Thank Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⣀⡀⠀⣀⣀⡤⠤⠤⠤⠤⣄⣀
⠀⢀⡤⠄⢀⠄⠂⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⣠⠎⠁⣠⠟⡏⠁⠀⠀⣀⣤⡤⠶⠶⣶⡬⠁⠀⢠⠆
⠀⢋⡔⣰⢫⠎⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⡼⠁⠀⠘⠧⠔⠁⠀⠀⠈⠋⠁⠠⠞⠋⠕⠂⠀⢠⠇⠀⢀⠤
⠀⡾⢰⡇⣿⠈⣄⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠁⠻⠃⢿⣄⠈⠲⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡇⠀⠀⠀⠀⠐⠀⠀⠀⢤⠀⠀⠀⠀⣀⡀⠀⠀⢀⡇⠀⠀⢤
⠀⠀⠀⠀⠈⠙⠳⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢸⠃⠀⠈⢦⠀⠀⢀⣠⣄⣸⠀⠀⢰⠋⠁⠈⡇⠀⢸⠀⡀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⠀⠀⠀⡾⠀⣴⠋⠀⢀⡟⠀⠀⡏⠀⠀⡜⠀⠀⡟⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⡟⠀⠀⣸⠃⠀⢷⡀⠀⢸⡇⢀⡜⠀⠀⢰⡇⠀⡸⠁⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⡼⠁⠀⠀⠻⠄⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠁⡾⠒⠒⠢⡄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡸⠃⢀⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⢻
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⡤⠞⠋⠉⠉⣧⠀⠀⠀⠀⢀⡠⠖⠂⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⣸
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⢀⠎⠀⣀⠀⠀⢠⡏⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⣑⣓⣋⡥
⠀⠀⠀⠀⠀⠛⠦⣄⣀⡀⠀⠀⠀⠀⢀⠄⠸⡄⠞⠁⠀⠀⡞⠀⠀⠀⢀⡟⠀⠀⠀⠀⣀⠀⠀⠀⢠⡄⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣼⠁⠀⡔⠁⠀⢸⡆⠀⠀⢸⠃⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠈⠓⠶⠶⠶⠾⠛⠋⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢰⡏⠀⣸⠁⠀⠀⢸⡇⠀⢀⡏⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠘⣧⣿⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⣾⠀⠀⢻⣄⣀⣠⠟⠀⠀⢸⡃⠀⠀⢸⡇⠀⠀⠀⠐⠊⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠑⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣴⠚⡉⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⣀⣀⣀⣀⣀⡤⠴⠚⢉⣠⡄⠀⠳⠴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣠⣤⣴⣾⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠯⠭

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠐⠀⠀⠀⠀⢃⠀⠀⠀⣠⠀⡀⣤⡀⠀⠠⡆⠀⣀⠀⠀⢀⠎⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⣀⡀⠀⠀⢳⢦⢸⠒⠽⠘⡅⡉⠁⠀⠀⠀⠀⡏⠀⡠⠁⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠣⠉⠀⠀⣀⣀⡀⠀⠀⢀⠀⠀⠀⠀⡁⠈⠀⠀⠋⠀⠁⠀⠀⠐⠐⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠑⡀⠠⠐⠂⠀⠉⠀⠀⠀⠀⠀⢸⠀⣇⢀⡇⡘⡆⢸⠀⡇⣧⠎⠀⠀⠀⠀⢀⣠⡠⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠆⠀⠀⠀⠀⠀⠸⠀⠏⠀⠇⠁⠹⠼⠈⠇⠏⠣⠀⠀⠀⠀⠈⠉⠙⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠴⠐⠆⠀⠀⠀⠀⠀⠀⠀⢦⣠⢂⠒⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⠀⡀⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢘⡀⣠⢀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢄⡛⠲⡦⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠁⠀⠀⠄⠀⢄⣀⠀⠀⠀⠃⠈⠂⠂⠘⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⢸⠐⠆⠀⠂⠀⠠⠀⠄⠀⠀⠰⠠⠀⠀⠀⠀⣦⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⣛⠈⠀⡤⠘⠃⠈⠋⠐⢤⠀⠀⠘⠃⠆⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢂⡀⠛⠀⠀⠤⠀⠀⠀⠀⣠⠘⠀⠠⠆⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠨⡄⠂⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈




⣏⠉⣹⣛⣛⣛⣛⣛⣛⣛⣛⣻⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣻⣿⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⡿⠁⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣾⠃⢀⠎⢀⡤⠀⠀⠀⠀⠀⠀⣰⡏⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡟⠀⠀⢸⡏⡠⠁⢠⡟⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣾⡇⠀⠀⣾⠏⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣿⡀⠀⠈⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⢁⢂⡿
⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⣿⠀⠀⠀⣿⢠⡆⢀⡴⢂⡀⢰⣦⢺⡆⢸⣿⢀⡾⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⢻⣿⢸⣇⣿⠁⢸⡇⣾⠃⣾⣿⡏⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⡿⠈⠿⠁⠀⠙⠃⠀⠀⣿⡼⢹⡟⣿⡀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣈⡀⠀⠀⢀⠄⠀⠀⠀⠀⢀⠈⠁⠘⠁⠈⠓⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠈⣿⠀⣿⠈⢆⣾⠁⡧⢰⣿⠀⣿⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⡄⣿⣇⠘⣿⠀⡅⢸⡇⢸⣿⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠟⠸⣿⠀⠙⠊⠀⠈⠓⠉⣯⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢿⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠁


⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣈⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣁
⠀⠀⠀⠀⠀⡇⠀⠀⠠⢤⣤⠄⠀⣠⡀⠀⡀⠀⠀⣤⠀⠀⠀⣤⠀⢀⠀⢠⡀⠀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⣿⡇⠀⡇⠀⢀⣿⡇⠀⠀⣿⡄⢨⠀⢸⡇⠠⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⣿⡧⠴⡇⠀⠸⢼⣇⠀⠀⢿⣇⢸⠀⢸⣷⡁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⡇⠀⠀⣿⡇⠀⡇⠀⡆⠸⣿⠀⠀⠈⣿⢸⠀⢸⡇⢃⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸⡇⠀⠀⣿⡇⠀⡇⠀⠇⠀⣿⡀⠀⠀⢿⣷⠀⢸⡇⠘⡄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠃⠀⠀⠙⠃⠀⠁⠘⠀⠀⠙⠃⠀⠀⠘⠛⠀⠘⠃⠀⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣴⣄⠀⠀⣿⡇⠀⠀⢠⡴⠂⡀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⠀⠸⣿⡇⠀⢀⣿⠃⠀⠉⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⠀⠁⣿⡇⠀⠈⣿⡀⠀⠀⠀⠀⣿⠀⠈⣿⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠙⠀⠀⣿⡧⠀⠀⠉⠓⠀⠀⠀⠀⠙⠃⠀⢿⡇⠀⠄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢈⡑⡄⠀⠀⠀⢀⠄⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⢠⠊⡅
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠙⠉⠈⢹⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣠⡿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣒⣚⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠏⠀⠈⠉⠘⡀⢰⠂⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠐⠂⠈⠀⠃⠀⠀⠀⢀⢡⣀⡄⠀⠀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⢈⠀⠀⠀⡑
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⡘⠀⠀⠀⢹⣆⠀⠀⠀⢀⣮⢬⠇⠀⠀⣾⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠂⠀⠀⠀⢀⠀⠠⠐⠈⠀⠀⠐
⢴⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣤⡴⠊
⡄⠂⢀⣠⡄⠀⠀⠘⣏⡐⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⣖⠲⠀⠀⠀⠆⠀⠀⠀⠀⡿⠀⠀⠀⠀⢠⡆⠀⠀⠀⣠⠀⠀⠀⢰⠿⠛⠉
⠀⣨⢁⣱⡆⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢸⠀⠀⢀⠇⠄⢡⣀⣀⣸⠀⣄⣀⣀⡇⢠⠀⠀⠀⡞⠀⠀⠀⢠⠋
⠀⠉⠁⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣤⣿⡵⠔⢖⠆⣼⣉⠉⠉⠀⢀⠮⠦⢄⡄⣶⣀⣔⡍⢁⣀⠉⠉⣴⡃⠦⢄⣀⠟
⠀⠀⠀⠀⠀⠄⢀⣀⠤⢼⠀⠀⣢⡽⠴⡜⠸⠟⠈⠉⠉⠁⠉⠉⢀⠄⠁⠀⠀⠀⠈⠢⠀⠀⠠⠇⠀⠈⠉⠛⢢⡤⢔⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠦⠥⠖⠃⠀⡸⠢⡀⠀⠈⠣⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⢀⢄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠐⢆⣉⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣇⡀⠁⠀⠀⠀⡆⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠑⠞⠑⠊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⡅⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⡇⠉⠀⠀⠀⣻⡟⠀⠀⠀⢸⢃⡞⣱⠃⠀⠀⠈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⡇⠰⠀⠀⠀⠀⠒⠂⠀⠀⠀⢠⢡⠁⠀⠀⠀⡽⠁⠀⠀⢀⡈⡈⢠⠇⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⡟⠰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠤⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⢆⠘⠦⣀⣀⣀⣀⣠⣴⠋⠯⠈⢆⠀⠀⠀⠀⠀⢀⡔⠀⣯⠖⠒⢬⡽⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⢉⣉⣉⠍⠀⠀⠈⠲⢔⣀⣀⡠⠴⠚⠁⠀⠘⢄⡀⠉⠒⠒⢒⡶⠋⡠⠪⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⣅⠀⠑⠤⣀⡤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢀⣀⡀⠠⣶⣦⢀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⠀⠀⠀⢠⣤⡀⠀⣾⡿⠇⠀⠀⠠⣾⣿⣿⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⠉⠀⠀⠀⠀⠀⠘⠛⠿⠀⠉⠀⠀⠀⠀⠀⠸⠟⠿⢋⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣾⣁⡈⢳⡄⠀⠀⣿⡆⠀⠀⠀⠀⠀⠐⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣤⡀⠀⠀⠂⠄⠤⠐⠂⠉⠀⠀⠻⠿⠇⠀⡇⠀⠀⠈⠀⢠⠞⠉⠀⠀⠲⣄⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⣿⣦⠀⠘⣦⣴⣦⡀⠀⠈⢧⠀⢿
⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣿⡏⣿⡿⠒⠲⠴⠶⠷⠦⠤⠤⠤⠒⠋⠀⠀⠀⣿⠇⠀⠀⠈⠙⠋⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⣿⠀⣿⡇⡀⢀⠀⢀⣤⣴⢤⡀⢠⣀⠤⠀⣀⠀⣿⠀⣷⠀⠀⢀⣄⣐⠋⠀⠀⡿⢰⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠉⣡⡀⠀⠀⠀⣿⠀⣿⡏⠀⠈⣷⠙⠛⠁⠀⣿⢸⡇⠀⠀⢹⡄⣿⠞⠁⠀⠀⢻⣿⣿⣀⠀⣰⠇⠋⢁⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⣿⠀⣿⡇⠀⠀⣿⠀⡤⠒⠘⣿⢽⡇⠀⢀⣿⡇⣿⠳⡄⠀⠀⠀⠉⠀⢉⡴⠋⠀⢲⣄⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠿⠀⠻⠇⠀⠀⠿⠘⠧⠀⠴⠿⠸⠃⠀⠸⠿⠃⠿⠀⠈⠑⠀⠀⠐⢚⣿⡆⠀⠀⠘⣿⡿
⠀⠀⠀⠀⠀⢀⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⢰⠀⣰⠊⠁⠉⢷⡄⣶⣶⠄⠀⢰⡦⠀⠀⠀⣸⣿⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠙⠿⠋⠀⣴⣾⡟⠁⣀⠀⠀⢸⣿⠀⠀⠀⣸⠀⡇⠀⠀⠀⢸⣷⣿⡏⠀⠀⢸⡟⠀⠀⢀⣿⡇⠀⠀⢀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠘⠿⠀⠀⠀⠻⢄⣀⡴⢿⠀⢻⡀⠀⠀⣼⠏⢿⡁⠀⢀⣿⡇⠀⠀⣸⣿⠀⠀⠘⠁⠀⣴⡖
⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⣀⠀⣾⣿⣗⢡⣤⣄⠀⠀⠀⣿⠀⠀⠈⠀⠚⠉⠀⠈⠙⠛⠉⠈⠁⠀⠀⠛⠃⠀⠀⣾⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠘⠛⠛⠙⠛⠉⣀⡬⠄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠺⠀⢠⢀⠀⠀⠀⠀⣠⣾⣇⠀⠀⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⢠⡏⠑⠦⣀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⠛⠋⢠⠀⠈⢻⠛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣸⠃⢀⡀⡈⠻⢿⣿⣷⠀⠀⠀⣀⡀⠀⠀⠀⠀⡆⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⢀⡴⠋⢠⣾⣿⣿⡄⠀⠀⢠⡀⠙⠿⠿⠟⠀⠀⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠙⠛⠟⠀⠀⠀⣿⣷⠀⣧⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠐⢸⢦⡀⠀⠀⠀⠀⡖⢴⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠀⠀⠀⡀⠠⣤⠀⠀⠀⠐⠤⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠒⠚⢀⠀⠀⠀⢠⡧⠚⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠈⠙⡦⡁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢀⣟⠀⠀⠀⠀⠀⢀⡔⣙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣧⠀⠀⠘⠁⠀⠀⠀⠀⢨⢹⣀⣀⣠⠊⡵⠄⠀⠀⢱⢙⡄⠀⠀⠀⢖⣦⠀⠀⢸⢹⠀⠀⢸⣸⠀⠀⠀⠀⡠⠋⡰⠃
