Princess Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡠⠤⣤⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣹⣷⠐⡿⢶⣿⣆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣤⣼⣿⣯⢸⣟⣽⠀⡿⠻⣿⠿⢌⣳⡀
⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⣴⣙⠿⢽⠁⢹⣦⣧⡸⣾⠷⠤⠾⠤⣾⣝⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢹⣦⠼⠓⠋⠉⠀⠀⠀⠀⠀⠰⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⢤⠚⠀⢄⠄
⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠃⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠌
⢀⡄⢀⠀⠀⠀⠀⠀⠀⠆⠀⠁⠀⠐⢠⡄⠀⠀⠀⠀⠀⠀⠀⣀⠠⠲⠴⠈⠒⠂⠥⠴⣤⠄
⣞⠂⠈⠀⢂⠀⠀⠀⠀⠠⠀⠀⡀⢄⣢⡶⠄⣴⡉⠉⠈⠈⠁⠀⠀⠀⠀⠘⠒⠒⠒⣒⡍⠆
⠀⠀⠐⠠⠃⠀⠀⠀⠀⠐⠼⢛⣉⡀⠠⠤⠒⠈⠑⠄⠀⠆⣤⢋⠀⠄⠀⠀⠋⠉⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⡄⠀⠀⠒⣲⢆⠀⠀⠀⠈⠤⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠄⠨⠀⠂⡀⠀⠈⠂⢀⠁⣀⠴⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠄⠀⡱⠄⠈⠁⠑⠒⠒⠛⠋⠁⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠞⠀⣀⠤⠔⠒⠦⡀⠀⠀⠀⠒⠐⠒⠒⠒⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠉⢬⡔⠁⠆⣤⠤⠔⠒⠒⠢⡄⣀⠀⢀⣠⠴⠒⠲⠤⣄⣀⠤⠊
⠀⠀⠀⠀⠠⢂⠀⠿⠜⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣄⠀⠀⠀⢀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠁⠀⠀⠀⠉⠒⠤⠤⠤⠒⠉⠀⠀⠀⠉⠐⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⡀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠠⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠒⠒⠛⠉⠉⠀⠀⠈⠑⠦⢄⣀⣀⡠⠔⠉⠀⠀⠉⠙⠒⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣄⣠⠤⠖⠒⠂⠒⠠⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠦⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠐⠂⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠐⠄⣀⠄
⠀⠀⠀⠀⠀⢀⠀⠁⠀⠈⡀⠳⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠄⡐
⠀⠀⠀⠀⠀⠘⠀⠀⠠⠄⣇⢀⡤⠀⠁⠀⠀⠐⠂⠀⠀⠑⠂⠀⠂
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠙⠂⠀⠀⠠
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⡀⢀⠀⠐⢦⠀⠀⠂⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⡀⠀⠄⠀⠁⣸⠀⠀⠀⡄⠀⠀⡀⠀⠄⠀⠈⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠘⢀⢦⠵⠶⠀⠘⠛⠛⠛⠃⠀⠡⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣄⠀⠀⠀⣶⣿⠓⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⢈⠂
⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠜⠀⠀⠀⠀⠀⡤⣙⠆⠀⠘⢇⡐⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠎⠀⠀⠠⡾⠁⠀⠣⠀⠀⢀⠀⡀⠀⠙⠠⠆⠀⠄⠈⠀⠀⠀⠀⠆
⠀⠀⢀⠀⠀⣈⠄⠂⠈⠉⠃⠀⠘⠇⠠⣀⡖⠍⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡀
⠀⠀⠈⠙⠄⠀⠀⠚⠁⠲⠀⢸⠄⠆⠰⠈⠀⠀⠈⠀⡐⠀⠂⠀⠠⠀⠀⠀⠂⠀⡀⠀⠠⠃⠀⠀⠀⠀⠆
⠀⠋⠀⡀⠀⠀⢀⠀⠀⠐⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠁⠀⡆⠀⠀⠀⠀⠀⡀⠐⠃⠈⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠠⠐⠇⠀⡐⠦⡔⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣠⠄⠑⢀⠃⠤⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠢⠀⠙⠂⠑⠀⣬⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⠀⠰⡤⠈⠀⠀⠀⠀⠀⡠⠀⠆
⠀⠀⠀⡀⠔⠀⠀⠰⠐⡄⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢐⠐⠶⡀
⠀⠀⠀⠃⠀⠀⠀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐
⠀⠀⠀⠀⠀⠐⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠇
⠠⠀⠀⠠⠴⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⠈⠈⠀⠀⠀⠣⡀
⠄⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠈⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⢀⢀⣀⠀⠀⣸⣇⠀⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠛⠧⠀⠀⠀⠀⠠⠈⠁⢄⠀⠀⠀⠀⠘⢿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠁⠀⠀⠀⠄⠈⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠰⣄⠑⠆⡀⠀⣰⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠒⠒⠒⠒⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠁⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠤⠆⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠚⣀⠀⠀⠀⠀⠒⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡀⠈⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⣰⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠰⢆⠀⠀⠀⢰⣀⣴
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⡀⠀⢠⠐⠒⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠃⠀⠀⠷
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠁⠀⠀⠀⣤
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠒⡀⠀⠀⡴⣀⠀⡀⠐⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢣⡀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠶⠶⠆⠀⡠⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠁⡠⠚⢀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠚⡀⠀⠀⠀⠀⠀⠆⠀⠈⠉⠦⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠱⠄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠂⠀⠀⠀⠀⠠⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠉⠠⠄⠀⡀⢁⣴⠀⡀⠀⠀⠀⢉⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⠁⠀⠀⣀⠀⠀⣀⣱⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⢁⡄⠀⠀⠀⢦⡀⠂⠁⠀⠙⠛⣿⣿⢿⣷⣖⣿⣦⣿⡟⠛⠀⠈⠀⠰⠂⠁⠀⠀⣈⠁⠲⣄⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⣼⠏⠀⢠⡾⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⡀⠘⢷⡄⠀⠘⢷⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⣰⠟⠀⢀⡤⢚⠃⠉⠀⣤⠄⠀⠀⠀⠀⠀⢀⠀⠦⡀⠉⠓⠒⠚⢧⡀⠀⠹⢆⠀⠈⢷⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠂⢰⡇⠀⢀⠟⠀⢀⡼⠃⢠⠀⠀⠀⠀⠘⠋⢶⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⢻⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡈⡇⠀⢾⠀⠀⡜⠃⣠⠆⠀⠀⠀⠀⠀⠀⠀⠐⢆⡘⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⢳⡄⠀⣇⠀⢰⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠛⠀⠺⣧⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠀⠛⠀⠻⣆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⣛⠛⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠻⠋⡘⠋⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠉⢡⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢤⠀⠀⠀⠠⠀⠀⠀⠀⣤⠒⠀⠃⢠⡔⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠁⠀⠀⠀⠉⠀⢹⡇⠀⣀⠀⠶⣤⣸⣷⠤⠤⠀⣤⠋⠀⠀⠀⠀⣄⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⣤⠴⣾⠟⠃⠀⠀⠀⠙⠃⣄⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠴⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⣠⣀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢙⠓⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠈⢁⠉⠉⠁⣻⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡟⠀⠇⢠⠀⠀⠀⠆⢀⠀⠀⠀⠀⠓⠉⠰⠀⢠⣿⡇⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠈⠀⠀⠆⠀⠢⠀⠀⠀⠀⠀⠀⣀⡶⠴⠋⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠇⠀⠀⢠⠀⠀⢃⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠄⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⠀⠀⣠⠂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠈⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣼⠀⠀⠀⠀⠀⠄⠀⠉⠀⠀⠀⠀⡀⠜⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⠠⠄⠀⠀⠀⠀⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠉⠀⠐⠂⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⢀⡀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠤
⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠐⠂⠀⠠⠄⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢤⠄⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠀⠤⠤⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠠⠤⠤⠀⠈⠉⠀⠉⠁

⠀⠀⠀⣰⣿⠿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⢿⣿⣆
⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⡿⢿⣟⣲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣖⣻⡿⢿⣿⣿⣿⣿⡿⣿⣿
⠀⠀⠀⠙⣿⣟⣿⣿⠉⣹⣷⣾⡿⢏⣙⣿⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢞⣿⣋⡹⢿⣷⣾⣏⠉⣻⣿⣻⣿⠋
⠀⠀⠀⠀⠈⠻⣿⡿⣿⡟⠉⠙⠛⠶⡟⠉⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠉⢻⠷⠛⠋⠉⢻⣿⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠖⠒⠢⠤⠷⣄⠀⠀⠈⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⣠⠾⠤⠔⠒⠲⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣀⣀⣀⣀⣀⣈⣑⣦⣀⠀⠀⠙⢷⣄⠀⢀⡀⠀⣠⡾⠋⠀⠀⣀⣴⣊⣁⣀⣀⣀⣀⣀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣀⠙⢦⣾⣷⡴⠋⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⠈⠙⣲⣿⣿⣖⠋⠁⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⡿⠿⠿⠛⠻⢿⣛⡻⡿⠿⠿⣿⣿⣿⣿⠻⠿⢿⣟⣛⡿⠟⠛⠿⠿⢿⣯⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⠤⠴⠒⢒⡲⠋⠀⠀⢀⡠⠚⣹⣿⣿⣏⠓⢤⡀⠀⠀⠙⢶⡒⠒⠦⠤⣽⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢋⣀⠤⠔⢺⠏⠀⠀⣀⠔⠉⢀⠜⡸⣿⣿⢏⠣⡀⠉⠢⣀⠀⠀⠹⡗⠢⠤⣀⡙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠉⢀⡠⠖⢻⠖⠒⣹⠃⠀⣠⠋⡰⠡⣿⣿⠈⢆⠙⣄⠀⠘⣏⠒⠲⡟⠲⢄⡀⠉⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢶⡋⠀⢠⠋⠀⢰⠃⠀⡼⠁⣰⠃⠀⣿⣿⠀⠘⡆⠈⢧⠀⠘⡆⠀⠙⡄⠀⢙⡶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⢶⡇⠀⣠⠃⠀⡜⠀⢠⡇⠀⠀⢻⡟⠀⠀⢸⡄⠀⢣⡀⠘⣄⠀⢸⡶⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⣿⣦⢾⣀⣠⠟⠀⠀⠀⠘⠃⠀⠀⠀⠻⣄⣀⡷⣴⣿⣽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⠿⢻⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⠀⠀⢸⠟⠻⡟⠙⢿⠻⣏⣵⣼⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠟⠻⡉⢻⠙⣿⣦⣿⡇⠀⡇⠀⠎⢀⢿⣧⢽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡋⠓⢄⠀⣈⡃⠡⢸⣿⠁⠀⠁⢀⠶⠚⣻⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠉⠲⢦⣝⡇⠙⠦⣼⣿⠀⠀⡴⠃⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣉⠓⠦⣌⠻⣄⠀⢿⡇⠀⠘⠁⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠈⠑⢈⣳⣼⣇⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠒⠶⢿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠂⣠⠔⣨⠞⢿⡏⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠤⠒⢋⣥⡞⠁⢀⣿⡇⠀⢠⡀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠴⠚⢋⢴⣀⡴⠋⢿⣇⠀⠀⠳⡀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣤⠚⢁⠌⢰⠀⡆⣼⣿⠀⠀⠀⠘⠲⣤⡝⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣮⣤⣯⣼⠿⠋⣿⠀⢸⠀⠀⡆⢰⣾⣛⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢿⣦⣾⣦⣴⣷⣾⡉⡏⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣷⣧⣦⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⠇

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠒⠠⡀⠀⠀⠀⠀⢀⡤⠒⠠⠀⠀⠀⣀⠀⣤⠀⠀⠀⠀⠀⢀⣀⠄⡀
⠀⠀⠀⠀⠈⠀⠀⠀⢰⡆⢀⠀⠀⠀⠀⠀⡀⠠⠀⠈⢀⠀⠈⠆⠀⠠⠀⡞⠠⠀⠈⠀⠀⢉⡉⣠⣅⢠⡄⠀⠀⡔⢎⠀⢸⢖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠅⣾⠀⠀⠀⠀⠀⠀⠍⢠⡌⢡⡄⠀⠀⠀⠻⣬⠑⡯⠃
⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠅⠀⢠⠀⠀⠡⡈⠀⠘⠀⠄⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢁⠉⠀⠀⠀⠈⠀⠀⠀⠒⠊⠀⠀⠀⠀⢀⠐⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠃⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠚⡆⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠠⠀⢀⡈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠐⠀⠀⠀⠁⢸⣏⠀⠀⠀⡀⢀⠀⢑⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠆⠐⠤⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⡀⢰⠀⠀⠀⢼⠁⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⠀⠐⢄⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠆⠀⢀⡁⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠈⠃⠀⡂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠂⠄⠀⠀⠀⠸⠀⠀⠁⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⠠⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⡀⠀⠱⣀⢀⣀⣤⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣇⠔⠁
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠐⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡠⠂⠉⣩⠉⠑⠠⡀⠀⠀⠀⠰⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠂⢄⢀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠉⣐⣀⠔⠁⠀⠀⠠⢄⠈⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠔⠉⡑⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⣃⠀⠰⠀⠀⠀⠂⠀⠀⠀⠀⠀⡆⠀⠑⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠃⠂⢀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠊⡀⠀⣀⠈⠳⣄⠀⠰⠌⡤⠂⡐⡄⠀⠀⠛⠀⢠⡷⢾⡇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠉⠁⠢⠀⡇⠈⠋⠀⠀⠀⠀⠀⠀⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠈⠇⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠁
⠀⠀⠀⢠⡀⠢⡈⠀⠀⠰⠂⠀⠀⠀⠀⠐⢁⡄⠀⠑⡈⠀⡠⠁⠀⠀⠀⠀⠀⢀⠀⢠
⠀⠀⠈⠒⠴⣦⣿⣔⡾⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡷⠈⠀⡌⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠈⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃

⢼⣶⣀⡀⠀⠀⠀⣀⣲⣿⠀⢸⡿⣒⣄⠀⠀⠀⠀⣀⡲⢶⡆⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠐⣿⣷⠦⡀⠀⠀⢴⣿
⢸⣛⣭⣵⣄⣤⣮⣭⣍⣻⠀⠀⡿⠉⠛⢷⡀⢠⠞⠛⠛⣿⠀⠈⠳⢉⣾⣿⣶⣴⣶⣾⣿⡌⠼⠁⠀⠹⢿⣀⣱⣤⣀⣠⡿
⠀⢿⣿⣿⠟⡟⢿⣿⡿⠄⠀⠀⢈⠔⠂⠀⢹⡏⠀⠀⢠⠁⠀⠀⠀⠘⠙⠉⢸⡿⣿⠈⠋⠟⠀⠀⠀⠀⣞⠁⠀⠋⠀⠙⣷
⠀⠀⠻⠇⠀⠁⠈⡿⠃⠀⠀⠀⢸⡀⠀⠀⠈⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠂⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⠷⠆⠀⠳⠿⠁
⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠉⠑⠀⠀⠀⠐⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⡾⠛⠁⢀⠀⠀⢀⠀⠉⠛⡇⠀⠹⣿⢶⣄⠀⠀⠀⠀⣠⡾⠿⠃⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⢰⡿⠒⠀⠀⠀⠀⠀⠒⠻
⠁⢴⣿⡁⠀⡄⠀⣽⣷⠄⠀⠀⠀⢻⣆⣻⣷⣀⣠⣾⡏⠸⡎⠀⠀⠀⠀⣠⣾⣤⣶⣀⠀⠀⠀⠈⢀⣴⡖⠁⣀⠈⢑⣶⡄
⢰⠻⣿⣥⡴⡷⣄⣽⡿⠰⠀⠀⠀⠰⠋⣀⠘⠻⠻⢃⣄⠱⠀⠀⠀⠀⢼⡙⠟⠉⠿⢙⡆⠀⠀⠀⠾⣿⣏⣠⣿⣄⣹⣿⠇
⠀⠀⠈⠙⠁⠁⠙⠉⠀⠀⠀⠀⠀⠀⠣⡴⠟⠀⠐⠿⢆⠊⠀⠀⠀⠠⠜⠛⠀⠀⠘⠛⢥⠀⠀⠀⠁⠈⠛⠋⠈⠘⠟⠋
⣠⢤⣀⡀⠀⠀⠀⠀⢀⣄⡦⣄⠀⠄⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢤⣄⠀⠀⠀⠀⠀⠀⠀⢠
⣷⠛⠉⣀⡀⣀⣀⢀⣀⠉⠛⡎⠀⠀⢸⣧⡀⠀⠀⢀⣾⠄⠀⠀⢸⣿⠿⣢⠀⠀⣠⡺⢻⡿⠀⠸⣄⣾⣦⠀⠀⠀⣠⣶⢠
⠙⢒⣻⣟⣯⣿⣟⣟⣿⡟⡒⠃⠀⠹⣟⣙⣿⣤⣴⣿⣉⣿⠇⠀⠀⠙⡆⠛⣷⣶⠛⢠⠛⠁⠀⠀⠻⡎⢻⣷⣤⣼⡟⢩⡞
⠀⢿⡿⣿⡾⢙⠹⣿⣿⣧⡗⠀⠀⢀⡾⢿⡿⢻⡿⣿⡿⣦⠀⠀⠀⢸⣿⠸⠁⠉⢇⣼⠇⠀⠀⠀⠀⣾⣟⡉⢻⢉⣟⣶
⠀⠈⠙⠛⠁⠀⠀⠈⠋⠉⠀⠀⠀⠈⠻⠞⠁⠀⠀⠘⠻⠛⠀⠀⠀⠐⠙⠀⠀⠀⠀⠋⠃⠀⠀⠀⠀⠈⠋⠀⠀⠀⠛
⠐⠰⣠⡀⠀⠀⠀⣀⠠⠒⠀⠀⢠⣤⣄⡀⠀⠀⠀⣠⣴⡆⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠤⡄⠀⢰⣦⣤⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠈⠈⢢⣦⡚⠈⠀⠀⠀⠀⠀⣏⡉⠉⢀⡀⠈⠉⠙⡇⠀⠀⡂⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠘⣿⢰⠋⠀⣠⠀⠘⢷⢹
⠀⠀⠌⠃⠺⡟⠃⠯⡠⠀⠀⠀⠀⢉⡷⠾⢿⡿⠗⠶⣌⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⢨⣾⠟⠉⢹⠉⠳⣾⡎
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠷⡴⠋⠙⢳⡴⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠧⣀⠀⠘⠀⣠⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠿⠿⠿⢿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡗⠐⠋⣠⠀⣀⣤⣤⣤⣌⠙⠻⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠋⣠⣶⡿⢡⣾⣿⣿⣿⠿⢿⣿⣆⠈⠻⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⠀⣼⣿⡿⢀⣿⡿⢋⣥⡶⠶⣶⠆⠙⠇⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀⣿⣿⣷⢸⣿⠁⣾⡟⠐⠺⢯⣳⡄⢠⣾⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢿⣿⣷⡈⢿⣿⣆⢻⠀⣿⡇⢹⣿⡈⣳⠇⠘⣿⣿⣿⣿⡟⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡙⢿⣿⣆⠙⢿⣦⠰⣿⣿⣦⣬⡍⠁⣤⡀⢹⣿⣿⠋⡀⢸⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣌⠻⣿⡇⠰⣭⣀⣉⣉⣉⣡⣴⣾⣿⣷⠀⠻⢃⣾⡇⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠘⢃⣀⡈⠻⠿⣿⣿⣿⣿⣿⣿⠟⠀⣠⣿⡿⢠⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⢰⣿⣿⣿⣿⣶⣦⣭⣍⣉⣉⣡⣴⣾⣿⡿⠁⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣤⣀⣤⣤⣤⣬⣭⡛⠻⠿⠿⠿⠿⠿⠋⢀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠛⠛⠿⣦⡐⢶⣶⣶⣶⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⠿⠟⣋⣤⡈⠀⢠⣬⣭⣝⣋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⢉⣴⣦⣿⣿⡇⣿⣷⣦⡙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⢁⣶⣼⣿⣿⣿⣿⡇⢿⣿⣿⣿⣦⠙⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠏⢠⣻⣿⣿⣿⣿⣿⡿⠁⠈⠻⣿⣿⣿⣧⡘⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠃⣠⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⠛⠿⢿⣬⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢁⣴⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢋⡴⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⢀⣤⠖⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡆⠀⠀⣤
⠀⠀⠀⠀⢠⣿⡇⠐⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠃⠀⠀⠀⠀⢀⢠⡀⡄⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠙⠶⠞⠃
⠀⠀⠀⠀⣾⣿⠓⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠾⠁
⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣷
⠀⠀⠀⠀⠛⠛⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠩⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢀⠀⠀⠀⠀⠀⢈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣸⢀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠅
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠻⣦⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠿⠿⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢾⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿⣿⣿⣿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠉⠉⠉


⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⡿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⡿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣯⣽⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿⣿⣿⣿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉⠉⠉⠉


⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⣿⣷⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⣿⣿⣿⣿⣶⡷⢿⣾⣿⡿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣷⡾⠿⠿⠶⡿⠷⣶⡿⠷⢾⠿⠿⠿⢿

