Gems Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⣡⢻⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⡰⠃⡏⢸⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠑⠒⠂⣴⠁⢀⠇⠈⡆⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠑⡎⢩⣒⠤⣄⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠃⠳⣸⣠⠴⡷⠤⣘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡱⣄⡈⠁⠀⠉⣷⠀⠀⠀⠀⡞⠀⠀⠀⡎⠀⢀⡏⠀⢸⠀⠀⡴⠍
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⣰⠁⠀⠉⠓⠦⡼⠀⡆⠀⠀⢀⡇⠀⠀⢸⠁⠀⡸⠀⠀⡇⠀⡰⡹
⠀⠀⠀⠀⠀⠀⠀⢸⡑⠦⣤⠃⠀⠀⠀⠀⠀⣿⠀⣇⠀⠀⢸⠀⠀⢀⠇⠀⢠⠇⠀⣸⠁⠀⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠸⡄⠀⠀⠀⠀⠀⢻⠀⢸⠀⠀⡏⠀⠀⡼⠀⠀⡼⠀⢀⡇⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢧⠀⠀⠀⠀⠀⢸⠀⠸⡀⢠⠃⠀⢠⠇⠀⢰⠃⠀⢸⠀⠈⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠸⡆⠀⠀⠀⠀⢸⠀⠀⡇⣼⠀⠀⡼⠀⠀⡞⠀⠀⡇⠀⡸⠀⠀⠀⣀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⣀⣀⣀⣀⠀⠸⡄⠀⢳⠀⠀⠀⠀⢸⠀⠀⢷⡇⡎⢀⠇⠀⢰⠃⠀⢸⠁⢠⡧⠖⠚⠉⣀⢾⠒⠋⡹⠙⡆
⠀⠀⠀⢠⠿⡙⠮⣝⠉⢩⢷⠀⠘⡇⠀⠀⠀⢸⠀⠀⢸⣱⡀⢸⠀⣀⣏⠀⠀⡏⠀⡾⣀⡤⠖⠋⠀⠀⠑⡶⠥⢤⠟
⠀⠀⠀⢸⠀⢣⠀⢀⡹⢧⠸⡆⠀⢻⠀⠀⠀⢸⡆⠀⢸⣯⣃⣿⣍⠀⠀⢙⣶⡧⠚⢯⡁⠀⠀⠀⠀⢀⡞⢡⡾⠋
⠀⠀⠀⣾⣠⠤⢷⠋⠀⠈⢇⢻⠀⠘⡇⠀⠀⣸⡇⠀⠀⡟⠁⠸⡄⣹⠚⠉⠘⡇⠀⢀⣵⡀⠀⠀⢠⠏⣠⠟
⠀⠀⠀⠈⠢⡀⠀⠳⡀⠀⠈⢿⣇⠀⢹⣀⣀⡿⠧⠴⠧⣷⣠⠤⠟⠳⠤⢤⣀⡧⠖⠉⠀⢣⠀⣰⠋⡴⠃
⠀⠀⠀⠀⠀⠈⠳⣄⠙⢆⣀⠤⠟⠚⠉⠁⠀⢀⣀⡤⠖⠊⢳⡀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠘⣴⢧⡞
⠀⠀⠀⠀⠀⠀⠀⢈⡟⠯⣄⡀⣀⡤⠴⠒⠋⠉⠀⠀⢀⣠⠴⡇⠀⠀⠀⠀⠀⠘⡆⠀⢀⡞⠀⠎⡇
⠀⠀⠀⠀⠀⠀⢠⡿⢀⡠⠖⠻⡀⠀⠀⠀⣀⡤⠴⠚⠉⡀⢸⠁⠀⠠⠄⠀⠀⠀⢹⣀⠞⠀⢀⣀⡇
⠀⠀⠀⠀⠀⠐⢷⡾⠥⠤⠄⡀⣧⠴⠒⠋⠁⠀⣀⣠⠴⠒⠙⣏⠉⠛⠓⠒⠒⠒⣲⠟⡊⣉⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠢⣔⠀⡰⢃⣀⣤⠶⠞⠉⠉⠒⠤⣀⠀⠘⣆⠀⠀⣀⠴⠋⣐⠽⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠈⠉⠓⠲⠤⣄⣀⡀⠙⠒⠾⡦⢊⣡⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠋⠉

⠀⠀⠀⠀⢀⢠⠒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡖⢄
⠀⠀⠀⠀⠋⠉⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠐⢠⠄⠂⠁⠂⠤⠐⠆⠀⠀⠀⠀⠀⢀⠀⡀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⢣⠊⠈⢠⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⢗⠒⠗⠒⠒⠗⢒⠗⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠦⣤⠀⠰⡤⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠂⠄⢂⠁⠔⠃⠀⠀⠀⠀⠀⠀⠁⢈⠀⢐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⢎⠢⡠⢊⠘
⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠓⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⠻⠄⠀⠀⢼⠃⠀⠀⠀⠀⠀⠀⠐⠃⢀⠜⠙⢄⠀⠓⠀⠀⠀⠀⠀⠀⢀⠆⡨⠁⠹⡐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠳⡀
⠀⠀⠀⠁⠄⠀⠀⠀⠈⢄⠡⠀⠀⠀⠀⠮⠀⠴⠡⠤⠤⠤⠰⠆⢨⠆⠀⠀⠀⢠⠵⠂⠀⠀⠀⠈⠢⢡⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄
⠀⠀⢉⠁⠄⠀⠀⠀⠀⠔⠩⠁⠀⠀⠀⠀⠐⢄⠢⠀⠀⠠⢂⠔⠁⠀⠀⠀⠀⠰⠠⡀⠀⠀⠀⠀⡠⠰⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠍
⠀⠀⠀⠡⣠⠄⠀⠀⢼⡐⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⠲⠀⢰⢂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢲⣠⠃
⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠔⠩⠀⠀⠀⠤⠑⠄⠀⠀⠀⠀⠀⣠⢼⡅⢈⣏⠀⢽⣤⡀⠀⠀⠀⠀⣠⠞⠉⠀⠰⠈⠁⠙⢦⡀⠀⠀⠀⠀⠀⠴⣈⡀⡇⣌⡰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡌⠀⠀⠈⣄⣠⠇⠀⠀⠀⠘⢁⠒⠘⡃⠒⠂⡛⠐⢒⠝⠀⠀⠀⠀⣌⣐⣊⢢⣧⢊⣓⣈⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⡡⢀⣀⠠⣁⣈⡇⠀⠀⠀⠀⠀⠑⢀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠡⠀⣢⡊⡍⣢⡖⠠⠁
⠀⠀⠀⠑⢬⡁⠀⠀⣉⠜⠁⠀⠀⠀⠀⠀⠈⠹⣅⣠⢧⣀⡽⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⢦⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢍⣇⠡⠘⠃


⠀⠀⠀⠀⣠⡄⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠤⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠄⠀⢠
⠀⠀⠀⠄⣁⠠⠒⠢⢀⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡀⠀⠀⠀⠀⠀⢠⠚⠀⡴⠀⠐⡄⠐⢢⠀⠀⠀⠀⡠⠊⢀⠂⠀⠀⠀⢂⠈⠢⡀
⠀⠀⣖⠀⠁⠀⠀⠀⠀⠁⢸⡄⠀⠀⠀⠀⡤⠤⠔⠁⠀⠑⠤⠬⡄⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠑⢀⠈⠅⠀⠀⠀⠍⢀⠀⠁
⠀⠀⠀⠄⠓⠀⣀⡠⠐⠃⠌⠀⠀⠀⠀⠀⠈⠢⡀⠁⡄⠁⡠⠊⠀⠀⠀⠀⠀⠰⡀⠈⢆⠀⢀⠎⠀⡰⠀⠀⠀⠀⠀⠀⠑⢌⠀⠀⠌⠔⠁
⠀⠀⠀⠀⠷⠂⠉⠑⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠇⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠁

⠀⠀⠀⠀⠀⣤⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⠀⠀⠰⡆⠀⠄
⠀⠀⠀⠁⠀⠀⠋⠀⠀⠀⠀⢠⠄⠀⠂⠀⡠⠀⢀⠙⠛⠋⠀⠀⠀⠀⠀⠃⠜⠀⠐⠃⠀⠀⠀⠈⠁⠀⠻⠔⠀⠀⠀⠀⠸⠷⠆⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠡⣄⡀
⠀⠀⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠒⠁⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠈⠃⠀⠀⠀⠈⠁⠀⠀⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⣀⣀
⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠐⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡍⠉⠐⣇⠀⡉⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⠀⠠⠀⠈⠓⢠⠜⠃⠀⡱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠧⠘⠂⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠢⡀⠀⠀⠒⠄⠀⢁⠈⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠙⠀⠇⠀⠘⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠐⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⡄⠀⠀⠀⢰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⡀
⠀⠀⠿⠈⠁⠀⠀⠤⠁⠀⠀⠀⠀⠀⠃⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡐⠀⠀⠠⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⠀⢹
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠀⠀⠀⠑⠢⣀⠾
⠀⠀⠀⠈⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉
⠀⠀⠈⠂⠒⠀⠚⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⢃
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠭⡀⠋⠀⠀⠀⠀⠀⠀⠐⢆⠐⠀⡴⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⠀⡠⢈⡶⠀⠀⠀⠒⠠⠤⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢦⣀⡤⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠈⠀⠰⠆⠀⠀⠀⠲⡶⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠠⠒⠆⠠⠀⠷
⠀⠀⠉⠉⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠠⠄⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⡀⠀⣌⢣⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣀⡉⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡀⠀⠀⠀⣀⡀⠀⡼⢀⠀⠀⠁⠘⠃⠀⢠⠀⠀⠀⠀⠀⠀⡄⠀⠸⢇⠀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠄⠀⠀⢀⠄⠁⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⢡⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠣⠤⠀⠐⠓⠉⠀⢀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠏⠀⠀⠀⣄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠞⢁⠔⠂⠒⣄
⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡈⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⡏⠀⠀⠀⠈⡃
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢣⢀⡀⢀⡶
⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠂⠐⠀⢡⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠠⠶⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣰⢫⠄⠀⠤⠹⢦⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡀⠈⠁⠀⠁⠀⠀⠀⢠⠂⠃⢀⠀⢀⡀⠈⠀⠀⠉⢀⡀⢸⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠰⠀⠀⠀⠁⢡⡄⠁⠠⠄⠋⠀⠀⠀⠀⠀⠀⠀⠚⡍⠉⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠴⠀⠀⠠⠀⠀⠀⣤⣤⠇⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠴⠒⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠁⠒⠉⠄⠀⠀⠀⠀⠀⠠
⠀⢠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⣈⠠⠈⠀⠁⠄⢨⡄⠀⠐
⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡆⢀⠀⠀⠀⠈⠀⢀⠀⠀⠀⢠⣶⣶⣶⣄⠀⠂⠀⠀⠂⠁⠠⠜⢀⠐⡀⠘⢁⠐⡀⠄
⠀⠀⠀⠀⡀⠤⢀⡀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠀⠀⣀⡃⠀⠈⠈⣁⡀⠀⠀⠀⠀⠀⠀⠀⣷⠁⠀⠈⣿⠀⠀⠠⠐⠀⠀⠀⠀⠉⠈⡁⠒⣈⠁⡍
⠀⠀⠆⠘⢁⠀⠀⠙⠋⠀⣄⠀⠀⢀⡀⠀⠀⢄⠀⠉⡄⠀⠀⢀⡉⠁⠀⠀⡀⠀⠀⠀⠀⠹⣷⣤⠾⠟⠀⠀⠀⠀⠤⠀⠐⡀⠓⠀⠁⣀⠈
⠀⠀⡔⠀⠀⠀⡀⠀⠁⠀⣨⠀⠀⠀⠈⠠⢀⣀⠶⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⣰⠀⠐⠠⠀⠀⢀
⠀⠀⠀⠒⠀⠀⠀⠀⠄⠀⠀⠀⢠⣔⠳⣦⠀⠀⡠⠆⠌⠑⠠⠀⠀⠀⢆⠀⠀⠀⠀⣤⠂⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠁⠀⡏⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⢀⡀⢠⡎⠀⣤⢆⠸⠇⡀⠁⠀⠂⠀⠀⠀⠀⠘⠇⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⢀⡀⠀⠀⠀⠀⠠⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠚⠛⠀⠀⠀⠈⠱⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠀⠉⠁

⠀⠀⠀⠀⡀⠐⢲⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀
⠀⠀⢠⡆⢘⡧⠌⡃⠘⠆⠀⠀⠀⠴⠊⠱⣀⡈⠶⠁⠢⡄⠀⠀⠀⠀⠀⠀⠀⣎⣩⢢⠀⠀⠀⠀⠀⠀⡠⢹⠆⡙⠆
⠀⠀⢿⡤⠎⠀⠀⠱⣤⡌⠀⢀⣦⣀⡠⠂⠁⠀⠀⢢⠄⡟⠂⠀⠀⠀⠀⠔⢠⠂⠈⣌⠳⡀⠀⠀⠀⠠⡧⠂⠀⠘⣮⡀
⠀⠀⡄⢰⠀⠀⠀⠀⣇⢘⠂⠸⣁⠠⠀⠀⠀⠀⠀⠀⠄⢀⡶⠀⠀⢀⠆⢠⠂⠀⠀⠘⣆⠀⠀⠀⠀⢰⠻⠀⠀⠀⡇⡳
⠀⠀⢴⠒⢇⠀⠀⡠⠸⣆⠀⠀⢤⡇⠀⢄⡀⠀⢀⠴⠒⠃⠀⠀⠀⡞⠀⠁⠀⠀⠀⠀⠘⢇⠳⠀⠀⠨⡼⡄⠀⢠⢾
⠀⠀⠘⠄⢈⡔⢺⡁⣠⠇⠀⠀⠈⠣⠀⠰⡍⠁⠶⡤⠐⠃⠀⠀⣼⣓⠶⠒⠒⠀⠀⠒⢖⣸⡙⣧⠀⠀⢣⣼⢦⣀⡌
⠀⠀⠀⠀⠰⢥⡀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠑⠄⠃
⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡀⠀⠀⠀⠀⢀⡀⢀⠀⣀
⠀⠀⠀⠀⠐⡘⢣⡠⠀⠀⠀⠀⡠⠀⡒⠖⢤⡀⠐⠀⠧⠤⡀⠀⠀⡐⠀⠲⢄⡀⠀⠁⠠⠀⠘⡀⠀⠀⢸⡇⠉⠳⣧
⠀⠀⠀⡜⠋⠌⠠⡇⠱⡀⠀⠀⢓⡀⠟⠉⠑⠂⠉⠑⠄⣀⠀⠀⠀⠈⢳⠖⠆⠈⠉⠓⣆⠀⠃⡀⠀⠀⠠⠤⠶⠚⠤
⠀⠀⢠⣤⠊⠀⠀⠘⣄⠁⠀⠀⠛⢃⠃⠀⠀⠀⠀⠀⢎⠵⠃⠀⢰⡀⠀⣂⠀⠀⠀⠀⢸⠀⠀⠸
⠀⠀⣀⢀⠀⠀⠀⠀⡏⢲⠀⠀⠀⠐⢜⠦⠀⣀⡤⠃⡁⠀⠀⠀⠠⠑⡤⠉⠁⠀⣀⡤⠦⢤⡀⠀⠀⠀⢀⡈⠂⢌⠠
⠀⠀⠉⡛⢣⣀⡀⡰⢾⠊⠀⠀⠀⠀⠈⠙⢦⣈⠓⠋⠀⠀⠀⠀⠀⢡⣀⠴⣀⠀⠀⢀⠰⣤⣤⠁⠀⠀⢤⣧⡀⡠⠤
⠀⠀⠀⠈⠁⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠁⠀⠈⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠍⠐⠒⠷⡉⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣠⡀⠉⠀⣼⠋⠑⠀⠀⠀⢈⣈⠓⠀⠀⠀⠀⡰⣆⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠛⣀⣀⡀⢂⡒⠠⣀⣀⠱⡆
⠀⠀⡠⠤⠃⠈⠉⠁⠈⠁⣇⠰⡀⠀⠋⢙⣷⠂⠲⣌⡀⠐⢀⡠⠀⢸⣄⠀⠀⠀⠀⠀⠛⡀⠂⠀⠀⠀⠀⠀⠀⢘⠢