⠀⠰⡤⠤⡆⠀⠀⢀⣖⠺⣣⡇⠀⠀⠀⣀⠤⣄⠀⠀⢨⠈⡛⠮⢾⠿⠂⠀⠀⠀⢸⠀⡇⠀⠀⢰⢨⠀⠀⠀⢸⣼⠀⠀⡾⠋⠀⠀⠀⡞⣡⠎
⠀⠀⠘⠚⠃⠀⠀⢸⠸⡏⠉⠁⠀⠀⢠⢃⡎⠈⠀⠀⡆⢸⠆⠈⠀⠀⣠⠀⠀⠀⢸⢨⠃⠀⠀⢸⠨⠀⠀⠀⣘⡇⠀⠀⠁⠀⠀⠀⠀⢶⠁
⠀⠀⠀⠀⠀⠀⠀⢸⢘⠀⠀⠀⠀⠀⠸⢸⠀⠀⠀⠀⢁⠊⠀⠀⢠⢪⠘⠀⠀⠀⠀⠸⠀⠀⠀⢸⡀⠀⠀⠀⣳⠁⠀⠀⢀⠔⢫⡀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠘⣐⡀⠀⠘⣉⣛⣷⡇⠀⠀⠀⢰⡰⠀⠀⠀⠈⠉⠀⡀⠀⠀⢘⡆⠀⠀⠀⢰⡅⠀⠀⢀⣮⠀⠀⢰⣁⠔⠁⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡸⠄⠀⠀⠀⡀⠀⢨⠘⠗⢤⡄⣀⠤⠚⢙⢆⣤⠋⠈⣶⠢⠤⢧⡇⢦⠤⢼⣣⡀⣠⡯⠇⠀⠀⠀⠀⠀⡤⠚⢳⠄
⠀⠀⠀⠀⠀⢢⡀⠀⠀⢀⡠⠜⠁⡸⠀⠀⠘⢖⣒⣺⣰⠀⠀⠙⠒⠐⠊⠁⠀⠙⠓⠋⠀⠓⠚⠛⠃⠐⠒⠺⢏⣱⣤⡽⠀⠀⠀⣀⡀⠈⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠯⠷⠻⠊⠉⡙⢄⠀⠈⠉⠉⢹⣯⡀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⠂⠁⠀⢹⡄⠀⠀⡆⠀⢀⡧⡀⠀⠀⠈⠀⠀⣼⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⠎⠀⠀⠀⠀⠀⡆⡇⠀⠀⠀⢀⢠⣀⠀⠀⠀⠘⡷⡀⠀⠀⢸⢳⠀⠀⡇⠀⠀⡃⡅⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠸⠀⠀⠀⠀⠀⠀⣅⠃⠀⠀⢠⢁⡤⠚⢳⠀⠀⠀⠱⡟⠀⠀⡘⡸⠀⠀⠃⠀⠀⢘⠇⠀⠀⠀⠀⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠀⠀⠀⠀⠀⠀⢯⡇⠀⠀⢸⡜⠀⠀⠀⠀⠀⠀⡈⡃⠀⠀⡃⠂⠀⠀⠀⠀⢸⢔⠀⠀⢀⣀⠀⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣷⠀⠀⠀⠁⠀⠀⠀⠀⠀⡐⣡⡇⠀⠀⠳⠄⠀⠀⠀⠀⢘⢜⡀⠀⠀⡱⠚⠭⣥⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡰⡦⠴⢒⡇⠀⠀⢀⢁⠃⠣⣄⡀⠀⠀⠀⣀⠄⢊⡰⠁⢧⡀⠀⠀⠀⠀⣀⠀⠀⠀⣷⡆⠀⠀⠀⠀⠀⢹⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢀⠊⡜⠀⠀⠙⠒⠬⠭⠥⠔⠒⠁⠀⠀⠀⠻⣕⣐⠒⣈⡩⠗⢒⠒⢻⡇⠀⠐⢤⡀⡀⠀⡘
⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠱⣦⣤⣀⣀⣀⣀⡠⠄⠊⡡⠊
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠉⠒⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠄⠠⠀⠀⡠⠀⠄⠠⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⣿⢹⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⣠⣿⠇⠀⠀⠙⢷⣍⢷⡄⢹⣿⢀⡶⠟⣩⠟⠀⠀⠀⠀⣀⠀⢠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢶⣿⣷⣦⣴⣿⣯⣀⣀⠀⠀⠀⠙⠛⠻⠂⠉⠻⠓⠋⠁⠀⠀⣀⣤⠞⠁⢠⣿⡟⠀⠰⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⢸⣿⠀⠀⣿⡟⠉⠛⠛⠿⠿⣶⣶⣶⣦⣤⣤⣤⣤⣴⣶⠾⠟⠋⠁⠀⠀⣾⡿⠀⠀⢰⣀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⣿⡟⠀⢸⣿⠁⣀⡀⠀⠀⠀⠀⠀⢀⣈⡉⢉⣭⠀⠀⠀⠀⠀⣠⣤⡀⢠⣿⢃⡠⢤⣄⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠊⢽⠀⠀⣿⡇⠀⢸⣏⠞⢉⣿⠀⠀⠀⣠⡾⠟⠁⣹⣿⠏⠀⢠⣾⢢⠞⣿⡟⠀⢸⣿⡎⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡴⠚⠁⠀⣿⡇⠀⠸⡿⠀⢸⣿⠀⠀⣸⡟⠁⡠⠊⣿⡏⠀⢠⣾⣿⠏⢸⡿⠀⢘⡿⣿⣶⠞⠋⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⢸⡏⠀⡰⠛⠗⠋⠀⠀⠻⣤⠔⠁⢿⡟⠀⠸⣧⠴⠋⠀⠈⠹⣧⠀⠀⣠⠏⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠲⣄⡘⢦⡀⠙⠻⠂⠀⠀⠈⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠊⠁⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣮⣿⡶⣿⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢋⡾⠋⣴⠟⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣈⣉⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⢀⣤⣶⣶⣶⡦⠀⢀⣀⣀⣰⣾⣿⡆⠀⠀⠀⠀⠀⣰⣶⣶⡄⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⣰⣿⣿⣿⠏⠀⠸⣿⡟⠛⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⢀⣴⠟⠁⣿⣿⣿⢰⣿⣿⣿⡏⠀⠀⠀⢻⣿⡄⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⡇⠈⡁⡬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠛⠁⠀⢰⣿⣿⣿⢸⣿⣿⣿⡇⠀⠀⠀⢸⣿⡇⠘⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⣼⣿⣿⠇⠘⣿⣿⣿⡇⠀⠀⠀⣼⣿⠇⠀⢻⣿⣿⣿⠀⠀⠀⣰⡿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠉⠉⠛⣿⣿⣿⣟⠀⠀⠙⢿⣿⣿⣄⣀⣴⣿⠟⠀⠀⠀⠻⣿⣿⣷⣄⣴⡟⠁⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⣀⣴⣿⣿⠟⠛⠃⠀⠀⠀⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠘⠿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠛⠋

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡀⠀⡁⠱⠎⢘⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⡤⠊
⠀⠀⠑⣄⢈⡖⢢⠋⣠⠊⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠤⠐⠒⠢⡀⠀⠈⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⢄⡈⡠⠤⡄⢉⡩⠂
⠀⠀⠮⠤⠌⢁⠛⢤⠀⠥⠀⠀⠀⠀⡠⠄⠈⠑⢲⠀⠀⠀⠀⠀⣈⣀⡀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠀⠀⠖⠒⠁⠑⢄⡀⠀⠀⠀⠀⢠⣊⣁⠛⠲⢁⡈⢑
⠀⠀⠀⠀⠤⠊⠁⠜⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠂⠀⠀⠀⠠⠊⠀⠀⠈⠲⠒⢃⣀⠠⠂⠈⢂⠀⠀⠀⢸⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⠠⠓⢄⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠈⠈⠁⠀⠀⠀⠀⡀⢀⠄⠀⠃⡤⠴⡀⠀⠀⢀⠌⠀⠀⠀⠈⠁⠈⠚
⠀⠀⡠⠀⢄⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠠⡄⠀⠈⢉⠀⠀⠀⠀⠀⠈⠐⠒⠁⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⡀⠀⠀⠀⠰⠆
⠀⠀⠁⠤⠊⠀⠀⠀⠀⠀⡐⠰⠅⠱⠂⠀⠄⠒⡀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠶⠄⣀⠠⠂⠀⠀⠀⠀⡀⠰⠀⠀⠨⡄⠀⢨⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⢑⡀⠀⢓⠀⢰⠖⠈⠁⡇⠀⠀⠀⠀⢠⢀⠀⠀⢘⠀⠀⠀⢠⠀⠀⠀⢘⠀⠀⠜⢁⠤⢄⠈⠃⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠐⢄⠈⠀⠉⡒⠉⠈⢣⡠⠴⢀⡠⠃⠀⠀⠀⠀⠄⠈⠠⣈⡐⠀⢀⠂⠀⠀⠀⢠⠃⠙⡀⠃⠀⢀⠃⠐⠒⠂⠀⠀⠀⡀⢀⢤
⠀⢀⡤⠋⠀⠰⠀⠀⡎⢁⠖⠂⠣⣀⣀⠴⢄⣀⢀⡈⠄⠀⠀⠀⠀⠀⠁⠂⢻⠒⠂⠁⠀⠀⠀⠀⠐⢀⣠⠓⠠⢀⠠⠔⢅⣀⠀⠀⠀⠀⢡⠀⠀⡰⠂
⠀⠀⠁⡄⠀⠥⠀⠀⢨⣁⡀⠤⡎⠀⢰⡀⠀⢡⣈⡆⠀⠀⠀⠀⢠⠀⡀⠀⢸⠀⠀⡀⢤⠀⠀⠀⠀⠀⠐⢄⣀⣼⢄⣀⠘⠀⠀⠀⠀⠀⠁⠈⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠔⠇⠀⣦⢈⠦⠠⠀⠀⠀⠀⠀⠀⠀⢄⠈⠢⣘⡐⠁⢀⠂⠀⠀⠀⣀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠁⡆⠈⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠁⠂⠻⠄⠂⠁⠀⠀⠀⠀⢆⠈⠐⢄⠀⢸⠀⡀⠔⠈⢀⠅⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠰⠀⠀⠀⠀⢀⠀⠈⠐⢄⠀⡇⢀⠀⠊⠀⢀⠂⠀⠀⠀⢠⢀⠀⠀⠸⠀⠀⡀⢀⠀⠀⠀⠈⠂⡀⠀⠑⣌⡐⠀⠀⡠⠊⠀⠀⠠⠊⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢂⣇⠊⠀⢀⠠⠃⠀⠀⠀⠀⠀⢄⠈⠢⣘⡐⠈⢀⠂⠀⠀⠀⠀⠀⠈⠁⠂⢺⠐⠂⠁⠀⠀⠀⠀⢀⠀⠄⠀⢀⠀⠘
⠀⠀⠀⢀⠠⠤⢀⠀⠀⠀⠀⠁⠀⠐⡟⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⠒⠂⠁⠀⠀⠀⠓⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⢀⠡⠔⠁
⠀⠀⡔⠁⠀⠀⠀⠑⡄⠀⢠⠀⠀⠀⠇⠀⠀⢤⣀⣀⠀⠀⣀⣀⡀⠀⠀⡄⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠄⠲⠄⠀⡠⠢⡀
⠀⠀⠆⠀⡀⠀⡀⠀⠄⠀⠠⠀⢀⠀⠀⢀⠀⡔⠀⢸⠀⢨⠀⠀⠁⠀⠌⠀⠀⠀⢠⠀⡇⠀⠁⢄⠀⠀⠀⠀⡁⠀⡄⠂⠀⢀⠜⠀⠀⢀⠀⡀
⠀⠀⠈⠢⠄⠁⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠂⠐⠀⠀⢀⠘⠀⢀⠉⡄⠀⢂⠁⠀⠀⠀⠑⢤⠀⠀⠂⠀⠀⠀⠰⡁⠀⠀⠀⢇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⢀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠘⠇⠀⠠⣄⠀⠀⠀⠀⠇⠀⡔⢄⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⡇⠀⢸⠀⢸⠀⠀⢀⢀⠎⠈⠀⠉⡀⠀⣠⠀⠀⠀⠱⠀⠀⠀⣆⣀⠀⠀⠢⣀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣄⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠑⠒⠋⠀⠈⠀⠐⠁⠀⠀⠀⠀⠀⠈⠀⠑⠒⠊⠀⠀⠀⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀
⠀⠀⠀⠲⢀⡠⠌⠆⠤⡍⠀⢀⡀⠀⠀⠰⠀⠀⠀⢀⢀⠀⠀⢀⣀⠀⢀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠘⠀⠀⠀⠲⠄⡀⠌⠤⠴⡉⠀⢀⡀
⠀⢠⡀⣠⠋⠠⠀⠒⠠⡀⠡⠊⠀⠀⠀⠀⠀⠀⢋⠀⠀⢂⢀⠂⠀⠨⠃⠀⢀⠀⠀⠈⠺⠀⠉⠀⠀⡁⠀⠈⠀⠀⠀⠀⢀⡀⢀⠊⢀⠄⠀⠠⡈⠫⡈⠁
⠀⠀⠀⡃⠀⡁⢌⢈⠄⠰⠀⡉⠴⠂⠀⠀⠀⠀⠀⠢⠀⠀⠃⠀⡰⠁⢀⠊⠀⠈⠂⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣚⠀⡁⢐⠉⠆⠀⠀⣃⠲⠆
⠀⠐⠂⠐⣄⠐⠠⠠⠔⠁⣴⢢⡀⠀⠀⢀⠄⠄⠀⠀⠀⠀⠀⠐⢃⠀⠀⠢⠀⠠⠂⠀⢀⠃⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠑⣀⠑⠄⠀⠤⠃⣠⢢⡀
⠀⠀⠀⢠⠄⠃⠖⡔⠲⣙⠀⠀⠁⠀⠀⠐⠄⠠⠀⠀⠀⠀⠀⡀⠀⠒⢄⠀⠀⠀⢀⠠⠈⢂⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢠⠍⠓⠆⡤⠲⣘⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢠⣴⠾⠿⠿⣿⣿⡿⠿⠃⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⡰⣿⣿⠁⢀⣄⡀⠀⢀⣤⣤⡀⣠⣄⠀⢠⣤⡄⠀⣤⡀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡼⠁⣿⡿⢠⢿⣿⠃⠀⣾⡿⠁⣿⣿⡟⠀⣾⣿⠃⣾⣿⡇⢰⣿⠇⡴⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⢀⣿⣧⡏⢸⣿⠀⢸⣿⠇⠀⣿⡿⠀⡼⢹⣿⡼⢹⣿⠀⣼⣿⣜⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⡿⠀⠀⢸⣿⡿⠀⢸⣿⡴⠻⣿⣀⡜⢿⣧⡞⠁⣾⣿⡇⠸⣿⠀⣿⣿⠙⢿⣦⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠈⠉⠁⠀⠀⠉⠀⠀⠈⠉⠀⠈⠉⠀⠀⠈⠉⠁⠀⠹⣆⠉⠁⠀⣀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣠⣀⠀⣠⡞⠛⠛⢶⡄⠀⢀⣀⠀⠀⣀⠈⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠹⣿⡇⢀⣿⣿⠱⣿⣶⡿⠀⠀⣿⢀⣾⣿⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⣿⡇⡼⣿⡟⠀⣿⣿⣧⣤⣤⡟⢋⣿⡇⢀⣾⡏⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢱⣿⠁⠀⢿⣿⣄⣀⠞⠀⢸⣿⣥⠞⣿⠁⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣾⣇⣀⣀⣀⣉⣉⣁⣀⡀⠀⠉⠁⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡚⠛⢉⡽⠋⠉⠉⠉⠉⠙⠛⠛⠛⠿⠿⣿⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠇





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⡀⢐⡂⠐⠈⢩⡇⢀⠈⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠐⠂⢴⣄⠀⠀⠈⠀⠈⢢⡄⠀⠀⠀⣸⠃⠀⠀⢸⡃⠂⢠⡞⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠄⠀⣶⠀⠠⠁⢀⡟⠀⠀⠀⢀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠙⣆⠀⠀⣿⠀⠂⠀⠚⠁⢰⠟
⠀⠀⠔⠄⠀⠀⠀⠀⢰⡇⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⣾⢱⠀⠀⢹⡄⠀⠀⢰⢄⠀⢹⡇⠀⡿⢠⠀⠀⣄⠀⠹⣇
⠀⠀⣀⣄⠀⠀⢠⠤⠾⠀⠀⠀⠓⠂⠁⠀⣸⠀⠀⠀⠀⠈⠀⠀⠀⠈⡇⠀⠀⢸⠀⡄⠀⠀⢰⡇⠘⠀⢸⡏⠄⠀⢻⡄
⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⢠⢤⣤⡀⠀⣿⠀⠂⠀⣲⠞⠛⡄⠀⠀⣿⠀⠀⢸⠀⠰⠀⠀⢸⡇⠀⠀⢸⡇⠰⠀⠌⣷
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸⠁⠀⠀⠀⡟⠈⠀⢀⡏⠀⠀⠀⢀⣀⡏⢀⣤⣼⠀⠀⠴⠶⠾⠃⠐⠚⠛⠁⠀⠙⠉⠙⠁⠀⣀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⠀⠀⢀⣢⡇⠠⠴⠾⠃⠀⠀⠘⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠤⠄⣤⠀⠀⡐⠁⠀⢀⡞