⠀⢀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⡀
⠀⢾⡿⢍⠳⠈⠛⠙⢶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡶⠋⠟⠡⠞⡩⢿⡇
⠀⠸⣗⠄⡱⣚⠭⠭⠶⢷⣬⣟⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣛⣥⡾⠶⠭⠭⣓⣎⠠⣻⠃
⠀⠀⠹⡗⢽⣱⢊⣭⠤⠬⢜⣛⣿⢷⣽⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣯⣾⣽⣋⡡⠥⠬⣭⡑⣾⡇⣺⠏
⠀⠀⠀⠹⡆⢿⢺⠀⢲⡖⠐⠠⠭⡝⡿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿⣿⢿⢫⠭⠄⠂⢲⡖⢀⡇⡿⢰⠏
⠀⠀⠀⠀⢹⡄⢦⠑⢤⣙⡢⢄⣀⠀⠁⠂⠝⣺⣻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣿⣝⡫⠒⠍⠀⣀⡠⢔⣃⡤⠋⡼⣠⠏
⠀⠀⠀⠀⠀⣷⠈⡷⣄⡤⠉⣑⠒⠡⠕⣴⣄⡈⠚⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣛⡝⠓⠁⣀⣦⠪⠘⠒⣈⠉⢄⣠⣾⠡⡾
⠀⠀⠀⠀⠀⢸⡅⢻⣦⣉⢉⠈⠳⠥⠤⠶⡉⡙⠷⣠⡛⣽⢟⣷⡀⠀⠀⠀⠀⠀⠀⢀⣞⡿⣫⢋⣤⠖⢋⢉⠖⠤⠭⠞⠡⡉⣉⣴⡟⢨⡇
⠀⠀⠀⠀⠀⠸⣇⢸⠟⣩⡥⠤⡤⠤⣀⡀⠙⠢⠄⢂⠙⠿⣿⡿⣿⡄⠀⢀⡀⠀⢠⣟⢯⣿⠟⠋⡐⠠⠔⠋⢀⣀⠤⠤⠤⢬⣍⠻⡇⣺⠇
⠀⠀⠀⠀⠀⠀⢿⡼⣜⢧⣠⣰⣰⣀⣸⣈⣹⡐⢠⢈⡳⢅⠨⠻⣼⣿⡔⣿⣿⢢⣿⣳⠟⠅⡸⢞⠀⡄⢒⣏⣀⣅⣀⣇⣆⣄⡼⣣⢧⡟
⠀⠀⠀⠀⠀⠀⠀⠙⠮⣓⣤⣀⡉⠀⠀⢀⣀⠈⠉⠓⠺⠶⣄⡀⠘⢿⣷⣿⣿⣾⡿⠁⢀⣠⠶⠓⠊⠉⠁⣀⣀⠀⠀⢉⣀⣴⣛⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢲⣴⣶⢢⣤⣤⣩⣵⣄⣀⣩⣷⡾⣿⣧⣾⡿⢷⣾⣍⣀⣠⣮⣁⣥⣥⡔⣶⣦⡖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡉⢱⢁⡛⠀⡇⢻⠙⠉⢹⣿⣿⣮⡿⣿⣿⢿⣤⣿⣿⡏⠉⠋⡟⢹⠀⢛⡈⡌⣉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠠⢇⠀⡇⢼⡐⠂⠀⠸⠛⣿⡇⣿⣇⢸⣿⠛⠇⠀⠐⢂⡇⢸⠀⡼⠄⠁⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⣠⢣⠈⣻⡀⠹⡀⢹⡀⠂⠀⠀⢹⠀⣿⣿⠈⡏⠀⠀⠒⢀⡏⢀⠏⢀⣟⠀⡜⣄⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⢀⡒⡀⠐⢣⡀⠙⣄⠉⠱⣄⣡⠇⠀⣿⣿⠀⠸⣌⣠⠊⠉⡠⠋⢀⡜⠢⢀⢒⡀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀⢘⡒⡄⠉⠷⣄⠀⠙⠲⢼⠏⠀⠀⢻⡗⠀⠀⠹⡦⠖⠋⢀⣠⠾⠉⡠⢐⡁⢀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠤⠦⣀⠁⠟⢲⡾⠁⠀⠀⠀⠈⠁⠀⠀⠀⠘⢷⡖⠻⠈⡠⠴⠥⠀⢸⠉
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⣜⢂⣭⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣭⡐⣣⠒⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⢿⡟⠈⠳⣄⠀⠀⠀⠀⡤⠊⠁⣻⠗⠀⠀⠀⣿⡇⣶⣤⡀⠀⠀⠀⠀⠀⣠⣴⡆⣿⡇⠀⠀⠘⢻⡷⡦⣄⠀⠀⠀⠀⠀⣠⣴⡾⣿⠓
⠀⠀⠀⡉⠁⠀⠈⠁⣴⡄⠊⠀⠀⠈⣩⠀⠀⠀⠀⠸⣷⡙⠻⣤⣇⢀⣄⢀⣧⡼⠛⣱⡿⠀⠀⠀⠀⠫⢿⡹⡟⠀⣀⣸⣀⡠⠘⡟⣽⠯⠃
⠀⠀⠀⠛⣳⠖⠶⠖⣿⡗⠲⠖⠲⡛⠋⠀⠀⠀⠀⠀⠙⣷⡾⠉⠉⣹⣿⡉⠉⢹⣾⡟⠁⠀⠀⠀⠀⠀⠻⣿⣛⡈⣹⣿⣏⠁⣘⣿⡟⠁
⠀⠀⠀⠘⡀⢠⠔⠀⣿⡇⠑⢤⠀⣈⠀⠀⠀⠀⠀⠀⠸⣿⣷⠘⠻⠏⠏⠿⠛⢸⣿⡿⠀⠀⠀⠀⠀⢠⣿⣿⣿⡤⠁⢸⠈⢠⣟⣿⣿⣆
⠀⠀⠀⠀⢳⣀⣀⠂⠀⠀⠂⣀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡞⠂⠀⠛⣾⣿⡟⠃⠀⠀⠀⠀⠀⠸⣨⣻⣴⠇⠀⠀⠀⠘⣧⣝⣉⡇
⠀⠀⠀⠀⠞⠉⠉⠀⠀⠀⠀⠉⠉⠆⠀⠀⠀⠀⠀⠀⠀⠸⠁⠁⠀⠀⠀⠀⠀⠁⠹⠀⠀⠀⠀⠀⠀⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠱
⠀⢿⣿⣶⣦⢀⠀⠀⠀⠀⢀⠀⡠⣴⣾⣿⡇⠀⠰⣄⣀⣶⣶⢤⡀⠀⠀⠀⣠⢴⣶⣆⣀⡶
⠀⠈⣿⡯⠨⠈⠳⣄⠀⠀⡠⠋⠩⠁⣿⡏⠀⠀⠀⠘⢷⣮⡁⠀⠈⣶⣷⡎⠀⠀⣩⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⢸⣿⣀⣈⣀⣈⣶⣞⣁⣊⣀⣰⣿⠃⠀⠀⠀⠀⠈⢿⡿⠛⣋⣹⣿⣉⡛⠻⣿⠏⠀⠀⠀⠀⠳⣦⠀⠀⠀⠀⢺⣿⡗⠂⠀⠀⠀⡰⡾
⠀⠀⠀⣿⠁⠈⣉⠉⣿⣏⢉⡉⠀⠹⣯⠀⠀⠀⠀⠀⠀⠸⣇⠀⢉⡉⠃⣉⠁⢠⡿⠀⠀⠀⠀⠀⠀⠈⠀⡤⡖⠉⠘⣿⡇⠈⢐⣤⡄⠋
⠀⠀⠀⢿⣥⣀⡀⠘⠙⠙⡀⣁⣡⣼⡟⠀⠀⠀⠀⠀⠀⠀⣸⠲⠚⠁⠀⠙⠲⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠿⠄⠀⠀⠄
⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢀⠀⠀⠀⣾⣷⠶⣄⡀⠀⠀⠀⠀⠀⠀⣀⠴⣾⣿
⠀⠴⠀⠶⣤⢀⠀⠠⢴⡤⠀⢀⡀⡴⠖⠰⣄⠀⠀⡏⠁⠂⠀⠉⠢⣠⣦⡠⠚⠁⠀⠂⠉⡇⠀⠀⠹⡶⠻⠹⠊⠶⡄⠀⢀⡶⠂⠏⠝⠳⡏
⠀⠻⣷⡀⠀⢀⣠⠔⢻⡃⢤⣄⡀⠀⡐⡾⠋⠀⠀⠑⠒⣶⠶⠦⠤⣾⣿⡦⠤⠴⢶⠒⠒⠁⠀⠀⠀⠷⣀⣀⣀⣀⣸⣶⣏⣀⣀⣀⣀⠸⠃
⠀⠀⠈⢃⠈⠉⠀⠀⣼⡄⠀⠈⠉⠀⠛⠁⠀⠀⠀⠀⠘⠁⢀⠄⢀⡿⡿⣇⠀⢤⠀⠙⠀⠀⠀⠀⠀⢰⡏⠀⠈⡀⠘⣿⡧⠀⡉⠀⢘⣦
⠀⠀⠀⠈⠢⢀⠠⠜⠁⠈⠢⢀⠀⠘⠀⠀⠀⠀⠀⠀⣀⡦⠀⠠⠃⠀⠀⠈⠣⠀⠠⣆⡀⠀⠀⠀⠀⠸⣇⡀⠀⠀⠋⠹⠙⠀⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠈⠛⠛⠁
⢀⣤⠂⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⣄⠀⠀⢰⣿⣿⠳⢄⠀⠀⠀⠀⢀⠴⢻⣿⣷⠀⠀⠀⢾⣷⣶⣤⣀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣷
⠀⢿⠂⠀⠙⢦⡀⠀⠀⠀⠀⢠⠞⠁⠀⢘⠟⠀⠀⠘⣿⡏⠂⠀⠐⠀⠀⠀⠀⠀⠊⣿⡟⠀⠀⠀⠘⣿⣿⠷⣟⣳⣄⠀⢠⣖⣻⡾⣻⣿⡏
⠀⠀⡛⢐⠢⠀⠈⠀⢰⡄⠔⠁⠠⠐⠘⠋⠀⠀⠀⠀⠹⢿⡥⠄⠐⢶⣷⠖⠀⠤⣽⠟⠁⠀⠀⠀⠀⠘⣿⣷⡉⣿⣿⣿⣿⣿⣉⣴⣿⠏
⠀⠀⠈⠂⢠⡤⠀⢠⣾⣧⡄⠠⣤⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠾⡟⠆⠀⠂⠈⣷⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⣼⣿⣧⡀⢸⣿⡅
⠀⠀⠀⢰⠏⠀⠀⠀⢿⡇⠀⠀⠀⢵⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⡾⠀⠁⠸⣦⣤⣼⠟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣟⠉⢹⣿⣿⡿⠃
⠀⠀⠀⠈⠃⠼⠄⠀⠀⠀⠀⠤⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⣹⠁⠀⠀⠀⠀⠀⢩⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠁⠀⠀⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠊⡿⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⠛⢃⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣏⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣽⢛⣿⠀⠀⠠⠆⠀⠀⢀⠀⠈⡀⢀⠀⠀⠘⠛⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠋⣥⠀⣄⡖⠃⠀⠀⠁⠀⠀⠀⣾⠀⠀⡰⠉⠀⠀⠀⠀⠀⠀⢀⣀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢾⠖⢠⡆⠀⢰⡾⠁⠀⣼⠀⣠⡷⢠⢤⣤⣤⡤⠀⣤⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⢦⡘⢿⠀⣸⠙⢤⣿⣷⣮⣿⢋⣼⣿⣷⣧⣾⣿⡟⠒⠉
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠐⠻⠟⠿⢿⣿⣿⣌⢷⣴⣤⣾⣿⡿⠟⠁⢉⣿⣿⡟⠉⠁⠀⠀⣀
⠀⠀⠀⠀⠄⣀⣀⣀⣈⣰⣤⣤⣤⣤⣼⣿⣿⣿⡆⢿⣽⠃⠀⠀⠀⣠⠊⠁⠈⠛⠋⠳⣶⠊⠀⠛⢲⡞
⠀⠀⠀⠀⠀⣈⠉⠉⢉⣽⠟⠛⠙⠏⠉⣿⠟⡻⣦⡰⠿⠋⣹⠾⠛⢻⣶⣤⣤⣄⣀⠀⠈⣷⠀⠀⠀⡻⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠔⠁⠀⠐⠇⠀⠀⠉⠀⣴⡶⠾⢉⣀⡌⣩⣽⡿⠛⢿⣦⠀⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠐⠀⠀⠀⠀⠀⣀⣶⠀⢸⠛⢁⡴⢛⣼⣽⣶⣿⢦⡴⠀⠀⢻⢿⣿⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠐⠂⢠⡄⠒⢦⡄⣻⡞⠉⢳⡀⣿⣄⣼⢷⢸⣭⣿⡏⢻⡏⠐⠓⢻⠟⠀⢻⢿⡆⠀⠀⠀⢱
⠀⠀⠀⠀⠀⢰⠀⠈⠀⠀⠀⠺⠛⢛⣶⣷⣿⠂⠀⠈⢿⣿⢻⡏⢾⣼⣽⡿⢅⣏⠛⠁⠀⠃⠀⠀⣷⠸⣿⡄⠀⣀⡞⡠
⠀⠀⠀⠀⠀⢘⣦⣀⣞⠀⢀⣤⣤⡼⠇⠈⠉⣆⠀⠀⢸⡣⡘⢷⠒⠭⠾⠓⢀⣁⠀⠀⣸⠄⠀⡐⠁⠀⠻⣿⢶⣿⣿⠁
⠀⠀⠀⠀⠀⠁⢺⣿⣿⠀⣿⣾⠋⠀⠀⢠⠞⠛⠁⠀⢸⡇⠈⢦⣧⣀⣀⡀⣿⡟⠁⠁⠀⠀⢰⠇⠀⠀⣼⡿⣿⣿⣷⠶⢶⣤⠀⡾
⠀⠀⠀⠐⢉⠛⠉⣡⣬⢷⣿⠉⠁⢂⡀⠈⠛⠲⣤⠀⠻⢷⣄⠀⣶⠈⠙⠛⠳⣤⡀⠀⠀⢠⣿⠀⣴⣼⣿⡽⠋⠀⠀⠀⠀⠘⡟⠁
⠀⢀⡀⠂⠀⠠⢞⡿⢳⠀⠉⠳⡄⠀⠀⠀⠀⠀⠈⢧⡀⠀⠹⣶⣬⠿⠿⠿⠛⠉⠛⠷⣤⣼⡟⢀⣿⣿⣿⡷⠄⠰⣴⣶⠶⠚⠁⠀⠀⠀⠐
⠀⠈⠀⠀⠀⠰⢿⠃⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠁⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⢀⡤⠠⡤⠄
⠀⠀⠀⠀⠀⠀⣆⠀⣆⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠷⠶⣶⣦⣴⣶⣾⣶⣶⠾⣿⡿⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣠⡘⣧⡤
⠀⠀⠀⠀⠀⠀⣿⡟⠋⣀⣀⡀⢠⣤⣤⣀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠈⠉⠛⠁⠙⠿⣶⣶⣌⠀⠀⣀⢀⣠⡴⠋⠀⠀⠀⢀⡀⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠠⠜⡛⠄⠂⣉⣤⣬⣹⣿⣶⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠉⠉⠉⠙⠛⠳⢶⣶⠮⣉⠡⢶⣶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠴⢾⣶⢆⣿⣿⠯⢺⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⢸⣿⡆⠙⢆⠈⠃⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠉⠉⣽⡶⣛⣻⣿⣿⣷⠠⠤⢴⡀⠀⠀⠀⠀⠀⠀⢀⠸⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠁⠀⢁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢀⠐⠢⣀⠀⠠⣤⡘⣦⣀⣿⣿⣿⣿⣿⠙⣿⡄⠀⠀⠙⠳⣄⠀⠀⣀⡄⢁⡀⠀⠀⣀⡤⢘⡩⢉⠛⠀⡀⠀⠀⠀⠀⠀⠣⡈⣧⡀
⠀⠀⠀⠀⠀⢀⣠⠒⠺⠋⠀⡴⠎⠉⡉⣹⣿⣿⣿⠸⣧⣿⣿⣦⠀⠀⠀⠀⠈⣴⠟⠁⣼⣿⡷⣾⣿⠞⠛⣯⠙⣩⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⢀⣠⠋⡌⢀⣤⠀⠖⠀⠀⢲⣿⣿⣿⣿⠿⠖⠻⢿⡿⠀⢀⣁⣡⠤⢶⣧⣄⡀⢱⣿⣿⣯⠛⢧⡉⠉⠀⠉⠁⡀⡴⢆⣀⣴⣦⣤⣤⣀
⠀⠀⠀⣾⠃⠚⠁⠉⠀⠀⠀⠀⠀⣿⣿⣿⠟⢻⡦⠀⠀⠈⠳⣦⣉⣽⠄⢀⡼⢿⣿⣁⠞⢻⡇⠀⢳⡄⠙⢦⡀⣠⣾⣶⣴⠟⠋⢉⡁⠉⠀⠀⢱
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣿⡏⠠⠿⠃⣀⠀⠀⠀⠉⠀⠀⠀⢸⡇⠈⢻⣿⠀⠞⣿⣄⠈⠀⠀⠈⠻⡈⠙⠻⠷⠒⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⠁⠀⢰⡏⠢⢄⣀⡀⠀⠀⠀⢮⠙⠄⠀⠉⠀⠀⠈⠏⢻⡆⠀⠀⠀⢹⣆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠰⣤⣄⣙⠋⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠲⢰⣼⠇⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡿⣉⣩⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠑⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠐⢒⠺⠓⠢⠒⠘⠏⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⣀⡀⠀⠀⡰⣴⡄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠰⡤⠤⠀⠤⡴⠀⠀⢠⠂⠁⠀⢀⠔⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡛⠚⠒⠐⠢⠐⠚⠁⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠔⠛⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠀⠀⠠⠇⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠛⠀⠀⠷⠀⠀⠀⢀⣠⠖⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠂⢠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢳⣶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠠⡴⠿⠁⠙⠉⠁⠀⠀⠀⠩⠆⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠙⠉⠃
⠀⠀⠀⠀⠀⠀⢐⠀⢓⠀⠀⠀⠀⠀⠘⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠜⡁⡐⠲⠂⠀⠀⠀⠈⠇⢀⣄⠀⠀⠀⠀⠀⠀⢰⡶⣶
⠀⠀⠀⠀⠀⠀⠈⢤⠀⠀⠀⠀⠀⠀⡀⣈⠙⠀⠀⢐⣖⣶⡞⠆⠀⠀⠀⠀⢤⠚⣁⡚⣠⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⢀⠌⣄⡀⠀⠈⠉⠈⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠯⣣⠅⠀⠀⠀⠀⠀⠀⠀⣩⠃
⠀⠀⠀⠀⠀⠈⠛⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⡴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠰⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠄⢺⠠⠄⠀⠀⠀⠁⢀⣦⢤⣤⡤⣤⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠜⠀⠀⣠⠰⠿⠒⠛⠋⡉⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢤⡘⡛⡀⠜⠁
⠀⠀⠀⠀⠤⠴⠦⣐⡀⠁⣠⠦⠤⢀⣀⡸⠂⠘⠀⠙⠤⠖⠀⠀⠀⠛⠋⠙⠁⠀⠀⠀⢀⡀⠀⣴⠀⠀⠀⠀⢀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢐⡀⠀⠀⠆⣄⠈⠀⣠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⡀⠀⠀⠀⠀⠙⣃⠅⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠐⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠈⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠑⡐⠋⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠈⠄⠀⠀⠀⠀⣤⢘⠃⠀⡀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡄⠀⠀⠀⠀⠠⣶⢈⠀⣠⢫⠄⠀⠀⠀⠀⠒⠤⢄⣀⠠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⡌⠰⠀⠀⠀⠀⠀⠲⢿⡆⣀⡌⠀⠀⠀⠀⠀⠀⠐⠘⠛⡀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⣁⢴⡂⠀⠀⠀⠀⠀⢭⣿⠋⠁⠀⠀⠀⠀⠀⢀⡤⠤⣤⠤⡀⠀⠀⠀⠀⠀⠀⠠⢴⣶⠄⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠋⠀⠁⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⣘⠉⠀⣚⠀⠛⣄⠀⠀⠀⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⠅⣈⡰⠁⠀⢀⠀⢀⡀⠀⠠⡄⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡤⢀⡇⠀⠰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠀⣡⠶⠜⡁⠀⡀⠐⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣴⣤⠀⠀⠀⢨⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠻⡃⣼⠂⣴⠀⡙⠄⣀⡁⠀⠂⠁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠤⢒⠀⢠⡀⢠⡖⠀⠠⠀⠀⢀⣸⣆⣀⢤⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠐⠱⠟⠀⠁⠒
⠀⠀⠀⣀⢠⡀⠀⢀⠠⢄⠀⠀⠙⠅⢿⡀⠀⢸⡇⢹⡌⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠐⠲⠂
⠀⠀⠀⠀⠘⠡⠒⣈⠣⣤⢑⠀⠀⣀⢸⡗⠁⠸⠇⠈⠰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠁⠄
⠀⠀⠀⠀⠀⠨⠀⠀⠀⢙⣏⠀⠀⠉⢺⡇⣠⡀⠐⢹⡶⠃⠀⠀⠀⠀⠀⠀⠀⡀⠴⠾⡤⠛
⠀⠀⠀⢀⠇⠗⠚⠓⢀⣀⡁⠀⠀⠀⢹⡷⠼⠿⡧⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠄⠻⠷⣴⡆⠀⢰⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠁⠉⠋⠛⣟⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠁⡀⠛⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⡀⣂⠠⡦⡄⠘⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⠀⠒⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⡘⠄⣽⠋⠁⣌⡃⢨⡀⠡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣄⡿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠠⣛⣡⣆⡶⠻⢿⡇⠛⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢈⣷⣈⠡⠌⠟⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠈⠇⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⣀⡀⢀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢀⣠⠄⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠰⠆⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠐⢀⣄⠀⡂⢀⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠘⠙⠀⠀⠈⠃⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂

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

⢰⣶⡶⠖⠛⠛⠒⠒⠲⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠒⠒⠛⠓⠶⣶⣶
⣿⡋⡉⠀⠀⠀⠀⠔⠂⠀⠀⠈⠙⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠒⠄⠀⠀⠀⠈⡉⣻
⢻⣀⡀⠠⠄⠐⠀⠂⠈⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠤⠀⢀⣸
⠀⠛⢦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠀⢠⣴⣤⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠞⠃
⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⣀⠠⠀⠀⠉⠐⠀⠤⢀⣀⣙⣷⣴⣿⣷⣴⣟⣁⣀⠠⠄⠀⠈⠁⠀⠠⢀⡀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠈⢶⡖⠒⠉⠁⠀⠀⠀⠀⢀⣠⡤⠖⠚⠛⠛⠻⣻⣿⣿⠛⠏⠛⠛⠒⠦⣤⣀⠀⠀⠀⠀⠀⠉⠑⠒⣶⠎
⠀⠀⠀⠀⠀⠀⠳⣦⣀⠀⠀⢀⣠⡶⠋⠁⡀⠄⠤⠀⠀⢀⡞⣿⡟⣆⠀⠀⠠⠄⠄⠀⠉⠳⣦⣀⠀⠀⢀⣠⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⡟⠉⠀⠀⠀⠀⠄⠀⠀⢀⣾⠐⣿⡇⢸⣆⠀⠀⠀⠄⠀⠀⠀⠀⠙⢿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠃⠀⠠⠂⠀⠀⠀⠄⢸⣿⠀⢿⠇⢸⣿⠁⠄⠀⠀⠀⠢⠀⠀⠱⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠁⠀⡠⠁⢀⠀⠀⠀⠀⠀⢻⠀⠘⠀⢸⠇⠀⠀⠀⠀⠀⠀⠱⡀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⡐⠀⢀⠂⠀⠀⠀⠀⠀⠈⡇⠀⠀⡏⠀⠀⠀⠀⠀⠀⢣⠀⠐⡄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢀⠆⠀⠀⠀⡆⠀⢀⠀⣃⠀⢀⡇⠀⠀⠀⠆⠀⠀⠀⢂⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡜⠀⠰⠀⠀⠆⠀⢸⣠⡏⠀⠈⣧⣸⠀⠀⠂⠀⠘⡀⠈⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⡇⠀⢠⠀⢀⣼⠋⠀⠀⠀⠈⢻⣄⠀⢰⠀⠀⢇⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠿⢾⡿⠛⠛⠀⠀⠀⠀⠀⠘⠛⠻⣿⠾⢿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠆⠌⠌⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠀⠀⢰⠃⡞⢀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠟⠈⡱⠋⠀⣄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠘⠰⠁⠀⠀⢸⡇⠁⢀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⠔⠊⠉⠉⠉⠙⢭⡉⠑⢦⡇⠀⢀⠀⠀⠀⠀⢠⣃⠴⠓⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⡠⠚⠉⢀⡀⠴⠥⢄⣀⣀⡀⠀⠀⠀⠙⡄⠀⠹⣄⠘⠶⠤⠤⠰⠋⠤⣖⠉
⠀⠀⠀⠀⠀⠰⡎⠉⠀⠀⠀⠀⠀⠀⠉⢢⠞⠁⠀⢠⠋⠀⠔⠀⠉⡀⠀⡀⠈⠤⡀⠀⠘⡄⠀⠱⣉⡶⠒⠒⠒⠲⢤⡀⠃
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠐⠢⢤⣀⣹⡄⠀⠀⠈⠀⣠⢆⢀⢪⠄⠀⢈⡆⠀⠘⠆⠀⡇⠀⠀⠏⠉⠒⢤⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⠀⠀⣠⠔⠋⠀⢡⠀⠀⠀⠰⡏⢆⠙⠤⠤⠖⢈⣃⠄⢈⠀⣠⠃⠀⠀⢰⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⡜⠁⠈⢑⡞⠁⠀⠀⠀⠀⡆⠀⠀⢀⠆⠈⠢⡀⢀⠀⠈⠁⠀⢸⡜⠁⠀⠀⠀⡎⠀⠀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠉⡄⢠⠖⠉⠀⠀⠙⣄⠀⠸⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡃⠀⣀⢠⡌⠀⠀⠀⠀⠀⢰⣆⣠⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠐⠦⢤⣄⣀⣀⣱⠁⠀⠀⠀⠀⠀⢈⠳⣬⡄⠀⠀⠀⠡⠀⠀⠀⢀⡠⠖⢋⠔⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠧⠒⠢⡀⠀⠀⠰⠛⠓⠲⣄⠀⠀⠈⠁⠓⠂⠉⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢀⣼⣡⣔⠈⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⣀⣀⣃⠀⠀⠀⠀⠀⠀⠈⠻⢔⡂⠤⠤⢀⣲⡞⠉⠀⠀⠀⠀⠀⣀⡤⡶⠋⠀⠀⠈⠙⢦⣠⠞
⠀⠀⠀⠀⠀⠰⣅⠀⠀⠀⠀⠁⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⢈⠟⠈⠒⠒⠒⠛⠉⠁⣴⠛⠒⠄⡀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⡀⢀⡤⠔⠒⢺⣷⠤⢄⣀⣀⣀⣀⣀⠠⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⢀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⠋⠀⠀⡴⠃⠈⡄⠀⠀⠋⠀⠀⢸⠓⠦⢤⣀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠓⢤⣀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠜⠁⠀⠀⣿⢄⡀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣰⠇⠀⠉⠓⠶⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣀⠠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠿⠿⠿⠿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⢖⣶⣿⣿⣿⣶⣌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⣿⣿⣿⣿⠿⣟⡿⢵⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⢻⡿⣡⠞⠛⠉⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠈⠃⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⣀⠤⢤⡾⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠈⠓⢶⡖⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠋⢥⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢹⡀
⢠⣾⣿⣿⣷⣄⣀⣤⣀⠀⣴⣾⣿⣷⣦⠀⡼⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⢀⡠⣿⣆⠀⠀⢸⡇
⣿⣿⣿⣿⣿⠁⠈⠀⠸⢸⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⢰⣿⣷⣦⣤⣴⣿⢟⣽⣿⣿⡬⡄⢸⠃
⠹⣿⣿⣿⣿⠎⠣⣄⠀⠈⢿⣿⣿⣿⡟⠁⡇⠀⠀⠀⣾⣿⣿⣿⣿⣶⢖⣿⣿⣿⣿⡇⣇⢸⡄
⠀⠀⠉⠉⠁⠀⠀⠀⠉⢀⡀⠪⢍⣁⠀⠀⠇⠀⢠⡇⢿⣿⣿⣿⣿⣫⣾⣿⣿⣿⣿⢃⣿⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣄⠈⠙⠒⠀⢀⣾⠃⠐⣿⣿⣿⣿⣿⣿⣿⠿⣛⠁⣾⣿⡄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣀⣠⣾⠃⠀⣸⣿⣿⣿⣿⣿⣯⣶⣿⠏⠀⢻⣿⣇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣌⣛⠻⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣦⣤⣈⡉⠉⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣟⣩⣶⣾⣿⣿⣿⣿⣶⣶⣦⣄⢛⣤⣄⢀⣀⡀⠀⠀⠀⣠⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠇⠉⢉⣡⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⢓⣈⣤⠴⠚⠋⠁

