Clash royale Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠑⠂⠚⠂⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠐⠈⠁⣀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⢠⠉⣴⣴⡀⢴⢊⡳⣄⠀⠀⠀⠜⡀⠀⠀⢀⠐⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢐⠐⠀⠀⢺⡀⠇⢠⠀⠀⠀⠀⠀⢱⠀⠐⢠⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⢀⠜⠁⡀⠀⠀⠀⠀⡀⣘⠉⠀⠣⢄⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠁⠉⢉⣀⣤⠀⠈⠰⣈⠑⡒⠐⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⡐⠈⠈⠀⡰⠋⡰⠀⠇⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡧⠋⠠⠀⠀⠀⡇⠞⢠⠔⠈⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡇⠀⠃⠀⠀⠀⠀⣹⠶⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠤⣄⡀⢰⠊⠀⠘⢅⡀⢀⠀⠀⣀⣤⠧⡤⠵⠒⠊⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⠈⠉⠢⡀⠀⣾⡷⠏⠯⢻⡏⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠟⠣⠤⠤⠜⢓⠐⠂⠆⠐⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡄⠀⠠⠀⠀⠆⡈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠄⠂⡀⠁⠀⡀⠂⠠⠈⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⢴⣀⣀⠂⣀⣀⣘⣠⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠙⠙⡉⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⡃⠀⠰⠤⠤⠤⠒⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡰⠀⠀⠀⢡⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠃⠀⠀⠀⠀⢧⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡎⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠀⢀⡇⠀⠀⠀⠀⠀⠀⢱⠀⠀⠸⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⠴⠂
⠰⠦⠤⠄⠤⠤⠠⠦⠦⠤⠤⠤⠴⠠⠤⡭⠼⠯⠩⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠤⠤⠤⠜⠃⠀⠀⠀⠀⠀⠀⠐⠉⠷⠥⠾⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠐⠀⠀⢠⠤⠤⠤⠄⠀⡀⠀⠢⢀⠀⠠⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⢠⠀⠈⠀⠀⠀⢸⠀⠀⠻⢿⠀⠈⠉⠀⢸⠀⠀⠀⠂⠊⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠃⢰⠀⠈⠂⡆⢀⣀⡀⠈⠟⠛⠀⣸⠀⠐⠛⠀⢸
⠀⠀⠐⠒⠂⢄⠀⠀⠃⠀⠀⠌⠁⠀⠀⠁⠈⠉⠁⠀⠧⠄⠀⢻⡆⠀⠀⠀⠸
⠱⠀⠀⠁⠀⠈⠆⠀⠀⠀⠀⠰⡄⠀⠀⠀⣤⠀⠰⠀⠀⠀⠀⠰⣧⠀⠀⢀⣰
⠀⠀⢀⡀⠀⢠⡆⠀⠀⠀⠀⢰⠙⠀⠀⡜⡁⠀⠀⠀⠀⣇⠀⠠⢼⠀⢠⣴⠽
⣄⠀⠀⣻⣄⠀⠙⣄⠀⠀⢀⡰⢇⠀⠀⣻⠀⢠⠴⢤⠀⣻⣀⣀⣸⣀⣀⣀⣰⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞
⠈⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠀⠈⠉⠁⠀⠀⠀⠉⠉⠉⠁⠀⠉⠓⠦⣄⡀⠀⢀⣠⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠈⠀⠀⠀⠈⠀⠖⠈⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠄⠀⠀⠀⢀⠀⠀⠀⠀⣨⡀⣀⡀⠤⠀⠐⠂⠀⢄⣀⠠⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠡⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡐⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠳⠀⣀⠀⣐⠂⠀⠀⣘⡆⡙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢺⡀⠠⡆⢀⣌⣉⣁⣀⣀⣀⡉⠀⠀⠀⠀⡠⠖⠒⠒⢀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡘⠀⢀⠀⠀⠀⠀⠀⠀⠈⢀⠀⢃⣠⠎⣁⠀⢄⠀⠁⡄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⠀⠀⠀⢠⠁⠀⠰⠀⠀⠀⠀⢂⣠⠔⡫⠖⠉⠀⠀⠀⠑⠄⢀⠜⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢣⣀⣀⣠⠤⠒⠛⠉⢀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠀⠒⠈⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠟⡳⣀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠢⡫⣹⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠰⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡂⠁⢢⠀⠀⠄⡰⠁⠂⠀⠀⠤⠤⠀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⣂⠔⠁⠀⠀⠈⡗⠤⠤⠀⡀⣀⢀⠴⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢏⠁⠀⠀⠀⠀⣠⠓⡈⠄⠒⠔⠢⢊⢄⠇⣫⡷⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠑⠠⠤⠖⠊⠧⣁⠄⠂⠅⠂⣥⣣⡾⠚⠉⠐⠀⢱⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠉⠈⠉⠉⠀⠀⠀⢀⡞⠀⢀⣵⡀
⠀⠀⠀⠀⠈⠃⢋⣀⠀⠀⠁⠀⠀⢀⡀⠤⠂⠈⢄⠀⠀⠀⠀⠀⠀⠀⡰⠃⢣⣈⣀⠴⠃
⠀⠀⠀⠀⠀⢀⠉⢁⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠄⠀⡀
⠀⠀⠀⠠⠤⠤⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠤⠤⠤⠤⠀⠀⠄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⡀⠀⢀⣀⡀⡀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠠⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡁⠀⠀⠁⠈⠀⠀⠀⠀⠀⢀⡀⠈⠁⠈⠀⠀⠀⠀⠀⠀⢐⠀⠀⠈
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⢀⠀⡠⢊⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⡆⠀⠀⠀⠀⠀⠀⠸⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢤⣤⣀⠀⠀⠀⠠⠀⠀⠀⠘⡀⠀⠀⠀⣀⣤⠤⠀⠐⠰⠃⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠙⠀⠀⠀⠀⠞⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠉⠁⠀⠀⠀⠀⡀⠀⠬⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄
⠀⢀⣰⠀⠰⠂⠀⠀⠀⠀⠀⠠⠄⠐⠂⠰⠀⠀⠀⠀⠀⠑⠏⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠁⠈⡋⠀⡀⠐⠀⠀⠀⠀⡔⠀⠀⠒⠀⠀⠀⠀⠒⠂⠀⡞⠁⠀⡀⡁
⠐⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠇⡀⠐⢤⡄⢀⠀⠠⠂⠚⢆⢐⠃⠀⠈
⠀⠀⣀⠀⠀⠀⠤⠀⠀⡀⠄⠀⠀⠀⠈⠀⠀⠀⢀⠀⢀⣀⣀⣃⡀⠀⠈⠀⠀⠀⡕⠀⠐⠲⠀⠀⢁⢀⣶⡄⠀⠀⠦⠰⠀⠀⠀⠘⠈⡀
⠉⠉⠠⠰⠒⠀⠚⠀⠀⠀⠀⠀⠀⡀⡀⠂⠀⢱⠁⠀⠠⡏⠀⣨⠀⠐⠀⠀⠀⠀⠑⠖⠠⠀⠀⠀⡨⣄⠓⠺⠦⡀⠀⠀⠀⠀⠀⣅⠀⠁⠀⠀⠤
⠐⢈⡐⠀⠀⢐⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⡿⠀⠀⠀⠀⡀⡊⠂⠠⢷⠀⠂⠀⡀⠀⠈⠀⠀⢰⠂⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⠐⠆⠀⢀
⠀⠀⠀⢐⠀⢂⠀⠀⢘⡀⠀⢄⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣄⠀⠈⠂⠀⡀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⣠⠌⠀⠀⠀⠀⢠⠜⠀⠛⠶⢺⠆
⠀⠀⠀⠀⠔⢨⡳⠀⡈⠠⠋⣀⠀⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⢄⠀⠂⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠠⠀⡀⠀⠈⠂⠁⢀⠁⠈
⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⢀⡐⢀⠄⠀⠀⠀⠀⠀⠒⠁⠂⠀⠀⠀⠤⠄⠄⢇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠈⠀⠀⠀⠀⢈⠀⠁⠀⠀⠐⠀⠀⠅⠂⠈⠀⠀⠀⠠⠀⠀⡐⠀⠀⠀⠀⠠⣀⠀⠀⠀⠠⠒⠀⢀⡀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⢀⡴⠀⠡⠀⣠⡤⣍⢀⠰⡠⠀⠀⡠⠒⠃⠐⠀⠀⠈⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠀⠀⢀⡤⠉⠀⠂
⡀⠀⠀⣰⢀⣴⠟⠁⠀⠀⠀⢠⣠⣿⠂⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠉⢁⣤⣴⠏⣤⡄⠀⠀⣀⠀⠀⠀⠈⠋⠀⣀⣠⡷⠶⡋⡀⢈⣀⡀
