨⠞⣩⣌⠣⡴⣿⣄⠀⠀⠀⠀⠀⠉⠫⣸⢳⡄
⠠⣖⠩⠉⠃⠀⡎⠀⠀⠀⠈⠛⠛⠛⢿⣿⣼⡟⡟⡟⢰⣧⠘⣹⢱⡿⣷⢫⠽⣦⡀⠀⠀⠀⠀⠀⠈⣿⣻
⠀⠛⠦⠤⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣅⢻⣽⡄⠈⠓⢿⡌⣁⣾⣿⣦⡟⠿⡆⠀⠀⠀⠀⠀⣮⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣛⡙⣜⢟⣊⣙⣒⢮⣛⣷⠾⠛⢦⣭⡳⣶⡉⡢⣄⣀⢀⣴⣙⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢦⣤⣜⡳⠾⠍⠬⠻⡉⠁⠀⠀⠀⠈⠉⠻⣝⡻⠦⢼⣧⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠥⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠐⠊⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢧⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢷⣾⡟⢯⡓⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡠⢀⡀⠀⢸⣿⣿⠸⠀⠘⠓⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠘⢧⢸⠀⠀⠈⠉⠛⠀⠀⠀⠳⣅⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⣈⡃⢇⠁⠀⠀⠀⠀⢀⠀⠀⠈⠉⠁⠲⡟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⠓⠍⠈⠿⡌⣆⠀⠀⠀⠀⠈⠣⠀⡀⠀⠀⠀⡇⢼⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢀⡀⠀⠞⢂⡀⠠⠀⠀⠀⣬⠇⠀⠀⠘⢡⡏⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣸⣿⣿⠆⠻⣏⠀⣴⠖⠒⠋⢉⡀⠀⢀⣴⠋⠀⡀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⡤⣲⠞⢋⢁⣖⡫⠟⢁⠀⠈⢁⡤⠀⡙⠉⠉⠙⠛⢦⡘⠀⢀⡘⠈⠀⠀⣠⠎⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⣯⠁⢸⡝⠀⡶⢡⡟⣉⣴⠾⣯⠖⢁⡾⠁⢰⠁⠀⠠⣤⣄⠀⠙⢷⡀⢄⠀⢠⡾⠋⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢸⣼⡘⣷⢄⠀⢷⡄⠇⢁⡞⡟⣡⡕⠁⢠⢿⠃⢀⡟⠀⠀⠀⠀⠙⠳⡀⠀⠑⠞⠀⠀⠀⡠⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢶⣶⡆⠹⣼⣾⠀⠀⡇⢰⢸⣷⠃⡟⠀⢠⣧⠇⠀⣸⠇⡄⠘⠛⠛⠲⢄⠀⠀⠀⠀⢰⢀⠄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⢌⣧⢠⣽⠃⠀⣰⠇⢻⡸⡏⢠⡇⣼⠸⡏⠀⢀⡿⠀⠁⠀⠀⠀⡀⠀⠀⠀⢀⣶⣼⡞⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢶⠛⢟⠛⠆⠘⠃⢼⡋⠀⠘⠋⠀⠀⢳⡁⠸⣇⢹⡄⢻⡇⠈⠁⠀⠀⠀⠀⠼⠀⠀⠔⠀⠙⠛⠛⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡾⠉⠀⠀⠀⠀⠛⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠈⠳⡄⠙⠦⠿⠆⠳⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐
⠀⣀⣠⣄⠀⢠⣤⡀⠲⡿⠿⠞⠁⠀⠀⣀⡀⠀⠀⠹⠗⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⣤⡀⠀⡀⢀⡀⡈⣠⠾⠤⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢤⣄⡀⠀⠀⠀⣤⣄⣆⣐⣉⣿⣿⣿⣭⣆⣰⣠⣤⠀⠀⠀⣀⣠⡤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣀⣀⠀⠸⣯⡑⠊⠁⠠⣬⡭⠷⢿⣋⣿⣔⡷⠾⢯⣤⠄⠈⠑⢊⡽⠇⠐⣀⣀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣿⣿⡶⠦⠉⠐⠛⠛⣋⣴⠶⠛⣻⠿⣟⠛⠶⣦⣙⠛⠛⠀⠉⠷⢷⣿⣿⡭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠁⠉⣰⠶⠒⢉⣥⠶⣞⣛⣿⠀⣿⣛⣓⡶⣬⡉⠓⣶⣆⠉⠉⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣴⠞⣹⠇⠀⠋⡴⠛⢡⣿⡇⠶⢸⣿⡌⠛⢦⠙⠀⠺⣏⠳⣦⡀⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⣼⡟⠀⢠⡞⠁⢰⠇⡼⠂⠀⠒⢇⢸⡆⠘⢻⡄⠀⢻⣧⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢀⣀⠉⣗⠘⠛⠓⠀⣾⣀⠀⠀⠀⠀⠀⣠⡷⠀⠚⠛⠃⣻⠉⣀⡀⣿⡦⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⢻⣿⣸⡟⠸⣿⡳⣿⣟⣦⠘⣿⡆⠀⠀⠀⢸⣿⠃⣴⣚⣿⢚⣿⠇⢿⡇⣿⡟⠲⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣠⣾⣯⢹⡇⢦⣀⡙⠦⠉⣿⠀⣿⡟⠀⠀⠀⢻⣿⠐⣿⠁⠴⢉⣠⡜⢸⡇⣿⣷⣄⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⢿⣿⡿⢸⡅⠀⢉⡉⠀⠀⠸⢀⡏⠀⠀⠀⠀⠀⢻⡐⡇⠀⠀⢉⡉⠀⢸⡇⣿⣿⡿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⣿⢸⣷⣾⣬⣵⠖⡰⠀⢠⠁⠀⠀⠀⠀⠀⠈⡄⠀⢄⠲⣦⣤⣷⣾⡇⣿⣿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣸⣿⠿⢘⣇⡼⠁⠀⠠⠀⠀⠀⠀⠀⠀⠐⠄⠀⠈⢧⣸⡃⠿⣿⣇⣿⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⣿⣿⡿⠶⠾⣿⢂⠀⠀⢨⣅⠀⠀⣶⠀⠀⣨⡄⠀⠀⢐⣿⠷⠾⢯⣿⣿⡍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⣿⠿⣿⣿⣗⣬⠇⠒⠦⡀⠹⢷⣌⠉⣠⡾⠏⢀⠴⠂⠘⣥⣻⣿⣟⢿⣿⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⢿⠟⠋⠟⡼⣛⠲⠶⠀⠀⠉⠚⠉⠀⠐⠶⢖⣛⢧⠿⠙⠛⢿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠛⠃⢀⠀⠀⠉⣦⣤⣁⣀⣴⣿⣦⣀⣈⣥⣶⠉⠀⠀⡀⠈⠋⠀⠘⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡆⠀⠀⠀⠈⢻⣷⣄⡾⠛⠛⠉⠉⠛⠉⠉⠛⠛⢷⣠⣶⠟⠀⠀⠀⠀⢸⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⣧⠀⠀⠀⠐⠟⣿⣷⣦⣀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠿⠂⠀⠀⠀⣼⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠓⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠊⡹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠻⠿⠟⠉⠉




⣿⠿⠿⠿⡿⡿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣛⣿⣻⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢠⣤⣑⢢⣀⠀⠀⠤⠶⢒⣲⡶⣶⣲⡒⠠⠀⣀⡔⣊⣭⣤⣮⠛⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⣾⣿⣿⣿⡟⣉⡀⠦⠭⠭⢍⣹⠒⠿⠿⠷⠚⣁⣾⣿⣿⣿⣿⠆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢾⣿⣿⣿⠋⣵⣂⣀⡴⠂⣾⡹⠟⠓⢦⡀⢹⡆⠉⢛⣻⣿⣿⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣬⣽⠟⢋⡤⡾⠁⢨⣴⠶⠚⢙⠒⠳⠶⠄⠘⢻⡢⣄⡈⠉⠻⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠊⢠⡶⢋⣼⠀⠀⣠⡤⠖⠽⠹⣧⠤⢀⣤⡀⠈⢿⡎⠫⣀⡀⠉⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣴⣟⡀⠈⡧⣤⣋⡠⢀⡼⡷⠈⢬⡦⠈⡇⣥⡤⢳⠀⢰⡌⣿⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣸⠇⣞⡣⡤⣬⡉⠀⠀⠀⠀⠀⠁⢀⣥⣦⡔⠛⡣⠘⣷⠘⣷⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⡿⠀⣽⠀⢿⠘⢿⡟⢿⡀⠀⠀⠀⠀⠀⡾⠟⠻⠾⢙⣷⠀⢹⠀⢹⡀⢠⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⡇⠀⢿⠀⠀⠲⠈⠀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠈⠀⠾⠁⢀⣾⠀⣸⠇⢸⡆⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣿⡄⢸⡷⢶⠒⢫⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⠂⡴⢻⠿⢀⣿⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣿⣿⡀⠙⣤⠞⠁⠀⠀⡏⠀⠀⠀⠀⠸⠆⠀⠀⠈⠛⣠⣃⣤⣿⡿⠀⠈⡇⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡀⠀⠸⣿⣧⡴⢿⡆⠰⢄⠀⢦⡠⣀⢀⠤⣠⠂⢀⣈⡀⢸⡿⠛⡿⠟⠁⠀⢠⡇⠀⣼⣷
⠀⠀⠀⠀⢀⣠⡾⠁⠀⠹⣷⣄⡀⠀⠉⠃⠘⢷⡰⢷⣀⡀⠙⠦⣀⠏⠁⢀⠤⣔⢀⣾⡇⠀⠀⠀⢀⣴⠟⠀⢀⣿⣿⡀
⠀⠀⢀⠴⠋⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣄⡀⠘⣿⣦⣭⡅⠠⠴⠷⠤⠠⢠⣭⣵⣿⣿⣤⣤⣴⣾⠟⠉⠀⢠⣾⣿⠋⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠀⠙⠿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⠉⠀⠀⢠⣴⣿⡿⠃⠀⣼⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠛⠿⠶⠴⠤⣶⣶⣿⠛⠉⠙⠋⠁⠀⠀⠀⢠⣿⡿⠋⠀⠀⠞⠁⠋
⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠋
⣧⡈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣦⣀⣱⣄
⡿⡿⣿⣿⠿⢿⣷⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⢶⣶⣶⠶⡶⣶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⢮⢤⡙⣧⢹⡀⣿⢠⢻⡘⡇⢲⣶⣠⢤⡖⣴⡿⢃⢎⡿⢒⡔⢲⣦⠏⢀
⠀⠀⠀⠀⠀⠀⢀⡎⢳⢹⡄⡁⠇⢻⢸⡆⡅⣿⠘⣿⡟⠀⢿⢿⠁⡟⢸⢹⡇⢁⡞⢱⠋⡤⠸⢯⢠⣉⡑⡆
⠀⠀⠀⠀⠀⠀⣶⣈⢞⠸⠁⡇⠈⢸⡞⡇⣇⠹⢀⠀⡇⢀⠈⡎⣆⡳⡜⣄⢇⠈⠀⠟⢸⡇⡀⡆⡸⠀⠁⠐
⠀⠀⠀⠀⠀⠀⡛⣻⢄⢦⢰⠇⡄⣎⢇⠑⢸⣆⡎⠀⡄⢸⠀⣸⠹⡇⢹⡌⣆⠀⢰⡀⡀⡣⣀⡿⠦⠐⢢⠈⠁
⠀⠀⠀⠀⠀⢠⡙⢯⣱⡌⢺⣠⡇⣈⠢⣀⠈⡯⢁⣼⣱⣿⡰⠃⠐⠁⠈⣇⣿⡄⠈⠳⠌⠀⠈⠁
⠀⠀⠀⠀⠀⡾⠛⠇⠱⡌⠊⠈⢒⣶⣭⡙⠭⠃⠀⠀⠀⠈⠁⠂⠀⣠⡤⣎⠁⠑⠀⠀⠂
⠀⠀⠀⣀⣠⣛⠏⠀⠀⠀⠀⠀⡘⢶⣄⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⠑⠀⠑⠮⣂⠀⠘⢄
⠀⠀⠘⠛⠋⣇⠀⠀⠀⠀⠀⠘⡮⢵⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⡀⠀⠈⠑⡄⠀⠁
⠀⠀⠀⠀⠀⢱⡀⡑⡀⠀⠀⠀⠈⠢⡀⠓⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⠲⠀⠀⠐⠢⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡛⢀⣅⡦⢄⣿⣶⡦⣄⠀⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣧⡉⣽⠝⣊⣌⣦⢀⢸⣇⠸
⠀⠀⠀⠀⠀⢀⡀⠠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⢧⡋⠀⠀⠀⠉⡳⢹⢾⡇⡀
⠀⠀⠀⠀⡄⠀⢠⣾⡿⠛⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣠⡀⠀⠀⡄⠐⠙⠋⠞⢁⠃
⠀⠀⠀⠀⠙⠢⠾⠿⢇⠀⣠⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡉⠢⢀⠀⣼⠀⠀⡠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠋⠉⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠘⡦⣀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⣯⣧⣇⢒⠀⡀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⠎⣿⠸⡇⠏⢿⣌⣿⢣⠀⠀⣀⠀⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⡟⠀⠀⠀⠀⠀⣠⠶⣿⣷⠘⣧⡹⡆⠹⢰⠀⡻⡟⢮⡁⢆⠆⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠐⠁⠀⠀⡠⣾⡇⣿⡈⢻⡈⣧⠘⣧⢻⢠⡞⠀⢻⠘⡌⢣⠈⢠⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⠗⠀⠀⢀⢾⣆⠸⣇⢹⡇⢸⣧⠘⣇⠹⠀⠀⠁⣷⠟⠛⠓⢄⢣⡀
⠀⠀⠀⠀⠀⠀⢀⢾⣶⣤⠂⠀⠀⣰⣿⡌⠻⣆⠙⠂⠀⣷⠹⣆⠙⠂⠀⠀⠀⠇⣠⣄⡀⢦⡀⣧⡞
⠀⠀⠀⠀⠀⠀⡆⠀⢨⠃⠀⠀⣼⣧⠉⠻⠆⠀⠀⠀⠠⢼⣧⡈⠀⠀⠀⠀⠰⡮⠅⠈⠉⠀⣹⣿⠃
⠀⠀⠀⠀⠀⢸⠿⠿⡏⠀⠀⣼⣎⠉⠛⠦⠀⠀⠙⠒⢦⣤⣻⡷⠄⠀⠀⠀⠀⣿⡛⠉⢁⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣤⣤⡇⠀⢠⣆⡉⠛⠒⠀⠀⠐⠚⠛⢦⣭⣻⡗⡀⠀⠀⠀⠼⠛⡟⠉⠉⠒⣿⣿
⠀⠀⠀⠀⠀⠸⣁⣀⣇⠀⢸⣌⡛⠓⠂⠀⠀⠈⠉⠛⢶⣌⣻⠃⠀⠀⡠⠂⠀⠀⢹⣛⣛⠁⣿⣿
⠀⠀⠀⠀⠀⠀⡟⠉⣙⣆⣘⣟⡛⠲⠄⠀⠀⠒⠶⣶⣦⣙⢏⣠⠔⠀⠀⠀⠀⠀⠸⠉⠵⠖⢻⣿
⠀⠀⠀⠀⠀⠀⠹⣾⡿⠉⣽⡿⠛⠷⠄⠀⠀⠀⣒⡦⠿⣿⠿⢿⠿⠷⣶⣶⣶⣦⢸⠛⠛⠁⠘⢿⡷⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠛⠳⣴⠦⠀⠀⠀⢀⣿⡇⢼⠁⠀⠀⠦⠼⡐⢤⠙⠉⠈⠢⣄⠀⠀⠀⢝⢍⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠈⠁⠀⠀⠉⠉⠉⠉⠒⠒⠒⠁⠁⠀⠀⠀⠀⠈⠉⠃⠐⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣭⡑⣀⣀⣄⢤⡤⢪⣤⣮⡳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣣⢠⠉⣏⠷⣆⠻⣿⣿⢇⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡆⡆⢙⢰⢁⠸⠳⠨⠯⢨⡝⢿⢦⣀⣀⢤⣖⠚⡛⠋⠉⠻⢏⠲⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠃⢀⣼⢖⠚⢰⢹⣀⢀⢿⠈⡷⡟⠿⢆⠈⠛⡙⣆⠐⡄⢀⠁⠘⠇⢙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⢈⠁⢠⡥⢰⠬⢸⡟⡾⠀⢠⠘⡆⢢⡀⠀⢻⡈⡁⢸⡌⠃⠸⡸⡜⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠲⠖⢴⣅⣠⣍⣠⢞⡽⢡⠃⢠⢆⠃⠸⡇⣀⠈⠇⠱⡀⢳⠀⡀⡇⠇⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠍⠈⣽⣯⡳⢁⠞⢡⣯⠄⠌⠘⢀⠆⡀⣿⠀⠐⠀⠃⠨⠁⠃⠠⣤⡦⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣍⠺⠂⠛⢡⠴⠂⢠⠟⠀⣿⠇⡶⠸⠀⠀⡰⠃⠈⣯⣿⠞⣩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⡓⠀⠰⠁⡀⠴⠂⠀⠠⢹⡰⠃⠀⢀⣴⡶⠣⢎⡾⢹⣟⢃⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣩⣿⡀⠠⣘⠃⠀⠀⠀⢸⣷⠾⠖⣿⣯⡒⠯⢶⡇⠀⠻⣏⣀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢩⣿⡿⢿⣞⠃⠀⠀⡀⠀⠀⠀⢸⡿⠷⠂⣸⠑⠀⠀⠈⠻⢤⣼⣃⠖⠒⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⣸⣧⣤⡀⢀⡇⠀⠀⠀⣼⣉⠀⣩⡍⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡄⣻⣷⠀⠀⠸⠀⠀⠀⠼⠋⠉⠀⡾⠅⠂
⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣶⣧⣄⣄⣈⠁⡈⠁⠀⣇⠠⣯⣰⣀⡀⢀⣼⣷⠶⠒
⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠛⠛⣻⣦⡛⢆⣚⡙⠁⠀⠉⠉⠉⠉⠁⠐⠂⠀⠀⠈
⠐⠐⠀⠈⠢⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣿⠛⠛⣷⣖⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠌⠋⢾⢿⡟⡤⡼⠡⣬⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⢤⣤⣤⡤⡤⣤⢴⠺⣧⣰⢠⡇⣤⡂⡤⢃⡡⣄⢄⣬⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⡖⠻⣯⢟⡴⢃⢋⡆⡸⠁⣰⢹⡀⡻⢸⡇⢹⡟⠀⠙⢮⢧⣍⣿⣇⢚⡺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠞⠁⡁⡆⠈⠘⢱⡏⠘⣴⢀⠆⣿⠈⠀⡇⠀⠃⠞⠄⡠⠀⠸⢎⢫⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡜⢸⠀⣇⢠⡇⣼⢳⢸⡿⡀⣰⡟⢀⡆⠀⡆⠀⡅⣀⢡⠀⡀⢄⡀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡏⢷⠹⣿⢧⡇⣼⣌⢠⡇⡏⠃⣾⠀⣦⠳⢰⣇⠙⠀⢀⢳⣒⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣺⠏⢳⣘⣧⢻⣴⣷⠉⠉⠓⠳⢷⣼⡷⣶⣟⣲⠾⠿⡲⠀⠈⢨⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢦⡜⢯⣹⣿⠯⠎⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢉⡁⠀⣏⡀
⠀⠀⠀⠀⠀⢠⣿⠃⢀⣾⣽⠲⣶⣿⡻⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢤⡇
⠀⠀⠀⠀⠀⠈⠻⠽⢧⡋⠰⠎⠘⢿⠳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢀⠺⠗⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⣀⠀⣣⣌⠆⣀⣀⡀⠀⠀⠀⢀⠀⠀⢀⣐⣂⣀⠈⣉⡳⠴⠴⠋⠭⠍⠀⠀⠒
⠱⢄⠀⠀⠀⠀⠀⠀⠛⠛⠂⠷⠾⠛⠋⠋⠉⠉⠉⠉⠉⠉⠙⠛⠋⠉⠁
⠀⠀⠀⠄

⠀⠀⠀⣠⣾⣿⣶⡄⠀⠛⠓⢶⣴⣿⠃⠀⣶⣶⣶⣶⣶⢶⣶⣾⡆⠀⠘⣦⠾⠚⠀⠀⣾⣷⣶⣶⣦⠰⣿⣿⣿⣿⣿⣿⣿
⢠⣤⣾⣿⣿⣿⣿⣷⣶⡶⠶⠦⡝⡏⠀⣼⣿⠿⣿⢿⣿⣟⢿⣿⣿⠀⠀⠣⢾⣿⣿⡿⣿⣿⣧⠙⣿⡀⣽⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣷⣽⡈⣿⡀⠓⠀⢸⣄⠠⣿⡷⣿⣿⣿⠇⠉⠻⢿⣿⠀⠀⠘⠀⣿⣿⠀⣿⣿⠈⠀⠹⡇⢰⣿⣿⣿⣿⣿⣿
⠀⣿⡷⣷⣾⣿⣿⣷⣌⠻⠶⣶⣿⣿⣶⣿⣿⠋⠉⠀⠀⠀⠀⠀⠙⢠⣷⣶⡾⠛⢁⣾⣿⡟⢀⠀⠀⣷⠘⣿⣿⣿⣿⣿⣿
⠀⣿⣾⣿⣿⣷⣟⣿⣿⣿⣶⣎⢹⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣏⣴⣶⡿⣿⣫⣾⡇⠀⢠⠋⠀⣿⣿⣿⣿⣿⣿
⠀⠙⠏⠀⢻⣿⣿⣿⢿⣿⣟⣻⣿⣿⣿⡿⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠛⠋⡁⠀⡀⡀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⢚⣛⣾⣿⣿⡽⣿⣿⣿⣿⣿⣧⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣍⠒⠤⣞⠋⣴⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿
⢸⣶⣿⣿⣿⡿⠛⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠈⠚⠁⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠸⠿⠟⠉⢹⡇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠘⣷⡀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⡀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢛⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠹⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣟⠀⠹⣧⣤⣀⠀⠀⠠⠀⠀⢀⡰⠁⢀⣤⡞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⠬⢿⣿⣿⣿⣿⣿⣿⣿⡝⠛⠂⠀⠈⠙⢿⣿⡄⠀⣰⡞⠉⠀⠐⠋⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠶⢦⣤⡀⠀⠈⠛⢷⠿⠋⠀⠀⠤⠴⠞⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⠶⠖⠦⠴⠀⠀⠀⣠⡀⠀⠒⠒⢶⣒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡀⠀⠰⠶⠻⠿⠿⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢷
⠀⠀⠀⠀⠀⠀⠳⠦⠤⣀⡀⠀⠀⠠⠤⢒⣛⣛⣛⣹⣍⣝⣃⣐⡤⢤⢄⣤⠶⠋⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠞⠋⣁⣠⣄⢈⣍⡈⣁⣈⡛⠶⡝⢦⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⢚⡄⠀⠀⠈⢩⠈⠀⢈⣁⢩⡌⠉⠍⡀⠀⠈⠇⠀⢀⡆
⠀⠀⠀⠀⠀⢀⡼⠂⣠⠄⠀⡿⣷⠀⠻⠦⡀⡄⠘⣆⡇⠠⡱⠖⠐⡆⣰⠄⡾⠄⡈⠷⡀
⠀⠀⠀⠀⣰⠋⠀⣼⠋⢠⡿⣠⠟⠢⣴⠶⠦⡀⠀⢀⠀⠀⠀⠂⠀⡠⢤⡄⠴⡴⡎⢳⡟⡄
⠀⠀⠀⣰⠃⠀⠸⡇⠀⣾⠃⠹⣿⠥⠜⠤⠠⣿⡶⠇⠀⠀⠀⠀⢺⡤⠤⣧⠁⡿⢹⡈⣧⢸⡄
⠀⠀⢠⠇⠀⠀⠘⡿⠀⡏⡠⣄⣀⣓⣽⠾⢠⡉⠀⠳⡄⠀⠴⠀⡀⠀⣀⠀⠀⠀⡀⢠⡿⠀⠉⣄
⠀⠀⣺⠀⠀⠀⠖⣀⠀⠼⠄⠔⠀⠈⢠⠀⢌⠳⠀⢀⢇⡑⠀⠂⠀⠀⠞⣠⠀⡍⢹⠀⡇⠀⠀⠣
⠀⠀⠿⢴⡃⠀⣿⣇⢀⣀⠀⠀⣶⣦⢝⠳⢌⠳⣄⠘⣤⡉⠀⢀⠀⢠⠞⣡⡶⢠⡎⡰⣷⣀⣀⢰⡇
⠀⠀⠀⢻⡇⠚⠉⢙⣦⡉⠀⠀⢻⣧⣌⠛⠦⠀⠀⠀⠈⢣⡤⠊⠀⠀⠀⠜⠁⠘⣡⡿⠮⠁⠿⠌⠁
⠀⠀⠀⠙⠷⡀⠀⠀⠈⠙⠲⡀⠻⣜⢿⠐⣿⠀⢀⣬⠳⠾⣷⢶⡞⢻⣿⣧⡴⠿⣛⣠⡖⠚⠙
⠀⠀⠀⠀⠐⠻⣶⣶⣤⡀⠀⠴⢦⡹⣿⣧⡙⢠⣸⣿⣿⣿⣿⣿⡇⣜⠉⠀⠀⢸⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣆⡀⠈⠙⠻⣿⡏⣼⣿⣿⣿⣿⣿⡏⣿⠿⠀⢠⢴⠾⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣤⡀⢿⣿⣾⢻⣿⣿⣿⡿⢻⠁⢀⣤⡾⣎⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠹⣷⣤⣭⣵⣦⣄⣧⣴⣿⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠈⠙⠛⠛⠛⢉⣾⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣶⣶⣶⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠉⠻⠦⠀⠀⣠⣴⣶⣶⣶⡤⢶⣶⣶⣶⣤⣀⠀⠠⠶⠛⠁⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⢀⡀⠀⠀⠀⣶⠀⡠⠚⠉⠉⠁⠈⢁⣴⣄⣀⠀⠀⠉⠻⠷⡄⢰⣧⠀⠀⠀⠀⡀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢺⣧⣤⡶⠚⠁⢀⠐⢚⡽⠿⠿⠿⠛⠁⠙⠛⠛⠻⢶⣄⠀⢄⡀⠉⠳⣤⣼⣿⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⠛⠛⡅⠀⣾⠋⠀⢲⣤⣀⡀⢀⣴⠁⢻⣆⠀⣀⣀⡨⠔⠀⢻⡇⠀⢾⡛⢋⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢠⠞⠠⠼⢋⣤⣤⣤⡍⠙⡿⠛⢉⡴⢨⡛⠻⣿⠉⣤⣤⣤⣌⠻⠦⣄⠹⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡠⠀⡄⠀⠾⠋⠉⣉⡑⠆⠁⡴⠻⠃⢸⠻⡆⠁⠒⢋⣉⠉⠛⠦⠀⡀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⣴⢡⠀⢿⣆⠀⠶⣏⠹⠿⣂⠀⡇⠀⠀⠀⠀⢻⢀⡞⠿⢋⡷⠆⢀⣾⠇⣄⠘⣦⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠠⡟⠀⢸⡇⣿⡆⠘⢿⣿⡆⠀⠉⣿⢏⠄⠙⠀⠀⠀⠀⠘⢨⡿⡏⠁⠀⣾⣿⡟⠀⢸⡄⢹⡇⠀⣷