⠀⠀⣁⣤⡇⠀⠀⠀⠀⠀⠈⢢⡁⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠂⡄⠄⠀⡀⢀⣄⣀⡀⣀⠀⠀⣀⢼⡀⣦
⠀⠀⢇⡈⡣⠀⠀⠀⠀⠀⣔⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣇⠀⠀⠀⠀⢀⠂⠀⠀⠙⠡⠤⠤⠤⠶⠶⠦⠤⠤⠄
⠀⠀⠀⠁⢉⡉⠓⢤⡈⠁⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡤⠄⠀⢠⡀
⠀⠀⠀⠀⠀⠈⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠂⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠤⣤⡀⠀⠀⠀⠀⠀⣀⢴⢄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⢸
⠀⠀⠀⡠⠊⢇⡜⠉⢢⡜⠑⢄⠀⠀⠀⡾⢤⠗⠒⠒⣥⠼⡆⠀⠀⣰⣊⢁⠼⢄⢉⣢⠀⠀⠀⢀⡞⢅⡠⠷⢄⡨⢳⡀⠀⠀⢸
⠀⠀⠈⠫⡉⠹⡉⠉⢩⠏⢉⠝⠁⠀⠀⡇⢸⠀⠀⠀⢸⠀⡇⠀⠀⡇⠀⡇⠀⠀⡇⢀⠀⠀⠀⣼⢠⡏⠀⠀⠀⢱⡄⣧⠀⠀⢸
⠀⠀⠀⠀⠙⢦⣣⠀⣎⡴⠁⠀⠀⠀⠀⣇⣸⡀⠀⠀⣼⣀⡇⠀⠀⢧⠤⠣⣀⡠⠣⢤⠀⠀⠀⠸⡀⡱⢄⣀⡠⢎⢠⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠙⢤⣏⣉⣉⣆⠜⠁⠀⠀⠀⠑⠦⣸⡠⠖⠁⠀⠀⠀⠀⠙⠲⠤⣯⠤⠔⠋⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠙⠋⠲⡄
⠀⠀⠀⠀⢀⡠⠊⠓⢄⠀⠀⠀⠀⠀⠀⠀⠞⢁⠀⠊⠀⢀⠙⠆⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⢰⠉⢀⠀⠀⡀⠘⡆
⠀⠀⠀⠀⡜⣀⠐⠃⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⡁⡆⠑⡈⣥⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡀⢸
⠀⠀⠀⠀⠳⣀⣘⣃⠰⠃⠀⠀⠀⠀⠀⠸⠀⡠⠀⠀⠀⠤⡀⠇⠀⠀⠀⠀⠀⠀⠈⢦⡁⣊⡠⠃⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠐⠀⣀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⠐⠂⠑⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠔⠁
⠀⠀⠀⠀⢀⡀⠀⠤⣤⡤⠤⢤⡀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⣄
⠀⠀⠀⢠⠎⠐⣀⠔⠀⠐⣀⠀⠘⣄⠀⠀⠀⠀⡰⠁⠱⡀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠠⠈⠀⢳⠀⠀⠀⠀⠀⠀⡴⢁⠐⠄⠀⠠⢈⢷
⠀⠀⠀⠈⢆⠀⠘⠀⠀⠀⠁⠀⡠⠃⠀⠀⠀⢰⠁⢀⠀⢱⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠈⢣⠀⠀⠀⠐⠀⡔⠁⠀⠀⠀⢠⠋⠖⠈⠐⠁⢣⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⡀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠱⡀⠀⢠⠎⠀⠀⠀⠀⠀⢸⠀⢂⡀⡀⠂⢸⠀⠀⠀⠀⠀⠀⠙⠢⡈⠀⠌⡠⠋⠀⠀⠀⠀⠀⠀⣧⠀⠃⠄⠀⠄⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠘⠾⠁⠀⠀⠀⠀⠀⠀⠀⠑⢌⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡄⠤⠤⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢀⠶⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠈⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⡈⣧⠀⠀⠀⠀⠀⢠⠖⠒⠉⠁⠉⠇
⠀⠀⠀⠀⡬⢠⠰⠌⡇⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠠⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠁⡆⠀⠀⠀⠀⠀⡌⠀⠖
⠀⠀⠀⠀⢡⠀⠀⠀⡼⢚⢍⢻⠀⠀⠀⡇⠀⠄⠆⠀⠀⠈⠁⠀⣃⠀⠀⠀⠀⠀⢀⠎⠀⠁⢰⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⣠⠖
⠀⠀⠀⠀⠀⡇⢀⢼⢁⡤⢊⠎⠀⠀⠀⠣⡀⠀⠀⠆⠀⠘⠀⣠⠋⠀⠀⠀⠀⠀⠘⡓⠂⢠⠞⠀⠀⠀⠀⠀⢸⠈⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠈⠚⠚⠚⠒⠋⠀⠀⠀⠀⠀⠘⢤⣀⣀⣀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠳⠚⠁⠀⠀⠀⠀⠀⠀⠿⠚⠁

⠀⠀⠠⠂⠀⠉⠀⠂⠀⠀⠀⠠⠐⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐
⠀⠠⠁⡀⠁⠈⢢⠀⠂⠀⠀⢀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠈⠀⠀⠊⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠜⠁⠀⠀⠀⠀⠀⢀⠁⠀⠀⡆
⠀⠀⠂⠀⠐⠒⠊⠀⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⢀⠀⠀⠀⠀⢀⠈⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠠⣀⠄
⠀⠀⠀⠈⠀⡀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⠀⠀⠀⠀⢀⣀⡀⠁
⠀⠀⠀⠀⠀⠃⠈⠂⠀⠀⠀⠀⠀⠀⠀⡠⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢂⠉⡁⠈⠙⡀⠀⠀⡰⠁⠀⠀⠹⡄
⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠂⠀⠀⠉⠠⣀⠀⠃⠀⠀⢇⠀⠉⠀⠀⢶⠈⠈⠂
⠀⢀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⠁⠁⠲⠈⠉⠃⠀⠀⠀⠀⠀⠀⢡⠀⠠⠇⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⢠⠃⠀⢀⠈⢤⠀⠀⠀⠀⠀⠀⢰
⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠸⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⡄⠀⠀⠀⡀⢀⠤⡅
⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⡠⠊⠀⠀⠀⠀⠉⠀⠄⠀⠄⠈⠟⠀⠠⠂
⠀⠀⠀⠀⣀⣠⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠠⢀⠀⠀⠀⠀⠀⠀⢠
⣀⠔⠒⠉⠠⠁⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⡀⠃⠀⠆⠀⡀⠀⠀⢀⠎⠀⠄⠀⠈⠱⢦
⢰⠙⠢⣀⠃⠀⡐⠀⠀⢂⠀⠀⠀⠀⠀⠀⡀⠊⠀⠂⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠆⠄⠀⠀⣾⠀⠀⠘⠒⠒⠆⠀⣄⡀⠀⠀⠀⠀⠀⠂⡀⠀⠀⢀⡀
⠀⡆⠀⠀⠑⠲⠂⠒⢒⠴⠂⠀⠀⠀⠠⠌⠉⢢⠀⢀⠀⠀⠀⠀⠂⠐⠀⠀⠀⣀⠀⠄⠀⠀⠘⡄⠈⠢⠀⠀⠠⠰⠃⡠⠀⠀⠀⠀⠀⠀⠈⠲⠄⠀⠡
⠀⢃⡘⠀⠀⣀⠠⠂⠁⠀⠀⠀⠀⠀⠘⠆⠀⠀⡁⠀⠀⠀⠀⠀⠑⠀⠃⠐⠂⠁⠀⠀⠀⠀⠀⠘⠀⠀⠐⠀⠀⣰⡔⠁⠀⠀⠀⠀⠀⠁⠤⢀⠀⠀⣐
⠀⠀⠓⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠛⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⢀⠴⠂⠒⠀⠐⠒⢠⡀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠁⠀⠐⢠⠀⠀⠀⠀⢀⡴⠁⢀
⢠⠃⠀⠘⠁⠀⠀⠓⠁⠐⠀⠀⠈⠁⠂⢤⠊⠀⡄⠉⠀⠀⠀⠀⠇⠀⠈⠴⠄⡰⢀⢀⡄⠀⠀⠀⡠⠊⠀⠀⢀⠀⠀⠘⠀⠀⠀⣠⠂⠀⠀⠀⠑⡀
⠅⠘⠀⠀⠀⠀⠀⢀⡄⠒⠁⢀⡀⠠⠀⢀⡀⠀⠁⠀⣀⡀⠀⡀⢤⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠔⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡿⠀⠀⠀⢀⠌⠁
⢃⣀⢡⠀⢀⠀⡠⠂⠀⡙⠀⠀⠀⠈⠛⠀⠀⠂⠀⠀⢀⠂⠀⢧⠊⠀⠀⠀⠀⠀⠀⠲⡀⠀⠘⡄⠂⠁⢀⠀⠀⢀⠀⠋⠀⠀⠀⡄⠀⠋⠀⠁⠀⡀
⠀⠑⠤⢀⢀⠈⢡⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠆⠉⠁⠂⠀⠀⠀⠂⢀⢀⣀⠀⡁⢀⢀⠀⠀⣟⡀⠠⠀⠁⠠⠊⠁⠀⠀⠀⠀⠀⠈⢄⡀⠀⢀⠘⠁
⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⣀⠈⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠁⠀⡉
⠀⠀⠀⡠⠊⠈⠂⠀⠀⠀⠀⢸⠀⠀⠀⠰⠄⣠⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠁⠀⢩⠀⠀⠀⣴⠀⠉⠀⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⡄⠀⠀⠁⢸⠁⠀⠀⢈⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠑⡀⠂⠀⠔⠀⡌⠀⠀⠀⠇⠁⠄⣀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠂⠀⡠⡘⡅⠠⡀⠘⠃⠀⠀⠀⠁⠂⠀⠀⠀⠁⠀⠀⠀⠀⠜⠀⠃⠈⠢⠄⠀⢠⠁⠀⠀⢸⠀⠀⠀⠌⠈⠉⢀⠃
⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠄⠁⠈⢷⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠈⣁⡠⠝⠋⠀⠀⠀⠘⡀⠀⡐⠀⠀⠀⡐
⠀⠀⠀⠀⠠⠄⠁⠀⠀⠀⠀⠀⠈⠂⠀⠀⠤⠀⠠⠠⠼⠀⠀⠀⠀⠀⠢⠀⠠⠀⠀⠀⠀⠀⠷⠆⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠃⠈⠀⠶⠁
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣶⣄⠀⠀⠀⠀⠀⠀⠁⠄⠄⠀⢀⣴⣿⣿⣷⣄⠀⠀⠀⠤⠀⠐⠂⠀⠤⠀⠀⣴⣶⣶⣶⣶⣦
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠌⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⡁⠀⠀⠄⠁⠀⠀⠀⠠⡄⠀⣿⣿⣿⣿⣿⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠃⠀⠀⠈⠀⠀⠀⠀⠈⠀⠙⢿⣿⣿⣿⠟⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠄

⠀⠀⠀⠄⠠⠀⠀⠄⠄⠀⠀⢀⣤⣶⣶⣶⣄⡀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⢀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠐⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⢀⣾⣿⣿⣷⡀⠀⢀⣄⠈⠁⠈⠀⢤⠄⠀⣴⣾⣿⣿⣿⣷⣦
⠀⠀⠀⠄⠠⠀⠀⠀⠄⠀⠀⠛⢿⣿⣿⣿⠿⠃⠀⣀⠀⠀⡀⡀⠀⢀⠀⠀⣿⣿⣿⣿⣿⡷⠀⠀⠀⠘⠂⠐⠁⠀⠀⠀⠈⠙⠛⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠢⠂⠂
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⡀⠄⠠⣀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⢀⠠⡀⡀⠀⠀⠀⠀⣀⣀⣠⣀
⠀⠀⠂⠁⠀⠀⠀⠀⠱⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⡀⠀⠀⢀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠐⣬⠀⠁⠀⠀⠂⠀⢀⡴⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠃⠀⠀⠀⠀⠘⡀⢰⣿⣿⣿⣿⣿⣧⠀⠈⠐⠂⠢⠀⠄⠅⠀⠀⠈⠻⠿⣻⣿⠿⠋
⠀⠀⠁⠀⠀⠀⠀⠀⠋⠀⠀⠛⠿⠿⠿⠿⠿⠛⠁⠀⠁⠁⠀⠀⠈⠁⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⠠⠒⠀⠀⣤⣾⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠨⠘⠁⠀⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⢂⠀⠰⠂⠀⠀⠈⢻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠐⠂

⢄⠀⠀⢷⠇⠀⠀⠀⠀⠁⠃⠁⠀⠀⠙⢄⠀⠀⢀⠼⠀⢠⡁⠀⠈⠀⠀⠠⠀⠀⢀⠀⠀⡀⠈⠈⠀⢀⠠⠊⠀⠀⠀⠁⠀⠀⠁⠈⡄⠀⠀⣠⠐⠈⡀
⠀⠇⠀⠀⠀⢀⠄⠤⢄⡀⠀⡞⢂⠦⡀⠀⠙⠋⢁⡠⣀⡀⠑⡀⠀⠀⠆⠀⠀⡠⠋⠀⠀⠉⠐⠂⠛⠁⠀⠀⣀⠀⠀⢆⠁⠀⠀⡠⠃⠀⢀
⠀⠃⠀⠀⠠⠃⠀⠄⠀⠹⡄⠙⡀⠀⠘⢄⠀⢀⡋⠄⠠⠉⡄⠈⠒⠀⠀⠐⠊⠀⢀⠄⠒⠒⠐⠢⡄⠀⢠⠊⢠⠑⢆⠀⠉⠀⠈⠀⠀⠀⣌⠀⠄
⡤⠀⠀⠀⣆⢀⠀⠀⠈⠀⣰⠀⠐⡄⠀⠀⢵⠀⠢⣁⡂⠔⠀⠀⠀⠀⠀⠀⢀⠔⠁⠄⠀⠀⠀⠀⢈⠀⢨⠐⠀⠄⡠⠀⠀⡀⠀⠶⡄⠀⠑⢄⠀⠂
⠠⢤⡀⠀⠇⠈⠀⠀⠀⠀⠸⠀⠀⠈⠒⠥⣼⠀⠀⠀⠀⣠⠐⠚⠛⢄⠀⠀⡜⠀⠂⠀⠀⣀⠈⢀⠃⠀⠀⠑⠚⠈⠀⠀⢰⠀⠠⠀⠈⠢⡀⠀⠑⠒⠈
⡄⠒⠘⡂⠘⡄⠀⠀⠀⣠⠃⠀⡤⠄⠠⢄⠀⠀⠀⠀⠀⠁⠈⠠⠀⠀⠧⠀⢣⡀⠀⠐⠀⡠⠔⠁⣠⠤⠄⠀⢤⠀⠀⢀⠋⠀⠀⠀⠀⠀⠐⢄⠀⠀⠠
⢀⣈⠠⠇⠀⠈⠐⠐⠊⠁⠀⠎⠠⠉⠈⢀⠱⡄⠀⠀⠰⠀⠀⠀⠀⢀⠃⠀⠀⠈⠀⠉⣁⠀⠀⠎⢀⠀⠀⠄⠀⢱⠀⢨⠀⠘⠀⠀⠀⠀⡀⠼⠗⠀⠐
⣄⠀⠀⢀⡄⠀⠒⠒⠢⡀⠀⠡⡄⠀⠀⠘⠀⠘⠄⠀⢧⠠⠐⣀⠀⠌⠀⠀⠀⠀⠔⡉⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⢂⡈⠁⠀⠀⠀⢀⠤
⠈⠄⠀⠈⠀⠂⠈⠁⠀⠈⠢⡄⠀⠁⠒⠂⠀⠀⠼⠄⠈⢤⡤⠔⠋⠀⠠⠖⡠⣜⠀⠀⠁⠃⠀⡀⠄⠀⠀⢀⠀⡆⠀⠀⡴⠒⠉⠀⠉⠐⠠⡀⠠⡅⠈
⠚⠀⠀⢦⠀⠂⠀⠀⠀⠈⠀⡀⠀⠀⠴⣄⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠘⠍⢠⡈⣆⠀⡼⠀⠀⠣⣈⣀⣈⣀⡰⠃⠀⡘⠀⠀⠄⠀⠃⠀⠀⢠⠀⠑⠠
⢠⣦⣀⠀⠑⠢⡀⠐⠀⣀⠠⠆⠀⢸⠀⠂⠣⠀⠀⡠⠚⠀⠀⡀⠈⠑⢄⠈⠒⠛⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠐⠀⢀⠀⠀⠀⢨
⠎⠀⠀⠑⢠⠀⠀⠉⠁⠀⠀⠀⠀⠘⡀⠀⠀⠀⠈⠁⠀⠠⠀⠀⠀⠄⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⡖⠨⡍⠒⠄⠀⠀⠀⠱⣄⡀⠈⠀⣀⠔⠁
⠀⡄⠀⠂⠀⠀⠀⣠⠐⠒⠂⠀⢤⠀⠰⡀⡄⡅⠀⣀⠀⠀⠠⠀⠀⠀⠀⠂⢀⠚⠁⠐⢢⠀⠀⠀⠆⠰⠀⢃⠍⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣤⡀
⠢⡀⠀⠀⢰⠀⠀⠁⠀⠊⠀⠐⡀⠵⠀⠑⠤⠅⠀⠈⠂⢄⣀⢀⡀⠤⠎⡠⠃⠀⠘⠂⠀⢦⠀⠀⠈⠆⠂⠁⠀⠀⠀⠀⠀⢸⠋⠩⠅⠢⡜⠆⠚
⠀⠈⠢⡀⡄⠀⡘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⣀⠀⠈⠀⠀⠀⡰⠁⠀⠀⠀⠀⣄⠀⢣⠀⠀⣀⠤⠐⠂⠐⠒⠢⡀⠀⠢⡁⠀⠀⢠⡠⣦⠇
⠤⡀⠀⠙⠃⠀⡇⠀⠀⠀⡀⠄⢠⠀⠀⠀⠀⠐⠡⠒⢠⢱⠀⠀⠀⠘⠇⠀⠤⠀⣀⡀⠀⣀⠌⢀⠌⢀⠀⠂⠀⠁⠀⠀⠸⠀⠀⠀⠙⠢⠀⠞⠁⢰⠦
⠀⠈⠒⢄⠀⠀⠐⠂⠀⠠⠤⠔⠃⢀⠶⢄⠀⠈⠤⣀⡠⠞⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠀⠄⠀⠠⢀⡀⠀⠀⠁⡰⠁⠀⠀⠀⣀⠠⠤⢀⠀⠀⢦
⠂⢄⡰⠄⣡⠀⠀⠀⠀⠀⠀⠀⠐⠣⠄⠄⡃⠀⠀⠀⠀⠀⢀⠔⠁⠀⢄⡊⠀⠐⡖⡏⠀⠂⡄⠈⠢⠤⠄⠀⠤⠐⠈⢀⣤⠤⠂⠉⠀⠀⠂⠀⠑⣄
⠀⠀⠈⠉⠉⢠⠔⡉⣉⠙⡇⠀⢠⠆⠀⢠⠷⡆⢶⠀⠀⠔⡁⠀⢈⠤⠊⠀⠀⢀⠸⠦⠄⣽⢻⠀⠀⠀⠀⡀⠤⠄⡀⠀⠈⠑⠠⢀⠀⠰⠀⠀⡀⠞⠁
⠉⠉⠢⡀⠀⠸⣄⠠⠀⢀⠇⠀⠘⢅⠘⣃⠄⢈⠗⠀⠸⠂⠰⠊⠁⠀⠀⠀⢐⠡⢀⠀⢀⣠⠜⠀⠀⡤⢊⠀⠂⠀⠉⡆⠀⠀⠀⠀⠈⠐⠒⠈⠀⠀⡠
⠈⠈⠀⡈⢦⠀⠀⠁⠚⠁⡀⠤⢀⠀⠉⠉⠛⠁⠀⠀⣀⣠⠀⠰⠢⡀⠀⠀⠛⠂⠰⠐⠉⠀⠀⡠⠊⠀⠀⢀⠀⠄⢁⠃⠀⢠⠄⠶⢄⠀⠀⢀⡔⠊
⠀⠀⠐⢠⠎⠀⠀⢀⠖⠁⠀⠀⠀⠈⠲⠀⠀⢀⠊⠁⡀⠀⠀⠆⠀⠸⠀⠀⢀⠄⠤⢀⠀⠀⠘⠓⠀⠀⠀⠒⠀⠚⠁⠀⠐⡧⠆⢈⠈⡁⠀⣌⠀⠐
⠀⡠⠚⠁⠀⠀⠀⡈⠀⢀⠀⠁⠀⠆⠀⠆⠀⠰⣀⠈⠁⠀⠀⠀⠀⠁⠀⡐⠀⠀⠀⡈⠑⢄⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠈⠣⠠⠤⠄⠆⠀⠈⠢⡀
⠋⠀⢀⣄⠀⠀⠀⢓⠀⠀⠀⠀⠠⠀⢀⠇⠀⠀⠈⠑⢄⠀⠀⠀⡘⠀⠀⠃⠀⠂⠀⠀⠰⠈⢂⠀⠸⣁⠐⠀⠀⠀⠀⠙⢠⡀⠀⢀⡀⠀⠀⠀⠀⠈⠑
⠀⡠⠊⠈⠑⠄⠀⠀⠑⣀⠀⠀⠀⣠⠊⠀⢀⡠⢆⠀⠀⠑⠦⣴⠁⠀⠀⠈⠄⠐⠀⠀⠀⠂⢈⠀⠀⠀⠉⠐⠂⠀⠰⠇⠋⠁⠀⠋⠁⡕⢆⠀⢀⣄
⢰⠁⡀⠀⢠⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠔⠡⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠁⢀⠌⠀⢀⠤⠠⢄⣀⠀⠀⢀⡀⠀⠀⢃⠁⠀⠀⠏⠓⠝⠆