⠿⠟⠿⢿⠯⠁⠀⠀⠀⠀⠀⠂⠈⠠⣿⠆⠀⠀⡁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⣡⠞⠁⣠⡄⠀⠀⠀⠈⢀⣀⠠⠐⠉⢁⣀⡀⠀⠄⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠈⠂⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⢰⡞⣩⣿⡓⠠⠿⣀⠀⠸⠑⠖⠋⠁⠀⠀⠀⠈⠉⡛⢰⡆
⠔⠒⠀⡀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⢀⡤⠐⢠⠀⡾⢻⣷⣿⣷⣿⣿⣯⣂⣈⡠⠄⠀⠦⠂⠨⢆⠀⠀⢉⣴⣦⠀⢠⠀⠈
⢀⡴⠃⠀⢀⣀⡙⠂⠀⠋⢠⣻⡆⠀⠀⠤⠀⠖⠋⠂⠀⠀⢀⡀⠀⠀⢀⣤⠾⡕⠿⠿⠛⠙⠉⠉⠁⠈⠉⢠⠀⢀⣤⠹⠔⠛⣦⡀⣨⠭⠉⢠⡎⠀⠠
⢀⣀⣤⠞⠉⠉⠙⠶⠾⠀⠀⢀⠠⠀⠐⡀⠰⠂⠀⠀⣠⣤⢤⡌⠳⣄⠀⢀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠰⠰⠍⠱⠘⠙⠀⠰⣗⠛⠛⠀⡀⡶⠋⡴⢤⣤
⣾⠋⠀⢀⡶⠄⠀⠀⠨⠒⠂⠁⣶⡦⠌⠁⠀⠀⣰⣸⠋⠀⠠⠀⠀⠀⠀⡰⢆⡀⢀⠀⠠⠆⠀⠐⠜⠒⠀⠀⠀⠀⠀⠘⠳⠇⠀⢀⣰⢋⡶⠞⡴⠋
⠇⡤⠈⣹⢲⣿⣿⣿⠃⠲⣀⠾⠛⣿⢤⠤⠀⠀⠀⠛⠀⠀⢰⠐⠀⢀⡠⠡⣶⡏⠀⠀⠀⠘⠇⠠⠀⠀⠀⠀⠀⠀⠀⠀⡰⣶⢘⠩⣄⠘⠁⠼⢀
⠐⢀⡟⠉⠈⣨⣅⡹⠀⢀⡬⠔⠚⠡⣿⣤⠀⠜⠀⠈⠃⠀⣠⣔⠂⢁⠶⠆⢽⠇⠀⠀⡀⠀⠀⠀⠤⠀⠈⠀⠀⠀⠀⠀⢀⠔⠉⠀⠈⢀⣀⢲⣀⡀⠄
⡕⣿⠇⠐⠾⠄⠠⢀⢐⠀⠀⠓⢀⣙⡿⣿⠀⠀⠀⠰⠀⢢⣼⡯⠾⠷⠀⠖⠀⠀⠀⠁⠀⠀⠰⠠⠂⠀⡄⠀⠀⠀⡠⠀⠀⠀⢄⠀⠀⠈⡄⡈⠛⢉⣬
⡾⠃⠐⠓⠀⡐⠤⠂⢬⡀⣀⡸⠖⣋⠈⠋⠐⠐⠂⢤⡺⠋⠙⠠⠀⠀⠀⠀⠀⠒⢀⡀⣄⠀⠀⢎⠢⠈⢀⠀⢠⠦⡀⠰⠀⠀⠀⠘⣿⠼⠃⣈⡶⢾⠛
⣷⡀⠀⣴⠀⢠⣞⡀⠠⠟⠈⠀⠀⢀⠒⣯⡔⣧⡀⢿⡇⠬⢱⡶⠀⠀⠠⠂⠀⣴⠋⠀⠀⠐⠠⠄⢀⠐⠞⠳⠛⣧⠞⢲⣤⣀⣀⣴⠟⠀⢼⣇⣀⠞⠉
⠋⠛⢀⠀⣠⣶⡏⠀⢤⠥⠄⠀⠀⠀⢵⢦⠤⣙⣃⠠⠀⠀⠂⢰⠀⠀⠀⡄⠾⠥⠀⠀⠀⠀⣠⣠⠴⢤⠑⠲⠀⠁⠒⠂⠛⠃⠈⠁⠀⠀⠿⠛⠛
⠀⡴⣶⡛⠉⠻⠀⠀⢸⡦⠀⠆⠁⣈⠎⠁⠀⠘⠁⠀⠀⢀⣰⠂⡴⠶⣤⣀⠀⡄⡲⠒⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠁⣠⣠⡤
⡀⠘⢿⣡⢂⡢⠐⠂⠉⠁⢐⠻⠟⠁⠀⢠⠀⠀⠀⡠⠀⢠⠦⠚⠉⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀⠀⠀⠟⠉
⠟⠀⠠⠒⢊⣵⣟⠁⠀⠀⠀⠈⢿⡇⠀⠉⠀⠀⠀⠈⠀⠀⠀⠸⠉⠁⠀⠀⣿⡖⠋⠀⣀⢠⡀⠶⠀⠀⠀⠀⠁⠀⠀⢀⡰⠛⠙⢷⣆⣸⠋
⠔⠛⠀⠞⠉⠉⠀⠀⠀⠀⠀⠀⠈⠛⡑⢤⠀⠂⣠⣶⠃⠀⣠⠐⠶⣀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⣹⣷⣴⡦⠂⠀⠐⠉⠀⠀⠀⠰⣭⡿⠉
⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⡄⠴⠁⣄⣀⣠⣶⣤⣏⣷⡏⠀⠀⠀⠀⠀⠀⢚⣿⡿⠟⠛⠁⠀⠀⠀⢾⣆⠀⠀⠀⠀⣀⢠⣄⡠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢀⠀⠀⠤⠤⠤⢀⠀⣀⢰⠇⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢼⠁⠲⠶⠒⡀⡵⠔⠋⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣫⣨⣏⡀⣀⠀⠀⠀⠤⣧⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠐⠉⠉⠀⠀⠀⠉⠙⡂⠀⠀⣴⠍⠂⡝⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⢶⣦⡈⠓⠉⡔⠐⠒⠐⠒⠂⣪⠁⡾⣠⣟⡀⠴⡷⠃
⠀⠀⠀⠀⠀⢠⡀⠀⠀⢧⡀⣥⣇⡰⠠⠗⠓⠂⠀⠲⣅⠹⡄⠗⢇⢀⡴⠊
⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⢸⠣⣌⣹⠁⠀⠀⣀⣀⢨⢉⣀⡠⠔⠊⠁⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠌⢦⡠⠤⠺⠤⣄⢙⡌⠁⠠⡁⠀⣄⣁⡟⢢⡤⢤⣼⠃⠀⠀⢻
⠀⠀⠀⠀⠀⢀⠼⠋⠀⠀⠐⡀⢽⡿⠃⠉⠀⢁⡞⠉⠉⢈⣼⠃⠀⡋⠀⣀⠂⡼⠀⡀
⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⢰⠛⠧⡬⡤⠦⡼⠁⡐⠠⠊⢣⡤⠚⢉⠜⢁⡼⠣⣰⠏
⠀⠀⠀⠀⢱⠤⢄⡀⠀⠀⠀⠨⠀⠀⡜⠀⣀⣀⠙⠀⠀⢰⠋⠀⠀⠉⠤⠞⠀⠀⢣⠴⣃⠀⠆
⠀⠀⠀⠰⠁⠀⠀⠈⠙⡆⠀⠁⠀⠑⠗⠈⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⢀⠚⢁⡀⠀⠰⡳
⠀⠀⠀⢳⠤⠚⠓⣐⣆⣽⢄⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠀⠀⠠⢄⠀⠀⠀⠀⠸⠊⠁⠀⠀⣷⠀⣧⡀
⠀⠀⠀⠹⡀⠘⠥⠾⠚⣏⠇⠒⠉⠁⠀⠂⢄⡀⠈⠊⠀⢀⠡⠚⠉⡝⠒⠀⠐⠚⡶⠊⠀⠀⠸⢀⣿⠍
⠀⠀⠀⠀⠙⢦⡀⢪⠴⢽⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠒⠉⢢⡀⠀⠈⠣⢴⠉⠀⣱⠿⠴⠞
⠀⠀⠀⠀⠀⢀⣙⣤⠔⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢈⠑⢦⣾⡬⡭⠥⠬⢭⡤⠃
⠀⠀⠀⠀⢩⡁⠈⠉⢀⣰⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠌⠱⡀⠀⠉⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠛⠉⠛⠉⠸⠓⠢⠷⢄⠀⠀⠀⠀⢀⣀⡤⠔⠖⠚⠉⠀⣀⠴⢇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠎⡓⢤⠔⠊⠁⡆⡀⠀⠨⠛⠊⠉⠀⠀⡬⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⡃⠐⢀⡀⠄⢀⡟⡀⠀⠑⠒⠒⢈⠇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⡗⠢⠭⠴⠖⠚⠁⠀⠈⢲⠲⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⠑⠠⢠⠶⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣠⠶⠛⢶⢦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠠⢠⠰⠂⡀⣦⣶⡟⢳⣶⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡠⠚⠡⡴⠛⠲⢦⠙⢿⣿⣦⣤⡀⠀⠀⢠⣄⣄⣟⣑⢛⣟⡛⣋⡟⣽⣿⣇⣀⣼⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⣧⣸⣿⡟⠛⠃⠀⠠⣽⢯⠯⡧⠯⣽⡽⠿⠷⠧⠿⠿⣟⡿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡤⠃⢐⠀⠠⣰⠋⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠨⡇⠀⠀⠀⠁⣘⣨⣿⣿⣏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⡀⡧⠤⠀⠀⢹⣻⣵⣯⡿⠁⠿⠛⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣿⡷⠀⠀⠀⠀⠈⣉⣹⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⢠⣞⠛⠙⣧⡀⠀⠀⡀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⣨⣿⣷⣛⣿⠈⢻⣿⡷⠞⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣌⢻⣿⣆⣀⠀⢀⣯⠉⣿⣿⡏⠀⣾⡿⠗⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⣾⡷⠀⢹⣿⣿⣿⣿⣿⠷⠀⠉⠉⠀⠉⣀⡴⢻⣿⠀⣾⣧⡀
⠀⠀⠀⢀⡴⢹⣷⣞⡛⢋⣹⠗⠉⠁⠀⡸⠟⠛⠛⠛⠋⠀⠀⠀⠠⠴⠞⠋⠀⠘⢿⣶⡿⠛⠁
⠀⠀⠀⠸⢿⡿⣿⣿⣶⡿⠁⠀⠀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠒⣶⠶⠶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣤⣀⡤⡴⠶⢶⡶⠶⠶⡖⠶⡶⠦⢤⣤⣤⢠⣤⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣼⣈⠳⣤⣜⢦⣼⡇⠀⢠⣧⢾⣷⣤⣶⣣⣸⣿⣿⣿⣄⡀⠀⢸⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣶⣿⣿⡿⠃⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣦⡸⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠘⠁⠀⠈⠁⠀⠀⠀⠈⠁⠀⠈⠉⠛⠢⠀⠀⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢶⣿⣆⠀⠀⣀⣀⠀⠀⣠⣤⣤⣤⡀⠀⠀⣠⣖⡶⣶⢿⣿⢡⡯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣌⠻⣧⠈⠉⢉⠅⠩⣿⣿⣟⢻⣷⡿⠯⢙⠽⢅⠈⠿⠃⢈⣿⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣶⣿⣿⣷⡿⠿⠿⠿⠿⠿⠿⠿⢿⣷⣿⣷⣶⣿⣿⣿⠏⢻⣷⣄⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⠃⠠⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣾⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡞⢹⠀⠀⠹⣿⣿⣿⢸⡿⢿⣿⣿⣿⣿⣿⡿⠇⣀⡿⠃⠀⠀⢠⣿⡙⠛⠿⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣿⣼⣿⡄⠀⠀⠘⠻⣷⡀⠉⠁⠛⠃⠈⠉⠁⠀⠒⠉⠀⠀⠀⣠⠛⠡⠤⣈⣴⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡫⠘⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⣟⢦⢁⣰⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⣀⠔⠙⣦⣀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⣀⠤⠺⣥⣦⣡⣶⣿⣿⣿⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣯⣠⠚⣿⡟⣿⣿⠉⢻⢍⠉⠍⢿⡿⡟⣅⠳⣄⢁⣤⣾⣿⣿⣿⣿⡟⠉⠈⠒⠲
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣵⠛⢂⡏⠈⣼⠀⠀⠀⢨⡇⣧⠹⣦⣼⣿⣿⣿⣿⣿⠟⠷⣄
⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠙⢿⣿⣿⣾⣄⠀⡇⠀⠐⠀⣸⣧⣾⣾⣿⣿⣿⣿⠿⠋⠀⠈⠢⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠐⡄⠀⠀⠀⢀⠎⠈⠑⢦⣀⠀⠉⠻⣿⣿⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⠿⢋⣁⠤⠔⢄⠀⠀⠈⢦⡀⠀⠀⠀⠀⢀⣠⣦⡥⢂
⠀⠀⠀⠀⠈⠆⠀⢠⠃⠀⠀⠀⠀⠈⣷⣦⡄⣼⢿⣿⣿⣿⣿⣿⣿⣿⠿⡫⠕⠒⠉⠀⠀⠀⡈⢣⠀⡀⠦⠉⠁⢀⣠⡞⠓⢍⡯⣷⠞