⠀⠀⠀⠀⠀⠀⢀⣿⢀⣿⡇⢻⣷⡀⠀⠙⠿⣄⠀⠁⢸⠆⡀⠀⠀⠀⠀⠀⠘⡇⠈⢀⡴⠟⠁⠀⠀⣾⠇⢸⣷⡀⣏
⠀⠀⠀⠀⠀⠀⣿⠁⣸⣿⡇⠘⣿⣿⣦⣄⣀⣤⣀⠀⠋⠘⠁⠀⠀⠀⠀⠘⡄⠀⢀⣀⣀⣠⣤⣤⣾⡟⠀⢸⣿⡇⠘⣧
⠀⠀⠀⠀⠀⢸⡇⠀⢹⣿⣇⠀⢘⣿⣿⣿⠏⠁⠀⠀⠀⣿⣤⣀⡀⢀⣀⣤⡗⠀⠀⠈⠉⢻⣿⣿⠟⠀⠀⣸⣿⡇⠀⣿⡄
⠀⠀⠀⠀⠀⠀⢿⡀⠈⣿⣿⡎⠁⠀⠙⠻⢦⣴⠀⢀⠒⠈⠙⠻⣿⡿⠛⢉⠀⠂⠀⠀⡄⠼⠟⠁⠀⠀⢸⣿⣿⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠈⠻⣆⠹⣿⡄⠀⠀⠀⠀⠀⢿⣄⠀⠡⠀⠀⠀⢸⡀⠀⠀⠄⠄⢀⣠⡏⠈⠀⢰⠀⡀⢸⡿⠋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠘⢳⡀⠈⢷⣴⠒⠉⠻⢷⣤⣶⠥⠖⠛⠛⠢⢤⣤⣤⡶⠋⠁⠀⣀⣼⠃⢨⠟⠁⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣁⠀⠈⠈⣧⡀⠀⡄⠠⠔⠀⠀⠀⠀⠑⠂⠀⠚⡁⠀⠴⠛⠉⠁⢀⣡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢦⠀⠀⠉⠀⠘⣦⣀⠀⠀⠀⠀⠀⢀⣠⡞⠁⠀⠀⠀⢀⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⢿⣶⣶⠟⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠔⣈⣁⣬⣽⣯⣥⣄⣈⡁⠂⢀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡈⢿⣿⠃⠚⠉⠁⢈⣉⠀⣰⣷⠖⠀⠀⠀⠉⠀⠒⠀⣶⡾⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣇⠀⠙⠃⢀⣀⣴⠬⠤⠬⣩⣏⡶⠦⢬⣔⣀⠀⠐⠛⣩⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⠀⠀⣀⢄⣠⡶⠟⠙⢛⡛⠋⠻⢦⣄⢠⣀⠀⠀⣠⣾⢁⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠈⢁⠀⠺⠃⠈⠡⠶⠿⠛⢺⡗⠘⠿⠶⢌⠀⠹⠃⠀⠘⠟⡸⢎⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⣴⠋⣠⣆⠀⠀⠰⠚⠡⠖⠋⠙⠳⡌⠓⠆⠀⠀⣶⡄⠱⠄⢱⡄⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢡⡾⣣⢰⡉⣇⠰⠆⠁⠂⢟⡀⠀⠀⠀⡺⠀⠀⠴⠆⡛⢁⡐⡞⢦⡙⡆⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⡇⠻⢸⢋⡿⠻⡆⢂⣄⠈⠀⠀⠀⠀⠁⣀⠐⣲⠛⢟⢺⠇⡷⣾⡇⢙⠀⡄⠈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣿⠃⠀⢨⠘⣇⠀⠊⠙⡿⠀⠀⠀⠀⠀⠀⡿⠋⠑⠂⡼⠀⠀⠁⢿⡧⠸⠀⠁⠆⠃⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢻⣧⣠⣼⣦⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣠⣾⣤⢂⣾⠗⠸⠆⠀⠸⡀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠈⠻⣿⡏⠃⣈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢫⡄⠉⣿⣿⠟⠀⡰⠀⠀⠀⡇⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⡀⠘⠻⠶⣬⣷⠦⠀⠀⣄⠀⠀⠀⠀⣠⠀⣀⠶⢾⣥⣾⠟⣉⠤⠋⠁⠀⠀⠀⡇⠀⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠀⠀⠀⠀⢙⡳⠆⠀⠈⠻⢆⡀⠟⠋⠀⠴⢖⡋⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢦⡀⠀⠀⢻⣭⠔⠀⢀⣨⣅⡀⠀⠠⣭⠟⢠⡶⠞⠁⠀⠀⣴⠀⠀⠀⡠⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠳⣄⠀⠈⠹⡟⠛⠋⠉⠉⠉⠙⠻⠋⠀⠋⠀⠀⠀⠀⢸⡟⠀⠀⠀⡁⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠘⢧⠀⠀⠙⠦⢀⡀⣀⡤⠤⠂⢀⡀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠁⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⢷⡀⠀⠘⣧⠀⠀⠀⠘⢦⡀⠀⣠⡶⠋⠀⠀⢀⠀⣠⡟⠁⠀⠀⠀⢀⣴⠟⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢳⡀⠀⠙⢷⣄⠀⠀⠀⠉⠀⠉⠀⠀⣀⠔⢁⡼⠋⠀⠀⠀⠀⠀⣼⢃⡴⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠹⡄⠀⠀⠙⣦⡀⠀⠀⠀⣠⡴⠛⣡⠴⠋⠀⠀⠀⠀⡌⠀⡼⠻⠋⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠘⢦⠀⠀⠈⠳⣤⠀⠐⢁⡾⠋⠀⠀⠀⠀⠀⢠⡞⠀⡘⠀⠶⣺⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⣄⠀⠀⠀⠘⣧⠀⠀⠀⠈⠇⠀⠎⠀⠀⠀⠀⠀⣀⣴⠟⠀⢠⠁⠰⠞⠉⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⣀⠀⠈⠳⢤⡀⠀⠘⠀⠀⠀⢀⣠⣴⡾⠛⠁⠀⡠⠊⠀⢀⣀⣤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⡀⠐⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣁⠲⠆⣀⠀⠀⢀⣠⠤⠂⠀⠀⠀⠀⢀⣀⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣯⠿⠷⠟⢟⣰⠏⠀⠀⠀⠀⠀⠀⢀⡚⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠈⠦⠀⠀⢦⡤⠖⢛⡥⠆⠀⠀⠀⠀⠀⠀⠸⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⡀⠀⠀⠉⠀⠘⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠀⠀⠀⠉⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠀⠀⠀⠤⡀⠂⠀⠆⠀⠀⠀⠀⠀⠀⠀⡌⢀⠀⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠘⠉⠸⠀⠀⠠⡀⠀⠀⠂⠐⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠂⠈⡤⢁⣀⡀⣶⣀⠤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣀⣤⡀⣿⠀⠀⣠⠀⠀⣰⠀⠀⡤⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠑⠒⠳⠶⠾⠿⠞⠋⠴⠶⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢠⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⢀⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠏⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⠞⠛⠿⢛⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣀⣤⡖⠂⠈⣿⣿⡃⠀⠀⣿⣿⣄⣀⡰⠋⢀⡠⣴⣶⣺⢟⣫⣽⠿⢛⣫⣽⠶⠿⠟⠛⠓⠒⠤⣄⡀
⠀⠀⢀⠔⠉⣿⣿⣧⣀⠠⠿⠟⠓⠒⠒⢚⠟⠋⢉⡒⢴⣫⣾⡿⠋⣱⣿⡟⣠⣾⡟⠉⠀⣀⣤⣶⣾⡿⠿⠿⠿⢿⣶⣄
⠀⢠⣿⡀⠀⢨⠟⠋⠀⠀⠀⠀⠀⠀⢀⣎⡤⢚⣁⡈⢿⣿⡟⠀⣴⡿⢋⣼⣿⠏⠀⣠⣾⡿⠛⠉⠀⠀⢀⣠⣤⣤⣤⣬⣑⣄
⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⡛⢿⣡⠟⠉⣹⣶⣻⣇⢸⡟⠀⣼⣿⠏⠀⣴⣿⠏⠀⠀⢀⣤⣾⡿⠛⠉⠀⣀⣀⣉⡙⢳⣄
⠀⡀⠈⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡞⢃⡶⠿⠿⠿⣿⠇⢸⡇⢰⣿⡿⠀⣼⣿⡏⠀⣴⢟⣩⠾⣫⠄⣠⣴⣿⠿⠛⠛⠛⢿⣟⣳⡀
⠀⢧⣄⣠⣼⣧⣀⡀⠀⠀⢀⣀⣴⣿⣿⣷⣮⠔⣀⣈⣻⣿⣇⣿⠁⣾⢹⡇⠀⢿⣹⡇⣸⣧⣿⡁⠚⣡⣞⣭⠭⠀⠀⠀⠀⠀⠀⠹⢿⣿⣤⡀
⠀⠈⠿⡿⠿⠃⠈⣿⣿⡇⠈⢹⣿⣿⣿⣿⣿⡾⣿⡿⢿⣿⣿⣿⠀⣿⢸⡇⡇⢸⣯⡿⡛⠀⡈⠛⣻⣿⣭⣥⣤⣶⣾⣿⣿⣿⣷⣦⡀⠉⠙⢿⡀
⠀⠀⠀⠈⠒⠠⠴⠿⠿⠣⠀⠞⠋⠉⠻⠉⡟⠀⢠⠂⠀⠀⠘⣿⣇⢻⡄⢿⣿⡞⣵⠏⣽⠿⣤⡾⢋⡽⣻⡿⠛⠉⠉⠉⠉⠉⠉⠙⢷⣄⣀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣇⡠⢘⡆⢰⡆⢠⡿⠿⣿⣿⣾⣿⢸⡏⣸⠁⣠⢀⣴⢏⡼⠋⣠⣤⣶⣶⣶⣤⣤⣄⠀⠈⠛⢿⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⠙⠎⠋⠛⠁⠀⠀⠙⠻⣿⣿⡇⠁⣾⡁⣾⣿⣾⠶⠛⠉⠁⠀⠀⠀⠉⢻⣿⣦⡀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣀⣿⣿⢛⣻⣁⣠⠶⠛⠛⠛⠻⣶⡀⠀⠟⠛⢿⣷⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⣿⣉⠍⠳⠚⢛⣛⠳⢦⣼⣟⠻⢷⣄⠀⢿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡛⢿⣿⡄⠛⢫⠔⢠⠦⠤⣍⠳⠶⠦⡍⢳⡄⣻⣄⣾⣧⡾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢿⡇⠰⢶⣠⡐⢤⠐⡦⠈⡉⠙⢦⡀⠈⢉⠹⣯⡹⣟⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⣰⢾⡶⠢⣅⣴⡦⢀⡁⠠⠛⡅⠈⡰⡆⢸⡶⠛⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢹⠇⢸⣏⢸⣿⡴⠏⣶⠃⠀⠉⠀⣶⡄⠲⠄⣤⢀⣶⣞⣋⡉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⡀⢿⢸⣿⣿⠁⠙⣆⢠⠤⠞⣼⡄⣚⣤⢠⢠⣿⡟⠻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡙⠎⠀⢻⢁⣭⣙⡻⢤⣤⣌⣿⡾⠿⢃⣼⠃⢰⣇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡉⡾⡬⠁⠈⠹⡏⣠⠟⣫⡤⠶⠛⠁⢀⣾⣿⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣄⠷⣶⣦⣵⢾⠡⠆⠱⠶⢶⣀⣴⣿⣯⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠛⠷⣦⣬⡥⢠⣴⡟⢛⣿⣿⡿⢛⡁⢨⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡻⠦⣀⣀⣠⣴⠿⣿⣇⡼⠋⡽⢃⣉⠙⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠈⠛⠀⢉⡿⣤⠇⠈⠁⠈⢷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢸⣶⣹⣆⣷⣰⡈⣆⠜⢱⠇⠀⡀⠀⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠀⠘⠀⠀⡸⠀⠀⠃⢠⠀⠈⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠁⠀⠓⠘⢂⠑⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠐⡤⠀⠈⠄⠀⢰⡄⢈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⣥⢷⡌⣠⣾⢁⡟⢻⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠊⠁⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠠⠀⠀⠀⠀⠠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠀⠠⠄⠀⠠⠀⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⠛⠻⣿⣿⣶⣄⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⣠⣶⣿⣿⠟⠛⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣦⠀⠙⢿⣿⣿⣶⣶⣿⣿⠿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣶⣶⣿⣿⡿⠋⠀⣴⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⢀⣴⣿⠟⠉⠉⢉⣠⠶⣿⣿⣿⣿⣿⣿⣿⣿⠶⣄⡉⠉⠉⠻⣿⣦⡀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⣴⣿⡟⠁⠀⠀⠐⠋⣴⡿⣛⣉⡉⠉⠉⢉⣙⣛⢿⣦⠙⠀⠀⠀⠈⠻⣿⣦⣹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠏⠀⣰⠃⠀⢀⢞⣵⡿⢋⣴⣾⣿⣿⣷⣦⡙⢿⣮⡳⡀⠀⠈⣆⠀⠹⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡏⠀⠀⣿⠀⠀⢀⣿⡏⢠⣿⠏⠁⠀⠀⠈⠹⣿⡄⢹⣿⡀⠀⠀⣿⠀⠀⢹⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣴⣾⣿⠟⣿⣿⠀⠀⠀⠻⠿⠿⠾⣿⡇⣸⠃⠀⠀⠀⠀⠀⠀⠘⡇⢸⣿⠷⠿⠿⠟⠀⠀⠀⣿⣿⠻⣿⣷⣦
⠀⠀⠀⢀⣾⣿⣿⡏⢸⣿⡇⢀⡆⠀⠀⣤⣶⣦⣤⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⣤⣴⣶⣤⠀⠀⢰⡀⢸⣿⡇⢹⣿⣿⣷⡀
⠀⠀⠀⣼⠏⣿⡿⠀⣿⣿⠁⣼⣗⠀⠀⢻⡟⢧⣛⣹⣿⣦⠀⠀⠀⠀⠀⠀⣴⣿⣏⣛⡸⢻⡟⠀⠀⣻⣧⠈⣿⣿⠀⢿⣿⠹⣧
⠀⠀⠀⠋⢸⣿⡇⠀⣿⣿⡀⣿⣟⡄⣀⣤⣭⣆⡈⡉⣿⡏⠀⠀⠀⠀⠀⠈⢹⣿⢉⢁⣰⣭⣤⣀⢠⣻⣿⢀⣿⣿⠀⢸⣿⡇⠘
⠀⠀⠀⠀⢸⣿⡇⠀⢹⡇⠁⣿⣿⡶⠀⠀⠠⠾⠋⠡⢻⠇⠀⠀⠀⠀⠀⠀⠸⡟⠎⠙⠷⠄⠀⠀⢶⣿⣿⠈⢸⡏⠀⢸⣿⡇
⠀⠀⠀⠀⢸⣿⡇⠀⠘⣿⡄⠸⣿⣧⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣠⣼⣿⠇⢠⣿⠃⠀⢸⣿⡇
⠀⠀⠀⠀⢸⣿⡇⠀⠀⢻⡿⡄⠙⣿⡏⠁⢀⡀⠀⢸⣧⡖⠀⠀⠀⠀⠀⠀⢲⣼⡇⠀⢀⡀⠈⢹⣿⠋⠠⢾⡟⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠘⣿⣧⣿⡀⠈⢷⡀⠀⠈⠃⢠⡞⠀⠀⠘⣿⣧⣀⣀⣀⣀⣀⣀⣼⣿⠃⠀⠀⢳⡄⠘⠁⠀⢀⡿⠁⢀⣿⣼⣿⠃
⠀⠀⠀⠀⠀⢹⣿⣿⣧⠀⠈⢿⣆⡀⠀⣾⠛⠶⢤⣀⠀⠉⠛⠿⣿⣿⠿⠛⠉⠀⣀⡤⠶⠛⣷⠀⢀⣰⡿⠁⠀⣼⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀⠀⠙⢿⣦⣿⣷⣤⣀⣀⡀⠀⠀⠀⢹⡏⠀⠀⠀⢀⣀⣀⣤⣾⣿⣴⡿⠋⠀⠀⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠈⢻⡘⣿⣷⣄⠀⡀⠈⠙⢿⣤⣀⣀⣤⠄⠀⢠⣿⣿⡄⠀⠠⣤⣀⣠⣤⡿⠋⠁⢀⠀⣠⣾⣿⢃⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣷⡄⠀⠈⠙⠿⣷⣶⣶⡾⠿⠟⠻⠿⢷⣶⣶⣾⠿⠋⠁⠀⢠⣾⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣦⣤⣴⣿⣯⠖⠋⠁⠀⠀⠈⠑⠲⣽⣿⣦⣤⣴⣶⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣶⣬⣭⣝⣫⣭⣥⣶⣶⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⢛⡢⠀⠀⠀⣠⠭⣭⣾⣭⣄⡀⠀⠀⠀⣈⣋⡳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣬⣻⠇⠀⠴⠶⢒⣰⣶⣀⠚⠻⠾⠟⢻⣩⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⣡⡶⠟⢫⡾⠛⣩⡻⠯⠙⣶⠘⡳⠄⠻⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢮⡾⠋⠊⠀⢠⣶⠾⠿⡹⠾⢷⡆⠀⠙⡈⢦⡀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⡿⠁⣼⡇⡄⡴⠒⣠⠞⢻⣆⠰⠆⣠⢸⣧⠀⠻⣄⠛⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢲⣿⠁⣼⣸⣇⡛⠞⢸⠇⠂⠠⠳⠀⠑⢛⣸⡇⢼⡀⢿⡆⢠⡧
⠀⠀⠀⠀⠀⠀⠀⢰⡏⢘⣿⡇⠏⢰⢾⣱⢴⡌⠀⠀⠀⠁⣰⡦⣾⠳⡇⢸⢁⣾⡇⢸⣧
⠀⠀⠀⠀⠀⠀⠀⣻⡧⢈⣻⣧⢣⣀⠛⠄⠈⠁⠀⠀⠀⠀⠹⠄⢁⠞⣀⡈⢨⣿⠇⠚⣿⡄
⠀⠀⠀⠀⠀⠀⠈⠻⣷⡍⢻⣿⡜⠉⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣾⠟⢠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡉⠙⠳⣮⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠴⠻⡁⣼⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⣀⢠⡑⠀⠐⢄⠀⢀⠔⠃⠔⢠⠚⠉⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣧⣅⡀⠀⣡⡁⠀⣀⣤⣾⣿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣯⣀⠉⠉⠙⠋⢙⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⢶⠞⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣖⢻⣟⣩⡟⠛⡷⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⡴⠷⣦⡟⠋⠉⠉⠉⠛⠳⢾⣏⣸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣷⠶⠾⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣾⠉⣷⠶⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢤⣾⣏⣨⡽⠟⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣷⠿⠷⠿⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢁⡤⡂⠤⠽⢦⣐⠻⣟⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢱⢱⠏⡎⣠⢞⡥⢂⠽⢛⡦⠿⠝⣶⣤⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⡏⡏⢻⠘⡇⣿⠘⢰⠇⡼⣁⠀⣠⠴⠒⡁⠈⣋⡽⠋⣩⠝⢳⣶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⢀⣼⠋⢟⠀⣼⠈⡇⠘⠇⠁⢁⠀⠜⠈⣴⠃⡴⠁⡠⢊⡴⠋⡠⠒⣈⣥⠚⣩⣉⠐⠛⢙⣲⣄
⠀⠀⠀⠀⠀⠀⣼⢣⢦⠎⢀⣿⠀⢻⠀⠀⡆⡏⠀⣠⢠⢧⠁⡜⠰⢡⠎⠀⣼⢁⡞⢱⡿⣚⣫⣭⣗⡲⠉⠴⣻⣧⡀
⠀⠀⠀⢀⣀⣴⢃⡟⠊⠀⣾⣿⠀⣼⣤⠰⠑⡁⣼⠁⡼⣸⢰⢡⠃⣼⠀⣰⢻⣿⢶⣯⡾⢟⡿⠿⠝⠛⢶⣾⣭⢽⣷⣤⣄
⠀⠀⢰⡏⠉⠀⣼⡇⡄⣶⢸⡏⠰⢳⡇⣠⢰⠃⣏⠀⢡⡏⡜⣾⢀⡟⢰⡇⣸⣯⠛⢻⢞⡍⢚⡋⡉⡁⣺⣿⠛⠲⢄⠙⢿⣦⣠⣤⡀
⠀⠀⠘⢷⡄⠀⢹⣇⣯⠻⣘⣷⣴⣾⣷⢸⣸⢦⡿⢠⡟⣼⠁⡿⢸⠇⢸⡇⣇⢻⡦⢈⠘⢤⡯⣧⡉⠎⣧⠃⠠⡼⡆⡄⢰⢹⠿⢫⡇
⠀⠀⠀⠀⠙⠛⠛⠙⠛⠛⠛⠉⠁⠀⢻⣿⣀⡟⢸⠸⠇⢿⢠⠃⡿⠀⠈⡇⣹⣾⠃⣸⠐⣆⠡⠼⠇⠤⢌⣀⢣⠖⢺⣛⡟⢧⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣇⠀⠀⢿⡈⢆⢳⡀⢰⡇⣯⣿⠁⣧⢹⠇⢀⠐⠃⢀⣃⠹⡎⢙⡖⢠⠠⡆⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢦⣤⣬⣿⡆⠀⠳⣌⢷⡸⣧⠀⢺⡀⣅⢵⠘⢶⡀⣤⡤⠃⠐⢷⡎⣰⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⡴⠚⠉⣙⣿⣦⣤⣼⣆⣙⣿⣿⣄⣡⢸⣶⢤⣴⣻⣥⣀⣀⡄⢊⡴⢣⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢰⠃⠊⠁⠒⠛⠛⢻⣌⠉⠀⠈⠙⢿⡼⡿⡞⠉⠁⣧⡟⣡⢐⣭⡾⠟⢡⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣿⠔⡀⠀⢠⡀⠐⠂⠈⢳⡀⠀⠀⠘⣿⣧⢽⣿⣏⣹⣿⡟⢋⡵⢒⠊⣠⡤⠽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡁⠀⠀⣄⢠⣸⣿⠿⠀⠀⠀⠀⠻⠶⣤⣤⣩⠟⠸⣧⣸⢡⠃⢈⢀⠴⢒⣚⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⡼⠦⢷⠞⠚⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢾⣤⣇⠀⠀⠀⠀⠘⠉⠙⠳⠖⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢶⣀⣴⣼⢀⡀⡴⠀⡠⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠹⠿⢿⣵⣦⣧⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉

⠀⠀⠀⠀⠀⡰⠒⠉⠙⠛⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠉⠉⠒⢆
⠀⠀⠀⠀⢠⠇⠀⠀⣠⣤⣤⣄⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢁⣠⣤⣤⣄⠀⠀⣼⡄
⠀⠀⠀⢀⡟⠀⣀⣽⣿⣿⣿⣿⣷⣆⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢐⡶⢶⡶⠶⢆⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡖⠀⣠⣿⣿⣿⣿⣿⣿⡀⠈⢷
⠀⠀⠀⢸⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⢦⡤⣴⡖⠒⠛⣋⣉⣉⣉⣉⣛⢚⣛⣛⣋⣉⣉⣉⣙⠛⠛⣷⣶⣴⣶⠋⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⡇
⠀⠀⠀⠀⠣⠀⣼⣿⣿⣿⣿⣿⣿⢿⣿⡆⠀⣠⡖⠀⢀⡴⠿⠛⠛⠉⣁⣍⣟⡁⣍⣻⣩⣌⠙⠛⠛⠿⢦⡀⠀⢰⣅⠀⢸⢿⠿⣿⣿⣿⣿⣿⣿⣧⠀⠜
⠀⠀⠀⠀⠀⠱⣽⣿⣿⣿⣿⣿⠿⠀⠀⡀⠚⠉⠀⠴⠉⢀⣴⣶⡿⠿⠛⠋⠙⢃⡘⠋⠉⠛⠛⣿⣶⣦⡀⠙⢦⠀⠉⠓⢀⠀⠀⠻⣿⣿⣿⣿⣿⣯⠎
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡆⠀⣠⠎⢠⡖⠀⠀⢀⡴⠛⠋⠁⡀⠀⣤⠾⠋⡌⠛⠻⠷⣦⠀⣀⠈⠙⠻⢦⡀⠁⠀⢶⡀⠱⣄⠀⢰⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠠⣿⡿⠛⠋⢁⡜⠀⢠⡟⠀⠀⠠⠋⢀⣠⠾⠟⢉⣤⣤⣤⠆⠃⠃⢻⣷⣤⣤⡉⠻⠷⣄⡀⠛⡄⠀⠀⢻⡄⠈⢧⡌⠙⠛⢿⣷⠆
⠀⠀⠀⠀⠀⠀⠐⣯⡀⠀⣴⡟⠁⢠⣿⠀⠀⠀⠀⠀⠞⠁⣴⠀⠈⢀⡿⢡⡖⡀⠠⡈⠌⢿⡀⠁⠐⣆⠈⠓⠀⠈⠀⠀⠀⣿⡄⠈⢿⣷⠀⢀⣵⠂
⠀⠀⠀⠀⠀⠀⠀⠿⠁⢸⡟⠀⠀⣿⣿⡆⢀⣤⣀⣤⣄⠐⣿⠀⠀⣾⡶⠸⠇⠇⠀⠓⠀⢳⢻⠀⠀⣿⠀⣠⣤⣀⣤⡀⢸⣿⣿⠀⡈⢿⡇⠩⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣰⠀⠟⢻⡅⠈⠙⠋⢙⡛⠂⠹⢆⠀⠀⠀⠟⠀⠀⠀⢀⠀⠳⠀⠀⠀⠋⠐⢛⡋⠉⠉⠉⢸⡟⠻⠀⣇⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⣿⡄⠀⣸⡿⠤⣶⡿⣿⣿⢷⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⠴⢿⣇⠀⢠⣿⠀⢿⣿⡀⡀