⠀⠀⠀⢀⣤⡤⠏⠀⠀⠚⠛⠉⠀⢀⡉⠁⠀⠠⠠⠀⠐⡦⠀⠀⠐⠀⠰⣦⡀⠀⢀⠁⠀⣾⠀⠀⠀⠀⠀⡿⠀⠀⠁⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢾⡀⠀⠆⠀⠀⣼⠃⠄⠀⣀⣄⠀⠀⢻⡄⠀⠀⢠⡇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⢷⡄⠀⠀⢠⡏⠌⠀⣼⠏⠀⠑⠀⠈⣷⡀⠀⢸⡇⠀⠀⠀⠀⣸⠁⠀⠰⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠁⠀⠀⣾⠀⠀⢰⡏⠀⠀⠀⠀⠀⣿⠃⠀⣙⠁⠀⡎⠀⢠⡿⠀⠀⠈⣩⠭⣭⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⢰⠇⠈⠀⢸⡇⠀⠀⠈⠀⢸⣿⠀⠀⠨⡴⠆⠀⠠⣬⠁⠀⠠⠈⠀⠀⠌⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡿⠀⢐⠠⠀⠁⠂⠊⠀⢠⡿⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⡀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠇⠀⠀⠡⣤⣀⣀⣀⣴⠟⠀⠀⠱⢦⣤⣤⠴⠟⠁⠀⠀⠀⠈⠛⠓⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⣤⠷⠟⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠈⠈⠁⠈⠀⠈⠉⠀⠈⠈⠀⠈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⢀⠄⠠⠀⡀⠀⠀⢠⣎⠤⠤⠤⢄⡀⠀⠀⢀⠀⠀⠀⢣⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⣀⣀⣀⣀⡀⠀⠀⠱⡄⢀⠀⠢⡀⠀⣸⡴⠚⣿⠀⠀⠀⠀⠀⢹⡆⠀⠈⠢⠀⠀⠌⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⣠⠴⠛⠫⡙⠉⠉⠉⠉⠉⠉⠋⠉⠛⠳⢺⡷⠤⢤⣴⣋⣀⡀⠸⡄⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢀⡀⠀⠀⠀⠀⣼⠃
⡀⠀⠀⠀⣼⠁⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢠⣦⡿⠀⣰⡟⠁⠀⠀⠀⠀⠈⠓⠒⠖⠛⠁⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠙⠒⠲⠒⠋⠁
⢧⡀⠀⠀⠹⣄⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⢀⡴⣻⡟⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠙⠲⠤⣀⣈⣉⣉⡉⣁⣀⣀⣀⠤⠔⠚⠁⣰⠟⢀⣾⠟⢲⡆⠀⠀⢠⠔⠒⣦⡴⠀⢰⣤⠖⢲⡄⠀⢠⣾⠗⢲⣶⠀⠀⠀⣀⠤⠖⠒⠢⠤⣀
⠀⠀⠀⠀⠀⣀⡤⠿⠿⠯⣄⠀⠀⠀⠀⢀⣼⠋⠀⣾⠃⠀⣸⠇⠀⣰⠏⠀⢠⡿⠁⢠⡾⠁⢀⣾⠃⢀⣿⡡⠔⠋⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠈⢳⠀⠀⣰⠟⠁⠀⢸⡏⠀⠀⣿⠀⡠⣿⠀⣠⣿⠁⡰⡿⠁⠀⢸⠏⡠⢾⡏⢧⣀⠀⢀⡴⠁⠀⠀⣠⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠘⣇⡀⠀⠀⠀⢀⣨⣷⠛⠁⠀⠀⣀⣠⡥⣤⣄⣈⣈⡀⠈⠉⠀⠈⠉⠀⠁⠀⠀⠈⠉⠀⠀⠁⠀⠈⠉⠉⠀⠀⠀⢀⡻⡀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠉⠐⠛⠉⠉⠀⠸⡄⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠈⢉⣴⠄⠀⠀⠀⢀⡴⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠙⢎⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡇⠀⠘⣇⠀⠀⠀⠀⠀⡀⢀⣶⠟⠁⠀⠀⠀⣠⡞⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢏⠀⠀⠀⠁⠂⠾⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣇⠀⠀⠈⠳⠶⠶⠶⠊⣴⡟⠁⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠑⢄⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⡠⣿⠏⠀⣠⢴⢶⡄⣀⣰⠆⠀⣰⡄⠀⠀⡠⠐⠀⠀⢢⠀⠘⡄
⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⣼⡏⠀⠀⠀⢀⠞⣱⠏⠀⣼⠃⠈⣻⠏⣡⠏⠀⢰⡟⠀⡠⠊⠀⠀⢀⣀⠼⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⣿⠀⠀⠀⡴⠋⣰⠏⠀⢸⡇⠀⣰⠏⠀⣟⠀⣠⡟⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⠤⠔⠊⠀⣼⠏⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠉⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠑⠠⠀⠘⡄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠑⠦⡀⠀⠀⠀⣠⠟⠁⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⡀⠀⠀⠀⠀⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠈⢦⣠⠞⠋⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⠠⢀⡇⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⣀⣀⣀⣤⠴⠛⠉⠐⠠⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⢈⠀⠀⠀⡘

⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡘⢡
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣛⡹⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⢀⣬⠑⠀⠀⣠⣿⣼⣇
⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠀⢠⠿⠿⠁⠀⠀⡀⠀⠀⠀⢀⡡⠤⠀⠀⠀⠀⠐⣤⠇⠸⢿⠀⠂⠔⣿⣟⡠⠞⣷
⠀⠀⠀⠀⠀⠀⢸⡰⡆⠀⠀⠀⠀⢀⣶⡶⠀⠀⠀⠀⣳⡜⠀⠀⢘⡁⢠⡦⠀⡀⠀⠸⡆⡾⠀⠣⠈⠠⣼⣿⠟⠁⠀⣠⡇
⠀⠀⠀⠀⠀⣴⡾⠀⠀⠀⡀⠀⠀⠚⡉⠀⠀⠤⡄⠀⡶⢰⡖⣠⡜⠃⠀⠁⠘⢇⣠⡴⠇⠽⢤⣀⠀⡇⠿⢃⣤⠶⠋⠁⣿⠀⢸⡀
⠀⠀⠠⠁⣿⣿⠟⢉⡁⢈⣯⡠⠰⡿⠇⠀⢀⣶⡇⢠⣧⣼⡅⠘⠀⣤⣼⡟⣴⣿⣁⣀⣀⣀⣤⡬⠷⠁⢴⠛⣵⠀⣀⠴⠀⢀⣎⢸⡄
⠀⠀⣇⢰⣏⡩⣶⢁⠀⡂⠀⡱⣤⠁⠸⠿⠤⠙⠁⡞⠁⠈⣧⠀⠀⠏⠙⠃⣾⣅⡀⣀⡀⣀⡄⡠⣾⣷⠈⢆⣿⠊⢉⠄⠀⢘⡁⢀⣙
⠀⠀⠸⡢⣿⣧⡜⢂⣉⠔⣤⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡀⠀⠀⠀⢻⣯⣽⣯⣼⣧⠯⠻⢿⠇⠀⠀⠡⣔⠉⠀⠀⣫⡀⢀⣈⣇
⠀⠀⠀⠘⠻⢿⡿⠧⠁⠈⠔⠁⠀⠀⢀⣼⣤⣀⣀⠀⠀⠀⠀⡟⢃⠀⠀⢀⠀⠙⠶⣶⠶⠖⢒⡾⠋⠀⠀⠀⠀⠀⠀⣠⣾⣯⣥⣤⣤⣭⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣏⠉⢄⠀⠀⢰⠃⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠂⠘⣧⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠌⡌⠐⠀⠆⠱⠈⠆⡆⠀⢘⠀⠠⠋⠰⠈⠀⠘⢠⠁⠚⠛⢠⢰⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⢀⠀⠀⣸⠀⠘⠛⠛⠛⣧⠀⢰⡆
⠀⠀⢀⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⢠⠄⣀⠀⡀⠀⡄⢠⠀⠲⠈⠁⢀⣿⡇⠀⢠⣤⣄⠈
⠀⠀⠈⣡⡤⢠⠄⠀⣴⡇⠀⠀⠀⠀⠀⢠⡄⠀⡤⡀⢄⠀⠁⠀⠁⠀⠀⠀⠀⠀⣸⣿⣿⠀⠹⠿⠟⠀⠀⢀⣄
⠀⠀⠀⠀⠰⠈⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠰⡿⣄⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠉⠁⠈⠉⠀⠁⠡⠶⢿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠐⡅⠀⢠⠃⠀⠀⠃⠈⢀⣴⣷⡀⠛⠛⢁⣀⣀⡀⠀⢀⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠑⢸⠘⠀⠀⠐⠰⠾⣿⡿⠆⠀⠀⠀⠀⠈⠀⠈⠁⠀⠐⢛⡉⣉⢳⡀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠻⠀⠀⢀⣀⠀⠀⢠⣈⣠⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠖⢳⡆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠈⠀⠀⠀⠀⠀⠙⠀⠀⠘⠖⠃⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⢀⣠⣶⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠠⢄⡒⠀⠀⠸⠀⠀⠀⠚⠁⠀⠛
⠀⠀⠀⠛⠛⠿⠇⠀⠛⠋⣤⡶⠀⡀⠀⠀⠈⠥⠀⠘⠂⠀⠀⢄⡐⠀⠀⠀⠸⡀⠀⠀⠀⡀⠀⠀⠛⠀⢀⢀⣀
⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠉⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⡀⠀⠀⠁⢀⠀⠀⠀⠛⠛⠛⠃
⠀⠀⠻⣿⣿⣿⣄⠀⠀⣶⡄⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⠀⠸⠇⡌
⠀⠀⠀⠻⠿⢿⣿⡷⠾⠛⠀⠀⢨⣯⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⡎⠀⠀⠀⣌⠀⠤⠀⠀⢠⡄⣬⠀⠀⢠⡆⠅
⠀⠀⠀⠈⠁⠈⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉

⣀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠿⠿⣿⠿⠗⠀⠀⠀⠀⠉⠀⠀⢀⣴⣄⠀⠹⠇⢀⡀⠀⢰⣿⣿⣷
⣿⡀⠀⠀⣿⣿⣿⠄⠀⠆⠀⣴⡁⠀⠀⠀⣾⣿⣷⠄⠦⠀⣾⣿⣿⠆⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⠀⠉
⣿⣷⡀⢴⣿⣿⣿⣧⠀⠀⣼⣿⣷⡀⠀⣠⣿⣿⣿⡄⠀⠰⣿⣿⣿⡷⠀⢀⣄⣀⠺⠿⢿⣿⠿⠟⠂
⠻⠋⠁⣼⡿⣿⣿⣷⠀⢀⣼⣿⣷⡀⠀⣹⣿⣿⣿⡏⠀⠼⠿⣿⠿⠿⠄⣹⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⢈
⠀⠠⠄⠀⠀⠙⢠⡄⠀⢉⣿⣿⣿⡉⠀⠛⠛⣿⠛⠛⠂⣄⢠⠘⠀⠀⠰⣿⣿⣿⠧⠀⠉⣀⠀⠐⢻⣤⡞
⣤⣤⣤⠄⠀⠀⣾⣿⡀⠚⠛⣿⠛⠛⠂⠀⠀⠉⠀⣸⡄⣏⢹⠀⣼⡆⠼⠿⣿⠟⠷⢀⣾⣿⣷⡀⠿⠛⣿
⠿⢿⢿⠀⠀⣼⣿⣿⣧⠀⠀⠉⠀⢦⡼⣆⠀⠃⢠⣿⣧⠈⠉⣸⣿⣿⡀⠀⡉⠀⠀⣸⣿⣿⣿⡇⠀⠀⣿
⠀⠸⢸⠀⣰⣿⣿⣿⣿⣇⠀⠋⠀⣾⡿⠉⣀⠀⠛⢿⠿⠓⢰⣿⣿⣿⣷⠀⠉⠀⠰⢿⡿⣷⣿⡿⠆⠀⠏
⠀⠀⣰⡀⠛⠛⢻⡿⠛⠋⠀⠀⠀⠙⠶⠿⢫⣾⣿⣄⠀⢀⣿⣿⣿⣿⣿⣇⢰⡆⢰⣿⣿⣿⣿⣿⡆
⠀⣰⣿⣷⡀⠀⡀⡀⠀⠀⣴⣶⣶⡀⠀⠀⢿⣿⣿⣿⠆⠀⠀⠉⠻⠉⠁⠀⣾⣷⡀⠀⠀⠟⠀⠀⠀⠀⠈
⠀⣹⣿⣿⡉⢰⡍⣵⠀⢈⣿⣿⣿⡅⠀⣰⣿⣿⣿⣿⢧⠠⢶⣀⡴⠃⠀⠾⢿⡿⠷⠀⢀⡄⠀⣼⣶⣶⡀
⠴⣿⣿⣿⡿⠆⠉⠁⠀⢾⣿⣿⣿⡿⠄⣹⣿⣽⣿⣽⣯⠀⣾⢿⣷⣀⣁⠀⢀⡀⠀⢠⠀⠀⢠⣿⣿⣿⡄
⣰⣿⣿⣿⣷⣄⠀⠂⢀⣾⣿⣿⣿⣷⡄⠛⠛⢻⡟⠛⠛⠃⡄⠀⣿⣿⣿⣿⣿⠀⢠⣿⣧⡀⢻⣿⣿⣿⡟
⠀⠀⢻⠁⠀⠀⠀⠀⠈⠁⠀⢿⠀⠀⣄⠀⢄⠈⠁⢀⠀⢀⣿⡀⡟⡇⠀⢸⢸⠀⣠⣿⣿⡀⠟⠛⣿⠛⠛
⠀⣧⠀⠀⠂⣰⣶⣶⡀⠀⠃⠀⠀⠀⣸⣶⣏⠁⠀⣀⢀⣾⣿⣧⠀⠁⠀⠈⠈⠘⣻⣿⣿⡛⠀⠀⣉⠀⠤
⣼⣿⣆⠀⠀⣽⣿⣿⡏⠀⣶⣶⣶⣶⣿⠋⠙⠁⢠⣿⣎⠙⠟⠉⠁⢠⣾⣦⡀⠘⠛⢻⠛⠛⠂⣴⣿⣷⡀
⠻⡿⠟⠂⢾⣿⣿⣿⡿⠄⡟⡟⠛⢻⣿⠀⠀⠐⢻⣿⣟⠂⠀⠀⢰⣯⣿⣿⣷⡀⠀⡈⠀⠀⢠⣿⣿⣿⡅
⢠⡄⣀⠀⣼⣿⣿⣿⣿⣄⠧⠃⣤⠘⠟⠀⢀⣠⣿⣿⣿⣦⡀⠀⣴⢿⣷⢿⣿⣄⢰⡟⣳⠀⣹⣿⣿⣿⣏
⢾⣽⡅⠈⠁⠀⢹⠁⠀⠀⠀⣸⣿⡆⠀⠤⠀⣰⣿⣿⣿⣆⠀⠸⣿⡿⣿⣿⢿⡿⠀⠓⠃⡄⠉⠉⢿⠉⠉
⣤⣙⡟⠀⠐⠂⠀⠀⠀⠀⢰⣿⣿⣿⡄⠀⠘⠋⠉⣿⠉⠉⠃⣰⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢀⣜⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠔⣠⣤⠊⣠⠀⠀⣨⡕⢶⣤⠤⣤⠣⠁⢨⣄⡀⢀⣀⣀⣀⣀⡄⢀⣀
⠀⠀⠀⠀⠈⢢⡉⠠⠈⠻⣄⠀⠙⢆⠀⠐⡄⠈⠉⠓⠀⠀⠀⠈⢰⢧⠀⠈⠀⠐⠈⠒⠀⡀⠀⠈⠁⠉⢸
⠀⠀⠀⠀⠀⠂⢀⣀⠈⠉⠀⠀⠁⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢶⡦
⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡄⢃⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠁⠀⢀⡀⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠬⠥⠴⠤⠤⠴⠧⠤⠴⠾⠄⠀⣶⣾⡄⠀⠀⠤⠔⠒⡲⢀⠾⣆⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠅⠀⠀⠀⠔⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢀⣀⣀⣴⣤⣉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⠛⠛⠻⢿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⢸⣿⠏⠀⠀⠀⠀⣠⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣿⣿⠀⠲⣦⣠⡾⠁⠀⢨⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀⠈⠋⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡍⢿⣿⣶⣶⣶⣾⣿⠏⠁
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢡⣦⣤⡌⠙⠋⣤⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢿⡟⠀⠀⠀⠈⢿⡿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣠⣿⡇⠀⠀⠀⠀⠀⡇⠰⠖⠘⡸⢙⡤⢤⢐
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠙⠋⠀⠀⠀⠀⠘⠐⠻⠈⠒⠀⠱⢎⣀⢒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢧⠀⠀⠀⠀⣰⣀⡀⢠⡴⡴⢤⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠖
⠀⠀⠀⠀⠀⠀⠀⣿⣾⢿⣽⠀⠀⠀⠀⠩⠸⠿⣿⡖⣲⡀⠿⡗⠳⠗
⠀⠀⠀⠀⠀⠀⣴⣯⣿⠿⣷⠆⠀⠀⠀⢴⣶⢶⡂⣟⣸⣶⣶⡶⠲⠶⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠀⡀
⠀⠀⠀⠀⠀⠐⣿⣯⣿⢿⣿⣾⠄⠀⠀⢸⡿⣢⣴⣷⣶⣶⣶⡔⠤⠖⠀⠀⠀⠀⡼⠀⠀⠀⠔⠀⡰
⠀⠀⠀⠀⠀⣼⣹⣹⣿⣿⢻⣿⣦⠀⠀⠐⣪⣼⣿⣿⠟⢻⣿⡇⠄⡀⠀⠤⠀⠈⠑⠀⢀⣴⠃⢀
⠀⠀⠀⠀⢠⣟⣻⣿⣿⢿⣿⢿⡾⢀⠀⠈⠁⠐⣿⠁⢀⡈⢻⣇⠈⡇⢀⡰⢄⣠⣦⣾⢟⠋⢀⠄
⠀⠀⠀⠀⡷⣿⣿⣿⡏⠈⣹⣗⣿⠟⠢⣤⡀⠈⡿⡬⠿⠧⣿⡇⠀⠃⠀⠀⠈⠀⠁⢸⠁⣆⠊⣀⡀
⠀⠀⠀⠀⢛⠻⠁⢘⠟⢱⡏⠛⠀⡟⢰⡄⢀⠠⡴⣦⣾⡧⠾⠭⣦⠀⠀⠀⠀⠀⠀⠈⡇⡃⠀⠈⣤⠰⡃
⠀⠀⠀⠀⢷⡤⠀⣰⠀⠈⠀⢀⣿⡟⣾⠁⣸⡇⠠⠾⠿⠷⠶⠶⠶⠶⠺⠁⠀⠂⡤⠈⠁⠀⣿⠀⢻⠞⣧
⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠉⠀⠉⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠦⠉⠉⠟⠛⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⠶⠆⠀⠀⠀⠀⠀⠀⢀⣖⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠓⠲⠶⠄⠀⢂⣬⢆⣀⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢀⠰⣝⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢀⣤⣶⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠉⠛⠛⠷⠶⠤⣤⣤⣀⠀⠀⠀⣀⣤⡶⣉⡙⠒⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⡀⠀⠀⠀⠂⠄⢀⠈⠉⠙⠓⠶⠻⠭⣬⣉⣛⢳⣦⣄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠿⣶⣦⣤⣝⣒⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠉⡉⠙⠛⠻⢷⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠉⠛⠻⠿⣿⣿⣷⣶⣦⣤⣂⣄⠀⠐⠂⠤⣄⣀⣀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠉⣹⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣖⣟⢲⡀⢦⡍⣉⠋⠉⠛⠛⠻⢿⡷⣶⣶⣦⣤⣅⣈⠁⠐⠂⠀⠀⠀⠀⢀⡾⠃⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⡲⠿⠌⣹⣞⢷⣿⡀⣞⠳⡄⢠⣄⡀⠙⠓⠿⢿⡿⢿⣶⣶⣤⢤⣴⣿⠃⠀⢤⡀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⢤⣤⣙⡃⠘⠧⢿⠎⢷⠻⣄⢟⢳⡄⣤⢤⡀⠉⠉⠃⠙⢻⣧⠐⠈⢆⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⠦⢬⣅⣉⣀⠀⠹⠈⠉⢿⡌⣯⢳⡀⠈⢻⣆⠐⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠤⣅⣘⡋⠳⠀⠀⢻⣆⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠲⠿⠟


⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠄⠀⣀⡄⢀⡉⠉⣉⣉⡁⠉⢐⣒⡒⠒⠒⠒⠒⠂⠤⠤⠄⠠⠤⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⣤⠶⢛⣿⡟⢁⣤⠾⠧⠖⠋⣠⡾⠯⠴⠛⣰⣿⣍⣹⠟⢀⣴⡟⠙⣦⠀⢰⣦⠀⣴⣤⢀⣤⡤⠄⠉⢩⣭⣭⣍⡈