⠀⢆⠀⠀⠀⡘⠀⠀⡰⢊⢍⠰⡀⠀⠀⠀⠀⠈⠀⠀⠇⠀⠀⣀⠤⠀⠲⠠⣀⠀⠀⠉⠈⠁⢀⠔⠁⠀⡂⡀⠩⠀⠀⡈⠉⠢⡀⠀⠳⡀⡸⣤⢇⡜
⠀⠀⢂⠀⣀⠁⠀⠀⢇⠢⡠⢀⠇⠀⠘⠀⠀⡀⠀⠀⠀⠀⡘⠁⠀⠀⢀⠀⠀⠙⡆⠀⠀⠴⠁⠀⠀⠊⠀⠀⡰⠀⠀⠃⠀⡀⠐⠄⠀⠉⠉⠉⠁⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⣤⣤⢤⣤⡤⠤⣤⡤⠤⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢉⡿⡋⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⠴⠤⣤⠤⣤⣤⣄⡀
⠀⠀⠀⣼⢯⡉⠒⠀⠀⣀⣀⡀⠀⠐⠊⢁⡽⡆⠀⠀⠀⠀⠀⠀⣠⡿⠋⠁⠛⠁⠛⠂⠛⢂⠀⠀⠀⠀⠀⠀⠀⣜⡏⠈⠋⠁⠀⠀⠀⠀⠀⠐⠋⢹⣻⡄
⠀⠀⠀⣿⠀⠁⠈⠀⠀⠈⠉⠀⠀⠊⠀⠘⢦⣷⠀⠀⠀⠀⠀⣰⡯⣀⡄⠀⠀⠆⠀⠀⢤⡐⢂⠀⠀⠀⠀⠀⠀⣿⠟⠦⣄⠀⡀⠀⠀⠀⠀⣀⠤⢻⣽⡇
⠀⠀⠀⡿⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢠⣿⠜⠉⠁⠀⠀⠁⣀⡀⢜⠓⢸⡆⠀⠀⠀⠀⢰⡟⠀⠀⠈⠳⢤⠄⢠⡔⠊⠁⠀⠀⢿⡇
⠀⠀⠀⣿⣆⢠⡃⠀⠀⠀⠀⠀⠀⠀⢁⠀⣸⣿⠀⠀⠀⠀⢸⣧⣄⠀⢀⡿⠀⠀⠸⢅⢸⣇⣸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⣤⡴⠇⠀⠀⠀⠀⣸⠇
⠀⠀⠀⣿⣻⣿⡶⠃⠀⣀⡀⠀⠀⢠⣼⣷⠏⡟⠀⠀⠀⠀⢸⣿⣿⣿⣧⡀⢶⣠⡇⣌⣻⣟⣿⠇⠀⠀⠀⠀⢸⣿⣄⣤⠖⣠⠎⠀⠀⠐⢄⠀⢄⣰⣿
⠀⠀⠀⢿⣿⣴⣿⣞⠋⠀⠀⢙⣲⣾⣿⣻⣷⠇⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣾⣿⡶⣟⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣤⣔⣁⠀⠀⠀⠀⣈⣳⣤⣿⣿
⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠿⠽⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠷⠶⠿⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠜⠑⠖⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⠄⠀⠰⠄⢠⣀⣀
⠀⠀⠀⠀⡐⠁⠀⠀⢀⠤⠀⠐⠂⠀⠀⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢏⡀⠀⠀⠀⠀⠄⠀⠈⠋⠉⠉⢄
⠀⠀⠀⢀⡠⠐⣀⠋⠀⠀⠀⠀⠙⢆⠐⠃⠀⠀⠀⠀⠀⠀⢀⣤⣦⠄⣴⡅⢠⣄⠀⢠⡄⠀⢄⠀⠀⠀⠀⠀⢠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢸⡀
⠀⠀⠀⢧⣀⠀⢇⠀⠀⠀⠀⠀⠀⠸⣆⣀⣤⠗⠀⠀⠀⠀⣸⢷⠀⢠⠇⠀⡠⣅⠀⡀⢣⠀⠸⡆⠀⠀⠀⠀⢸⡷⣄⠌⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣸⡇
⠀⠀⠀⠈⢿⣿⠛⢳⡀⣀⣀⠀⣶⠉⢻⣯⠏⠀⠀⠀⠀⠀⡏⠘⣄⡞⠸⣄⠇⢰⣠⠃⢸⢀⠇⢡⠀⠀⠀⠀⠘⣿⣿⠃⢶⠀⢀⡀⣀⡀⢠⣦⣼⣾⣿
⠀⠀⠀⠀⠈⢿⣤⣶⣿⡍⢀⣽⣛⣶⡿⠟⠀⠀⠀⠀⠀⠘⠓⠶⠟⠳⠒⠛⠲⠚⠻⠶⠾⠿⠶⠶⠂⠀⠀⠀⠀⠘⠿⣿⣿⣿⣯⣷⣽⣷⣿⣿⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⣲⢶⡒⢢⡄
⠀⠀⠀⣴⠫⠀⠀⢤⡄⠀⠀⠉⠀⣀⣴⡳⢦⡀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠘⠀⠀⢀⡂⢄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠃⠀⡄⠀⠀⢡⡈⠀⠍⣀
⠀⠀⠀⡇⠓⣦⠀⠠⠀⠀⠠⠄⠠⢉⠁⢰⣿⡇⠀⠀⠀⠀⠀⠀⡙⠢⡀⠑⣠⡄⠈⢀⡵⠛⠀⠀⠀⠀⠀⠀⠀⡼⢁⣇⢀⣠⠴⠚⠛⠢⣄⠀⢠⡏
⠀⠀⠀⡧⠈⠁⢸⠀⠀⠀⠀⠀⠀⢸⣷⣿⣯⣡⠀⠀⠀⠀⣔⠴⠀⠠⠞⢧⣸⠁⡹⠛⠀⠔⠄⠃⠀⠀⠀⠀⢰⣁⣤⠜⣿⠃⠀⠀⠀⠀⠘⣿⠛⢴⣦⡀
⠀⠀⠀⡷⡀⢀⢾⠀⠀⠀⠀⠀⠀⢸⡿⠙⣟⣿⠀⠀⠀⠐⢓⡒⢒⣿⠓⢶⣿⣿⠦⠼⣿⣶⠶⣾⠆⠀⠀⠀⢸⣿⣯⢀⣿⠀⠀⠀⠀⠀⢀⣿⠀⣀⣽⠇
⠀⠀⠀⣇⣵⠾⢿⣦⣀⣀⣀⣀⣠⣾⣿⣦⠋⡿⠀⠀⠀⠀⢀⡞⢻⣾⣮⣱⠏⢿⣛⣾⡧⠼⣿⡿⠀⠀⠀⠀⠈⣿⣷⣿⠿⣧⣀⠀⠀⣀⣼⠿⣿⣽⠻
⠀⠀⠀⢿⣏⣀⣸⣿⠟⠁⠈⠙⢿⣧⣈⢻⣷⡇⠀⠀⠀⠀⣴⣞⣉⡿⠗⡿⣟⡿⣿⢾⣿⣧⣿⠇⠀⠀⠀⠀⠀⠹⣿⣯⣤⣼⡿⠛⠻⣿⣃⣤⣹⡷⠃
⠀⠀⠀⠀⠙⠿⣿⣿⣷⣤⣤⣴⣯⣽⣿⠿⠋⠀⠀⠀⠀⠀⠀⠙⠻⣷⣸⣤⣿⣧⣹⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⠿⣏⣿⣷⣄⣾⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠟⠛⠋

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⢷⡄⢀⠀⠀⠀⠀⢀⣠⢉⡀⠰⡄
⠀⠀⠀⢀⡀⠀⠀⣾⠀⢠⡆⢀⡖⠀⠀⠀⠃⢸⡇⠈⢺⠀⠀⠀⠈⡇⠈⠀⢸⡇
⠀⠀⠀⠀⠸⣶⡄⢿⠀⢠⣧⢫⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠤⠈⢿⠗⠀⣘⠷⡁⠀⠀⠀⠀⠀⢸⡇⠀⡆⠀⠀⠀⢀⠀⣀⣘⣼⡇⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠐⠒⠚⠱⠾⠻⠟⠁⠀⠀⠀⠀⠀⠘⠷⠘⠁⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⢐⡄
⠀⠀⠀⠀⠆⡀⠀⠐⠃⠀⠀⠰⠀⠀⠀⠀⡁⠀⠀⠈⠕⠄⠀⠀⠐⠀⠀⢀⡈⡀
⠀⠀⠀⠀⠀⢹⠀⠀⢀⣾⠁⢲⠀⠀⠀⠀⠉⠦⠀⡀⢀⠀⠀⠀⢰⠀⠀⠈⠀⠃⠀⠀⠀⠀⢰
⠀⠀⠀⠀⣿⠀⠀⠀⢸⡏⠀⠋⠀⠀⠀⠀⠀⠀⠀⣷⡌⠀⠀⠀⢸⠀⠀⠸⠸⠀⠀⠀⠀⠀⠛⠀⠀⡀
⠀⠀⠀⠀⢸⡦⣀⠔⢺⣷⡎⢠⡾⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠸⡀⠀⣬⡼⠀⠀⠀⠀⠀⠟⠀⠸
⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⣷⠀⠀⠀⢀⠀⠀⠁⣠⡀
⠀⠀⠀⠀⠁⠀⡴⠀⠀⠀⢹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⠀⠘⣿⠇
⠀⠀⠀⠀⠀⠚⠥⠐⠊⠁⠉⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠡⡀⠐⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠘⢄⢱⠀⢳⡀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢄⠀⠸⣧⣄⡀⠀⠈⠂⢇⠀⢳⠀⠀⠀⡠⠞⠀⣟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⢆⡆⠀⠈⠙⠒⠤⠀⠘⣆⠈⣧⣄⡀⠁⠀⠀⣹⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣨⡇⠀⠀⠀⠀⠀⠀⠀⡸⠋⢹⡇⠀⠀⠀⢀⡟⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠒⠀⠈⠸⠁⢾⠀⠀⠀⠀⠀⣰⠁⢠⢻⣷⠀⠀⠀⣞⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣰⠇⢰⡇⣾⡿⠀⠀⡜⣸⣸⠙⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠈⡑⢿⡀⠀⠀⡀⠸⢸⡄⠀⠀⢰⡟⢠⡏⢣⡏⡇⠀⡼⢠⣇⣿⠀⠒⡹⠺⡌⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠉⠁⢀⠉⠳⡉⡇⠀⠀⣇⡀⣼⡇⠀⢠⣿⢡⡏⢷⣘⣹⡇⡼⣑⣿⡟⡝⠁⠂⠀⠀⠱⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡝⠁⠀⠀⠡⢻⢀⣴⡏⠻⡿⡇⢠⣿⢧⣟⠐⢾⣿⣿⠿⠛⢩⠻⡋⢷⣇⠆⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡀⠀⠀⠀⠡⠹⣿⣿⡇⠀⠙⣷⣾⣿⡿⠋⠸⣷⠋⠁⠀⠠⢆⠀⢑⢄⢿⡄⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠬⢲⡄⠀⠢⡹⣿⣿⡇⠀⠀⣿⣿⡿⢡⠞⠀⡿⠈⡆⠀⠀⠀⢑⣷⣾⣿⡇⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⢀⠇⠒⠒⢦⣽⣿⣧⣀⡀⣹⣿⡷⣇⠀⠀⣷⣄⢸⡄⢀⣴⣿⠿⣿⣌⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠛⠛⠛⠛⠋⠙⠻⠷⣽⡟⠿⠿⢷⡾⠋⠙⢿⣷⣾⡿⠗⠺⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠒⠒⠀⠉⠁⠀⠀⠀⠁⠈⠉⠀⠒⠂⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⣦⡀
⠀⠀⠀⠀⠀⠀⣠⠔⢋⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠳⢄⡀
⠀⠀⠀⠀⣠⠞⠁⠀⡼⠁⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡷⣤⣄⣙⠲⣄
⠀⢀⡴⠋⠀⠀⠀⣰⠃⠀⠀⠈⠙⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠚⠁⠀⣧⠀⠈⠉⠛⠺⠿⣦⡀
⢰⠋⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠈⣹⡶⡶⠦⠤⠤⣤⣤⣄⣀⣀⣀⣠⣤⣤⠤⣤⣶⡒⠋⠉⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢳
⡏⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠙⢦⡀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠈
⣇⠀⠀⠀⠀⡼⠀⠀⠀⠀⣀⣴⠞⠉⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢀
⠹⡄⠀⠀⣸⠃⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡜
⠀⠱⡄⢰⣏⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⣇⠀⠀⠀⣠⠞
⠀⠀⠙⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣿⢀⣠⠞⠁
⠀⠀⠀⠈⠙⢷⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠙⠦⣈⠙⠲⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠉⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠻⣟⠓⠶⠶⠦⠤⠤⠤⠤⣤⣿⡥⠤⠤⠤⠴⠶⠒⠚⢩⠟⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠙⢆⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢀⡼⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡈⠳⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡞⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⢦⡀⠀⠀⢸⡆⠀⠀⣰⠏⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣝⣦⠀⢸⡇⢀⡴⣣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣌⣷⣾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠘⢣⠦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⢠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣔⠳⠀⠀⢒⠊⠀⠀⠀⠉⠁⠀⠀⠘⡀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢶⠀⠀⠀⠉⠀⠀⠀⠁⢘⠂⠀⠍⠁⠀⠀⠀⠀⠃⠀⠐⡀
⠀⠀⠀⠀⠀⠐⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⡆⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠈⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⣄⠉⠂⡀⠀⢤⠀⠀⠐⠉⢀⠀⠀⠺⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⢠⡁⠀⠀⠘⠂⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡰⠁⠂⠀⠀⠀⠀⢠⠠⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡤⠃⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⣤⠀⠁

⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠀⠀⠈⠍⠁⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⢀⠠⠂⠀⠀⠀⠀⡴⠤⠤⠤⠀⠀⠀⠀⠀⠀⠰⡄⠲⠀⠀⠀⠀⡨⠆⠀⢀⡠⠀⠀⠀⠀⠀⠀⠘
⠒⠄⠠⠀⡰⠀⠀⠀⠀⢻⣤⠋⣐⡂⠲⡀⠀⠀⠀⠀⠐⠣⣀⠀⠉⠓⣀⢠⡄⠈⠁⠁⠀⠀⠀⠀⠀⢇⠀⠄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⢀⠂⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠂⠂⡂⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢤⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⢀
⠀⠀⡀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⡀⠐
⠀⠠⢀⠖⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⢀
⠀⡤⠊⢰⠀⠀⠀⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠔
⠀⠁⠀⡘⠀⠀⠀⠂⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠁⢀⠀⠀⠀⠈⠢⢄⡀⠀⡄
⠀⠀⠀⠃⠀⠘⠃⡠⠀⠀⠀⠀⠀⠀⠀⠈⠃⠂⠀⠀⢠⡀⠀⠄⠁⠈⠀⠀⠀⠀⠀⠀⠈⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠖⠀⠀⠀⠀⠀⡀⠀⢔⡆
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⡌⠀⠀⠀⠀⢀⠸⠩⢐⠨⡂
⠀⠀⠀⠀⠀⢸⠞⠄⠀⡠⠛⠄⠈⠹⢷⠀⠀⠀⠀⠀⠀⠀⢀⡤⢠⠀⠈⠄⡞⠁⠀⠀⠀⠀⠤⢊⠀⠄⠉⣂
⠀⠀⠀⠀⠀⢠⢀⠄⠀⠀⠀⠀⠀⡀⠸⠀⠀⠀⠀⠀⠀⢀⠀⠄⡄⡁⢢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⢸⠃⠄⠀⠀⠀⠀⠀⡨⠆⠀⠀⠀⠀⠀⠀⢈⠒⠂⣄⡰⠁
⠀⠀⠀⠀⠀⢸⢄⠄⠐⢄⢀⠄⠀⢀⣠⠀⠀⠀⠀⠀⠀⠘⠣⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠈⠁⠀⠀⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗
⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢘⡈⠉⠁⠰⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⣧⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⠁⣤⢰⣼⣿⡇⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⣶⡹⣿⡟⠉⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⢀⠛⣧⣜⢰⣿⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠈⠒⠿⠷⢶⣶⣶⣤⣝⡘⠁⣿⡟⠘⠁⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠠⠄
⠀⠀⠀⠀⢠⣀⣤⣤⣶⣶⣦⣌⣉⡁⠀⢹⣷⢟⣴⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠐
⠀⠀⠀⠀⠀⢉⣩⣭⣽⢝⠛⣋⣭⠗⠀⠈⠱⢟⠯⠉⠉⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢀⣀⣤⣴⣾⠀⠼⠛⢁⡼⣿⣿⣷⡚⠷⢶⣤⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠒⠚⠛⠋⠉⠀⠀⢀⡼⠛⢿⡻⢿⢿⣮⠀⢀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠊⠀⠀⠀⠁⠀⠀⠉⠂⠀⠀⠈⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠠⢖⠆⠀⠀⠀⠀⠀⠀⠀⠀⣖⣰⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⡀⠀⡠⠠⠀⠀⢆⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⡀
⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⡎⠀⡱⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠄⢀⠈⡄⠀⠄⠀⠀⠀⠀⠀⠀⠠⣄⠀⣀
⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠐⠀⠀⠀⣀
⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⡆
⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠁⠒⠁
⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠄⠠⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣀⠀⡀⡢⠀⠀⠠⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠼⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠓⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⡀⠀⠀⠰⠄⠀⠀⠶⠂⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠦⠐⠄⠀⠆
⠀⠀⠀⠀⠀⠀⡠⠀⠀⢄⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠠⠊⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢁⠈
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢁⠔⠁⠘⢢
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⢤⡀⢀⠌
⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠡⣀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠐⢀⠀⠀⡒⠲⠀⠀⠀⠀⠀⠀⢀
⠀⡀⠀⠐⠑⡀⠈⡈⠗⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠐⠀⠃⢐
⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⢀⠀⣈⠐⠸⠄⠈
⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠂⠃⠐⠀⠀⠀⠀⠀⠀⣰⠋⠉⣷⠀⠀⠀⠀⠀⠀⠀⠂⠄⠂
⠀⠀⠘⠁⠀⠑⠂⢀⠀⠀⣀⠀⠀⠀⠩⠀⠀⠘⠁⠀⠀⠀⠀⠀⠹⠦⠴⠟⠀⠀⠀⠄⠀⠀⠂⠁⠄⠁⠁
⠀⠐⢀⠀⠀⠈⠀⠀⠀⠀⣀⠀⠤⠚⠀⠄⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⢁⠀⢈⡈⠤⠁⠀⠀⠁⠀⠀⠸⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠋⠀⠀⠩⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠄⠀⠀⡀⠀⠀⠀⠐⠂⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢀⣠⠖⠂⠀⠈⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⠀⠀⠀⠒⣤⣀⡀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠠⠌⣀⠰⠨⠰⠖⢠⠓⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡜⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠿⠀⠃⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠃⡄⠊⢛⠚⠓⣔⠺⠂⠀⠀⠀⠀⠀⠀⠁⠐⠂⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠀⣀⣁⢀⣼⠒⠰⠟⠦⠔⢲⣏⢠⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢩⠈⠀⢁⣀⣨⡤⠴⣤⣴⠾⠙⣤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢁⠀⠱⢉⣃⣤⡾⠁⢦⢸⣅⡀⠲⡅⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡄⠀⠈⢁⠜⡁⠚⢂⠤⠛⢄⠀⣀⣀⠍⠙⢋⠘⢰⡔
⠀⠀⠀⠀⠉⠐⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠘⠠⠄⡀⠀⠂⠜⠶⠀⢦⠒⠻⠁⠙⣏⡉⢸⡃⠉⠀⠄
⠀⠀⠀⠀⠀⠀⡄⠀⠆⠀⠐⠹⣇⣀⣴⢆⢠⡤⠂⠀⠂⠀⠀⠀⠀⠈⠐⢀⠀⠐⠃⠊⢿⠷⠀⡘⠮⠔⠃⢀⡰
⠀⠀⠀⠀⠀⠂⠀⠀⢀⣔⢶⣁⠘⠀⠁⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠄⢀⢀⣀⣠⠤⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠘⠂⠛⠛⠋⠙⠃⠐⠒⠒⠛⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⡀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⢠⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⡀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⣵⢀⠀⠀⠀⡂⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡂⠈⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠀⠀⠀⠣⠀⠀⠙⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⢀⡆⠀⠀⠘⠆⢁⠀⠀⢀⠀⡐⠊⠹⠂⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠀⠀⠀⠀⠀⠫⡀⠀⠀⣾⠉⠀⠐⠞⠀⠀⠀⠀⡠⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⣀⠀⠀⠀⠀⠁⡁⡀⢀⠇⠀⠀⠈⣄⡀⠀⠀⠐⠂⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⠉⠢⡀⠀⠀⠀⠀⢀⡎⠀⠀⡰⠊⠁⢻⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢸⠂⠀⠀⣀⢨⠃⢀⣀⠀⠀⠀⡲⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣦⠀⠀⠀⠀⢮⠁⠈⠈⠃⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢦⠀⠀⢘⠀⠀⠀⠀⠲⡿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠈⣿⣦⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡀⠀⠀⠀⠀⢸⣿⣶⣦⣤⡇⠀⠈⠻⣄⡶⠿⢿⠁⠀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣷⣴⣶⣒⡆⢸⢿⣿⣿⣿⣇⠀⠀⠀⠹⡀⠀⣇⠠⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢿⣿⡙⠃⢺⠀⣿⣿⣿⣿⡄⠀⠀⠀⠠⣀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢌⣻⠷⠲⣄⠀⢸⣿⣿⣿⡿⢦⡀⠀⠀⢻⠍⠟⢹⣧⢀⣈⡄⠀⠀⢀⣀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣖⠒⠒⠂⢤⡈⠁⠀⠀⣉⠂⡀⢿⣿⣿⣧⣀⣸⣶⣤⠉⠸⠀⣾⣿⠟⢿⠇⠀⣰⣦⡴⢒⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢦⡔⢻⣿⠀⠀⠀⣼⣷⣮⡻⣿⡇⠈⣿⣿⣿⡟⠁⠂⠀⣿⣿⠀⢸⢀⣾⣿⠏⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠘⡷⠀⢃⠀⢻⣄⠀⠀⣿⣿⣿⡛⠻⢷⡀⠉⢻⣿⡁⠈⠀⠀⢿⣿⠀⣼⣿⠟⠁⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠰⡸⡌⢧⠀⢻⡟⢺⣿⡿⠯⠙⠀⢠⠷⠒⠋⠉⠑⡀⠀⠀⠀⠇⢠⡿⠋⢀⠊⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢍⣒⣧⣧⡸⣷⡀⣿⣮⣿⣧⣀⠀⠀⠃⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢘⣴⡆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⢿⠿⠛⠿⠿⣿⣿⠛⠛⡛⠓⢷⣴⣿⡀⢀⣀⣤⣾⣿⣇⠀⣀⣴⣿⣿⣧⡴⢶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠷⠶⠷⣿⣿⣿⣯⠉⠁⠀⠀⣿⣿⡿⠋⠘⠙⣿⠸⣿⡾⠛⣿⠟⠉⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣸⡇⠀⠀⠈⣙⣏⠹⣿⣧⣶⣾⣿⡿⠃⠀⠀⠀⡯⠀⣬⢠⡔⠁⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠛⢛⣻⣿⣿⣿⣿⠗⢻⠻⢿⣿⣯⡇⢀⠀⠀⢀⠈⢀⡋⠀⠀⠉⢤⣾⡄⢒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠖⠿⣿⠟⠋⢀⣰⣿⣦⣴⣿⣿⣿⡋⠉⠀⢸⡉⢾⣿⣧⣄⣠⣾⢝⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⢿⣿⠋⠛⠛⣿⣿⠟⠿⠿⣿⣿⣿⣿⣄⣀⣳⣄⣿⣿⠙⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡼⣆⡴⠿⠛⠻⣧⣄⡴⣿⣿⣿⣿⣿⡛⠿⠛⠻⢯⠜⠃⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠤⠤⠿⠃⠻⣾⠉⠛⠻⢿⣷⡆⠺⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⣠⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠁⢀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⡠⠒⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢼⡅⠀⠀⠹⠀⢀
⠀⠀⠀⠀⠀⠀⣠⣴⠘⢳⠃⡆⠀⠀⠀⠰⠀⢰⠀⠀⠀⠀⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢻⣼⠀⠀⠀⠀⡤⡄
⠀⠀⠀⠀⠀⠁⠉⢹⠀⠀⢀⠇⠀⠀⠀⠁⠀⢻⢠⠀⠀⣠⠧⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠈⣿⠀⠀⠀⠀⠃⡁⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠈⠀⠀⠀⡄⠀⣿⠘⠉⠛⢍⢀⠨⡄⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣿⢀⣠⠃⠀⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⢠⣾⠀⠀⠀⢳⣴⠁⠔⠀⢘⢻⢹⠄⢋⣸⣠⠁⠀⠀⠀⢀⠀⠀⠀⠀⠰⣣⡾⠙⣌⡃⣴⣾⢣⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⡿⠻⠀⠀⠀⠀⢘⣧⠠⣄⣘⣻⢀⡃⣚⣿⠄⠀⠀⠀⠀⣀⡂⠀⠀⠀⠙⣧⣼⣾⣏⠱⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡄⠀⠀⠀⠀⠁⠛⠽⢧⡀⢩⢱⠾⠷⠛⠁⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠂⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣴⢲⠓⠊⡷⢋⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡄⡰⠀⠀⠀⠀⠁⠤⠘⠋⠀⠀⠀⣀⠀⠀⠀⠒⠀⠞⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⣧⡀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠸⠸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⢣⢸⣷⠀⣀⣼⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣀⡄
⠀⠀⠀⠀⠀⢀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⠀⠀⣤⡶⣼⡀⠰⡆⠀⣿⠛⠠⠴⠃⠀⠀⠀⠀⠀⠸⣿⣀⣴⣿⠃
⠀⠀⠀⠀⠀⠈⢟⢣⣠⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡝⠛⣫⡶⠳⡄⢿⠋⠀⠀⠀⠀⠀⠀⠀⠐⢤⣽⡟⠋⠛
⠀⠀⠀⠀⠀⠀⠘⠦⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢪⠿⠇⠉⣧⠄⡓⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⠖⠒⢞⠋⠑⣖⠲⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠒⠛⢤⠀⠀⣱⠀⣸⠇⣀⡟⠀⣸⠄⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣏⡀⠀⢹⡄⣸⣧⠴⠛⠛⠛⠛⠛⠶⢾⣯⣴⣿⣿⣿⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡁⠀⠀⢹⣤⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠁⢀⣈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠈⢳⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡞⠋⠙⢦⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠞⠋⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⢾⡋⠀⠈⢳⣀⣀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠿⣄⠀⠀⣿⣀⣤⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠴⣋⠉⠉⡆⠀⢸⡦⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠁⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡖⠉⠉⠑⣆⠀⢸⣆⣴⠷⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠓⠒⢦⡼⠃
⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠈⣷⠀⣠⡿⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢻⡍⠛⣾⢿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠦⠤⣄⣸⡇
⠀⠀⠀⠀⣰⠟⠉⠙⢶⡀⣠⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠀⠀⢸⡟⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠈⣯
⠀⠀⣀⡤⠿⢤⡀⠀⣼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⡀⢀⣠⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠒⠦⣼⠏
⠀⢰⡏⠀⠀⠀⢹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⢀⣿