⠀⠀⠀⠀⠀⢠⠀⣸⣿⡇⠀⣿⠇⢰⡿⣷⣄⠈⢷⣘⠛⢛⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡛⠛⣣⡾⠁⣠⣾⢿⡆⢸⣿⠀⢸⣿⣇⠐⡀
⠀⠀⠀⠀⠀⡘⢀⣿⣿⡇⠀⢸⠀⠀⡇⠈⠛⢧⣄⣉⠉⠉⢿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⡿⠉⢉⣉⣤⡾⠋⠀⢸⠅⢘⡇⠀⢸⣿⣿⡀⠃
⠀⠀⠀⠀⡴⠀⢸⣿⣿⠃⠀⢸⠆⠀⣿⡄⠳⣤⣬⠉⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠑⠀⠈⠉⣥⣴⠎⢰⡿⠀⢸⡇⠀⢸⣿⣿⡇⠈⢆
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⢘⡇⣦⠈⢻⣆⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⣰⠟⠁⡶⢸⠃⠀⠈⣿⣿⣿⡄
⠀⠀⡰⠂⠀⢸⣿⣿⣿⠀⠀⣸⡇⠹⠀⣤⡉⢉⠌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠦⢣⡉⢁⣴⠀⠏⣸⡇⠀⠠⣿⣿⣿⡅⠀⠘⢆
⠀⢠⠁⠀⠀⠀⣿⣿⣷⠆⠀⢿⣿⡈⣷⡝⢷⢊⠀⣠⠞⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠈⠈⠓⠷⡑⠿⢣⣾⢡⣿⣗⠀⢰⣾⣿⣿⠀⠀⠀⠐⡄
⠀⣿⠂⠀⠀⠀⢿⣿⣿⡆⠀⢹⣿⡇⠘⠷⠀⠀⣴⠃⡼⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠐⣦⢀⠀⡾⠁⣼⣿⡏⠀⢸⣿⣿⡷⠀⠀⠀⠐⣷
⠀⢏⠜⠀⠀⠀⠈⣿⣿⣿⣄⠀⠻⣿⡄⠀⢦⣽⠇⢀⡴⠀⠀⠀⣦⣀⣀⣀⣀⠀⠀⢀⣀⣀⣠⣿⣿⢧⠀⣤⡀⠸⣧⡜⠀⣠⣿⠟⠁⣠⣿⣿⣿⠀⠀⠀⠀⠢⡹
⠀⢿⣟⠀⠀⠀⠀⠸⣿⣿⣿⣄⣀⠈⠳⣦⡀⠙⢶⡿⠃⠐⠃⠀⢿⣁⣀⡈⠉⠛⠛⠉⢁⣀⣈⡿⡿⠘⠂⠘⣿⣶⣫⢄⣴⡟⠁⣀⣴⣿⣿⣿⠇⠀⠀⠀⠀⣳⡿
⠀⠸⢮⠇⠀⠀⠀⠀⠋⠻⣿⣿⣿⣷⣄⠈⠻⣄⠈⠙⠟⠶⠶⢄⡈⠛⢿⣿⡇⠀⠀⢼⣿⡿⠛⢁⡠⠶⠶⠻⠋⢉⣡⠟⢁⣴⣾⣿⣿⣿⠟⠙⠀⠀⠀⠀⢸⡿⠇
⠀⠀⠈⢤⣤⡀⠀⠀⠀⠀⠉⠙⠋⢹⣿⣿⣦⣬⣿⠷⢶⣶⣤⣤⣀⢀⠀⠈⠓⢶⡶⠚⠁⠀⣀⣠⣤⣤⣶⠶⢿⣿⣥⣾⣿⣿⡏⠛⠋⠉⠀⠀⠀⠀⢀⣤⡤⠁
⠀⠀⠀⠘⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⡤⠄⡤⠠⠰⠀⠀⠀⢀⣼⣧⠀⠀⠀⠀⠆⠄⢠⠠⣴⣾⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃
⠀⠀⠀⠀⠀⠻⣿⡄⣰⡀⠀⠀⢀⠀⠀⠈⠁⠹⠿⢿⣶⣤⣦⣄⣀⣀⣤⠼⠻⣿⣿⠛⠶⣤⣅⣀⣠⣶⣶⣾⣿⣿⡟⢉⣁⣾⠀⡀⠀⠀⢀⣆⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠁⢿⣿⣶⣶⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠱⣀⠀⠘⠃⢀⣠⠏⠈⣿⣿⣿⣿⣿⣿⠀⣀⠘⠋⠁⠀⣿⣶⣶⣿⡿⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⢿⣶⡄⢀⣴⣷⣆⣤⣬⣿⣿⣿⣿⣤⣼⣯⣯⣯⣿⣽⣼⣶⣶⣿⣿⣿⣿⣿⣶⣶⣿⣷⣄⣠⣶⣿⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠋⠀⠉⠉⠀⣠⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠋⠀⠙⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⣝⣵⠻⣿⣟⣿⣿⠿⣟⣻⣿⠷⣮⣫⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣤⣏⠀⠈⠈⠃⠁⠚⠚⢁⠓⢀⣽⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠼⠷⢤⡴⠾⠦⠟

⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣫⣿⢟⣯⣶⡶⢿⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢙⣿⣶⣌⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠊⠁⢸⠟⣡⠟⠉⣠⠀⠐⣛⣷⡮⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣰⡏⢱⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣾⣾⡿⣿⣿⢇⡜⡀⠘⠀⠁⠀⡎⣿⣷⢆⣉⣉⣠⠄⢈⣙⠳⣠⣾⠆
⠀⠀⠀⢀⣴⢯⣹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⡾⣿⠋⢰⢋⡿⣾⢃⣇⠀⠀⣦⠀⢹⠞⠁⣩⢶⡒⠒⡄⣰⠶⢭⠈⢿⡼
⠀⠀⣴⣛⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⢻⡇⠇⢸⡆⠀⡜⠁⢻⣆⢻⡆⢷⢻⡦⠀⠊⠀⡘⡉⢉⠹⠆⠹⠳⢦⠁⢸⡀
⠀⠀⣧⣤⣿⡀⠀⠀⠀⠀⣀⣤⢶⡏⣿⢃⣼⣿⢹⣿⠈⠀⣿⠀⠈⠁⢀⠀⠀⠀⢻⣿⣿⣼⣬⡅⠀⣴⠀⡃⢖⣲⠉⠂⠀⢠⡀⠙⠊⢿⡆
⠀⠀⠸⣟⣩⡷⡤⡴⣶⡛⣿⣥⠿⢟⣿⣿⣻⡏⡘⣜⢧⠀⠀⣆⢀⡾⢁⣴⠎⠀⠈⠉⣙⣿⣿⣖⢤⠻⢦⠑⠀⠀⠀⠀⠀⠉⠁⢾⡡⣾⣻⣆⡀
⠀⠀⠀⠈⠳⠼⠥⣧⠿⠟⠉⠀⡴⣻⠏⣿⣿⠈⣧⡈⠈⡇⣸⣯⢻⠁⡞⣡⡴⢋⠀⠈⠉⠉⠉⠉⠑⣖⠦⡀⡄⠀⠲⠀⢠⠆⡄⠊⢰⠳⠟⣿⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⢋⠀⠉⠘⣧⠈⢻⣆⡿⡿⠀⢸⣆⣾⡏⢰⡏⢰⣶⣶⠃⠀⣀⢀⠈⣷⣿⣜⢳⡴⢶⡦⠾⣅⣸⢹⠀⢸⠏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠋⢀⠀⡀⢸⡆⡆⣿⠀⠁⠀⢀⡨⡻⣿⡟⠛⠛⠛⠓⠢⠀⠈⡇⣙⣈⢱⣘⡯⣁⣹⡀⠀⠀⠙⢾⠀⠀⠀⠋⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⢴⡷⢣⢠⡇⢸⠇⣧⠇⢀⣠⠜⣋⣠⣾⣿⠀⠀⠀⠀⠀⠀⠳⠗⠣⠾⠷⠞⠫⡁⠀⣩⠃⠀⠀⠀⡄⡄⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡼⣡⡞⢁⡏⡼⠀⠘⣸⣿⢊⠀⠰⣤⣀⣀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠞⠁⠀⡀⢤⢀⡦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠃⣿⣷⡼⣷⣄⣀⡴⣋⡜⠆⣷⣤⣘⣻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⢠⣄⠈⣀⠡⣸
⠀⠀⠀⠀⠀⠀⣠⠔⠙⠏⢛⠟⠉⠉⠉⣩⠋⠀⠈⠙⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠿⠾⠓⠋
⠀⠀⠀⠀⢀⡆⢀⠄⠀⢠⠏⠸⠿⣴⠦⠃
⠀⠀⠀⠀⠈⢷⣊⣔⣠⠎
⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⡴⣿⢉⡿⣍⣇
⠀⠀⠀⠀⠀⢀⡞⠀⣾⡇⠀⣿⣿⠏⠘⣳⡙⠽⠷⢦⡀
⠀⠀⠀⠀⠀⣿⡅⢢⠉⠻⡄⠘⠛⢀⡀⡈⣅⡐⢾⡀⢳⡀
⠀⠀⠀⠀⢦⡈⢻⡌⡇⢠⡇⠀⢄⡾⢡⡗⠠⠟⢛⠃⠀⠳⡄
⠀⠀⠰⠦⣄⡙⢦⠙⡇⣾⠀⡘⡾⠠⠞⠛⠓⠒⠤⠆⠀⠠⠈⢆
⠘⠛⣛⠦⣄⡉⠓⠄⠀⢷⡀⢷⠹⣤⡀⢠⠈⡄⣈⠀⠈⠤⠰⣿⠃
⢾⣛⣭⠤⠤⣭⣍⣑⠂⠀⠑⠀⢠⣀⠉⠲⢱⡀⠈⠿⠿⠟⣻⠁
⢹⣇⣶⡾⣛⣩⣥⡾⣃⣤⡴⠖⣂⣈⣉⣛⣀⡀⠀⠐⠒⠚⠁
⣸⡟⢻⣿⡟⢋⣥⡾⠋⢀⣴⡿⠛⣹⠃⠀⣠⡤⠶⠖⣢⠤⠀⠀⣀⣄⠀⠀⣀⣀⣤⠄⠀⠀⠀⡀⠀⠀⢀⣠⠴⠒⠂⠀⣀⡀
⠿⠁⣿⢻⡇⢀⣽⣷⣶⡿⠋⣠⣾⠃⣴⡟⠁⠀⢀⡞⠁⣠⡶⣻⠟⢁⡴⣫⡟⢋⣴⢞⣡⢶⣿⠁⠀⣴⡟⠁⢀⡴⠿⠟⠛⠛⠻⠶⠶⣤⡀
⢤⡀⠇⢸⠇⣸⡿⢉⣿⠓⣶⣿⣥⣾⠟⠀⠀⣠⡟⠀⣸⣟⣴⠟⠰⠋⣰⡏⢠⣟⣡⠞⠁⣼⠏⠀⣰⡿⠀⣴⡟⠁⣀⣠⣴⣶⣦⣤⣀⠈⠙
⡶⠳⣄⢸⡀⣿⡇⣸⡿⠀⡿⢿⡉⢀⣴⣶⠿⠛⢀⣤⣶⡿⠋⠀⠀⣴⡟⢠⣾⠋⠀⢀⣾⠃⣀⣼⡿⢁⣾⢟⡴⠛⣩⣴⡶⠶⠄⠉⠛⠿⠶
⡶⢇⡌⢦⡁⠹⣧⠻⡇⠸⣇⠘⣧⠈⣿⣄⠀⢾⣿⡋⣡⣶⡟⣠⣾⣟⣴⣿⣁⣀⣤⣿⣥⣾⣿⣧⣾⣿⣿⣯⣤⣀⣀⣤⣴⠶⠖⢚⣀⡀
⣴⡿⠃⠀⠙⠶⣬⣧⡑⢄⠀⠀⢿⡄⠈⢿⣦⠀⠹⣷⣿⣯⡉⠻⣯⠻⠟⠿⣶⡌⠙⢿⣿⣿⡿⣾⣿⣿⣿⣿⣷⣤⣉⡁⠀⠴⠟⢻⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⠤⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡃⠶⠌⠙⣀⢁⠸⠀⢿⡿⠷⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⢈⡭⣧⠈⠍⢉⡸⠂⢰⠀⠒⠁⣰⢸⠇⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢡⣄⠈⠁⠘⢁⠏⠀⠀⢀⢹⡎⠂⢘⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⠀⠉⠉⠒⢀⡇⠈⢸⢁⢰⡘⣶⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⢊⠙⡖⢤⡞⠀⠀⠘⠘⣇⠃⡟⢘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⢁⣸⡷⡈⡎⠀⠀⠀⠀⣿⠀⠀⡏⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⢸⡟⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠿⠙⣇⣄⠑⣌⠂⠀⠀⠀⠀⣷⢡⡆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢹⠻⠆⣧⢸⡛⡄⠹⠄⠀⠀⠀⠀⡏⠈⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣤⠴⣮⣉⠖⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⣾⠁⣿⠀⡔⢶⡈⠀⠛⠻⡄⢆⠀⠀⠀⠀⢀⡟⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠲⣏⣹⠦⠄⠒⠉⠀⠀⠀⠀⢀⢤⡴⣶⢋⣽⠋⣿⠀⣿⠀⣿⠀⡘⡄⢻⡄⢄⢦⡀⠀⠀⠀⠀⠀⡞⣸⣿⡇
⠀⠀⠀⠀⠀⠀⢠⣎⣉⡻⠊⠁⠀⠀⠀⠀⠀⠀⣠⢾⢃⡎⠸⣰⠃⡎⢸⠀⢂⡞⠱⢸⠛⢂⠻⣇⠀⠇⠈⠀⠙⠀⠀⠀⠀⠀⢠⠟⢃
⠀⠀⠀⠀⠀⢠⠋⣡⡝⠀⠀⠀⠀⠀⠀⣀⢤⡞⣇⣌⠈⣿⠀⣿⠀⢣⡇⠀⣼⣰⠀⠀⡄⠸⡆⠈⢳⡄⢠⠀⠀⠀⠀⠀⠀⣰⠟⣣⠟
⠀⠀⠀⠀⠀⠈⢶⡄⢸⠖⢢⡤⠰⣖⢿⣤⡎⢠⢹⡎⠆⣿⠀⠙⢆⢸⣰⠆⠇⠹⣀⠟⣔⣄⡙⢦⡈⠃⡘⠀⠀⠀⢀⣦⠞⣡⣚⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠚⠦⠤⠔⠒⠉⢀⡎⠁⢸⡀⠅⣆⠻⡄⠀⠀⠀⠛⠇⠂⠀⠹⡆⣌⡉⠑⠄⠻⠐⡇⠀⣠⠶⠋⠐⠊⣩⡅⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⢧⢠⡀⢹⡄⠻⣄⠈⢂⠀⠀⠀⠀⠀⠀⠑⢦⠀⠉⠁⠀⠀⢀⡗⠋⠁⠀⡄⠘⢂⡴⠋⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠀⠰⣌⠈⠳⣄⠙⠂⠈⠁⠀⣠⠤⠖⠒⠒⠀⠤⠜⣂⠀⠉⠓⠂⠀⡇⠀⠀⢰⠉⠀⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠁⢀⣀⣀⡀⠀⣀⡉⠴⠋⠀⠀⠀⡀⠠⠬⠶⡾⠛⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⣠⠊⠁⠀⠀⠈⠀⠹⣄⡀⠀⠀⠀⣀⡈⠤⠒⠉⠀⠀⢃⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠉⢇⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠠⣄⠀⠀⡆⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠎⢀⡄⣄⢠⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⣇⠀⢀⡀⣸⢦⢠⡃⠠⡤⡄⢼⢢
⠀⠀⠀⠀⠀⠀⠸⣀⣶⡆⣬⡇⣸⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⢐⡶⢘⣾⣿⠆⠀⠀⠀⠀⠈⠢⣀⣸⣼⣷⢷⠷⠼⠧⠻⠚⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠁⠙⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⡀⠀⣤⣤⠄⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠮⡥⠉⢡⡽⠷⡜⠁⣤⢾⣷⡈⠟⡃⣸⡷⢂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣏⢈⣧⣶⢶⡰⣟⣽⢳⣧⢻⣿⢯⣶⣷⣾⡽⣿⡿⠈⠽⠛⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣏⣏⡬⢿⣿⠛⠓⠈⠀⠀⢀⣀⣠⣤⣀⣉⡉⠁⠻⣿⣃⣴⣿⣼⠏⢤⡀
⠀⠀⠀⠀⠀⠀⣼⣃⡏⢰⣿⣶⠊⠁⠀⢀⣤⢞⡟⢋⣹⠯⣌⣿⣷⣿⣂⣦⠀⠐⡍⢻⣟⠁⢃⠷⡀
⠀⠀⠀⠀⠀⢸⡩⢮⡕⠆⣻⠁⠀⣠⡾⡹⢿⣭⡽⣶⣿⣿⡶⠟⡛⠈⠀⠁⠀⠀⠐⠀⠘⣿⣯⠚⡧
⠀⠀⠀⠀⠀⢺⣶⢄⡟⢈⣿⠀⠀⣿⣟⣷⢭⣍⡁⠻⣿⣿⣷⣋⢽⣀⡀⠀⢀⡔⠀⠈⠀⢸⡷⢾⡶
⠀⠀⠀⠀⠀⢨⡹⠾⣷⡈⠿⣦⡴⣿⡋⠀⠠⣄⠴⠷⣌⠳⣤⡘⢦⣈⠙⠓⠋⠀⠀⠃⠀⠐⡷⢶⡁
⠀⠀⠀⠀⠀⠀⢻⡄⠾⣛⠛⣫⣽⡏⠂⢀⣲⡃⠀⠀⠀⠙⠚⠻⠿⠿⠀⠀⠀⠀⠀⠀⠀⣼⡯⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠨⢙⠘⠛⠛⠊⠁⠀⣤⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣸⡷⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⠆⠐⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⡞⣩⣹⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢖⣻⢯⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣠⠆⠳⣿⣵⡸⠏⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣤⣴⣴⢶⣾⣾⠉⢿⣿⣣⣾⣾⣿⣿⣿⣿⣿⡶⢦⢤⣀⡀
⠀⠀⠀⠀⠈⠀⠀⢠⡤⣦⢦⣼⠿⢛⡻⠟⣷⣀⣪⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣸⣿⣟⡷⢼⠯⠇⢀⣦⣄
⠀⠀⠈⢀⣤⣶⠿⠿⠳⣷⣿⠝⠓⠉⠉⢁⡴⢻⡟⣿⣿⡿⠟⠋⠉⡁⠀⠠⠠⠠⠠⠡⠉⠛⠷⣤⣶⢿⣮⣛⣉⣡⡄
⠀⢀⠶⣿⠯⣍⢿⣿⠟⠉⠀⠀⠀⠀⢠⣯⣷⣮⣛⡿⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢿⡃⠛⠋⢩⣿⡆
⠀⣼⠲⠞⠧⠙⣼⡏⠀⠀⠀⠀⠀⠀⣾⡌⢻⣿⣿⣇⡀⠀⠀⢀⣀⣠⣤⡔⢲⣖⣶⣶⣶⡄⣀⠀⠀⠈⡿⣿⣿⡷⣿⢛
⠀⣿⠛⡿⢷⡞⢿⠃⠀⠀⠀⠀⠀⠀⢺⣵⡆⢥⡄⣿⣷⠶⢋⡽⠛⢛⣯⠒⣩⡭⣬⠉⣷⠀⣾⣗⣄⠀⣷⣮⣁⠸⢿⡞
⠀⢹⣺⢳⣿⢏⡐⣜⡦⠀⠀⠀⠀⠀⠈⢷⣶⣗⣲⢿⡶⢃⣴⣲⣮⣅⣀⡼⠿⠿⠯⢿⣯⠈⢀⣡⣥⣿⣭⣻⣭⣧⡍⣠
⠀⠈⢿⣿⣥⢾⣿⢩⢮⢀⣷⣄⡀⠀⠀⠀⠉⠻⠿⢮⢡⣼⠽⠿⠛⠉⠁⠀⠀⠀⠀⢀⣨⣿⢮⡽⢿⣿⣆⣫⣭⠟⢠⠇
⠀⠀⠀⠻⣿⢛⣏⡘⢫⡠⣽⡶⢶⣝⠒⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣯⠿⣉⡧⠔⠘⣇⢻⡟⠋⣰⠃
⠀⠀⠀⠀⠈⠙⡯⣿⣌⣱⣮⠿⣑⡛⢈⡳⢠⣾⢻⣿⠱⡴⢇⣾⣉⣻⣻⣿⣿⣿⣿⣿⣷⣯⣼⢀⡜⣿⣶⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠍⡙⠓⠾⢿⣿⣌⣡⣿⡴⢟⣙⡃⢀⣾⣟⣻⣿⣓⡿⣿⣿⣿⣿⠿⠞⢹⠌⢻⡾⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⢀⡉⠉⠁⠙⠛⠻⠿⠛⠿⠟⠟⠇⠃⠛⠉⢉⡀⠄⠒⡧⢀⣼⡃⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠂⠀⠈⠈⠀⠀⠀⢜⡑⢿⢐⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠃⡀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣠⢦⣤⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢀⠶⣆⣰⣯⡿⠟⢻⣽⣿⣦⣅⠀⢀⡠⢲⣭⣵⣟⣻⡿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢽⣿⢿⣁⣀⣀⣀⣀⣩⣥⡿⣸⡆⢣⣵⣟⣻⣾⡡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢀⣻⣖⣎⣝⢣⠮⣝⣿⣿⡆⡾⣷⡸⣃⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠇⣉⡛⣩⣟⡿⠛⠉⣿⣿⢚⡷⠟⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠀⣀⣼⣫⠇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣽⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢂⠀⠉⠀⠀⠀⣄⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢶⢹⠉⠀⠀⠠⠀⠾⣀⣠⠘⡰⢀⡀⠀⠁
⠀⠀⣴⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠊⠈⠀⠈⠢⠀⠀⠀⠀⠂⠀⠋⠁⠁
⣰⣦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⠰⢆⠣⠣⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠁⠃⠄⠀⠀⠀⠀⠀⠀⠀⠘
⣤⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⢤⣤⡤⡖⡼⣾⠃⠡⠀⡀⠀⢊⠀⡄⠀⠀⠀⠀⠦⠀⠀⡄⠀⠀⠀⠀⡀⢀⢀⣠⣠⠄⠀⢀⠄
⠙⢩⣤⡄⣀⡀⢀⣤⡔⣿⡴⢾⠀⠀⠎⠝⡱⡣⠁⢡⠆⡀⣎⠀⢀⠌⠀⠃⡄⠀⠈⠑⠀⠀⢠⠔⢆⣄⠠⠅⠚⠈⠁
⠀⠈⠻⠄⠿⠷⠌⠛⠉⠀⢠⠻⠀⠐⠀⠀⠐⡀⢰⠘⣸⢀⣏⠀⢺⠀⢰⠀⡸⢬⣒⣰⠶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠚⠀⠚⣴⡀⢀⢕⣧⠼⠏⠼⠇⠠⠼⠾⠦⠷⠈⠃⠉
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢠⠀⡇⣨⣏⠯⠈⠁
⠀⠀⠀⠀⠀⠀⢄⢠⣱⡌⡯⠇⠟⠋⠁
⠀⠀⠀⠀⠀⠙⠈⠉⠁

⣀⣐⣤⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣛⣛⣙⣛⣟⣻⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣴⣶⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⣴⡾⠀⠀⠀⣠⢰⣏⠽⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣆
⠀⠀⠀⠀⠐⣟⠄⡀⢰⡤⠛⠉⠀⢰⣿⣿⣿⣿⣿⢟⡿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠋⡙⣻⢛⠓⣾⣿⣟⡶⠄
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣾⣿⣿⣿⢿⣧⡈⡧⠄⢿⢠⡼⢯⡹⢻⣿⣿⣿⢿⠀⠯⢹⣼⣷⣾⣉⢤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⣿⢾⠿⠿⣽⣷⠚⠷⠷⠾⠷⣀⣿⣿⣿⠀⠀⠐⢋⠻⣭⠏⠰⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣧⣛⡪⠛⠁⠀⣗⢲⣬⠇⠀⠀⠀⠀⠀⠈⡈⣿⣿⠉⠲⢏⣨⡕⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠉⠀⠀⠀⠀⡿⣐⡎⠀⠀⠀⠀⠀⠀⠀⣄⣿⡏⠀⠀⠀⠈⠀⢤⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠹⣧⠀⠀⠀⠀⠀⠀⠁⢤⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡤⢠⢖⣲⢖⣰⠒⢲⡦⢤⠤⡤⠴⠆⢶⣴⣤⠤⠀⢀
⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⢀⡀⢶⡀⢿⢀⢸⢣⠃⡏⡞⣡⢺⠁⣾⠊⠀⠾⠀⢡⠀⠀⠀⠀⠐⣶⢋⠁⣱⡄
⠀⠀⠀⠀⠀⢸⣫⢀⡀⣴⡨⠛⠉⠀⡰⣄⢹⢸⢠⡷⢡⢀⢧⡆⠃⢠⠇⡄⠁⠀⠀⠀⠀⠀⢀⡌⠁⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠉⠚⠉⠀⠀⠀⠀⢠⡀⣇⠟⡐⢉⣄⡘⠄⠸⡇⣠⢻⣂⠕⣀⠀⠀⡀⠀⠀⢏⡃⣿⣠⡄⡀⢤⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⡐⢲⡵⡟⠽⢭⣱⡖⠺⠼⠦⠻⢄⡄⠀⠀⠈⠈⠀⠂⠸⢫⡉⠋⠰⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣌⣃⡹⠊⠀⢸⠀⢤⣬⠀⠀⠀⠀⠀⠀⢃⠀⠀⡌⠑⠴⢀⠀⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠊⠁⠀⠀⠀⢰⠇⢠⠇⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠈⠙⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠈⠢⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⠠⠴⠜


⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠀⠀⢶⡿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠁⣀⣀⣼⠃⠀⣄⠠⠤⢶⢀⡉⠀⠀⢀⣦⢀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⢿⣿⠀⢰⣿⠀⠀⠀⠋⠈⠁⠈⡤⠟⢻⣿⡇⠀⠀⠀⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢻⡀⡙⣄⢼⣏⡀⠀⠀⠠⠑⢲⡁⠠⠾⠾⢿⡇⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⠀⠸⡇⠀⠘⣿⣦⣤⡀⠀⠨⠦⠀⠄⠀⠀⠉⠙⠁⠉⡏⣶⠂⠀⠀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢳⣭⣇⠀⢷⡀⠀⠘⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠱⣦⣤⣄⠀⠀⠀⢀⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⠀⢸⣿⣤⣀⠹⣿⣿⢷⣄⠀⠀⠀⠀⠀⠀⠰⠟⠛⠁⠀⢀⣠⡾⠟⠛⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠄⠀⠈⠛⠷⣝⣟⠻⣷⣟⣷⣤⡀⠀⠂⠁⠀⠀⢀⣠⢴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣀⠀⠈⠛⠿⣿⣿⣏⣉⠀⠀⠀⢀⣠⣴⣿⣿⠋⠀⢀⣤⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠑⢦⣀⡀⠈⠛⢿⣿⣷⣤⣀⣀⣀⣴⡿⢁⣤⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡀⠀⠀⠁⣽⣦⣤⣤⠛⣩⣿⡿⠿⠿⠛⠂⠉⡉⠁⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠙⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠚⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⣦⡀⠀⠀⠀⠀⠀⣀⣠⣤⣠⣄⣄⢠⣄⣤⣄⢀⡀⠀⠀⠀⣀⢤⣿⠅⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠻⠶⠤⡞⠛⠙⠛⡉⢙⠉⠻⠛⠛⠉⠋⠉⠛⠛⠖⠒⠉⢠⡟⢻⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⣗⡄⠀⣀⡤⠶⠂⠋⠁⠉⡉⢿⠟⠋⡛⠓⠳⢶⣤⡀⠶⢶⠟⠻⠃⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠴⣾⠝⠛⢋⡔⠜⠛⠛⠛⠛⣡⣴⣌⠛⠙⠛⠶⢤⣤⣀⠀⠏⡔⠁⠤⢴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢀⠭⠃⠐⢋⡤⠀⢀⣶⣶⡿⠛⣉⠻⣷⣄⢰⣄⠀⢬⣭⣄⡈⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⣥⠝⠂⠀⣘⣱⢶⡼⠋⠀⠀⣠⣾⠉⢧⣀⣈⠁⠙⠷⠆⠙⠻⣧⠀⠀⠠⣇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⣀⡴⠟⣩⡀⠀⢀⣤⡾⠟⠉⠉⡆⢨⡍⠙⠿⠦⠄⠀⢸⣦⠉⠳⣄⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⡎⣠⡞⠁⠀⣰⡿⠁⠀⢉⣽⡆⠀⣀⡴⠳⣠⣅⠀⢰⣦⡄⠀⠀⢻⣶⠄⠈⢳⣆⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠬⠀⣿⡇⣶⡄⠙⠁⣴⣄⠈⢤⠀⣈⢁⡇⢠⣼⡉⣴⠀⡄⢀⣤⡶⢤⡏⢀⣶⡄⣿⣆⠀⠂
⠀⠀⠀⠀⠀⠰⢋⠀⠈⣿⠀⢿⡇⣤⠄⠈⠙⠃⠟⢰⡏⠘⣁⠈⣿⠃⢸⡆⠋⣈⢁⡀⠀⠻⡘⣿⠃⣿⣯
⠀⠀⠀⠀⠀⠠⠛⠁⠀⣿⠀⢸⠁⡛⠠⡘⣇⣛⣢⡀⠣⠀⠈⠐⠈⠀⢈⢃⣮⣩⡼⢣⠂⢹⡆⢹⡀⢹⣿⠀⠀⢬⡀