⠀⠀⣀⣀⣉⣀⣀⣈⣉⣀⣉⣁⣀⡀⠀⠚⠁⠀⠀⠀⠰⠟⠀⠠⡿⠀⢻⣿⣀⣴⡟⠀⠘⣿⣶⣿⠃⢸⣿⡷⠒⠀⠘⣿⣆⠈⢿⣦⡀
⠈⠉⠈⠉⠉⠉⠉⠉⠉⠉⠐⠒⠈⠩⠍⠉⠛⠛⠓⠛⠛⠿⠿⠷⠷⢶⣶⣶⣯⣥⣤⣤⣤⣉⣙⣁⣀⣈⣙⣛⣛⣒⡀⠛⠻⠶⠟⠛⠃
⢀⣀⣀⣀⢀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠉⢉⣉⡙⢛⠛⠛⠛⠻⠛⢛⠓⠒⠲⠶⠦⡤
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀
⠀⠀⠀⠋⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠐⠄⠃⠔
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠭⢹⠀⠀⠀⢘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄⠀⠀⠀⠀⠀⠄⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠹⠒⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠀⠀⠀⢰⠄⠀⢀⠀⠀⠠⢠⠀⠀⠀⢀⠀⢸⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠐⠀⠀⠀⠀⠠⠉⠀⡀⠀⡄⠀⡀⠘⠀⠀⠘⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⢀⡈⡴⢶⡎⣀⠀⠠⠄⠀⠔⠁⠑⠄⠀⠁⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡙⡚⠣⡀⠀⠀⠀⠀⠢⠀⠠⠃⠀⠀⠀⠀⠁⠀⠀⠲⠀⣨⠡⡠⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢴⣟⣳⠡⠠⠤⠀⠀⠀⠀⠀⠁
⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡄⠀⠀⠀⢀⠀⠀⣠⠐⠫⠁⠃⡄⠀⢠⠀⢀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢃
⠀⠀⠀⠠⢔⡀⠄⠀⠀⠤⠀⠌⢢⣀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠐⢨⢇⠜⡕⠂⠀⠀⣀⠀⠀⠈⠑⠀⠀⠀⠠
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹⠄⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡁⠀⡱⠒⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⡀⠈⡂⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠂⠀⠀⠂⠖⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⠄⠛⠈⠐⢂⣀⣼⠯⣼⡀⠀⠌⠁⠀⣸⠆⠐⠴⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢧⠄⣤⠀⠐⠎⠀⠀⠳⠀⠈⡁⠀⢀⡴⠔⠀⠈⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣍⠀⠀⠛⠀⠀⢰⠂⢂⠩⡀⠀⠠⠀⠀⠰⠉⠂⢀⢓⠀⠀⠀⠀⠀⡁⠀⠀⠐⠘⠳⠦⠄⢀⠔⡀⠀⣠⠀⠀⢀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠰⠄⢊⠀⠂⠀⡇⠂⠁⣶⣀⠀⠠⠀⠀⠀⢠⠀⡀⠀⠐⠒⢦⣀⠀⠀⢀⡀⠀⢀⣀⡀⠼⢇⣀⡀⣈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡏⣠⣄⠈⠀⠀⣰⣾⠉⠀⠐⠠⡄⠦⠀⠀⠀⡠⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢸⡆⠈⡁⠁⠈⡠⠊⠁⠈⠑⠀⠀⢀⢁⡀⠋⠈⠩⠁⠀⠀⠥⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠈⠂⠀⠀⠀⠅⡆⠀⠀⠀⠥⠀⠀⠄⠄⠀⠀⢤⡀⠠⠀⠀⠀⠀⠁⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠒⠶⠦⣠⢀⠀⣡⡈⠀⠀⠀⢀⠀⣀⠀⠃⢀⠀⠀⣰⣀⠀⢀⡀⠙⠆⠀⠀⠀⠀⠧⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠆⠆⠈⠋⣃⠉⠀⡀⢰⡟⠀⠁⠀⢀⠍⡀⠊⠁⠀⠀⠚⠄⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠠⣗⠀⠀⠀⠀⠀⢭⡀⠰⠛⠸⠇⠀⠀⠀⠉⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⢠⢠⡖⠡⣄⠠⠀⠙⡠⠀⠀⠈⠪⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⡄⠐⢶⠀⠱⠆⢸⠂⠀⠀⠉⢈⡁⠂⣴⠆⠀⠀⠐⠲⡈⠀⠐⡊⠄⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠤⣁⣀⣀⣀⠀⠀⠀⠀⢧⡀⠈⠫⠁⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠉⠙⠛⡦⠴⠖⠒⠋⠀⠀⠀⢠⠀⠀⠠⠐⠀⠀⠂⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠂⡀⢉⠴⠡⠄⠀⡠⠀⠑⠄⠀⡀⠀⠈⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠄⠀⠀⠀⡤⠀⢀⡀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠿⠀⠄⠀⡁⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠈⡄⠁⠀⠄⢦⡰⠀⠙⠂⠉⠀⠴⢠⡀⣀⠀⠚⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣈⠀⢢⡀⠀⠀⡀⣘⡄⠀⠀⠀⠀⠀⢆⡇⠀⡀⠀⡀⠸⠋⠶⠆⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠒⡐⠋⡉⠉⠐⠉⠑⢳⣦⣴⣤⣚⡉⠀⠀⢈⡁⢆⠀⠀⠀⡅⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠈⠋⠔⡲⠦⠄⢸⣇⢧⠙⡇⠐⠀⠉⠀⡈⡗⢀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠂⠀⠀⠀⠀⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⣄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⣀⣤⠶⠂⠐⠁
⠀⠀⠀⠀⠀⠀⠤⠤⢀⢀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡔
⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠄⡀⠂⠀⠄⠀⢀⠀⢘⡀⠀⠀⠀⡠⠀⠀⠨⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠊⢁⡀⡋⠁⠀⠈⠂⠀⠀⢠⠃⠀⠀⠉⠀⢤⠈⠀⠀⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⢄⠀⠀⠀⢐⢯⠀⠀⠀⠀⠖⠀⠀⣀⠀⠐⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣶⣾⣧⣜⢦⠀⠀⣞⠀⣬⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠁⠀⠀⠀⠈⠙⢦⣠⠻⣧⣾⠇⠀⠀⠀⠀⡀⠀⠠⠂⢀⠀⠀⠀⠺
⠠⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠇⠀⠀⠀⢰⣧⣼⡦⢿⣦⣼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠠⠀⠀⠀⠀⠁
⠀⠹⢄⠀⠀⠀⡄⠀⢳⠀⠀⠀⠀⣠⡆⠀⣨⣍⣭⠖⣩⡿⠉⠀⠀⠀⠀⢀⠀⠀⠀⣀⠶⠁⠀⠀⠐⠁
⠀⠀⠀⠛⠢⡈⢧⠀⠘⠀⠀⠀⠀⠉⢃⠀⠙⠛⢿⣶⣿⡇⠀⠀⠀⢀⠔⣙⣀⡚⣀⢠⠀⠀⢀⣠⡦⣉⣠⠊
⠠⡄⠀⢀⠻⣤⠿⠗⠀⠘⠄⠀⠀⠀⠀⣠⠋⠀⠀⠀⢸⡷⠀⣠⡴⠟⠛⠛⠙⡁⠉⣠⣦⣴⣿⢿⠔⣠⠃
⠀⠀⠀⠀⠄⠻⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢠⡄⣦⡀⠸⢿⠟⠢⢀⠀⠐⠗⠀⠻⠛⠋⣹⣿⡿⠀⢀⡿⠤⠄
⠀⠀⠀⠄⠈⠂⢒⣇⠀⠀⠀⠠⠀⣼⣷⠄⠘⠿⠟⢹⣶⣿⠂⠀⠀⠀⠀⠀⠠⡀⠀⠀⠸⡟⢐⠀⠈⠁
⠀⠀⠀⠀⠐⠌⣻⣿⣦⡀⣠⢤⡾⠋⠀⠀⠀⣶⣤⣷⡟⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⡤
⠀⠀⠀⠀⠀⠀⠀⠹⣍⡻⠦⠈⠁⠐⠒⠀⠀⠈⠉⠉⣶⣤⣿⠀⠀⠀⣀⠀⠀⠠⠐⢀⠀⠀⠀⠝
⠀⠀⠀⠀⠀⠀⣶⡿⠃⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢠⡞⠉⠁⠀⠀⠀⠛⢠⣤⣀⠀⠀⠙⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠁⠀⢸⡟⡤⠄⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⠣⣀⣀⡈⢒⠀⠐⠀⠀⠀⡀⠀⠊
⠠⠒⠂⠀⣰⠏⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠂⡾⠀⢀⣄⣶⣤⣀⣦⢀⡾⠁⡌⠸⠛⠉⠠⠘⠋⠀⠀⠄⠘
⠀⠀⠀⠐⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢈⣻⡿⠍⢻⣿⡊⠀⠀⠀⠊⠁⠠⢄⠀⡠⠒⠀⠉⠛
⠀⠀⠀⢇⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⡁⣨⡴⠚⠍⠉⢐⠦⣄⠈⠑⢦⡀⠀⠤⠒⠉⠉⠑⠒
⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠍⠀⢾⣦⡷⠻⣾⡿⠀⠀⠀⠁⠀⠢⣤⣞⡁
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠷⠲⢤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⢠⣶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢬⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠀⣷⡇⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⢀⡀⠀⣿⠇⠀⠀⠀⠀⠀⠤⠄⣼⠇
⠀⣶⣶⡾⠿⠿⣿⣿⠀⠀⠀⣿⡿⢷⣶⣶⣤⣤⠀⢀⣀⣠⣤⣤⣶⣧⠀⠀⠀⣿⣿⠿⣿⡿⣿⣷⠀⠀⢰⣿⣿⣶⣦⣤⣀
⠀⣿⣿⣶⡆⣿⣿⣿⡆⠀⢸⣿⠇⠺⠿⢩⣿⡇⠀⢻⣿⣿⢉⡹⣿⣿⡄⠀⠀⣿⣿⢠⡹⡇⣿⣿⠀⢀⣾⣿⠁⠟⣋⣽⣿
⠀⣿⣿⣿⣇⣿⣿⣿⡇⠀⣿⣿⣰⣿⡇⣼⣿⠀⠀⠘⣿⣿⢈⣣⣌⣿⣧⠀⠀⣿⣿⣸⣷⣀⣿⣿⠀⣸⣿⣇⣶⡆⢻⣿⡏
⠀⠸⠿⠿⠿⠿⠟⠛⠃⠀⠉⠙⠛⠛⠿⠿⡏⠀⠀⠀⢿⣿⣾⣿⠿⠿⠛⠀⠀⠛⠛⠛⠛⠛⠛⠃⠀⠈⠉⠛⠻⠿⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡆⠀⠀⠀⠀⠀⠀⠀⢰⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⣤⣤⣤⠀⢀⣤⣤⣤⣤⣤⣾⡅⠀⢠⣤⣤⣤⣶⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣏⢻⠟⣻⣿⠀⢸⣿⠏⣥⣬⠙⣿⡇⠀⠀⣿⡏⢻⣿⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣾⣿⣿⠀⠘⣿⣆⠻⠿⢃⣿⡇⠀⠀⣿⣷⠸⠿⢃⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠾⢿⣿⡏⠀⠀⣿⣿⣷⡾⠿⠿⠷⠀⠀⢿⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⣠⡿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢲⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⢰⡿⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⠇
⠀⠀⠀⠀⠀⢠⣶⣿⣿⣾⡏⠀⠀⣿⠃⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣏⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢰⣟⣜⣡⡀⠀⠀⣴⠾⠿⣿⣿⠀⢸⣿⡶⠾⣷⡄⠀⣾⣋⣉⣩⡿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢀⣼⡏⠉⢹⣿⠀⣼⠏⠀⢠⣿⣿⠀⢸⣿⠀⠀⣿⡇⠀⣿⠏⢻⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣆⣀⣴⠟⣿⡇⠀⢸⡟⣠⣿⣄⣠⣿⢻⣿⣤⣾⣿⠀⠀⣿⣦⣾⣿⠀⠀⣿⡇⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠁⠸⠿⠇⠀⠸⠿⠋⠈⠛⠛⠁⠈⠛⠋⠘⠿⠀⠀⠛⠋⠸⠟⠀⠀⠛⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⣶⡆⠀⢀⡴⣶⣦⡄⠈⣷⡆⠀⣰⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⠁⢠⡟⠀⠉⢹⡇⢠⣿⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣸⣿⢀⣾⣇⠀⣠⡿⠁⢸⡇⣰⠟⣿⡀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣻⡿⠋⠈⠛⠟⠋⠀⠀⠘⠛⠋⠀⠘⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣴⠟

⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⣄
⠀⠀⠀⠀⢰⣿⠭⠵⠖⠲⣌⡷⣄
⠀⠀⠀⠀⢸⢫⠄⠀⠚⠛⢻⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣿⠀⠞⠂⣉⣉⠙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⢁⣀⣀⣀⣠⡴⠊
⠀⠀⠀⠀⡇⠀⠀⠐⠻⣭⡼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⡇⢰⡂⠀⠀⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⣀
⠀⠀⠀⠀⢷⡈⠙⢛⣯⡵⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠰⣫⠿⠭⠋⠁
⠀⠀⠀⠀⠈⣇⢀⠀⠈⠘⣆⠻⡄⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠙⠛⠾⣷⡶⣄⠀⢤⡀
⠀⠀⠀⠀⠀⣿⠀⢷⡀⠀⠈⠃⠹⣦⡀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⡀⠹⣦⡀
⠀⠀⠀⠀⠀⣿⠀⠈⢧⠀⠀⠀⠀⠈⠻⣦⡿⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡈⠻⣦⣀
⠀⠀⠀⠀⠀⣿⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⠻⣶⣀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⠳⣄⠉⠛⠛⠒⠒⠒
⠀⠀⠀⠀⠀⢻⡰⡀⠘⣽⢦⠀⠀⠀⠀⠀⠀⢹⡍⢷⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⡇⣸⠀⠛
⠀⠀⠀⠀⠀⠘⣧⠫⠀⣿⠙⠿⠟⠂⠀⠀⠀⢨⣷⢾⠠⢤⣤⣤⣤⠞⠋⣠⣴⠄⠀⣧⡏
⠀⠀⠀⠀⠀⠀⠸⣆⠀⠹⣆⡀⠀⠀⠀⠠⠴⠚⠸⡇⠀⠀⠀⠀⣀⢄⡰⡝⠁⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠨⡉⠛⠛⠒⠒⠀⠀⠘⢁⡼⠀⠀⠀⠀⠑⠒⠺⠀⢀⣼⠋⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠘⢦⣀⣀⣀⠀⠔⠋⠉⠀⠀⠀⠀⠀⢀⣀⣤⡴⠟⠁⠀⠈⠙⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣬⣉⢁⣠⡴⠶⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⢰⣦⠀⡟⢦⣠⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠑⣤⡭⠧⣧⡚⠁⠀⢹⠁⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠲⣦⣄⡀⢇⠀⢰⠍⠀⠀⠀⠙⢆⠀⠀⠀⠀⢨⡦⡴⢤⣀⣀⢀⣀⠤⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠓⠦⣀⠀⠈⢇⠈⢻⣄⣸⣆⠀⠀⠀⠀⠈⠀⣄⣆⣠⠋⠀⠀⠀⠋⠘⢿⣇⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⣾⣧⡴⠚⠿⣿⣿⡿⠿⣄⣖⠙⠢⣄⠀⠉⠛⢿⣦⡀⣠⠖⠛⠛⠻⣿⠓⠒⠲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⡿⠁⠀⣠⠿⣯⠄⠀⠘⠫⠿⢶⢤⣿⢿⣇⠀⣠⣄⣠⣾⣥⠴⠚⠋⠉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠛⢷⡀⠀⠀⠇⠀⠞⠁⠀⡼⠷⢖⣰⣋⠙⢻⡀⠁⠀⠈⣾⠃⠀⠈⠛⠖⣤⣴⡊⠉⣻⠟⠉
⠀⠀⠀⠀⠀⢀⣠⣤⠒⣾⠀⠀⠀⠀⠀⠁⠐⢓⡀⠀⣀⡤⠾⢧⠀⣜⠉⠉⠉⢢⠱⣄⠀⢀⡎⠀⠠⠄⠀⠈⠉⠛⣇⠴⠁
⠀⠀⠀⠀⠀⠈⠉⢉⣲⣿⣄⣀⡠⠲⡤⣥⣚⣛⣉⠵⠿⠀⠀⣰⠋⣹⣤⠶⣦⣸⣶⠿⣶⣿⣦⠀⠀⣀⣠⣤⣤⣴⣧⠤⣀⡀