⢠⡞⠋⠉⠓⣦⣼⠇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣝⣛⠲⢤⡀⠀⠀⠀⢀⡴⠾⢿⠓⢶⡦⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⢳⡟⠋
⣿⠀⢀⣀⣀⣿⠁⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⢿⣿⣋⢉⣹⣿⡷⠀⣿⠀⠀⠀⡞⠀⠀⠘⠁⢸⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⣿⣀⡀⢀⣾⠇
⣸⠟⠉⠀⠙⣧⠀⠀⠀⠀⠀⢠⣾⣿⠟⠉⣠⣾⣿⠿⠻⢿⢿⣷⣤⡿⠀⠀⠀⠹⣄⠀⢀⣀⣼⣿⠟⠻⠿⡿⠃⠀⠀⠀⢰⠏⠁⠀⠈⣿⠁
⠹⡆⠀⣀⣀⣿⡀⠀⠀⠀⠀⠸⡞⣧⣀⣿⣿⣿⠁⠀⢀⠼⠀⢹⣿⡀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⡼⠖⠦⣄⣤⠿
⠀⢨⡟⠁⠀⠀⢹⡆⠀⠀⠀⠀⠙⠶⣍⣹⣿⣿⣆⠀⠀⠀⣠⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣀⠀⠀⣸⡆
⠀⠸⣇⠀⡴⠂⠉⠉⢳⡀⠀⠀⠀⠀⠈⠹⠿⣿⣿⣿⣶⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠉⠙⡞⠋
⠀⠀⠀⠹⡄⠀⠀⣠⠞⠋⠙⣦⡀⢀⡀⠀⠀⠈⠻⠿⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠛⠲⣄⠀⣰⡟
⠀⠀⠀⠀⠙⠲⣾⡁⠀⠀⢠⠞⠋⠉⠙⣦⣤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣴⠛⠉⠙⢦⡀⠀⣿⠞⠋
⠀⠀⠀⠀⠀⠀⠘⠧⣀⣀⣿⠀⠀⠀⣾⠁⠀⠀⣼⠛⠋⠛⣶⡶⠛⠉⠛⣶⠞⠋⠉⢙⡾⠁⠀⠀⢹⡆⠀⠀⢸⣧⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⡤⣿⠀⠀⢸⡇⠀⠀⠀⣿⡀⠀⠀⠸⡏⠀⠀⠀⠘⣧⠀⠀⣀⣼⣇⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠓⠦⠤⠖⠛⠻⢦⣤⡶⠟⠶⠶⠾⠛⠉⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠠⠈⠁⠈⡞⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠁⢠⠀⠀⠀⠀⣨⠀⠁⠀⠀⠁⡦⠀⠰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠓⠀⡀⠀⠠⡐⠆⠀⠠⠦⢀⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⢰⡄⠀⠀⢠⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠂⠁⠀⣠⣴⣶⣶⣤⡀⠀⠀⠀⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢰⠀⢰⠀⢢⠀⠀⠀⠁⠀⠀⠀⠀⠐⠁⠁⠀⠀⠀⡀⠈⠀⡈⢀⠀⢸⣷⣿⣿⣿⣷⡄⠀⠈⠦⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣼⠀⢈⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠋⢀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡁⠀⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠘⡆⠀⣀⡀⠀⠐⠢⢀⢐⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⣿⠆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢂⠀⠀⠔⠀⠀⠀⠀⠀⠐⠖⠀⠀⡀⠀⠁⠀⠀⠇⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⡀⠀⡀⠀⠠
⠀⠀⠀⠀⠀⢿⠅⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⢀⠀⠈⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡄⠀⠀⠀⠐⠑⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠏⠀⠀⡠⣘⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠢⠀⡀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠰⠀⠁⡀⠀⠀⠀⠀⡌⠂⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠰⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠐
⠀⠀⠀⠰⡇⠀⡆⠀⠀⠸⡄⠀⠀⠀⢰⠁⠈⠀⠕⠀⠁⢠⠀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠇⠀⠀⡀⠀⠀⠀⡊⠁
⠀⠀⠀⠀⠉⠀⡇⢀⣄⣀⠀⠀⠀⠀⠀⠐⠄⠂⠤⡀⠰⠂⠀⠀⠂⣀⠆⠀⠀⠀⠀⣉⣀⠲⢀⠤⠆⠀⠃⠄⠀⠻⣟⠀⠀⠀⠀⠀⠀⠄⠄⠂⣀⡀
⠀⠀⠀⠀⣠⡄⠀⢀⡀⠀⣀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⣀⠄⠁⠀⠼⠟⠋⠛⠋⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⢀⠔⠒⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠃⠀⠀⠊⠑⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠘⠁⠀⠀⠀⠀⠀⠀⢈⡿⠁
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠘
⠀⠀⠀⢀⡆⠁⢀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠁⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠓⠂⠀⠐⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⠦⠀⠀⠀⡞⠄⣁⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠃⠀⠀⠀⠀⢦⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡂⡄⡀⠋⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⢀⣤⠃⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠄⠀⠀⠈⠠⠘⠘⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢸⣧⣱⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣍⢺⣿⣏⢻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⢟⣽⡟⡇⣸⣿⣿⡀⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⣎⣿⡿⢹⡇⣿⡟⡏⢷⠘⢿⡟⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡛⠿⣧⡾⢃⣇⣀⣤⣤⣓⢦⣠⣱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⣷⣦⡔⣹⣿⣿⣿⣷⠉⡷⢸⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⢟⣳⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠨⣿⡏⣷⠸⣿⣿⣿⡿⢰⡇⣼⣷⣿⠀⠀⠀⠀⠀⠀⠀⣠⣿⠗⣡⣿⢋⣥⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢻⡇⣿⡄⢻⣿⣿⡇⢸⢀⣿⡏⣿⡄⠀⠀⠀⠀⢀⣾⣿⢃⣼⢟⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣷⢸⡇⢸⣿⣿⡇⡜⢸⣿⡇⢻⡇⡠⢰⡄⢀⢾⡟⣡⢟⣵⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣞⣿⢸⣿⣿⠃⢃⣿⣿⡷⣮⡵⣣⣿⣷⣤⢋⣾⣵⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⣄⣹⣄⣘⣿⣿⣿⠘⣿⣿⠀⢸⣿⣧⡴⠏⣰⣿⡿⡇⢻⣻⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢸⣿⠹⣟⠿⣿⣿⣿⡆⣿⣿⢀⣿⣿⣿⣣⣾⣿⣿⠷⠶⠼⠏⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣿⡆⢿⣆⢿⣔⢻⣿⣿⣧⣿⣏⣼⣿⣟⣿⢣⣶⣶⠖⣿⠟⠜⢀⡴⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠚⣽⣿⣳⣶⣤⡴⣾⡟⣿⣿⣿⡟⣹⣿⣿⣾⠏⣼⣿⡟⣸⢁⣬⣤⢾⣧⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⣿⢻⣧⢿⣿⡇⣿⣿⢿⣿⣿⢀⣿⣿⣿⣟⢀⣿⡿⢡⢃⣾⣿⢏⡾⢁⢞⣾⣿⣶⣶⠒⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠸⣿⡏⢻⣌⣿⣧⢻⣿⣾⣿⣟⣸⣿⣿⡿⡏⣸⣿⠃⣼⣾⡟⣡⡾⢇⢎⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣶⣤⣽⣿⡈⢿⣽⣿⡘⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⠇⣼⣿⠏⣰⣿⣼⡷⠛⠛⠃⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢣⡹⣻⣿⡹⣷⠈⣿⣿⣧⣹⣿⣿⣿⣿⣿⢿⠇⣼⠃⣼⡟⣡⡾⣟⣿⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢿⣧⡹⣿⡇⢿⣇⢹⣸⣿⡼⣿⣿⣿⣿⣿⣧⣀⣿⣾⣿⣾⣿⣵⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢻⣷⣹⣿⢸⣿⡄⢻⣿⡇⢿⡿⢿⣿⣿⠞⠋⠉⠹⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⢙⣿⣧⠀⣿⣿⣸⠟⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠧⠼⠋⠁
⣀⣀⣀⣀⡀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀
⣿⣿⠿⡻⢿⠛⡿⢿⢿⣻⡿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡟⣦⠀⠀⠀⠀⠀⠀⠀⡄⡇
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠄⢹⣿⢽⣷⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠆⠁⠄⠀⠀⠠⠄⠀⠀⢀⠄
⠀⠀⢸⣴⢀⠀⣄⠀⠀⠀⢠⠀⠀⢸⣿⣯⣯⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠈⠽⢹⠀⠀⠀⠀⠀⡄⠀⠀⣽⣾⣼⣙⣙⣷⠀⠀⠀⠀⡗⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀⣀⢠
⠀⠀⠀⢀⠐⠁⠀⠀⠀⢀⠁⠀⠀⢿⣽⣯⣿⣿⣵⣄⠀⠀⠀⠡⠨⢷⡈⠀⠀⠀⠀⠀⠀⢀⡠⠬⠐⠂⡇
⠀⠀⠈⢀⠀⠠⠀⠀⠀⡌⠀⠀⠀⣿⣾⣷⣥⣿⣾⡟⠀⠀⠦⠄⠉⡁⠦⠀⣀⠀⠀⠀⠀⢦⢰⣛⡹⢃⠦
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠳⠀⠀⠀⠈⡛⢉⠃⡛⠁⠀⠀⠀⠈⠃⠁⠀⠀⠀⠁⠀⠀⠀⠈⢣⣗⡝⡖⠕⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⡀⠀⠀⠀⠂⠀⢈⠁⡲⢱⣠⠀⠀⠀⠀⠴⠂⣂⢀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠈⠀⢀⡀⠀⠀⠀⠘⢀⠓⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡰⣀⢀⠀⠈⡰⠑⢂
⠀⠀⠀⠀⠪⠀⠀⠀⣀⡀⠀⠀⠀⠉⠉⠓⠐⠀⠅⠽⣠⣦⠃⠐⠶⣤⣀⣠⡤⠀⠀⠐⡈⠀⠄⡌⡡⠵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠐⠼⣷⣶⣶⣾⣿⣍⣛⣿⣿⠯⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣂
⠀⠀⠀⠀⠀⠀⣈⠉⠛⠻⠛⢉⣀⡦⠤⡟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣸⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣼⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠴⢷⣤⡀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⣾⡇
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠁⠀⠀⡜⠀⠀⠀⠀⠀⠀⢠⣄⣠⣀⠀⠀⠀⠀⠀⠀⣠⣄⣀⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠁⠁⠁⠀⠀⣠⣼⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠓⠂⠀⠂⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣺⣿⣥⣵⣄⡐⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢖⠳⣤⠊⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠉⠛⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⣠⠜⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⢠⣼⣿⣇⡂⣠⡇
⠀⠠⠀⠀⠀⠀⠀⠀⢠⣤⠼⠱⠀⠀⠀⠀⠀⠀⠀⠤⢄⡀⢹⣷⣦⡀⠀⠀⠀⠸⡈⠀⠀⠀⠉⠙⢿⣿⠙⣿⠁
⠀⠀⠀⠀⠀⡀⠾⢦⡸⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⠑⠀⠀⠀⠀⠘⣆⢀⡀⠀⠀⢨⣧⡤⠁
⠀⠀⠀⠀⠀⠀⠤⠞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠈⠙⠻⠦⠴⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢄⢠⢀
⠀⠀⠀⠀⠐⠤⠠⢠⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠷⠈⠀⣶⠂⠄
⠀⠀⠀⠀⠀⠈⣁⡚⠠⢔⡀⠋⠻⡀⠀⠀⢀⠄⠀⠀⠀⠀⢀⠔⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠀⠌⢢⡙⢃⣤
⠀⠀⠀⠀⢀⢼⠉⢋⠺⡌⠉⠐⢖⢇⠂⠇⠐⠂⠀⠀⠀⢰⢧⠼⣀⡤⠜⡆⠀⡀⠀⠀⠀⠀⠀⡴⢄⠀⠀⠀⠀⢃⠘⠂⠙⠴⣉⠊⠘
⠀⠀⠀⠀⡃⡖⠀⠀⡏⣡⠠⣦⣏⣘⠀⠁⠈⠀⠀⠀⠀⠈⠀⢶⠁⠀⠀⡇⠐⢀⠂⠀⠀⢀⡈⠀⠀⠥⠄⠀⠀⠀⠁⠡⢸⡀⠋⠜⡰⠂
⠀⠀⠀⠀⢁⢠⣴⠂⠇⠛⠢⣀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⡇⢚⠀⠀⠀⠀⠈⠀⡄⠂⣠⠀⠀⠀⠀⠀⠱⣼⣧⡮⠈
⠀⠀⠀⠀⠈⠀⡌⠁⠀⠀⡠⢊⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠇⠀⣿⠅⠈⡀⠀⠀⠀⡀⠀⢈⠓⠀⠀⠀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⢆⢤⠀⡴⣬⠔⠁⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠦⣬⣀⣥⠤⠃⠁⠀⠀⠀⠀⠀⠠⠀⠂⠀⠒⠁
⠀⠀⠀⠀⠀⠈⠒⠶⠋⠀⠀⠀⠀⠀⡠⠻⡶⡄⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠁⠰⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⢰⡔⠢⡱⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠋⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⡝⠁⠣⡄⢧⠭
⠀⠀⠀⠀⠔⠇⠙⢄⠀⠀⠀⠀⠀⠀⠑⢄⡥⠊⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠦⠀⠇⣷⠰⡦⠉⠀⠀⠀⠀⠸⠈⡞⠤⢠⡄⢿⠍
⠀⠀⠀⠞⠘⢆⡰⠨⣆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢴⠢⠐⢄⡀⢢⡸⢯⣿⡀⠀⠀⠀⠀⠀⠆⢠⣶⠂⡐⠀⣴⢰⣇⡚
⠀⠀⠀⠐⡈⢺⡄⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡀⠰⠈⣠⢡⡔⣁⠂⣱⠀⠀⠀⠀⠸⠄⠦⠬⢱⡁⣰⠭⠛