⠀⠀⠀⠀⠀⢀⢞⡁⠀⣿⡧⠘⠀⢿⣄⡘⠚⠙⢻⡧⠐⠀⠀⠀⠀⠀⠀⠸⣿⠉⠀⠓⣠⡟⠁⣼⠀⣸⡇⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠸⠇⠀⠘⢷⡀⢤⠀⠈⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠉⠁⠀⣸⠇⢰⡿⠇⠀⠀⣹⠆
⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⣶⣌⠳⠦⢿⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠛⠛⠉⡿⣤⣾⠄⠀⠀⠄⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠙⢿⣷⣦⣈⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⡗⣾⡷⠀⠁⠀⠀⣴⠞⠃
⠀⠀⠀⠀⠄⠒⠒⠒⠺⣿⡶⠤⠤⠤⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡴⠋⠀⠀⠀⠢⠠⠁
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠼⠶⠶⠂⠀⠀⠽⣿⡃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢜⠯⠠⣀⣠⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡤⠴⠦⡷⢬⡻⣦⡄⣀⣀⣄⣠⣤⣠⠄⠈⠘⣈⣛⠛⠉⠂⠤⣀⡀⠀⠂⠄⣁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠠⠐⣊⠽⠗⣚⡽⣃⡦⠈⠙⠤⠴⠋⠀⠀⣀⣿⣿⠍⠂⢌⡁⠂⠤⣈⠒⢄⡀
⠀⠀⠀⠀⠀⠐⠈⠁⠀⠐⢊⡥⠖⣉⠄⡠⢂⢜⢽⣿⡷⠶⢶⠾⠿⠶⠶⢿⢿⡿⣽⠣⠀⠢⡈⠒⠄⡀⠉⠢⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⡤⠊⢠⠊⠀⠉⡌⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣧⢠⠀⠀⢀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡰⠀⠀⠈⠀⠀⠀⠖⠀⠰⠃⠀⠸⠁⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⢐⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢳⣵⢿⠘⣡⠀⢗⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠳⣌⣧⣿⣾⡇⢁⢸⣃⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⢦⡝⣷⢹⡜⣮⣷⡄⠀⠀⡶⢂⣀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣽⣭⣭⣭⣉⠙⠻⣦⣝⠷⣤⣄⢠⣀⣀⡀⣀⡀⢀⠀⡄⣄⡬⣎⢷⠸⣇⢻⡜⣟⢆⠀⠂⠗⡭⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠛⠛⠛⠻⣿⣿⣦⠈⢿⣿⣄⠉⢿⡏⣻⢃⣿⠁⣿⢠⡇⣿⢷⢻⠸⣇⢹⣆⢻⣜⡆⠀⠀⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⡈⢴⠾⠷⣶⣶⣦⣄⡈⠻⢿⣷⡀⠹⣿⣧⠘⣿⡏⢸⡟⢸⡇⣼⠁⡿⢸⡜⡆⢻⣆⢻⣇⠈⠁
⠀⠀⠀⠀⠀⠀⣺⠀⣤⣤⣤⣈⣉⠛⠿⣶⣆⠙⣿⡄⠸⣿⠀⣿⠁⣿⠃⣾⢀⡟⣸⠇⡌⣧⢻⡌⢻⣆⠙
⠀⠀⠀⠀⠀⣸⣿⠀⠀⢀⣉⣉⣙⡛⠷⡄⠋⡇⢹⡇⠀⣿⢠⣿⠀⣿⠀⡿⢸⡇⠏⣼⣻⡘⢧⡹⡄⠉
⠀⠀⠀⠀⢰⣿⣿⡀⠀⠉⠙⠮⢭⡙⠃⠀⠀⢫⠸⡇⢸⡇⢸⡿⢠⡟⢸⡇⢸⠀⢞⣩⣍⡛⢎⢳⠘
⠀⠀⠀⠀⢼⣿⣿⡇⠀⢨⣉⣛⡓⠄⠀⠀⠀⠀⠀⠃⠘⠇⠸⠁⢸⡇⠸⠆⠘⠄⠐⣶⡖⠭
⠀⠀⠀⠀⠘⣿⣿⠃⢀⣲⣶⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏
⠀⠀⠀⠀⠀⠘⣿⠇⢽⣿⠯⠑⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣯⠁
⠀⠀⠀⠀⠀⠀⠈⠀⢸⣻⡁⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⡆⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⣦⠠⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠘⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠛⢲⠤⢤⣤⢤⠤⠤⠔⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡰⠁⠀⠀⠋⠀⠠⠄⠸⡀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣶⡆⠀⠀⠀⣶⡄⠀⠱⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⠦⢀⡀⠀⠀⠀⠀⠀⣀⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠘⢬⡉⠭⠏⠀⡰⠉⠃⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠆⠒⠓⠤⠤⠄⡀⠤⢴⢳⢛⡖⢲⢦⣀⢀⣤⡤⡖⠒⡖⡶⠒⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⠤⠔⠋⠀⠀⢸⡏⣸⠁⢻⡏⠑⡀⢳⠹⣇⠈⣷⠃⠘⢡⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢀⡗⠁⠀⢸⠀⢀⡇⡼⠀⢸⠀⢹⡇⢠⠇⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠳⠀⠀⠀⢰⠻⢁⡄⠀⡞⠀⡜⢰⠃⠀⢾⠀⠈⡇⢸⠀⢠⡏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡆⠀⠀⠀⠀⣧⠎⠀⠀⣠⠀⠀⠀⠀⠀⢸⠀⣼⠃⢸⠀⠞⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⡄⠀⠀⠀⢧⡀⢀⡴⠃⠀⠀⠀⡼⠀⡾⡞⠁⢀⠎⠀⡀⢨⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⣑⣄⠀⠀⠀⢷⠋⠠⠔⠚⠛⠻⡧⠞⠋⢱⡀⣁⣤⠞⢀⢾⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⠉⠉⠲⠦⣄⣸⠀⢀⣠⣔⡊⣹⢧⣴⡎⠁⠹⡔⠁⢀⡀⢼⣙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡭⠿⠷⠦⡜⠈⣆⣉⣥⣤⣭⡇⠈⢶⠲⠖⠒⢻⡏⠉⣀⣸⡤⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠤⠤⡇⠀⡟⠋⠁⠀⢰⠀⠀⠀⠑⡖⠊⠁⡟⠉⠁⢈⡷⡞⣳⢴⡞⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠴⠶⠦⡄⠀⢸⠛⣛⠓⢸⠀⠀⠀⠀⣙⠉⠁⣏⣉⣉⣨⠁⠈⠛⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⠶⠶⠆⡇⠀⢸⠝⠛⠛⢃⠀⣴⠖⠦⣏⢈⣠⣇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢠⠊⠙⠲⣤⠃⢠⢞⠖⠲⠒⡞⢶⠯⠼⠀⣼⠋⡏⡜⠉⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠤⠤⠤⠞⠁⠸⣸⡀⣆⢀⣇⡸⠀⠀⠀⠈⠓⠓⠛⠒⠊⠁

⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⢠⡞⠁⠐⠂⠬⢍⣒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⣋⠭⠄⠂⠈⠙⣦
⠀⠀⠀⢸⡖⠚⢋⣉⣓⡒⠦⢝⡮⠷⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠴⠭⣞⠥⠖⣚⣋⣙⠛⠒⣿
⠀⠀⠀⠈⢷⡉⣉⠀⠨⢭⣍⣻⡄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣼⣋⣭⠍⠀⣈⡉⣸⠇
⠀⠀⠀⠀⠘⢧⡠⠤⠖⠒⠒⠒⠛⠦⣄⠀⠀⠙⢦⠀⠀⠀⠀⣠⠞⠁⠀⣀⡴⠞⠒⠒⠒⠒⠦⠄⣰⠏
⠀⠀⠀⠀⠀⠈⢷⣐⠊⠉⢉⣉⣉⡙⠛⠛⠒⠦⣄⡳⣐⣢⡴⣁⡤⠖⠛⠛⠛⣉⣉⣉⠉⠉⢒⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠻⠧⣤⣤⠬⣭⣭⣭⠯⠭⢽⣏⢘⣿⠭⠭⣯⣭⣭⡭⢤⣤⡬⠿⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣁⠤⠄⠐⣶⠤⠒⠊⡝⣿⢾⡿⡑⠒⠤⢴⡒⠀⠤⢄⣉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠗⣉⠤⠒⢈⡏⠀⠀⣠⢾⢀⡏⡘⡇⠹⢆⡀⠀⠙⣏⠐⠢⢌⠓⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⠤⠂⡩⠳⡴⢺⠁⠀⣸⢀⢃⢹⠸⠀⢻⠲⡴⠫⡁⠢⣄⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠁⢠⠊⠀⡜⠀⠇⠀⢰⠇⠈⠃⠈⣿⠀⠈⡄⠑⡀⠈⢦⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣇⠀⡘⠀⠀⡆⢀⡞⠀⠀⠀⠀⠸⣆⠀⠇⠀⢸⠀⢈⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠦⠶⠚⠋⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⠶⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢸⣷⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⢲⡄⠀⠈⢿⣷⡀⢻⣇⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⣤⡴⠶⠿⣿
⠀⠀⠀⠀⠀⠘⣿⣆⠀⠈⢻⣿⣄⢻⣆⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠀⠀⡀⢂⡀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⣀⣤⣴⣿⡀
⠀⠀⠀⠀⢤⡀⠘⢿⣷⣄⠀⠹⣿⣦⣻⣿⣿⣧⡀⠀⠀⢀⠰⠖⠁⢀⡄⠀⠀⢠⡶⣻⣆⠀⠀⠀⠀⠀⠀⣠⡴⠟⣋⠵⣾⣿⡇
⠀⠀⠀⠀⠈⢻⣦⣈⠻⢿⣷⣦⣈⠛⢿⣿⣿⣿⣿⣆⠠⠎⠀⣴⠀⠀⣠⣀⠀⠀⠈⠉⠉⠐⠀⠠⣄⣴⠞⢉⡴⠚⣡⣾⣿⣿
⠀⠀⠀⢀⠀⠀⠙⠿⣷⣤⣙⠻⢿⣷⣦⣝⣿⣿⣿⣿⠀⠀⣈⣿⠦⠶⣿⠟⠂⠀⠀⠀⠀⠙⠀⠸⠏⢀⡴⠋⣠⣾⣻⣿⣿⣿
⠀⠀⠀⠈⠻⠷⣶⣤⣌⣙⠻⠿⣶⣬⣭⣿⣿⣿⣿⡿⠀⠀⣴⣷⠀⠀⠰⣆⠀⠀⠁⠀⠀⢠⣤⣀⣴⡟⣡⣾⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢀⡀⠀⠉⠛⠛⠿⠿⠷⠶⠿⠿⣿⣿⣿⣿⡆⠀⣿⣮⠞⠡⣼⠏⠀⠐⠀⠀⠀⢀⣩⣿⣿⣿⣿⣥⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠙⠛⠿⠶⠶⢶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣾⣿⣧⣴⣾⣿⣶⣦⠀⠀⠀⠀⢡⠿⢳⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠐⠶⠶⠶⠶⠶⠾⢟⣛⣭⠷⣿⣫⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢰⡍⣶⣿⣽⣿⣿⡟⣹⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠠⢴⠶⠖⠻⠛⣩⡴⢾⣿⣿⣷⡾⣿⣿⣿⡏⣿⣿⣿⢿⣿⣿⣀⣄⢸⣿⣿⣿⣿⣿⡿⣱⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⣉⡥⠾⣫⢴⣿⢿⡔⣿⣿⡏⡁⣼⢿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣊⡵⢊⠵⢮⡾⠋⡈⠀⠀⠘⢻⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⡿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⢿⣿⣿⣧⡿⢠⣿⡿⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣋⣿⣿⣿⡿⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣟⡙⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣢⣶⣶⣾⠆⣽⡿⢫⡆⣠⣨⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠟⢛⣻⣿⣿⣿⣿⣿⡿⣫⣾⣿⣷⣿⣱⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠰⢟⣉⠁⠒⠚⢛⣩⣽⣟⣻⡛⠟⠉⣶⣫⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⣀⣤⡾⢛⣹⣿⣿⣿⠟⣴⡇⣿⣿⡿⣿⢻⡟
⠀⠀⠀⠀⠀⠸⠁⢀⣤⠾⠛⣡⣴⢟⣿⣿⣿⣿⣿⣿⣧⣿⣿⢰⣏⡼⠁
⠀⠀⠀⠀⠀⠀⡰⠋⠀⢠⡾⢋⣴⣿⢿⣿⢿⣿⡿⣿⢿⣿⡇⣿⣿⠁
⠀⠀⠀⠀⠀⣸⠇⠀⠰⠋⣰⡿⠉⢡⣿⠏⠸⡿⣡⣿⢿⣿⡇⣿⣿⣷⡄
⠀⠀⠀⠀⠀⢿⠀⠀⠀⢰⡟⠀⠀⣾⣿⡄⠀⢰⣿⢣⣿⣿⡇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢸⡏⣿⠀⠀⢸⣿⣿⣿⠈⣿⣿⣯⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⢸⠏⣿⠐⢸⡄⢿⣿⣿⠂⣿⣿⣿⣿⣷
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠘⠀⣿⠀⠙⠿⠟⣿⢹⡀⣿⣿⣿⣿⢿⣦⣀⣠⠏
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣀⠀⠐⣿⡈⠑⣿⡌⢿⣿⡀⠙⠟⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⣆⠀⠹⣧⡀⢿⣇⠀⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢿⣆⠀⠈⠛⠘⣿⡄⠀⠁⠊⠛⠂⠤⣠⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠘⢿⣦⣀⠀⠈⠉⠉⠉⠉⠁
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠠
⠀⠠

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣷⣾⣷⣦⣐⣤⡉⠻⣿⣿⣿⣿⡿⠿⠟⣛⣛⣛⣛⣿⣾⣯⣭⣭⣈⠉⠙⠛⠿⣿⡿⠛⣡⡾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⢹⣿⣿⣷⣤⣈⣻⣿⡝⢦⠀⠙⠁⠀⠴⠶⣛⣛⣛⣛⣛⠛⣻⣟⣥⣬⣭⣓⣤⣤⠶⠂⠀⣼⢿⣶⣿⣿⣿⣿⣿⣿⠂⢨⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣍⠙⣻⣿⣿⣿⣧⡀⠀⠾⠿⠛⠛⠛⠛⠛⣻⣶⣿⣈⠉⠛⠛⠛⠻⠄⠀⠙⢻⣿⣟⣛⣿⣿⣿⣿⣿⣿⣂⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠋⣉⣤⡀⠀⠀⢀⣴⣾⠟⢻⣿⣿⣿⣟⠿⢿⣦⡀⠀⢀⣹⡆⠀⠙⢿⡛⠋⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⣈⣿⣿⡟⠁⠀⠾⠟⣁⣤⠟⣽⣿⣧⡉⣤⣌⡙⠿⠀⠘⣿⣿⣷⣄⣈⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢟⣵⡿⢿⣿⠟⠀⠀⣴⣿⣿⠿⠟⠿⣿⡿⠓⠻⢿⣿⣷⡀⠀⠈⢻⣿⡿⣿⣄⡀⠈⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣠⣶⡿⠋⣠⣿⠁⠀⠀⠀⠀⠀⣠⠀⢀⣰⡿⢆⡀⢀⡀⠀⢀⡀⠀⠀⠘⣿⣿⣿⠻⢿⣦⡀⢀⡿⠟⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢀⣾⡿⠋⢠⣿⣿⡏⠀⠀⣠⣴⠶⠈⠃⢰⣟⠃⣡⣼⡏⠈⠛⠀⠈⠻⣷⠀⠀⢸⡿⠿⠀⠈⢻⣿⣿⡆⠀⠈⠛⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣴⣿⡿⣵⣶⠈⠙⣿⣁⣠⡀⡏⢠⠂⠀⣠⣼⡿⢱⣿⣿⡍⢦⠀⠀⣦⠀⣹⣧⣶⡌⣷⡀⠀⣿⣧⡙⣿⣿⡀⠀⠀⠙⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠃⠀⠀⣼⣿⡟⢠⣿⡗⢀⣼⣿⡈⠙⠛⠿⢹⡄⢠⡟⠁⣧⣾⣿⣦⣽⣿⡀⠀⣸⠀⠉⠉⠁⣠⣿⣷⡀⢸⣿⡇⠹⣿⣷⡄⠀⠀⠈⠻⣿⣿
⣿⣿⣿⣿⣿⠃⠀⠀⢰⣿⣿⠁⣼⣿⠃⠞⣛⣹⡷⣶⣶⣶⣤⠀⠸⣷⣶⣿⣿⣿⣿⣿⣿⡇⠀⣰⣿⣿⣿⡿⢛⣏⣉⠃⠘⣿⣿⠀⠹⣿⣷⠀⠀⠀⠀⢿⣿
⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⡟⠀⣿⡟⠀⣸⣿⡟⢻⣿⣿⣿⣿⣷⡀⣿⣿⣿⣏⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣷⠞⣿⣿⡀⠀⢸⣿⠀⠀⢿⣿⡆⠀⠀⠀⠈⢿
⣿⣿⣿⣿⠃⠀⠀⢀⣿⣿⠀⠀⣿⣇⠀⠘⢿⣏⠛⣿⣿⣏⠉⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡏⠀⣿⣿⡿⠠⣿⣿⠃⠀⢸⣿⠀⠀⣾⣿⡇⠀⠀⠀⠀⠸
⣿⣿⣿⣿⠁⠀⠀⠸⣿⣿⠁⠀⢸⣿⡀⠀⠀⠻⢿⣿⣿⠟⣸⣿⣿⠃⣿⣿⠿⡟⣽⣶⣿⣿⣿⣿⡄⠛⢿⣿⠾⣿⠁⠀⠀⢾⣿⠀⠀⣿⣿⠀⠀⠸⠀⠀⢀
⣿⣿⣿⡇⠀⠀⠀⣰⣿⣿⠀⠀⣾⣿⣧⣤⣤⣤⣴⠾⢟⣠⣿⣿⠏⢠⣿⡿⠀⠀⢹⣿⣿⣿⣿⣿⣿⢆⠲⢦⣄⠀⠀⣠⣶⣿⣿⡄⢠⣿⣿⠀⠀⢸⡀
⣿⣿⣿⡅⠀⠀⠀⢰⣿⣿⣿⠀⣿⣿⣿⠛⠿⠁⣴⣶⠟⣿⣿⡏⣰⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡁⠳⣄⡙⢳⣿⢛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⡇
⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣾⡾⠙⠿⣷⣤⣼⠿⠋⢰⣿⠛⣿⣿⡿⠋⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠙⠛⢷⣡⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠁
⣿⣿⣧⡆⠀⠀⠀⢸⣿⣿⣿⣿⣷⣼⣾⣿⣿⠀⠀⢀⣯⡁⢴⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀⣩⣦⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⡇⠀⠀⠀⠈⢛⣿⣿⣿⣿⢿⡿⢿⣿⣇⠀⠘⣧⣁⠀⠘⣿⡀⠀⠀⠒⠄⠀⢀⣠⡿⠁⠈⣘⣥⣾⣿⢀⣿⣿⣿⣿⠿⢿⣿⣿⡿⠧
⣿⣿⣿⣿⡄⠀⠀⠀⠀⠹⠟⠋⠁⠀⠀⢨⣿⣷⣦⣽⣦⡙⠃⠀⠈⠻⢷⣦⣼⣦⣴⡿⠋⠁⠀⠚⠛⣁⣾⠖⢰⣿⣿⣿⣿⣛⡛⠛⠁
⣿⣿⣿⣿⣷⡄⠀⠀⠰⣾⠋⠀⠀⠀⠀⠈⠛⠛⠩⠈⠛⠛⠲⠖⠂⠀⠀⠻⣿⡿⠟⠀⠀⠤⠴⠖⠛⠋⠀⠰⣿⣿⣿⣷⣂⠀⠀⠠⢀⣄⣄⠀⠀⠀⠀⠀⣰
⣿⣿⣿⣿⣿⣷⣂⣤⣾⣧⣤⣶⣾⠇⠀⠀⠀⠀⣠⡛⣴⣭⣅⣠⣀⢀⣀⣠⣾⣷⣤⣄⣶⣶⣶⣾⣿⣶⣼⣷⣍⢿⣿⠿⢛⡻⣷⣶⣾⣿⣿⠃⠀⠀⢀⣶⣿
⣿⣿⣿⣿⡿⠿⠟⠉⠀⠁⠘⠻⣯⣶⣶⣾⣦⣶⣿⣿⣿⢿⠟⠛⠛⠟⠻⠋⠀⠻⠛⢿⢻⠛⠛⢿⣿⣿⣿⣿⣿⣷⣿⣆⢬⣷⣾⣿⣿⣿⡟⠀⢀⣠⣿⣿⣿
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣶⣿⣿⠫⠛⠍⠻⠟⠁⠀⢀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⡀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠑⠀⠰⣶⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⡟⠋⠉⠀⠀⠈⠀⠀⠀⢠⣷⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣯⢙⣏⠈⢹⡿⠟⠿⢿⣿⣯⠋⠈⢠⠀⠀⠀⠀⠀⣴⠀⣶⣴⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣄⠿⣿⣿⡆⠀⠀⠀⢠⣶⣿⣿⣿⣿⣏⣠⣦⣤⣶⣾⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣧⣝⣿⣧⡀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣿⠟⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⣤⣿
⠀⠀⠀⠀⠀⢀⡀⢠⣤⡤⠀⢰⣶⠉⠉⡩⠀⠀⣀⣀⣤⣤⣤⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠰⣾⣏⠀⢸⣿⠧⠠⠼⣿⠷⠮⢡⣖⣽⡿⢋⣵⠟⣩⡶⠛⠉⣉⣤⣤⣤⣬⣶⣤⡀
⠀⣴⡇⠀⡹⠛⠉⠀⠀⠀⠀⣰⣡⢒⣈⢻⣿⡏⢠⡿⢫⣾⡟⠀⣴⡿⠛⠉⠁⢀⣠⣤⣬⣍⣢⡀
⢀⠻⣿⣿⠀⠀⠀⠀⠀⠀⣨⢙⡷⢋⣤⣿⣻⡇⣿⠀⣿⡟⢀⣾⡟⠀⣀⣤⣾⠟⠉⣀⣤⣤⣤⣙⣦⡀
⠰⡀⠀⣸⡄⠀⠀⠀⠀⣀⣿⣾⣡⡋⠉⢭⣿⣀⡟⣸⢿⠃⢸⣿⠀⣞⡵⠋⠕⣣⣾⡛⠋⠀⠀⠙⢷⣷⣄
⠀⠻⡿⠿⠋⢸⣶⡆⠹⣿⣿⣿⣿⣶⣿⢿⣿⣿⡇⣿⢸⣤⢸⣿⡖⠋⡙⠳⣿⣿⣭⣤⣶⣶⣶⣶⣤⠉⠙⢷
⠀⠀⠀⠀⠒⠚⠛⠁⠘⠉⠉⡏⠙⠀⠐⠀⠀⠘⣷⣹⣎⣿⡟⡽⣩⠟⠶⢟⡽⣻⠟⠉⠁⠀⠀⠈⠙⢷⣤⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠿⣤⡧⣌⠧⡼⠋⠛⠿⣿⣿⡇⢃⡴⢱⣏⣞⣡⠶⠟⠛⠻⢿⣷⡄⠀⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣸⣷⢿⣟⢉⡤⠶⠶⠶⣤⠀⠿⠿⣶⡄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡏⣿⡩⠙⠒⢯⣟⠶⠼⣟⠳⣆⠘⡇⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣮⣿⠇⡉⠐⠁⢃⡚⠮⢭⡓⠎⠧⢽⡶⣷⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠏⣩⣤⢩⢊⣌⠁⠁⠰⢆⠘⣠⠰⣬⠷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡇⣿⣴⠹⠇⠀⠁⢠⡆⠲⢠⠀⣷⣞⣉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣄⠃⢻⡗⣅⣡⡔⠒⣹⣆⣽⠆⡆⢛⡋⠻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡐⣸⡐⠛⠲⡽⢻⠾⣛⣩⠾⠃⣼⣶⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠷⣦⣴⠴⠡⠀⠤⢤⣠⣾⣯⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡈⠛⠲⠾⣰⣾⠉⣿⣿⠏⣅⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢹⠉⠒⠐⡾⠛⢻⡞⡁⠫⠒⢦⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢶⣴⣆⢠⡁⣀⠘⣼⠁⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢠⠇⠀⡁⢀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠀⣌⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣀⣇⢀⣰⢀⠻⠶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡴⠶⠶⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠉⠁⡰⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣄⡀
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢀⣤⠒⠋⠉⠀⠀⠉⠲⣄
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⡀⠬⠳⡀
⠀⠀⠀⠀⡼⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⡇⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⢤⡀⠀⠀⣠⡇⠀⠲⣄⠀⠀⣠⡟⣡⡞⢀⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⣇⢠⣀⠀⣀⣹⢦⡀⠻⣄⣴⠟⡇⠀⠀⠹⡳⡜⡝⡴⢹⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⣿⢀⣙⠻⡦⣹⣾⣌⡦⠾⠴⠴⠣⠶⣦⣄⣸⢠⡷⢁⠟⣿⡤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⢹⡀⠉⢳⣝⣜⢿⠏⠀⠀⠀⠠⠊⠀⠈⢷⡇⢸⡇⡜⢸⣿⢡⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠄
⠀⠀⠀⠀⠀⢱⠛⠍⠉⢻⣾⡀⠀⠀⠀⠀⠀⠀⣀⣼⣇⣸⣷⠋⠉⠉⣹⠉⢹⡄⠀⡇⠀⢀⣀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠉⠓⠚⠁⠀⠉⠑⠚⠉⠉⠉⠉⠀⠀⠈⠁⠈⠓⠒⠚⠉⠀⠉⠉⠉⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⡀⠀⠀⠀⡀⡀⡀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠇⢠⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢃⠈⣧⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢷⡀⠈⡀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠘⣇⠀⠠⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⡔⢿⣆⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠻⣌⠻⡆⠣⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⢦⡘⢦⠹⡆⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⡌⠂⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢀⡊⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢦⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡜⠡⠞⢀⠔⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠳⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠳⣄⠈⠓⠆⠀⠀⠀⠀⠀⣠⣆⡴⠛⠉⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣾⡟⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠲⢌⣁⠀⠀⠀⠀⠀⠀⢰⠟⠋⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⢀⡄⣼⣿⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣌⠁⣈⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠦⡀⢤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠟⠳⠶⠖⠈⠑⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣞⣁⣀⣤⠤⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⠀⠁⣠⣤⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠀⠀⢀⣠⣤⠾⠛⠉⠉⠉⠙⠙⠛⠻⢿⣿⢿⣦⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣀⡀⣀⣤⣠⣾⠿⢋⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠙⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠒⠂⣀⣴⣿⣿⣿⣿⣿⣿⣿⠟⣿⣟⣯⡥⢶⣟⠛⠻⣿⣿⣿⡓⠀⠀⠀⠀⠀⠀⢀⠹⣦⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡤⠖⠋⢡⢿⣿⣿⣿⡿⠁⠿⢷⣦⣭⣭⣤⣤⣤⣬⣥⡀⠈⠿⠀⠃⠀⠀⠀⠀⠀⠀⢸⣦⣿⣷⡀⠀⢸⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣤⠔⢃⣾⡿⢻⣿⠃⠀⠀⠀⠀⠀⢠⠾⠛⠋⠹⣿⢿⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣀⠀⢻⣿⣿⣿⣿⣿⠃
⠀⠀⢲⣄⡀⠀⠀⠀⠰⣤⣀⡈⠀⠉⠙⠃⠈⠛⠁⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⡈⢳⠌⠙⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣛⣯⠀⠀⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠹⢿⣷⣶⣤⣀⣈⠙⠿⣿⣶⣶⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣮⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⢀⣼⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣦⣄⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣄⣈⠉⠉⠛⠛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠙⠛⣛⣛⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠟⢿⡿⠿⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⢛⢦⡀⠀⠀⠀⢀⢔⣉⢱⡀
⠀⠀⠀⠀⠀⠀⠀⣸⢱⣿⣷⣤⣄⠀⠴⣧⣾⣿⡇⢧
⠀⠀⠀⠀⠀⠀⠀⡷⠟⠛⢩⢓⢦⢀⢖⣲⡄⠈⣙⣾⣄
⠀⠀⠀⠀⠀⢀⡾⠷⠦⠀⠱⠭⢔⣈⠒⠕⠁⠀⢉⣭⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀
⠀⠀⢄⣀⣀⣿⣟⡓⠂⣀⡄⠀⢻⡿⠃⠀⢦⣄⣠⠤⠴⢻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡛⠻⣏⠀⢹⣿⣦⣄
⠀⠀⣀⣀⣈⣇⣉⣉⣽⣭⣥⠀⠀⡇⠀⠨⠥⢾⣖⣒⣛⣹⣋⠉⠉⠀⠀⠀⠀⠀⠀⣰⣍⢙⡷⠚⠉⠉⠛⠻⠿⠟
⠀⠀⠀⠀⠀⢹⣄⡀⠼⢶⠂⠀⣠⢧⣀⣀⣩⠟⠁⢀⣴⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⣏⠉⡟
⠀⠀⠀⠀⠈⠀⠉⠓⠤⣀⣉⣉⣳⣴⣁⣀⣤⠴⠞⠋⣿⣿⢸⣿⡟⢸⣿⡶⣄⢀⣼⠛⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡉⠉⠁⠀⠀⠀⠀⠀⣿⠇⢸⣿⠁⢸⣿⠁⠈⠉⠙⣦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⡀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠃⠀⠸⠇⠀⢰⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣶⣟⠷⢹⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣣⢈⣛⡴⢋⣼⢷⡄⣠⠤⠤⠤⣤⣀⣤⡤⢴⡶⣾⣣⡤⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⡰⠛⠛⠆⢠⠃⠀⠀⠀⠀⢀⣿⣯⡈⡇⠹⣏⣠⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠥⣦⠴⠃⠀⠀⠀⠀⠀⢸⣥⣠⣠⠃⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⢀⣤⣶⣾⠿⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢀⣾⣿⣿⣤⣀⡀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠫⢋⣥⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣝⠊⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠐⢫⣷⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣍⠃⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⠙⣿⠟⠛⢷⣦⡄⠀⠀⠀⣀⠀⠀⠘⠛⠻⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠹⢿⣿⣿⣤⣄⠀⠀⠀⠀⡀⠀⠚⣉⣀⣤⣀⡾⠀⣿⣦⣤⣤⣤⣈⡁⠀⠈⠉⠛⢣⣤⣀⠀⢿⣿⣿⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠸⠛⣿⠟⠋⠀⣠⠆⠐⠁⠀⠀⢉⣠⣄⣀⡀⢠⡟⢷⣄⡀⠀⠉⡁⠀⠀⠀⠀⠀⢀⠉⠷⣦⡉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠁⠀⢀⣀⡰⠋⠈⣠⠤⠟⢳⣿⢷⠆⠙⢿⣆⢠⡿⣦⠀⢀⠀⣶⣌⠙⠲⣄⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢴⣿⡛⠃⠀⠐⡡⠂⣴⠏⠀⠈⢷⠀⠀⡃⠀⠁⠿⠚⠻⠟⢸⠟⠀⡀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⢀⣧⣤⣤⣭⣄⠀⠸⠁⠀⠀⠀⠀⠀⠀⢤⣀⣡⠀⣀⣤⣤⣤⣤⣾⡆⢸⣿⡄⠘⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡇⣼⠇⠀⢠⣦⡙⠾⣿⣷⠀⠁⠀⠀⠀⠀⠀⠀⠀⠿⠁⣼⣿⠾⠿⢁⣼⡟⠀⣦⢻⣷⠀⢻⡇⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⣼⠃⣿⠀⣄⠀⠈⠭⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⣀⣿⠀⣿⡆⠈⣿⠀⠀⠻⡗
⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⠀⠉⢻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣛⠁⡟⠀⣿⡇⠀⣿⡇⠀⠐⢿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⠁⢻⠀⠀⠠⠖⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠲⡌⠉⡜⠁⢀⣿⠀⠀⣿⡇⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⣹⣿⠀⢘⡷⠲⠖⢀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡕⢦⣴⠀⠀⣼⡇⠀⠀⣿⠃⠀⠀⠈⠻⣷
⠀⠀⠀⠀⠀⢀⣾⣿⡇⠸⣷⠀⠸⠋⣀⠀⠀⠀⣀⣀⣤⣀⣀⣀⣠⣤⣤⣤⠀⠀⠀⠀⡀⠈⣦⡟⠀⠀⣿⣷⠀⣸⡏
⠀⠀⠀⠀⡀⠀⠙⢿⣷⠀⠙⢆⠀⠈⠁⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⡀⢀⠁⠀⠈⠀⠀⠴⠋⠛⠂⣿⡀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⣇⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⡠⠖⠀⠀⠀⠀⠀⡀⠀⠛⠃⠀⠀⠀⢠⣣
⠀⠀⠀⢀⡿⠀⠀⠀⠀⢿⡟⠀⠠⣤⣌⣙⣉⣀⣀⢈⠀⠀⢹⡏⠀⢀⡀⠀⠀⠈⠋⢉⣠⠄⠀⢀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⠂
⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠁⠀⠀⠠⢀⣈⣉⣉⡁⠀⣠⣶⣿⣷⣄⡈⠙⠛⣋⣉⣉⡁⣄⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠡⠴⠾⠛⠛⠚⠛⠛⠛⠿⠦⣌⡻⣿⡝⠃⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠈⢷⠘⡷⣄⠀⠀⠀⢠⠸
⠀⠀⠀⠀⠀⠻⢿⣦⠀⠀⠀⠀⠀⠀⠀⠘⢯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠸⠧⠀⢀⡞
⠀⠀⠀⢀⠀⠀⠈⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣥⣤⣤⣶⣶⡶⠄⠀⠀⠀⠀⠀⠀⢀⣠⡾⠁
⠀⣿⡄⠘⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠃⠀⢐⣠⣶⣿⠿⢛⣭⣶⠟⠋⠀⠀⠀⣀⣠⣤⡶⠾⠛⠉⠀⠀⣠⡴⠇
⠀⢻⣿⡀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠉⢠⣶⡿⠋⢁⣀⣤⡶⠾⠛⠋⠉⠀⢀⣀⣠⣼⣷⠶⠏
⠀⠈⢿⣷⡀⠘⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁⠀⢀⡴⠋⣡⡴⠞⠛⠉⠀⠀⢀⣠⣤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢲
⠀⠀⠈⠻⣷⡄⠈⢻⣷⣦⣤⣄⣀⣀⣀⣠⣤⣶⣿⡿⠟⠁⠀⠀⡠⠋⣰⠟⠉⠀⠀⠀⣀⣴⡾⠛⠉⣀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠙⣿⣦⡀⠙⢷⣄⠉⠉⠉⠉⠙⠛⠉⠉⠀⠀⠀⣠⠞⠁⠀⠁⠀⠀⢀⣠⣾⠿⢋⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠘⣿⣿⣦⣄⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⣴⡿⠟⢁⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⣠⣤⡾⠋⠀⠀⠀⠀⠀⣠⡾⠋⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠋⠀⠀⢀⣀⣠⠤⣤⣤⣤⣤⣶⠶⠾⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠲⢤⡀⠀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠋⠁

⠀⠀⠀⠀⡔⠊⠉⠉⠛⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠉⠑⢢
⠀⠀⠀⣰⠃⠀⣤⣶⣶⣤⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⣴⣶⣶⣤⡄⠾⣆
⠀⠀⠀⡇⠀⣾⣿⣿⣿⣿⣿⣆⠀⢦⣀⣀⡠⠤⠴⠖⠒⠶⠾⠽⠯⠭⠖⠒⠒⠦⠤⢤⣀⣠⡴⠃⣰⣿⣿⣿⣿⣿⣷⠀⢹
⠀⠀⠀⠣⠀⣿⣿⣿⣿⣿⡿⡿⡄⢀⡭⠈⢁⠴⠿⠛⠛⣉⣛⣃⣙⣛⣉⠛⠛⠷⢦⡈⠉⣍⡁⢰⢿⢿⣿⣿⣿⣿⣿⠀⠜
⠀⠀⠀⠀⢰⣿⣿⣿⡿⠿⠁⠀⠀⠉⠀⠐⢁⣰⣶⠿⠛⠋⣉⠉⣜⣉⠉⠙⠿⣶⣄⡈⠢⠀⠙⠀⠀⠘⠻⣿⣿⣿⣯⡆
⠀⠀⠀⠀⠘⠛⣿⣿⡿⠀⡔⠁⡴⠃⠀⣠⠋⢁⣠⠤⠐⠚⠁⠆⡉⣝⡛⠂⠤⣤⡈⠻⣄⠀⠘⣆⠈⢆⠀⢿⣿⣿⡛⠁
⠀⠀⠀⠀⠀⢸⠋⠀⣠⡞⠀⣼⠁⠀⠀⠀⡴⠋⡄⠐⠉⡟⣡⠀⠀⠛⢻⠙⠂⢠⠙⢢⠈⠀⠀⠈⣧⠀⢷⣄⠀⢙⡇
⠀⠀⠀⠀⠀⠨⠍⢰⡟⠀⢰⣿⡄⢀⣄⣤⡄⢸⡇⠀⣾⠄⠗⠇⠘⠆⠰⢳⠀⢸⡇⢠⣄⣠⡀⢰⣿⡆⠀⢻⡄⢩⠅
⠀⠀⠀⠀⠀⠀⢀⣾⠁⡆⠘⢻⡄⠈⢉⣉⣙⠈⠳⡀⠀⠘⠀⠀⠀⠀⠘⠂⠀⠘⢀⣉⣉⡉⠉⢸⡟⠃⣸⠈⣿⡀
⠀⠀⠀⠀⠀⠀⣾⡗⠐⣿⠀⣼⣟⠛⣿⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⠟⣿⠛⣻⣧⠀⣿⠀⢻⣷
⠀⠀⠀⠀⠈⢐⣿⡇⠀⡟⠀⡏⠙⢧⣈⠓⠶⠺⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠗⠖⠚⣁⡾⠋⢹⠀⣿⠀⢸⣿⡂⠃
⠀⠀⠀⠠⠀⣸⣿⡇⠀⣿⠀⢷⡀⢦⣭⠙⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉⠀⠈⠋⣭⡴⢠⡞⠀⣿⠀⢸⣿⣇⠀⠄
⠀⠀⠀⠀⢰⣿⣿⠁⠀⢹⢰⠀⠻⣄⡔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⣠⠟⠀⡆⡏⠀⠈⣿⣿⡆
⠀⠰⠁⠀⠸⣿⣿⡀⠀⣿⡌⣄⣷⣄⠎⠈⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣱⡱⣠⡾⣠⢡⣿⠀⢘⣿⣿⠇⠀⠘⡆
⠀⡦⠀⠀⠈⣿⣿⡇⠀⣿⣷⠸⡇⠁⢀⡞⡱⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢠⡁⠈⣸⠇⣾⣿⠀⢸⣿⣿⠁⠀⠀⢴
⠸⡣⠂⠀⠀⢹⣿⣷⡀⠙⢿⡄⠀⣌⡏⢀⡄⠀⠀⣤⣀⣀⣀⡀⠀⣀⣀⣀⣿⡷⡀⢤⡀⢹⣴⠀⣰⡿⠋⢠⣾⣿⠇⠀⠀⠐⢘
⠐⣿⡁⠀⠀⠀⢻⣿⣷⣤⡀⠹⢦⡈⢱⣿⡁⠘⠀⠹⣤⣄⡈⠙⠋⢉⣤⣤⠟⠃⠃⣘⣿⣮⢗⡴⠏⣠⣴⣿⣿⡟⠀⠀⠀⢈⣾
⠀⠉⠏⠀⠀⠀⠀⠘⠿⢿⠿⣶⣄⡙⢦⣌⣉⡉⠑⠂⠈⠻⢿⣀⣀⡿⠛⠁⠐⠊⢉⣉⣡⡴⢋⣤⣾⢿⣿⠿⠁⠀⠀⠀⠀⠛⠉
⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣇⣉⢉⢉⠁⠀⠀⠀⣸⡇⠀⠀⠀⠉⡉⡉⣉⣼⣿⣿⣿⠛⠀⠀⠀⠀⠀⢀⣴⣿⠂
⠀⠀⠀⠈⠻⣧⢀⡄⠀⠀⡀⠀⠈⠉⠿⢿⣦⣤⣄⣀⣀⡠⠾⣿⡟⠲⢤⣀⣀⣤⣤⣼⣿⡿⠋⣁⣴⠀⠀⠀⢀⡀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠸⣿⣾⣾⡇⠀⠀⢀⠀⠘⢿⣿⣿⣿⠀⢡⣄⣈⣁⣠⡎⠀⣿⣿⣿⣿⠇⢠⡈⠉⠀⢸⣷⣾⣿⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠧⡴⠻⠷⠖⢲⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠟⢷⠾⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⢻⢿⣿⢿⣿⣿⡿⣿⣿⡝⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢯⣍⠀⠋⠋⠉⠲⠋⠙⢀⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⡀⣀⠀⠀⣀⢀⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠋⣥⢠⢠⣤⡀⠤⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⠱⣜⠛⡇⢊⣽⠀⣯⣬⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢃⣏⡰⣟⣻⠡⣎⡓⢢⢼⣯⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢧⡾⠷⠤⣶⠦⡷⢭⣭⣠⠗⠓⠐⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡿⡪⣔⣴⣦⡤⢿⣭⡾⠁
⠀⠀⠀⠀⠀⠀⢀⡞⢫⠞⢩⠾⢛⡿⠿⢶⣽⣦
⠀⠀⠀⠀⠀⠀⢸⡇⣾⠀⣣⡶⠟⣀⣦⣌⣉⣙⣆
⠀⠀⠀⠀⠀⠀⢸⡇⡿⣼⢋⡴⠛⠉⣡⠶⡚⢛⣛⣳⣄⡀
⠀⠀⠀⠀⠀⠀⣼⢹⡷⡻⢾⠇⣴⡿⢁⡼⢻⢯⣥⠴⢶⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⠄
⠀⠀⠀⠀⠀⠀⣇⠸⣷⠅⡞⡼⣿⢠⡟⣡⠏⣼⢋⣉⣉⣩⣭⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣻⡟⠁
⠀⠀⠀⠀⠀⢀⡇⢠⢻⣼⡇⠁⣏⡞⢸⠃⢺⡏⣸⠏⣴⡶⠶⣒⣾⣿⣖⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿
⠀⠀⠀⠀⠀⢸⠆⡎⢩⣿⡇⣀⣿⣇⣟⢸⢼⢰⢿⢰⡼⢱⢸⣣⣿⠟⢋⡗⣪⢭⠷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠸⡶⠾⣆
⠀⠀⠀⠀⠀⡜⠘⡘⣠⠟⠳⣼⡿⡇⢽⣾⢸⡟⣸⢿⡅⡇⣿⡏⣿⠃⡎⡴⠳⢉⢗⣙⠹⣷⡀⠀⠀⠀⠀⠀⠀⠑⢶⡟⢳⢄
⠀⠀⣠⠤⢀⡇⠀⢡⠇⠀⠀⠀⠿⣿⣾⣿⣿⣿⣸⡘⣿⣾⣿⣿⠏⣠⢋⢡⢿⡿⡡⣽⢉⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⢯⣠⣷
⠀⢻⡕⠂⠀⠀⢄⡜⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣻⡇⣏⢿⡀⠿⢸⠀⣼⢀⡇⠻⣿⣴⠚⢻⣶⡄⠀⠀⠀⠀⠀⠀⠀⢻⣴
⠀⠉⠓⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡽⣄⣻⣮⣧⡀⢈⡛⢻⡦⢥⣼⣿⣿⣷⡟⠙⢿⡄⠀⠀⠀⠀⠀⠀⡾⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢋⣋⢳⡸⣟⠊⠉⠓⠶⣬⡟⢷⣶⠟⠳⣆⣬⡻⢶⣎⠉⡢⣄⡀⠀⢀⣴⡙⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣏⢈⡁⠽⣦⣭⡝⢉⣹⢾⠛⠋⠀⠀⠀⠀⠉⠛⠒⣝⠳⢾⣍⣩⣿⣉⣺⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠲⠤⣤⣐⠈⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⡉⠩⣉⡳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⡑⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠋⡧⠁⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⠤⠤⠬⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣠⡀⠀⠀⣤
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⢻⣧⣰⣿⣿
⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢆⣀⣤⣷⣿⣿⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣷⣦⣀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⣟⢿⣿⣄
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣇⢉⠀⠉⠻
⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⣿⣿⣿⣿⣽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⡀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣿⣿⣿⠟⣀⠈⠉⠻⠟⣩⣿⠿⣿⡻⢿⣿⣿⣿⣿⣿⡇⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣵⣿⣿⣿⣿⢏⡞⢹⣇⣴⣶⢰⣿⣿⣧⡿⣷⣾⡈⢻⣿⣿⣿⣿⣁⡀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠙⣿⣿⣿⣿⣿⣿⣼⣵⣟⡛⠉⣩⡾⣻⣿⡛⠛⢿⣿⢃⠀⢻⣿⣿⣿⡿⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠟⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣭⣀⠀⢸⣿⣾⢷⢸⣿⡿⣿⣿⣊⠻⣿
⠂⢹⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⢁⣼⣿⣿⣿⡿⠛⣛⣥⣾⣿⣿⣿⣿⣿⣏⠀⣰⣿⣿⡘⠸⣿⣿⡎⢿⣿⡄⠙
⠆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⣰⣿⣿⣿⣿⣿⣷⣜⠋⣽⣿⠿⠻⠿⢸⣿⠋⠉⠙⣿⡿⣧⠘⣿⣿⡗⠀⢻⣷
⠀⡠⠆⠀⠐⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣝⣿⣫⣠⣤⣶⣶⣾⣥⡀⠀⢸⣿⠁⠀⠀⢹⡇⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣾⣿⣿⣿⡿⠄⠞⣿⣿⣿⣿⣿⣿⣿⣭⢀⣈⡻⠟⠁⠀⢈⣿⠀⠀⠀⠸⣷⠀⠀⣸⣿⡇
⣀⠼⠀⠀⠀⠀⠀⠀⠀⡻⠋⠁⢠⣬⣽⣏⣽⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣠⣿⢺⣿⣷⡄⠀⠀⣿⡇⢰⣿⣿⣷
⣁⠀⠀⠀⠀⠀⠀⠀⠀⢾⣧⡔⣐⠒⠶⠾⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡄⢿⣿⡇⠀⠀⣿⠁⢾⣿⣿⣿
⢻⠀⠀⠀⠀⠀⠀⠠⠀⢸⠿⣿⣯⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠈⢻⡔⢙⣧⠂⡀⠀⠀⠀⠹⣿⣿
⣌⠀⠀⠀⠀⢠⢠⣾⡆⠸⠀⠉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⡠⢔⣶⣄⠀⠠⠟⠈⠉⠀⠁⠀⠀⣷⢰⢿⣿
⢿⡂⡆⢰⣆⠀⣼⣿⣧⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣦⣸⣅⣠⡿⠤⠛⡀⠀⢀⠀⠀⣄⢀⣠⠀⣿⣼⣿⣿
⣼⡇⣿⢈⣿⣸⣧⣿⣿⠀⡄⠎⡀⢀⣈⠉⠋⣉⣤⡀⢻⡏⢿⡌⣷⠸⣻⡇⠀⣼⡇⠀⣾⠀⣾⢳⣿⣣⠔⣿⣿⣿⣿
⡏⣿⣿⢈⣿⣿⣿⢻⣿⣿⣇⣼⣧⣿⣿⣷⣿⣿⣆⢻⣎⣿⠀⢠⣿⣧⣿⡇⣼⣿⠉⣠⣿⢀⣿⣿⣿⣏⢸⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣠⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢂⠀⠁⠀⠀⠀⡌⠄⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⢹⠈⠀⠀⠠⠀⠣⢠⣤⠉⡒⣄⡀
⠀⠀⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠀⠈⠀⠈⠣⠀⠀⠀⠀⠂⢈⠈⠀⠁