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

⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⣰⠏⣠⠞⢙⢒⣙⣧⡀
⠀⠀⠀⠀⠀⣼⠃⣼⡃⣰⠋⠉⠙⣎⣷
⠀⠀⠀⠀⣸⠇⣸⠇⡼⠁⣀⣄⡀⠸⣾⡇
⠀⠀⠀⢠⡏⢠⡿⣹⢡⡞⣡⢤⣙⡆⣿⣿
⠀⠀⠀⣸⠁⣾⠃⡇⡾⡾⢁⣀⠹⣿⢸⣿⡆
⠀⠀⠀⣿⢀⡟⣸⢹⢿⣧⢯⡿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣚⣖⣖⣲⣟⡿⠃
⠀⠀⠀⣿⢸⡏⣹⢸⣽⢸⢸⣿⣿⣿⠷⣿⡗⠒⠒⠒⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⣝⣹⣋⣙⣭⣳
⠀⠀⠀⣿⢸⣧⢺⢸⢿⠸⣼⢯⢇⣿⢸⣿⡇
⠀⠀⠀⣿⠈⣷⢺⠸⡾⣆⠙⠋⣼⡏⢸⣿
⠀⠀⠀⢸⡄⢿⡜⡇⢳⡜⠦⠜⡿⢁⢿⡟
⠀⠀⠀⠈⣧⢸⡗⣹⡀⠙⠒⠛⢁⡞⣼⠇
⠀⠀⠀⠀⢹⡆⢷⡑⠳⣤⣀⣴⡫⣷⠋
⠀⠀⠀⠀⠀⠻⣎⢻⣔⠤⠊⣪⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⣤⡀⠀⢀⣠⣤⡴⠶⢶⡶⡶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡖⠲⠞⠁⡠⠟⠛⢫⣀⡤⠬⠧⠦⠷⠼⢤⣥⣹⢹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡷⠀⠐⠿⣍⡷⠋⠸⣄⠀⠀⠀⠀⠀⠀⠀⠙⢾⣀⢷⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣋⣤⣤⠀⠀⣀⠀⢿⠓⠾⠀⠀⠀⢀⣤⣴⠶⠶⠿⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠁⠀⢸⢠⠞⠉⠓⠾⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⢀⣀⣠⣤⡼⠿⠛⠛⠁⠀⠀⠀⠉⠙⠛⠻⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣷⠀⠀⠀⠀⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢁⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠁⠀⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡛⠋⢙⡿⠁⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢀⣴⠋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⠛⠉⠀⠀⠉⠛⢷⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢀⡾⠁⠀⣿⡇⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣾⢁⣶⣷⢻⡀⠀⢠⡇⢀⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡏⣼⣿⡟⢈⣿⠞⠁⠉⣏⠀⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣽⡇⢿⠿⢁⣾⠇⠀⠀⠀⢿⠀⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠸⣷⣤⣴⠿⠁⠀⠀⠀⠀⠸⣧⠹⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠾⣫⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣟⡛⠛⠛⠛⠉⠉⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠂⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠈⠉⠉⠉⠛⠳⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠃⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⣀⠀⠀⠀⠀⠙⠿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣄⡀⠀⠈⠛⠿⣿⣿⣿⡟⠛⠛⠛⢻⡍⠀⢀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣤⣤⣤⣤⣤⣿⡒⠦⣄⣀⢻⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢸⣇⠀⠀⠈⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠛⠛⠒⠾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢀⣴⠶⠾⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⣥⣤⣴⠟⠁
⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⡿⢿⡿⠿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠁⠀⠀⠀⡇⠀⠀⠀⠉⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⣀⣤⣤⣶⣷⣦⣤⣀⠀⠀⠀⠉⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⣠⣾⠿⠛⠉⠉⡏⠉⠙⠻⣿⣦⡀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⣼⡿⠃⠀⠀⣀⣤⣧⣄⡀⠀⠈⠻⣿⡄⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢰⣿⠃⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⠀⢻⣷⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠘⠛⣿⡟⠛⠛⢻⣿⡛⠛⠛⣿⣿⣿⣿⣿⣿⡟⠛⠛⣻⣿⠛⠛⠛⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠈⢿⣧⠀⠀⠈⠻⢿⣿⠿⠋⠀⠀⢠⣿⠇⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠈⢿⣷⣄⡀⠀⠀⡇⠀⠀⣀⣴⣿⠋⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠉⠻⠿⣷⣶⣷⣶⡿⠿⠋⠁⠀⠀⣠⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣦⣤⣤⣧⣤⣤⣶⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀
⠀⠀⠀⠀⠀⢤⡤⣤⣤⠄⣀⢠⣤⣤⣄⣤⢀⡀⣤⢤⣥⣴⣞⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠐⠛⠁⠀⠘⠃⠛⠘⠛⠈⠘⠃⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠀⠀⠀⠀⠙⠲⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡴⠶⠶⠛⠛⠉⠁⠀⠀⢀⣰⠖⢦⡀⠀⠀⠀⠈⠉⠛⠛⠲⠶⠶⠶⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠾⠋⠁⢸⠀⠙⠳⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⠶⠶⠶⠞⠛⠉⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⢶⣦⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡰⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣰⡍⠁⠀⠀⡐⠀⠀⠀⠀⢰⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠰⠁⠀⠀⠀⢀⣾⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠁⠄⠘⠀⢀⢺⠇⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠸⡶⠶⠶⠲⠒⠒⠺⠒⠒⣻⠚⠓⠒⠒⠶⠾⠿⠟⢛⡟⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠹⣆⠀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠹⣎⢃⠂⡔⡰⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠙⣆⠀⠰⢁⠀⡀⣿⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠘⢧⡀⠀⡴⠀⢻⠀⠀⠀⠀⣠⡞⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠻⣶⣁⠀⢻⠀⠀⢀⡴⠋⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠙⠷⣾⣤⣴⠟⠁⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⠉⠀⠀⣠⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣤⡶⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⡀⠀⠀⣀⣀⣀⢀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⠚⠀⠂⠀⠉⠱⠟⠃⠈⠉⠋⠀⠛⠀⠈⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⣞⠉⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡔⠒⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠐⡀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠁⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣋⡄⠀⠠⠆⠀⠀⠀⠀⠀⡂⣺⠦⠋⠄⠀⠄⠀⠉⢍⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⢀⢶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅⣀⣑⠂⠀⠀⠀⠀⠾⠟⠻⣷⡀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣷⠲⠀⠀⠀⠀⠀⠀⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣀⠂⠐⠒⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠐⠀⠀⠙⠁⡀⡀⠄⣰⠦⠤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⠤⠖⢇⣠⣀⡤⣧⠀⠀⠀⠀⠀⢠⣅⣀⡤⠐⠛⠲⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⡆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⠑⠊⡀⢿⠃⡀⠀⠀⠀⣿⠉⠑⠋⠉⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⣀⣀⡀⠀⠘⠋⠙⠆⢉⠒⠛⠐⠁⢀⡄⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠴⠴⡾⠹⠤⣀⣰⣠⠖⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⣀⠀⠀⠀⣠⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⠤⢤⡖⠒⠖⡇⠀⢀⠀⣿⠈⠑⠒⡋⠁⠈⠉⡦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠕⠀⡠⠒⠊⠉⠀⠔⠓⡴⣉⡊⠁⠃⠀⠒⠀⠀⠀⠐⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠰⠀⠀⠔⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣴⡃
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠴⠋⠁⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠂⠒⠐⠒⠒⠂⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠐⠒⠒⠈⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠛⠛⠋⠙⠛⠛⠻⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⣀⣴⠾⠛⠋⠉⠉⠉⠛⠳⢦⣄⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⢠⡾⠋⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⢰⡟⠀⠀⠀⣠⠾⠛⠉⠉⠛⠳⣦⡀⠀⠀⠹⣆⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⠀⠀⠀⣼⠃⠀⠀⣀⣀⠀⠀⠈⣷⠀⠀⠀⢻⡄⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠸⣇⠀⠀⠀⣿⠀⠀⠸⣏⣹⡇⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⠀⠀⠀⢻⣄⠀⠀⠈⠉⠀⠀⢠⡿⠀⠀⠀⣾⠁⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠘⣧⡀⠀⠀⠙⠷⣤⣤⣤⣤⠾⠋⠀⠀⠀⣼⠏⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠈⠛⠶⣤⣤⣄⣠⣤⣤⠶⠟⠉⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣤⣤⣤⣤⣤⣶⡾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣁⣉⣉⢉⣉⣏⣉⣉⣉⣷⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠀⠚⠚⠛⠛⠛⠛⠁

⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡾
⠀⠀⠙⠷⡄⠀⣧⡀⠀⠀⠋⠀⣠⠄
⠀⠀⠀⠀⠀⠀⢻⠻⢦⠴⢲⡟⠁⠀⢀⣤⣤⣤⠄⠀⣀⠄⡖⢰⢂⡐⠀⠤⡀
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠺⣤⣄⣀⠀⠀⠀⣠⠔⠃⣹⠔⠋⠁⠀⠀⠹⡄⠘⡄
⠲⠖⠒⠂⣠⣞⠁⠀⠀⣤⡾⠻⠥⠤⢰⠊⣇⠠⠖⠉⠀⠀⠀⠀⠀⠀⠀⡗⠈⡃
⠀⠀⠴⠚⠋⠉⠉⢻⣴⠋⣯⠘⠃⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣗⣉⣅⣀⣀
⠀⢀⣠⠀⠀⣴⠀⠘⠏⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠿⠛⠛⠋⠉⠉⠉⠙⠛⠛⠻⢷⡆
⠴⠋⠁⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣤⡤⠶⠶⠶⠶⠶⠶⠶⢤⣤⣼⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⢀⣠⣤⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⡷⠶⠤⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠴⠚⠛⠛⡟⠛⠿⠿⠿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣿⠀⠀⣆⣤⣴⣾⡿⠿⠟⠛⠋⠉⠀⣷⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠘⢽⣿⣿⠏⠉⠙⠛⠛⣿⠀⠀⢻⢿⣿⣯⠁⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⣀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠈⠛⠲⠶⠶⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⣼⡇⠀⠀⠀⠐⠋⣿⠛⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠛⣶⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠴⢶⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⡿⠀⠀⠀⠉⢹⡏⠉⠉⠉⠉⢹⡏⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣷⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⡀⣾⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣽⠞⠹⡆⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢤⣄⣀⠀⠀⠀⣿⣀⣀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⠴⠶⠞⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠁⠈⢿⣿⣦⡀
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋⠀⠀⠀⠀⠙⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⢰⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠟⠋⠀⠀⣠⣾⣷⣄⠀⠀⠙⠻⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡆
⠀⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣴⣶⣿⣿⡿⠟⠋⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⣦⡀⠀⠀⠙⠻⢿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿
⢠⣿⡏⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⣀⣤⣾⡿⠿⠿⠛⠛⠛⠛⠿⠿⣿⣷⣦⣀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⢹⣿
⢸⣿⠇⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢸⣿
⣸⣿⠀⠀⣼⠋⠉⠉⠙⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠋⠉⠉⠙⣧⠀⠀⣿
⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿
⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸
⣿⣇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸
⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⢹⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⢸⣿⡀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢀⣿
⠘⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿
⠀⢿⣷⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⡿
⠀⠸⣿⡆⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢰⣿⠇
⠀⠀⢿⣷⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣾⡿
⠀⠀⠘⣿⣇⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣸⣿⠃
⠀⠀⠀⢹⣿⡄⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢠⣿⡏
⠀⠀⠀⠀⢻⣿⡄⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢠⣿⡟
⠀⠀⠀⠀⠀⢻⣿⡄⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣤⡀⠀⠉⠛⢶⣤⣀⠀⠀⣀⣤⡶⠛⠉⠀⢀⣤⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣤⣀⠀⠈⠙⠛⠛⠋⠁⠀⣀⣴⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣤⣄⣠⣤⣶⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⠿⠛⠉⠀⣶⣭⣛⠿⢶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣾⣭⣭⣭⣭⣭⣿⣿⣿⡛⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⢻⡇⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢹⡟
⠀⠀⠀⠀⠀⠀⢸⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⢿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⡻⣿⣿⣿⣿⠀⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣭⣻⠿⠀⣀⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠋⣿⠉⠙⠻⣶⠾⢿⣬⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢧⣴⠟⠛⠳⠶⣼⣧⣀⣤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⠶⢿⣴⣾⣿⣷⣤⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡴⢋⡥⠿⢠⡙⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⠵⢺⠳⢭⡳⣄
⠀⠀⠀⠀⠀⠀⣼⣥⡏⠀⣤⡀⢙⣤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣏⠀⠀⠀⢀⣳⣽
⠀⠀⠀⠀⠀⠀⠹⡄⠲⣄⢈⢀⡴⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢧⡀⢀⠀⣀⠎⡼
⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣿⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢭⣽⣯⡵⠞⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢊⠠⠀⠠⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣸⡇⠈⠹⣦
⠀⠀⠀⠀⠀⠐⠢⡁⠄⠀⠴⠀⠀⢈⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⠤⢴⣿⣿⠶⠶⠾
⠀⠀⠀⠀⠀⠀⠀⠐⢌⠂⠠⠐⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢹⡇⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠛⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣷⣀⣀⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠿⠿⠁⠙⠛⢛⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠉⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣤⠀⣶⡶⠾⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠛⠋⢉⣿⢻⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣤⣀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣺⣿⡿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⢛⣛⣛⣛⣛⠛⠻⠶⣯⣽⣻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⣩⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣌⡙⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣰⡟⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣦
⠀⠀⠀⠀⠀⠀⣼⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⣧
⠀⠀⠀⠀⠀⣸⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠹⣧
⠀⠀⠀⠀⢀⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⡆
⠀⠀⠀⠀⢸⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⡇
⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⡇
⠀⠀⠀⠀⢸⣧⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⣿⡀⣿⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⠃
⠀⠀⠀⠀⠀⠸⣧⠘⣿⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⡏
⠀⠀⠀⠀⠀⠀⠹⣧⡘⢿⣦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣌⠻⣿⣦⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⠙⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣌⣙⠛⠿⠿⣿⣿⣿⣿⣿⠿⠿⠛⢋⣡⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⣶⣦⣤⣴⣶⠶⠾⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⣠⣾⣿⣿⡀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠿⠿⠛⠛⠿⠿⢿⣿⣿⣶⡄⣾⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠇⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣤⠀⣠⣾⡿⢛⣛⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⢀⣾⣿⡿⠛⠉⠀⠀⠀⠀⠉⠛⣫⣾⡿⠋⠀⠈⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⢠⣿⣿⠋⠀⠀⣀⣤⣶⣶⡄⣠⣾⡿⠋⣾⣿⡄⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⠃⠀⠀⣼⣿⠟⠛⣩⣾⡿⣋⠀⠀⠸⣿⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⠀⢸⣿⣿⠀⠸⠿⠋⣼⣿⡇⠀⠀⣿⣿⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⡄⠀⠀⢻⣿⣦⣤⣤⣴⣿⡟⠀⠀⢠⣿⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠘⣿⣿⣄⠀⠀⠉⠛⠿⠿⠛⠉⠀⠀⣠⣿⣿⠃⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠈⢻⣿⣷⣤⣀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠁⠀⢀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⣠⣬⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣷⣶⣶⣤⣤⣶⣶⣾⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢀⡀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠴⠚⠉⢀⣠⠖⠋⠙⠲⣄⡀⠙⠓⠦⢤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢀⣀⣠⠤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣄⣀⡀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠈⠳⣄⠀⠀⠀⠀⣠⠞⠁⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠙⠦⠴⠋⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⣠⠖⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⠟⠉⢀⣤⣄⠈⠙⠿⣶⣤⣄⡀
⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⠶⠾⠿⠛⠛⠉⢀⣀⡤⠞⠋⢹⠉⠛⠦⣄⣀⠈⠙⠛⠻⠿⠶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⣿⠇⠀⢠⣤⣤⣤⣤⣤⠤⠶⠖⠚⠋⠁⠀⠀⠀⢸⠀⠀⠀⠀⠉⠛⠒⠶⠦⢤⣤⣤⣤⣤⣤⠀⠀⢿⡇
⠀⠀⢠⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⡇
⠀⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡿
⠀⠀⠘⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⡇
⠀⠀⠀⣿⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣿⡇
⠀⠀⠀⢿⡇⠀⢸⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢾⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿⠀⠀⣿⠃
⠀⠀⠀⢸⣷⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢸⣿
⠀⠀⠀⠈⣿⡄⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣾⡇
⠀⠀⠀⠀⠸⣷⡀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⣸⡿
⠀⠀⠀⠀⠀⠹⣷⡄⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠉⠛⠶⢤⣄⣀⠀⠀⢸⠀⠀⢀⣀⣤⠴⠞⠋⠀⢀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣀⡀⠀⠉⠙⠛⠛⠛⠛⠉⠁⠀⣀⣠⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⢶⣶⣤⣤⣤⣴⣶⠾⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠻⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢴⠊⢿⣿⣿⣿⣧⡈⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⢁⠍⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣼⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⣿⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢾⣅⡐⣿⣿⣿⣿⣯⡐⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡨⢉⣤⣿⠏⠙⣿⣿⣿⣿⣿⣇⠀⠀⠰⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢀⡾⢃⣾⣿⠤⠤⣾⣇⠉⠻⢿⣿⣿⣷⡀⠀⠐⠆⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠸⠇⠸⣿⣠⠀⠠⠋⠙⠃⠀⠀⠉⠻⣿⣷⣶⣾⣶⠛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⣠⣬⣿⣄⣀⣤⡾⡿⢿⣾⠃⣀⣉⠐⢆⠀⠀⠀⠈⣿⣿⣿⣿⡀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡍⢻⣦⢉⣿⣿⠀⠀⠰⢾⡏⠀⠛⠉⠀⠀⠀⠀⣀⣄⠘⣿⣿⣿⣿⣷⣾⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣿⡷⣾⠋⠉⠶⠄⠀⡸⠰⡟⠀⠀⠀⢀⣦⣄⣤⠀⣄⠀⠟⠻⣿⣿⣿⣆⠀⣉⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠘⡟⢀⣴⣤⣷⡴⣿⠈⢻⣶⣶⣄⣠⣿⣿⡶⠀⢸⡇⠀⠀⠉⢹⣿⣿⣿⡟⠁⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠘⢷⣏⣙⣿⠋⠛⠷⣤⣤⣄⢿⣿⠛⠛⡿⢿⢷⡎⠀⠈⠰⣤⣷⣶⢿⣿⣿⣄⢀⠰⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠰⠛⠻⠿⣤⣶⣤⠀⠈⠟⣠⣿⠇⣠⣿⠒⡿⠃⣀⣛⣿⠿⠿⠏⠀⢹⣿⡿⠿⢷⣴⠖⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠆⠀⠀⢀⡀⢀⣄⠀⣀⣤⠀⢺⡿⢿⣿⣿⣿⣧⡀⢰⣿⡟⡟⠃⠀⠐⠛⠿⣿⡇⢀⣾⡅⢀⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣤⠀⣴⠞⣿⢧⣤⣶⣿⣏⡉⠻⣧⠽⣿⣿⣿⣿⣿⣿⣿⣽⢻⣤⢛⣼⣿⣷⠋⣠⣾⣿⣷⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣷⣤⣿⡄⠉⠐⠉⢿⣷⡿⠋⣀⣹⣶⣾⣿⣿⣽⠟⣭⣿⠏⠸⣿⣿⡝⠋⣹⣤⣽⡛⠛⣯⡀⠀⢈⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢰⣿⣿⣷⢆⣤⣥⣿⣿⣿⡀⢉⡀⢺⣿⣟⣩⣿⣿⣿⣿⣶⣿⣿⣶⠷⢎⡁⠀⠚⠉⠙⠛⢿⡿⠄⢁⣤⠺⣿⠆
⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠈⣿⣿⣿⣤⣤⣈⣀⣨⡉⢿⡿⠉⢻⡿⢿⣿⠟⠛⠿⢟⢻⡇⠻⠛⢠⣀⣿⠀⠀⠀⢺⡆⢼⣧⣄⡈⢉⣥⡀
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣯⣥⠘⣷⣀⣼⠓⢂⣠⣶⠶⡶⠋⠈⠿⠀⠀⣟⠻⢻⣤⠄⠀⠀⠛⣮⣉⣾⣧⣤⣽⣿⡇
⠀⠀⠀⠀⠀⠀⡀⠀⢀⠘⠙⢿⣿⣿⣿⣿⣿⢿⣿⣿⣾⣿⣿⣿⡷⢏⣹⣿⣿⣧⣼⣇⠀⠀⠾⣧⣴⣿⡁⠀⠀⠀⠀⠉⠁⢩⣙⣿⠟⠉⠀⣡
⠀⠀⠀⠀⡀⢀⡇⣀⣼⣧⣷⣤⣿⣿⡿⠛⣿⣿⠉⣿⣿⡿⠛⢿⣤⣾⣿⣿⣿⣿⣿⡻⣿⣶⣾⡏⢁⣄⠙⢓⣤⣤⠄⣤⣴⠛⠛⠻⣶⣾⣷⡿
⠀⠀⠀⠀⣷⣾⣿⣿⣿⣿⣿⡙⣻⣿⢁⣀⠁⠙⡟⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡴⠟⢻⣧⣤⣶⣤⣉⣋⣛⣯⣤⣾⡇⢠⣿⣿⣿⣇
⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣉⣿⣿⠖⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢙⣷⠂⣹⣿⢉⠽⢿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣶⣷⣄
⠈⠿⠿⢻⣿⣿⣿⠛⡜⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⡿⠋⠙⣿⣶⣿⡁⢙⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟
⠀⠀⠀⠀⠉⠙⠃⠰⠿⠿⢿⣿⣯⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⢿⣿⡿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⣾⠿⠿⣿⡟⣛⣀⣸⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠈⠛⠿⠟⠿⠿⠛⠛⠛⠻⣿⣿⠷⠿⣿⣟⣿⠖⠋⠉⠉⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⠏⠙⢻⡏⠉⣙⠛⢛⣏⠛⢹⣽⠟⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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







⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣶⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢲⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠛⠛⠿⠿⢷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣶⠂⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⣿⠟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣾⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢀⣿⡟⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⣿⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣸⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⡶⢒⠀⠈⢰⢠⣷⣄⠴⠖⣲⣶⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣞⠫⣅⠢⣷⡓⠀⠀⠃⠠⣼⠟⢿⣿⣿⣿⠿⣍⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢝⣥⣏⡙⠛⣿⣧⣽⡧⢤⡤⢀⣽⣧⠀⣉⠁⡈⢰⣿⡿⡟⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⣥⡾⣿⣦⣩⡿⢶⠏⣻⣷⣽⣿⣓⣚⠋⠻⣷⡟⢻⡇⠀⣗⠀⣼⣉⣳⣿⣦⡀
⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⠜⡋⣹⣾⡟⣃⢌⣹⣽⠟⣿⠂⠿⣿⡟⢿⣿⢿⣿⣹⣬⡻⣄⣷⣤⣉⡄⠙⣿⣏⢅⠙⢿⣶⡄
⠀⠀⠀⠰⠟⠩⣍⣩⡿⢧⡡⣿⡿⢿⣼⠃⠀⣀⣨⠀⣿⡜⣿⣷⡷⣾⣿⣿⠿⣿⣿⣿⣮⣿⡟⠻⠿⣶⣎⢻⣎⡙⢾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠛⠀⠀⠀⠀⠙⠛⠋⢗⢈⣇⠸⣿⣷⡹⢻⣿⣶⣮⣿⡿⣿⣿⣷⣿⣷⣾⣿⣿⣿⣩⣄⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡉⢻⡓⠉⠹⢿⠿⣿⣿⣞⣷⣶⣌⠻⠿⠿⣿⡿⠯⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠨⠀⠀⢀⠘⠀⠛⠩⠻⢿⣏⡿⢷⣿⠓⠪⠱⣼⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠊⠀⠀⠉⠉


⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣦⣷⣴⣤⣶⣤⣾⣵⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣠⣤⣤⣤⣀⢠⢠⣖⣸⡭⣭⡥⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠗⣌⠹⣻⠋⢿⢀⡼⢯⡀⠀⠀⠀⠙⢋⣓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣾⠋⠀⠈⠓⠈⡙⠨⠟⣿⣟⡿⣷⣌⠀⠀⠀⢩⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠀⠀⠀⠒⠙⠁⠁⣼⡄⠀⠀⠀⠀⠀⠀⠐⠖⠀⠈⡈⣉⣡⡔⠀⠀⠀⢋⢁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣛⣻⡅⠀⠀⠀⠀⠠⣌⡀
⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣴⣿⢇⡀⠀⠀⠀⠀⢢⢥⡀
⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠠⢤⣀⡀⠀⢠⣿⣷⠛⠋⠃⢹⣄⠀⠀⠀⠀⠢⡴⢄
⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠈⢧⠀⠀⠀⠀⠈⠲⣛⢢
⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠉
⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠄⡏
⠀⠱⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡞
⠀⠀⠹⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡜
⠀⠀⠀⠘⢦⡈⠦⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣠⠋
⠀⠀⠀⠀⠀⠙⢦⡉⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡠⢠⡐⠊⠣⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠆⠝⣘⠥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢬⣑⡤⣀⣉⠡⠔⠍⠄⣀⡀⣂⠀⠀⠀⢐⡤⠔⠊⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣿⣿⣿⣶⣶⣶⣶⣶⣶⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣀⣩⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠰⣏⣝⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⣍⣹
⠀⠈⠻⠻⣿⣵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢿⡿⠟⠟
⠀⠀⠀⠀⠀⠻⢯⡷⣄⡀⢀⢠⠠⢀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡠⠤⡄⡀⢀⣴⢮⡽⠋
⠀⠀⠀⠀⠀⠀⠈⠹⢿⣏⠟⣴⠟⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣦⠻⣙⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣙⣣⣼⢟⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣻⣧⡜⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣧⠋⠈⢻⣯⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡟⠁⠙⣌⠂
⠀⠀⠀⠀⠀⠀⠀⡺⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⠑⢄⠀⠀⡠⠊⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠑⢎⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢿⣧⣀⠙⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⣾⡿⢻⣧⡀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⣾⡿⠋⠀⠀⠙⢿⣦⡄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠙⢿⣶⡀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠑⢄
⠀⠀⠀⠀⠀⠀⡠⠊⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠑⢄
⠀⠀⠀⠀⢠⣾⢞⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡳⣷⡄
⠀⠀⠀⣰⠟⣱⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣎⠻⢆
⠀⠀⠐⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⡤⠴⣯⣤⡶⠿⠉⢱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡎⠁⠽⢶⣤⣽⠦⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠣⠤⠼⣧⣄⡠⠾⠻⣿⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣿⠟⠷⢄⣠⣽⠦⠄⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⡤⠂⢀⠟⠀⢙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡋⠀⠻⡀⠸⢤⣬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⠀⢀⡾⡟⠉⠀⠀⣤⡀⠀⣀⠀⠀⡀⠀⢀⣤⠀⠀⠉⠻⢷⡀⠀⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣾⡇⠈⣧⣥⠀⠀⠀⢸⡇⠀⢾⡁⣀⡷⢀⣸⠇⠀⠀⠀⣈⣼⠁⢸⣷⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢆⣸⣅⠷⣄⣀⣌⢉⣅⣈⣉⣯⣥⣼⣯⣱⣀⣠⡾⣨⣇⡰⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⠀⣿⣧⡤⠞⠁⣽⣿⠈⠣⣤⣬⣿⢀⣴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⣿⡗⢀⡸⢃⡈⠤⢘⡇⠁⢩⣛⡏⣿⣻⡯⢿⣏⡇⠤⢁⡘⡇⡀⢚⣿⠷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣆⡈⠠⣼⣌⣰⠤⠛⣥⣶⠿⠀⣀⣄⠀⠀⣿⢈⣐⣸⡇⠿⣶⣼⠛⠴⣆⣡⣧⠄⢁⣱⠶
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢻⠞⠋⣩⠿⢠⡀⢉⣿⡛⠀⠐⠁⠀⠀⣿⠀⠈⢺⡇⢚⣿⡈⢀⡄⠿⣍⠙⠷⡟⠀⣀
⠀⠀⠀⠀⠀⠀⣀⠄⣉⠛⠉⣠⣾⠗⣦⣼⠟⣋⠛⠣⢌⣁⣀⠄⠀⢻⠀⣂⣨⡭⠜⠛⣙⠻⣧⣴⠺⣷⣄⠉⠛⣉⠠⣀
⠀⠀⠀⠀⠀⡾⢿⠀⠻⣀⣠⣮⡍⢽⡟⠡⠞⠁⠉⠉⠈⠉⠉⠙⠳⠞⠋⠉⠉⠁⠉⠈⠈⠳⠌⢻⡯⠉⣵⣄⣀⠟⠀⡿⢷
⠀⠀⠀⠀⠀⠁⠀⢀⣾⣿⣿⠇⠀⣠⣿⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣄⠀⠸⣿⣿⣷⡀⠀⠈
⠀⠀⠀⠀⠀⠐⣊⣯⣭⡁⠀⠀⣰⡿⢛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡛⢿⣆⠀⠀⢀⣭⣽⣛⠂
⠀⠀⠀⠀⢀⡜⠛⢉⣽⡿⢃⡾⠁⣵⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣮⠈⢷⡘⢿⣯⡉⠛⢣⡀
⠀⠀⠀⠚⢩⣧⣴⡉⠛⠉⡏⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⢹⠈⠛⢉⡦⣼⡍⠓
⠀⠀⢲⡴⡟⠁⢘⠏⢠⡶⠶⢻⡗⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⢼⠛⠶⢶⡄⠹⡓⠈⢻⢦⡞
⠀⠀⠘⣆⣀⣶⠇⠐⠊⠠⠰⣤⡗⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣤⠆⠄⢑⠂⠸⣶⣀⣼⠃
⠀⠀⠀⠈⠻⠿⡶⢴⣶⣤⢠⣿⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣿⡄⣤⣶⡦⢶⠿⠟⠁
⠀⠀⠀⠀⠀⠠⣦⢀⣿⣿⣮⡁⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⢨⣵⣿⣿⡀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠍⠹⢁⡻⣿⡆⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⢰⣿⢟⡉⠏⠩
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⠷⢿⣷⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣾⡿⠾⡇⠀⠀⢀
⠀⠀⢀⡄⠈⢀⣿⣄⢰⣤⡆⠀⢻⡿⣷⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣾⠿⡟⠀⢰⣤⡆⣠⣿⡀⠁⠠⡀
⠀⠀⠘⠟⠛⠙⢿⣿⢮⠀⢤⣀⢀⣀⣸⣦⠟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠻⣶⣇⣀⣀⣀⡦⠀⠴⣿⡿⠋⠛⠻⠃
⠀⠀⠀⠀⠀⠀⠸⠙⠇⠀⣏⠈⢿⠟⠛⣿⣦⡈⠢⣄⠀⠄⡀⠀⠀⠀⠀⢀⠀⠀⣠⠔⢁⣴⣿⠛⠻⡿⠉⣹⠀⠸⠛⠇
⠀⠀⠀⠀⠀⠀⠘⠋⠋⠀⣨⣿⡿⠴⡿⠋⠻⡿⣄⠈⢻⣦⣤⣀⡀⢀⣈⣤⣴⡟⠁⣠⢿⠟⠙⣿⠦⢿⣿⣅⠀⠙⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠸⠆⢰⠗⠀⣀⠀⣿⣶⠿⣈⣿⣀⣥⣤⣤⣿⣁⠻⣶⣿⡀⣀⠀⠺⡆⠰⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠽⠾⠿⠟⠃⠙⠛⠉⠉⠉⠙⠛⠋⠘⠻⠿⠥⠯⠜⠁

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

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡛⣙⣟⣩⡛⣻⣛⣻⣟⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣾⣿⠿⠟⠋⠛⠿⣿⣿⣶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠐⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠿⢿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠰⣿⣇⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣤⣀⣠⣴⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⠿⠛⠉