⠀⠀⠀⠀⠱⡂⡴⠃⠀⠀⠀⠀⠀⢀⠠⠖⡤⡀⠀⠀⠀⠰⠄⣬⠀⠀⢀⡄⠃⡠⠀⠋⠰⠁⠀⠀⠀⠀⠀⠱⣌⣱⡡⠜⠁
⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠴⢡⠆⠀⢤⠄⠲⠀⠀⠀⠈⠯⠿⣼⠤⠟⡴⠀⠌⡴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢀⠀⠀⠀⠀⠀⠆⡀⡄⠀⠀⠀⠉⠙⠶⣺⣗⡾⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺⣸⡀⠳⣏⠀⢀⣦⡟⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠏⢙⢂
⠀⠀⠀⠀⠀⡤⠤⠀⢀⠀⠀⠀⠚⠏⣠⠀⢀⡸⠒⠀⠀⠀⠀⠣⢰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠺⠙⠕⢀⠀⠀⠀⠀⢰⡏⠈⢢⠊⠉⠃
⠀⠀⠀⠀⢐⢐⡈⣶⠈⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⡳⢀⠌⣀⡀⠀⠀⠀⠀⠐⠃⡇⡄⢚⠁⡄⠀⠀⠀⠲⣷⢃⠘
⠀⠀⠀⠀⠘⡀⠰⣬⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣄⡐⢢⢾⠃⣳⡀⠀⠀⠀⠀⠃⢑⠠⡈⢆⠁⠀⠀⠀⠘⡷⠏⣶⠀⠀⡇
⠀⠀⠀⠀⠀⠐⠀⢳⣵⢇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄⣘⠉⢻⠀⠙⠀⠁⠀⠀⠀⠀⠈⠈⡀⡘⡡⠆⠀⠀⠀⠀⠉⠛⣡⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢌⣳⠟⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⢄⠀⢣⣤⢀⡇⠀⠀⠀⠀⠀⢥⠖⠺⣳⠆⠀⠀⠀⠀⠓⣒⡁⡷⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⣨⠑⡿⡴⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠉⠉⠓⢦⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⠖⠋⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣀⣀⡀
⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⢳⡄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠻⢤⡀⠀⢀⣀⣠⣤⠤⠴⠶⠶⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⠦⠤⢤⣄⣀⣀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⢘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠀⠀⠀⠀⠀⠈⠉⠙⠺⢯⡁
⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠘⢧⣀⠀⠀⠀⠀⠀⢀⣴⠏⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠸⡏⠓⠦⣤⣀⣀⠀⠀⠠⡇⠀⠀⠀⠀⠈⠛⠒⠶⠖⠚⠉⠀⠀⠀⠀⠈⡇⠀⠀⢀⣀⣠⡤⠖⢋⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠉⠉⠙⠛⠛⠒⠶⠶⠶⠶⠶⠦⠤⠤⠶⠶⠶⠶⠶⠒⠚⠛⠛⠉⠉⠁⠀⢀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠦⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠤⠶⠖⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢉⡜⡿⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⢀⠞⢠⠇⢧⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠈⠉⢁⢮⡀⢸⠀⢸⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢱⠐⠭⠑⠢⢄⡀⠀⠀⠀⠀⢸⠀⠀⠀⡸⠀⠱⡮⠔⢻⠙⠒⠼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡸⠓⢤⣀⠀⠀⡾⡄⠀⠀⠀⡏⠀⠀⢠⠃⠀⢰⠁⠀⡏⠀⢠⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡀⠀⢠⠃⠀⠀⠈⠙⢺⠀⡇⠀⠀⢠⠃⠀⠀⡜⠀⢀⡇⠀⢸⠁⢠⠣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠓⡇⠀⠀⠀⠀⠀⢸⠀⢱⠀⠀⣸⠀⠀⢰⠁⠀⡸⠀⠀⡇⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢳⠀⠀⠀⠀⠀⢸⠀⢸⡀⠀⡇⠀⠀⡎⠀⢠⠇⠀⢸⠁⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠘⡆⠀⠀⠀⠀⢸⡆⠀⡇⢰⠁⠀⣸⠀⠀⡼⠀⠀⡇⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢻⠀⠀⠀⠀⢸⡇⠀⡇⡌⡀⠀⡇⠀⢠⠇⠀⢸⠁⢠⠇⣀⡤⠴⢒⣋⣹⠿⡷⡆
⠀⠀⠀⠀⠀⢰⡶⣖⠲⠦⠤⢿⠀⠈⣇⠀⠀⠀⢸⡇⠀⢸⣇⠇⢸⠁⠀⡜⠀⠀⡎⠀⣞⠉⢀⡠⠔⠊⠣⣄⡼⢁⣹
⠀⠀⠀⠀⠀⣸⠹⡀⠉⠲⣤⢋⣇⠀⢹⡀⠀⠀⠸⡇⠀⢸⡎⡆⣾⠤⠚⠓⢤⣸⣁⣼⡕⠚⠁⠀⠀⠀⢀⡜⢉⡥⠋
⠀⠀⠀⠀⠀⡇⠀⢳⡠⠞⠉⢧⢹⡀⠈⣇⠀⠀⠀⡇⠀⠈⣿⠊⢹⡑⢦⡤⠖⢻⠁⠀⠑⣄⠀⠀⢀⢠⠎⢰⠟⠁
⠀⠀⠀⠀⠀⠫⡉⠉⠳⡄⠀⠈⢦⣧⠀⢹⡀⠀⢰⣇⣀⣀⣇⠀⣀⣧⣎⣀⠀⢸⣀⡤⠚⠙⡀⠀⣰⠃⡴⠃
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠘⢆⠀⢀⣻⠤⠴⠓⠋⠉⠀⢉⣩⠽⢿⠁⠀⠀⠈⠉⠙⡅⠀⠀⠀⢇⣰⣣⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⢴⡋⠉⠀⠀⣀⡤⠤⠒⠋⠉⠀⠀⣈⡇⠀⠀⠀⠀⠀⢱⠀⠀⢀⡞⢩⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⣨⠗⡎⠉⠀⠀⠀⢀⣠⠴⠚⠉⢰⠃⠀⢀⡀⠀⠀⠈⣇⢀⡞⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢰⣯⣖⣉⣀⣀⣹⣀⠤⠖⠊⠉⠀⣀⣠⠥⠺⡖⠒⠲⠶⠤⠤⠤⣼⠾⠒⢒⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⢀⡟⠀⣀⣤⡴⠒⠛⠯⣄⡀⠀⠹⡄⠀⠀⢀⡤⠚⢑⡮⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠚⠉⠉⠙⠒⠦⢤⣀⡀⠉⠓⠦⢽⡤⠖⣉⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠴⠓⠉

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⣉⠂⠀⠀⠀⠀⢀⡎⡁⠀⣄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣤⠀⢠⠇⠀⠀⠀⠃⣿⡇⠘⢺⡀⠀⠀⠈⣿⠐⠃⠀⣿
⠀⠀⠀⠈⢩⣦⡀⢸⠀⠀⣽⡡⣻⠀⠀⠀⠀⠀⣿⡇⢠⠀⠁⠀⠀⠀⠹⠀⠰⠀⣿
⠀⠀⠀⠀⣀⠙⢿⣾⠀⠀⢿⡕⠁⠀⠀⠀⠀⠀⣿⠇⠠⡄⠀⠀⠀⠀⠀⠀⠀⢄⣿⠀⠀⠀⠀⠀⠀⡕
⠀⠀⠀⠀⠠⠤⢨⣇⣤⣾⣷⡶⠀⠀⠀⠀⠀⠀⢿⣇⢲⠃⠀⠀⠀⠀⠀⢸⠷⠞⠋⠀⠀⠀⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡄⠀⠀⠀⣰⠂⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠳⢄⡀⠀⠀⠀⠀⠈⠁⠰⠂⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠉⢳⠀⠀⠀⣀⡄⠀⣁⠀⠀⠀⠸⢆⡀⠀⠀⠁⠁⠀⠀⠀⡅⠀⠀⡖⢰⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣤⠈⠆⠀⠀⣿⠇⢠⢇⠀⠀⠀⠀⠀⠉⠀⡆⢰⠀⠀⠀⠀⡇⠀⠀⡇⡆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢹⡇⠀⠀⢀⣿⣀⠅⢈⣀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡇⠀⠀⠁⠃⠀⠀⠀⠀⠀⡅⠀⣠
⠀⠀⠀⠀⠈⡿⠢⠞⠁⣿⠿⢀⡾⠃⠀⠀⠀⠀⠀⣄⠽⠁⠀⠀⠀⠀⠣⢀⡴⠖⠀⠀⠀⠀⠀⠀⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠐⠀⠀⢾⣆⠀⠀⠀⠠⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⣼⠁⠀⢀⠠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠙⠃⠒⠊⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡀⠀⠀⣨⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣷⡄⢠⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠨⠟⠋⠙⣯⠀⣿⣿⣿⣿⣿⡠⡟⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣘⠃⠆⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⢀⠠⠤⠰⠀⠲⠶⠋⣙⠛⠋⠉⠉⣿⣿⣿⣿⣤⡥⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡀⠀⠂⠀⢸⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⠈⠠⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠧⣀⡀⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠃⠀⠈⠁⠂⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⢀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣶⠂⠈⣠⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣾⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣼⣿⡞⣷⡘⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⣼⣿⣿⡿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⣰⡹⠧⣿⣽⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⠟⠉⠈⢟⠀⠀⢀⣼⢃⢃⣶⡟⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⡤⠀⢾⡟⢋⡌⠦⣿⣻⣭⣿⡿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣿⠈⠁⠀⠀⠀⠀⠀⠻⣟⡼⣴⣏⣷⣿⣿⡔⢛⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣼⣿⣿⣿⣼⣿⣶⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⢧⣴⣦⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣬⣿⢺⣡⣾⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣾⡿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⡈⠀⠠⠄⠈⢁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠌⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠐⠂⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠐⠄⠀⣀⠐⠀⡀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⢀⠄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠠⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠡⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠐⠀⠀⠒⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠁⠀⠁⠈⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡄⠀⠀⠀⠀⠐⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⡀⠐⠀⠀⠀⠀⠈⠆⣀
⠀⠀⠀⠠⠐⠈⠠⠄⠀⠀⠀⠄⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⠂⢀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠄⠀⠀⠀⠠⠀⠤⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⢀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠀⠤⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠄⠐⠂
⠀⠀⠀⠀⠀⡀⠀⠘⠀⠐⠀⠀⠀⠂⠀⠓⠀⢀
⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⣿⣯⣿⣋⣏⣽⣹⣼⣹⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠂⠀⠀⠁⠀⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⢀⡀
⠀⠀⢰⣿⠉⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖
⠀⠀⢸⣿⣿⣀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠸⠟⢃⣀⠠
⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⣿⠀⠀⠀⢀⠀⠀⠀⠀⠓⠥⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡄⠀⠀⠀⠀⢹⣟⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣠⣀⠀⣀⠀⠀⠀⠀⠈⢻⡄⡔⠁⢀⣀⠄⠀⠀⠀⠀⠀⠀⢀⡾⠛⠀⠀⠀⠀⠋⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠀⠀⠀⠀⢀⣀⢿⣷⣀⢀⡾⠿⠀⠀⡠⠀⠘⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡿⢙⢻⣿⣋⡰⡇⠀⠀⠸⢳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡅⠀⠹⢇⣾⡇⠀⠀⠀⢃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⣀⢠⣾⢏⣗⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠃
⠀⠀⠀⠂⠀⠀⠄⢀⡀⠀⢀⠀⠀⠀⠀⠛⠗⠒⠓⠚⠓⠋⠁⠀⠀⠀⠀⠙⠻⠿⠿⠟⠟⠃
⠀⠀⠀⢰⠀⠀⠀⣿⢻⡓⠎⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠛⠛⠛⠳⣟⠿⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⣸⡇⠀⠀⡠⡼⠀⠀⠀⠀⡄⠀⣠⡄
⠀⠀⠀⣀⣓⡀⠀⢠⣄⡀⠀⢀⣤⠂⣁⣼⣤⠆⠀⠀⠀⠀⢀⠴⠄⠆⠀⠻⡾⣀⡀⡘⠫⣴⠖⢶⣤⣄⣄⡘⠋
⠀⠀⠀⢙⣯⠻⣄⠀⢻⣿⣶⣠⡯⠈⠉⣰⠂⠀⠀⠀⠀⣴⣦⣄⡀⠀⢠⡼⢻⠿⣤⡅⠠⣿⣀⠀⣉⠀⠀⠈⠄
⠀⠀⠀⠀⠛⣷⡝⢧⡀⢻⣿⣿⠀⠘⣴⣧⣶⡶⡡⠀⠐⣿⣀⠀⠀⠀⠸⣆⡄⠀⢀⣆⠚⢸⠫⠞⢻⠖⢛⣡
⠀⠀⠀⠠⠴⠛⠿⣌⣿⣿⠟⣛⣛⡟⢛⣿⠉⠇⠀⠀⠀⠙⠻⢶⢂⣼⣶⠵⢏⣿⠧⣤⣠⠿⠓⠢⠶⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠶⠆⠉⠃⠈⠋⠉