⡴⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠂⢆⠙⠘⠌⠒⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠐⠡⠅⠁
⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠂⣲⣶⢶⢰⢻⠏⠩⠂⡠⠀⢈⠀⡄⠀⠀⢀⡀⠃⠀⠀⠄⠀⠀⢀⠀⡀⣀⣤⠦⠤⠀⠀⠠
⠉⣠⣶⠄⣄⠀⢠⣶⣘⡷⠗⣿⠀⢸⠑⠣⢿⠂⣆⡞⡰⣾⠀⢀⡆⠀⠃⣆⠀⠀⠉⠀⢀⡠⠚⠦⡦⠖⠂⠉
⠀⠈⠙⠀⠿⠗⠈⠉⠁⠀⡌⣟⠙⠁⠀⠐⢱⢤⠇⣡⠇⣿⠄⢸⡇⡸⡄⢜⡳⣭⠼⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢁⠐⢡⣧⡀⣔⡽⠖⠛⠐⠛⠀⠚⠛⠛⠛⠂⠉
⠀⠀⠀⠀⠀⠀⠀⢲⠀⢀⣇⢸⣠⣼⠜⠃⠁
⠀⠀⠀⠀⠀⣀⣦⣢⠼⠜⠚⠚⠉
⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢀⢀
⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⠶⢶⣄⡀⠀⠠⠀⠄⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣽⠇⠀⠀⣐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⢀⡀⠀⠀⠀⠦⠹⠴⠋
⠀⠀⠀⠀⢷⡶⠃⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⠻⡆⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠖⠀⠀⠀⠀⣴⡀⠀⠀⠓⠚⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⠉⠉⠤⠄⠈⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠟⡆⠀⠀⠀⠀⠀⠀⠉⠀⡄⠀⠀⠀⡰⠃⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠑⠐⠂⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠆⠀⠀⠀⠀⢄⣶⣿⣿⣤⣰⣿⡇
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣟⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢰⣿⣿⡏⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣠⠴⠦⣀⢲⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⡁⠚⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣛⣓⠒⠀⠱⡀⠰⠆⠀⠀⢀⡀⠀⠀⠠⠄⠀⠀⠈⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡴⠎⢩⡽⠿⠇⢷⣀⠈⠹⣯⡀⣀⣀⡀⠀⠀⢀⠈⠀⣡⠖⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡐⢤⣴⡏⠀⢠⠎⠀⠀⠁⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⠀⠀⣀⣴⡋⣁⠀⠈⠉⠑⠢⡀
⠀⠀⠀⠀⠀⢸⡇⠀⢸⡁⠀⠛⠀⠀⠀⠀⠀⢀⡛⠂⠀⠀⠀⠠⢀⣤⣾⢤⠿⠛⠛⠉⠉⠁⠉⠘⠦⣄⠀⠀⠘⡆
⠀⠀⠀⠀⠀⢼⣧⠀⠘⢧⣄⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠈⠁⠐⢈⣂⠴⠆⠐⠲⠀⠀⠀⢸⠁⠀⠀⢹
⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⠙⠴⣄⠐⠀⠠⠀⠀⠀⣒⠂⠈⢀⠠⠂⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠱⣈⠙⢦⣀⠀⠈⠑⠲⠶⠤⠐⠚⠁⠀⠀⠀⠠⠆⠀⠀⠀⡠⠖⠊⠲⠶⢆⡀⡤⠀⠟⠀⠀⠀⣼
⠀⠀⠀⠈⠀⠁⠀⠸⡌⠚⠺⣶⠤⣀⡀⠀⠀⠀⠀⠀⢀⠐⠛⠃⠨⠀⠀⡞⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠠⠤⠂⠀⠀⠙⠄⠀⠏⠀⢀⠀⠁⢈⡉⢐⠄⠀⠀⠤⠐⠶⠀⠸⡇⡀⠀⠀⠀⠠⠀⠀⠀⢀⣠⠀⠈⠅
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢚⠃⠀⠀⠀⠐⣤⣿⣦⡄⠀⠀⠈⠀⠀⠀⠸⠇⢁⡀⠀⢠⠴⠆⠀⠈⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⡬⠥⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⡀⠠⣤⠀⠴⣶⠆⠄⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡭⣤⣃⡀⠀⠀⢄⠠⣒⠠⢤⣝⢢⠁⠓⢉⠰⣆⢩⢐⠨⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢀⢄⣠⣦⠴⠵⠒⠲⣌⣓⠲⡄⠁⢁⠄⢈⣀⠎⢒⠐⢠⣀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠴⠡⠞⣀⠐⠲⠖⠓⠦⠤⡈⢷⣌⠀⢀⢠⠈⠍⠠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⢴⡥⠶⢊⡉⠛⠒⢦⡙⣦⡀⠁⠈⡀⠁⠘⠤⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⣖⠚⠉⠙⠛⢶⣤⡛⠿⢙⠲⢴⡌⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢋⣥⡞⠛⠛⠙⠠⣌⡙⠆⠀⠙⠆⣀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⣋⡴⠲⠶⠦⣲⡌⠑⠀⡃⠸⢾⠹⡄⠘⡆⢀⣤⡀⠰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⣈⣉⣩⣙⠦⠝⢂⠈⠀⠐⠠⡠⠁⡇⠸⠃⡀⠀⠀⢹⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⡜⠁⢉⣀⡉⠛⠲⣄⠁⠀⠀⠀⠈⠉⠑⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢂⡞⠛⣉⣉⣓⠒⠒⠁⠀⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⠋⢠⡾⠋⣉⡉⠉⠀⢹⣶⡭⣙⠳⡌⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠱⢋⣤⡴⢋⣠⡼⠋⠛⠛⠿⠉⠳⣤⣈⠳⠘⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⡁⣤⠎⢀⣰⠿⠛⠛⢒⠂⠰⣀⠅⢠⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠞⣥⠞⣡⠖⢉⣥⡤⠾⠟⠉⣰⠋⠡⠞⢁⡀⠰⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠁⡸⠃⠞⠁⠴⠋⢀⠐⠂⠴⠾⠃⢙⡄⠀⠀⠀⠀⠈⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠶⠛⠁⣁⠁⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡓⠾⠂⠁⠀⢀⣀⠀⠀⠀⠀⠀⠰⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠐⠁⠀⢸⣿⣷⠀⠀⠀⠀⠀⢂⠠⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠆⠀⢀⡜⠛⠟⠀⠀⠀⠀⠀⠘⠷⠂
⠀⠀⠀⠀⠀⠀⣠⠏⠀⠘⠁⠀⢐⠃⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⢰⣦⡴
⠀⠀⠀⠀⠀⠈⣹⠀⠀⠄⢀⠀⠁⠀⠠⠖⠂⠀⠀⠀⠀⠀⠀⢀⡂⢈⠃
⠀⠀⠀⠀⠀⠀⠉⠸⠆⠐⠁⠀⠀⠀⠀⢠⡶⢄⠀⠀⠀⢀⢠⡌⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣿⣆⢘⡷⠌⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⢀⠙⢦⡀⠀⠀⠀⣀⠠⣄⣐⡀⣤⣤⣦⡤⢀⣂⣠⠄⡀⠀⠀⠀⢀⡴⠋⡀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠑⢤⡘⣦⣦⡌⢂⡦⠟⠛⣩⠭⠶⠒⠒⠛⠒⠒⠒⠶⠭⣝⠛⠻⢴⡒⢣⣴⣴⢃⡤⠊⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠠⣔⣤⣽⣿⡿⢛⡁⠖⠉⣁⣴⢖⣒⣶⠶⠟⠻⠶⣶⣒⡲⣦⣈⠉⠢⢈⡛⢿⣿⣯⣤⣠⠄⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⣨⣽⠿⣋⡴⢋⣀⠀⢊⡥⠖⠈⢀⣤⡶⠶⠶⠶⣤⡀⠀⠲⢬⡑⠀⣀⣙⢦⡙⠿⣯⣅⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠻⢋⣾⠏⡴⢋⡴⠂⠈⣠⣶⠖⣀⣠⠶⠞⠳⠦⢤⣀⠲⣶⣄⠁⠐⢦⡙⢦⠹⣷⡙⠟⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣿⢟⡞⠐⣿⠀⠠⠊⢡⡔⢀⡅⢠⡜⣋⣙⢣⡄⢠⡀⢢⡌⠑⠄⠀⣿⠂⢳⡻⣿⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣭⠀⣸⠂⠜⠡⠾⠗⠢⠘⠂⠟⡀⠟⠠⠉⠁⠤⠻⢀⡻⠐⠃⠰⠺⠷⠌⠣⠐⣧⠀⣭⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⣰⣿⠁⣸⠃⣠⠀⠒⢿⡋⣹⣿⣦⠸⠇⠐⠃⠀⠀⠀⠀⠐⠃⣴⣿⣏⢙⡿⠒⠀⣄⠸⣇⠈⣿⣆⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⣿⡟⢠⡟⢀⠙⠀⠱⣜⢧⣬⣥⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣬⣭⠾⣣⠎⠀⠋⡀⢻⡄⢻⣿⡄⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢸⣿⠁⣸⡇⢾⠘⢶⣄⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⣠⡶⠃⡷⢸⣇⠈⣿⡇⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢸⣿⡆⣿⣧⠈⢷⣄⢨⣥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣬⡅⣠⡾⠁⣼⣿⢸⣿⡇⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⣿⣇⠸⣿⣦⠈⠻⣧⠁⢫⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡝⠈⣼⠟⠁⣴⣿⠇⣸⣿⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠙⣿⡀⠙⠻⢇⣤⡀⠰⠏⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠹⠆⢀⣠⡸⠟⠋⢀⣿⠇⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢳⡘⡧⢻⣶⣌⠛⠿⣆⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⠿⠛⣡⣶⡟⢼⢃⡞⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⢠⡀⠙⢿⣿⣷⡜⠀⠀⠀⠀⠹⣶⣶⣤⣀⣀⣤⣶⣶⠏⠀⠀⠀⠀⢳⣾⣿⠿⠋⢀⡄⣿⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⡈⠻⣷⣦⣬⣽⣛⠀⢀⠀⠀⠀⠀⠉⠻⣿⣿⡟⠉⠀⠀⠀⠀⡀⠐⣛⣯⣥⣴⣾⠟⢁⣱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣤⣌⠉⠛⠛⣉⠐⠠⠀⠀⠀⠈⠀⠀⣹⣏⠀⠀⠁⠀⠀⠀⠄⠂⣉⠛⠛⠉⣡⣴⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠓⠖⠻⠾⣂⣂⣐⣂⠠⠄⠞⠛⠛⠓⠢⠄⢐⣂⠒⣀⠷⠟⠲⠚⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⣄⣀⣀⣀⣀⣀⡤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⠀⠁⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣉⠃⠀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠄⠀⠀⢀⣠⠆⡃⣠⣀⢰⠀⠀⢈⠴⠁⢁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠃⠀⢰⣚⣩⠅⠀⠀⠈⠀⠄⠐⠂⠐⠁⠀⠀⠐⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⠠⡤⢀⡉⠀⠒⠁⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠰⢀⠀⠀⠒⣢⠊⠁⠀⠈⠑⠠⠖⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠰⠀⠐⠀⠀⠀⠀⠀⠘⠃⡖⠠⢄⡀⢀⡀⢀⣄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢩⡀⠈⢯⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⢈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣃⠀⢦⣄⠀⠀⡈⠀⣄⠀⠀⠀⠀⠀⠀⠸⠂⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠙⠛⠷⣄⡀⠀⠀⠧⡄⠤⣽⡿⠂⢧⣀⠘⠀⠀⠀⠀⠰⠍⠀⠤⠖⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣀⣀⣐⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣟⣫⣛⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣽⣽⣽⣿⣿⣿⣿

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄
⡤⠰⢾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃
⠛⠀⠘⣰⣶⡅⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣤⡔⢤⣄⣀⡴⠃
⣥⠀⠞⠙⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠸⣦⣸⣿⣟⣿⠋
⠐⣆⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠢⣄⡀⣿⡿⡻⢛⡋⣠
⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠏⠤⢀⣾⡇⣸⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣶⣦⣀
⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡀⠀⢹⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⣡⠀⠡⠀⠂⠠⠶⣖⠈⠀⠀⠀⠿⠤⠂⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠇
⢀⠀⣿⠀⠘⠀⠀⠻⡍⢀⣷⣤⣤⠶⠲⣦⠀⠀⠀⠘⣿⣿⣿⠟⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠟⢩⡟⣿⠋⡦
⠘⠀⣿⠀⠀⠀⠀⠀⢷⣿⣽⢆⣿⣷⣶⣿⠀⠀⠀⠀⠘⣿⣿⣶⣿⣧⢾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⠏⣤⡿⡙⢱⡇
⣿⡀⣧⡄⢠⣶⣜⢃⡈⢿⣧⣈⣿⢿⣿⡏⠠⠄⠀⠀⠀⠈⠙⣿⣿⠿⠞⠛⠿⠿⠿⠽⠿⠾⠛⠋⠙⢿⣿⣿⣧⢿⣿⣿
⣿⢷⣿⡇⠿⠿⠛⠉⠁⠈⡟⢻⠉⠁⠼⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠈⠻⣯
⡉⢻⣿⣧⡀⢜⡀⠀⠀⠀⡅⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⠧⠀⠈⢆
⠛⠿⡻⠻⠛⠻⠿⠿⠢⢴⡧⢣⠄⢰⡀⠀⠀⢈⣰⣦⣞⡂⣿⢛⣿⣆⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠃⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⢀⣠⣤⣜⣱⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⠽⣿⢢⣤⣤⣆⣀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠃
⠀⢰⡆⠀⠀⡀⡠⠴⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⡟⣍⢻⢿⣦⡴⣀⢹⣻⣇⢀⡴⠂⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠋⠀⠉⠁⠙⠉⠋⠉⠙⠟⢷⣸⡇⠁⢈⣀⡉⠀⠀⠀⠉⠙⠛⠳⠶⢄⠀⡠⠇⠀⠀⠈⠐⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠧⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠅⠀⠀⠀⠀⠀⠈⠁
⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡄
⠀⠀⡄⠉
⠀⠀⠘⢂⣠⣴⡀
⠀⠀⠀⢈⠋⠉⠃
⠀⠀⡰⠟⢿⡶
⠀⣠⣷⣤⡴
⠀⢉⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣤⠔⠒⣶⣶⠶⡦⠤⢀
⠀⢸⣾⠟⠛⠄⡀⠀⠀⢀⡀⢤⣾⠋⠀⢿⣇⠀⢸⣿⠀⠀⡴⠶⠿⠿⢷⣄⡀
⠀⠀⠃⠀⢠⣾⠟⠛⣻⣟⠀⠘⢿⣦⠄⠀⠉⠁⠀⠉⢛⣦⣠⡶⠦⣤⣄⣉⡀⠓⠶⣄
⠀⠀⠀⠀⠙⠿⠄⠀⠙⠿⠷⠀⠁⠀⠀⠀⠀⠀⢀⣴⢯⡟⢁⣴⠟⣁⠀⠀⠀⠙⢢⣴⠟⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣱⠋⠀⡾⡵⠛⣁⣤⣶⠶⢶⣦⣄⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢠⡏⠀⣼⠛⢀⡞⠉⠀⢀⣀⣤⣤⣉⠻⣶⠾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⣧⣼⠏⢠⡆⠀⣠⠾⠛⠉⠉⠉⠛⠂⣥⣀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢒⣤⡟⢹⡄⣿⡇⠀⠘⣧⡞⠁⠀⣀⣠⣤⣤⣤⡀⠹⠏⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⠀⠛⢣⡾⠁⣿⠇⠀⡴⢛⢀⠴⠟⠉⠉⠀⠈⠉⠛⢦⣄⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⣇⢸⡇⢰⡇⠀⣾⠀⠟⠁⠀⢀⣤⣤⣤⣤⣤⣄⠀⠙⠉⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠲⢤⣀⢙⣀⣳⣶⠀⠀⠀⣀⣴⣿⡿⠛⠛⠛⠻⠿⣤⣤⣠⣤⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠷⣦⡼⠟⠀⣽⠁⠀⢠⣾⡿⠟⠁⠀⣀⣤⣤⣀⡀⠈⢿⠋⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠳⠶⠖⠓⣴⠇⢀⣴⠟⠁⠀⢠⡶⠟⠉⠉⠉⠙⠻⣦⣾⡴⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢈⠉⠉⡿⠀⡼⠃⠀⠀⣴⠟⠁⠀⢀⣤⣤⣦⣤⡘⠿⠃⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠐⠨⠃⠐⡇⠀⠁⠀⢀⡼⢁⡀⠠⠴⠛⢉⠤⢤⣀⣉⠳⢤⠶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢇⣀⣤⣜⣋⣤⠊⠁⠀⢀⣀⣠⠄⣠⣿⠭⠷⠶⠶⠶⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠇⠀⠀⠈⢋⠀⢀⣀⣤⠔⣴⡻⠉⠁⠜⠁⣠⡶⠖⢋⣉⡀⠉⠛⠁⠠⣤⡀⠀⠀⠀⠀⢠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠘⢁⣼⠛⠉⠁⢀⣤⣿⠇⠀⢀⣾⠏⠀⠀⡀⢠⡌⢻⣎⣻⠑⠶⠒⠞⠉⠀⠛⢤⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠃⢀⡜⣡⡾⢀⣠⡾⣏⢡⡆⠀⣼⡏⠀⣰⡆⢀⠸⣷⣰⠟⣱⡾⢀⣟⡵⠀⣹⠷⢶⡸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠛⠘⢀⡿⠀⠉⠀⣿⠉⠀⢂⠘⡹⢦⣿⡇⢠⡟⠁⢈⡶⠛⢫⡤⣹⣇⠘⠯⣷⡄⠙⣄⠈⣤⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢷⣤⣴⣦⠀⠀⣿⢠⠙⢷⣆⠈⢿⡃⢀⠙⠧⢈⠀⢀⡞⢠⡔⣠⠄⣡⠀⢠⡖⡉⢠⣀⣭⠀⣀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⢦⣤⠶⠀⢰⡀⢻⣌⠷⣤⣿⣷⡈⢧⠈⢷⡀⠀⠀⢸⠀⣼⢀⡏⢼⡠⠖⠾⠀⠁⠀⠻⠟⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢴⠆⠀⢈⠸⣦⣽⣷⣤⣈⡉⢳⡌⢷⣤⣿⡀⢀⣸⠀⢿⠸⣿⠘⣧⡀⠀⢀⡄⣀⠄⠠⠄⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣧⠀⠈⠓⢤⣌⣉⠻⡆⢻⡄⠉⠻⢧⡈⠻⣆⠘⢷⣙⠧⡤⠩⣄⠸⠃⢿⣂⡀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠉⠹⡄⢹⣀⡙⠫⣀⣉⡉⠛⠛⣳⣆⡉⠛⠛⠃⠉⣀⣠⣚⣉⠤⠄⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠⠀⢀⠠⠀⡇⠀⠀⠀⠀⠀⠛⠀⠀⠙⠃⣠⣥⠈⠉⠁⠀⢀⣤⣜⣽⣯⣿⠀⠀⠉⢁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠒⢀⡛⣨⡂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠑⢦⠈⠃⣠⡴⠖⢀⡙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢨⣇⡀⠁⠶⢛⡋⠉⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⡎⠑⢦⡀⠉⣉⠲⢲⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢄⠀⠉⠳⣌⠛⢋⢭⣉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⢉⠀⠛⠉⠁⣈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣬⠂⠀⠀⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠆⠀⠀⠘⣄⢈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢀⣆⢘⣧⠘⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠄⠠⠠⠤⠀⢀
⠀⢀⣰⣶⣟⠲⢶⢖⠳⣘⣫⣶⠿⠿⠞⠛⢓⢹⠄⠂⡈⣡⢰⣺⣦⣷⣠⡄⠒⠚⠚⠇⡴⡂⢄⣃⣀⡀⢀
⠀⣠⡼⢖⣀⣤⣯⣥⠴⠂⣿⠃⠀⣀⠀⣄⣾⢻⠀⣀⠝⠨⠧⢸⡽⣏⠉⠳⢄⣄⣤⢤⡀⣤⣴⣛⣃⢼⣌⡙⣤
⢀⠏⡀⠈⠁⢈⢇⣘⣆⢀⡼⡆⠒⠉⢣⣀⢯⡘⡆⠀⠠⠤⠀⠈⢃⡷⠲⠆⠀⠀⠐⠊⠏⠁⠀⠉⠹⡀⠀⢈⣛⠁
⠊⢿⡾⠠⣿⣾⣹⡽⣝⢧⣀⣈⣀⠀⣉⡠⠀⠘⣇⠀⠐⢠⣯⠴⣟⢲⣄⢀⣐⣆⡀⢀⠶⠂⠈⠛⠂⠀⠃⣀⠉
⠀⢀⠇⠀⠀⡞⡩⠙⣶⡾⠟⠛⠻⡛⠻⣟⡣⢾⣿⣭⣶⣿⠋⠛⠉⣠⣟⠦⢌⠿⣻⣿⣾⠛⡯⡀⠠⠂⠀⠀⢀
⠀⢨⠔⠊⡰⣠⠇⢡⣿⠷⣶⡶⠀⠹⢷⡟⠙⠷⢼⣮⢻⣻⣧⠄⠞⢻⣯⣿⣃⣼⠇⠀⠈⠛⣧⣼⡁⠀⠀⠀⢨⢰⡀
⠰⠖⠶⠂⠤⠀⠀⠈⣩⡗⠈⠀⢴⡄⠀⡓⢊⠒⠶⠶⣾⡽⡈⠋⣄⣀⡏⣩⣷⡋⠀⢀⣀⣀⢸⣿⣖⡆⢸⣄⠱⣣⠂
⠀⠰⠀⠀⢘⠄⠀⠀⠀⠱⢤⣀⠤⡄⣰⡀⠙⢂⠀⠀⢪⡄⠇⡠⡤⠀⣤⢸⡂⠛⠃⢀⠁⢉⠾⣟⣿⠇⠀⠈⣄⠉
⠀⠃⣈⠉⠩⠓⠒⢲⡞⢁⠘⢿⣟⣻⠷⠖⢶⣿⣦⣐⣿⣧⣤⣀⢀⡼⠗⠛⠗⠢⡄⠛⠋⠜⠃⣁⣀⡀⠀⣀⡄⢀
⠀⢶⠉⡚⡶⠞⠶⡖⡽⠎⠃⠼⢸⣵⠴⠚⠛⠛⠿⢏⡙⠛⡛⠛⣻⠆⠀⠀⠀⠀⠙⢶⣵⣧⣼⡿⣭⣙⢷⣄⣀⠆⣃
⠀⠈⢻⠉⠀⠀⠃⠞⠀⠀⠀⠀⢈⢻⣾⣷⠄⠺⣿⡆⣿⡇⠉⣉⣿⠆⠂⠰⠶⠈⠐⢀⣏⣽⠻⠋⣹⡛⠿⠻⡆⠀⣹
⠀⠀⢩⠁⠀⠀⠀⠀⣀⡀⡵⠖⣶⠞⣇⠀⢀⣀⠀⢀⡋⠀⠘⠛⠣⡄⠷⠀⠀⠀⠀⠊⠉⠈⡆⣀⣭⣩⠀⠜⠀⠙⠃
⠀⠀⢨⡇⠤⢖⠨⠱⢠⠀⠀⠀⠀⠀⣨⣁⠠⣠⠀⡈⠀⠀⠀⠀⣰⣬⠀⠂⢀⠀⠀⠀⠀⠀⣙⢏⣁⠤⠀⠰
⠀⠀⣚⠦⣿⡴⣴⠂⠟⠀⠸⠁⠀⠀⣸⣭⠓⠻⢺⣾⡃⢤⢠⢤⣼⣿⣲⢶⠃⠘⠿⠗⢀⣶⠳⠾⠲⣄⠀⠒⠿⢻
⠀⠀⠀⡞⢿⣠⣤⠠⠒⠓⡆⠈⠀⣜⢟⣁⡈⠚⠓⢋⣷⠻⠇⡆⠨⡿⢿⠀⠀⠀⠀⠀⠀⣹⠈⠁⠰⠟⠛⡖⣺⣿⢧
⠀⠀⠀⢀⠈⠎⠘⢲⣥⠀⢈⢶⣺⢶⠊⠛⡛⡁⠸⡈⢻⠀⠀⠓⠼⠀⢸⡏⣡⠶⠄⠤⣸⠛⠟⢀⡄⠀⠀⢰⠿⠛⠈
⠀⠀⠀⠉⢠⡔⠓⠂⣶⠒⡡⡶⠀⠛⠀⠀⢀⡁⠀⢉⢠⠀⠀⠚⠻⢂⡞⠼⢿⡷⢶⣟⡹⢠⡀⠀⠀⠊⡠⠀⠆⠄