⠀⠀⠀⢀⣠⠖⠛⣿⡆
⢀⡴⣾⣿⣷⣶⣾⣿⣦⡀
⣿⡟⠁⠀⠀⠘⣧⠤⣾⣿⡄
⢹⣦⠀⠀⠀⠀⠘⣷⠟⠋⣹⡄
⠀⢻⡀⠀⠀⠀⠀⠘⢷⣽⣿⣿⡄
⠀⠀⢻⣆⠀⠀⠀⠀⠈⢻⣦⡿⠟⣛⣙⣛⡓⢦⡀
⠀⠀⠀⠹⣕⡤⣤⣤⡴⢞⣩⣶⣿⣿⣧⡀⠉⣳⠇
⠀⠀⠀⠀⠈⠙⠛⠿⠚⠋⠁⠻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠻⣟⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡜⢦⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡙⠦⡀⠈⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡉⠢⡀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡈⠢⡀⠈⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢈⠒⢄⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡁⠢⣄⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣙⠢⣄⣙⠲⠦⣍⡒⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢭⣛⣶⣬⣟⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⣿⣶⣤⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠇⠀⠀⢠⠀⠀⠀⠀⣀⠶⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⢧⠀⢿⣶⠆
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⢀⠀⢠⡟⠀⡴⢃⡴⠛⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠔⣡⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢹⡀⠀⠘⢀⠞⠱⠋⠀⠀⠀⠀⠀⠀⠀⡀⠘⠁⠀⠀⢀⣀⠀⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠒⠌⠉⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠬⠰⠂⠀⠰⠀⠀⠈⠛⠛⠷⠶⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⢀⠀⠀⢀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠉⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠈⠙⠒⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⢀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠉⠲⡄⢤⡀⢀⡀⢀⡰⠒⠚⠁⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⣾⣿⡿⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠤⠂⠐⠐⠒⢆⣀⡀⠀⠀⠀⠀⠀⠀⠰⠆⠙⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠀⠉⠙⠂⠀⠀⠀⠀⠄⠀⠈⠀⢀⡒
⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡀⣁⢀⡀⠀⡀⠀⣀⠤⢤⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣸⠏⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀⡉⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠐⠁
⠀⠀⠀⠀⠀⠀⣾⣤⣷⣶⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠐⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠠⣄⡀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⢿⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢊⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠘⠣⢔⠂⢀⠀⠠⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢠⡶⠤⠤⠤⠀⠀⢴⣭⠷⣤⠀⠈⠒⠛⠀⠀⠀⠀⣤⠞⠠⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⢀⣠⠄⣀⠸⠛⠃⠒⠀⠒⠒⢍⡀
⠀⠀⢰⡦⢒⠂⠀⠀⢂⠀⠺⠈⠀⠀⠠⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠤⠀⠀⠑⢄⣤⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠷⠂⠀⠈⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⢈⣰⠃⠀⠾⠆⠁⠈⠈⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⡀⠀⣀⡀⠀⡄⢠⣶
⠀⢈⠀⠀⠀⠈⠇⠀⠀⢀⣀⡀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠡⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠒⢖⣨⠖⠉⠉⠀⠀⠈⠂⠑⢎⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢰⠋⠀⠀⠸⣷⠀⠀⠀⠰⠆⠀⠱⠄⠀⠀⠀⢀⡀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢊⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠤⠄⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⠀⠈
⠀⠀⠀⠀⠀⠑⠂⠒⠀⠘⠎⠁⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

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


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢀⣟⣆⢸⣭⡝⢸⠉⣥⢸⠭⠅⢙⡏⠀⠀⡇⡞⠉⠁⡏⠉⡇⣿⢦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠈⠀⠁⠈⠙⠉⠈⠛⠃⠈⠁⠀⠀⠁⠈⠛⠁⠉⠋⠁⠉⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠠⠒⠁⠙⠒⠁⣿⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠟⠀⣀⣠⢦⣠⠀⠈⢉⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡆⠀⣠⠟⠀⠀⠈⡗⠀⠈⠻⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣚⠁⠀⢀⡷⠤⡠⣴⠛⠀⠀⣰⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⠀⠸⣯⡀⢧⡀⠀⠀⣠⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠷⠲⣦⡿⢿⣌⡛⣦⢤⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⣷⡉⣿⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⢾⠁⣴⣧⣈⣿⣯⢹⡷⢶⣦⣤⡀⠀⠀⠀⠀⠀⢰⡟⠉⠋⠉⠛⠛⠳⡄
⠀⠀⢠⡞⣉⠀⢻⠀⢹⠑⢲⡄⠀⠀⠀⣠⡶⠟⠉⠀⡀⣼⠳⢬⣛⣛⣛⣩⣼⣷⣄⠀⠉⠻⣷⣦⡀⠀⠀⣼⠁⡈⠀⢰⠀⢀⡀⠹⡄
⠀⠀⣼⠁⢿⣀⣼⣀⣼⣀⣸⡇⠀⢠⡾⠋⠀⠀⢰⣾⡸⣧⡀⠀⠘⣿⣿⣿⣸⣿⣿⠃⠀⠀⠀⠻⣿⣆⠀⠻⣦⡽⢦⣈⠦⠤⠃⡀⢹⡆
⠀⣼⠛⠀⠀⣉⣛⣧⣄⣨⡟⢀⣴⠟⠛⢶⡄⠀⠘⣿⣷⣽⣿⣿⣾⣿⣿⣿⢿⠿⠋⠀⠀⡄⠀⠀⢼⣿⣧⠀⠙⠶⠶⢾⣶⠳⠛⠁⠀⢳⡀
⢀⣿⠃⠀⠀⠈⢻⡟⠉⠉⠀⢸⡟⠀⠀⠀⠁⠀⠀⠈⠛⠿⣿⣿⣿⣋⡿⠋⠉⠀⠀⠀⠘⣷⡀⢀⣽⣿⣿⣧⣀⣀⡀⢸⡇⠀⠀⠀⠀⠈⢳
⣼⠇⠀⠀⠀⠀⢸⣿⣤⣤⣤⣼⣿⠰⣿⣿⣦⠀⠀⠀⠀⠙⢿⣿⠿⠁⠀⠀⠀⠀⠀⠒⠚⠛⠻⣾⣿⣿⣟⣿⠟⠛⠛⠻⣧⡀⠀⠀⠀⠀⢨
⣿⡀⠀⠀⠀⣠⡿⠛⠉⠈⣉⣿⡟⠇⣿⡃⣼⣧⠀⠀⢰⠀⠀⢠⠀⠀⠀⠀⢀⣀⣤⣄⠀⠀⠀⠈⣿⣿⡾⡁⠀⠀⠀⠀⠈⠑⠢
⠘⣷⡀⠀⠀⠀⠀⢤⣤⣴⣿⣿⡇⠀⢸⣧⣻⠿⢷⣤⣼⢠⡀⣏⣀⡀⣠⡶⣿⣯⢏⡽⠟⠒⢀⣼⡹⣿⣿⣷⣤⣀⣀⣀⣴⣀⣠⣠⡄⣀⣤
⠀⠘⠷⣤⣶⣶⣶⣶⣿⣿⣿⣿⣷⣠⠏⠉⠉⠛⠏⢙⣿⡷⠓⠾⢻⣟⡓⠒⠚⢛⡿⠚⠉⠉⢽⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⠀⠀⣰⠀⠀⠉⢧⣍⠀⣠⣤⣼⠟⠉⠀⠁⢀⣀⣨⡿⠎⢿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣧⣦⣘⣶⡶⢤⣀⠚⠿⠟⠋⣀⣠⠤⠖⠋⢉⡽⣰⠃⣠⣾⣿⠟⢋⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⢿⣿⣿⣿⣦⣈⣉⣛⣋⣉⣉⣀⡤⠔⠶⣋⠔⣡⣾⢿⠟⢁⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣇⠀⠿⣏⣀⠉⠉⠉⢁⣀⣠⠴⠚⠁⣠⢜⡵⣋⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣀⡈⠉⠉⠉⠉⢁⣀⣤⣶⣿⣿⠿⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣻⣿⣿⣿⣿⣛⣛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠆⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡆⢀⢠⣦⡀⠀⢀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⣿⡟⠙⣿⣇⠀⠀⠀⠀⠀⠠⠃⠈⣿⣿⡿⠟⢛⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠙⡿⣫⡷⢟⣛⣛⠿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢰⣿⡇⢰⣿⡿⠀⠀⣀⡀⠖⣃⣀⣴⣿⣯⣶⣿⣿⣿⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⣀⣿⣿⣿⣿⣾⣿⣿⠟⢃⠄⣷⣄⢀⢸⣿⣶⠀⣶⣿⠇⠀⠀⢉⠛⠛⠉⠉⣸⣿⣛⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣽⣿⣷⣿⣿⡯⢀⣤⣶⣿⣼⡿⢙⣃⣿⡏⠀⣿⣿⢀⡂⣲⣿⣿⣶⣄⡀⢿⣿⣿⣿⣿⣿⣿⣿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣋⠏⣰⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⣿⣿⣟⠋⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⣿⣇⢸⣿⣿⣿⡟⡿⢿⣿⣦⣾⣿⣿⢶⡿⣷⣶⣾⣷⠛⡟⣿⣿⣿⣿⣆⢳⠈⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⣴⣿⡿⣿⡇⢀⣾⣿⣿⣿⣿⣯⢸⡇⡟⠿⣿⣿⡆⠀⣿⣿⣿⣷⡏⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢩⣿⢿⣷⣿⡿⢿⠿⣇⣘⣿⣯⣿⣿⣷⣿⣹⣷⣿⣴⣬⣿⣥⣄⣿⡿⣿⣿⠷⣏⡈⠻⣦⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣏⣿⡟⠻⠿⠿⠟⠛⠛⠉⠈⠙⠛⠿⠷⠿⠿⠿⠟⠋⠁⠉⠙⠛⠻⠿⠿⠟⢻⣿⠆⠈⡀
⢀⡀⠀⠀⠀⢰⡇⠀⠀⠀⠂⢿⣿⣞⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣳⣆⠀⠁⠀⠀⢸⡄⠀⠀⠀⢀
⠀⠙⢶⡄⠀⣿⣿⡄⠀⠀⠀⠘⢿⣿⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿⣿⡆⠀⠀⢠⣿⣿⠀⣠⡾⠋
⠀⠀⠀⠈⠳⣿⣿⣿⣄⡠⠊⠡⡘⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠙⢄⣠⣿⣿⣿⠞⠁
⠀⣀⡀⠀⠀⠈⢿⣿⣿⠁⠀⠀⠈⠻⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠁⠀⠈⣿⣿⡟⠁⠀⠀⢀⣀
⠀⠀⠙⠛⠶⠤⣈⣿⠏⠲⣄⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⣠⠖⠹⣿⣁⠤⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⡟⠉⠒⠢⢷⣤⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡿⠔⠚⠉⢻⡀
⠀⠀⠀⠀⠀⣠⠌⠀⠀⠀⠀⠰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠳⢾⣿⣿⣦⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⣤⣾⣿⡷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣭⣛⡀⣹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⢀⣛⣩⣅
⠀⠀⠀⠀⠐⢤⣤⣤⡞⠉⠻⢿⣷⠋⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠹⣾⣿⠟⠋⠰⣦⣀⡤⠂
⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠚⠻⣿⣶⣤⣀⡀⠈⠐⠂⠄⠀⠀⠀⠀⠀⠀⠁⣀⣠⣤⣾⡿⠟⠓⣴⠂⠉⠀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠀⠀⠒⠀⠒⠠⠄⠘⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣲⣦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⣿⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡼⠛⠉⠁⠀⠀⠘⢿⡯⠉⠐⠒⠒⠈⠓⠀⠢⠤⠴⠖⠒⠒⠒⠊⢹⡿⠃⠀⠀⠈⠉⠛⢆⠆
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⠿⢛⣡⣍⠛⠿⣿⣶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠛⢛⣋⣭⣴⣾⣿⣿⣿⣿⣶⣦⣍⣙⡛⠻⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣤⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣙⠻⠿⣿⣿⠿⠛⣩⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣦⣶⣾⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠠⠀⠁⠀⠀⠀⠀⠀⠐⢈⠐⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡠⠂⠀⡀⠔⠈⠀⠀⠀⠄⠀⠒⢀⠒⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠢⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⡠⠊⠀⠀⠈⠀⠠⠀⠀⠀⠀⠄⠐⠂⢀⠀⠀⠀⠄⢀⠀⠀⠢⠀⠀⠀⠀⠈⠢⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠠⠀⠀⠐⠀⢀⠄⠂⠀⡀⠀⠀⠀⢈⠀⠀⠀⠀⡀⠀⠀⢄⠀⠐⢄⠀⠠⠀⠐⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠌⠀⠐⠀⠀⠀⠀⠔⠁⠀⠐⠀⠀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠐⠀⠀⠑⠄⠀⠢⠀⠐⠀⠈⠄⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠔⠀⢀⣴⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣄⠀⠐⠄⠀⢂⠀⠡⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠂⠀⠈⠀⢠⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣽⣿⣧⠀⠈⠀⠀⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⠈⠀⠈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠀⠈⠀⠸⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⢸⣿⣿⣯⣿⣿⣯⠀⠀⠀⢨⣿⣿⣯⣿⣿⣿⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⠀⢠⠀⢀⠀⠀⠀⠈⣿⣿⣿⣿⣻⣿⣶⡤⣴⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⠀⢠⠀⢠⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠄⠀⢂⠀⠘⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⢀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠈⠄⠀⠠⡀⠈⠻⢿⣿⣿⣿⣷⣿⣿⣿⣿⠿⠋⠀⡠⠂⢀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢂⠀⠠⡀⠀⠄⠀⠀⡀⠈⠂⢀⠀⠉⠙⠛⢛⠛⠛⠉⠀⠀⠀⠊⠀⡠⠀⠀⠄⠀⡠⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢄⠀⠀⠀⠈⠀⠄⡀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⡀⠄⠈⠀⠀⠀⢀⠔⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⢄⠀⠑⢄⠀⠑⠀⠀⠀⠁⠂⠀⠀⠈⠀⠀⠀⠂⠁⠀⠀⠐⠁⢀⠔⠁⢀⠄⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⡀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠐⠂⠈⠀⠀⠀⠂⠀⡀⠄⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⢈⠀⠀⠐⠂⠀⠀⢀⠠⠐⠈⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⣀⠀⢀⠀⠀⢀⡞⠁
⠀⠀⠉⠂⢸⣦⣀⣈⣠⠖⠀⠀⢀⡀⠀⠀⢀⡀⡀⠀⢀
⠀⠀⠀⠀⢠⠁⠉⠀⢇⣀⡀⠉⠉⡁⠔⢺⠼⠒⠀⠑⢮⠱
⠒⠒⢂⣴⣏⣀⢀⣴⠛⡅⡄⣆⠧⠐⠈⠀⠀⠀⠀⠀⢘⢈⡀
⠀⠈⠉⠀⡀⠘⡿⠸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠾⠶⠶⠤⣤⣤⣀
⡤⠞⠁⡼⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⠀⠀⣀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⠿⠛⠛⠛⠛⠛⠛⠛⠿⣿⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠁⢚⠥⠒⠀⠢⣀⠀⠀⣀⠀⠀⡈⠀⠀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⡰⠃⠀⠀⠀⠀⠈⢣⠊⠀⠀⠀⠈⠲⡀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⢰⠃⠀⠀⠀⣠⡄⠀⠀⡇⣀⡀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⣭⡿⠀⠀⡗⣼⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠛⠁⠀⢠⡇⠈⠁⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⣠⠋⠙⢄⡀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠊⠁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠒⠖⠢⠤⢄⣀
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠄⠀⠀⠀⠀⠉⡗
⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⠠⠠⢤⡤⠤⡀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⢸⠀⢀⡀⢐⠈⠀⣃⠀⢀⡁⡁⣐⣀⣀⣀⣳⣄⡀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⣤⣤⣀⣀⣀⣤⣤⠤⠶⠚⠋⠁