⠀⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠒⠀⠀⠀⠀⠠⠆⠀⠀⠀⡀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠄⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠄⠀⠀⠠⠀⠑⠀⠀⠀⠈⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠠⠈⠀⠈⠁⠀⡄⠆⠃⠀⠀⡄⠀⠐⠄⠩⠠⠄⡘⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⡄⠂⡀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠰⠄⠀⠀⠀⠀⢈⠀⡀⠀⠀⠀⠨⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡐⠁⡀⠈⠁⠀⠀⠀⢀⡀⠀⠀⠐⠄
⠀⠀⠀⠀⠔⠀⠐⠒⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠋⠀⠀⠈⠀⠀⠐⠄⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠐⠁⠀⠀⠀⠀⠢⠀⠀⠀⢰⠀⠀⡄⠀⠐
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠠⢀⡰⡠⠈⠀⠐⡀⠀⠍

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠈⠁⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⡆⠀⠀⠑⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠞⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⡀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠖⠀⠀⠆⠙⠀⣀⡁
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠀⣈⠀⠱⣄⠀⠀⢀⠈⠀⠀⠐⠄⠉⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⡃⠀⠀⠀⠀⠀⠀⠊⠁⠠⠀⠀⠀⠈⠀⠀⢹⠀⠀⠊⠀⠀⠀⠀⢀⠑⠁⠀⠀⠀⠀⠀⠀⡃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⡶⠙⠠⠀⠈⡆⠀⠀⠀⠀⠠⠚⠉⠰⠀⠀⠀⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⡠⡀⠸⢀⠀⠀⠲⠀⠀⠈⠁⠀⠀⠀⠀⡀⢀⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣀⠀⠀⠐⢃⠀⠀⠰⠿⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠠⠀⠀⠀⠀⠀⠀⠉⠁⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠶⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠰⠖⠒⠚⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢤⠀⠀⠀⠀⠀⢠⠄⠚⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣿⣿⢿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣻⣷⣿⣼⣿⣷⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣽⣻⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣯⣿⣿⣿⡿⣫⣿⡿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⣯⣻⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⢟⣽⣿⣿⣿⢿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⢞⣽⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣯⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣽⣿⣟⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣷⣾⣝⢿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣮⣿⣿⢻⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢸⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣼⣿⣾⣿⣿⡿⣿⣯⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⡟⣿⣯⣿⣿⣿⣯⣟⣛⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣻⣿⣻⣿⣿⣿⣟⣿⣿⢿⣟⣿⣿⣿⣿⣿⢽⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⡯⣿⣿⣿⢿⣿⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣷⣿⣟⣿⣿⣿⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣯⢟⣿⣿⡿⣿⣿⣾⣟⣿⣷⣽⣿⣿⣿⣿⣿⢿⣿⣿⡿⣻⣿⣿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣻⣿⣿⣽⣿⢿⣿⣿⣿⣿⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣞⣿⣿⣿⣿⣷⣿⣿⣿⣿⣽⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣻⣵⣿⣿⣿⣿⡿⣟⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣽⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣟⢿⣺⣿⢾⣿⣷⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣾⣿⣿⡟⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢸⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣸⡄⠀⢑⣆⡶⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⢸⠁⠀⠈⣩⣄⠀⠀⠀⠀⣠⢄⣿⠿⠂⠀⠀⣲⡀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⢼⠀⠀⠐⣏⣸⡇⠀⠀⡼⠋⢸⣿⣀⡆⠀⠀⠈⢷⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⢸⠀⠀⠀⠈⠉⠀⠀⠀⠁⠀⢸⣿⣿⣧⡀⠀⠀⢸⢻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⠂⠀⢸⣿⡏⠈⡇⠀⡄⢎⠚⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⡿⠛⠋⠀⠉⢹⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠿⠗⠀⠐⠠⠚⢦⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⣸⡇⠀⠀⢀⣀⡾⠃⠀⠐⠄⣶⣤⣄⣀⣀⠀⢸⣿⡶⠁⠀⠀⠀⢾⠀⠀⠃⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⢸⠇⠀⢠⣭⡍⣄⠀⠀⠀⠒⠀⠉⠉⢧⠀⡆⢸⣿⣣⡇⠀⠀⠀⠸⢷⣷⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⡀⠀⢼⡇⠀⠀⢹⣷⣹⣦⡀⠀⠀⠀⠀⠀⠘⠀⡗⠀⣿⣿⠃⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣿⠀⢸⡇⠀⠀⣮⢿⡿⣟⡣⠀⠀⠀⠀⠀⠐⢂⣇⠀⣿⣿⡆⠀⠀⠀⠀⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡀⢸⡇⠀⠀⠙⠾⠿⣿⣶⣶⣶⣶⠶⠻⠟⠛⠋⠀⢻⣿⡆⣠⣄⠀⠀⠀⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⡇⣀⣟⢻⣲⣤⢦⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⠛⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢹⡷⣼⡇⠀⠀⠀⠀⠀⠘⡷⣿⠯⠚⣁⡴⣾⢿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢟⡐⢫⣏⠠⠴⠟⣡⡶⠀⠀⣷⣴⣿⡅⠀⠀⠀⢀⣤⡶⢛⣥⣶⢯⢟⣽⣷⣿⢿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⣶⣭⣿⡷⠶⠾⠋⠀⠈⢿⣦⠀⠰⣟⣿⣟⣿⣛⢿⣿⣿⢫⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⠈⠿⣷⡄⠀⠀⠀⠀⠹⣧⠀⢨⣯⣿⣿⡟⠻⠾⢻⡭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣾⠆⢿⡇⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠸⣿⡄⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠙⠳⣄⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠟⠛⠦⠛⠀⠀⠀⠀⠀⠘⠿⣦⡀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡟⠋⠑⢶⣤⣀⡺⠷⣛⣿⣿⡇⠀⠀⠀⠀⠈⠻⣦⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠾⠿⠿⠿⠿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣈⠛⠛⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⣰⣿⠀⣀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠰⠀⠇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⣂⠤⣄⢉⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠋⠉

⠀⠀⠀⠀⠰⢀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠁⣮⠊⠀⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⡀
⠀⠀⠀⠀⠀⠚⠛⣤⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢀⡄⠑⠂⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠇⠰
⠀⠀⠀⠀⠐⢲⠂⠸⠿⠷⠇⠀⠁⠀⠀⠀⠀⠀⠀⠊⠀⠰⡀⠀⠄⢀⠀⢤⠀⠀⠀⠀⠀⠀⡀⠠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢈⠒⠀⠀⠀⠀⡀⣐⠀⠀⠀⠀⠀⠈⡐⠰⠀⠀⠀⠰⠱⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠨
⠀⠀⠀⠀⠠⢾⡌⠄⠀⢀⡀⣘⠋⠅⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠀⠀⠀⠀⠀⠀⠀⠂⢜⠀⢀⣀⡁
⠀⠀⠀⣠⢀⡉⠡⠿⢐⠃⠬⣤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠙⠇⢤⡤⠹⠒⠶⠮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠀⠀⠀⠀⡀⠀⢾⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠠⠰⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⡔⠀⠐⠀⠀⠀⠀⠁⣀⠀⠀⢀
⠀⠀⠀⠘⠐⠀⠀⢵⠀⠀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡌⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡁⠀⠀⠀⠠⣄⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠁⠀⠀⢘⠂⠀⠀⠀⠀⠀⠀⠀⢠⡴
⠀⠀⠀⠀⠀⠘⠀⠒⠀⠀⠁⠀⠀⠀⠀⠉⢀⣰⠀⡌⢉⠀⠀⠀⠀⠀⠀⠀⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⠔⣰⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⡶⠂⠀⠈⢻⠷⠄⠀⠀⠀⢰⡒⠺⠉⠀⠚⢉⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠂⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⢀⣄⠀⠀⣤⣠⡄⠀⠀⠀⠀⢨⡀⣄⠀⠀⣰⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⡟⠉⢀⠀⠙⢿⣇⠀⠀⠀⠀⠀⠀⠉⠳⠰⠀⢀⠃⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣧⣄⠀⠀⠙⠀⠀⠀⠀⠀⠈⠧⢀⣄⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣤⠀⢀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢿⣃⠘⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢶⡆⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣠⡏⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣰⠶⠶⠟⠛⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠛⠛⠛⠛⢷⡄
⠀⠀⠀⠀⠀⣿⣄⠀⠘⠿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⠾⠀⢀⣀⣼⠇
⠀⠀⠀⠀⠀⠈⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠐⠲⠶⠤⠤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢀⣀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡶⠛⠉⠁⠀⠀⠀⠉⠙⢳⣄
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠛⠻⢷⣄⠀⠀⠀⠘⣷
⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡾⠇⠀⠀⠀⠀⠙⣧⠀⠀⠀⢹⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠘⣧
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢰⡏
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣸⠇
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡴⠃⠀⠀⢠⡟
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣄⣀⡴⠟⠁⠀⠀⢠⡿⠁
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣴⠟
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠁
⢰⡟⣿⠀⠀⠀⢀⡴⠒⢦⡀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠈⣿⣛⠛⠛⠋⠉
⠸⣷⠇⠀⠀⠀⠸⣄⣀⣠⠇⠀⠀⠀⠀⢸⡁⠀⠈⣷⠀⠀⠀⠀⢰⡇⠀⠀⢙⡇⠀⠀⠀⠀⢹⡉⣷
⠀⣿⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠙⠲⠚⠁⠀⠀⠀⠀⠀⠙⠲⠶⠛⠀⠀⠀⠀⠀⠀⣿⠋
⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⢸⡏⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠺⣧
⠀⠈⠻⠶⣶⣶⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣶⠶⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠈⢀⠐⣿⡇⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⢩⠀⠀⢘⣧⣤⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠛⠉⠉
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠
⠀⠀⠀⠀⠀⢦⡀⠀⠈⢧⡀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⠀⠀⠈⣧⠀⠀⡰⠀⠀⢀⡔
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠅⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠺⣱⡀⠀⣣⣄⠀⠈⣷⠏⠀⠾⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠒⠀⣤⠈⠋⣀
⠀⠀⠀⠀⠀⠀⠙⣲⠉⠙⢀⡀⢻⠖⢾⠀⠨⠋⠉⢠⡴⠂⢀⡠⠊⠀⠀⠀⠀⠀⠀⠆⠈⠃⠘⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠦⢀⡴⢻⡋⢠⠃⠀⢀⣠⠄⢸⡵⠞⠁⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⣿⣯⠀⠄
⠀⠀⠀⠀⠂⠄⠀⠀⡀⡈⠃⢈⡤⠂⣁⠀⣈⣁⠐⢯⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣠⠀⢼⠇⠀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠓⠛⣐⣏⠨⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠭⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⡄⠀⠀⠀⠀⠀⣰⣦⠀⡄⠀⠀⠀⠠⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⣴⢿⣿⠿⣿⡳⡄⠀⠀⠀⢀⣼⣏⠀⠀⠀⠈⣼⡿⣠⣶⠐⡟⠿⡻⣿⡆⠀⠀⢱⡻⢉⣾⣾⣄⠀⠀⠀⠀⢀⣾⡟⣭⣱⡄⠀⠀⠀⢠⣿⡀
⠀⠀⢴⣷⣴⣾⢀⣼⣷⣧⠀⠀⠐⢿⣿⡯⣄⠀⠀⠠⣬⣛⠀⢸⣄⣴⡾⣾⣿⠃⠀⢰⣾⣁⠈⢾⣿⣿⡅⠀⠀⠀⣖⣴⣿⣷⣿⣿⠀⠀⠀⣼⣯⡁
⠀⠀⡖⢻⡿⠀⢺⣿⣿⣿⣄⠀⢠⣾⠋⢻⣕⢀⣿⣦⠛⠋⠀⣰⡍⣻⣴⡾⠃⠀⠀⠀⣙⡷⠒⢿⣿⣆⣿⡄⠀⠀⢻⣇⣯⣍⣿⠿⣷⣶⣦⡇⠀⡁
⠀⠀⡔⣸⣇⣤⢾⡛⠭⣻⣿⣿⣿⡅⠀⠀⠙⣷⣿⣿⣁⠀⣨⠻⠿⡿⡟⠁⠀⠀⠀⠀⠸⡿⣶⣴⡿⠳⠁⠀⠀⠀⡠⠟⠀⣿⣈⡾⠻⣿⣿⣽⣶⣥
⠀⠀⠀⠈⡯⢫⣄⠀⠰⡌⢻⣿⡿⠆⠀⠀⠀⠈⣿⣿⠿⡿⠧⣹⣾⠏⠀⠀⠀⠀⠀⠀⠐⠘⢻⣿⠊⠀⠀⠀⠀⠀⡇⢄⠀⠹⡻⡿⠾⡦⣊⣁⠰⠟⠂
⠀⠀⠀⠀⣿⣈⣗⣇⡵⢣⠎⠋⣹⡀⠀⠀⠀⠀⠐⡇⠀⠀⣀⣉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠹⠈⢳⡶⠃⠠⠜⢛⢽⣅
⠀⠀⠀⠀⢰⣈⣯⠿⠒⠋⣀⢐⣯⣿⡄⠀⠀⠀⠀⢣⣤⠴⢃⣯⣿⣦⡀⠀⠀⠀⠀⢤⡊⠀⠈⠀⠀⠀⡄⠀⠀⠀⠈⡇⠛⢐⣈⣠⣴⣋⣆⣿⣦⡀
⠀⠀⠀⠀⠈⠻⠇⠀⠀⠸⠙⣾⣿⣿⣿⡀⠀⠀⠀⠀⣧⣄⣘⣽⣿⣿⣿⣆⠀⠀⠀⠿⢢⡄⡀⠄⡦⡤⠁⠀⠀⠀⠀⠈⠙⠛⣹⣿⣿⣿⢿⠿⣧⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣛⠛⡿⠒⠀⠀⢨⣽⣏⡌⠛⠃⣿⣿⣆⠀⠀⠀⠈⠙⠛⢱⠂⣜⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⡿⠛⠉⢈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⣽⣿⣿⣤⣤⣤⠀⠘⣯⣛⡔⣡⢰⣿⣿⡟⠀⠉⠀⠙⢲⣄⠂⢈⣩⢣⠄⣠⣤⡀⠀⠀⠈⠁⠰⠥⠄⢚⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠀⣇⠀⠁⠀⠀⠚⣷⡌⠞⢿⠛⡍⠴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠉⠢⣅⠠⢀⠀⢠⣤⣶⣿⣆⢠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠁⠀⠀⠀⠀⠀⠉⠀⠀⢠⠃⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠘⠶⣭⡀⡀⠐⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠁⠀⠀⠀⡄⠀⡆⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⣿⣴⣤⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣸⣾⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⠀⢸⠀⠀⠀⣨⠓⢾⠁⠀⠀⠀⠀⠀⠀⠐⢇⠀⠀⠀⢤⣙⢧⠀⠑⠢⣌⠴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠘⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⠁⠀⠀⠀⢿⠈⠓⠀⠀⠘⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢿⠂⠀⠀⠀⠀⠀⠀⠚⠀⠐⠐⠀⠐⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠠⠀⠀⠈⠀⠀⠃⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢸⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠇⠀⠇⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠰⠀⠀⠈⢷⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⡇⠃⠀⠀⠀⠀⠀⠀⢨⢰⠃⠀⠀⠠⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢧⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⡀⢠⣤⣀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢈⠑⠀⠀⠐⠘⠀⠀⢀⠁
⠀⠀⢠⣥⠶⢤⣀⣤⡑⢦⠴⣈⣠⡀⡀⠶⠱⣄⢀⢄⠀⠘⢄⢀⠀⣠⠞⠢⠤⠜⠙⠲⢺⠇⠀⠀⠀⠀⠀⠀⡀⠠⢀⣀⠀⠀⠄⣀⠀⠄⢀
⠀⠀⣷⡁⠀⠉⠝⠺⠯⢠⡤⡽⠟⠁⠀⢶⠀⣛⠈⠘⢦⡤⠊⢠⠁⢀⡐⠤⠀⠠⣥⣤⣼⡄⠀⠀⠀⠀⣠⣾⣤⠄⠴⠁⣤⣠⣤⠀⢦⠄⣀⡷⢄
⠀⠀⠻⣄⡠⣤⣶⣷⣤⣈⣠⣤⡏⣿⣶⢤⣤⡽⠁⠀⠀⣿⣶⣾⣯⠶⣲⡛⠋⠉⡙⣉⡀⠀⠉⢣⡀⢾⠁⠘⠁⠀⠀⠚⠛⠛⠛⠂⠀⠀⠈⠁⠀⡷
⠀⠀⠀⠙⢇⠀⠈⠺⠛⠛⠛⠛⠗⠀⠀⢈⠏⠀⠀⠀⠀⠘⡛⠉⣏⣬⣉⣁⣙⣏⣁⣉⣡⣬⠁⠘⠓⠀⠡⣀⣠⡀⠀⠀⠀⣄⠀⠀⠀⢀⡄⢀⠞⠁
⠀⠀⠀⠀⠈⠢⡀⠀⣄⠀⠀⢠⣦⣀⡴⠁⠀⠀⠀⠀⠀⠀⠈⢶⡎⢻⠛⠋⠛⠘⠙⠋⢹⢱⣀⠊⠀⠀⠀⠈⠻⣷⣶⣶⣦⣿⣤⣿⣶⣾⡷⠁
⠀⠀⠀⠀⠀⠀⠑⣾⡾⣷⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠈⣆⠀⠀⠀⠀⢠⠇⡾⠁⠀⠀⠀⠀⠀⠀⠙⢄⠙⡿⠈⢿⠏⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⡿⡿⠃⠀⢀⣠⣄⣀⡠⠄⣀⠀⠀⠀⠀⠁⣸⠀⣠⣧⠐⣻⡔⠁⠀⣀⠄⠄⠠⠄⢀⡀⠀⠠⣤⣀⣤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⡠⢰⠯⠛⢼⠋⠀⠀⠀⠀⠻⣶⣤⡀⠀⠘⢧⢹⡿⢰⠏⡠⠒⢻⣅⠺⢧⣤⣀⡌⠻⣶⣄⠈⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡍⠀⠰⠀⠓⢤⡤⣤⣤⣤⣾⣿⠟⣆⠀⠈⢣⣷⠃⡔⠁⠀⠈⡹⠓⠀⠃⠁⢀⠀⠈⠿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢭⣴⡤⢠⡄⠀⠈⠅⠁⠐⠒⢂⠛⠉⢣⠀⠀⠁⢰⣷⣦⠈⠃⠀⠀⠀⠀⠀⠀⠁⢨⠇⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠱⠚⠦⣄⣄⣀⢠⡄⠈⠀⢺⡀⡇⠀⠀⠸⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣿⣄⠀⡈⠀⠈⠒⠊⠙⡿⠤⠚⠁⠀⠀⠀⣤⣜⣇⠠⡄⠀⠀⠀⠀⢀⣤⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⢧⣿⣶⡿⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠘⢏⠀⠀⠀⣰⣶⣲⠎⠈⠋⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡛⡃⢀⣠⡴⠄⠊
⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀⡠⠄⠤⣠⣠⡀⠀⠀⢀⡀⡶⠛⣉⡙⠉⠉⢈⣷⠄⠀⠿⠉⠂⢄⠀⠀⠀⠀⠀⣀⣤⡤⠤⠤⢄⣀⡀
⠀⠀⠀⠀⣠⣮⠄⠀⢠⣽⡆⠀⣛⢁⣬⣙⣆⠴⣿⣷⣤⠤⣌⠠⠾⠷⢈⣡⣴⡟⠓⠤⡤⠴⡧⠆⢰⠖⠉⠉⠉⠓⢖⣠⣠⣤⣽⣿⣶⠦⣄⡀
⠀⠀⠀⠀⣯⣿⠄⠽⣿⠛⠓⠺⣟⣯⡤⠈⣼⠀⠈⠫⡃⠀⠀⢀⢀⣀⣾⡿⠛⣇⡀⢀⣄⠔⠀⠀⠈⣏⠙⠲⣄⢄⣀⠀⠀⠈⠙⠻⠰⠛⠻⠷⡄
⠀⠀⠀⠀⣿⠇⠀⠀⠁⠀⠀⠀⠈⢿⣥⠸⣿⠀⠀⠀⠈⠀⢄⣿⡿⡟⠙⠀⢰⡏⠠⠟⠁⠀⠀⠀⠀⠸⡄⠀⠈⠈⠉⠁⠈⠀⠀⣤⢠⣀⠀⢴⠟⣆
⠀⠀⠀⠀⣿⠀⢹⡀⠀⠀⠀⠀⠀⢰⣅⣀⢿⠀⠀⠀⠀⠀⠈⠙⢿⣄⣀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢰⡀⠀⠀⠀⠀⠀⠁⠀⠀⣸⠟⠁
⠀⠀⠀⠀⡟⠀⠰⠀⠀⠀⠀⠀⠀⢨⠈⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣼⣷⣤⣤⡴⣡⣄⣄⡤⠊
⠀⠀⠀⠀⣿⣆⠀⠘⣦⠀⠀⠀⣴⣇⠀⣷⠘⠀⠀⠀⠀⠀⠴⠟⢙⣃⣈⣟⠉⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⣵⣿⡿⠋
⠀⠀⠀⠀⡿⢿⢡⠛⢻⠃⠙⠻⠋⠉⡿⢉⣻⠀⠀⠀⠀⠰⣶⣶⡚⠉⠉⠙⣳⢶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⣿⢏⣾⠟⠋
⠀⠀⠀⠀⠈⠻⣤⡴⠛⠀⢠⣴⣿⢶⣧⠜⠁⠀⠀⠀⠀⠀⠈⠁⠑⣄⣀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⡶⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⢰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣗⡊⠙⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠀⠀⠈⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢿⣶⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣯⣶⡂⠀⠀⠈⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣟⡄⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣀⣤⡶⠀⣾⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢀⣄⡀⠀⠉⠹⠟⠽⣿⣿⡿⠟⠘⢿⣿⡿⠈⠁
⠀⠀⠀⠀⢀⣼⣿⣿⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣴⣿⣏⠀⣴⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⡿⣻⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣷⣿⣇⣴⣶⣶⣦⣤⣀⡀⢀⣸⠄
⠀⠀⢀⡟⢰⣿⢿⡿⡆⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣦⡀
⠀⠀⠸⡀⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⣿⠟⣽⠟⡁⡈⠉⠀⠉⠛⢿⣿⣿⡿⠿⠋⣼⡿⢫⠟⠁⠘⣿⣿⣿⣿⣿⣄
⠀⠀⠀⢳⣿⣿⣿⣿⢇⡀⠀⠀⢸⣿⣿⣿⢁⣴⡏⠀⠻⣿⠳⢿⡦⠶⢤⢛⠛⢷⠐⠚⠉⣠⣤⠶⠖⢿⣿⣿⣿⣿⡻⢿⣧
⠀⠀⠀⢸⣿⡿⣿⣿⣿⣯⡆⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠸⠎⠀⠀⠀⠀⣼⣯⡷⢲⣧⣼⣿⣿⣿⠇⠁⠀⢻⣧
⠀⠀⠀⠘⣿⠀⣿⣿⣿⣿⣧⠀⠀⠈⠘⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢸⣿⣿⣿⠟⠀⠀⣆⠀⣿⡆
⠀⠀⠀⠀⢹⡆⣿⣿⣿⣿⣿⣤⡄⣼⣷⠙⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠟⠃⢀⡄⠀⣿⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⣀⠀⠀⢤⣴⣿⣿⣾⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢿⡸⣿⣿⣿⣿⣿⣷⣧⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠏⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣿⣿⣟⣿⡏⢷⡀⠀⠀⠀⠀⠰⡙⠳⢶⣤⣄⣠⠔⠉⣠⣿⣷⣶⢀⣤⣦⣬⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣿⣿⡘⣿⡄⠱⣄⠀⠀⠀⠀⠈⠀⠠⠉⡉⠀⠀⣴⣿⣧⣄⠻⣿⣿⣽⣿⣿⡿⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠙⠿⣧⡌⠛⠓⠘⠦⡀⢀⣴⣆⡔⣠⠆⣀⠂⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣤⢂⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣙⣿⡿⢐⣇⢰⣿⣿⣿⣿⣿⢟⣽⠿⠋
⠀⠀⢀⣠⣴⣾⠟⣻⠇⣾⠃⠀⠀⠀⠀⠀⠁⠀⠀⠠⠤⡶⠶⣒⠉⠀⠙⣿⡧⡿⠈⠁⠁⠀⠄⠀⡀⠀⠀⠀⠤⠀⢤⡄⡀
⣴⣾⠿⡛⣭⣶⣾⠏⣸⠏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢰⣿⣧⠀⡠⠛⠉⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠄
⣿⣧⣱⣼⣿⣿⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢷⣄⡀⠘⠿⠏⠀⠀⠀⠀⠀⠀⢠⡇
⣿⣿⣿⣿⡿⠛⠁⡀⠀⠀⠄⠀⠀⠀⠀⠿⠷⠦⠀⠀⢺⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⠏⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰⣄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⣿⠟⠁⠀⠐⠀⣹⡇⢀⠇⠀⠀⠀⠀⠀⠀⢐⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡾⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⡟⢷⡸⠀⠀⢀⣼⡟⠃⢴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡷⡿⢳⠀⠀⠀⠀⠀⠀⠸⣦⣄
⠀⠀⠀⠀⠀⠈⣽⣿⡇⠀⠰⠿⠋⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⢧⡿⠛⡇⠉⠀⠀⠀⠀⠀⠀⠀⢿⣏
⠀⠀⠀⠀⢰⡿⢻⣷⠀⡼⢋⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣯⡿⠚⡶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⣸⠀⢸⣿⡶⠁⡿⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣥⡿⠺⠄⠊⠀⠀⠀⡇⠀⠀⠀⠀⠀⢿⣶⡆⣿⣷
⠀⠀⡿⠀⣿⡟⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⡿⣏⠠⠔⠁⠀⠀⠀⠀⠀⢀⢀⣠⣶⣆⣼⣿⡇⣿⣟⡴⠃⡀
⠀⠀⡇⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⠛⠁⢠⣤⣀⣀⡀⣤⢠⡄⢸⣿⣿⣿⣿⣿⣿⣿⢀⣿⣫⡴⠟⠁
⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⢠⣁⠀⠀⠀⠀⠀⣴⣿⢻⠋⠒⣰⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣄⡀
⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⡇⠀⠀⢠⣸⣷⢾⠃⢠⣴⣿⣿⣿⣿⣿⣿⣿⠏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⣀
⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⢷⡄⠀⢸⣧⣽⡟⠋⢠⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣍⡉⠉⠙⠓