⠀⠀⠀⢀⣤⣴⣞⣁⠬⠿⠛⠛⢣⡄⡠⠋⠁⠀⢀⠀⠀⢀⡾⠁⠀⠙⢦⣴⠄⠌⠃⠲⣶⣾⠻⡏⠉⠁⠀⠀⠹⣿⣏⣀⣀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠦⠔⠋⠉⠓⠋⠀⠀⠀⠀⠀⠙⠶⢦⣖⡆⠄⣅⣸⡧⠀⢀⣀⠀⠀⠀⣽⣿⣿⣋⠉⠉⠉⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠾⠿⢤⡀⠀⢘⡇⠀⠀⣿⣿⣯⠛⠻⣕⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠧⠴⣾⣿⣿⣷⡀⠀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠌⢿⡌⠙⠒⠒⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣀⠀⢀⣀⡀
⠀⠀⠿⠯⢠⣾⣧⡀⠐⠀⠀⣾⠁⢨⡷⠀⣴⢒⣦⠀⢉⡀⢰⢿⠂⣰⡿⣛⠻⣇⠀⡞⠀⠈⢳⠋⠀⠙⡆
⠀⠀⠀⣰⣿⡟⣿⣷⡀⠀⠀⠹⢤⣀⡀⠀⢻⣌⣉⢰⠫⣽⠂⠀⠀⠹⣷⣭⣾⡏⠀⠳⡀⠀⢺⠀⠀⡸⠃
⠀⠀⣴⣿⣷⡅⣥⣿⣿⣄⠀⣶⠆⢨⠟⣉⠉⠉⡉⠙⢳⡀⠀⠃⠀⠐⢶⠭⠶⠆⠀⠀⠙⢦⣸⣠⠞⠁
⠀⠈⢉⣽⡿⠇⡿⣿⣏⠉⠀⡀⠀⠘⠦⠿⠀⠀⣉⣀⣰⣧⣄⣀⣀⡘⠻⠖⠿⠃⢀⣤⡀⠀⠙⣡⡶⣤⡀
⠀⠠⠾⢿⣿⡆⣾⣿⡿⠧⠀⡁⢀⠀⠀⣀⣶⣀⠙⣿⣿⣿⣿⣿⡿⠟⠀⠄⠀⠀⠈⠛⠃⠀⠸⣕⡿⣫⡇
⠀⠀⣠⣿⣯⡃⢋⣿⣷⡀⢸⣎⣹⡁⠐⣺⣿⣗⠂⢸⣿⣿⡟⠁⠀⢠⡄⢶⢦⣤⠀⠸⣿⠟⠀⢉⣉⠉
⠀⠐⢛⠛⠛⣷⡟⠛⠛⠛⠈⠑⣋⡁⠀⠀⠛⠀⠀⢸⣿⣿⣧⠀⢸⡗⢠⣶⣦⠐⣷⠀⠀⠀⣰⢿⣿⡷
⠀⠀⣉⠠⡄⢉⠁⠀⣠⡀⠠⣾⣿⣿⣆⠀⠀⠙⠀⢸⡿⡟⡿⣧⠘⢫⡄⣩⣡⣬⠋⠀⢼⣿⣇⣠⡿⠃
⠀⢠⣭⡷⢳⣯⣄⠘⠿⠏⠀⠘⢿⣄⣸⣿⣯⠄⢀⣿⡁⠀⠀⣽⣧⠀⠀⠉⠁⠀⠀⠄⠀⠀⠉⣉⠀⢠
⠀⠀⠴⢋⡏⠳⠀⠀⢀⠀⠀⢀⣀⣉⣉⣉⣤⣶⣿⡿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣦⠀⠀⢀⣼⣿⣦
⠀⠀⠀⢠⣤⡄⠘⠁⠘⢷⣾⣿⣿⣿⠿⠻⣻⣿⡃⠀⢐⣻⣿⣿⡿⠛⠉⢀⣿⠏⣿⡆⢠⣾⣯⣩⣿⣷⡀
⠀⢰⣿⡟⣙⢻⣷⠄⠀⢸⣿⣿⣿⣧⣀⢀⢸⣿⣷⣦⣷⣿⡿⠋⠀⠘⠃⢸⡿⠀⣿⠇⢀⣼⣿⢙⣿⣧⡀
⠀⠀⢽⣧⣭⣾⡏⠀⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣁⡤⢤⣀⠀⣰⡞⠁⣴⠟⠀⠀⣼⣟⠛⣿⣇
⠀⢰⣶⣭⢀⣭⣶⡆⠀⢰⣿⣿⣿⣿⠋⠉⠀⣠⣀⠀⡼⢃⢮⣷⡂⢧⠈⡀⠀⢡⡀⠀⠈⠉⠉⡿⠉⠉⠁
⠀⠈⠻⠿⠿⠿⠛⠀⢠⣿⢣⣿⡟⠁⠖⠀⠀⠛⠋⠀⠸⣆⡛⢟⣂⠏⠈⠁⣰⣿⣿⡄⢀⡄⠀⠠⡞⢳⠄
⠀⠀⠠⠀⠀⠒⣠⣴⡿⠃⣼⡟⠀⣰⠚⣶⣴⣾⣶⡀⠀⠀⣍⢉⠀⠀⠀⠐⣿⣧⣾⡟⠂⠀⢀⡀⢉⠉
⠀⢠⡶⣲⢶⣰⡿⠋⣠⣾⠟⢁⠀⠹⣾⣿⣿⣿⡿⠀⠐⢶⡿⢻⡷⠂⠀⠰⣿⣧⣾⡿⠂⠐⠶⢟⡻⠶⠂
⠀⠸⣞⣿⣳⠇⠀⠀⡿⠋⠐⣏⣱⠀⠘⢿⡿⠋⠀⠆⠐⠛⡿⢿⠛⠃⠀⠰⠛⢧⡾⠿⠂⠐⢋⡶⢾⠙
⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢰⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⢁⠉⠑⢀⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣹⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⣎⣁⣰⣷⣿⡆⠀⠀⠀⠀⠀⣽⣿⣿⣛⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠟⠀⢠⣆⠻⢿⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⢿⣿⢿⠀⠀⠀⠀⠀⠀⠉⣿⣟⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣤⡉⠣⣤⠂⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣼⣿⣿⣿⣧⠁⠀⠀⠀⠀⠀⣀⠀⠈⠉⠉⠁
⠀⠀⠠⡎⠈⠂⠀⢸⣿⡿⣿⡻⢿⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠨⠁
⠀⠀⠈⡇⠀⠀⠀⢸⣾⣟⢎⢱⡿⠓⡶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠐⠀⠠⠞⠉⠙⠛⠉⢲⡔⠀⡑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠛⠻⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠂⡞⠉⢄⣀⣤⣼⡿⠟⠋⠻⣽⣷⡀⠀⠀⠘⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠢⠑⠜⠿⠷⠤⡶⠀⠀⠀⠀⠀⠀⠀⠈⠒⢲⣿⣿⣿⡿⠁⠀⠀⠀⠀⠘⣿⡇⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠙⠀⠀⠀⠀⠀⠀⠁⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⢰⣿⠃⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠸⠟⠀⠀⣠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟⢀⣀⡀⠀⣠⣶⣄⢰⣿⣿⣿⡿⠛⣡⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠏⢀⣿⣿⡿⢠⣿⣿⡟⠘⠛⠋⣥⣶⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡄⣼⣿⣿⠃⣾⣿⣿⢁⣾⣿⣦⢹⣿⠟⣋⣥⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⢰⣿⣿⡟⢸⣿⣿⡏⣸⣿⣿⠇⣨⣴⣾⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠻⣿⣿⣿⣿⠃⣿⣿⣿⢁⣿⣿⡿⢠⣿⣿⡟⢠⣶⣦⡙⢛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡈⣿⣿⡏⣸⣿⣿⡏⣼⣿⣿⠇⣾⣿⣿⢃⣿⣿⣿⢠⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⢸⣿⢁⣿⣿⣿⣠⣿⣿⡟⢸⣿⣿⡏⣼⣿⣿⠇⡼⠟⠉⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡈⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⡿⠀⠀⠀⠀⠈⠛⠻⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠃⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣶⡀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢿⣧⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠻⢀⠘⡀⠃⠀⠶⠧⠊⠃⢡⡴⠀⠶
⠀⠡⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣼⠁⠀⠠⣤⢠⣆⣃⠦⢯⢡⠑⣄⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠓⠒⠁⠀⠀⠀⠀⠀⠀⠉⠓⠁⠈⠀⠀⠘⠑⠀⡄⠉⠉⢠⠀⠊⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠩⠁⠀⠒⠐⠊
⠀⠀⢠⡀⣠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⡀⠡⠀⠀⠀⠂⠀⠀⠀⠠⣤⡄
⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠑⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣦⢤⡶⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇⠤⡨⠂⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⢰⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠑⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡤⠔⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣐⣂⣀⠀⠀⠀⠀⠀⠀⣒⣒⠂⠂⠀⢒⠐⠰⢂⣀⣀⣠⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⣦⣶⣶⣾⣾⣦⣤⣄⣠⣴⣾⣿⣽⣶⣶⣤⣭⣷⣶⣾⣷⣯⣽⣶⣶⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠈⠑⠐⠋⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣧⣶⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣧⣀⣀⠀⠀⠀⠀⠀⠠⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠲⠀⠠⢀⣀⡠⠤⠤⠰⠦⣤⠤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⡷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣴⣿⣿⣿⣯⣤⣯⣽⣿⣿⣗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣲⣖⣒⢚⣸⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⡆⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠿⠛⠿⠿⠿⠿⠟⠛⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣛⣿⣹⣻⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣽⣿⣽⣿⣿⣿⣿⣭⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣽⣿⣿⣿⣦⡀⢀⣾⣿⣿⣿⣿⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣟⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣻⣿⣯⣵⣶⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣽⣿⣿⣷⣝⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣾⢿⣿⣿⣿⣿⣿⢻⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡷⠶⢟⣼⣿⣿⣭⣭⣭⡾⢿⣾⣻⣶⣿⣽⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢏⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⡇⣿⣿⣿⣯⣿⢧⣿⣿⣻⣿⣿⣿⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⣻⣵⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⢿⣿⣻⢿⣾⣽⣿⣿⢋⣾⣿⡿⣿⣿⣿⣿⣴⢿⣛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣶⣯⣿⡷⣾⢯⣿⣿⣿⡎⣿⣇⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣷⢿⣧⣟⣻⣿⡿⣯⣾⣷⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣽⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣯⣽⣟⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡟⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢘⡔⢁⠀⠀⡠⠃⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣶⣾⣛⠀⠈⠢
⠀⠀⠀⠀⢀⡈⠀⡜⢀⠴⠡⣚⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠂⠄⠐⠖⠋⠀⠘⣿⠋
⠀⠀⠀⢠⣼⣧⡄⠀⠀⠀⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠰⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠏⠉⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⡗
⣶⣤⣾⠂⠀⠒⡄
⠉⢻⡿⠃
⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⠦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠤⣉⠊⡆
⣀⣴⣄⣠⠔⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⣁
⠀⣽⣿⡏⠁⠐⠄⠀⠀⡠⠊⠠⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⣷⣶⡾⠆
⠴⠋⠀⠀⠀⢀⡁⢀⣌⠀⢐⠀⠀⠠⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⣿⠟
⠀⠀⠀⠀⡠⠜⢻⣿⡇⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⣠⡀⠀⠀⢠⣶⠶⣦⡀⠀⣧⣿⠀⠀⣠⡴⢶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⢀⣾⣿⠃⠀⠀⠀⠻⣷⣜⣷⣄⢻⣿⢠⡾⢋⣠⠞⠃⠀⠀⠀⠀⣠⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⣿⡿⠷⣶⣾⣿⣧⣤⣀⣀⠀⠀⠀⠉⠛⠛⠀⠁⠙⠛⠉⠀⠀⠀⢀⣠⡴⠟⠁⢠⣿⡿⠁⠀⢳⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢰⣿⡇⠀⢸⣿⠏⠉⠛⠛⠿⠿⠿⣷⣶⣶⣶⣦⣤⣤⣴⣶⣶⡶⠿⠛⠉⠀⠀⠀⣼⣿⠃⠀⠀⣾⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⣼⣿⠀⠀⣾⡟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠉⢉⣭⠁⠀⠀⠀⠀⠀⣠⣤⠀⢠⣿⡇⣀⣤⣄⠀⠙⠻
⠀⠀⠀⠀⠀⣤⡤⠚⣿⠀⠀⣿⣿⠀⠀⣿⢇⡞⢹⣿⡄⠀⠀⢀⣴⡾⠟⠉⣳⣾⡟⠀⠀⣴⡖⣠⢋⣾⡿⠀⢸⣿⡴⠁⢀⣿⡇
⠀⠀⠀⠀⠀⢹⣆⣠⠾⠂⠀⣿⣇⠀⠀⢿⡟⠀⢸⣿⠁⠀⢀⣾⠟⠁⣠⠞⣿⡟⠀⠀⣼⣿⣵⠃⣾⡿⠁⢲⣿⣿⣧⣴⠿⠛⠀⠀⢠⠆
⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⢿⣿⠀⠀⠈⠁⠀⣿⡿⠀⢀⣼⣯⡤⠞⠁⠀⣿⠁⣠⠞⢿⣿⠃⠀⣿⠁⣠⠞⠁⠛⢻⣇⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⡄⠈⠻⣷⣄⠀⠀⠀⠻⣧⡤⠊⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠘⠋⠀⠀⠈⠋⠁⠀⠀⠀⠀⠻⢧⣤⡴⠋⠀⢶⡀
⠀⠀⠀⠀⠛⠷⢦⣌⠳⣤⡙⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄
⠀⠀⠀⠀⠀⠀⢘⡿⢻⡿⠛⣻⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣶
⠀⠀⠀⠀⢠⡶⠋⠰⠟⢁⣾⠏⠀⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣭⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⢀⣴⣶⣿⣿⡿⠗⣀⣀⣀⣀⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⣿⣿⡄⠰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⣰⣿⣿⣿⡿⠃⠀⠸⣿⣟⠉⠉⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⣠⣾⠟⢸⣿⣿⣿⢀⣿⣿⣿⣿⠁⠀⠀⠀⢻⣿⡆⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⢸⠀⣬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⠶⠾⠛⠁⠀⢸⣿⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣧⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠈⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⡇⠀⠸⣿⣿⣿⣧⠀⠀⠀⢀⣾⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠛⠻⠿⣶⣾⣿⣿⣿⠁⠀⠹⣿⣿⣿⣧⠀⠀⣠⣿⣿⠁⠀⠀⠹⣿⣿⣿⣆⠀⣠⣾⠏⠈⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣼⣿⣿⡿⢷⠦⠀⠀⠈⠛⠿⠿⣿⣾⠿⠟⠁⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠀⠀⠘⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⣴⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⣄⣠⣾⣿⣿⣷⣤⡀⢤⣶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠄⣾⠿⢛⣛⣩⣭⣭⣤⡭⠭⣭⣭⣭⣍⣛⡛⠿⣷⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⣋⡤⠀⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠄⣨⣙⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡖⠼⣋⡴⠟⠉⠀⠀⠀⠀⡀⡄⠀⠴⢲⠀⠀⢀⣴⡀⣤⣄⠀⠀⠀⠀⠉⠻⢦⣝⠻⡶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⣁⠆⠀⠀⠀⠀⢠⠒⡌⢲⡇⠻⠔⠘⠊⠀⠀⠊⠉⠓⠋⠉⠾⠽⢢⢤⡀⠀⠀⠈⠳⣄⠺⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⣣⡾⠋⠀⠀⣀⠠⡽⠆⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⡵⢒⠄⠀⠀⠈⢳⣌⢿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⣴⠏⠀⠀⣠⣜⢾⠁⠁⠀⠀⠀⢀⣠⠴⠖⠛⠛⠛⠛⠛⠛⠲⢦⣄⡀⠀⠀⠀⠉⠉⣼⡡⢄⠀⠀⠙⣦⠹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠏⣼⠃⠀⠀⡀⡓⡇⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⢖⠋⠃⠀⠀⠈⣧⡹⣟