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



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠛⠉⠉⠁⠈⠉⠉⠛⠻⢿⡿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⢀⣠⣤⣶⣶⣶⣶⣤⣄⠀⣠⣿⣬⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⢀⣴⣿⣿⠿⠛⠛⠛⠛⠿⣿⣯⢟⠟⠁⠹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⢀⣾⣿⠟⠁⠀⣀⣤⣤⡀⣠⠞⠹⣿⣷⡀⠀⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⢸⣿⡟⠀⠀⣾⣿⡿⣿⣿⣷⠀⠀⢻⣿⡇⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢻⣿⣇⠀⠀⣿⣿⣦⣵⣿⣿⠀⠀⣸⣿⡟⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠘⣿⣿⣄⠀⠈⠛⠿⠿⠛⠁⠀⣠⣿⣿⠃⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠘⢿⣿⣷⣤⣀⣀⣀⣀⣤⣾⣿⡿⠃⠀⢠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⡀⠀⠙⠻⠿⣿⣿⣿⣿⠿⠟⠋⠀⢀⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⡛⠋⠉⠛⡲⠤⣄⡀⠀⠀⢀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⠁⠀⠰⠁⠀⣀⠊⠀⠀⣀⠉⠶⢄⡈⠑⠤⠞⠁⠀⠹⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣠⠞⠛⠉⠉⠙⠲⢤⣀⠀⠀⠄⠙⠲⢤⠀⡤⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠟⡄⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⡳⢦⣀⣀⣾⠀⣳⡄⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠋⠉⠉⡟⠀⠡⢀⡾⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⣤⠈⠍⢁⣸⠇⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣻⠹⣄⡀⠀⠀⠙⠦⠤⠞⠁⠀⠈⢳⡤⢄⡀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠋⠀⠀⢀⣀⢸
⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⢻⣀⠀⠉⠓⠶⠤⠤⠤⠤⠤⠴⠒⢫⠇⠀⠈⠓⢦⣄⠀⠀⠀⠸⠖⠋⠙⢦⣀⡟⠈⠛
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⣀⣀⣀⣀⣠⣤⠴⠋⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⣰⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⠟⠀⣠⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠁⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠋⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⠆⠀⣠⣾⡿⠋⢀⣴⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠁⠀⠀⣠⣾⣿⣿⡿⠟⠛⠋⠙⠛⠛⠁⣠⣾⡿⠋⠀⠀⠈⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⠀⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⢀⣴⣆⠀⠀⠈⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢠⣿⣿⣿⠁⠀⠀⣰⣾⣿⣿⣿⣿⠋⠀⠀⣿⣿⣿⡄⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣏⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣹⣿⣿⡇⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠘⣿⣿⣿⡀⠀⠀⠹⢿⣿⣿⡿⠋⠀⠀⢀⣿⣿⣿⠃⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏⠀⠀⢀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⡀⠀⠀⠙⢿⣿⣿⣷⣦⣤⣄⣠⣤⣴⣾⣿⣿⣿⠋⠀⠀⢀⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⣠⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⢀⣤⣾⣿⣷⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣦⣤⣀⣀⣀⣀⣀⣀⣤⣴⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣄⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠛⢻⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡏⠉⠁⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣄⠘⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡿⢿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣀⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⢿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣴⡞⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠟⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⢠⣴⡄⠀⠀⠀⠀⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣴⣤⡿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⣄⣀⣀⠀⠀⢀⡄⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠋⠉⠉⠙⢋⣀⠀⢈⣀⠈⠛⠛⣶⣶⣶⣦⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⣀⢸⣧⣀⣠⣶⣦⠸⠿⣿⡟⠛⠿⢆⡾⠉⠀⢀⣿⡟⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⠈⢻⣿⡏⠉⠀⡄⠉⢡⣤⡀⢸⣿⣿⢻⣿⡏⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡄⠀⠈⠿⠃⠀⢀⣤⠘⢿⡟⠁⠀⠈⠁⠸⣿⠏⢹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣴⡿⠃⠀⣀⠀⢰⣿⣿⡟⠓⠀⠀⣴⡦⠤⠀⠀⢀⣾⣿⣉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢃⠀⠸⣿⣿⣞⠛⢿⣦⡀⠀⠀⠀⣤⡀⣠⣶⡟⠋⠹⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⡇⠀⠈⠛⣿⡦⠀⠉⢹⣶⣦⣠⣿⡿⠉⠉⠷⠂⠀⣀⣀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠀⠀⠀⠙⢷⣤⡀⠈⠻⣿⠟⠁⠀⠸⠇⢀⣴⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⢰⣦⣀⣠⡀⣨⣿⣿⠿⠃⠀⠀⠀⣀⣀⣰⣿⡿⠿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⣤⣾⠏⢀⣀⠀⢶⡟⠙⠛⠋⠀⢻⣿⢧⣴⣶⡿⣿⣿⡟⠛⠋⠀⠀⣤⣼⠋
⠀⠀⠀⠀⠂⠀⢀⣴⡿⠁⠀⠀⠀⣀⣼⣿⡿⢿⣤⣴⠗⢠⣤⡶⠊⠁⠀⣹⡿⠁⢀⣿⡿⠀⠀⠀⠀⠀⠉⠀⠈
⠀⠀⢰⣶⡆⠀⠈⢙⣥⣶⠟⢳⣶⠟⠛⠻⣇⠀⠻⢿⣤⡾⠿⠃⢀⠀⠀⢻⡿⠀⠀⠙⠁
⠀⠀⠈⠉⠀⠀⠻⠟⠋⠀⠀⠀⢠⣶⣦⠀⠈⠀⣀⣠⣿⣿⠀⠀⣿
⠀⠀⠀⠀⢿⣶⠄⠠⠶⠄⢰⣿⣿⠟⠉⠀⣀⣀⣿⠏⠀⣿⠆⠘
⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⣿⡟⠉⠀⣀⣴⣿⠿⠁⠀⢸⣿⡆⠀⢠⡄⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠏⠁⠰⣿⠟⠉⠀⠀⠀⣶⣿⡋⠀⠀⠈⠁⠀⣤⣀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣤⠀⠘⠛⢂⣤⡄⠀⣀⠀⢀⣤⣴⣿⠛⠉⠙⠛⠓⢠⣤⡄⠀⣿⣿⡗⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠈⠉⠻⢿⣿⣿⣶⣆⠀⠀⠀⠻⠇⠀⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⡿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⢹⣿⡏⠉⠁
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢀⡼⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡋⠀⢠⡄⠀⣄⠀⠀⠈⠉⡷⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⠛⠀⢀⡀⠀⠀⠀⠈⢹⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢀⣄⠀⢻⣷⡄⠀⠀⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠙⢻⣦⣀⠘⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⢹⠟⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣿⠀⠘⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠆⠀⠘⠇⠀⢿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⡀⠀⢴⣦⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠷⠀⠙⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⢰⡆⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠿


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠻⠿⠟⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣴⣦⣤⣤⣤⣤⣤⣶⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⢀⣠⠖⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠈⠳⠤⠋⢀⡀⠘⣆⣠⣤⠤⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⠀⡴⣄⠀⡴⠋⡇⢀⣀⣤⡄⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢉⡀⡇⠈⠛⠁⠀⠙⠉⠰⠯⢤⣄⡉⠙⠒⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢰⠈⠁⠀⣀⢠⠀⡀⠀⢠⠖⢋⣩⠤⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠈⣣⠀⠀⢻⣛⠛⡇⠀⠈⠙⢮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠮⢤⣘⣛⡳⠤⠤⡼⠨⢠⠇⠺⠿⣝⢛⣁⣘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢑⡏⠀⣾⣛⣛⣛⣋⣁⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠈⡸⠃⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣤⠚⠁⠈⠙⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣏⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆
⠀⠀⠀⠀⠀⠀⣰⠟⠁⣠⡤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣶⡛⣷⠀⠀⢻⡆
⠀⠀⠀⠀⠀⣼⠏⠀⡴⠋⠀⢀⣿⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠈⢻⡄⠀⠀⠈⣷
⠀⠀⠀⠀⢸⡟⠀⣸⠃⠀⢰⣿⣿⣀⣠⡄⣠⣴⣿⣇⠀⠀⠀⠀⢸⣷⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠈⠉⣿⠁⢹⠻⢿⡿⠟⠀⠀⠀⠀⣸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⣷⠀⢻⣄⠀⠀⠀⣰⡏⠀⢸⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠹⣦⠀⠉⠛⠓⠛⣋⣀⣀⠘⣷⡀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠉⠉⠹⡷⠈⠛⠷⠶⡶⠟⠋⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣶⣤⣤⣄⣀⣀⣀⣀⣠⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁
⣿⣿⣿⣿⣛⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣻⣿⣛⣻

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⢓⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⠋⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⣿⢧⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⢿⣿⣯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⣭⣽⢪⣵⣶⠧⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡠⣷⣾⣭⢺⣭⣍⢦⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣎⡧⠿⢿⡉⠢⣈⡦⣐⣬⣽⠶⠾⣿⣿⣿⡿⠶⢾⣭⣖⡠⣎⡠⠊⣹⠿⠧⣏⣾⣿⣿⣷⣦⣀
⠀⠀⢀⣠⠴⢾⡏⣩⣿⣿⣿⢿⠏⠀⠀⢀⡹⣪⣷⢟⡫⠵⠊⠉⠹⣿⣿⣿⠉⠉⠉⠒⠭⣛⢷⣯⡺⡁⠀⠀⠈⢾⢿⣿⣿⣯⡉⣿⠶⢤⣀
⡔⢻⣿⣷⣿⣷⠛⣡⠍⠙⢻⠏⠀⠀⡠⣫⡾⣫⠖⣿⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠑⢮⡻⣮⡢⡀⠀⠈⢿⠛⠉⢥⡙⢳⣿⡷⣿⣿⠓
⠈⠢⣙⠻⣆⣶⣧⠻⠾⢃⡏⠀⠀⣜⣼⢏⡞⠀⠀⠉⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⢿⣞⣄⠀⠈⣇⠻⠾⢣⣷⣆⠾⢛⡡⠊
⠀⠀⠈⠓⢦⡐⠿⢛⣿⡿⠀⠀⣎⣾⢣⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢣⢻⣞⡆⠀⠸⣿⣞⠿⠗⣠⠖⠋
⠀⠀⠀⠀⠀⠈⠓⠮⠽⠃⠀⡸⣼⡏⠇⠀⡇⢠⠞⠁⠀⠊⠀⢀⣴⣾⣯⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⢏⣿⡼⡀⠀⠻⠭⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣸⠀⠀⣷⠋⠀⠀⠀⡀⣰⣿⣿⡿⠷⠿⣿⣿⣷⣀⡀⣠⠀⠀⢀⡇⠀⢸⣸⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣟⣿⠀⢀⣠⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⢻⠛⠛⠟⡿⠛⠛⠛⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠟⢿⡿⢛⡿⠟⠛⢻⢻⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢿⡞⡄⠀⡁⠃⠀⠀⠀⠈⠹⣿⣿⣿⣷⣿⣿⣿⠿⠋⠀⠈⠁⡜⠁⡇⠀⡜⣾⢯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⡱⡀⡇⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⠋⠁⠀⠀⠀⠀⠜⠀⠀⡇⡰⣹⡟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⢷⡕⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⣵⢟⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣮⡻⣮⡳⣄⠀⡆⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢀⡴⣫⡾⣫⣎⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⣾⠃⠈⠪⡻⢶⣕⡣⢤⣀⣸⡀⢸⣿⣿⠀⠀⢀⣠⠤⣒⣵⠾⡫⠈⠀⢻⣆⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⣾⠃⠀⠀⠀⠈⠑⠫⢛⡷⢶⣯⣥⣿⣿⣿⣧⣭⣷⠶⣟⠫⠑⠁⠀⠀⠀⠀⢻⣆⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⣤⣾⠇⣄⠀⠉⢳⠄⠈⠀⠀⠨⠉⠒⠚⠛⠛⠛⠛⠒⠊⡉⠰⡆⠀⠀⠀⠀⠀⠀⠀⢿⣦⣄⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⠷⠏⠀⠘⢦⡀⠂⠲⠀⣤⡀⢰⠀⡦⠀⡆⡰⠀⡆⠀⠈⠈⠓⠸⡀⠐⢤⠂⡔⠀⠀⠈⠷⠿⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠉⠈⠀⠁⠀⠁⠈⢀⠇⠀⠀⠉⠀⠀⠁⠈⠀⠁⠈
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣵⣶⣦⣾⣵⣿⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠙⠷⡄⠀⢷⡀⠀⠀⠚⠁⢀⡠
⠀⠀⠀⠀⠀⠀⢸⡟⣦⣤⠤⣶⠏⠀⠀⢀⣠⣤⣄⠀⠀⣀⡠⡄⢰⢂⡲⠂⣤⡀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠰⣧⣀⣀⡀⠉⠉⠀⣠⠴⠊⣩⠰⠓⠉⠉⠁⠻⡤⠙⡆
⠴⠶⠶⠆⢀⣴⠃⠀⠀⢀⣴⡾⣏⢉⡅⡤⢲⡉⣥⠔⠋⠁⠀⠀⠀⠀⠀⠀⡦⠘⡇
⠀⠀⢠⠶⠛⠛⠛⢻⣆⡟⣹⠂⠖⠰⠆⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠚⣇
⠀⠀⢀⡀⠀⢠⠄⠀⣿⠁⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡶⠾⠿⠛⠛⠛⠛⠛⠿⠿⢶⣶⣄
⣠⡶⠋⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣶⣆⣀⣀⣀⣀⣀⣀⣠⣶⣦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣶⣿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠉⠉⠙⢿⡿⠶⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠟⣡⠤⠐⠂⠤⣀⠀⠀⠀⠀⠀⣀⡀⠀⠉⠀⠀⠈⠙⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠈⠳⡄⣠⠖⠉⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠟⠁⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⣷⢀⣠⡀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⣹⣿⠀⠀⠀⣿⢨⣹⣧⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿⠟⠀⠀⠀⡾⠈⠿⠇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⡴⠋⠈⠳⣄⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣤⠴⠋⠀⠀⠀⠀⠈⠙⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠚⠉⠛⠙⠛⠲⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⣀⢀⠀⢀⡀⠀⠠⠄⠀⠀⠉⢻⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣀⡠⢤⡀⠀⣀⣀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡀⠶⠀⠰⠀⠈⠋⡤⠈⠓⢀⡀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣀⣠⣌⣤⣥⣀⣄⣤⣤⣤⣤⣥⠤⡤⠼⠤⠤⠴⠦⠤⠼⠶⢶⡄⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⡴⠶⠞⠛⠉

⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⢠⠏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠹⡄
⠀⠀⠀⡾⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢷
⠀⠀⠀⡇⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢸
⠀⠀⠀⡇⠀⡄⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢠⠀⢸
⠀⠀⠀⢧⠀⠸⡄⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢠⠇⠀⡼
⠀⠀⠀⢸⡆⠀⠹⡄⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢠⠋⠀⢰⡇
⠀⠀⠀⠀⢧⠀⠀⠈⠂⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠐⠁⠀⠀⡼
⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⢄⠀⠀⠈⠑⢦⡴⠚⠁⠀⠀⡀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠈⠢⣀⠀⠀⠙⠲⣄⡔⠁⠀⣀⠴⠋
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⣳⢤⡀⠈⠑⠤⡀⠀⠈⠙⠶⣞⠁⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⣟⢿⣿⣦⠀⠀⢀⣠⠖⠋⠁⠀⣈⠷⢦⣄⠈⠑⠠⣀⠀⠈⠙⠲⢄⡀⠀⠀⣴⣿⡿⣻
⠀⠀⠀⠀⠙⢮⣿⣿⣷⠚⠉⠀⠀⠀⠀⢈⣀⡤⠖⠋⠙⠲⢤⣀⠉⠂⠀⠀⠀⠉⠓⣾⣿⣿⡵⠋
⠀⠀⠀⠀⠀⣠⢾⢿⣿⢷⣄⣀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣠⣾⣿⣿⡷⣄⡀
⣴⣶⣶⡴⢟⣫⡴⠞⠛⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⣽⣿⠛⠳⢦⣝⠻⢦⣶⣶
⢿⣿⣿⣿⡟⠉⠀⠀⠀⠙⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠋⠀⠀⠀⠉⢻⣿⣿⣿
⠀⠙⠻⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣶⣶⣼⣧⡙⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣷⣍⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠄⠒⠒⠠⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠓⢬⡳⢄⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣑⢦⡀⣠⠖⠁⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣍⠣⣀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠑⢮⡳⢾⣿⣿⣿⣿⠿⠛⠛⠋⠉⠛⠛⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⣰⣿⣦⣙⢿⡋⠀⢀⣤⣴⣶⣶⣶⣤⣄⠀⠈⠻⣿⣿⣿⣷⡀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣰⣿⣿⣿⠏⠓⣍⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠘⢿⣿⣿⣷⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣿⣿⣿⡏⠀⢰⣿⣷⣮⡛⢏⣁⣀⡉⠻⣿⣿⣿⣧⠀⠘⣿⣿⣿⡇⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⠁⠀⣿⣿⣿⡟⠉⣦⣙⢿⣿⡆⢸⣿⣿⣿⡆⠀⣿⣿⣿⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⣿⣿⣿⡆⠀⢻⣿⣿⣷⡀⠻⣿⣿⡿⠁⣸⣿⣿⣿⠁⠀⣿⣿⣿⡿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣿⣿⣿⣷⠀⠈⢿⣿⣿⣿⣦⣤⣤⣤⣾⣿⣿⣿⠏⠀⣰⣿⣿⣿⠇⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠘⣿⣿⣿⣷⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣴⣿⣿⣿⡟⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠘⢿⣿⣿⣿⣦⣄⡀⠈⠉⠉⠉⠉⠉⠀⣀⣴⣾⣿⣿⣿⠏⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⠀⠀⠈⠉⠉⢻⣿⣿⡏⠁⠀⠀⠀⠀⠈⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