⣰⠋⡻⠻⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠟⢟⠙
⣿⣷⡿⣖⣿⠿⣆⡙⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⢋⣰⠿⣿⣲⢿⣾
⠻⣿⣍⣺⣿⣷⣾⠟⠛⠉⠃⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠘⠉⠛⠻⣷⣾⣿⣗⣩⣿
⠀⠹⣿⣿⣿⣿⠍⢑⣒⣤⣤⠾⣦⣟⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣻⣴⠷⣤⣤⣖⡊⠩⣿⣿⣿⣿⡏
⠀⠀⢹⣿⡏⣙⣶⣶⣾⣿⣿⣶⣾⡿⠷⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠾⢿⣷⣶⣿⣿⣷⣶⣶⣋⢹⣿⡏
⠀⠀⠀⢻⣿⡍⣽⣿⠿⠛⠁⠀⠈⢧⡀⠈⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⡼⠁⠀⠈⠛⠿⣿⣯⢩⣿⡟
⠀⠀⠀⠸⣿⣶⡿⣇⠀⠀⠀⠀⠀⠀⠈⠤⠀⠀⠹⣿⣧⡀⢀⡀⢀⣼⣿⠏⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⣸⢿⣶⣿⠇
⠀⠀⠀⠀⠹⣄⣷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣾⣠⠏
⠀⠀⠀⠀⠐⣿⣿⣄⣀⣀⣀⣀⣀⣤⣤⣤⣀⣀⣀⣥⣤⠿⣿⣿⠿⣤⣬⣀⣀⣀⣤⣤⣤⣀⣀⣀⣀⣀⣠⣿⣿⠂
⠀⠀⠀⠀⠀⠈⠛⠛⣻⡿⢿⣟⡛⠛⠿⢛⡿⠟⠉⠁⠀⠀⣿⣿⠀⠀⠈⠉⠻⢿⡛⠿⠛⢛⣻⡿⢿⣟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⡰⣿⠖⠊⠈⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠹⠦⠀⠀⠁⠑⠲⣿⢆
⠀⠀⠀⠀⠀⠀⠀⡟⢹⣡⠄⠀⠀⠀⠼⠓⠒⠂⠀⠀⠀⠀⣿⡯⠀⠀⠀⠀⠐⠒⠺⠧⠀⠀⠀⠠⣬⡏⢻
⠀⠀⠀⠀⠀⠀⠀⢻⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣼⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠙⠃⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠗⢦⡆⠀⠀⢠⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⡄⠀⠀⢰⡴⢺⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣟⣿⣖⣻⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣟⣲⣿⣻⡽⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡴⠰⢀⢠⠅⢀⣻⡉⠑⠓⢄⣌⣀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠤⠁⠺⢦⢁⡴⠀⠂⣁⣀⠈⣹⡯⣷⣦⣖⣀⠌⡛⣆
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡄⠐⠦⢻⡦⠀⣀⣀⣆⠀⠙⠇⡛⣿⠝⢿⣟⣿⣼⢖⡙⣈
⠀⠀⠀⠀⠀⠀⠐⠈⠀⢀⠀⣰⠟⠀⠁⢛⣦⣿⡍⠉⣷⠴⡆⠈⢺⡇⠆⠋⠻⠐⢿⠟⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡭⠀⠀⣼⣻⣿⠿⠀⡀⡤⠀⢳⠀⠀⣟⠈⠳⢆⢠⠄⠀⠡⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⢀⠐⢁⡾⣿⣷⠌⡡⣧⠃⢄⠀⣇⠻⢆⠁⠸⠃⣤⣌⠀⣰⡁⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠡⠖⠀⠐⠉⢬⠳⡛⡀⢁⡤⠠⣮⠶⢉⣄⣀⡀⡟⠊⢵⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢲⣄⣠⡄⢸⡄⣿⡀⡘⠂⢀⠀⢠⠞⢿⣏⠀⢢⡄⠘⠂⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⢣⣀⠠⢻⣷⢀⠉⢹⠶⣎⠁⠡⡠⣾⣼⡋⠡⣶⣤⠲⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠤⢸⠉⢠⡊⣐⡈⠁⢠⢠⡇⡈⠃⠀⠈⢟⣇⠀⠘⢁⢹⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⢑⡀⣞⣶⡙⢁⡶⠏⠈⢹⡁⠂⡁⢱⡞⡁⠀⠒⠀⣀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⢹⠿⠈⢡⢡⣶⣦⣤⢸⣿⠦⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡾⠉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⡄⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡷⠎⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠫⣿⠏⣷⠸⡤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⠘⠃⠝⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⡤⠶⠛⠛⠛⠛⠛⠛⠒⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠖⠒⠶⠶⢤⣄
⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⣀⡴⠿⠛⠛⠉⠉⠉⠉⠉⠛⠛⠲⠶⢤⣄⣀⠀⠀⠈⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⣀⣠⣤⠴⠶⠒⠛⠛⠛⠛⠛⠒⠿⢷⣄⡀
⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⣄⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⣠⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠈⠳⣤⣤⡤⢤⣾⠁⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⢸⡿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣾⠁⠀⠀⠀⠈⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣿⠁
⠀⡇⠀⠉⠛⠿⠶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠶⠞⠛⠉⠀⣿
⢀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿
⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣇⠀⠀⠀⠀⢸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⢋⣽⡟⠙⠳⠶⠶⠶⠟⢿⡍⠙⢻⡶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⢻⡿⠁⠀⢀⡴⠋⣸⠃⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢻⡀⠈⠙⢻⡷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞
⠀⠈⠛⢶⣤⣤⣤⣤⣤⣴⣶⠶⠿⠛⠋⠁⠀⣰⠟⠀⠀⣠⠞⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢸⣧⠀⠀⠈⢷⡀⠈⠉⠛⠻⠷⠶⣶⣶⣶⣶⠶⠟⠋
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⣴⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠈⣿⡆⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⢀⡾⢻⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣷⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⣠⡿⠁⣾⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⣿⣇⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠞⠉⠀⠀⠀⢀⣴⠟⠀⣰⠇⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⡏⣿⡄⠀⠀⠀⠹⣆
⠀⠈⠛⠿⣿⣭⣉⣁⣀⣀⣀⠀⠀⠀⣠⡾⠃⠀⣰⠏⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢿⡘⣷⡀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠈⠉⠉⢉⣽⠃⠀⣠⡾⠋⠀⢀⡴⠋⣠⣤⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⣧⠹⣧⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢀⣠⡴⢛⣡⣴⠞⢋⣠⣤⣞⣫⣴⠞⠋⡿⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠹⣆⠹⣧⡀⠀⠀⠀⠀⠈⠳⣤⡀
⠀⠀⠀⠶⠾⠿⠷⠛⠋⠉⠀⠀⠈⠉⠉⠉⠉⠀⢀⡾⠁⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠙⣧⡘⢷⡄⠀⠀⠀⡀⠀⠈⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠈⠻⣮⡻⣦⡀⠀⠹⣷⡶⣶⣶⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡷⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⣤⣄⣀⣬⡿⠋⠻⢶⣄⡈⠙⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢿⡏⠉⠁⠀⠀⠀⠀⠉⠛⠿⠶⣶⣭⣽⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠈⠻⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣤⣤⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣹⣄⠀⠰⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠁⡀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡏⢿⣆⣆⣀⠻⣿⣦⣄⣀⠀⢀⣠⡤⡀⠀⠀⣼⡅⠀⠀⠀⠀⠠⠶⣿⠤⠆⢀⣬⢃⠀⣀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣯⣍⠙⣿⣿⣿⣿⣻⣦⣄⡈⠁⣤⠀⣀⣠⣾⣿⣡⡤⢶⡷⢏⣁⠚⠀⣩⡤⠀⠤
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣴⣽⡟⣿⣿⣿⡟⣿⠿⣿⣿⣿⣿⠿⠿⣿⣿⣯⣥⣼⣿⠽⠒⠛⠁⠀⣁⠀⠉⣁⠔⠃⠠⠄
⠀⠀⠀⠀⠀⢤⣸⠇⣤⣤⣬⣶⣿⣿⣿⣿⣿⣿⣰⣯⣽⣏⣻⣀⠙⠉⠱⣼⡿⠿⢿⣿⣿⣍⢣⣶⡿⠿⠷⠤⢀⣒⣠⠋
⠀⠀⠀⠀⠀⠀⠙⠳⠾⠷⢿⣿⣿⣿⣿⣯⣵⣦⡿⣯⢹⣦⣥⣿⡆⠀⠀⠘⠷⢄⡀⣀⣠⠌⠀⢈⣶⣦⣤⢀⠀⢀⣥⣤⠃⠀⣀⠤⠄⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢹⣿⠛⣻⣿⣿⣿⣯⣺⣿⣿⡏⠁⣴⣿⣤⣀⢿⣷⣿⡿⠆⣀⡉⢛⠷⣩⣯⢠⣿⠟⡛⡀⠰⠁⠐⠀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠿⣿⠛⠉⠓⢸⣿⣿⣿⣇⣠⣽⣿⢿⡿⠟⢀⡴⠛⠀⢉⣌⠢⡥⢀⡲⠤⢠⡾⠟⠃⣦⡁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢈⣶⣿⠄⠀⠀⠚⣻⡹⣿⣿⣿⣿⢿⠀⠐⢰⡏⠀⣠⠀⠛⠛⣶⢴⣿⣷⣤⠈⠡⠠⠶⠿⠍⠂⢀⠠⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠻⣿⣷⠖⡂⠙⣿⣷⣼⣿⣿⠋⠀⠀⣤⢴⣄⣸⠏⡀⠀⠀⠃⢸⠿⠇⠀⠀⣴⣬⣄⣴⣂⣠⣜⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠙⠀⠙⠀⠈⣿⢿⢇⠈⡄⠀⠀⠀⣼⣿⣿⡿⣣⣀⣤⣀⢀⡀⠀⠀⠘⠛⣿⡟⢻⣿⠛⡤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠁⠀⣤⡚⣠⠙⠊⡇⠀⠀⢠⠁⠺⠀⠺⠛⠋⠀⠀⢪⠉⠉⠹⠟⢉⠉⣁⣠⡾⡛⠛⠛⠛⠉⠑⠂⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⡆⠀⠀⠙⣿⣧⣼⣤⡗⢠⠀⢈⣾⠀⠐⠠⣶⣄⠀⠀⣦⣀⡤⠀⠈⢁⣀⢈⡁⠙⢾⣴⡇⡀⠀⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡀⠀⢿⣿⣿⣿⣿⣾⣿⠁⠀⠹⡟⠀⢿⣧⣵⣲⠀⠉⢀⢴⣿⣶⠊⡠⠏⡀⠀⢻⣾⠛⠛⠒⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠈⠁⢀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⢀⡈⠉⠋⠉⠀⡍⣺⣿⣿⣯⣷⢤⣯⣴⣶⡿⠿⣧⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡐⠒⠀⣰⣧⣞⣴⣾⠃⠸⣿⣽⣿⣿⣿⣿⠃⠀⣰⣶⣄⠘⠙⣿⣦⡀⠀⢻⣿⣿⣿⣿⣷⣿⣿⣿⣿⡷⠀⢸⠂⢤⡴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢴⣿⣻⣿⡏⠠⠀⣾⣿⣿⣿⣿⣋⡟⠀⠀⣿⣿⣿⣦⡀⠛⠁⣉⣀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠛⢿⣶⣾⣶⣭⣝⣛⠟⠉⠠⣶⣤⣿⣿⣿⣯⡷⠐⢦⣼⣿⣮⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠁⠀⠀⠈⠛⣿⣿⣿⣿⣿⣷⣶⣤⣬⣙⡛⠿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣍⣛⠛⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠍⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣆⠀⠀⠈⢿⣿⣿⢿⣿⡟⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢶⡆⢭⣙⠻⠿⣿⣿⣻⡿⣿⡏⣿⡘⢯⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣷⣄⠀⠀⠻⣿⣾⣿⠀⠀⠀⠀⣼⣿⠏⠙⡇⠚⡹⢏⣴⢦⣌⢻⣿⣿⣷⣶⣬⣁⠛⠶⠴⣎⢿⣿⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠸⣦⣟⣷⣤⣴⣿⣾⡇⠀⠀⠀⠜⠛⠛⠃⠘⠛⠿⣿⣟⢳⣠⣿⣿⣿⣿⣿⣿⣿⣿⠃⠙⣷⣶⣴⣌⣷⣬⡀
⠀⠀⠀⠀⠀⠀⢀⡄⠀⣤⡎⠘⣿⠐⠛⢹⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⢻⣛⣿⡤⣿⣿⣿⣿⣿⡉⠀⠀⠚⣿⣿⣿⡷⣿⡂
⠀⠀⠀⠀⠀⠀⠉⠡⠀⡠⢠⣍⡽⠧⡀⢸⣿⢽⣟⡃⠀⣤⣤⣘⣯⢶⠉⣻⣸⣿⣉⠶⢧⣈⣿⣿⡈⢹⡂⠍⣿⣿⣷⠄⠀⠀⠘⣻⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣴⠁⠂⢦⡾⠀⢠⣟⣿⣿⠿⣄⠀⣀⣠⣧⠙⡗⣧⢸⣿⢿⡛⢹⡁⣾⣿⠟⠭⠿⠾⣇⣀⠀⠹⠟⡆⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠰⠾⠆⠀⠈⠁⠀⠀⠉⠁⠈⠀⠀⠉⠛⠛⠛⠉⠙⠛⠛⠋⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣶⡶⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⠺⠀⢠⠄⢹⠧⠱⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠧⠰⠉⠀⡀⠨⠦⡈⣄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢔⣤⠀⠀⠢⠀⣈⠶⠀⡟⠂⠀⠀⢀⠴⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⡁⠀⠀⠀⠳⡆⢠⡏⠀⠀⠐⠆⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠠⢯⠀⢩⡖⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⠀⠁⣀⠀⡱⢆⢹⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⣤⠔⠓⢠⠒⠠⠈⠘⠀⠉⠙⢉⡦⣀⠀⠀⠀⠀⠀⠈⠓⡶⢤⣨⡞⢳⠖⠼⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠏⣵⢖⣀⡄⠐⠀⠀⢉⣤⡀⠘⣌⠃⠀⠀⠀⠀⠀⠀⠘⠂⠉⠉⣁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠠⡞⢷⠀⠀⠉⠒⠧⣦⡼⠁⠻⣏⣱⠄⠀⠀⣀⣤⣤⡀⠀⣀⠴⠁⠠⠤⡀⠈⣳⠃⠀⠀⢀⡰⡀⠂⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢺⣟⠉⠉⠁⠐⠼⡧⠀⡀⠈⠑⢤⠞⣹⠓⣉⠁⢹⣄⣌⠀⠄⣀⣀⣈⢇⣘⠔⠀⠈⠘⣠⠃⠀⣀⣀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⢣⣀⣀⣀⠀⣹⠀⠀⠁⠀⠀⠙⣾⠀⠀⠀⠢⣀⣸⣄⠀⠀⣠⣾⣿⣿⣿⣷⣾⣶⣛⣤⡫⠏⣧⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣭⠄⠀⠈⢨⡆⠀⢀⠀⠀⠀⠈⢳⡁⡀⠀⢀⠡⢨⣳⣮⣤⣤⣭⣭⣄⣈⡛⠟⠉⢿⠁⡀⢡⡀⠿⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠉⠚⠓⢲⠏⣤⡄⠀⠀⠙⠂⠀⣀⠹⣄⠀⠜⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠾⠂⢀⠀⠀⡀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⢧⠀⢀⣀⠀⢱⠉⠁⠀⠉⠲⡇⠀⠈⠣⡘⣆⣰⣾⣿⣻⣿⣿⢿⡟⣿⢻⠟⢙⡃⡴⠒⣀⠀⣤⠤⣤⣧⠋
⠀⠀⠀⠀⣤⠤⣾⠁⢝⣦⠔⢮⠱⡏⠀⠀⠈⢣⠤⠄⠤⠄⢠⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣸⣿⣿⠜⡷⠀⢀⣍⣀⣉⡐⠡⢴⡥⠊
⠀⠀⢀⡤⠿⢀⠬⢀⠈⠙⠀⠚⢱⡧⠀⠀⠀⡧⠀⠀⠠⣤⠄⣁⠀⠀⠀⠈⣿⣿⣿⣿⣿⢿⡟⣿⡃⠀⠀⡰⠃⠀⠃⠈⠉⠒⠐⠃
⠀⠀⣿⡖⢀⠤⠀⡀⠐⠀⠀⠂⣿⢱⣷⠀⢸⡀⢾⡗⠀⠀⢢⠀⠉⠢⠀⠀⢸⣿⣿⣿⣿⣾⣣⣿⣷⣤⣈⣀⠀⢠
⠀⠀⠘⡴⣤⠄⣤⠤⣀⠉⣤⡀⠈⢦⡴⠊⠀⠁⢆⠉⠀⠀⠈⠁⠀⠀⠀⠀⢸⣿⡟⢸⣿⠋⠉⠛⢿⣷⢹⢄⠁⠂⠈⢂
⠀⠀⠀⠙⢤⡦⢌⢂⣉⣀⣡⡄⣙⣤⣷⣤⡤⠔⠚⠓⢤⡀⠀⡀⠱⢄⠀⠀⣾⣿⣵⣿⠁⠀⠀⠀⠀⣿⣫⣐⠀⠉⠢
⠀⠀⠀⠀⠘⠠⠐⠋⠁⠈⣠⣿⣿⡿⠛⠁⠀⠀⡀⠠⠄⠠⠭⠀⡒⠢⣴⣤⣿⣽⢞⠜⠀⠀⠀⠀⠀⢸⣷⣏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣩⠏⣰⣦⡄⢀⣆⠀⡀⢠⣄⠀⠀⠈⠀⠀⣼⣿⡞⠁⠀⢀⠃⠀⠀⢀⣿⣿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣏⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣿⣇⠹⡄⢀⡎⠀⠀⠀⣼⢿⣿⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢛⡇⣀⠀⣢⠀⠀⠞⠀⠀⠀⠀⠀⠐⠀⠀⠈⢿⡟⢳⡈⡟⠀⠀⠀⡘⠙⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡘⠛⠁⠀⠀⡈⠀⠀⠀⠀⢀⡄⠠⠀⠀⢠⡎⢧⠞⡙⠀⠀⠀⡔⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⣿⠀⢀⠀⠈⡅⢀⢀⡀⠀⢠⠀⠀⠑⠠⣾⣋⣠⢶⡇⠀⠀⠀⣷⣇⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⣡⣄⡁⠀⠔⠋⠀⡌⠀⠀⣈⠀⠠⢤⡾⠁⣸⠁⠞⡅⠀⠀⠀⡧⠄⡙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⡙⠋⠉⠃⠀⠀⠰⢄⠀⠀⠀⠁⣠⣾⠁⠀⠉⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠈⠓⠦⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠠⣶⣶⡄⠀⠀⢴⣶⢶⡴⠁⠈⠀⠀⠀⠀⠀⢡⠀⠀⠀⠋⠀⠀⢀⠀⠀⠀⠀⠀⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⣀⣈⠉⢀⣠⠶⣄⠀⡎⣷⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀⠀⠀⠀⠀⣀⣀⡀⠀⠉⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢃⣴⡏⠉⠉⠙⠉⠀⠀⠈⠉⣠⠿⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⢈⡰⠖⠚⠉⠉⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡞⢿⣧⠀⠀⠀⠀⠀⣀⠞⣉⡀⠀⠙⢢⣠⠔⠒⠤⠤⢤⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠘⠃⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠉⠀⠀⣀⣠⠞⠀⢀⡥⣤⠤⠤⠐⠒⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠰⠁⠒⠂⠀⠀⣀⡜⢁⡀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⠯⠛⠀⠉