⠀⠀⠀⠀⠀⣠⣾⡟⣼⠃⠀⠀⠀⠻⡏⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠈⢲⣉⡇⠀⠀⠘⣧⢹⣷⣄
⠀⠀⠀⠀⢸⡏⢸⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⢙⡆⢿⣿⡇
⠀⠀⠀⠀⠀⢿⡇⣾⠁⠀⠀⣀⡀⠀⠀⣀⣀⣀⠀⠀⣀⣀⣀⠀⠀⣀⣀⣀⡀⠀⠀⣀⣀⡀⠀⣀⠀⠀⣀⡀⣀⣀⣀⣀⢀⣀⣀⡀⠀⠈⢿⢸⣿⠁
⠀⠀⠀⠀⣠⣿⡇⣿⠀⠀⢠⣿⣷⠀⠀⣿⠛⠛⣷⠀⣿⠛⠛⣿⠀⣿⠛⠻⣿⠀⣾⠟⠛⢿⡄⢿⡆⢀⣿⠃⣿⠟⠛⠋⢸⣿⠛⢿⣧⠀⢻⠈⣿⣆
⠀⠀⠀⠰⣿⣿⠀⣿⠀⠀⣾⣏⣿⣇⠀⣿⡷⠾⠟⠀⣿⡷⠾⠟⠀⣿⡷⣾⡟⢰⣿⠀⠀⣾⡇⠸⣿⣼⡟⠀⣿⡿⠿⠀⢸⣿⠀⢘⣿⠀⢀⡀⣿⣿⡇
⠀⠀⠀⠀⠙⣿⠄⣿⠀⢸⡿⠉⠙⣿⡀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⢹⣧⠀⢿⣦⣠⣿⠃⠀⢿⣿⠃⠀⣿⣇⣤⣤⢸⣿⣤⣼⡏⠀⣼⢡⣿⠏
⠀⠀⠀⠀⠀⣾⠀⢿⡀⠉⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠙⠋⠁⠀⠀⠈⠉⠀⠀⠉⠉⠉⠉⠈⠉⠉⠉⠀⠀⣿⢸⣿
⠀⠀⠀⠀⢸⣿⣶⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⣿⡇
⠀⠀⠀⠀⠀⠛⢿⣇⢻⡄⠀⠀⢰⣋⡷⡀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⢐⣆⠀⠀⠀⢠⡟⣸⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣆⢻⡄⠀⠀⢡⣠⡕⠀⠀⠀⠀⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⢐⣍⡉⠁⠀⢀⡈⣱⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⠻⣄⠀⠀⠁⠒⡟⣀⣀⠀⠀⠀⠉⠛⠶⢦⣤⣄⣀⣀⣠⣤⠤⠶⠛⠉⠀⠀⠀⠀⠀⡳⡜⠊⠀⠀⣠⡟⣱⡛⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣧⡙⢧⡀⠀⠀⠀⠧⠜⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡰⣜⡦⠛⠁⠀⢀⣴⠋⣼⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡙⢦⣀⠀⠀⠈⠳⠋⣖⡶⢀⣠⠄⣀⣀⠀⠀⣠⣄⠤⢦⢰⡦⡘⠤⠇⠈⠀⠀⢀⡴⢟⠱⠞⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣦⠁⠀⢠⣀⠀⠀⠈⠁⠙⠚⠀⠿⠁⠀⠀⠧⠼⠠⠝⠈⠁⠀⠀⠀⠀⣤⠾⣋⣴⠿⠷⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣦⣝⡳⠶⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠖⢠⣴⣾⣥⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⢷⣆⣠⣍⣛⣛⣛⠲⠶⠶⠖⣛⣛⣛⣩⣭⣶⡾⠛⠓⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⢿⣿⣿⡿⠟⠛⠛⠽⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⠛⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⣿⠛⠻⣦⡄⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⠀⠀⠈⣿⡄⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⡿⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⣾⠃⠀⠀⠀⢸⡇⠸⠶⠶⠶⠶⠶⠶⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠞⠋⣠⡾⠃⠀⠀⠀⠀⠸⠷⢶⣶⡶⠶⠶⠶⠶⢶⣦⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⣤⣤⣤⣤⣤⣤⣤⣤⣄⢠⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠈⣿⡀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠹⣦⣀⣀⣀⣀⣀⣀⣴⡿⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣠⡾⠛⠛⠛⠙⠛⠛⠛⠛⢷⡄⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢴⠾⠋⠀⠀⠈⣻⣶⣶⣶⣶⣶⣶⣶⡶⠟⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠈⣿⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⠀⠀⠀⠀⢀⣠⡿⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠛⠛⠛⠛⢿⡏⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣿⣤⣤⣤⣤⣤⣤⣼⡿⠀⠙⠻⠷⢶⣦⣤⣤⣤⣤⣤⣤⣿⣶⣤⣤⣤⣴⠟⢁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣤⣤⣤⣤⣤⣤⣤⠤⠞⠛⠓⠶⠦⢤⣤⣤⣤⡤⠤⠤⣤⣤⣤⣤⡤⠤⠶⠛⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⡴⣖⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣲⢦⡀⠀⠀⠀⢸⣿⣿⣿⡿⢋⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⢍⡛⢿⣿⣿⣿
⠀⠀⠀⡿⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠈⢻⣿⠀⠀⠀⢸⣿⣿⣿⢠⢱⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣷⡽⠈⣿⣿⣿
⠀⠀⠀⡇⡇⠀⠀⣠⣶⣄⠀⢀⣴⣿⣿⠟⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⢸⢸⣿⣿⠟⠉⠻⣿⡿⠋⠀⢀⣼⣿⡇⠀⣿⣿⣿
⠀⠀⠀⡇⡇⠀⠀⠙⢿⣿⣷⣿⣿⠟⠁⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⢸⢸⣿⣿⣦⡀⠀⠈⠀⢀⣴⣿⣿⣿⡇⠀⣿⣿⣿
⠀⠀⠀⡇⡇⠀⠀⠀⠀⠙⢿⠟⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⢸⢸⣿⣿⣿⣿⣦⣀⣠⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿
⠀⠀⠀⡇⡇⠀⡄⣠⣠⣄⣄⣠⣀⣀⡄⣠⡀⢸⣿⠀⠀⠀⢸⣿⣿⣿⢸⣸⣿⢿⠿⠿⠿⠿⠿⣿⢿⣿⠿⣿⣧⡄⣿⣿⣿
⠀⠀⠀⣇⡇⠠⠿⡟⢹⠹⠯⢿⠻⠇⡇⣿⠆⢸⣿⠀⠀⠀⢸⣿⣿⣿⢸⢴⣖⣐⣰⣦⣶⣸⣋⣧⣿⣺⣁⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠹⣾⣢⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣖⣵⠏⠀⠀⠀⢸⣿⣿⣿⣆⠣⠝⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠯⢊⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠠⢀⠀⠀⠀⠀⡀⠀⢀⠀⠐⢠⡄⠀⠀⠀⠠⣸⣀⠤⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢄⣸⣠⠄⠀⠀⠀⢀⡄⢂⠀⡀⠀⢀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠱⠘⠀⠀⠀⠠⠄⣻⠄⠑⠆⣲⢒⡐⠂⠀⠐⠛⡝⠒⠀⠈⠒⣀⢀⠰⢀⠄⡠⠎⠀⠐⠊⡍⠓⠀⠀⠀⢂⡚⢖⠀⠎⠡⣞⠠⠄⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠀⠀⠂⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠲⢈⡁⠆⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠐⠀⠀⠈⠁⠂
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠠⠀⠀⠀⠘⢘⡠⢣⢜⡳⠜⠀⠁⠁⠈⠀⠀⠄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠛⠀⠀⠄⡹⠃⡭⠀⠀⠀⢀⠐⠑⠠⠍⠂⠑⢦⡀⠀⠀⠨⢐⠟⡠⠀⠀⠛⠀⢀⠀⠀⢠⠀⠀⠀⠀⡀⠠⠄
⠀⢀⠀⢿⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠂⠀⠀⠐⠄⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠀⡠⠀⠀⠀⠀⠀⠂⣼⠆
⠀⠀⠂⠠⡄⠀⠀⡀⠀⠀⠠⡇⠀⠆⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠰⠆⢨⠅⠀⠀⠀⠀⠀⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⠤⠤⠢⠀⢠⠀⠀⠐⠀⢰⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⣆⠀⠀⠀⠀⢠⡆⠀⠀⠀⠈⡠⠀⠔⠤⠤⠄⠀⡄
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠐⠖⠂⠒⠀⣷⠀⠀⠀⠑⣄⠀⣀⠞⠁⠀⠀⠀⠀⠈⠳⣄⠀⣀⠌⠀⠀⠀⣴⠀⠔⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠒⣀⠋⠰⠀⠀⠙⠛⠀⢣⠆⠀⠀⠀⡄⠀⠀⠐⡞⠂⠛⠊⠀⠀⠒⠘⣀⠐⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⡄
⠀⠀⠀⠀⢤⠘⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠃⠀⠀⠀⠌⠀⠀⠀⠀⠀⠘⠁⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛⣠⠁
⠀⠀⠀⠀⠀⡀⠊⢠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠤⠑⢂⠄
⠀⠀⠀⠀⠀⢀⠐⠆⢀⡀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⡀
⠀⠀⠀⠀⠀⠀⠘⠢⢜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⡰⠀⠀⠀⠀⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⢃⠔⠛
⠀⠀⢠⡄⠀⠀⠀⠉⡈⠂⡑⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⠐⢃⡈⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⣶⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢰⠀⠈⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠤⠄
⠀⠀⠠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠
⠀⠀⠀⠄⠄⠡⠄⠤⠀⠀⠠⠀⠀⠂⠀⠀⠀⡈⢀⣀⠀⠄⢂⠀⠀⠀⠀⣀⡰⠤⡀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠃⠀⠀⠀⠀⠂⠀⠄⠀⠀⠤⠠⠤⠀⠠
⠀⠀⠀⠐⠈⢀⠂⠀⠀⠀⠀⠘⢣⣽⡀⣁⢒⢡⡤⠭⠒⢠⠊⠉⠀⠀⠀⢉⣇⣀⠟⠀⠀⠀⠘⡙⡄⠐⠭⠤⡌⠐⣀⢀⣼⣔⠃⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠡⠐⠋⣕⠉⠉⠀⡃⠠⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇⠘⡉⢢⠙⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠔⢲⢺⠀⡉⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡗⢒⠢⠔⠂⠀⠀⠀⠠⡄
⠀⠀⠀⢈⣰⠀⠀⠀⠀⠂⠒⢋⠁⡈⠐⠀⠀⠀⠀⠀⠀⠀⠗⠔⠃⠠⠄⠀⡀⠀⠀⠃⠘⠀⠃⠌⠀⠀⠀⠀⠀⠀⠈⠐⢉⠀⡉⠒⠀⠂⠀⠀⠁⣦⠀⠆
⠀⠀⠀⠈⡃⡄⠀⠀⠀⠈⠄⢨⠱⡀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡔⡁⠠⠁⠀⠀⠀⢁⢌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠃⡆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠄⠀⠄⠀⠠⠀⠀⠐⠀⠀⠀⠄⢰⡈⠣⢀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠓⡄⠀⠀⠀⠀⠐⠂⢲⠀⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠁⠀⠀⢀⠞⠁⠃⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠈⠙⢏⠛⠃⢤⠀⠀⠉⠉⠳⣄⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣶⡟
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠳⠀⢄⣠⣄⡈⢦⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⢺⠝⣧
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢦⣀⣃⠀⠉⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⣿⠞⠋⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠀⣨⠟⠒⢀⣀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠘⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠗⠒⠛⠉⠀⠈⠲⢝⢢⡀⠀⡀⠀⠀⣀⠀⡼⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠳⡑⡾⠁⠀⠀⠈⢏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠂⠛⠐⠒⠢⢄⣀⠀⠀⠙⣜⡄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠘⣞⡄⠐⡜⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡏
⠀⠀⢀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠤⠤⣄⡀⠀⢀⠀⠀⠀⢳⡀⠘⢂⡔⠓⠂⠀⠀⠀⠀⠠⠶⠊⠁⠀⣷
⠀⠀⠈⠑⠤⣄⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⡀⢳⠀⣄⢹⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡇⢰⠸⠀⠀⣠⠚⠁⠀⡀⡠⠊⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⢲⣄⣀⠠⣄⡰⠖⠛⠁⠈⠛⢦⡀⡆⢰⠃⠀⢀⢀⠟⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡤⠧⢤⣿⠀⠀⠈⠿⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠑⠚⠛⠒⠦⣄⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠓⢦⡦⣾⠤⠖⠛⠛⠛⠲⣄⠀⣀⣀⣀⡈⢳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠋⠉⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠃⠀⠀⢀⡀⠀⠀⠀⣼⢰⡖⣪⡅⠪⣽⢃⠀⢀⡤⠀⠀⠀⣤⣟