⠀⠀⠀⠀⠠⠱⡤⠀⠄⠀⡄⠀⠉⣥⠀⡠⢬⣁⣀⡠⠈⠀⠀⠤⠀⠈⠊⠉⠸⠉⠓⠛⠀⠀⠘⠃⠄⠀⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡒⣦⢀⣀
⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠛⠛⠀⠪⣡⡦
⠀⠀⠴⠚⣹⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⣷⣩⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠷⠦⢤⠄⠈⠀⣦⣀⠈⠲⣌⣠⠖⠂⠀⢀⣀⣀⠀⠀⠤⠐⡀⠝⠶⠦
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠀⠆⠀⠢⠀⠀⠀⠀⠀⠀⢸⡿⣷⢖⣶⣷⣆⠀⠙⠉⢀⡀⢹⡅⠀⢀⠈⠀⠀⠈⠓⢀⡔⠁
⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⡅⡀⡾⢟⣿⠃⠀⠀⠀⠳⣄⡁⣆⠀⠀⠀⠀⠀⠀⠈⢣
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠓⠳⠏⠠⣄⠀⠀⣀⠀⠈⠈⣿⠛⠂⠀⠀⠀⠀⠡⠀⠀⡇
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠖⠀⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⠃
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⡠
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡠⢐⡶⢄⣀⠀⣀⡀⠀⢠⣄⣀⡤⠔⠋⣸⡎
⠀⠀⠺⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⣀⣀⢊⡸⠗⠁⠀⠀⠀⠡⠋⠀⣴⠟⡹⠁⠀⠀⣠⡡⠃
⠀⠀⠀⠻⣿⣿⡀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠿⠟⠻⠿⣿⣿⣇⠀⠀⠀⠀⢯⣌⡰⠁⠀⠀⠀⠀⠀⡀⠀⠔⠉⠉⠙⠃⢀⡤⠊⠋
⠀⠀⠀⠀⠙⢿⣇⢀⠙⢿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡛⡡⠊⠀⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠰⠿⠿⠗⠀⢙⣿⣿⣶⠆⠀⠀⠀⠀⠀⠀⠘⠻⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⣠⣤⣠⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣦⡄
⠀⠀⠀⠀⠀⠼⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⣀⠤⠤⠦⠤⠠⠤⠴⠶⠤⣤⠀⠀⠰⣦⡄⠀⡶⠶⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠛⢷⣤⠶⠶⠛⠋⣛⢶⣶⣆⡛⠶⠶⠶⠶⠦⠴⠇⠀⠀⣤⣶⡆⠀⠀⠀⣤⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠉⠉⠀⠀⢀⠀⢀⣴⡶⣻⣿⡷⣿⡿⠷⠽⢷⣶⣄⠀⢠⡄⠀⠐⠿⠋⠓⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣉⠐⠛⠉⣀⣤⣤⣤⣿⣷⣶⣤⣤⣈⠙⠃⢶⣴⣻⣧⣄⠁⣤⣀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡿⠋⠀⠠⠾⠿⠛⠛⠻⣿⡟⢛⣻⡟⠛⠛⠀⠀⠙⣿⡟⢿⣇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢰⣿⡇⠀⠀⠀⠠⢦⠾⢻⣷⣿⣿⣾⡟⠻⣶⣦⣄⠀⠀⢻⣿⡆⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⡀⠙⢋⣧⣀⡀⠞⠀⠂⢠⡏⣿⣿⣿⣿⣿⣦⠀⠀⢈⣤⣴⣼⣟⠁⣤⡘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣸⣇⠀⣸⡇⠙⠛⠃⠀⠀⢺⣿⣻⣿⣿⣽⣿⣿⣄⠀⠘⡙⠋⢈⣿⡄⣹⣿⠸⡇
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣹⠇⠀⠟⢹⠛⣟⠻⢶⡀⠹⢿⣿⣿⣿⣿⣿⣿⢏⣴⡿⣻⡟⣻⣿⡧⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣿⠀⠀⣿⠘⣷⣌⡛⠻⣿⣆⠐⠉⣿⣿⣿⣿⣿⣾⡿⠛⣫⣾⣿⣿⡇⠀⣿⠀⢴⡆
⠀⠀⠀⠀⠀⠀⠀⢿⡧⠀⢿⠀⠀⢻⣧⠾⣿⡿⠀⠹⠿⠀⡰⣿⣿⢿⣿⣿⣿⣧⣾⣿⣿⣿⣿⠃⠀⣿⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠘⠀⠀⠀⡼⠟⣻⠟⠀⡘⠀⢠⡆⠉⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⣰⣏⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣿⡿⠾⠃⠈⢠⠴⠞⠁⠀⢀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡝⢯⡿⠻⢿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⡀⠙⢷⡄⠀⠐⠂⠀⠀⠀⠃⠈⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣿⢳⣄⣴⠿⠋⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣠⣬⣄⡀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⢿⣤⣿⣷⣬⣿⣿⣿⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠟⠉⠙⠃⠀⠐⠢⠀⠈⠢⣤⣠⣤⣤⣾⣿⠏⣸⡿⢫⣾⣾⠟⠋⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⢀⡀⡀⠈⠻⣿⠿⡋⣀⣀⣭⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣤⡀⠀⣠⣴⣿⣶⣤⣤⣤⣶⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⡉⡉⢉⢹⡏⠉⢻⣿⣿⣇⣴⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣰⣮⣰⣿⣾⡿⠋⠀⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⢿⣿⣿⣿⣿⣿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠉⠙⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣶⣶⣦⡀
⠀⠀⠀⢀⠀⠀⠀⢠⣧⣴⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠁⠀⠘⢿⣿⣶⣿⣿⣿⣇⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣤⠤⠤⣄⣀⣀⣤⣴⡶⣶⣿⣿⠿⠓
⠀⠀⢀⠀⢀⠀⠁⢾⡿⠁⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣭⣧⣶⣶⣶⣯⣿⡿⠿⢿⣭⣄⣀⣀⡀
⠀⠀⠀⠀⠤⡤⣬⡞⠱⠂⢸⣶⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⠿⠛⠛⣻⣿⣿⣿⣿⣿⣯⡤⢶⣿⡿⠿⠛⠛⠁
⠀⠀⢀⠓⠂⢠⡅⡀⠰⠠⠘⣿⣿⠟⠁⠀⠻⠿⣿⣿⣟⣉⣥⣤⣶⣿⣿⡿⠿⢻⣿⣿⣿⠗⠁
⠀⠀⠠⣤⣀⣻⣌⡀⠀⠠⠀⠜⢧⡀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠛⠛⠁⣠⣵⣾⠿⢋⢀⣤⣤⠭⠤⠤⠤
⠀⠀⠀⠀⢉⣁⣀⣀⣀⣀⣀⣀⣀⡁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡾⠿⢏⡀⠐⠚⡚⣿⡿⣶⠄⣀⡀
⠀⠀⢩⢿⡟⣛⣿⢿⣿⣻⣿⣿⣿⣿⣼⣿⣶⣶⣶⣶⡶⣶⣶⠶⠶⠲⠒⠒⠻⣿⡿⠪⣷⣿⣶⣶⣼⣫⣗⠢
⠀⠈⠉⠈⠛⠛⠈⠙⠛⣻⣿⡛⡿⠿⣿⣟⣿⡟⣿⠛⡛⠹⠃⠐⠀⢀⣀⣾⣤⠈⡏⣩⣮⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠀⠄⠤⠊⠋⠁⠒⠡⠖⠍⠽⠙⠋⢉⠀⢀⡴⢀⣠⣴⣿⡿⠿⠿⢀⡾⠿⢿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠚⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢸⣺⠵⠛⠋⠉⠉⠁⠂⠀⠀⡀⣰⣁⣠⣶⢾⣿⠟⠛⠃
⠀⠀⠔⠀⠀⣀⠀⠀⠀⠀⢦⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣾⣼⠟⠻⠯⡀
⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠸⠀⠁⠈⠀⠀⠀⠀⠡⠀⠀⠀⠀⢠⠃⠀⠄
⠀⠀⠀⢠⣄⣀⠀⢪⣩⣆⢠⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⡇⠰⠀⠀⠀⠐⠀⡔⠀⠁⠀⡁⠀⠆
⠀⣀⠐⢦⡀⠙⣷⣘⢳⠏⢰⢀⠏⠰⠀⠀⠀⠀⠀⡔⠡⡐⢤⠤⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢣⠀⠀⠈
⠀⠸⣆⠀⠙⠄⠈⣿⢼⠇⠰⣎⡴⠓⠄⢀⢔⣤⡞⠀⢀⠇⠈⡆⢠⠔⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸
⠀⠀⠈⠑⢄⢸⣆⢻⣶⡆⠐⣽⠁⠀⠀⢈⠘⣿⡇⠀⢨⡆⠀⢿⢀⡟⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠈⢦⠻⡈⣻⢃⢣⡏⠀⠀⠀⠀⠄⠻⣷⡄⠸⣆⣀⡞⣼⢁⠇⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⡄⠀⣄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠣⣷⣿⣾⠋⠀⠀⠀⠀⠀⠀⠣⠼⡿⠿⠋⠜⡿⠑⠁⠀⠀⠀⠀⠀⠀⠈⠯⣤⠀⢳⠆⠀⢰⡟⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣸⠘⠀⠀⠀⠀⠀⠀⡴⠒⠂⣴⠶⢄⡀⢳⣼⣇⣼⣿⠷⠚⠃⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠑⣄⡀⠈⠷⣇⡙⢶⣍⢯⠉⣤⣤⡶⠿⢛⡋⡳
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⢀⠀⠹⢦⣦⡭⣷⣶⠽⠷⠦⣤⠤⡤⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣉⣀⣀⣑⣀⣐⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⣟⡛⢻⡟⣻⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠷
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡟⠛⠀⠀⢸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣟⡂⠀⣤
⠀⠀⠀⠀⢀⣤⣾⡿⠿⣿⣿⢦⣄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣯⡀
⠀⠀⠀⢠⣾⣿⠏⠀⠀⠀⡹⡆⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⢈⣴⣾⣿⣿⣿⡿⠛⢹⣿⣿⣆
⠀⠀⢠⣿⣿⣿⡆⠀⠀⠀⡆⢹⠀⣇⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⣾⣤⡀⠈⠉⠉⠀⠘⣿⣽⣿⣷⣴⣾⣿⣿⣿⣄
⠀⢠⣿⣿⣿⣿⣧⣤⣼⣿⣇⣘⣿⣧⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠟⠉⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣟⡀⣽⣹⡿⢷⣿⣅⡀⠀⠀⠀⠀⢈⠟⢦⣄⡐⢀⠜⠁⠐⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠈⣿⣿⣿⣿⣿⠟⠛⠻⠿⣿⡟⣾⣿⣿⣶⣄⣠⣔⣡⢾⣷⣾⢡⠋⠀⠀⠠⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⣽⡷⢿⣿⣿⣿⠟⢁⣾⡁⠈⣿⡟⠀⠀⠀⠀⣠⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗
⠀⠀⠀⢰⣿⣿⣷⡀⠀⠠⣶⣿⣿⣿⣿⣿⢓⣤⣿⡿⠟⢖⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⣠⣿⣧⠶⠃⠀⠓⠀⣈⡽⠋⠛⢛⣽⣿⠿⢋⠂⠀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⣼⣯⣶⠧⠤⠚⠁⣈⣽⡟⠁⠀⣲⢿⣿⠡⣈⠤⡊⠉⠉⠉⠛⢆⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣧⣶⣷⣾⣿⣿⡟⠁⠀⠀⠲⢟⣁⣈⣶⠀⢴⡤⠶⠷⠠⠸⣧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠰⣿⣿⣿⣿⣿⣿⣿⢟⣴⣿⣷⠿⡿⠛⠉⣻⠁⣀⣸⠀⢀⣶⣤⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⣿⠶⠾⢿⠿⠛⡟⣟⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣴⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠻⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉
⠀⠙⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠈⠃⠈⠙⠛⠿⠿⠿⠿⠛⠁⠀⠀⠈⠉⠉⠉⠙⠛⠛⠂
⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⠿⠟⠛⠉⠀⠀⠈⠁

⠀⠀⠀⠀⠀⢀⡴⠚⠛⠛⠛⠛⡲⢦⣀⣀⣀⣉⣛⣛⡹⠷⠶⢶⣶⣤⡀⠀⣀⣤⠶⠶⠶⣦⣤⡀
⠀⠀⠀⠀⠀⠘⣇⠠⣄⡀⠀⢠⣿⢔⣛⠉⣉⣤⠶⠖⠛⠲⢶⠢⣌⠙⠛⢿⠁⠀⢀⣀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠘⢦⣹⣷⡖⠁⠀⡩⠕⢛⣡⣤⣤⣶⠏⠶⠤⢤⣌⡻⡗⠢⠁⢠⣤⣿⣇⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡩⠂⠀⣪⡾⠁⠋⢩⣥⠤⡀⢰⣄⡀⠀⠈⣉⠀⠈⢷⣄⠙⠛⠋⡎
⠀⠀⠀⠀⠀⠀⠀⡠⣊⣠⢄⣴⣿⠃⠠⠟⠛⠀⣾⡵⠲⣿⣯⠀⢿⡙⣀⠀⢸⡿⡎⢦⡀⠳⢄
⠀⠀⠀⠀⠀⣠⠀⣼⡟⢠⡞⠀⣿⠘⠛⠳⠄⣾⠉⠃⠀⢹⠎⠓⢸⠟⠉⠙⣸⣧⠀⡄⢹⡄⠀⠅
⠀⠀⠀⠀⣴⠁⢰⣿⡧⣾⡇⠀⢷⣌⢳⣿⣣⡈⠄⠀⠀⠀⠘⢂⣴⣛⡼⡡⠔⣉⠇⣿⡄⣧⢢⡈
⠀⠀⠀⠀⠇⠀⣸⣿⠃⢹⡇⢸⣦⡄⠀⠀⡿⠀⠀⠀⠀⠀⠀⡞⢻⢀⣿⡶⠾⠋⠀⣿⠇⢻⠈⣷⢰⡀
⠀⠀⠀⠀⠀⠀⢿⣿⠀⠈⢧⡀⠈⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠘⠍⢠⣀⣀⣠⣿⠀⣸⠀⣿⡄⢷
⠀⠀⠀⠀⡆⢠⡈⢿⣧⡠⢾⣿⠟⣡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠹⣦⣤⣿⣿⠁⢠⣿⢠⣿⠇⣸
⠀⠀⠀⠀⣇⢸⡇⠘⣿⣿⡆⢀⣀⠅⣀⡀⢠⡀⠀⠀⠀⠀⠀⡀⠀⣴⣤⡈⢹⣟⣣⠾⠟⠁⣾⣿⠀⠁
⠀⠀⠀⠀⠹⠌⣿⣦⢹⡿⣛⣿⣿⡉⡷⢤⠀⠻⣗⠠⠤⢒⡿⠃⢀⣠⠀⠀⣾⣏⠙⠛⠛⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠘⣟⠀⠈⠁⠈⢉⠤⠉⠓⠲⠀⠀⠳⡴⠋⠀⠄⣀⣴⣬⣾⡟⠃⠀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠙⢷⣦⣤⡤⠀⠚⠓⠀⠀⢦⣶⡶⠟⠛⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⣀⡀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⣿⣇⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⡀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠈⠀⠀⢣⠀⠀⢈⣥⣿⣥⠄
⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⡸⣿⣿⣿⢀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢤⣤⠔⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣻⣿⡟⠀⠀⠀⠈⠛⣣⡾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠉
⠀⠀⠀⠀⡂⠀⢘⠃⠀⠀⠀⠀⠀⣨⣿⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡤⠞⠛⠒⡤⠀⠀⢿⡄
⠀⠀⠀⠐⠀⠀⣾⡺⣆⠀⠀⠀⡀⠘⢿⠆⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢠⠎⠀⢀⡼⢸⣇⡀⠀⠃
⠀⠀⠀⠀⠀⢀⠏⢀⣄⣤⣠⣤⣿⣷⣦⢀⠀⢰⡇⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠂⣠⠎⠀⠀⠂⠀⡸⢿⣷⡿⠂
⠀⠀⠀⠀⠀⠀⠀⢨⡷⣿⣿⣿⠿⠿⢿⣻⣷⣿⠃⠀⠀⠇⢠⠀⠀⡼⠋⠀⠀⠀⠀⠀⢸⣿⣤⠃⢀⣄⢄⠀⡈⠀⠘⣯⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡅⢨⣼⡖⠶⢸⣿⣽⣿⣿⠀⠀⠀⠀⠆⠀⠀⠡⠀⠀⠀⠀⠀⠀⣈⠙⠇⣠⢿⠷⢶⡖⢁⠀⢜⣿⣶⠃
⠀⠀⠀⠀⠀⠀⠀⢁⣿⢸⣿⢹⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡀⠀⢸⠟⢡⠄⡠⠅⠀⠀⠀⠛⠃⢾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢠⡃⢸⣿⠸⣿⢯⡅⠉⠙⠟⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⢸⡟⠀⠂⠀⠀⠀⠂⠁⣾⣿⡇
⠀⠀⠀⠀⠀⠀⢠⡿⠁⣼⣿⢠⠏⢤⢃⡷⢾⡂⠀⠐⠦⣠⠤⠀⠸⠁⢀⡴⠀⠀⠀⠈⠀⣼⠀⠀⠀⠀⠀⠀⢸⡡⠋⢺
⠀⠀⠀⠀⠀⠒⠝⠁⣀⠘⢿⠷⣴⣤⢠⠿⠎⢷⠀⠀⠀⢈⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⣿⠉⠙⠒⠀⠀⠀⣾⡇⠆⠈
⠀⠀⠀⠀⠀⠀⢰⣾⡿⣷⡈⠀⡞⠛⠛⠂⡀⡈⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠀⠀⠀⠉⣿⠞
⠀⠀⠀⠀⠀⠀⠀⣯⣿⠈⠹⣠⣿⡿⡏⠀⠁⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣀⣿⠹⣦⢲⢿⡇⠁⠁⢀⡀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢿⠀⠀⡀⠀⠀⠀⠀⢸⠇⠘
⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⢰⡆⠻⠂⠚⠚⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢼⠶⣯⡵⠀⢀⣀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡄⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡠⠒⣶⣲⣟⠇⠀⠀⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⢇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⣿⠀⠀⠀⢸⡟⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣿⣿⠀⠀⠀⠈⣇⣤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣾⣿⠀⠀⠀⢀⣿⡷⢿⡄
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⡘⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠙⣷⣤⣿⠇⠀⠀⠘⢷⣀⣾⠛⣦⡀
⠀⠀⠀⠸⠁⠀⠀⠀⠐⠂⠈⠀⠀⠈⠉⠒⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠀⠀⣰⣲⡴⢦⣀⡀⠀⠀⠀⢀⡤⠖⠛⠛⠋⠉⠛⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠾⠥⣿⣀⠀⠀⠀⠀⣗⣻⣶⠛⣣⢛⡵⡄⣰⣏⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸⡄⠀⠉⠳⡄⠀⠀⠙⠶⣿⡀⠀⢉⡺⢷⡟⠸⣾⡇⢦⡀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⡆⢸⡇⠀⠀⠀⢹⣀⠀⣠⠾⢅⠉⣷⢅⡀⢸⣁⡀⠈⠁⠀⢹⣠⠇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⡇⠈⠀⠐⠞⠀⠀⣸⡶⠃⠀⢀⡽⠁⠀⠙⢺⠸⠀⠀⠀⠀⠙⢿⡴⠲⡄⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⡴⠾⠇⠀⠀⠀⠀⡴⠋⢨⠇⠀⣠⠞⠀⣠⣠⣤⡙⣄⣀⡀⠀⠀⠀⠘⠀⣠⠃⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠣⣄⡀⠀⠀⠀⠀⠀⣠⠎⣠⣾⠷⣶⢮⡇⠀⠀⢱⠙⢆⡉⠀⠀⢀⣀⣤⠽⣴⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠶⠲⣯⣤⣤⣤⣄⣤⣞⣥⣞⣁⡇⠀⠀⢨⡏⠙⠛⠛⠛⠚⠛⠛⠋⠉⠀⠀⠀⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠓⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣼⣇⣀⣀⣀⣀⣀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢀⢤⡤⠤⠤⠶⠖⠒⠛⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⣿⠉⠉⠙⠂⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠹⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠳⡄⠀⠀⠀⠀⠀⠀⢀⡴⠛
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠒⠋⠁⠀⠀⠀⠹⡄⢀⣀⣠⠴⠚⠉⠀⢰
⠀⠀⠀⠀⠀⠀⠸⣦⠤⠤⣴⠚⠋⠙⠒⠒⠒⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⣀⣀⡤⠴⠒⡻⠋⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢰⠋⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡟⢦⡀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⠀⠀⠀⣰⠃⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⢀⠼⠁⠀⠀⢠⡇⠀⠙⠦⡀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⡆⠀⠀⠀⡿⠀⠀⠀⡇⠀⠀⠀⢰⠋
⠀⠀⠀⠀⣠⠖⠋⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸⡄⠀⠀⠘⡇⠀⠀⠀⠀⠀⢿⢞⠯⣝⢧⡀⠀⠀⡇⠀⠀⠀⢳⠀⠀⠀⠈⢧
⠀⢀⣤⡞⠁⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣧⠀⠀⠀⠀⠀⠈⠫⣗⣤⡈⠉⠉⡟⠁⠀⠀⠀⠘⡇⠀⠀⠀⠈⢧
⣴⡁⠀⢻⣦⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣀⣴⠒⢦⠀⠀⠀⠀⠉⠲⢵⣴⠃⠀⠀⠀⠀⠀⢻⠀⠀⢀⣀⠼⣇
⠙⣷⡄⢸⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣠⣾⡥⠞⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⢉⡽⠁⠀⣨⣧
⠀⠘⠿⣮⣿⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⢀⣠⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣊⣷⣚⣡⠴⣒⡭⠖⠃
⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠛⠛⠒⠉⠁

⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠲⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⢀⢏⣤⣘⡿⠓⠶⣦⡀⠀⠀⠀⣸⢁⣤⡘⠏⠉⢳⡆⠀⠀⠀⢀⣴⠏⢀⢀⣽⣦⣄