⠀⢠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡄
⠀⠀⢻⣧⣏⡗⠚⠷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡿⠟⠲⣏⣯⣿⠁
⠀⠀⠈⣽⢤⣿⣋⣈⣽⡇⢨⣿⣷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣽⣯⠰⣿⣉⣉⣹⣥⣿⡇
⠀⠀⠀⠹⣯⣼⣯⣀⣨⣛⡧⠤⡿⠷⠮⢷⣄⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⠀⣠⣴⠯⠶⠿⡯⠴⣟⡯⣀⣨⣟⣼⡟
⠀⠀⠀⠀⠘⢿⣾⡉⡱⡗⡀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⢀⠀⠀⢀⣼⣿⡉⣳⣿⠏
⠀⠀⠀⠀⠀⠠⡿⣫⢽⣿⠛⠂⠀⠉⠒⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⠔⠋⠁⠀⠛⢾⣻⡽⣧⡟
⠀⠀⠀⠀⠀⠀⢹⣿⣤⢷⣀⠀⣀⣀⠤⠴⠦⠄⠀⠀⠈⠳⡀⢀⣀⢀⡴⠋⠀⠀⡀⠠⠶⠤⠄⢀⡀⢀⣸⢧⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠘⣾⣿⠎⢀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣤⣤⣶⣶⣶⣶⠒⠒⠤⣤⢤⣼⣿⣿⣷⣤⣤⠀⢀⣶⣶⣶⣶⣶⣤⣤⣴⣿⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⣠⠞⢿⣿⡟⢄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡽⠓⠂⠀⠀⠉⠀⠀⣀⡤⠊⠁⠄⢸⣿⠀⡀⠙⠢⣀⠀⠀⠈⠀⠀⠀⠒⠻⣜⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣻⣄⣀⠀⠰⢊⠠⠒⠋⠁⠀⠀⠜⠀⢹⣿⢠⠘⠄⠀⠀⠉⠒⠦⠘⠲⠀⣀⣀⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⡅⢀⡔⠁⠀⠀⠀⠀⠀⠀⣤⠃⠸⡟⠈⢷⡀⢀⠀⠀⠀⠀⠀⠱⣄⠀⣵⣹⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡿⣟⣿⣄⣀⣠⡆⠀⡰⠁⣰⠃⠀⠀⠀⠀⠈⢧⠀⢣⡀⠈⣦⣀⣀⣼⣛⡟⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⣻⣽⣿⣷⣺⣇⡴⠃⠀⠀⠀⠀⠀⠀⠈⠳⣤⣿⣲⣯⣿⣽⣿⠽⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠙⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⢀⠂⠀⠒⠁⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣀⡐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠓⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠁⠫⠀⠸⠀⣦⠀⢀⡥⠀⠈⠀⠀⠀⠀⡀⠀⠀⠐⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡖⠀⠘⡔⠄⠸⣄⣁⣸⣧⡑⣤⠀⠀⠂⠀⠀⠀⠒⢤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⣹⢷⠀⠀⠈⠚⢦⡹⡝⠉⠛⠳⢆⠳⠶⢴⣄⣠⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣮⣣⠈⢿⠦⣄⠀⣀⠉⠳⣶⡒⠂⠀⠐⠀⠰⠶⠟⠁⣠⡀⠀⢠⡆⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣯⢿⡇⠀⠸⣇⣦⠙⠉⠧⣄⣀⠉⠓⠤⢉⡀⠀⢲⣾⡟⠚⠀⠀⠋⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢰⡏⠨⢻⡄⠀⠘⢷⣀⣴⣠⣀⡀⠉⠃⠀⠰⣻⡿⢿⢛⠁⠀⠀⠀⠀⠀⡴⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⢧⡄⠀⠸⠿⡶⣤⣤⣉⠣⢴⡋⠉⠉⠛⠚⠈⠈⠉⠉⠁⠀⣀⣀⠦⣀⢸⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⠀⠹⣷⣄⣀⡀⢇⢿⣿⣷⣶⣮⢳⠀⢠⢈⡐⢲⣶⣶⣶⣮⠾⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⣶⣆⠸⠏⠉⠙⢿⣰⣿⡿⢿⢿⠀⡆⠈⣼⡰⠿⠛⠋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡵⣟⣿⣿⡻⣄⠀⢸⣿⣿⠡⡿⢿⣆⢱⡞⠡⠔⠊⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⠇⡈⣀⢸⣿⣧⠖⠋⠉⢁⡴⣿⢦⣤⢾⠯⠃
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣷⣭⣿⣇⠹⠀⢀⠀⠀⣿⢟⢻⣿⡿⠃
⠀⠀⠚⠛⠁⠁⠉⠛⠚⠓⠉⢁⣾⣿⢿⡿⣿⣿⣿⡲⣦⣾⠛⣿⣿⣷⡿⠛⠁
⠀⠀⠀⠀⠀⢤⣶⠶⠴⠖⠚⠋⠉⢀⡾⠀⡜⠁⠈⠉⠉⠛⠻⡟⣏⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠌⠀⠀⠀⠀⠀⠀⠀⠙⣼⣜⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣮⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠄⢀⠊⢀⠇⠀⠀⠀⡠⡞⣤⠀⠤⠀⢤⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠐⢄⠈⣼⠢⠁⠠⡄⠀⡜⠠⠁⡆⠟⢸⠇⣤⠄⢀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⣀⠀⠀⠀⠀⠀⡀⢡⠀⠠⠐⠒⠢⣨⠓⠤⠤⡐⠁⡘⠀⠀⠀⠱⠄⠀⣀⡁⠄⣡⡆⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⣈⠁⠒⠤⣀⠠⣀⠆⣀⣑⣒⠂⡏⠐⢄⣀⠸⢀⠁⠀⠃⢀⠄⠻⡀⠉⠠⢊⠜⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠔⠂⢹⠃⡀⠘⣀⣀⠸⡷⠌⣉⠀⣑⢘⠀⢈⣤⡀⠀⠀⢱⠔⢀⡊⠤⢀⠃⠀⠀⠀⡀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⠘⢦⡀⢡⠓⠀⠀⣷⣌⠉⠉⠂⣘⡀⢸⣈⢻⡄⠀⠀⡤⠊⠀⠀⠈⠀⠀⠆⠎⠀⢰⠊⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢐⠁⢨⠷⠤⣱⠛⡆⡴⠞⢰⢶⣞⠛⠿⣹⠏⠁⠁⠈⠙⣲⠚⡅⠀⠀⣀⠜⠀⣸⢀⣶⢡⡎⣵⠯⡉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢆⠀⠀⠱⠸⠓⠶⠶⠒⡋⠞⠋⠀⣰⠅⢺⢧⡩⢾⣛⠶⣤⠠⣴⠞⠋⠈⠙⢦⡹⠁⡴⠈⠳⡎⠈⢦⣨⢤⠄⠡⠚
⠀⠀⠀⠀⠀⠀⠀⢐⠉⠢⡀⢣⠀⠂⠣⡀⠄⢄⣀⠨⣴⣹⣄⡉⢙⠇⣠⡧⣈⢀⡀⣨⠧⠸⠇⠻⢩⡄⠀⠀⢘⠁⣰⠀⠀⠀⢀⠐⠊⡕
⠀⠀⠀⠀⠀⢀⣀⡈⠢⡀⠈⢆⠑⣤⡤⠘⠟⢍⣍⠣⣧⢞⠉⠉⠉⠉⠹⢀⣀⡋⠀⢱⠤⣴⡆⣴⠊⠙⣶⠶⡞⠃⣤⣢⣄⡠⠿⠔⠋⠉⠉⠠
⠀⠀⠀⠀⠀⠘⢄⠀⠁⠢⢅⡰⠻⡌⣤⡉⠳⠊⠉⠘⢏⢰⢏⠠⡆⠀⠀⢺⠁⠈⢰⣇⣀⠭⠹⢿⣄⡜⢁⠜⡉⢉⢴⠏⠀⠱⡖⠓⠶⠐⠊⠁
⠀⠀⠀⠀⢀⠤⠀⠨⠉⣈⠋⠍⠑⢳⢄⡙⢽⡀⠀⠀⢸⠏⠀⠀⢸⢀⡴⢛⢳⡤⠞⡍⡷⠖⠒⠁⢙⣃⠗⠁⢀⡼⠙⠤⠠⠚⡇⠀⠀⠂
⠀⠀⠀⠀⠈⠒⠀⠐⣾⠋⠑⢊⠢⣀⡇⠈⡁⠴⠤⠊⠉⣤⣤⠒⢁⡌⢀⠞⠁⠈⠻⢿⣼⣒⣒⡒⢈⠛⡍⣩⠟⠛⠛⣅⡩⠁⠘⠒⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠎⢰⠈⢄⠀⢱⠀⠀⠸⣀⢀⡠⠓⡖⠁⠈⢲⢩⡠⠛⡘⢄⠀⢀⡟⠁⠀⠀⢹⣀⣨⠿⡤⠠⣔⣸⡉⠉⠳⣀⠅⠒⠉⣠⠤
⠀⠀⠀⠀⠀⠀⠘⠀⢰⠀⠀⠉⠁⠀⠀⠀⠀⢰⠁⠀⠛⢦⣠⡼⠦⢷⡄⠋⠉⢉⠀⠈⣄⣀⡀⠬⠀⠉⢲⡖⠈⠀⣀⠼⠃⠎⠙⢫⣉⣁⢀⡀
⠀⠀⠀⠀⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⢀⡀⠨⠦⠤⠏⢙⠉⠂⢤⣜⠀⠀⣀⠌⠙⠁⠀⠙⢎⡈⠁⠢⣸⣈⠿⠘⠃⢺⢸⠀⡀⠘⡿⡁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⡴⠀⡀⢀⠈⡄⠰⠃⠸⠃⢈⠟⠀⢐⢇⡀⠀⢈⠋⠁⠠⣽⡁⠀⠀⠺⡁⠈⠶⠈⢀⠃⠙⠤⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⡚⠁⡾⠀⠇⡇⢠⢂⠔⣻⢟⠳⡙⢨⡉⠉⠭⠭⠤⢩⡿⠄⠐⠄⠐⠃⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠠⠚⠀⠛⢡⠊⡠⠙⠂⠑⢌⠢⡉⠒⣢⠶⠾⣽⣍⠢⠄⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡁⠜⠁⠘⡀⠀⠱⡄⠃⠘⠤⠐⠸⠇⠣⡘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠑⢄⠀⠘⡀⠀⠀⠀⡆⢠⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢁⠀⠀⠀⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢛⠁⢊⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠶⢾⣿⣋⣀⣀⠴⠾⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠈⢁⣀⠀⠻⣯⠫⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⡾⢇⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢠⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣍⠛⠂⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠐⠶⢦⣄⡠⣤⠀⠀⠀⠀⠀⠈⠀⠈⠻⣧⠰⠚⣓⠲⢥⣀⡢⢲⣤⣠⡀⢀
⠀⠀⠀⠀⠀⠀⠈⠙⠻⡎⢡⡀⢀⡀⢀⠈⠃⣠⡰⢟⣿⡶⢏⠢⡥⠶⡍⣿⢮⣿⣿⣤⠒⢠
⠀⠀⠀⠀⠙⢦⣔⠲⣤⣿⣈⡉⠉⠉⠀⠑⣠⣷⣳⣾⣿⣶⣦⣶⣷⡎⣿⣿⣿⣿⣿⣿⣶⢿⡤⡄
⠀⠀⠀⠀⠀⠈⠛⣷⣌⣻⣷⠵⡢⡂⠢⠁⠘⢙⣹⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌
⠀⠀⠀⠀⠀⠀⠱⣽⣿⣿⣿⡟⣓⠹⠌⣷⣈⠼⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⢦⠙⣿⣿⣿⣷⣯⣨⡾⣿⣟⡻⠷⣦⣜⣿⡿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠂⠱⣾⣿⣿⣿⣿⣷⣤⠀⠈⠙⢦⣌⠉⠻⣧⣄⢩⠿⠝⠯⠙⠛⠛⢛⡁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣤⣭⠻⣿⣷⡄⠠⣤⡛⠄⢹⢶⠂⠈⣿⢦⣤⠀⠛⠛⢿⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠙⠿⠿⣿⣿⣿⣿⣷⣾⣿⣂⠘⡁⢒⣀⡀⠈⢙⠤⢤⣄⣤⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⡀⡀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡼⢻⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⡀⢷⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿⢸⡇⠠⢺⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣷⡶⢄⠀⠘⢷⣿⡾⠁⢁⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢆⣑⣀⣘⣻⠔⠒⢮⠋⠕⢒⣒⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⢈⡶⠋⠁⢀⣈⢙⣷⡀⠘⠓⣌⠿⢿⠟⠁
⠀⠀⠀⠀⠀⠀⢀⡾⢣⢺⠓⣩⠤⣬⠓⡝⠆⠀⢸⠈⠙⢶⡀
⠀⠀⠀⠀⠀⣶⡫⠶⠋⠺⢷⡄⢰⣿⢀⡇⢰⣄⡞⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠙⣇⠀⠀⣸⣤⡭⠝⠃⡜⢠⠚⢉⠇⠀⣠⠞
⠀⠀⠀⠀⠀⠀⣰⠗⠮⢤⣀⣀⣤⣞⣁⠟⢰⣿⣠⠏⣰⠂⣠⡄
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣽⣋⣉⣁⣠⠴⠞⠁⢀⡴⢣⠞⣿⣷⡀
⠀⠀⠀⠀⣰⣯⣬⣣⡀⠀⠀⠀⢠⠟⠀⠀⣀⣀⣾⢁⡏⢸⣿⣿⡇
⠀⠀⠀⠈⠛⠛⠿⠿⠾⠗⠒⣈⢓⣒⡦⠭⠤⠤⠤⠸⠀⣾⣿⣿⢇⠤⢔⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣆⠻⢿⣿⣶⡿⠿⠶⢤⣘⡿⠋⠠⣾⣿⡿⠁
⠀⠀⣀⣠⡤⠤⠤⠤⣄⡘⠸⢟⣿⣤⣴⣟⣁⣀⠀⠀⠀⠀⠉⠛⢻⠟⠋
⠀⠀⠻⣿⣷⣷⣶⣦⡀⡈⢠⡿⠁⠀⣠⡤⢀⡉⠛⢦⣶⠦⣄⠀⠈⠲⣄⠀⠀⠀⣠⠴⣶⡖
⠀⠀⠀⠈⠻⢿⣿⣿⣿⡷⣺⣇⡤⡶⠃⣀⣴⠾⡟⢿⣻⣆⠈⠳⣦⣀⡈⣧⢠⠞⣡⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠉⡩⠚⣹⠋⢰⡇⣞⣽⣿⣿⣾⣆⣷⢻⡇⠀⠸⡇⠙⣧⠀⢰⣿⣿⠟⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⣿⣆⢸⣇⢻⣯⢞⡡⠏⣿⠃⣸⠀⠀⢠⡇⠀⢸⡀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣼⣁⣉⣜⡵⠆
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣿⠘⠻⣇⠙⠫⣭⡴⠞⣡⠞⢹⡗⠚⢩⠇⠀⣸⠇⢒⣊⣭⣷⡶⣰⢶⠊⢉⢉⡙⠓⠲⡞⣁⡀
⠀⠀⠀⠀⢀⣀⠀⣿⠃⠀⠻⣄⠀⠙⠲⠖⢋⣡⡾⠋⢀⣼⠃⣠⠏⠀⣰⣿⣰⣿⣿⣿⠟⣰⣏⣻⠟⡉⠉⡻⢟⡛⠹⣉⠉⣀⣩⣾⣿⠇
⠀⠀⠐⢾⣿⣶⣶⣜⢧⡀⠀⠈⣻⣖⠒⠊⠉⣁⣠⣴⣛⡵⠞⠁⠀⣾⣿⠃⠛⠛⠻⣤⡘⠿⢿⡉⣾⣷⣖⣋⠥⢚⣃⠿⠸⣿⡟⠛⠁
⠀⠀⠀⠀⠈⠛⠻⣿⠗⠑⠄⠀⢈⡩⠿⠿⢿⣿⣉⠉⠁⠀⠀⢀⡴⢿⣵⣷⣗⣦⢄⣀⠙⢦⡀⠉⢡⣍⣀⠐⢄⢠⣥⣤⣤⣀⣉⡓⢦⡀
⠀⠀⠀⠀⠀⣠⠎⣡⣴⣶⣿⠀⣍⢧⠀⠀⠀⢹⡿⠛⠛⢛⠋⣵⣿⠈⢿⣿⣿⣿⣿⣿⣶⣄⢻⣆⠘⢿⣿⣿⣎⣧⠻⣿⣿⣿⣿⣿⣶⣿⣄
⠀⠀⠀⠀⢰⣧⣾⣿⣿⠿⠋⡄⣿⣿⠛⠶⠶⠾⠀⠀⠀⣆⣼⣿⠟⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣿⡄⠀⠉⠛⠻⠿⠆⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠛⠛⠉⠉⠀⠀⠀⢳⡿⠃⠀⠀⠀⠀⠀⠀⠀⠹⠟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢤⠄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣰⣦⣉⣷⡞⣼⣻⡾⣸⣽⣮⣧⣾⠙⣒⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠎⣿⡗⢿⢿⣏⣎⠾⠌⠯⠥⠻⠴⠮⢗⣟⡷⡿⣽⣥⠯⡰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⢯⣹⡟⣿⡻⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠭⣄⡶⠽⣿⣿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢳⡿⡾⣉⠶⠊⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⢠⣄⣀⠀⠀⠀⠀⠈⠙⢿⣟⣗⣾⣓⡄
⠀⠀⠀⠀⠀⠀⠀⠴⣥⣬⡿⡵⠋⠀⠀⠀⠀⠀⠀⢠⣴⡞⣿⡽⣗⣿⡟⣿⣷⡀⠀⠀⠀⠀⠀⠙⣭⢛⣿⢞⣆
⠀⠀⠀⠀⠀⠀⣸⣢⣿⡾⡝⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣶⣿⠿⢿⣿⣟⣽⡄⠀⠀⠀⠀⠀⠈⢿⣿⣿⠽⠆
⠀⠀⠀⠀⠀⢠⡷⠺⣳⡼⠁⠀⠀⠀⠀⠀⠀⠀⣼⣯⣽⣿⣿⣭⣤⣤⣤⣬⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⡿⠿⢿⠿
⠀⠀⠀⠀⠀⢴⣽⣿⣦⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣯⡇
⠀⠀⠀⠀⠀⠟⣝⣫⣩⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡻⠀⠀⠚⠛⠥⠇⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣯⣟⣥⡅
⠀⠀⠀⠀⠀⠚⣻⣝⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⣿⡄⠀⠀⠸⣿⠇⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣙⣯⣣⡆
⠀⠀⠀⠀⠀⢟⣽⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠹⣷⣶⣤⣤⡤⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣷⡿⡇
⠀⠀⠀⠀⠀⠘⣶⣷⣶⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⣌⣿⡿⣋⡔⠂⣠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡛⣿⣦⢙
⠀⠀⠀⠀⠀⠀⢲⣸⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠙⣿⡘⠉⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⢠⣟⢾⣿⢵⠃
⠀⠀⠀⠀⠀⠀⠀⢫⣿⣯⣜⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣤⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⡰⣻⣞⡟⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣽⠯⣭⣧⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡠⣞⡡⢿⡾⡭⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣿⣿⡶⠭⢓⢢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣆⢿⣧⣾⣽⡯⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢝⡖⣋⣳⣶⣿⡻⣲⡲⢠⡤⢔⢶⠐⣆⡝⣿⣿⣧⢿⣏⠵⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠫⢥⢐⡿⢏⣿⡷⠋⡿⣯⡟⡽⣷⡙⠿⠑⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠑⠋⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣴⣸⡿⣿⣿⣷⡍⢉⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⠳⡌⠙⢿⣿⡿⠿⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣩⠯⠉⡇⠀⠀⣠⣼⡋⣴⣶⣤⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢧⣤⣀⣾⣶⣾⣿⣦⣀⡀⠈⠙⠛⣷⠀⠀⠀⣠⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢻⣿⣿⣽⠟⢹⡇⢻⢿⠿⣷⡆⣈⡀⢀⡆⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣴⣼⡿⢿⣯⣾⣴⣷⡼⠃⠈⠛⠛⣿⠃⠸⠀⠀⠀⠀⠀⣵⢦⡀
⠀⠀⠀⣀⣾⣷⡈⠙⢷⡀⢀⡿⢃⣿⣻⡿⡛⠁⠆⠀⠀⠘⠂⣤⣿⡆⢠⠸⠀⢀⠀⢰⠇⠈⠐
⠀⠀⠀⠙⠿⡌⠛⣗⣾⠗⣈⣡⣍⢿⣷⣿⣇⠀⠀⠀⠀⠀⠀⠈⠇⣵⠤⠦⣄⢉⡴⠁
⠀⠘⠉⢷⣤⣀⣀⣨⣽⣷⣿⣿⣿⣿⡿⠟⠻⢷⠀⠀⠀⠀⠀⠀⣻⢷⣟⣷⡌⡅⣀⠀⠀⠀⢀⡀
⠀⠀⡄⠉⣭⣭⡭⠖⣿⢿⡿⣿⣟⢯⡛⠳⡞⠀⠀⠀⠀⠀⢉⣫⣽⢻⡿⣿⣿⠳⠄⠀⠀⠀⠈
⠀⠀⠐⣶⣭⣡⠄⢊⡵⠋⣠⡉⣿⣄⠙⠂⠀⣂⢶⡄⢀⠀⠀⠀⢡⣿⠃⠛⠋⠓⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠉⠉⢰⣾⡶⣾⣿⣷⣬⣍⠠⣶⠿⣿⠇⢸⣿⣄⣀⠀⠋⠡⠤⠤⢀⣀⠀⢀⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠘⠷⠉⠘⢿⣃⠀⠀⠀⣿⠀⠈⠛⠿⣿⣟⣻⣶⣶⣾⣶⣶⣶⣬⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡈⠻⣦⣠⣤⣥⡀⠀⠈⠀⠁⢀⣵⣿⣿⡿⢿⡿⢿⣿⣟⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠹⣦⣿⣥⣟⣳⣽⣶⠂⠀⠀⠛⣿⣿⣿⣿⣦⣻⣦⡙⢻⣍⣛⣿⣛⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⢢⣤⣼⣿⣿⣿⣾⣧⣄⠀⠀⠀⠙⠛⠻⣿⣿⣿⣽⣻⣾⣥⣴⡮⠟⠿⠿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠋⡙⠻⠿⡎⠉⠓⠀⠀⠀⠀⢀⣤⣿⣿⣿⣷⣶⣾⣿⣷⣴⣾⣚⣓⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢻⠀⢀⡀⠘⢢⣤⣤⠀⠀⠀⠸⠉⠉⢹⢻⣿⣿⣯⣽⣿⣿⡟⣛⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏⡻⠃⠀⠀⠀⠀⠀⢠⠋⠀⠿⠟⠏⠳⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⠀⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠤⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⢠⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⢫⣧⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⣠⡇⠐⠙⢿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣥⣴⣾⠋⠀⠰⠷⠈⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⣋⣭⣵⣾⣯⡐⠷⠀⠀⡀⠀⣿⣿⣿⣿⣦⡀⠀⠘⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠛⠛⠉⣿⣦⣄⠈⠁⠀⠀⠉⠛⠿⣿⣿⣶⣶⢟⣿⠇⠀⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠅⠈⠀⠃⡸⠋⡣⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣏⣀⣠⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⣫⣿⠃⢀⠀⠐⠜⠂⠆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣽⣿⡿⢛⡛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠁⠀⠠⠀⠤⠜⠀⢀⡠⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⢹⡿⣷⣌⢻⣿⣿⣿⠿⠿⢿⣦⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⡀⠀⠀⠐⠀⠀⠠⠄⠅⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣾⣿⡟⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠵⡀⢄⣴⣶⣿⣿⠥⢀⠀⠄⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⣿⡿⣏⣿⡇⠀⠀⣀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣴⢬⣿⣿⣝⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⢰⣿⣿⠀⠻⣾⣿⣦⡀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⠋⠈⢿⣝⡻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣼⣿⣟⢇⠀⠀⠉⠉⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠉⠛⣿⣷⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠰⠿⠟⢻⣮⡓⠦⡤⣶⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⣴⡿⠟⠿⣶⡀⠙⠻⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣾⣿⠃⣴⢿⣷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠹⠦⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⢀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⢠⣾⡿⠙⣷⠀⣀⣤⣤⡴⠶⢦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⣴⣿⠟⠀⢀⣿⣿⣿⠟⠁⢀⣤⣾⣿⣿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣝⡲⠶⢶⣶⣶⠿⠟⠋⠀⢀⣠⣾⡿⠋⠀⣠⣾⣿⠟⠁⣠⣶⣿⣿⡿⠛⠁⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠳⣝⡶⣤⣤⣤⣤⣤⣴⣶⡿⠟⠋⣠⣴⣿⠿⠋⢁⣴⣾⣿⣿⠟⠋⠀⢀⣴⠶⠶⢤⡈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣛⠶⣯⣭⣍⣉⣩⣥⣤⡶⠿⠛⠉⢁⣤⣾⣿⡿⠟⠉⠀⠀⠀⠀⣾⡇⢰⣆⣼⡇⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣍⣉⣉⣁⣀⣤⣤⣶⣾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣉⣉⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉

⠀⠀⠀⢀⡴⠚⠉⠉⠉⠙⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠛⠓⠒⢤⡀
⠀⠀⣠⠿⠖⠒⠒⠒⠲⠦⠤⣄⣀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⣀⣠⠤⠤⠴⠶⠶⠤⢷⣀
⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠙⢦⡀⠀⠀⢀⠔⠋⣀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⢹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡜⠉⠉⠹⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟
⠀⢸⠀⠉⠛⠲⠦⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣰⠇⠀⠀⢀⣇⣀⣀⣀⣀⣀⣀⣀⣤⡤⠤⠴⠖⠛⠉⠀⡇
⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⢸⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⢚⡽⡟⠙⠒⠒⠊⣯⠉⢳⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠈⠳⣤⣀⣀⣀⣤⣤⠴⠖⠛⢩⠟⠀⣠⠊⢰⡇⠀⠀⠀⠀⢸⠀⠈⣇⠀⠘⡏⠛⠲⠶⣤⣤⣤⣤⡤⠞⠁
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⡰⠋⠀⣴⡇⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⣿⡄⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠀⢀⡞⢹⠀⠀⢸⠀⠀⠀⠀⠀⠸⡇⠀⢸⣧⠀⠀⢳⡀
⠀⠀⣀⣀⣀⡤⠤⠒⠉⠀⠀⣠⠏⢠⠏⠀⠀⣿⠀⠀⠀⠀⠀⠀⣇⠀⠸⡿⡆⠀⠀⠳⡀
⠀⠀⠀⠉⠛⠒⠖⡶⠀⣠⡾⠁⣠⠏⣀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⢳⢹⡄⠀⠀⠙⢄
⠀⠀⠀⢀⣀⣴⣪⡤⠞⠩⣴⣮⠵⠋⡽⢠⡟⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠈⢧⠻⡄⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⣠⢞⣵⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠈⠳⣝⣦⡀⠰⣤⣤⣬⡵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣤⣤⡬⠟⠙⢦⣌⣓⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠘⢦⣀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣷
⠀⠀⠐⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡟
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣇⡇
⠀⠀⠀⢻⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⣿⡇
⠀⠀⠉⠈⣇⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢦⢀⡞⠿
⠀⠀⠀⠀⢻⣇⠰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸⡏
⠀⠀⠀⠐⢦⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠩
⠀⠀⠀⠀⠀⠙⢟⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠱⡍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢼⣧⡄⠐⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠀⣀⠀⠀⠀⣸⣷⣿⠀⡄⠀⡼⠁⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠂⠸⣴⡏⠙⢀⠀⠉⠁⠙⣠⠀⢰⠁⡤
⠀⠀⠀⠀⠀⠀⠀⠘⠀⣴⡀⠀⠲⠒⢈⠻⠋⠛⠐⠛⢧⢸⣆⠚⠀⠀⠃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢳⣀⠀⠀⠈⠀⣶⡱⠀⣀⠸⢘⣭⠳⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡚⣡⠞⠠⣌⠋⠈⣽⠏⢈⠀⢠⠟⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⣰⠃⢀⣀⠀⠅⠀⠘⠀⡞⠀⠙⠀⠀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⡏⠀⠀⠰⡆⢃⠃⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡼⠃⡟⠀⠀⠀⠀⢹⣦⡐⠉⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉
⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⢸⡇⢸⠃⠂⠀⠀⠀⢨⡾⠉⢢⣀⡀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠐⠀⠀⢀⣴⡟⠁⣘⠀⠀⣄⠀⠀⢸⣯⡶⠀⠀⢷⡄⠀⠀⢀⡀⠀⢀⡹⣦⣄
⠀⠀⠀⠀⠀⣔⡠⢔⣉⠀⠀⢀⣽⠀⠀⠘⣆⠀⠸⣏⠀⠀⠀⠀⠈⢢⡿⠮⠁⠀⠀⠀⠆⠈⢳⡀
⠀⠀⠀⠠⠀⠈⡛⣴⠋⠀⠠⠃⠈⠀⠀⠀⢹⡀⠀⢻⣀⡠⠂⠀⠀⠀⢱⣄⠠⣈⡀⠒⡲⠖⢻⡷⣴⣦⣀
⠀⢀⠀⠋⠀⣀⠜⣱⣧⠐⠁⠀⠀⠀⠀⣰⣾⡀⠀⠀⠙⢦⠀⠀⠀⠀⠸⠮⢛⡿⠯⣉⠉⣭⠀⠀⠀⠀⢙⡄
⠀⠈⠙⠛⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⢲⠋⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⢈⠀⠘⡿⠂⠀⠠⣀⠀⢀⡀⠐⠂
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣐⠛⠀⠐⠂⠀⢦⣃⡴⠃⢄⢍⡠⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠁⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠈⠕⢢⠇⠠⠄⣨⢋⠡⡀⠀⡀⠁⡔⠂⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄⠜⡥⠚⠉⠐⢾⡴⠾⠒⠺⡅⠀⢲⠊⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠠⠀⠀⠐⠀⠀⠀⠈⡴⠊⠀⠀⠀⠀⡞⠀⠀⠀⠀⠻⡞⢁⣀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⠤⠚⠋⠀⢠⣐⣀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡵⠀⠒⢀⠈⠅⡄⣩⢥⡀⠈⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢲⠁⠀⠀⠀⡴⠋⠁⠀⠀⠙⠂⣀⣼⢴⣶⡦⢼⠖⠉⠀⠀⠀⠈⡄⠶⠃⠉⠁⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠄⠀⠀⠐⠉⡡⠼⠁⠀⠀⠀⠀⢸⣟⠕⠁⠀⠀⠈⠑⡘⢖⠁⠀⠀⠀⣽⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠌⠀⢀⣀⢲⣀⡠⠊⠀⠀⣸⠋⠀⢊⡀⠢⠐⠀⠐⣼⣢⠔⠒⠋⢹⡏⠀⠂⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⠀⣀⡀⠀⠀⠀⠀⣻⣶⡀⠀⠁⠁⠀⣠⣾⠟⠨⢀⣀⣀⡼⡁⠠⠀⢀⠀⠉⠓⠦⣤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⣂⠴⠉⢡⢀⣀⠐⠁⠙⠿⢯⣶⣒⠿⠋⠁⠀⢤⣀⣀⣴⢇⡓⡢⢀⡄⡀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠰⠲⣼⠒⣅⠀⠀⡰⠚⢇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⣆⠀⢀⡢⠛⠼⢇⢤⠖⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⢄⠀⠘⠉⢈⣑⠇⠀⠀⢀⠀⠢⠤⠤⠔⠁⠀⠀⣀⡠⢤⠴⢺⡍⢿⣷⣄⣄⠘⠀⠀⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠢⠀⠀⠀⠐⠀⠁⠾⠀⠑⠀⠈⠀⠀⠀⣐⠀⠰⡯⢩⢩⠀⠸⠇⠈⠁⠘⣍⢄⠀⠈⠃⠀⡀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠇⠀⠀⠆⠀⠀⡠⠑⣦⣾⠀⠖⠡⠸⠀⢀⠈⠙⢟⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠈⠀⠠⡄⠄⡀⠀⠉⠹⡀⠀⠀⠀⠐⠈⠀⠀⠨⢯⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣉⢉⠉⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⢿⣻⠿⠗⠊⠈⠀⠀⠀⠁⡈⠶⠂⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⢻⠟⠧⠈⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⠀⠀⠀⣠⣼⣿⣿⡿⡋⠓⠈⠀⠀⠀⠀⣀⠄⠂⠁⠀⠀⠀⢀⡀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣣⡀⣰⣿⣿⣟⠉⠈⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠱⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⢟⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢻⣿⣿⣿⡇⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡄
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⠋⣠⠴⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣹⡄⢸
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠟⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⢿⡿⣿⣯⣿⣾
⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣦⣄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠁⠀⠀⠀⠀⠙⣫⣽⠏
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣞⠁⠀⠀⢀⣀⡀⣠⣄⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⠾⠔⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠹⣎⣩⠉⢙⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠶⠾⢄
⠀⠀⠀⠀⠀⠘⣧⠬⢤⠠⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⠏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠶⠆⡸
⠀⠀⠀⠀⠀⠀⠈⡿⣌⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠁⠁⠀⠀⠀⠀⠀⠀⡀⠄⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠸⡌⢈⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⡟⠋⠋⠉⠀⠀⠀⠀⠀⢀⡠⠔⠂⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣘⣉⣀⣠⣤⣴⣶⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣥⡀⡄⠀⢀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣧⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣯⠾⠗⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⡿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡙⠿⠿⠿⠟⡛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠛⠑⠉⠀⢾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢗⡿⣽⡷⢌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⠟⠟⠁⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⡏⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠘⣦⣠⡀⠀⠀⣠⣴⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡋⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠬⠷⠄⠂⠉⠙⢿⣿⣿⣿⣿⣷⣄⠀⣀⣤⣴⣿⣿⡿⠛⡆⠈⠙⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣾⡿⠋⠙⢿⡉⠀⣀⣸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠄⠠⠀⠀⠀⠀⡠⠐⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠤⣀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠤⣀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⠊⠀⠀⠀⠒⠲⣄⠀⠀⠀⠀⠀⠀⡀⠀⠓⠠⠀⠨⠄⠂
⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠
⠀⠀⠀⠀⡠⠒⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⡀⠤⠀⠀⠈⠐⠀⠀⠈⠉⠉⠀⣀⡀
⠀⠀⠀⠀⠂⠀⠁⠉⠉⠀⡀⠠⠔⣈⡀⠀⡀⠀⠠⠄⢂⢠⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠨⡠⠤⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⢾⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠄⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠨⠤⢄⣤⣬⣥⣤⠄⠀⠀⠀⠀⢀⡀⠀⠀⠠⢔⣽⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠄⣀⠀⠉⠐⠒⠀⠄⠠⠤⠀⠀⠀⠀⠤⠄⠐⠷⢤⣤⣀⣀⣀⣀⣐⣐⣨⡧⢀⠠⣊⠔⠒⠉⠉⠉⠙⢌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠒⠒⠠⠄⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢁⠀⡀⠀⡴⠃⢀⠠⠀⠀⠄⠠⢌⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠄⡀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⢧⡔⡥⠚⠉⠉⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣈⠀⠀⠀⠀⠠⠀⠐⡀⠔⡯⠥⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣟⠒⠤⠤⣤⠭⢤⣴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣌⡀⠉⠉⠙⠛⠛⠛⠛⠛⢑⣂⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠲⠶⠖⠒⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠀⠀⠄⠠⠈⠠⠀⠀⠠⠂⠀⠀⠈