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣆⠀⣀⡇⠉⠓⣤⡾⢻⣌⠳⢭⣠⠞⠉⢧⠞⠁⠀⠀⠀⠀⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣨⠟⠋⠀⠀⣼⠋⠀⠀⠉⠳⣄⠟⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠤⠐⠒⠠⡏⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⡏⠀⠀⣠⠞⠒⣒⢦⡄⠀⣠⡶⠶⠋
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠹⣦⡀⠀⠀⣀⣉⠤⠞⠁⣠⠎⠹⣄⠀⢠⠏⠉⠳⣄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣄⣀⡠⠞⢋⠟⠉⠀⠀⠀⣀⡾⠁⠀⠀⠀⠉⠉⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⢤⣄⠀⠀⠀⠀⠰⢟⣁⢀⣠⢞⠟⠒⠒⠉⢩⠑⢀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣤⣀⣀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠉⣉⡩⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠶⠚⠉⠂⠈⠙⠓⠛⠛⠲⠶⠴⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⡯⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⣙⣳⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢀⡙⠿⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣋⣤⣴⣿⣷⣆⠈⠁⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠻⠟⢻⣿⠿⣿⣿⣿⣿⣶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⣠⠴⠛⠃⣤⣾⣿⣿⣿⣬⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⣧⠄⢀⣴⣿⣅⢀⣿⣿⣍⡻⡟⣳⣤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⢆⢀⡷⣼⣿⣿⡿⠟⢁⡰⠎⣩⣿⣿⠏⠀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⢿⣿⢿⣿⣿⡟⠉⣃⢲⡛⠛⠛⠻⢆⣈⣤⣤⠴⠋⣹⠇⠀⠀⢀⣶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⢀⢉⡼⠋⠁⢠⣾⣿⣯⠝⢶⡤⡴⠾⠿⠟⢽⢳⣾⣥⣤⣤⣶⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⢶⠞⠛⣿⡀⢀⡀⣀⣾⣿⣿⣿⣶⣤⣤⣤⣷⣶⣶⡘⣟⣿⢿⣿⠿⢿⣿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⣁⢀⣤⠂⠀⢀⣨⣷⣨⣿⣿⣿⣽⣿⣿⣿⡇⠀⢹⣿⡟⠿⡿⢧⣿⣶⣤⣴⣿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⢁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣒⠉⠙⠓⠲⠧⢬⣁⠛⠉⣫⣼⣄⡠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡿⠛⢹⢿⣻⣽⠟⠋⢱⣾⠿⢿⣦⡽⠟⠛⠿⣿⡷⣶⡄⢠⡼⢋⢀⡀⠀⣠⣶⢶⡌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡂⣀⠠⣦⠰⠟⠉⠀⣀⣠⣾⣿⣄⣼⣿⣖⠶⢤⣤⡬⢿⣶⠊⠁⠙⠿⣿⣿⣶⣟⣁⣾⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣴⡆⣉⢩⣅⠀⠀⠘⣧⡀⣠⣾⠟⠛⠋⣠⣦⠀⠛⢿⣦⣆⡀⠀⠀⠙⠿⣷⣠⣤⣀⠈⠉⣉⠉⣭⣁⣴⣶⣾⠇
⠀⠀⠀⠀⠀⡸⢸⣿⣿⣦⡆⠀⠙⠣⣾⠟⣿⡷⢀⣷⣷⡟⠾⠁⣀⣴⣿⠧⣿⣷⡀⠀⠙⣿⣿⠂⠀⠀⡖⠉⢻⡟⣿⣿⣶⣿⣶⡏⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠐⣷⣾⡿⢣⡟⠀⠀⠀⠀⠀⠈⠻⣿⣿⡟⠁⠀⠀⢻⣿⣥⣿⠒⢿⣿⡇⠀⠀⠈⢿⡿⣿⣇⠰⢲⠞⠀⠀⠙⢿⣇⡁⠀⠀⠀⠀⠀⣠⡄⢰⣞
⠀⠀⠀⠀⢀⡿⠙⢱⡟⠀⣴⣶⣶⣶⠀⣠⣴⠿⠋⢀⡰⣷⣾⣿⣿⠿⢿⠦⢾⣿⣷⣶⠀⢀⠈⠙⠻⢿⣿⣛⢿⡷⢦⣄⣠⣈⢉⠓⢦⣤⣤⣾⢣⢿⣼⣿⡇
⠀⠀⠀⠀⢸⠃⠀⡾⢸⣿⡘⣿⣿⣿⡟⢉⠀⠀⣰⣿⣷⡸⣿⣷⣿⣤⣴⣄⣴⣿⣟⣻⣾⣿⡆⢰⣶⣾⣯⠉⠳⣄⠸⠟⠛⠛⢾⣿⣤⣦⣤⣿⣿⡜⠛⡿⠤⠴⠂
⠀⠀⠀⠀⢸⡆⢸⡇⠀⣿⣧⠹⣿⣿⣿⡘⢷⣿⠟⢛⣉⢷⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠙⣿⠇⣾⣿⣿⡟⢀⡼⠋⣀⣀⠀⠀⠀⣽⢻⡽⠿⣿⡍⠀⢸⠷⠿⠂
⠀⠀⠀⠀⢸⣇⠈⢷⡖⠛⡿⠃⠉⣀⣀⣰⣞⢳⣼⣿⣿⠿⠿⢿⣿⣿⡇⠀⢀⣤⣤⣄⢸⠟⠀⠿⢿⣿⣧⣾⣵⣿⠟⠻⣿⡆⠀⣷⢰⣇⣴⡟⣠⢆⡇
⠀⠀⢀⡴⠾⣷⡀⠈⢿⡾⣧⣴⣿⣿⠋⠉⣿⣿⣿⣿⡇⠀⠀⠸⡏⢿⡇⣰⠿⠋⠉⢻⡟⠶⠦⠶⣦⣿⣿⣿⣿⠀⠀⠀⢹⣿⢠⡷⠖⢛⣫⣾⣡⣾⣀⡀
⠀⠀⠈⢰⣿⣿⠧⡀⢨⢷⣿⣿⠷⠛⠀⠀⣸⣿⣿⡏⠤⠀⠀⠀⣿⡘⣹⣿⠀⠀⠀⣼⠀⠁⠀⠀⣜⢹⣿⠟⣿⠄⠰⠆⣼⣾⣯⠶⢒⣻⣿⣟⣥⣤⢀⡉⠁⣀
⠀⠀⠀⠀⠉⠃⠀⢻⣿⣼⣟⢣⣀⠐⣠⢤⣿⣿⣿⣿⠔⣄⠶⢰⣿⠇⢻⣿⠣⡜⠃⠻⡇⠶⠀⠀⠉⣻⣟⢦⡀⠶⣤⠴⠂⣠⢿⣾⡟⠋⢠⡅⠈⡿⠏⠛⠃
⠀⠀⠀⠀⠀⣼⢻⡏⠙⢯⠙⠿⢿⣯⣤⡞⠁⣉⣿⡀⠀⠀⠑⠉⠉⠀⣸⡈⣳⣶⣶⡾⠿⢆⠰⡶⠚⢿⣿⣿⣿⣶⣦⣀⠶⠋⣀⠬⠛⢁⡾⠶
⠀⠀⠀⠀⢰⡇⡀⠃⣀⢈⣷⣀⣀⠈⢩⡙⠚⠻⠿⣷⣤⣀⣀⣀⣄⣰⣿⣿⣯⢿⣿⣇⢀⡜⠉⢱⣄⣼⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⣸⣧⣄⠀⠈⡄
⠀⠀⠀⠀⣸⢟⣡⠋⣹⣿⣿⣿⡿⢣⢸⡏⡷⣶⠀⠀⠉⠉⠻⠿⠿⢿⣿⣿⡿⠿⠿⠿⠛⠛⠀⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡟⠀⠀⡧
⠀⠀⠀⢀⡾⢹⡇⠀⢿⢻⠝⡏⠀⠀⢸⡇⡇⣿⠀⣤⢀⠀⠀⠀⠀⠀⠀⠀⣤⢸⠆⢶⠀⠀⠀⠀⠀⠀⠀⣤⢀⣀⣠⡄⣲⠴⢷⠀⣸⡿⢥⣠⠔⠋
⠀⠀⠀⢘⣷⠟⢳⡀⢀⡟⣰⠀⠀⠀⠘⠃⠗⠿⢸⡏⢸⡇⢸⡇⢰⡆⡆⠀⣿⠀⠀⢼⠐⡆⣷⠁⣷⠛⣤⣿⢸⣿⣿⠷⠟⠃⠈⢠⡏⠀⢠⡗
⠀⠀⠀⢸⡏⠀⢸⣿⣼⠁⠈⠉⠛⠲⠦⠤⣤⣀⣀⡀⠈⠁⠈⠃⠈⠃⡇⠀⠙⠀⠀⠚⠚⠃⠛⠀⠉⠀⠉⠀⠀⠀⣀⣀⠤⠤⠒⠉⢷⣠⠟
⠀⠀⠀⠈⢿⣀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣄⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⢴⡦⠶⠶⠖⠙⠃⠉⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠡⠄⠈⠄⠀⠀⠀⠀⠀⠀⠀⡾⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠌⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠉⠈⠉⠟⠀⠀⠀⠀⠈⠀⡀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠉⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢀⣤⣤⠀⡆⠀⢀⠔⠀⠀⠀⠀⠔⣠⣤⣄⢠⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⡑⠛⠀⢀⣤⣾⣦⣠⣶⣦⡀⠀⠙⢂⣿⡆⠄⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠙⠻⠶⢿⠟⠋⠉⢈⡁⠉⠙⠻⡿⢶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠂⠄⠜⠣⠀⠄⠊⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣈⡄⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠘⠛⠛⠛⠢⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠛⠛⡄⠀⠀⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⣀⣀⣀⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⠛⠛⠛⠛⠛⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠸⠉⠉⢹⠀⠯⠉⠉⠽⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠠⡀⠀⡈⠀⠰⠀⠀⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣠⣄⣠⣄⣀⣀⣥⣀⣇⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⣿⣿⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠸⠟⠋⠁⠀⠀⠀⠈⠙⠻⠷⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠉⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠢⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡠⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⠀⢸⠀⡏⠀⠀⡰⣡⠔⠁⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢌⢇⠘⠀⠀⢀⣾⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡈⠓⠄⢀⠼⠚⠓⠒⠲⡟⠁⠠⠊⢀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡏⠀⢛⢀⠘⠃⢸⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⢒⣒⠭⠛⠧⡀⠘⠚⠀⢀⡼⢍⠑⠒⠤⣄⣀⣀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠁⢀⠤⠀⠀⢨⣷⠒⠒⠁⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠴⠁⡰⠁⢀⣿⣿⠀⢰⠀⠳⡀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠻⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡿⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡸⢰⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣀⠤⠒⠉⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠳⢄⡀⢀⡰⠁⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡠⠊⢁⡠⠖⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡇⠀⠣⡀⠀⢀⡠⠴⠊⠁⠀⣠⠊⢀⠴⠋⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠁⠀⠀⠀⢀⠜⢁⡔⠁⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠣⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡠⠃⠴⠋⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠢⣄⠀⠳⡄⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢀⠜⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡈⠁⠀⠈⠢⡀⠀⠀⠀⠘⡌⡄⠀⠀⠀⢠⠎⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠈⢦⡀⠀⠀⢃⢱⠀⠀⢠⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⠈⠢⣀⠸⡈⡆⢠⠇⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⡓⢧⠱⣎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣤⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⡿⠛⢋⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠘⡆
⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣀⠀⣿⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⡇⠀⣿⢀⣤⠀⣠⢴⡄⠀⣿⣠⠎⣿⠇⢻⡔⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠊⣿⢰⣇⡀⣿⡀⠿⠁⢰⡟⠀⢸⣇⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠛⠀⠛⠈⠉⠀⣀⠀⠀⠀⠘⠓⠀⠈⣿⠙⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⢸⡆⢰⡟⢯⣀⢰⡿⠀⣾⠆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⢼⡇⠘⣧⣀⠍⠸⣇⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣀⣀⣀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠋⠉⠉⠉⠉⠉⠛⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⠆⠀⠀⣿⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢀⡴⠋⠀⣀⠜⠉⢧⡀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⠴⠚⣉⣠⠴⠚⠁⠀⠀⠀⠙⢦⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣞⡥⠖⣋⣉⣀⠀⠀⠀⠀⣀⣀⡀⠀⠙⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠁⠀⢚⣡⣤⣀⠀⠀⠀⢈⣡⣄⡙⠂⠀⠸⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣄⠀⠀⠘⠛⠁⠀⠀⠀⠀⠙⠛⠀⠀⠀⡇⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣿⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⢸⡧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢀⣀⣭⣅⣀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠀⠘⢿⣛⣻⠟⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠳⣄⡀⠀⠀⣀⡴⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠙⠒⠋⠁⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⡆⢰⠏⢱⡞⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⠇⡎⠀⢸⠇⠀⣼⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢄⠀⢠⠎⠀⠀⡞⢰⠁⠀⡸⠀⠀⡏⠀⣧⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢳⠁⠀⠀⠐⣲⠃⠀⣰⠁⠀⢸⠁⢸⠙⡦⠴⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡆⠀⠀⡰⠁⠀⠰⠃⠀⠀⡎⠀⡆⢠⣧⣤⣔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢼⠀⠀⠀⢣⢀⠜⠁⠀⠀⠀⠀⠀⠘⠀⠀⠁⣸⣀⡠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡜⠁⢸⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣶⣦⣤⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣯⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣽⣿⣿⣭⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣴⠟⠋⠉⠉⠙⠻⣦⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣼⠏⠀⠀⠀⠀⢀⣤⠜⣷⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢿⡎⠻⣦⣠⣴⠟⠁⢀⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⢿⣄⡈⠉⠀⢀⣠⡾⠃⠀⠀⢸⣿⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠘⠟⢠⡾⠋⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠶⠶⠶⠶⠶⠶⠶⢀⣤⡾⠛⠛⢶⣤⡶⠛⢀