⠀⠀⠀⠀⠀⣾⣾⡷⠿⠀⠈⣠⣿⣧⠀⠀⠀⣿⣨⣍⣀⣦⣡⡾⣷⠀⠀⠠⡏⢁⣴⠞⠛⠁⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢻⣿⣿⣿⡇⠀⠀⠈⠉⠀⠉⠻⣿⣷⢿⣷⠀⠀⠛⠛⠁⣠⢤⣄⠀⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢹⣿⠏⠀⠀⠀⠀⠀⠀⠀⣾⠃⢸⡿⠀⠀⢠⣿⠀⠉⠚⢿⣿⡏⢹⡇
⠀⠀⠀⠀⠀⣴⠀⠀⠀⣰⠟⣱⡿⠋⠀⠀⠀⣰⡆⠀⠀⢰⠏⢠⡿⠁⠀⠀⢿⡇⠀⠀⠀⠀⡟⠀⢸⡇
⠀⠀⠀⠀⢸⢿⣄⠀⠔⣡⡾⠋⠀⠀⠀⠀⠀⢿⡄⠀⠀⠈⣠⡟⠀⠀⠀⠀⡎⢷⡀⠀⠀⡠⠇⢠⡿⠁
⠀⠀⠀⠀⠘⠳⠶⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠳⢬⣤⣤⠾⠋⠀⠀⠀⠀⠀⠘⢤⣉⣁⣀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⢀⡤⠶⣦⡀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣈⣉⣉⣁
⠀⠀⠀⠀⣴⡏⠙⣦⡴⠿⢿⣶⣦⡀⠀⣰⠏⠉⡻⠿⠿⡏⠉⡙⣷⡄⠀⢀⣾⠋⢁⣄⠈⠛⠿⣦⡀
⠀⠀⠀⠀⢹⣿⢺⣿⣿⠦⣾⠟⢿⡇⠀⢿⡀⠀⢰⣶⣶⡌⠲⢶⣿⣿⠀⢸⠁⢸⡟⠋⠛⠛⠶⠈⣷⡀
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⡼⠃⣸⣿⡀⠀⠹⣦⣼⣿⣿⣷⡴⣀⠈⣿⡇⠘⣗⠻⣿⣴⠃⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠈⠻⠿⢹⣿⣡⣾⠁⢹⡇⠀⠀⠀⠻⣿⣿⣿⣟⢉⣴⣿⡇⠀⠙⠺⠋⡽⢿⠋⢠⣀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠀⣾⠇⠀⠀⠀⠀⠀⢸⣿⠟⢿⣿⣿⠁⠀⣼⠃⠸⡇⣤⣴⣿⠏⢰⡿
⠀⠀⠀⠀⣴⠃⠀⠀⠀⢘⣿⡄⢰⡟⠀⠀⢠⡴⠒⠀⠀⡏⠀⣾⣿⠏⠀⢸⣇⠀⠀⠑⡀⢹⡏⠀⣼⠇
⠀⠀⠀⠀⠸⡄⠰⣄⠀⣼⠟⣰⡟⠁⠀⠀⣿⡁⣦⢀⣼⠃⣴⣿⠏⠀⠀⠸⡉⢲⣀⡀⢀⡼⠃⢰⡟
⠀⠀⠀⠆⠀⢄⣀⣿⣊⣵⠾⠋⠀⠀⠰⠂⢮⣿⣿⣿⣧⣾⠟⠁⠀⠀⠀⠄⠱⣘⠛⠛⠋⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⣴⠚⢳⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣎⢉⡷⣄⡀⠀⠀⠀⠀⠀⠀⡤⠶⢶⣦⣄
⠀⠀⠀⠀⣠⡾⠁⣠⣾⣿⣷⣤⡀⠀⠀⠀⢠⡴⣿⣿⣷⣤⠞⠻⣆⠀⠀⠀⠀⠀⣀⡀⠀⢹⣿⡇
⠀⠀⠀⣾⠃⣤⣄⠉⢸⡏⢁⡄⠹⣦⡀⠀⣿⡹⣿⡟⣿⠄⢠⣶⣿⡄⠀⠀⠀⢾⣭⣿⣦⡀⠻⡏
⠀⠀⠀⢿⡸⣿⣿⠀⣸⣧⣾⣁⠀⣿⣧⠀⠘⢷⣬⡶⢿⣄⣼⢻⣿⡇⠀⠀⠀⣸⣿⣿⣾⣿⣾⡇
⠀⠀⠀⠀⠹⣄⣰⡾⠋⠉⠉⢛⣷⣿⣿⡄⠀⠘⢧⢠⡿⠋⢁⡞⠙⣷⡀⠀⢶⡍⣠⡾⠋⠁⢻⣧
⠀⠀⠀⠀⠀⠙⠋⢀⣠⡴⠚⣉⢽⣿⣿⡇⠀⠀⠀⠛⣁⠴⠋⣠⠀⢹⣧⠀⣰⠟⣾⣇⣸⣷⣼⣿⣆
⠀⠀⠀⠀⢀⡴⠂⣿⠀⣀⣀⣤⡆⢀⠃⣤⠀⠀⠒⢳⡿⢶⣄⠙⠀⠀⣿⡆⠀⠀⣿⠙⠿⣿⣿⣿⣿⡀
⠀⠀⠀⢠⠏⠀⠀⣷⠘⠋⢻⣿⠃⡌⢠⣿⠀⢸⣤⣿⠀⠀⠙⢷⣤⣼⣿⣇⠀⠀⣿⡀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⢼⠀⢀⡄⢻⡀⠀⣸⣿⢀⠆⢸⡟⠀⠚⣿⣿⡄⠀⠀⢠⡀⣺⣿⡟⠀⠀⠹⣧⡀⣿⣿⣿⣿⡇
⠀⠀⠀⡜⣇⠘⣦⣌⡉⢿⣿⢏⡌⣡⡿⠃⠀⠀⡏⠙⠁⣰⡇⠸⣇⣾⣿⠧⢄⠸⣷⣹⡟⡛⣿⣿⣿⠇
⠀⠀⢤⠘⣎⡀⠀⡴⠏⣼⣿⣿⣿⠟⠁⠀⠠⡄⠁⣤⣾⣿⣿⣾⣿⡿⠋⠀⢈⠁⠈⣋⣼⣿⣿⣿⡟
⠀⠀⠀⠀⠈⠙⠲⠶⠾⠟⠛⠋⠁⠀⠀⠀⠀⠀⢤⣾⡿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠐⠐⠸⠟⠋

⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣶⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢄⠀⠀⢀⢀⣠⣆⣀⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠁⡚⠋⢽⣶⣳⠀⡍⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡐⣨⠀⠄⠀⠦⠈⠘⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢸⢰⠑⠶⠻⣄⣧⡄⢸⣧⠟⡷⠘⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⠁⠆⠸⠀⠀⠄⠁⣿⡿⠀⠀⠩⣿⠁⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⠀⠀⠀⡀⠖⠂⠘⠉⠇⠀⡀⢀⡷⡆⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡏⢐⡀⠐⡄⠀⠛⣤⠉⡀⠀⠈⠻⣬⠊⠀⠰⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠠⡕⠇⠈⠁⡀⢳⣆⠀⠀⠀⠈⢠⠀⠐⠛⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣁⠰⠺⠀⡗⡆⠀⠀⠑⡀⠙⢿⣄⣄⠀⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠈⠀⠉⠀⠆⡄⠁⠇⠀⠘⢧⡈⠢⡀⠙⢎⡦⣀⠁⣠⠄⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠢⢀⠀⠀⢰⠀⢱⢰⠀⠸⡆⠀⠹⣄⠈⠀⠀⠙⢢⡽⠟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡄⣦⠀⠃⠀⠀⣆⢰⣾⡇⠄⠰⡀⠀⠈⠻⣄⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠘⣧⢻⣆⠂⠹⡀⠙⢮⣿⢁⠀⠀⠙⠢⡀⡴⠉⠀⠀⠀⢠⠔⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠛⠳⡄⠸⡆⢇⠰⡀⠣⢃⠈⢧⡈⢄⠀⠀⠀⠈⠀⠀⠀⠀⣠⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠉⡀⠀⢻⡄⠀⢸⡆⠱⡀⠈⠣⡀⠁⠀⠀⠀⠀⠆⠀⠀⠀⠘⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⡂⠈⠒⢌⠑⠌⠂⣳⠀⢧⠀⠐⣥⠀⠀⠀⠀⠀⡀⠀⠀⡴⢀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠤⠽⠒⢎⡳⠭⠀⢠⣈⣆⠘⣆⡀⠀⠁⠀⢦⡄⠀⠁⡀⢸⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⣊⡑⠶⠦⢍⠳⠌⡖⠈⠿⣤⣀⠱⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⣀⣤⠹⠟⠲⠤⢆⠀⠀⠀⠉⠻⣄⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢀⣠⣤⡤⣤⡶⢤⣤⣤⠶⡏⢵⢉⠔⣩⡶⠀⠒⠒⣾⠀⠀⣸⢦⣀⡈⠓⠂⠀⠰⠄⠀⠀⢠⠀⢰⡀
⠀⠘⠄⠰⠏⠁⢯⠀⢇⠀⠳⠘⣏⢸⣯⠄⠀⠀⠉⠁⠀⠀⠁⠀⣿⢁⣪⠍⠉⡄⠀⠀⠀⠀⠀⠈⠣⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠔⠀⠤⠶⠀⢀⠀⡀⠀⠁⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣔⣂⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣣⣾⣀⣴⡅
⠀⠀⠀⠀⠀⠀⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣠⢀⠆
⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣯⡻⣿⣿⣿⣿⣿⡶⠟⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⢟⣽⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⡎⡻⣿⣿⣿⣶⣶⠶⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⢿⣿⣿⣿⠿⣿⣿⣷⢸⣿⣿⣿⣷⡝⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⣿⣿⠏⠀⣸⣿⡿⣼⣿⣿⣿⣛⣋⣈⢻⡿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⡷⢠⣿⣿⠿⣛⣿⣿⣿⣿⣿⣿⣧⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⢀⣤⣤⢄⣀⣈⠉⠁⣰⣾⡿⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣀⣄⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢷⣄
⠀⠀⢀⣠⣴⣾⣿⡟⢫⣍⣙⣿⢿⣿⣿⣷⡼⠛⣩⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣟⣿⣍⠛⢻⣿⢿⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⢠⣾⣿⡟⠉⠀⣼⣿⣿⣿⠿⢿⣷⣾⣭⣭⣥⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣮⢻⡆⠊⠙⠀⠀⡿⠸⢹⣿⣿⡿⣿⣿⢻⣿⣿⣿
⢻⣿⣯⠁⣠⣾⣿⠋⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣷⠀⠀⠀⠜⠁⠤⠟⣿⣿⡇⣿⡏⣼⣿⣿⣿
⡞⢡⡟⢠⡛⢻⣿⠆⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠋⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⢹⡿⣿⢠⡿⢹⡏⠁
⠻⠞⠀⠀⢹⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠩⣿⣿⣿⣎⠻⡼⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠃⠑⠝⠦⠓⠈⠷⠄
⠀⠀⠀⠀⢸⡋⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣦⡙⢿⣿⣿⣿⣿⣿⣶⡶⢦
⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣷⣯⣿⣿⠿⢿⣿⣿⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣧⠀⠈⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣀⠈⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡷⡏⠟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⡗⣴⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⣿⡏⢸⠹⠿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠒⠀⠢⣄⠀⠀⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡉⠁⠀⠀⠀⠀⢀⣈⠁⠢⠄
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠤⠖⠑⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⣄⣀⡁⠀⠁⢀⣀⠀⠘⠀⠈⠶
⠀⠀⠀⠀⠀⢀⠀⠈⠈⠠⠐⢦⣨⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡘⣆⣤⠋⡄⠐⠀⠀⠀⢌
⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠐⠀⠀⠀⠐⠀⡀⠚⠃
⠀⠀⠈⢀⠀⠀⠀⠀⠠⠀⠀⢠⠰⠈⠀⡄⠀⠀⠀⠀⠀⠄⢀⠀⢄⠠⢰⡀⠀⠀⢀⠱⠀⠀⠀⡀⣸⠠⠤⢆⠈
⠀⠀⠀⠸⠀⠀⠀⠈⠂⠄⠀⣐⠠⠀⠟⣡⡥⠤⠂⠨⠒⠚⠀⠀⠒⠒⠀⠘⠆⠲⢀⠛⠳⠃⠒⠊⡁⠂⠐⠀⡇
⠀⠀⠀⠁⠐⠄⡠⠬⠃⠐⠊⡡⠀⠘⠋⠉⠉⠇⠀⠀⠂⠀⠁⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠐⠀⢀⣀⣀⠀⠀⣀⣀⡤⠤⠞⠀⠀⠀⠀⢢⠶⢀⣀⠾⠀⠀⠒⠀⠀⠈⠋⠀⢄
⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠁⠈⠁⡿⠘⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠄⠀⠢⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡄
⠀⠀⠀⠀⠀⣇⠈⠈⠉⠀⠀⢲⠖⠚⠳⢠⢄⠀⠀⢀⠀⢠⡨⢦⠀⠀⠀⠀⠀⣰⠀⠉⠑⠀⠐⠆⡜⠉⠉⠁
⠀⠀⠀⠀⢀⡈⠕⠀⠀⠀⠀⠈⠀⠀⠣⢇⠈⠸⠁⠨⠨⠀⠀⠀⠉⠢⠤⢔⠝⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠶⠉⡀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠟⠀⢀⠠⠟⠢⠄⣀⣀⠀⠀⡇
⠀⠀⠀⠀⠀⢑⠄⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⢊⠄⠘⠀⠀⠖⠀⢤⠎⠀⠉⠉⠁
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⣴⣆⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠖⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⢠⣶⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣀⣴⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⣫⡖⣦⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢟⠵⣯⣼⣿⣿⢸⣧⡴⢞⠛⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡔⢻⣶⣿⣿⡿⣟⠈⢷⠄⠙⠃⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢀⣼⢋⣴⣉⣿⣿⠿⠋⣵⠄⠉⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣴⠟⣵⣧⣼⡿⢋⡅⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣿⠀⠀⠀⠀⢀⡾⢫⣾⣿⠟⠉⠶⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⡇⠀⠀⠀⣠⡟⣱⣿⡿⣁⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⠀⠀⣰⡟⣼⡿⢫⡄⠉⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⢸⣟⢱⡹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣧⠀⢰⡟⣼⠟⣥⡌⠀⠀⠀⠀⠀⣠⣾⡿⠿⣿⣿⣿⠿⣿⣿⣶⣄⠀⠀⣿⣿⣋⣣⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡻⣤⣿⢱⠏⣦⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⢸⣿⣿⠀⠈⢻⣿⣿⣦⣼⣿⣿⣏⣹⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⡴⠛⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣿⡿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⣹⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣷⣦⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠛⡟⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⢈⣿⣶⡄⠈⡳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣟⢛⡿⣱⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠉⣷⣦⣤⣟⢷⣭⡻⢶⣦⣤⣤⣀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡋⣻⢟⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠉⢻⣿⣿⣷⣬⡛⢶⣭⣛⠿⣍⣽⣿⠛⣿⠟⣿⠟⣿⣏⣹⣧⠼⣛⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣆⠈⠙⠻⠶⣮⣭⣽⣛⣓⣛⣛⣫⣭⣭⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠄⣀⠀⠀⣀
⠀⠀⠀⢀⠠⠲⠀⠒⠑⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠁⠀⠀⣀⡀⠑⢾⡅⡀
⠀⠀⣊⠀⠀⠔⠒⠈⠀⠈⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠐⠀⠀⠀⠀⠀⠀⠁⡀
⠠⡌⠀⠀⠀⡅⠀⠋⠀⢁⠠⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠄⠀⠀⠀⠀⠀⠀⡀⠀⡃⠀⠀⠀⢀
⠘⡠⠀⠀⠀⢀⠀⠀⢀⡀⠊⠓⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠒⣛⣯⠆⢈⠇⠀⠣⠀⠀⠠⠒
⠀⠈⡍⠀⠘⣎⠁⢟⢻⣻⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⡊⠁
⠀⠀⠀⠀⠉⠈⠐⡄⠉⠙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⣦⠤⢤⡊⠔⠀⠀⠀⠀⠀⢀⠠⢊⠄⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠘⠗⠲⠒⠁⡁⠂⠤⢀⠀⠀⠀⠀⢆⣀⠑⠋⠀⢀⡀⠈⡏⠀⠀⣀⢀⡀⠅⠂⠁⡴⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠀⢹⠎⠰⠐⠢⠘⠦⣀⣍⣩⡶⠓⢻⠀⠹⠀⣀⢠⠐⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠒⠤⣀⡀⠀⠀⢸⡀⠐⢨⠄⠠⠆⠀⠀⠀⠀⡖⠃⠐⠋⠁⢀⠂⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⡄⠉⠉⠉⠀⠉⠁⠀⠘⣄⠀⠀⠀⣠⠃⠀⠀⠀⢀⠌⠁⠀⠐⠚⠋⢩
⠀⠀⠀⠀⠀⠀⠀⠈⠰⡒⠒⠒⠈⠡⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⡆⠀⡱⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡌⠀⠀⠢⠑⡄⠀⠀⠀⠀⠀⠈⠛⠊⠈⠉⠁⠀⠀⠀⠀⠀⢸⠓⠒⠒⡖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡄⠀⠑⡘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠇⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⢪⣦⢀⡐⢤⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣴⢽⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣠⠖⠋⠀⠀⠈⢦⡇⠀⠀⠀⠀⠀⠀⠠⡌⠀⠈⠋⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠶⠞⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣤⡴⡴⡰⠠⠀⠀⠆⡄⡆⣰⢢⢤⢄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠖⠉⠑⢀⡀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⣇⠘⠒⠢⢄
⠀⠀⢀⠂⣀⡄⠀⠒⡛⠛⠒⠟⠘⠷⣼⣶⣦⣤⣤⠾⠏⠀⡿⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠠⠒⣠⢇
⠀⠀⠿⣿⡭⠛⠛⠛⢋⡓⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠇⢸⠇⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢐⠀⠀⠇
⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⠟⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡘⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣈⢠⠀⢀⠀⡀⠀⢀⠀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡱⣄⡤⣀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⡧⢶⣐⣄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠃⠙⢏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⢠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠁⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠄⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⢈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠰⠿⠿⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠀⠀⢠⣼⣿⣁

⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠰⢒⢤⠔⠴⠦⡴⠂⠉⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠄⠄
⢳⠄⠀⠘⠀⠐⠃⢰⠋⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠰⡞⠻⡖⠁⣠⠐⠀⠀⠀⢀⡀
⠈⠒⠀⢤⣤⣠⣄⠠⠆⠂⣀⣎⠉⠓⠦⢀⠀⠀⢠⣷⡀⠀⠑⡀⠀⠁⠀⠀⠀⠀⢱⠒⠒⠒⠒⠤⠤⣀
⠀⠀⠀⠀⠩⣙⣍⠷⣀⠀⠀⠈⠢⣄⣀⠀⠙⠢⣼⢉⠿⠆⠀⠨⢠⡀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢉⠛⠿⠀⠈⠉⠉⠸⡄⠀⡉⠂⠀⡬⠻⠀⠀⠤⣌⣢⣌⠛⠷⡆⠀⠘⢳⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠃⠑⢤⣤⡾⠃⡸⠉⠀⠻⠒⢦⠄⣄⡈⠠⣦⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠈⠄⠙⠒⠂⢰⠎⠁⠀⡄⠀⠠⠀⠀⢺⢻⡧⠄⠀⠠⢸⣀⡀⠀⡮⠀⠀⠀⣿⠀⠀⠀⠀⢀⠙
⠀⠀⠀⠀⠀⠙⢂⡴⠀⠀⠀⠀⠛⠠⠄⠀⠀⡀⢀⣾⢍⢢⡥⣐⠀⠄⣩⢿⡇⠄⠈⠀⡃⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠨⡟⢘⣀⣴⡋⡷⡶⣶⢾⢡⠸⠐⢸⠙⣦⣤⡶⠋
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⡿⢣⠀⠀⠈⡔⠀⠙⠙⠐⠇⠤⣹⣮⠽⠃⠀⠘⠆⠀⠀⠀⡐
⢀⠤⠢⣴⣦⡀⢌⣀⣀⣀⠀⠀⠀⠀⡁⢳⡈⡦⢥⡀⠀⡀⠀⡀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠁⠀⠀⠀⠙⢿⣦⠙⠳⣬⡍⠲⣄⠀⠀⠐⣟⢀⠠⠀⠂⡀⠀⠈⠃⠀⠈⠧⡄⢤⡀⠐⣾⡥⡘
⠀⠂⠰⣾⡇⠐⠙⢷⣤⡀⠁⠀⣸⡧⣾⣄⣈⠛⣴⠀⠀⢘⢀⡤⠴⠊⠀⠀⠀⡜⠉⢠⡟⡴⢻⠳⡄
⠀⠀⠂⣀⠁⠀⠀⠀⠹⣿⣶⠆⠈⡁⠉⠛⠋⠁⠈⠀⠉⠉⠧⡀⠀⠀⠀⠄⠀⠀⡼⠟⠇⢀⠀⡠⠋
⠀⠀⠀⠀⠀⢸⢷⣶⣉⣻⡗⠄⠀⣦⠆⠈⠁⡖⠀⠀⠀⠀⠀⠘⢢⡀⠀⠀⠀⠀⢠⡀⠂⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠠⣁⠀⠈⠐⢂⣴⡇⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠠⡈⠓⠶⠶⠛⠙⢿⣶⡆⠀⠀⡇⠀⠀⠀⣀⠠⠄⠐⠂⠀⠀⠀⠈⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠃⠀⠀⠠⡈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⣛⣻⡧
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⠀⠤⣄⣀⡙⢦⡀⠀⠅⠑⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