⠀⠀⠀⠀⠀⠀⡀⢀⠀⠠⠋⠁⢳⠀⠀⠀⠀⠀⠂⠀⠑⠀⠀⠀⣠⡀⠔⠄
⠀⠀⠀⠀⢐⠉⠈⠉⠒⠠⠥⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠉⠀⠐⠢⢤⡀
⠀⠀⠀⠀⠈⠒⠂⠐⠢⣀⠀⠈⠀⠀⢂⠀⠀⡀⠀⠀⢠⠊⠀⣀⠔⠊⠉⠲⡦⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣤⣄⠆⠀⠀⠀⢰⠃⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢉⣾⢿⠈⣀⠀⠀⠊⠀⠈⠣⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⣾⣷⣿⡤⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀⠀⡠⢶⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠰⠿⡸⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⡤⠤⠒⠊⠉⠐⢛⣾⠆
⠀⠀⠀⠀⠀⠀⣸⣧⠔⠙⠄⣰⡾⠃⠀⠀⠀⠀⣠⣾⣿⣯⣿⣿⠦⠶⠚⠉⠀⠀⠀⠀⠀⠀⢸⣿⣠⡀
⠀⠀⠀⠀⢀⠄⠛⠁⠀⠰⣷⣿⠁⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠾⠛⢋⠵⠧⡄
⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⠞⠛⠋⠉⠉⠀⠀⠀⡀⠀⣀⠇
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⠐⢻⡇⠀⠀⠁⢀⣿⣿⠃⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⡔⠲⣬⣦⡱
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣤⣴⣾⡿⠛⠁⠀⡀⠀⠀⠀⢰⡏⠀⠀⣰⠦⡀⠀⠀⡇
⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠿⢿⡏⠀⢀⡼⠋⠉⠀⠀⣠⣿⢃⡴⠞⠁⠀⠘⢢⣀⠆
⠀⠸⠀⠀⠀⠀⠀⣄⣠⣿⠋⠀⠀⠀⠈⠓⠠⣎⠀⠀⠀⠀⠀⠿⢷⣾⡁⠀⠀⠀⠀⠈⢹
⠀⠘⣂⠀⢀⣴⣾⠟⠁⡽⢄⠀⠀⠀⠀⠀⠀⡎⠱⣼⠧⢀⣄⠀⠈⣯⠀⡄⠀⠀⠀⠀⢨⠂
⠀⠀⢇⢀⣾⡏⠀⠐⠋⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣼⣧⣼⣄⡀⠀⢀⡾
⠀⠀⢈⣿⣿⠇⠀⠸⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠙⠻⣿⣿⣿⣿⣷⡀
⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⢆⠀⠀⠀⠀⠀⠼⢿⣇
⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢓⠔⠊⡋⡔⠁⠈⢧⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠒⣹⠞⠁⠀⡐⠀⠀⠀⠀⠘⡆⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⢁⢶⡀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⡜⡠⠁⠘⣧⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⡀⠀⠀⢀⡜⣰⠃⠀⠀⠈⠁⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀⠠⡶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠊⢠⠇⠹⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣦⣤⣤⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠸⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣿⣿⢙⣿⣿⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⠏⡘
⠀⠀⠀⠀⠀⠀⠀⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⢿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢱⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣵⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣷⣤⡀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢏⣼⣿⣧⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⡀⠀⠀⢀⣠⡴⠞⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠈⠻⣿⣿⣏⣭⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠸⣿⣝⣿⡀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⠀⠀⠀⣿⣿⠏⢧⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⠛⠿⠿⠿⢿⡿⢿⡿⠿⠿⣿⣄⣀⠹⢿⠛⠀⠀⠀⣿⣿⠂⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣦⣤⣀⡀⣀⡀⢀⠀⣀⢀⣰⣿⣿⣿⣿⡯⠉⠁⠀⢸⣿⣿⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣧⡀⠀⠿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣏⡉⢩⣍⣥⠂⠀⠀⢠⣿⣿⣿⠀⠸⣿⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣷⠈⢳⣦⣍⣛⣛⢿⠿⠿⠀⠿⠿⠿⠿⠿⢿⡇⠀⢀⣤⣄⣀⣽⣿⣿⣿⡿⠀⠀⡟⣸⣿⣿⣦⢠⣤⣀
⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣇⣠⣌⠁⢸⣿⣿⣿⣶⠀⣿⣶⣶⣶⣶⠻⣿⠴⠞⣛⣛⣩⣵⣿⣿⣿⠇⢠⣷⣶⣿⣿⣿⠏⣸⣿⣿⠃
⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⡛⠿⣦⣾⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣄⣶⣿⣿⣿⣿⣿⣿⡿⠛⠀⣀⣾⣿⣿⣿⡿⠋⣼⣿⡿⠋
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠓⣿⡿⣓⣸⡿⠋⣿⣷⣦⣭⣭⣙⠻⠿⠃⢹⡿⠿⠛⣛⣹⣿⡟⣛⠛⠛⠛⠁⠄⠀⠉⠻⣿⢏⣥⠛⣤⣾⣿⣿⠇
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⡂⠀⢸⣿⡇⠹⠿⠀⠀⢀⣼⣿⠿⣿⣿⣿⢶⠆⣸⣾⣿⣿⣿⣿⣤⣤⣿⣦⠀⠀⠀⠀⠀⠀⢰⣶⣿⡟⠀⠹⡿⠟⠁
⠀⠀⠈⠙⢿⣿⡿⠟⠉⠀⠀⠀⢾⣿⣦⣄⡀⠋⢀⣾⣿⠋⠀⠀⠀⠉⠈⠀⣼⡿⠿⠿⠿⠛⠋⠉⠁⠀⠆⠀⠀⣠⣦⣄⣾⣿⠿⠃
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠹⣧⣾⣿⣷⠃⠀⠀⠀⠀⠘⠀⠛⠛⣡⣤⣴⣶⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣦⡕⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠈⠵⠾⠿⠿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣬⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠛⠋

⠀⠀⠀⣀⣀⡀⠛⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣖⣾⣶⣶
⣴⣾⣿⣟⣟⠛⢿⠛⠟⠶⡦⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀⣴⣶⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⢶⡍⢑⣠⣤⣤⣴⣾⣿⠟
⠈⠻⣿⣿⣏⣙⣙⣉⠹⠊⠛⠒⣦⠀⠭⣐⡂⠤⡄⢀⠀⣿⡿⡿⠥⣬⢯⠙⠹⡿⣤⣄⢀⡀⣀⣤⣤⣶⣺⠍⠡⠴⣒⣮⠁⢀⡀⢘⢠⣤⣴⡾⠛⠁
⠀⠀⠀⠙⣿⣿⡼⡥⣠⢟⠀⠈⢹⢏⠑⣒⣒⡽⢯⣿⣿⣤⣿⣟⣻⠏⠀⢀⣽⠘⢓⠙⣂⠈⡯⠿⣟⣟⣛⡋⢯⣖⣚⣳⣖⣚⣳⣶⢾⣿⠁
⠀⠀⠀⠀⣿⡿⠿⠒⠓⠚⠒⠒⠒⠚⠐⠒⠒⠒⠓⠓⠫⠟⠋⠩⠝⡀⠀⡙⠟⠙⠊⠙⣀⠋⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⡀
⠀⠀⠀⡸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠈⠀⡀⢿⠗⠀⠐⠊⠄⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢹⣀⠔⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠙⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃

⠀⠀⠀⠀⠀⣴⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣦
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢀⠀⢀⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⢍⣴⡿⠀⠀⢿⣦⡩⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣰⠿⢿⣿⣿⣿⣛⣛⣿⣭⡷⣟⣵⣿⠟⠀⠀⠀⠀⠻⣿⣮⣻⢾⣭⣿⣛⣛⣿⣿⣿⡿⠿⣆
⠀⠀⠀⠀⠁⠿⣿⣿⡿⠿⢟⣻⣭⣷⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣾⣭⣟⡻⠿⣿⣿⣿⠿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⡀⠀⣠⣤⣤⣄⡀⠙⠏⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⢿⣿⣿⣿⣿⣿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⢀⣸⣧⡀⠙⠛⠛⠛⠁⠈⠋⠀⣀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠈⢻⡟⠉⠀⠀⠀⠰⠶⠀⠀⠀⠙⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠇⠀⠃⠀⠈⠁⢀⣤⣶⣷⣦⣄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣠⡀⠀⠀⠉⠉⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⡀⠀⠀⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠈⠋⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⠁⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠟⠉⠁⠉⠀⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣤⠀⠈⠋⠀⢰⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠰⣿⣿⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣟⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⡿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦⡀⣀⣤⣤⣄⣤⠤⠀⠀⠀⣀⠄⠘⠛⠉⠹⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡾⠟⠋⠀⠀⠀⠀⠀⠈⠛⠟⠀⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠻⢿⠛⡿⠿⣿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⢠⠞⢻⣭⠭⢽⡓⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣚⡯⠭⣭⡟⠳⡄
⠀⠀⠀⠀⣿⠀⠻⠿⠁⣀⣈⠑⢄⠙⠻⡢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⠿⠋⡠⠊⣁⣀⠀⠿⠟⠀⣿
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠻⠟⠁⠀⠑⣄⠈⠢⡑⢄⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠀⠀⡠⢊⠔⠁⣠⠊⠀⠈⠻⠟⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠹⡄⠀⣤⣤⠀⠀⠔⠋⠀⢱⣄⠈⢆⡑⣄⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⣠⢊⡴⠁⣠⡎⠁⠉⠢⡀⠀⣤⣤⠀⢀⠎
⠀⠀⠀⠀⠀⠀⡇⠀⠛⠛⠀⡌⠀⣀⣠⠃⠈⠳⣜⠛⢌⠳⡀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⠜⡡⠛⣣⠞⢁⠘⣄⣀⠀⢡⠀⠙⠛⠀⢸
⠀⠀⠀⠀⠀⠀⢧⠀⠀⣴⣤⡅⠘⠿⠟⠀⠋⠀⠈⢳⣄⠱⣝⢄⠀⠀⠱⡀⠀⠀⠀⠀⢀⠎⠀⠀⡠⣋⠎⢠⡞⠁⠀⠙⠀⠹⠿⠃⢈⣤⣦⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠈⠢⣄⠙⠋⠁⢀⣤⣤⠀⠀⠀⡰⢅⣈⠳⣌⠁⢧⡀⠀⠱⠀⢀⡀⠀⠎⠀⢀⡼⠛⣩⠞⣁⡈⠆⠀⠀⠀⣠⣤⡀⠸⠙⠋⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⡘⡈⠛⠛⡀⠀⠀⡇⠀⠋⠙⠪⣑⠦⣙⢦⡀⣨⣿⣿⣅⢀⡴⣋⠴⣊⠔⠊⠙⠁⢸⠀⠀⢀⠛⠛⢃⢂⣀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠇⠀⡀⠀⠡⣾⣿⠧⣀⣉⠉⣁⡲⣵⣬⣓⢿⣿⢻⡟⣿⡿⣞⣥⣮⣴⣊⡉⣉⣀⠸⣿⣷⡌⠀⢀⠀⠸⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⣄⡈⠄⠀⢣⣠⠤⠷⢒⠒⡉⠩⣿⣭⣍⣛⣿⣿⣿⣿⣛⣩⣭⡿⠍⢉⠐⡒⠾⠤⣤⡜⠀⠠⢃⣠⡴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡩⠟⠋⠁⣀⣠⣤⣈⡑⠾⢦⠶⢾⣿⣻⣿⣿⣿⣿⣿⣿⡷⢶⡴⠷⠊⣁⣤⣄⣀⠈⠙⠻⢍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡴⠊⠍⣙⡽⢃⠠⢀⣶⢶⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⡶⢦⡀⠄⡘⢯⣋⠩⠙⢦⡀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⣺⢟⣪⠴⠛⠉⢀⣠⣶⣫⣽⠿⣻⡿⠃⣸⣿⣿⣇⠈⢿⣯⠻⣼⣝⡶⣄⡀⠉⠛⠦⣕⡻⣗⢄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠙⢉⠁⠀⠀⡀⠘⠋⢉⠔⠁⡼⢻⠁⣠⢿⣿⣿⡿⣆⠈⡛⢷⠈⠢⡉⠙⠓⢄⠀⠁⠈⡉⠋⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠔⠁⠀⢀⢸⣿⠀⣐⠁⢠⠟⠄⡄⢠⠇⢸⣽⣯⡇⠸⡄⢡⠠⠻⡄⠈⣂⠀⣿⡇⠀⠀⠈⠢⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢀⠁⢸⡏⣸⡿⠀⣟⡜⡐⢀⡎⠀⢸⢾⡷⡇⠀⠱⡀⢂⢳⣳⠀⢿⣧⢹⡇⠈⠄⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣄⠂⠀⠈⢰⡿⠁⠀⠟⡰⠁⡸⠀⠀⠘⣿⣿⠇⠀⠀⢧⠈⢆⠻⠀⠈⢿⡆⠁⠀⠘⣀⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⢦⡀⠀⠆⠀⠀⠀⡰⢁⣶⠇⠀⠀⠀⠛⠛⠀⠀⠀⠘⣶⡈⢆⠀⠀⠀⠐⠀⢀⡴⣫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠳⠴⡀⠀⣀⣠⡷⢋⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡙⢾⣄⣀⠀⢀⡦⠞⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠙⠊⠉⠉⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠉⠉⠑⠋⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠰⡒⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⣽⣾⣷⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡄⠛⠍⢙⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠁⡀⣰⢀⠁⠁⠘⢧⠴⢦⣀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⣤⠟⣄⠠⠁⢠⠀⣠⠃⠀⠙⣴⣯⣾⣷⣡⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠠⣽⠷⠾⠓⠠⠼⣋⣁⣁⠠⠔⠉⠹⢿⠛⠭⡛⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡉⢀⠄⣀⡀⠀⣻⣗⣀⡈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠱⡐⠋⠉⠠⠆⠉⠿⢿⣃⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⢿⣀⠀⠈⣁⣠⡶⣶⣶⣏⠟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢻⡽⠿⠋⠻⣽⣟⣽⣠⢠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠲⣤⣶⠘⠟⣧⣷⣚⠁⠈⠁
⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⡿⣭⣀⡀⠀⠀⠈⢻⡄⠆⢹⡟⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠄⣈⡁⠒⢦⣆⣻⠈⠀⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡈⠛⣷⣰⣿⣷⠶⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣈⣽⣿⡽⠐⡏⠉⠃⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡻⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠁

⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢿⣿⣿⡷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣆⠶⣿⡿⣦
⠀⠀⠀⠀⠀⣿⣿⣿⡦⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣤⣦⣹⠆⢋⣾⣿⠞⠁
⠀⠀⠀⠀⠀⠈⢿⣿⡿⠲⣦⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⢿⣿⡏⠀⣰⣿⣯⠋
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡦⣄⡀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⢿⣮⡂⠀⡀⣿⣏⡇
⠀⠀⠀⢠⣤⣻⣿⡿⢆⣷⣿⣿⡾⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠻⣦⠝⠉⠛⠈⠘⢿⣷⢀⣴⣿⡗⡁
⠀⠀⢀⡦⣿⣿⣿⣀⠀⠀⠙⢿⣳⣼⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⢷⣉⣣⣤⣴⣶⣦⣔⣠⣤⡞⠉⢹⡿⠝⢄
⠀⠀⠀⠲⠙⡿⢻⡏⢴⣿⣿⠿⡻⠛⠋⠆⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡯⠿⠿⠛⠛⠼⡻⠟⡿⡻⠆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣬⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣰⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠂⠢⣄⢠⣀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⡈⢑⠀⠈⠀⠀⠀⣀⠀⢆⡀⠙⡿⠛⠁
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠨⠄⣶⣿⠁⠀⠰⣤⠺⠝⠋⠀⠀⠀⠀⢀⣤⣾⣯⢹
⠀⠸⣿⣏⢛⣳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⣴⣛⡯⢰⡯⣽
⠀⠀⠘⣿⣿⠩⠭⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⣿⣅⣿⣗⡏
⠀⠀⠀⠘⣷⠖⠂⣀⣀⣀⣀⣱⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠻⣯⣷⣈⣷⠙⣧⣀
⠀⠀⠀⠀⣿⡛⠻⠋⠉⢉⣩⣿⢿⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣦⡹⠿⠿⣿⣿⣧⡽⣳⠖⠛⠃
⠀⠀⠀⠀⠹⣧⣀⠘⢀⣾⡿⠃⢸⡇⠀⡈⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣄⠺⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠛⢻⡏⠠⠊⣸⡇⢀⢀⡤⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡛⠂⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣀⣘⣧⣼⣠⣧⣟⡻⣧⠀⠀⠀⠀⠀⠀⠀⠉⠩⠛⠛⢉⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠛⠻⢿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡰⠢⡴⠛⢶⠋⢲⠞⠳⡤⠲⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡖⠒⠇⠀⢣⠀⢠⠀⠈⠀⢸⠀⠸⠀⢀⠃⠀⠗⠒⣆⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠤⢏⠀⠱⡀⠈⠄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠌⠀⠈⠀⡰⠁⢈⠧⢤
⠀⠀⠀⠀⠀⠀⡶⠚⢄⠀⠣⡀⠈⠄⠀⡤⠔⠒⠃⠈⠉⠉⠀⠑⠒⠢⢌⡀⠌⠀⡰⠁⢀⠜⠲⡆
⠀⠀⠀⠀⢰⠚⠓⢄⠀⠑⢄⠈⡠⠚⠁⢀⡀⠤⠒⠂⠀⠀⠐⠂⠤⢀⠀⠈⠒⢎⠀⠔⠁⢀⠔⠛⢲
⠀⠀⠀⢰⠚⠓⠤⡀⠉⠢⣠⠋⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠑⢄⠊⠀⡠⠔⠛⢲
⠀⠀⢠⠚⠑⠠⠄⡀⠁⡰⠁⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⢂⠁⡀⠤⠖⠛⢦
⠀⠀⡴⠓⠂⠤⠀⠀⡰⠁⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢇⠀⠠⠔⠒⠳⡄
⠀⢀⡽⠒⠀⠀⠠⠄⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠤⠀⠀⠀⠺⣅
⠀⠈⡷⠤⠄⠠⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠠⠴⡇
⠀⠈⢣⠤⠀⠐⠂⠀⡃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠂⠒⠀⠠⢤⠋
⠀⠀⠳⡤⠄⠀⠂⠈⢱⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠂⠀⠤⡤⠃
⠀⠀⠘⢤⡠⠔⠂⠀⡀⠥⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡀⠀⠒⠤⣠⠜
⠀⠀⠀⠸⢄⡠⠐⠉⢀⠄⠓⣄⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⢄⠈⠑⠠⣀⠼
⠀⠀⠀⠀⠸⢤⡤⠊⠀⡠⠂⢀⠗⢄⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢆⠉⠢⡀⠉⠢⣤⡼
⠀⠀⠀⠀⢠⠞⡧⢤⠊⠀⡠⠁⢀⠂⢈⠒⠢⠄⣀⣀⠀⣀⢀⡀⢠⠄⢒⠉⢂⠀⠱⡀⠈⢢⠤⢆⠑⡄
⠀⠀⠀⡰⢃⠌⠀⠘⠒⢎⠀⡠⠁⢀⠂⠀⠃⠀⠀⠈⠀⢨⠀⠀⠀⠆⠀⢂⠀⠡⡀⠈⠖⠚⠀⠀⠑⡈⢆
⠀⠀⡜⢀⠂⠀⠀⠀⠀⠈⠉⠣⠠⡆⠀⡐⠀⠘⠀⢀⠀⢸⠀⢰⠀⠈⡄⠈⡦⠠⠋⠉⠀⠀⠀⠀⠀⠐⠄⠣
⠀⡘⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠔⠳⣤⠾⣄⣴⠤⣴⠓⠔⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢃
⢰⠁⠌⠀⠀⠀⣀⣠⠤⠤⢄⠀⠀⠀⠀⠀⠀⠄⢀⡜⠁⠈⠣⡀⠡⡀⠀⠀⠀⠀⠀⣠⠤⠤⣄⣀⠀⠀⠀⠱
⣌⣠⠤⠖⠊⠉⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠂⢠⠎⠀⠀⠀⠀⠙⣄⠐⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠑⠒⠤⣄
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⠂⢠⠃⠀⠀⠀⠀⠀⠀⠘⣆⠐⡀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠎⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠱⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢁⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢚⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣆⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⣴⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⢻⣆⠀⠀⠀⠀⢀⣾⠇⢠⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⠘⣿⡆⠀⠀⠀⣾⡟⠀⣾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡙⢿⣿⡗⠀⣿⣿⠀⠀⢸⣿⡇⢸⣿⣿⡿⣡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡙⢿⡀⣿⣿⣆⣀⣾⣿⡇⣼⠟⠡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⢿⣿⣿⣿⣿⣿⠟⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⡎⣿⣿⣿⣿⡏⢼⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣀⣿⣿⡿⣿⣇⣨⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠁⠀⠀⡀⠙⠻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢚⣻⣿⣿⠁⠀⠈⣛⠁⠀⢸⣿⣿⡓⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣽⣿⣿⣿⣷⣤⣘⣟⣃⣴⣿⣿⣿⣿⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠟⠻⠿⠟⠛⠋⠙⠉⠛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣟⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣥⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⠁⠈⠙⢿⣿⣿⣼⣿⣿⠟⠁⠀⢹⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠙⢤⣤⣤⡾⠛⠛⠛⠛⠷⡤⣤⣤⠎⠉⠛⠛⠉⠁




⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⣶⣶⠶⠶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠉⠁⠉⠉⠒⠂⠄⠀⣀⡀⠠⠠⠐⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠒⠄⢀⣀⣀⣠⠤⠤⠔⠲⡄⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠤⠀⣠⠊⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⡔⠁⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠉⠁⠒⢤⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⢀⠎⢀⠀⠀⠀⠀⡀⠒⣊⠉⠉⠉⠲⣄⠈⢳⠀⠀⠀⠉⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠘⠀⡊⠀⠀⠐⠈⠔⠀⢀⡉⠂⢄⠀⠀⡇⠈⡆⠀⠀⠀⠀⢷⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠂⢹⠀⠂⠀⡀⡄⠀⡈⠉⠓⠀⠁⠠⠇⢀⠇⠀⠀⠀⠀⢸⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠈⠑⢀⣰⠛⡁⠘⠀⠰⠮⢾⡠⠀⠀⡼⠀⠀⠀⠀⠀⡜⠀⠀⠀⣸⢀
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢰⠀⠀⠀⠀⠀⢤⡀⠀⠀⡇⣰⢷⠀⠈⠑⠀⠀⠀⠀⠀⠐⠋⠀⠀⣰⠁⠀⠀⠀⠀⡜⠁⠀⠀⣰⠁⠀⢡
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⠟⠀⠱⠀⠀⠀⠁⠀⠀⠀⠀⡠⢂⠔⣹⡀⠀⠀⡠⠊⠀⠀⢀⠴⡁⠀⠀⢸
⠀⠀⠀⠀⢀⠀⠙⢄⠀⠀⠀⠆⠀⠀⠀⠀⠀⡇⠀⠀⡷⣤⡀⠀⠈⠂⠄⠀⣀⣀⡀⠾⠐⣁⡴⠋⠀⠠⠔⡀⣀⠄⠊⠁⠀⠘⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠡⡀⠀⠈⢦⡀⠀⠀⠀⢇⠀⠀⠐⣼⣬⡁⠐⠒⠒⠒⠀⠀⠀⠚⢉⣡⠄⠂⣁⡼⠋⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⡈
⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠑⠀⢀⡙⢦⡀⠀⠈⠳⢄⣀⠈⠳⠀⠉⠉⠉⠀⠀⠈⠁⠠⠋⠤⠲⠋⠁⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠔
⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠘⠄⠙⢦⡀⠀⠀⠈⠉⠙⠂⠒⢎⡉⠉⠀⠀⠁⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⢸⠜⠁
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠘⢆⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠃⠀⢀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⣀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⡀⠀⠀⠉⠈⠉⠉⠉⠁⠀⠀⠀⢀⣀⡤⠔⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠘⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠻⠁⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠉⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠱⠦⠄⠤⠠⠔⠉⠀⡔⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⠀⠀⠀⠀⠀⠈⠉⠉⠝⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⣀⡠⠤⠐⠉⠂⠄⠀⠀⠤⠔⠒⠂⠀⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢤⡀⠋⠶⠴⠴⣄⡄⠀⠀⠧⢀⠀⡀⠑⢖⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠒⠂⢠⢀⣤⠀⠀⣰⠀⠘⣧⡄⠐⠛⠁⠛⠄⠀⣅⠂⠬⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠠⡔⡖⢻⢀⠠⠒⣄⢼⠝⠏⠋⠀⠀⠶⠋⠑⠒⠚⠷⠂⢀⣀⠀⠂⠰⣌⣆⠀⡀⠈⢹⣄⡄
⠀⠀⠀⠀⠀⠀⢠⠹⣦⣼⣧⣶⡿⠟⠉⠀⢓⡳⠂⠡⣄⠀⠀⠀⠀⠘⣧⠀⠀⢉⡧⢀⠀⢹⡦⣀⠀⠈⢿⡇⠀⡀
⠀⠀⠀⡀⢸⠀⠎⢀⣸⣿⢳⣏⣤⠤⠚⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠲⢇⣆⣷⢀⠁⠘⡧⢸⣦⡀⠎⢷⡴⢻⡆
⠀⠀⠀⣧⠀⡆⠀⡸⢋⡿⣾⣉⣆⢠⢠⡠⣴⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⢿⠳⠷⣧⡄⣣⡑⡄⢼⣷⣾⠁
⠀⠀⢀⠸⡔⡉⢶⡟⣹⣱⡟⠓⠁⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠵⠂⠳⣄⣏⠘⠻⢷⣿⣀⣿⡃⣨
⠀⢳⠈⡦⢻⣦⡟⣿⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⢸⣿⡝⣿⡷⡴⠂
⠀⠈⢷⡄⠈⢿⣾⢃⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⠳⣿⡇⢻⣇⢽⠄
⣄⠀⣸⢿⣆⣼⣟⣱⣿⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡑⢻⡷⣼⣿⣷
⠘⣧⡽⣎⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢟⣸⣿⣼⣿⠏
⠀⠘⣧⣿⢸⣿⣿⢀⣄⠀⢠⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⢹⣿⣿⡏
⠀⢀⢹⣾⢾⣿⣿⣨⠋⠡⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣀⠀⡓⢾⣿⣿⢳
⠐⢾⡤⣿⣤⣿⣿⡄⠀⢸⣿⣫⡀⠀⢠⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣟⡻⡟⣾⣿⣿⢸⠇
⠀⠸⣿⢏⢿⣿⣿⣧⠀⢒⢸⣟⡆⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⡇⢈⣿⣿⡇⢸⠀⠠
⠀⠀⢹⡥⡂⢻⣿⣿⣧⠀⢖⣿⢩⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣛⣿⠥⣼⣿⣿⣇⡏⠀⠏
⠀⠀⠀⠘⢷⡈⣿⣿⣿⣷⡨⣯⣾⣿⢘⣠⣀⡆⠀⠀⠀⠀⠀⠀⠀⢶⣷⣆⡀⠀⠈⢀⣤⡸⣿⣏⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣾⣿⣛⠛⣿⣻⣿⣶⣄⢀⠀⢀⠀⠀⠘⢝⢯⣇⢆⣇⡞⣿⠩⢿⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠻⣿⣷⣾⠼⠿⠿⠿⠯⣄⣠⣤⡄⢠⠴⠓⢉⣩⣍⠙⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠓⠦⠤⣼⣿⣥⠤⠄⣨⡤⠐⠀⠀⢈⠗⣅⠀⣲⣊⣹⣥⣾⣿⣿⣿⣿⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡏⠉⢻⣿⣟⣩⣹⣷⣶⣊⣠⠶⢻⣯⠟⠉⠀⠀⢤⣤⠼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠙⠿⠏⠀⠊⠁⠐⢤⠞⠂⠀⠐⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⢀⡀⠀⢀⠀⢀⠀⠀⢀⠀⢀⡀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠈⠒⠁⠀⠃⠀⠛⠂⠘⠙⠀⠘⠀⠑⠀⠀⠋⠂⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⡶⠀⠀⠀⠀⠀⠀⣴⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⠱⠊⠀⠄⠀⠀⠁⠖⠂⠀⠀⠀⠀⠀⢶⣄⣿⣿⠁⡾⠟⣴⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⣰⠖⠁⠀⠀⠀⠀⠀⠈⠀⠀⣰⣾⣿⡟⠉⣥⣠⣶⠃⠻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣀⣴⣞⠀⠀⠀⠀⡔⠃⠈⠋⠠⣵⠞⠩⢿⣧⣤⣙⠛⣡⣤⣶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠣⠀⠅⠀⠡⠀⠀⢀⡀⡆⠀⣠⣄⣤⣍⠁⣀⠉⢷⣼⣧⡶⢖⡀⢤⡦⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠛⠆⠀⠀⠀⠀⢀⠸⠷⠀⠀⣠⣿⣿⣿⡟⢈⡑⢢⠘⣫⠋⣁⣀⠈⠉⠛⠓⠙⢡⡞⠁⠮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠀⣄⠀⠀⠀⠀⠳⡟⠀⠀⠘⠿⣿⠿⠯⠠⡀⠌⢀⣰⡷⠀⠀⠁⠀⠀⠆⠀⣂⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣛⠺⢶⡆⠀⣤⠘⢅⡀⠀⡘⢡⡄⠓⠀⠘⡀⠉⠍⠀⢀⠔⠖⢸⡄⠀⡀⠉⣠⣠⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡋⢉⣤⡾⠃⠲⣏⠃⣸⢟⣄⡀⠄⠀⠈⠆⠘⠅⢀⡤⠀⠨⠀⣾⣿⣇⠄⠀⠐⢋⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⠡⡎⠀⠀⡋⢭⠍⠺⠃⠀⢄⠘⢂⡽⣶⣦⣄⠀⢸⣧⠀⠀⣌⠻⠿⠃⠁⠀⣀⣈⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢰⡾⠀⣘⠃⠀⢠⡀⠐⠂⠈⠒⢺⣿⣿⣿⣾⡇⠀⠻⡆⠤⣽⠏⠁⠔⠀⢀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠃⡁⠀⠂⠀⠈⠳⢿⡟⠛⠁⠀⠀⠙⠗⠂⠀⠀⢀⠀⠠⡄⠀⢠⣆⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢶⣎⠀⠀⠀⠈⢰⡀⠄⠀⠀⠀⠀⠀⢀⠀⢊⡰⢛⠃⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠟⠀⠀⠀⠀⠉⡐⠀⠄⢠⣤⣀⠖⠼⠁⠉⠀⢨⠉⠀⠀⠔⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣃⠰⠀⢀⣀⠀⠦⠨⠄⠀⢀⠀⠀⡀⠀⠀⣶⠞⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠶⠄⢈⣩⢻⠀⠀⠀⢻⡄⠉⢠⢙⢀⡂⠁⠀⠁⠀⠘⠣⢉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠐⠉⠀⠀⡤⠋⠀⣤⠐⣆⡁⠀⠀⠀⠘⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠜⣣⡄⠀⠙⠆
⠘⠀⠘⠂⠐⠊⠀⠊⠀⠃⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⠃⠀⠛⠀⠛⠀⠀⠀⠛⠀⠙⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢀⢠⣰⠶⢖⠐⢯⢢⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⡿⡣⠢⠄⣏⣱⢺⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠼⠀⠄⢀⣾⣸⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣁⡄⢀⡄⠀⠀⠀⠀⠀⠀⡇⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠐⠀⠀⠋⠈⡾⠈⢳⠀⠀⠀⠀⠀⠀⠀⠤⠤⢀⠴⠖⠚⠲⡆⠀⠀⠀⠀⠀⢠⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⣷⠀⠸⡆⠀⠀⠀⠀⠀⠀⢃⡖⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⡤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⣀⣼⠃⠀⠀⠀⠀⠀⢄⡴⠀⢉⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡚⠅⠀⠈⠈⠀⣶⡀⢱⢰⣝⣟⣹⣾⠉⠀⠀⠀⠀⣀⠤⢄⣄⡠⢖⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣼⣷⣢⢰⡆⡰⠀⣿⠀⠈⠀⡠⣬⣁⠍⠀⠀⠀⣠⡎⣼⡷⠰⢟⣴⣛⡢⢎⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠐⠃⠈⠻⢷⣬⣜⣿⣆⠀⣦⠄⢅⠐⠘⠂⢠⣾⣿⠑⠏⠛⡦⠘⣹⠦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠊⠀⢀⢀⣀⡀⠀⠘⠁⢿⣿⣿⠀⡇⠐⡀⠅⢁⡶⠟⠋⠹⣤⣯⠀⠥⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠠⠔⢆⠀⠁⠐⠀⠀⠀⠉⢣⠀⠀⡀⢀⣼⢻⠉⠉⣀⣫⣶⣶⠞⢉⢁⡠⢅⡀⠅⠀⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠠⣠⠂⠀⢠⣾⡇⢄⠨⠿⡃⣼⣿⣷⢯⡿⠍⢫⠔⠚⡰⣗⡦⠀⣤⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⣰⠀⠀⢸⡄⠐⣶⠾⠛⠟⠻⠯⢇⠀⠠⠰⢦⣄⢻⡽⢮⠒⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⡰⠋⠀⣠⣿⢐⡄⣿⠠⢀⡞⠻⡄⠠⠀⠀⠘⠦⠊⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⣰⣟⡿⢿⠀⠁⢀⠜⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣸⢡⡇⠃⠘⠟⠀⠊⠛
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣴⡇⢀⣯⠟⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠀⣘⠕⠠⢀⠈⢠⠂⡘⣸⠀⢸⣅
⠀⠀⠀⠀⠀⢸⠓⠈⠉⠲⡄⠌⣾⡿⡟⢀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⠙⣳⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡇⠀⠘⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢻⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⣼⣥⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣡⣏⣾⣥⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⢋⠏⢁⡼⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡯⠖⣦⠔⠉⡠⠞⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣿⠁⢰⣃⠔⠊⢀⣠⣾⠟⠁
⠀⠀⠐⣿⣿⣗⢶⣶⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡞⠀⢀⣴⣿⣟⣥⣴⣶⣤⣄
⠀⠀⠀⠈⠻⣦⣿⠧⣽⡿⠛⢿⣷⣦⣀⠢⠀⠀⠀⠀⠀⠀⢸⠀⡰⢀⣴⣿⡿⠛⣁⠤⠊⢉⡻⢿⣧
⠀⠀⠀⠀⠀⠈⠻⢿⣯⡉⠙⢻⣄⡉⠛⠻⢷⣤⣀⠀⢀⣀⣿⣠⣷⠿⡫⠾⠶⠭⠴⣂⣉⠠⠄⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣍⣀⠀⠭⠓⠒⠀⠤⠭⢿⣾⣿⣿⣯⣴⣫⡤⠤⠤⣤⡒⠉⠑⠢⢤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣤⣤⣴⣶⡿⠿⣋⠝⣿⣿⣿⣒⠤⢄⣀⠀⠈⠉⠒⢤⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠛⡻⢖⠉⠀⡌⢸⢻⢻⣖⠱⢦⣀⠉⠑⠒⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣀⠞⣄⣸⠀⠈⡆⢣⢿⣦⠀⠈⠉⠒⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣍⠣⠱⡀⠡⠀⢿⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠾⣦⣶⡾

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣶⡏⠀⠀⠀⠀⢹⣶⣶⣶⣶⡏⠀⠀⠀⠀⢸⣶⣶⣶⣾⣿⠀⠀⠀⠀⠈⣷⣶⣶⣾⣿⣟⠀⠀⠀⠁⠹⢹⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿
⠉⠛⠛⢳⣶⣶⣶⣦⣤⡜⠛⠛⠿⠿⠿⢇⣀⣀⣀⣀⡸⠿⠛⠛⠻⢇⣀⣀⣀⣀⡸⠿⠛⠛⠻⢿⣀⣀⣀⣀⣠⠿⠿⠿⠛⠛⣧⣤⣶⣶⣶⣶⡞⠛⠛
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣤⣤⣤⡼⠛⠛⠛⠛⠛⢿⣄⣀⣀⣀⣠⡜⠛⠛⠛⠛⢣⣄⣀⣀⣠⡜⠛⠛⠛⠛⢣⣤⣀⣀⣠⣼⠛⠛⠛⠛⠻⣤⣀⣀⣀⣠⡟⠛⠛⠛⠛⠛⣤⣤⣤
⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿
⠿⠿⠿⢧⣀⣀⣀⣀⣀⣸⠿⠿⠿⠿⠿⢇⣀⠀⣀⣀⡸⠿⠿⠿⠿⢇⣀⣀⣀⣀⡸⠿⠿⠿⠿⢟⣀⡀⠀⢀⣀⠿⠿⠿⠿⠿⣇⣀⣀⣀⣀⣀⠿⠿⠿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀
⣀⣀⣠⡼⠿⠿⠿⠿⠿⣇⣀⣀⣀⣀⣀⡼⠿⠿⠿⠿⢇⡀⠀⠀⢀⡸⠿⠿⠿⠿⢇⡀⠀⠀⢀⡸⠿⠿⠿⠿⠿⣀⣀⣀⣀⣀⡸⠿⠿⠿⠿⠿⢧⣀⣀
⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣇⣀⣀⣀⣀⣠⡿⠿⠿⠛⠛⠻⣧⣄⣀⣀⣤⡜⠛⠛⠛⠛⢧⣄⣀⣀⣠⡼⠛⠛⠛⠛⢿⣤⣀⣀⣠⣤⠟⠛⠛⠿⠿⢯⣄⣀⣀⣀⣀⣸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠔⠒⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣠⠀⠀⠉⢛⡀⠀⠚⠶⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠰⣂⠫⣀⠀⠸⠢⠁⡄⠀⠀⠀⠀⡀⠀⠙⠋⠀⠀⣶⢯⣤⡤⠤⡀⠈⣤
⠀⠀⠀⠀⠀⠀⠰⢇⢪⡏⠀⣀⡄⠾⠛⡯⢱⠀⡸⢀⠀⠀⠀⠀⠙⣿⣦⣄⡾⠀⢀⢴⡎⠁⠳⣔⠏⢠⠸
⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⣦⡌⣆⠳⠔⣡⡎⠀⠁⢀⠻⠀⠀⠀⢀⠈⢡⣾⠇⢰⣿⡀⠓⢀⢀⣼⠃⠸⠇⣠⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡈⠦⠙⢃⠤⠼⠭⠐⠋⠀⣠⣎⠄⠀⠀⢀⡴⠞⠋⢝⢌⡐⠻⠳⠒⣻⠗⠁⢀⣔⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠈⠉⠑⠠⡄⠹⣦⡀⡠⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠍⠢⠛⠉⠁⠐⠀⠀⠨⠁
⠀⠀⠀⠈⠷⣄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣤⣈⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⠀⡦⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢐⣠⡍⠁⠚⠉⠁
⠀⠀⠀⠚⠋⠁⠘⠛⢂⡠⠌⠙⠛⠆⠀⠀⠀⠃⠯⠊⠛⠛⠛⠚⠛⡟⠛⠁⠀⠀⣰⡟⠁⠀⠉⣉⣻⣾⠀⡀⠤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⣶⣯⣤⡖⠶⣤⡀⠀⠀⠀⠀⢠⢖⣅⢔⣀⡄⣀⡀⠀⠀⠀⠀⡍⠀⣠⣞⡑⡟⠓⣒⡦⣌⠃⠹⣾⣄
⠀⠀⠀⠀⣠⠊⠂⣡⣞⠉⠑⠮⣛⠀⣦⠀⠀⠀⠀⠘⠣⣜⡁⠋⠃⠋⠀⠀⠀⠀⢿⢰⠈⢋⡞⠁⠀⠨⠃⣹⣿⠀⡞⡳⡀
⠀⠀⠀⢸⣿⠀⣴⡆⠙⠀⡀⢠⡿⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠸⡇⠈⠻⣶⣰⣦⡶⠼⠟⢊⡴⡱⠁
⠀⠀⠀⠈⣏⠂⠘⣿⠤⠶⣻⠏⠀⠀⠀⠀⢀⠄⡀⠘⠣⠄⠀⠄⠀⠀⢀⣀⠀⠀⠙⠦⢰⣦⢀⠀⠉⠓⠶⠶⢖⠞⠰⠁
⠀⠀⠀⠈⠛⠕⡒⢄⠶⠚⠁⠀⠀⠀⠀⠐⢀⡘⠋⣀⣠⠂⣄⠀⠁⠻⠋⠀⠀⠀⠀⠀⠙⠉⢀⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡰⢄⠈⠆⢸⢹⠛⡯⣀⠀⠻⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣿⣷⡤⠀⢀⣤⠛
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⣤⠴⣧⣠⠀⠀⠼⠌⡒⢪⠝⣠⠀⣇⠜⠃⡀⠀⠀⠀⠀⣠⡴⠶⠙⣿⢀⣴⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠐⠹⣂⠞⢃⡴⠁⢰⣿⠁⠀⠀⠀⠐⠉⠀⠀⠀⢈⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠀⠀⠀⠀⠀⠀⠁⠐⠚⢃⠀⠐⠒⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂

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

⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣦⣤⡀
⠀⠀⠀⠀⠀⣠⡤⠞⢻⠃⠀⠀⠀⠀⠀⠀⠀⢰⣏⠳⣍⡽⣿⠀⠀⠀⠀⠀⠀⠀⣠⠚⡔⠿⠷⣨⠓⣦⠀⠀⠀⠀⠀⣰⣇⣸⣮⣁⣩⣿⠷⡶
⠀⠀⠀⠀⣜⡜⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⢨⠏⠀⠀⢳⠘⡄⠀⠀⠀⠀⠀⠀⠷⣤⡙⠶⣩⠕⠚⠁⠀⠀⠀⠀⠀⢹⠀⠙⠺⢤⣺⠏⠀⡇
⠀⠀⠀⠀⠘⠦⣄⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣘⡼⠁⠀⠀⠀⠀⠀⠀⠀⠳⣕⠀⠁⣀⡼⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⠀⠙⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣠⠤⠒⢐⣒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢤⠒⢲⡀⠀⠀⠀⠀⠀⣠⢴⣯⣭⣍⠓⠲⡄⠀⠀⠀⠀⠀⠀⢀⡴⠦⣖⣓⢦
⠀⠀⢸⣅⠀⢺⠟⠛⣷⡈⢧⠀⠀⠀⠀⠀⠀⣜⣥⡞⣩⠿⡇⣼⢩⡇⠀⠀⢀⡞⠱⣏⣶⠖⡟⢯⠑⣷⣄⠀⠀⠀⢀⡞⠉⡤⣞⠯⠏⣬⡓⣆
⠀⠀⢸⡈⢧⡈⢓⣖⣋⠗⢀⣧⠀⠀⠀⢠⠊⢺⣤⣵⣤⣤⠿⡻⢸⠁⠀⠀⠘⢦⠘⣍⠫⣝⠿⣫⣢⠏⣸⠆⠀⠀⠈⢧⢧⠹⠈⠥⣄⢋⣇⣸
⠀⠀⠀⠑⢤⠙⠀⠀⣉⡽⠋⠀⠀⠀⠀⠈⠙⢦⣐⠤⡤⠶⣚⡵⠋⠀⠀⠀⠀⠈⠹⣌⠑⠶⠚⢉⣇⠞⠁⠀⠀⠀⠀⠀⢯⠓⠚⢛⡋⢈⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⣠⠤⢤⣔⠒⠲⡄⠀⠀⠀⠀⠀⠀⣠⠤⣴⣒⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⠔⠒⣦⣄
⠀⠀⠀⣰⢃⡴⣯⠬⣝⢳⡗⢄⠀⠀⠀⠀⡴⠃⡼⣿⣻⠝⡎⠹⡄⠀⠀⠀⢀⡴⠋⣹⣷⡾⢿⣺⣟⡙⡆⠀⠀⠀⢀⡞⡱⣚⣾⡫⡉⣿⠳⣄
⠀⠀⣾⠀⡿⣌⣧⡼⢎⣿⠇⢸⠄⠀⠀⢰⡇⠀⡀⠈⠁⠴⠻⡄⣻⠀⠀⠀⠀⠳⣸⡟⡏⠓⠒⣺⢿⠇⢹⠀⠀⠀⡼⡷⠉⡧⣤⣨⠟⣮⢳⣈⡇
⠀⠀⠹⣄⣻⠮⠿⣛⣫⠾⡶⠋⠀⠀⠀⠸⡟⠲⣌⠓⠒⢂⡠⠃⣸⠃⠀⠀⠀⠸⡍⠓⠬⠲⡍⠒⠋⢛⡏⠀⠀⠀⠙⢿⢦⡙⢶⣶⠚⢁⡾⣿
⠀⠀⠀⠈⠉⠳⣄⣀⣤⠞⠁⠀⠀⠀⠀⠀⠙⠶⠬⠿⠿⣉⡤⠖⠃⠀⠀⠀⠀⠀⠙⠦⠤⠖⠳⠤⠞⠉⠀⠀⠀⠀⠀⠘⣦⣭⣭⠽⠯⠭⣥⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⢀⣤⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠹⠄⠀⠈⠙⠀⠉⢻⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡠⠴⠉⠑⡆⠀⣤⠀⠀⠠⠛⠉⢳⡄⠀⠀⠀⠀⠀⢸⣄⠀⡀⠉⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⣌⠑⠆⠠⠴⠃⠀⠈⢷⣄⡀⠀⠀⠈⡧⠀⠀⣾⣦⣴⣦⠈⠉⠈⢦⣀⡤⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⣀⡰⡁⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⢸⡏⡼⠏⠘⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⣠⡄⠰⠚⠲⢤⡀⠀⠀⠈⣴⠀⢀⡴⠋⠛⣦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⢰⠃⠀⠀⡀⠀⠀⠙⠲⣄⠀⠘⠶⠉⠀⠀⢀⡟⠀⣰⠟⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⢄⡠⠂⠀⢸⡇⠀⡼⠀⠀⠀⠷⠀⠀⠀⠀⢈⣀⠀⠀⠀⠀⠀⠉⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⣷⠀⠐⠛⡄⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⡽⢆⠀⠀⠀⠀⣾⠏⠀⠀⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡅⠀⠀⠀⢠⡀⣠⠇⠀⠀⢀⡄⠀⣤⠀⠀⠀⠀⣼⠃⠸⣿⣇⠀⠀⠀⢹⡀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠚⠀⠀⠉⠁⠂⢀⣀⡞⠀⠙⠀⠀⠀⠀⠘⣷⡐⠢⠿⠿⣿⠖⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠈⠀⠀⠈⠁⠁⠀⠀⢀⡀⠀⢠⣊⣀⣤⣬⣝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⣇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠚⠹⡄⠈⠉⠋⠁⠀⠀⠀⠀⢠⣄⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣭⣿⢻⡆⠀⠈⠓⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⢀⡏⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⡺⠈⣿⣤⠀⠀⠀⠀⠀⣠⡶⠀⠀⠈⠳⡄⠀⢠⡷⠤⠀⠀⣠⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠈⢻⣆⠀⠀⠀⠀⠈⠉⠲⠦⡀⠀⠀⠀⠀⠀⠀⠒⢺⣿⠁⠀⠀⢀⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⠐⠒⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠏⠀⠀⠀⠀⠒⠚⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣇⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⠀⣹⣿⣿⣿⣯⡟⢟⣿
⠀⠀⠀⠀⠀⠀⢠⡄⢈⡁⢉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⣿⠟⡿⢛⠛⠛⡍⠀⠀⠀⣿⣿⣾⣿⡛⠀⣴⣿
⠀⠀⠀⠀⠀⠀⣿⣶⠿⠷⠾⠿⣿⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣽⣛⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⢠⣑⡀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣴⣶⣤⣠⣴⣶⣦⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⠈⢹⠛⣿⣿⣿
⠀⠀⠀⠀⢀⣼⣿⡟⠀⠀⠀⠀⠀⠀⣿⣽⠷⠒⢲⣾⡿⢿⡏⠉⠉⠁⠙⠻⣿⣿⣿⣿⠟⠁⠈⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⣿⠀⠈⠉⠀⢹⣿
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢀⠠⡇⠀⠀⠀⡯⣀⣬⠁⢀⠀⠀⠗⠔⣿⣿⣿⣿⠀⠀⠀⠀⣰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠸⡇⣨⢋⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢼⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡅⠀⠀⠀⣿⣿⣿⣥⣀⣀⣀⣤⣿⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣾⣿⡇
⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⢀⣴⣼⡇⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⢠⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢿⣿⣷⡄
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⡿⢿⣷⠀⠀⠀⠀⠀⣛⣿⣧⣤⣤⣤⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⢈⣿⣿⠀⠀⠀⠀⠀⢰⡏⠀⠀⢀⣿⠡⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢣⣼⠿⠀⠀⠀⠀⢀⢐⢻⣿⣿⣿⣿⣿⡟⢧⠀⠀⠀⢀⡟⠙⠃⠽⠟⠁⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠙⠒⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠘⠀⢹⣿⣿⣿⢹⡇⠘⣇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣾⢼⡇⢸⡇⠀⠘⢧⣰⠏⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠿⣼⡇⣸⠃⠀⠀⢈⡿⣦⡀⠀⠀⠀⠀⣀⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⢸⣿⣷⣿⠀⠀⠀⡾⠁⠈⠙⠒⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢰⣿⣿⣿⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠋⢀⡄⣀⣠⣿⣯⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣀⣀⡠⠴⢚⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣡⡄⠀⠀⠀⠀⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⢠⣿⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠆⠀⠀⠀⣾⡿⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠹⠀⠀⠀⠀⠳⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠛⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿

⠀⣀⠤⠼⠏⠒⠤⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠔⢐⣀⠂⠀⠀⠒⠂⢈⡤⢉⡀⠀⠈⠄
⠎⠁⠀⠀⠀⠀⠀⠈⠉⠛⠁⠀⠀⠀⠀⠁⠀⠂⠀⠀⠠⠀⢀⠋⠉⠀⠀⠀⠀⠀⠀⠙⢣⡀⠁⣁⠀⠀⡀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠠⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⡀
⠁⢄⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠂
⠀⣠⠀⠢⠂⠤⠤⠤⠴⠒⠁⠁⡀⣀⣀⠀⢀⠀⠄⠀⣀⠀⢐⠀⠀⠀⣀⠀⠀⠀⠄⠀⠀⠈⠑⠠⠀⠀⠀⠈
⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠈⡄⠀⠄⠲⠀⣉⡀⠘⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⡼⠀⣀⠀⠀⠉⠐⠢
⠀⠀⠀⠀⢀⠒⠀⠀⠀⠀⠀⠀⠘⠠⠅⠀⠉⠄⢼⠀⠀⠐⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠑⠀⡈⠀⠀⠠⠄
⠣⡄⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⢂⠀⠘⠂⢠⠁⠌⠀⢀⠀⠀⠆⠀⠒⠀⢈⠄⣤⠀⠀⡐⠀⠀⠁⠐⠄⡄⢀
⠀⠀⡟⠀⣠⠕⣄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐⠀⠀⠀⠀⡇⠀⠁⠈⠀⠈⠀⠀⠀⠂⠤⡄⠀⠠⠄⠀⢰
⢠⠔⢧⠀⠀⡶⠀⢤⢀⠀⠂⠀⠀⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠁⠠⠀⡄
⠀⠀⠸⣄⠀⠖⠀⠸⡄⠀⠀⠀⠀⠈⠲⢤⢰⣤⡄⠀⠀⠀⢀⣤⡄⣠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⡄⠈⠁
⠀⠀⠀⠜⠲⢆⣄⠤⠓⠶⣦⣸⢁⠤⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡷⠀⠠⠀⠀⠀⠀⠀⠟⠃⠁
⠁⣢⠘⠀⠀⠀⠸⡄⠀⠀⠈⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢻⡵⠈⡂⠀⠀⠀⠀⣀⠙⠀⠂
⡎⠁⠣⣀⠀⠀⢀⠨⡦⢠⡄⠅⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠠⠾⠀⠀⡸⠲⢀⠀⠀⠀⣀⡀⠠
⠁⠀⠀⢈⣍⠁⠀⠀⠘⡇⠀⠂⠀⠘⢢⢳⡄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢶⡟⢠⡇⠰⠊⠀⠀⠈⠚⠲⠺⡁
⡀⠀⠀⢨⠉⢠⠀⠀⠀⡇⠀⠀⠂⠀⠀⡼⣧⠑⠄⠀⠀⠀⠀⠀⠂⠀⠘⠁⠐⠁⠀⠆⠀⠀⠀⠀⠀⠀⠐
⠣⣄⠀⠀⢘⠁⠀⢀⡴⠁⠀⠀⠄⠀⠀⠀⣿⠺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⢀⣈⢟⡒⠜⠂⠒⠋⠀⠲⣄⠀⠀⠀⠀⡀⢛⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠔⠃⠤⠤
⠁⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠀⠀⠀⠀⠀⠠⠲⠉⢡⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠨⠖⢀⠎⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⢰⡇
⠀⠀⠀⠀⠀⡐⠁⡐⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⡠⠴⠤⠄⣜⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢣⣄
⠀⠀⠀⠀⠉⠠⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠈⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘
⠀⠀⠁⠠⠄⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠘⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠁⠀⠀⠀⠀⠀⠀⡔
⠐⣾⣷⠀⠀⠰⠇⠀⠀⠀⠀⠰⢠⡀⠀⡆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠈⠁⠀⢠⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀
⢲⠒⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣘⣀⣁⣀⣀⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢦⣼⠀⡌⣿⣿⡆⢻⡰⣴⣃⡶⠋⠹⢲⡼⠀⢠⡸⠀⠀⢸⡄⢴⠥⣰⣷⡞⢻⡈⢸⣿⣿⣧⢸⣿⣀⢼⢿
⣛⣿⣇⡿⣿⣿⣷⠋⣷⠋⢸⠀⣥⠟⡼⠓⠂⢩⡤⣰⠀⠈⢷⡘⠮⢼⡞⣷⠀⢻⣾⣿⣿⣿⣾⣿⣸⣽⣿
⠘⢧⣸⣧⣿⣿⣿⣼⠉⣧⡯⣂⡴⠚⠁⠀⢐⠘⠆⣬⡳⢦⡈⢷⡤⣉⣿⡜⣄⡄⠹⣿⣿⣿⣿⣿⢉⣿⣿
⡦⣹⡟⠈⣿⣿⣿⣇⣾⣿⡞⠉⠀⢬⠌⣠⠀⠤⠄⠰⠭⠵⢿⣿⣷⣌⣐⠿⣎⠻⣄⣿⣿⣿⣿⣿⣼⣿⡷
⣷⣼⣷⣞⣿⣿⣿⠞⢡⡿⢀⣤⣉⣤⣞⠚⠯⠀⠀⠉⠊⠀⠀⠀⠉⠻⢾⣝⠾⣿⡟⣿⣿⣿⣿⣿⣿⣯⣏
⠸⣏⣿⣿⣿⣿⣿⢸⡿⣷⣩⣠⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣷⣿⣿⣿⣿⣿⣿⣦⣾
⠀⢹⣏⣸⣿⣿⣿⣿⣋⡽⠯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⢹
⢀⡾⠙⣿⣿⣿⣿⣏⠿⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⢸
⣼⠁⢰⣿⣿⣿⣿⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⡇⢸
⣏⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡜⣿⣿⣿⣿⣿⣧⢠
⣿⡟⢰⣿⣿⣿⣿⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠤⢻⣿⣿⣿⣿⣿⣿
⣿⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣻⣿⣿⣿⣿⣿⡏
⣿⣇⢸⣿⣿⣿⣿⣧⡀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡇⠉⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣾⣿⣿⣿⣿⣿⡘⣌⠂⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡇⣴⣿⣿⣿⣿⣿⣿⣇
⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⡿⣝⡞⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢰⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡃⢸⡷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢹⣸⣿⣿⣿⣿⢿⣿⣿⡏⣿⣿
⢋⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⡕⠀⠀⡀⢀⣀⣀⣠⣤⣤⡤⣶⣷⣿⣿⡟⢻⣿⣿⣆⣿⣿⣧⢻⣿
⣾⠃⣸⣾⢻⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣦⣴⡷⠛⢋⣭⢿⣉⣴⢿⣿⣿⣿⡿⣠⣾⣧⢻⣇⠟⣿⣞⣷⣻
⡟⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⣷⡟⢣⣾⣱⣷⣟⣿⣿⣿⢇⣿⣿⣿⣾⣿⣷⣻⣿⡟⣿
⣷⠀⣿⡟⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣿⣷⣿⣿⣿⣿⡏⣽⣿⣿⠸⣿⣿⣿⢣⣿⢹⣿⣿⣿⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡤⢦⣤⠞⠲⡴⠛⢲⡴⠛⢦⡤⢦⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡞⠉⠹⡁⠀⢹⠀⠀⠇⠀⢸⠀⠀⢸⠀⠀⡝⠉⠹⡤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠺⡁⠀⠘⡀⠀⢡⠀⠐⠂⠀⢀⠀⢸⠀⠀⡇⠀⠰⠀⠀⡜⠀⢀⡿⠒⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⠻⣄⠀⠘⢄⠀⠹⡀⠀⠆⠀⢁⠀⣸⣀⣈⡀⣀⠁⢠⠃⠀⡘⠀⢀⠎⠀⢀⠜⠛⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢴⠛⠛⢄⠀⠈⠢⡀⠈⢂⠀⣡⠤⠚⠂⠉⠁⠀⠀⠀⠀⠈⠉⠙⠒⠶⣀⡠⠂⠀⡰⠋⠀⣠⠞⠛⢲
⠀⠀⠀⠀⠀⢠⠖⠛⠦⡀⠀⠑⢦⡀⠘⣤⠔⠋⠀⠀⣀⠤⠔⠒⠒⠒⠒⠐⠒⠢⠤⣀⠀⠀⠉⠢⣎⠀⡠⠚⠁⢀⡠⠚⠓⣦
⠀⠀⠀⠀⣠⠼⠧⣄⠀⠈⠓⢄⡀⢁⠞⠁⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠈⠻⣄⡀⠔⠉⠀⣀⡤⠷⢤
⠀⠀⠀⢀⣹⣄⠀⠀⠉⠒⠄⡀⡸⠁⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠈⢢⡠⠔⠊⠀⠀⣀⣼⡀
⠀⠀⠀⢻⡀⠀⠉⠑⠂⠄⠀⡜⠁⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢣⡠⠄⠒⠉⠀⠀⣸
⠀⠀⢰⠋⠉⠁⠒⠂⠤⠄⣸⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⠄⠒⠊⠉⠙⣦
⠀⠀⣠⠗⠲⠤⠄⠀⠤⢀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⡄⠄⠠⠤⠤⠲⢧
⠀⠀⠹⣄⣀⣀⣀⣀⣀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⣀⣀⡜⠁
⠀⠀⢾⡀⠀⠀⢀⣀⠀⠠⡆⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣀⣀⠀⠀⠀⣹⠆
⠀⠀⢠⠟⠉⠁⠀⠀⠀⣀⣧⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠉⠙⣇
⠀⠀⠈⢳⠶⠒⠂⠉⠁⢀⠸⡄⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠉⠐⠒⠲⢶⠋
⠀⠀⠀⠻⣄⡠⠤⠒⠉⠀⢀⠰⡄⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡎⠀⠉⠐⠢⢄⣀⠼⠂
⠀⠀⠀⠀⢼⡀⢀⡠⠔⠊⠁⢀⠜⢆⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢇⠀⠉⠲⠤⣀⠀⣹
⠀⠀⠀⠀⠀⢸⡃⠀⢀⡤⠊⠁⢀⠔⠑⣄⠀⠀⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⡠⠞⢅⠀⠙⠢⣀⠀⠈⣏
⠀⠀⠀⠀⠀⠈⢙⡿⠁⠀⣠⠞⠁⢀⠔⠁⢙⠦⢄⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠊⠑⣄⠀⠑⢄⡀⠈⢹⠻⡅
⠀⠀⠀⠀⠀⣠⠏⡸⠒⢾⠁⠀⡰⠊⠀⡠⠁⢀⡎⠈⠱⠒⠤⠤⣀⢀⣀⡀⢤⠤⢲⠊⠙⡄⠀⢢⡀⠈⠢⡀⠀⢹⠖⠛⢆⠙⣄
⠀⠀⠀⠀⡴⠁⡜⠁⠀⠘⠓⢺⠀⢀⡜⠁⠀⡔⠀⢠⠁⠀⠆⠀⢸⠀⢰⠀⠀⡄⠀⢆⠀⠸⡄⠀⠱⡄⠀⢹⠒⠛⠀⠀⠀⠣⡈⢣⡀
⠀⠀⢀⡞⢀⠌⠀⠀⠀⠀⠀⠈⠉⠹⣄⢀⡜⠀⠀⠎⠀⢠⠃⠀⡀⠀⢸⠀⠀⢁⠀⠘⡄⠀⠹⣄⢀⡟⠉⠉⠀⠀⠀⠀⠀⠀⠱⡀⠱⡀
⠀⢀⡎⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠴⠺⣄⣀⣼⠀⢀⣇⠀⢘⡀⠀⣸⣄⣀⠖⠢⠞⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢹⡄
⠀⡼⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠝⠋⣨⠖⠻⣌⠛⠣⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⢣
⢠⠃⡘⠀⠀⠀⣀⣠⠤⠶⠒⠛⠛⡆⠀⠀⠀⠀⠀⠀⢀⠊⠀⡴⠁⠀⠀⠈⢧⡀⠑⡄⠀⠀⠀⠀⠀⠀⢠⡟⠛⠒⠶⠤⢄⣀⠀⠀⠀⢣⠈
⣘⣠⡤⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢠⠃⢀⠞⠀⠀⠀⠀⠀⠀⠳⡄⠈⢆⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⣄
⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢠⠃⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⢆⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢠⠇⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠘⡆⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⡎⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠒⠻⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠐⠚⢻⡿⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃


⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠚⢿⠟⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⣠⡀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠐⢺⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠀⠀⠀⠀⠀⠀⠺⣿⡿⠂⠐⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⣰⡄⠘⠃⠀⠀⠀⠀⠀⠀⠄⢀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠤⢾⣿⣿⡶⠄⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠠⠴⢾⣷⠶⠤
⠀⠀⠀⠀⠀⠁⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠰⡦⠈⢻⡿⢁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠇


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⠂⡸⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠻⡝⠻⢧⣄⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀⡏⢠⡎⠹⡆⠀⠀⠋⠒⢤⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠡⡘⢷⣠⡇⡀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣼⠸⣿⡀⠀⠈⡢⣝⠛⠧⢀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠙⠷⠾⠮⣅⣉⡒⣤⣀⠁⠓⠺⢅⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣤⠞⠟⠓⣲⣦⣤⣄⡀⠈⠙⠺⣟⡲⣦⡂⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠁⠀⢀⣽⡿⠛⠉⠈⠹⣆⠀⠀⠀⠹⡄⠙⢦⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⣸⣟⠂⠀⠀⠀⢠⡿⠀⠀⠀⠀⡇⠈⠈⢷⣁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢠⡋⠉⠙⢻⠒⢤⣾⡟⠁⠀⠀⣠⠞⠀⢀⠀⢸⣿⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⢄⡈⢿⡻⠶⠃⠀⠃⢈⢿⠿⢷⣿⣅⡀⠀⠈⢀⣾⠇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠓⢦⢹⡿⢽⣶⣄⣀⠀⠈⠁⠀⠀⠀⠈⠉⠓⠶⢮⣈⡴⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠆⠙⣿⠁⠄⠈⠹⣿⣭⡒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢻⣦⡀⠀⠀⠻⣷⡙⢦⡉⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢤⣀⠀⠀⠀⠀⠀⢈⡄⠀⠈⡆⠉⢳⠢⠄⡘⢷⡼⠟⠋⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢤⣝⢦⠈⠳⢤⣀⠀⠀⠀⢇⡀⠀⢱⣀⣨⠦⠖⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⡀⠀⠀⠈⠓⢄⣀⠼⠖⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡹⠶⠶⠚⠋⠉
⠀⠀⠀⠀⠀⢀⠴⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠄⠀⠀⠀⠀⠀⠀⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⡗⣊⣉⣦⢠⠤⠤⠤⠀⠛⠚⠉⠙⠛⠓⠒⠠⠤⠤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣭⣭⡵⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⠐⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠈⡿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⢳⠖⠀⠉⠛⠁⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣄⡀⠀⠀⠀⠀⣍⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢯⢿⡀⠿⣇⢟⡈⢿⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠞⠁⠀⠈⢛⠙⠋⡁⠀⠀⠀⠀⠀⠀⠨⠀⠀⠂⢀⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⠠⠀⡀⡆⢠⠀⠀⠀⠈⠀⠐⠋⢀⡠⡄⠀⠀⠀⠟⣁⡐⡑⠁⠐
⠀⠀⠀⠀⠀⠀⠀⢠⠀⢿⠄⠈⢀⠀⢺⣡⠋⡶⢸⢁⠂⠄⠀⠀⢛⣶⡶⠀⠻⠃⠀⠉⠋⠀⠐⠇
⠀⠀⠀⠀⠀⠀⣀⠛⢇⡺⡿⠃⡗⠄⢸⢋⣴⣤⡆⠺⠃⢈⡀⠀⠀⠀⠀⠀⣤⠀⡔⠁⠖⢠⡀
⠀⠀⠀⠀⠀⢠⡤⢶⣾⣡⠆⣻⣷⣾⠘⠟⠣⠶⠀⠀⠀⡀⠅⠀⡀⠀⠀⠀⢩⡴⠄⠄⠈⠌
⠀⠀⠀⠀⠀⠰⠙⣊⠸⣛⣿⣾⢾⣾⢢⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⡄⣜⠧⣻⡛
⠀⠀⠀⠀⠀⠀⠴⠿⢑⣮⣟⣵⣋⡉⠀⠀⢲⠀⢀⠀⢰⡄⠀⠀⠰⣼⢟⡟⡻⡧⢋⠴⠂
⠀⠀⠀⠀⠀⠀⢀⢷⠾⣿⠿⣿⣡⣙⠗⣶⠾⠂⠶⣽⡺⡸⠞⠁⠈⠽⢶⣮⠙⠥⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡟⠉⠁⠠⠸⣆⠀⠀⣈⣳⡅⠀⠀⠀⣠⠂⠀⠂⠐⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢀⣠⠴⠌⠓⠘⠄⠀⠀⠀⢹⠀⠀⠀⠄⠱⣶⠤⢿⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣟⡖⠄⢻⠀⠀⠠⣀⣷⠙⢦⢸⡇⠀⠤⠄⠀⠀⠀⠀⠈⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⢢⠈⠀⠀⠓⣾⠁⢀⡏⢾⡇⠀⠀⠀⠀⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠑⣤⣨⡒⣽⡄⠈⡧⠲⠿⠀⠈⠀⠀⠠⠄⠁⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠃⠀⠁⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⢀⠀⢀⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⢸⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠂⢸⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣠⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢋⡟⢻⢽⣶⡄⠀⠀⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⢰⠒⠊⡇⣰⡟⢧⡘⡴⠃⢹⣄⠀⠁⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠐⢯⣵⣼⠀⠀⣷⢳⠇⠀⠙⢷⡶⠟⠘⡇⠀⠀⠀⠃⠀⡀⠀⣠⠴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠋⠛⣏⠓⢦⣿⣖⠒⢒⣶⣿⣶⡖⢻⡅⠀⠀⣀⠀⠀⢿⡞⢹⡄⢹⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⣿⣠⣾⢯⣉⢱⡄⣏⠻⡍⠉⠉⠉⠉⢁⡜⢀⡠⠔⢹⡀⠀⣿⡇⣼⠃⣸⣷⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⣾⠀⣿⡇⢧⣾⠟⡟⢿⡟⠀⢹⠿⣯⣍⠉⠉⡰⠋⠀⠀⠈⡽⠀⣿⣿⣿⣾⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⢀⡟⠈⢣⣽⣧⣀⣹⡾⠷⢻⠃⣠⢯⠀⠈⣯⢻⣴⡇⢀⣼⠃⣸⢧⣠⠟⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣼⡀⠀⠈⠳⣤⣀⣀⣀⣠⣿⠞⠁⢸⡇⢀⣿⣼⡇⢳⣾⡷⣾⣵⣯⣤⣴⣤⡀
⠀⠀⠀⠀⠀⠠⡤⣤⣐⠒⢤⡀⢸⠀⠙⠶⢤⣀⣈⣻⡿⠟⠋⠁⠀⢀⡼⠀⣸⣭⣭⣿⠁⠒⠻⣥⣀⠙⠛⠉⠀⠙
⠀⠀⠀⠀⠀⠀⠑⠦⣬⣭⡱⢾⣘⣦⣀⠀⠀⠊⠉⠛⠛⠛⠒⢲⣶⣯⣥⣤⡟⠉⣧⠹⣤⠀⠢⣈⢿⢮⠀⢄
⠀⠀⠀⠀⠀⡠⠊⡩⠁⠀⣼⡟⠻⣶⣌⠙⠦⣄⠀⠀⠀⠀⣠⠞⢿⣿⣯⠀⠀⠐⢬⡳⡈⠻⠷⢬⡙⣮⢣⡀⠑⢄⢲⡄⠀⣠
⠀⠀⠀⠀⠀⢀⠎⢀⡼⠆⢿⣽⡀⢠⣽⠀⣦⣬⣿⣶⣶⣾⡿⢳⡀⠙⠿⠷⣤⣦⣀⣱⣇⠀⠀⠀⠈⢺⡇⠉⠒⠒⠋⠁⠉⠁
⠀⠀⠀⠠⠴⠧⠶⠟⠁⠀⠈⢧⡇⣸⢇⣴⡿⠋⣸⠁⠀⠙⡇⠘⢇⠀⠀⠀⠈⠀⠀⠉⠻⡆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⣡⣿⠋⠀⠀⢹⣦⠀⠀⢻⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡿⠁⠀⠀⠀⠀⠉⠻⢦⣸⡰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁

⠀⣤⣤⣤⢤⢀⣀
⠀⣿⣿⣻⣿⣶⣌⣙⣲⣤⣀
⠀⠙⣿⡟⢿⣿⡿⠿⣟⣿⣿⣷⣶⣄⡀
⠀⠀⢙⣿⣿⠿⣗⣀⣻⡏⠉⢉⣿⣿⣷⣄⢀⠀⠀⠀⠉⠂
⠀⠀⠀⢹⣿⣛⣿⡤⠜⠧⡀⢿⣿⠋⠉⣯⣳⣀
⠀⠀⠀⠈⢻⣟⣻⣷⡊⠈⣉⣒⣤⡀⢾⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄
⠀⠀⠀⠀⠨⣫⣭⣽⣯⣀⠀⣀⣹⣿⣷⣮⢅⡀⢻⣷⡀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠘⣷⠶⢾⡤⠀⠀⠠⠿⠿⢷⣄⣉⣳⣿⣧⣠⡞⣿⡿⠂⠀⠀⢀⣀⣠⣤⣤⣤⣀⣴⡴⠤⠤⢀⣀
⠀⠀⠀⠀⣠⡿⢻⣋⣉⣽⠖⠒⠉⠉⠉⠁⠐⠚⣭⣿⣿⣿⣿⣿⣷⣶⣟⡛⠋⠛⠉⣹⣿⡟⠓⣾⣯⠭⣝⡛⠶⣬⣻⡦⣤⡀
⠀⠀⠀⠀⢺⡿⢻⣧⠀⢇⠀⠀⠀⠀⣀⡴⠒⠉⢉⣽⡿⢽⣿⣿⡛⠿⣍⠉⠛⢀⣶⣿⣟⡁⢰⣿⠃⠀⢈⣿⡙⢻⡿⣿⣭⣿⠦
⠀⠀⠀⠀⣿⡟⣛⣿⡔⠉⡙⠓⢒⡿⠃⠀⢀⡔⣡⣟⣿⡿⠛⢡⡀⠀⠠⡙⠲⣾⣿⣿⠛⠟⠙⠗⠒⢶⡛⢤⣽⠿⣟⠻⣯⣹⡷
⠀⠀⠀⠰⣿⣟⣫⣿⣷⣾⣇⣠⣏⡀⢀⣴⠟⣰⣿⣿⠟⣰⠁⠀⣇⠀⠀⠘⣷⢌⣻⣧⣵⣄⢀⣤⣴⣶⡿⣿⣻⣧⡽⠗⠛⠃
⠀⠀⠀⠀⣼⠿⠛⣍⣿⡿⣻⣿⣿⣿⣺⡎⢰⣿⡿⠋⡼⠃⠀⢀⡟⣦⡀⢀⡜⢦⣹⣾⡿⠿⣿⢽⣷⠾⡿⠛⠛
⠀⠀⠀⣸⡡⠀⠀⠫⠋⠙⣿⠈⠉⢭⠎⠀⠈⠁⠀⣼⣟⢷⡄⢸⠀⣘⠈⡀⣧⣼⢻⣿⠇
⠀⠀⡼⠟⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡏⠘⣋⣾⣷⣾⣀⣿⣶⡿⢷⣙⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⢻⣿⣿⣏⣿⢸⣯⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⡿⣧⣿⣿⣿⣿⡿⠿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⡟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃

⠀⠀⠀⠙⠻⠿⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢿⡇⠙⣿⡀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠘⣿⡀⢀⣤⢤⡀
⠀⠀⣴⡶⣤⡀⠀⢀⡴⠒⠳⣦⢸⣿⠻⣦⢀⡤⢤⡀⠀⠸⣿⡀⢸⣧⠀⠁⣼⠀⠀⢀⣶⢿⣦⠀⠀⠀⠀⠸⣿⡀⢸⣧⠈⠀⢀⡷
⠀⠀⣿⡄⠈⢿⠄⠋⠀⠀⣸⠇⠀⢿⡆⠛⠀⠀⠀⡿⠀⠀⠹⣷⡈⠋⠀⣠⡏⠀⠀⠈⣿⡀⠹⣧⠀⣤⠶⣄⠻⣷⡘⡿⠀⣠⡞⠁
⣀⠀⠘⣿⡄⠀⠀⠀⢀⡾⠋⠀⠀⠘⣿⡄⠀⢀⣼⠃⠀⠀⠀⠻⣷⣤⡴⠋⠀⠀⠀⠀⢻⣧⠀⠻⠀⠀⢠⡿⠀⠙⠷⠶⠞⠋⢀⣀
⢹⡇⠀⠘⢿⣆⢀⣴⡟⠁⠀⠀⠀⠀⠘⠿⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣾⡟⣷⡄⠊
⠟⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⣠⠶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⢀⣀⠀⠀⠀⠀⠀⠸⣷⡈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠹⣧⡘⠁⣸⠇⠀⣴⣶⣆⠀⠀⠀⣠⣤⡀⠀⠀⢠⣿⠛⣷⡀⠀⢀⣤⡀⠙⣿⣶⡿
⠀⠀⠀⣴⡿⠷⣦⡈⠁⣸⠇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠙⠀⣰⠏⠀⠀⣿⡇⢻⣆⠀⠚⠁⢠⡿⠀⠀⠈⣿⡄⢸⣧⠀⠁⣸⡇
⠀⠀⠀⣿⡇⠀⠈⠃⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣼⡏⠀⠀⠀⠸⣷⡀⠿⠀⢀⣴⠏⠀⠀⠀⠀⠹⣿⡄⢀⣠⡾⠋
⠀⠀⠀⠘⢿⣦⣀⣾⠏⠀⣴⡿⢿⡄⠀⠀⣀⡀⠀⠀⠈⠻⠏⠀⠀⠀⠀⠀⠹⣷⣄⣴⠟⠁⠀⠀⠀⠀⠀⠀⠘⢿⠟⠁
⠀⠀⣠⣦⠀⠉⠛⠁⠀⠐⣿⡀⠀⣿⡄⠊⠁⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢷
⣷⡈⠀⣿⠀⠀⠀⠀⠀⠀⢻⣧⠀⠘⠁⠀⢀⡼⠃⠀⣴⡿⢷⡄⠀⢀⣠⡀⠀⠀⠀⠀⢠⣾⠶⣦⡀⡴⠛⠻⣆⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠈⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⣠⡞⠁⠀⠀⢿⡇⠀⢻⡆⠋⠀⣿⠀⠀⠀⠀⢸⣷⠀⠘⠏⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⣄⣠⡿⠀⠀⠀⠀⣠⣤⣄⠀⠈⢻⣷⡾⠋⠀⠀⠀⠀⠘⣿⣄⠈⠁⢠⡾⠁⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⢠⡟⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠻
⠻⠟⠀⢠⡾⢷⡔⠁⠀⣽⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⣴⠟⠀⠀⠀⣠⢶⡆⠀⠈⢿⣦⣀⣴⡟⠀⠀⢰⡿⠋⠻⣦⢠⠞⠉⢹⡆
⠀⠀⠀⠘⣿⣄⠀⠀⣰⠏⠀⠀⣠⣶⣤⡀⢀⣠⣤⠀⠀⠀⠈⠛⠁⣴⡿⢷⡜⠁⢸⡇⠀⠀⠀⠙⠛⠋⠀⠀⠀⢸⣇⠀⠀⠿⠁⠀⢀⡾⠁
⠀⠀⠀⠀⠈⢻⣦⣼⠟⠀⠀⠀⣿⡇⠈⣷⡋⠀⡿⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⣠⣄⠉⠋⠀⠀⠀⠀⢿⣇⠀⠙⠁⣼⠃⠀⠀⠀⠀⠀⠀⠸⣷⡀⠈⣸⠏⠀⠀⠀⣠⣄⡀⠀⣤⢦⡄⠀⠹⣿⣤⣴⡾⠋
⠻⣦⣄⠈⠀⢸⡇⠀⢀⡀⠀⠀⠘⢿⣦⣠⡾⠃⠀⣠⣤⡀⠀⠀⣀⠀⠙⣿⣾⠟⠀⠀⠀⣼⡟⠙⣷⠈⠁⢠⡗⠀⠀⠈⠉⠉⠀⠀⠀⠀⢸
⡀⠈⠉⠀⣠⡟⠀⢰⣿⢿⣆⠀⠀⡀⠉⠉⠀⠀⢸⣿⠉⢻⡶⠋⣿⠀⠀⠈⠁⠀⠀⠀⠀⢸⣧⠀⠈⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣷⡄⠀⣰⠟⠀⠀⠈⣿⡄⢻⡆⠋⠙⣦⠀⠀⠀⠘⣿⡀⠈⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⣠⡾⠁
⠙⠿⠿⠏⠀⠀⠀⠀⠹⣷⡈⠁⠀⣠⠏⠀⠀⠀⠀⢻⣷⣤⡾⠃⠀⠀⠀⣠⣄⠀⢀⣀⠀⠀⠀⢻⣿⠟⠁⠀⠀⢠⣿⢿⡀⠀⡴⠚⢻⡆
⠀⠀⠀⠀⠀⣠⠶⣦⡀⠙⣿⣤⡾⠋⣶⣦⡀⠀⡀⠀⠉⠉⠀⠀⠀⠀⢸⣿⠹⡗⠉⠉⣷⠀⠀⠀⠁⠀⠀⠀⠀⠸⣿⢸⡇⠈⢀⣴⠏
⠀⣾⠛⠿⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢿⡏⡿⠈⠉⣷⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⢀⣴⡟⠁
⠀⢿⣆⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠘⣿⣄⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠋
⠀⠈⢻⣦⡀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡄

⠀⠀⠀⢀⣀⣤⣤⣄⣀⣤⣄⠀⢀⣀⣀⣀⣀⣀⣀⠀⢀⣤⣄⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⡄⠀⠀⢀⡀
⠀⠐⠛⢛⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠛⠓⠀⠀⢰⣿⣿⣿⣿⣿⣿⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠐⠋⠁⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠉⠓⠀⠀⠀⢸⣿⡿⠟⠛⢻⣿⣿⣿⣿⣿⡿⠟⠋⠁⠘⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣦⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣇⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠈⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⣿⣿⣷⣿⣿⡿⠷⠂⠀⠀⢀⣀⣿⣿⣿⣿⣿⡉⠉⠁⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣷⣀
⠀⠀⠀⠀⢀⡼⠟⠋⠁⠘⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠉⠙⠉⠉⠁⠀⠀⠀⠴⡾⠛⠛⠃⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠘⠛⠻⣶⠄

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠄⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⢀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢙⣿⣿⣒⣦⡄⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣧⡤⠄⠀⠀⠀⠀⠀⠙⢿⣶⣦⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⣶⣶⣶⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠐⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⡟⠻⠿⣿⣿⣿⣿⣿⣶⣿⣿⣾⣿⣯⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⠿⠿⠿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⠏⠉⠉⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣷⣀⣀⣀⣀⣀⣀⣀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣛⡻⠏⠉⠉⠉⠉⠀⠈⠉⠉⣽⣿⣿⣿⣟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⢰⠆⠳⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⠃⠀⠀⠀⠀⠀⢤⢰⠀⠀⠀⠀⠀⠀⠀⠂⡘
⠀⢀⡎⠠⠀⢸⡁⠀⠀⠀⠀⠀⣄⠀⠺⢢⠚⠃⢀⡄⠀⠀⠀⠲⠀⣀⣀⠐⠃⠀⠀⠀⠠⠴⠀⣀⠄⠀⠀⠤⠀⠒⠂⠀⠀⠀⠈⡟⢻⠀⢐
⠀⠀⢶⣶⠟⡇⡏⠀⠀⠀⠀⠀⠘⡗⣬⣿⡹⡄⡯⠁⠀⢀⣐⠀⠃⢴⣄⠘⡁⢂⡀⠀⣰⣦⠀⣤⠟⠀⠚⡴⠂⠈⠀⠀⠀⠑⢘⣓⣘⡣⠊
⠀⠀⠨⣐⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠗⠉⠀⠀⠀⠀⠀⠠⠧⣙⣁⠴⠑⠂⠀⠈⠘⠁⠀⠀⠉⣀⡘⠁⠀⠀⠀⢠⠀⠀⠀⠏⠹⠄⠀⠀⢀⡀
⠀⠀⠀⢿⡵⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠶⠁⠀⠀⠘⠖⠀⠀⠀⡀⠀⠀⠀⠀⢭⡥⠀⠀⠀⠀⣡⢣⠀⠀⢀⣀⠀⢠⠌⠙⠆
⠀⠀⠀⣘⢠⠀⠀⠀⢀⡷⢯⡀⠀⠀⠀⢀⢀⠀⠀⣀⠤⠄⡄⡀⠀⠸⠗⠀⠀⡀⠠⠀⡁⠠⠀⠀⠀⢰⡆⠀⢀⠀⡘⠔⢥⡏⠀⠨⠍⠀⢰⢚⠀⠈⠀⠀⡀
⠀⠀⠀⢸⡖⠀⠠⣁⠁⣷⣯⡇⠀⠤⠀⠘⢉⠀⠮⢰⡶⠳⣶⠹⡄⠀⡂⠀⠀⠀⠛⠀⡅⠘⠃⠀⠀⠈⣷⠒⠋⠀⠀⣄⣢⠀⠀⢀⣆⠀⠀⠙⠶⣀⡈⠟⠁
⠀⠀⠀⢰⢺⠀⢄⡅⢰⢾⠿⡇⠤⠄⠀⠸⠚⠀⣇⢹⣦⣤⣟⢁⠃⠈⠋⠀⠠⠀⣀⠈⠂⢀⣀⠈⠀⠀⢸⠀⠀⠀⠀⠰⠖⠀⠀⠘⡞⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⢬⡷⣾⠔⠡⠀⠀⢰⣠⠀⠀⠃⠠⡅⠄⠋⠀⠀⠀⠀⠀⠐⠁⠀⡀⠸⠁⠂⠀⠀⡟⠀⠀⠀⠀⠈⡏⠀⠀⢀⢦⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⣴⠄⠀⢐⣸⠀⠐⠀⠀⢠⠀⡀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠰⠇⠀⠀⠀⡏⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠅⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢐⠀⠀⠀⠘⠿⠀⠀⠀⠀⢘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠁⠀⠀⠀⠘⠦⠆⠀⠀⠀⠆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠠⡄⡄⠀⠀⠀⡁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠰⡆⠀⠀⢠⠉⠄⠀⠀⠀⠘
⠀⠀⠀⢸⢉⠀⠀⠀⠖⠐⢠⠁⠀⠀⠀⠀⠇⠁⠀⠀⠀⠆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠷⡆⠀⠀⠀⠀⡇⠀⠀⠀⠉⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢦⡆⠀⠀⠀⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢐⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠁⠀⠀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠴⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⠰⠀⢠⢠⠄⢄⠄⠀⠀⠀⠀⠀⠀⢠⢠⠄⠀⢀⠄
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠄⠰⠒⠚⠀⠀⠀⠀⠀⠞⠀⠐⠀⠰⠠⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠈⠀⠀⠑⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠠⡀⠀⠀⠃⠀⠀⠢⠀⠀⠦⠦⠄⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⠀⠀⠈⠁⠀⠊⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠄⠀⠀⠀⠀⠀⣀⣲⡄⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠔⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠟⠀⠀⢀⠀⢀⠀⠀⢀⠀⢠⠄⠀⠀⡀⠐⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠈⠉⠈⠉⠉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠐⠒⠀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠉⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠿⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⣿⡿⠿⠶⣄⡀⢀⣼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⡷⠀⠰⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠈⢹⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⢦⣄⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢁⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣴⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡛⠛⢯⣏⡁⠉⣹⡏⠉⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣦⣙⣿⡿⢼⣿⣠⣽⣌⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣮⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⣼⣿⣿⣿⣿⡛⡟⢋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⣿⣿⣿⣿⣿⡟⠉⠉⠙⠻⣿⣿⣿⣿⡇
⠀⠀⣸⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣶⣿⣿⣿⣿⣿⣿⣆⠈⠻⣿⣷⣈⠛⢦⣄⡀⢈⣿⣿⣿⣿⣧⡀
⠀⢀⣿⡿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡄⠀⠈⠻⣍⡳⢤⣈⠙⣿⣿⣿⣿⣿⣿⣷
⠀⢸⣿⠁⠙⢺⠟⠛⠛⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡄⠀⠁⠀⠙⠀⠀⠀⠈⠙⠶⣝⠷⣾⣿⣿⣿⣿⣿⣿⡇
⠀⢸⡏⠀⠀⣿⠀⠀⠀⡇⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠸⣇⠀⢀⢀⡀⡆⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠟⠋
⠀⠸⣧⣀⣀⣯⣀⣀⣠⣧⣄⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣿⣶⣿⣿⣿⣷
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠿⠛⠛⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣿⠃⢹⡄⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⢇⣾⠏⠀⠀⣇⠀⠀⣰⡿⠋⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⡇⣼⣋⠑⠤⡀⢻⣤⠾⠋⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡿⣹⢏⡭⢒⣦⢿⣛⠉⢂⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠿⠛⠻⣿⣿⣿⣀⣴⠟⢋⡥⠨⣄⠈⡆⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠿⠿⠛⢷⣄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣄⠀⢒⡂⢺⡄⣨⣠⡟⠁
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣠⣾⣿⣿⣿⣿⣿⣿⡿⣿⣷⣬⣍⣰⣤⣾⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠉⠈⢿⣿⣿⣿⣿⣿⡛⠛⢿⣿⡉⡆⠘⠈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣌⣻⣧⡔⠀⡅⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣮⣸⣛⣿⣷⣄⣀⣀⣘⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠏⠉⣻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⣿⣿⠿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⢿⣷⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣾⣷⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣼⣄⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣠⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣷⠤⠀⠀⠹⠉⠀⠀⠀⠀⢠⣿⣧⡀
⠀⠐⠒⠺⢿⣿⣿⣿⣿⡷⠶⠆⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠰⠶⠾⣿⣿⣿⣿⡶⠶⠆
⠀⠀⠀⠀⠀⠹⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠻⠋⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣀⠀⠀⠀⠀⠀⠀⠈⢿⡏
⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠉⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣇⠀⢘⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⣠⠀⠀⢠⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢈⠿⠿⠛
⠀⠀⠛⣿⠟⠀⠀⠹⠃⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀
⠀⠀⠀⠈⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⣷⣤⣤⡀
⠀⠀⠀⠀⠙⣿⠛⠁⠀⠀⠀⠐⢦⣠⣿⣧⣴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⡉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠈⢿⡏⠉⠓⠀⠀⣰⣿⣶⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠘⠻⠓⠠⢴⣿⣯⠄⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⠈⠛⠁⠀⠀⠀⢀⣀⣼⣧⣀⡉⠀⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠂⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⢡⣤⣾⣧⣤⠄⠀⢤⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⠦
⠀⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⢹⡿⣿⡇⠀⠀⠀⠀⠀⠉⠉⣿⣿⠏⠉
⠀⠐⠒⠒⠿⠿⠿⣿⣿⠿⠿⠶⠖⠒⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣤⠀⠀⠀⠀⠀⠚⠻⠿⣿⣿⣿⣿⣿⠿⠛⠛⠀⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠰⠶⢾⣿⣿⡶⠶⠆
⠀⠀⠀⠀⠀⢰⠀⠀⠤⣤⣿⡤⠤⠀⠀⠀⠀⠀⠀⠈⢻⣿⠟⠀⠀⠀⠀⠀⠐⠶⢾⣿⣿⠷⠆⠀⠀⠀⠀⠀⠀⠲⠾⢿⣿⡿⠿⠒⠂⠀⢸⡇
⠀⠀⠀⠤⠤⣾⡦⠤⠄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⢸⡄⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⡄⠀⠀⠈⠃
⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣿⣿⣦⡤⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠠⢤⣼⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠏⠀⣀⣤⣾⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠶⠶⣿⣿⡷⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢻⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⣴⣻⣷⣆⠀⡠⣾⣿⠿⢿⡦⠀⠀⢰⠁⠀⠀⠈⢂⡠⠁⠀⠀⠀⡀⠀⠀⠀⣠⣤⣤⣤⡀⠀⣠⣴⣶⣆
⠀⠀⠀⣿⣿⠀⠻⣿⡾⠋⠀⠀⠸⢀⠆⠀⠀⢀⠀⠀⠀⠘⠡⠀⠀⠀⡰⠁⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⣻
⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⣠⢞⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠈⠻⣷⡀⢀⡤⣘⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠢⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠙⠿⣯⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣀⣴⣤⣀⡀⠀⢀⢀⡄⣤⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⣀⣤⣄⡁⠀⠀⠀⠀⢀⠀⠠⠄⠀⠀⠀⠠⣄⢀
⠀⠀⢠⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣷⠀⠀⠀⢰⣿⠉⢿⣿⡾⠉⠙⢿⣷⠀⠀⠀⠀⠄⢹⡗⠚⠋⠀⠀⠲⠀⠢⠆
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣇⣿⣿⡏⠀⠀⠂⠸⣿⣆⠈⠉⠁⠀⣴⡿⠃⠀⠀⠀⠀⠠⣀⠠⠆⠈⡉⠑⠒⠓⠴
⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠉⠻⣧⠀⢀⣾⠟⠁⠄⠀⠀⠀⠀⠀⠘⢃⡐⢂⠈⠡⠈⡀⠁
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠘⣳⡿⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⢡⠎
⠀⠀⠀⠀⠀⠀⠙⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⡀
⠀⠀⠀⢠⡾⠛⠛⢶⣄⡔⠋⠉⠙⢧⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢉⣀⠘⠁
⠀⠀⠀⣼⠀⠀⠀⠀⠁⠀⠀⠂⠀⢨⠀⠀⠀⠀⠀⡓⠀⠋⠀⠀⠀⡰⠀⠀⠀⠀⣠⠒⢶⣤⡎⠀⣸⠇⢀⣤⣤
⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠠⠀⢰⡀⠐⠀⠄⢠⡀⠀⠀⠀⠀⢻⡄⠀⠉⠀⣿⡿⣶⣿⣿⣿⠁
⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠢⠀⠰⠀⠄⠀⡟⠀⠀⠀⠀⠀⠀⢻⣄⠀⢀⣿⣷⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⠳⣄⠁⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⢧⠎⠀⠙⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡇
⠀⠀⠀⠠⠀⢠⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠶⠒⡄⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠈⠁⠀⡠⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠀⠒⠒⠀⠤⠀⢀⡀⠀⠀⠀⡇⣤⣴⣦⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⡖⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣀⣀⣀⣠⡤⠤⠤⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠉⠫⠭⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒⠂⠀⠀⠤⠄⠀⠠⠐⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠤⠒⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡨⠀⠀⠈⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣴⣭⣴⣭⣿⣽⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣾⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⡛⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⢻⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠲⠶⠶⠶⠶⠔⠒⠂⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠐⠲⠶⠶⠶⠶⠶⠂⠀⠀⠀⠛⠛⠿⠿⠿⠿⠿⠃


⣿⠿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣟⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡋⢙⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤⣀⠀⠀⠀⠀⠀⣾⣿⣿⣏⣹⣿⣿⣿⣿⣯⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⣽⣿⣷⣄⠀⠀⠀⠘⠛⠛⠛⠛⢿⠟⠛⢻⡟⠉⠉⠉⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢿⣿⣿⣿⣿⢿⣿⣦⠀⠀⠀⠀⣀⣀⡀⣼⠀⠀⢸⡇⢀⣴⣿⡿⠟⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣷⣾⣿⣿⠀⢀⣴⣿⠟⣿⣿⣿⡀⠀⢸⣧⣾⣿⣿⣿⣦⣿⣿⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⡍⠙⡏⠉⠉⠀⣴⣿⣿⣷⣦⣾⣿⣿⣿⡄⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢦⣄⠀⠈⡇⠀⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⣿⣷⣼⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣾⣿⣦⠀⣷⠀⢻⠀⣼⣿⣿⣿⣿⣯⡸⣿⣿⣿⣿⣿⡇⡿⠛⠛⣻⠛⠛⠛⡟⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣙⣿⣟⣡⣿⣿⣷⡰⡇⠘⠀⠘⠛⠛⠛⠻⡿⠿⠿⣿⠿⠿⠟⢡⡇⠀⠀⡏⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠹⠉⠉⠀⣃⣄⣀⣾⠂⠀⠀⠀⠀⡇⠀⠀⡟⠀⠀⠠⢸⠇⠀⢸⠱⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆⠀⠀⠁⢣⠀⠙⡆⠀⠀⠀⢰⡇⠀⢠⡇⠀⢀⡀⣾⠀⢀⡏⠁⢀⣴⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢰⣴⣶⣦⡘⡆⠀⢸⡀⠀⠀⢸⠀⠀⠘⣡⡾⣿⣿⡆⠀⡼⠀⢠⣾⣟⣿⣅⣽⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⣿⣿⣷⠀⠈⡇⠀⠀⡞⠀⢰⣾⣿⣿⡿⣿⣿⡌⠁⠀⠘⣻⠛⠿⠿⡿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⣿⠿⡟⠋⡇⠀⢸⣶⣶⡇⠀⢸⡟⣻⠛⢻⠿⢿⠇⠀⠀⢠⠇⡌⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢹⡀⢹⡄⢹⢀⣿⣧⣿⣿⠆⢸⠁⠇⠀⣾⡴⠃⠀⠀⢠⠏⣸⠁⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣄⢧⠘⢷⡘⡆⠀⡏⢸⠁⠀⣿⡜⠀⣴⠋⠀⠀⡠⣠⢳⣌⠁⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣼⣟⠈⢆⠀⢳⣇⠀⡇⢸⠀⢠⡿⠁⢰⡏⠀⣠⢞⡴⠇⡁⠈⢳⢤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣆⠈⢦⠘⣆⠀⠙⣄⡷⢸⠀⡼⠁⢀⡞⠀⡪⣐⢩⠴⠊⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣄⠀⠀⠈⠣⡈⠧⠈⢧⠀⠈⠃⠘⠋⠀⠀⠚⠋⠉⠈⠀⠀⣠⠔⠋⠀⠀⢠⡤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡀⠀⠀⠀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠆⠀⢸⣿⣷⡄⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠰⠀⠈⠛⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⠀⡀⠀⣼⣿⣿⣿⣿⣷⠀⢀⠀⠸⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠙⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⣦⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡟⠷⣖⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣷⠀⢸⠇⠀⠀⢀⣠⣴⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢿⣿⣆⣀⡀⢀⣴⣿⣿⣤⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣷⣾⣟⠋⣴⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣾⡯⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⢻⣿⣿⣿⣿⣿⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢻⣿⣿⣿⡀⠀⢿⣯⡙⢿⣿⣿⠟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣁⣿⣿⣿⣿⣿⣤⣀⠙⢷⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢻⣤⡀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣏⠀⢹⠃⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⡟⣿⣿⣿⣿⡿⢻⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⢁⡠⣄⠀⠀⡠⠤⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠉⠉⢼⠛⠐⠲⠁⠀⠈⣖⣚⢀⠀⠀⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣐⠁⠀⠀⠀⠀⠀⡇⠀⡐⠂⠀⢀⠉⠀⠑⣤⠄⠘⠂⠘⡆⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠒⢠⣄⠈⠢⡀⠀⠀⣠⠊⠁⠢⠈⠀⠀⠀⢆⠀⣰⠁⠀⠐⢠⠴⠁⠤⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣥⢀⠙⡤⢄⠀⠀⢀⢀⠀⣈⠁⠠⠬⠋⠒⠉⠎⣄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⣤⠀⠋⠉⠍⠲⡎⠀⠀⣁⠮⡰⠀⡖⠁⠀⠀⠀⠄⠀⠀⣅⠈⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⣉⠂⠀⠁⠶⠀⢻⢃⠺⠌⠀⠀⠙⡣⠀⠀⠀⠀⠀⠀⠀⠐⣥⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠀⠀⠀⠂⢀⠙⣗⠀⠈⠈⠠⠽⣀⠀⠀⠀⠀⠀⠀⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⡀⠃⠴⠀⠘⠺⡴⠦⠉⠁⢀⠧⠰⣀⢤⠤⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠑⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⢀⢀⡋⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣩⢦⢘⠨⣁⣀⣁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠈⠊⠈⡆⠠⠀⠘⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡇⢰⡀⢹⠸⠆⠀⠡⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢦⢧⢀⣧⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠉⠐⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣰⠖⠀⠀⠈⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⣿⠂⢠⡏⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠟⣤⠀⠀⠀⣸⡇⠀⠛⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⢰⣿⡆⣠⣾⠿⠁⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⢀⣴⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⣿⣻⣿⡿⠇⠀⢀⣠⠤⠤⢶⣦⣄⢀⣴⣽⣦⣤⡶⠛⠛⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣏⠀⣼⣿⣿⡟⠁⠀⣴⣿⣷⣦⣤⣤⣽⠿⠞⠛⠈⢁⣠⣤⣶⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠀⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⡿⠉⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠏⠀⣘⢿⣿⣿⡏⠀⢀⣿⣿⣿⣿⣿⡿⠀⠀⠀⣰⣿⠋⠉⠀⢩⡿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⠀⠈⠀⠚⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣇⡀⠀⠸⣿⣿⠀⠀⠀⠀⠀⣍⣻⣅⡀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡃⠀⠀⠰⠚⣿⣿⣟⡀⣼⣿⣿⣿⣿⣿⣶⠶⣤⣻⣿⣿⠀⠀⠀⠀⣿⡟⠻⠿⠾
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣥⡀⠠⣦⣤⣿⠟⠋⠉⠙⢿⣿⣿⣿⣿⠋⠀⣼⣿⣿⣿⣤⣀⣠⣄⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠉⢻⣿⡄⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢿⡀⠀⠀⠀⠀⠀⡜⠀⠙⠲⣬⠻⣿⣿⣿⣿⠃⠙⣿⣯
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡛⠁⠀⠀⠀⠀⠁⠘⠆⠀⠀⠀⠃⠈⢻⣿⡟⣗⢀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣞⣿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣛⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣦⣀⠀⠀⠀⢀⣦⡀⢀⣀⣠⣴⣿⠟⢻⣤⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡀⠀⠀⢀⡴⠟⠋⠉⣹⣿⠃⢀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡦⠐⡟⠀⠀⠀⢀⣿⡏⠀⣐⣬⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠎⠀⠀⢀⠀⣸⠟⠀⣀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⢄⠀⣼⡏⠀⢸⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣀⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣶⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⡖⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀

⠀⠀⠀⠀⣠⣤⢄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡄⠘⡄⢠⢃⡨⠛⠧⣽⡤⠃⠠⠿⠄⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⣧⡟⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠛⠯⠤⠤⠔⠊⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠰⢿⠀⠀⠀⣄⠫⠑⠀⡀⠀⠀⠀⠠⠀⠀⠈⠇⠒⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⢀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠀⠀⢿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠐⠐⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠀⠉⠉
⠀⠀⠄⠀⠀⠀⠀⠾⠆⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠠⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠄⢀⣴⣿⠟⠁
⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠁⠤⢘⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠇⠀⠀⠀⢻⣿⣿⡀
⠀⠀⠘⠀⡒⠈⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⡀⠀⠀⠀⣾⡇⠀⠀⢠⡶⣆⠀⠀⠀⠛⠛⠛
⠀⠐⠂⠀⠀⠀⠀⠳⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠀⠈⠀⠀⠀⢸⣽⣿⡇⠀⢀⢀
⠀⠀⠀⠀⠀⣀⡀⠳⠆⠀⠀⠀⠈⠀⠁⠀⠀⠀⡀⠀⠀⣠⣶⡧⠀⠀⠀⠀⠀⠻⠓⠀⠙⠛
⠠⠀⠀⠀⠀⢙⡃⠀⠀⠀⠐⠂⠀⢠⣤⡄⠀⠻⡟⠀⠀⠘⠁⠀⠀⡀⠀⢀⡴⡶⢢⠀⢀⣦⡀⠀⠀⠀⠀⢴⡷
⠀⠐⠢⠀⢰⣏⣷⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣤⣤⡄⠀⣾⠿⠀⠘⢷⣏⡿⠁⠈⠰
⠀⢈⠡⠀⠹⣾⡿⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠑⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠾⠮⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠛⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠆⠀⢰⠀⠀⠆⠀⠀⠈⠀⢀⡤⠒⡻⣏⠑⠢⣄⠀⠀⠀⠀⢒⠀⠗⠀⣀
⣐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⣏⣤⣤⡧⠼⣦⠤⢬⣇⠀⠀⠠⠈⠀⠀⠀⠐⠀⠀⢀⠠
⠀⠅⠀⠂⠀⢲⡶⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⠉⠲⣾⣀⠀⣹⡖⠉⢸⠀⠀⠙⠀⠀⠀⠁⣰⣰⡀⠘