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣀⣀⣀⣀⣀⡀⠀⣿⠉⠛⢶⣄⠀⠙⢷⣴⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠉⠉⠉⠉⠉⠁⠀⠹⣦⠀⠀⠙⢷⡀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⠘⢷⣄⠀⠈⣷⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠙⠳⠶⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠫⠉⠁⠀⠂⠐⠀⠈⠉⠝⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠂⠀⠀⢠⣤⡀⣶⣦⢠⣶⡄⣤⣀⠀⠀⠐⠉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⠀⠀⢀⣄⢺⣿⠌⣿⠃⣿⠷⢸⣿⢃⣿⠏⣼⡓⣠⡀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠘⢿⡷⠟⣀⠬⠔⠒⠒⠒⠒⠢⠍⣘⠃⣼⣿⠏⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣏⡄⣀⣀⣀⣀⣀⢈⣴⠊⣁⣀⣀⣀⣀⣀⣀⣀⣀⣈⠑⣤⣁⣀⣀⣀⣀⣀⢠⣹⣄⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣤⡀⢠⣤⣤⡀⣤⣤⣄⢠⣤⣤⡀⢀⣤⣤⡀⣤⡀⣠⣄⣤⣤⡀⣤⣤⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣿⣇⢸⣿⣹⡇⣿⣏⣿⢸⣿⣽⡗⢸⡏⣿⡇⣿⣇⣿⡇⣿⣏⠀⣿⢽⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⣿⣾⣿⢸⣿⠉⠁⣿⡏⠉⢸⣿⢹⣇⢸⣇⣿⡇⢸⣿⣿⠀⣿⣏⠀⣿⣾⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠛⠈⠛⠙⠛⠀⠀⠛⠃⠀⠘⠛⠘⠋⠈⠛⠛⠁⠈⠛⠋⠀⠛⠛⠁⠛⠛⠋⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠠⡄⠄⠂⠀⠀⠀⠀⠀⢤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡤⠀⠂⠀⠀⠀⠐⠠⢠⠄⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡔⠀⠀⠀⠀⢀⡴⣦⣉⠢⠤⣀⣀⣀⣀⣀⣀⠤⠔⣉⣴⣦⠀⠀⠀⠀⠠⣢⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠻⠿⢁⣾⢣⣶⠆⣤⡄⣤⣤⠀⣶⢀⣿⡌⠻⠇⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠉⠁⠛⠿⠸⣿⡇⢽⣿⠘⠿⠇⠙⠉⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠲⠶⠶⠖⠒⠚⠋⠉



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠸⠇⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠀⠀⠀⠀⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠛⠉⢧⠀⢀⣠⠴⠚⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠉⠀⠀⢀⣠⡾⠶⢯⣡⠖⠓⢦⡤⠞⠋⠉⠙⡆
⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⢀⣠⡴⠞⢉⡟⠀⠀⢸⠏⠀⠀⣸⣁⡀⢀⣠⡴⠃
⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣈⡁⠀⢀⡞⠀⠀⢠⠏⠀⠀⣰⠋⠀⠙⡏⠉⠹⡆
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⡼⠁⠙⢦⡞⠀⠀⢠⠏⠀⠀⣰⠃⠀⠀⡼⣁⡤⠞⠁⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡼⠁⠀⢀⡞⠀⠀⢠⠏⠀⠀⣰⠃⠀⠀⡼⠛⠛⣆⠠⣴⠶⠾⠛⠋⠁
⠀⠀⠀⠀⢸⡀⠀⠀⠀⡼⠁⠀⢀⡞⠀⠀⢠⠏⠀⠀⣰⠃⠀⠀⡼⠁⠀⢀⡟
⠀⠀⠀⠀⠀⢧⠀⠀⡼⠁⠀⢀⡞⠀⠀⠀⠈⠀⠀⢰⠃⠀⠀⡼⠁⠀⢀⡞⠀⢴⣤⣀
⠀⠀⠀⠀⠀⠈⠳⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⣞⡀⠀⠀⠈⠙⠻⢶⣤
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡞⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⣀⠀⠀⠀⣀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢰⠖⠟⠳⢲⡆⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⣰⣿⣿⣿⣿⣿⣦⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⢰⣶⣶⡆⢱⣶⣶⡆⠀⠀⠀⠀⠀⠇⠀⠀⡀⠀⠾⢽⢯⠷⢀⢀⠆
⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣼⣿⣿⣿⡷⠀⠀⢸⣿⣿⡇⢸⣿⣿⠁⠀⠀⢾⣦⡀⠀⠀⠀⠈⠀⢰⣿⢾⣿⣄
⠀⠹⣿⣿⣿⣿⣿⠟⢀⣴⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⡇⢸⣿⣿⠀⠀⠀⣸⣿⣧⣤⣄⠀⠀⠐⢿⠿⠀⠿⠿⠁
⠀⠀⠀⠉⠉⠉⠀⠀⠸⣿⣿⣿⠿⠋⠁⠀⠀⠀⠸⠿⠿⠇⠸⠿⠿⠀⠀⠿⠟⠛⠉⠛⠛⠃⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣉⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢠⣾⣿⡁
⠀⠀⠀⠀⣸⣇⠀⠀⠀⠈⣚⣷⡴⠀⠀⢦⣴⣗⠚⠀⠋⣤⠀⠀⠀⠀⠀⢈⡉⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⢀⡻⢟⡀⠀⠀⠈⠁⢖⣿⣶⣶⣾⣳⠋⠁⠀⠈⢃⡄⠀⠀⠀⠀⣈⡠⠄⠀⠸⠿⠆⠀⣀⠂⠀⡀⠀⠺⠿⠂
⠀⢻⣿⣸⣿⣿⣇⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣤⠄⠀⢀⣈⣁⡤⠖⠀⠀⠀⠀⠀⠈⠉⠹⣷
⠀⠈⠿⠋⠀⠀⠙⠻⠋⠀⠀⠈⣿⠛⠛⢻⠏⠀⢠⣦⠀⠀⢡⡆⠀⠈⣡⣀⡠⠵⠚⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣰⣾⣶⣶⣧⣄⠀⠀⠀⠀⠈⠓⠒⠉⠀⠀⠀⠀⠎⠸⠂⠀⠈⠈⠁⠀⠂⠤⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⣠⣶⣿⠓⠀⠀⠀⣠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣠⣾⣿⣿⠟⠃⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⠀⠐⠻⠿⠿⠀⠀⣤⣄⣻⣿⣿⣟⣠⣠⠀⠀⠀⢀⣴⣄⡘⠇
⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⡀⠂⠀⠀⠙⢿⣿⣷⣆⣹⡿⠋⠀⠀⣴⣿⣤⣬⣿⡆
⠀⠰⠿⠿⠿⠿⢿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣄⠀⠀⠀⣿⣿⠁⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⢼⣿⡿⠋⠈⠿⢿⠷⠀⠀⠿⠿⠀⠸⠿⠇
⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⢀⣬⠁⠱⠆⠀⠀⠀⠀⠀⠀⠀⣔⣰⣶⣠⣾⣧⢀⣤⠀⠀⣴⡟⠛⠉⠉⠙⢳⣆⠀⠀⢀⣴⣾⣦⡀
⠀⠀⠘⢆⡛⣡⡿⡿⠳⠇⢀⠀⠠⠀⠀⢀⣹⣷⣽⣿⣿⣿⣿⠃⠀⢘⣿⠀⠀⠀⠀⠀⠀⣯⠀⢠⣿⡿⠟⢻⣿⡆
⠀⠘⠛⣤⠢⣤⠷⢆⠈⣘⠋⠀⢇⠀⠀⠸⢿⣿⣿⠿⠿⠟⠃⠀⠀⠀⢿⣤⣀⡀⢀⡀⣰⡟⠀⢺⣿⣭⢀⠰⣿⣿
⠀⠀⠀⠉⠀⠀⠀⠘⠁⠙⠁⠀⠀⠑⠂⠤⠤⠤⠤⠤⠄⠂⠀⠀⠀⠀⠀⠉⠙⡿⡿⠛⠉⠀⠀⠈⠻⢿⣿⣿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⢿⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⡀⢀⡠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠁⢈⠉⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣧⠾⠻⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠀⠀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡴⣾⡃⠀⠀⠸⢻⣦⡀⠀⠀⠀⠀⠀⡴⡈⡲⠚⠋⠀⠀⢉⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⣹⣿⣭⣿⡟⣿⠟⠖⣾⢺⣿⢿⣿⣿⣦⡳⡀⠠⢿⣇⣀⠀⡆⡀⠈⣿⡍⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠡⡁⣐⣸⣿⣾⣿⣿⣏⡀⢀⣿⣌⣿⣾⣿⣿⣿⣧⡁⢠⣨⣽⡜⢀⣤⠀⣾⡇⠙⣷⠶⣶⠂
⠀⠀⠀⠀⠀⠀⢠⣤⣐⣥⣁⣴⡟⣿⣯⣿⣿⣿⠋⠙⠀⣿⠟⢻⡇⣿⣿⣿⣿⣿⣾⣿⣻⣩⡀⠉⠀⢀⡱⠾⢿⡄⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠰⣿⣯⣭⣿⣿⣹⣿⣿⡿⠈⣿⡏⠀⠀⠠⠛⠀⣿⣷⣿⣿⣿⣿⣿⣿⣿⠟⠛⣻⡖⢿⡏⠁⠀⠈⢻⣄⠀⠀⢇⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠈⢻⣷⡌⢻⣿⣿⣿⣧⣤⣿⠀⠀⠀⠠⡄⠀⠙⢻⣿⣿⢯⣿⢿⣿⣿⠀⠀⡏⠉⠉⠃⠀⠀⠘⠋⢹⣦⠀⣸⣧⣄⡀⣰⡆⠀⠁⣄
⠀⠀⠀⠀⠀⠀⠠⢠⣻⣴⣿⣭⣿⣿⢻⣿⣿⡗⠁⠀⠀⢀⠀⠰⣿⣿⠿⠞⢿⣿⣿⠃⠀⢀⡆⠀⠀⠀⠀⠀⠊⠀⠀⠈⣷⣾⡿⠛⠋⠁⠀⠀⢀⣿
⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⡏⢀⣦⣤⣀⠀⢀⣧⣀⣊⣿⣅⠀⠀⣼⣿⠃⢠⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠚⡹⠋⠀⢀⡀⠀⣠⣶⠟⠋
⠀⠀⠀⠀⣢⠰⠋⠉⠻⣿⡿⣿⡋⠉⠀⠀⢈⣿⠇⠈⠉⠄⠈⠀⠀⠘⣷⣾⠟⠁⠀⢸⡀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⠀⠀⣼⣿⣿⣿⣧
⠀⠀⠀⣠⠁⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣻⡯⡄⠀⠀⢂⣀⡀⠡⢽⡟⠁⠀⠀⠀⣼⡇⢘⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢢⣴⣦⣿⠉⠁⡘⢿⡄
⠀⠀⠘⠋⠀⠀⠀⠀⠀⣸⠋⠈⠀⠀⠸⣿⠍⢿⣦⢰⣀⣴⠟⣥⣤⣀⢀⣰⢤⣶⣿⣿⡄⣿⡁⠀⠀⠁⠂⠀⠀⠀⣀⠤⣀⣾⢼⣿⡔⠀⡇⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠂⠀⠀⠀⠀⠠⢤⡉⡸⢿⣧⠼⢿⡿⠷⣿⣿⣿⣿⣿⣿⡇⣿⣷⣤⣀⠀⣤⣀⣩⣭⠶⠚⠩⠀⠀⡝⣿⠀⡇⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠈⣾⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣿⡇⠀⠄⠀⢲⣾⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⡆⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⢷⠀⢧
⠀⠀⠀⠀⠂⠀⠀⠀⠹⣧⠀⠀⠀⣥⣤⡄⠀⣺⣿⣿⣇⡀⠀⠐⢄⣈⡉⢻⣿⣿⣿⣿⠂⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢹⠀⢸
⠀⠀⠀⠀⢰⠀⠀⠰⣀⣿⣆⠀⠀⠈⢧⠃⠀⠀⢿⣿⣏⡀⠀⠀⠀⢉⠙⢾⣿⣿⣿⣿⢼⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⣼⠀⢸
⠀⠀⠀⢀⢘⣦⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⣀⣲⠟⠉⠁⠀⠀⠀⠲⢆⠀⣼⠿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣴⣼⡆⠀⠀⠀⠀⠀⣀⣻⠀⠸⠆
⠀⠀⠀⠈⠰⣿⡇⠀⠀⠀⠻⣿⣿⣤⣀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠱⠷⢾⣿⡤⢤⣀⠙⢿⣿⣿⣿⠃⠀⠀⠀⠀⡌⣸⣧⠀⠀⠀⠀⠸⣿⣦⠀⠤⠂
⠀⠀⠀⠀⢸⣿⣿⢠⠀⠀⠀⠈⠛⠉⢹⡿⠒⠐⠒⠳⠂⠦⣀⠀⠈⡘⠀⠘⠒⡀⠀⠀⠀⠉⢿⣿⡀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⣿⣿⠔
⠀⠀⠀⠀⠀⠈⠉⠸⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠒⢦⣄⠠⠄⢹⠞⠁⣠⣤⣄⠀⠀⠀⠀⠀⠰⣿⣄⠀⠀⠀⠀⢘⣿⢧⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡦⠀⠀⠀⠀⠀⠀⠀⠈⣶⡎⠍⠁⠀⠀⠀⠀⠑⣄⠀⠀⠀⢢⠻⡛⢆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢏⠃⠀⠀⠀⠀⠀⠀⠠⠻⠇⠀⠀⠀⠐⠃⠌⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠐⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⢡⢠
⠀⠀⠘⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠆⠰⠈
⠀⠀⠀⠰⠀⠀⠀⠁⠀⠀⠛⡘⠛⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠰⡇⠀⠀⠠⠤⠖⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠆⠠⠄⠀⠀⠠⠠⠄⡄⠀⠀⠀⠀⡂⠆⠅⠀⠀⠀⠰⠰⠀⠀⠀⠀⡀⠀⠀⣠⢭⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠰⠠⠀⣃⣀⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⡀⠀⠀⡀⢀⢀⠀⠀⡀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⢸⣇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠒⡀⢇⣃⠸⡤⡀⣧⣅⠈⣆⠀⠀⠀⠁⠀⠀⠸⡿⠇⠀⠀⠀⠀⠀⡀
⠀⠀⣩⠔⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⢀⡄⡄⠀⣄⠀⢠⠀⡀⡀⢠⡀⠀⡄⠀⠀⢠⠀⠀⠀⢠⠀⠀⠀⢀⣿⡇⠀⠈⠫⣶⡽⠃
⠀⠀⡡⢖⠀⠀⠀⠀⠀⠀⢀⠀⠀⠣⡀⠐⠇⠧⠀⠷⠄⠸⠀⠬⠄⠀⠧⠀⠧⠉⠆⠮⠐⠦⠰⠥⠀⠀⠠⠻⠛⠃⠀⠀⠀⣿
⠀⠀⠖⠉⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠁⠈⠁⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠁⠀⠀⠈⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⢴⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠄⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⢄⠐⠀⣠⠆⠀⠀⠀⡆⠀⡆⠀⢀⢀⠀⠀⠀⢀⣀⡀⠀⠀⣄⠀⠀⠀⢰⡿⠁⠀⢈⠀⠄⠀⠀⠁⢈⠄
⠀⠀⠀⠛⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⠆

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠐⠀⣇⢯⣳⠲⣤⣄⡀⠀⢠⣺⠀⢀⣓⡄⠀⢀⣠⣤⠶⣞⡽⣹⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠠⠄⠀⠀⠈⢷⡛⠳⣴⣌⠻⣆⡇⢡⣂⣐⠍⢲⣰⢟⢡⣦⠞⢛⡾⢁⠂⠀⠠⠄⢀⠀⠀⠄
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠠⡙⢯⣤⣤⡛⢺⡌⢿⠁⠈⡯⢡⣗⢛⣤⣤⡼⢋⠄⡀⠀⣀⣀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⢀⡈⣙⠐⠂⠰⠀⣱⡜⢦⡀⠀⠀⣠⡤⠀⠉⠉⠈⡝⢉⣀⣤⣄⢌⠁⢀⠉⢀⢤⣄⠀⠀⢀⡴⢣⣎⠀⠆⠰⠆⣋⢁⡀
⠀⠀⠀⠀⠀⠀⠠⠄⠘⠋⠀⠀⠀⠀⣈⡶⠞⠁⠀⣰⠉⡀⡨⢻⣿⣫⣯⣼⡆⢂⠂⠁⠈⠁⠈⠳⢶⣁⠀⠀⠀⠀⠙⠃⠠
⠀⠀⠀⠀⠀⠀⢀⠔⣠⠴⠀⢀⣠⣾⠏⠀⠀⠀⢀⠔⠉⠁⠣⣀⠻⣟⠿⠉⢀⠈⠀⠁⠀⡀⠀⠀⠂⠹⣷⣄⣀⠀⠦⣅⠢⡀
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠊⠸⡿⡟⠀⠀⠀⠀⠀⠓⠈⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⠆⠑⠂⠀⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠉⠈⠁⠐⠂⡤⠄⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⢠⠁⡜⣁⢀⡀⠀⢀⠀⡀⢠⠋⡄⠀⠀⢀⡀⣠⠀⡠⠀⢀⡄⣠⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣰⠃⡜⢱⠃⡎⢰⢣⠞⠸⢡⠏⡄⠀⠀⠀⠟⢰⠃⢼⠡⠀⡞⠰⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁



⠀⠀⠀⠀⠀⠀⢀⠀⠠⢤⢰⣷⣧⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⡆⡠⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠈⠢⠙⠒⠀⠈⠙⢿⣆⠁⠀⠀⠈⠢⣀⡀⡔⠉⣴⣯⣶⣀⠈⢀⠀⡀⠀⠁⠀⠀⠈⣰⡿⠋⠁⠀⠖⠋⠔⠁
⠀⠀⠀⠀⠀⠀⠐⠂⢠⣄⠀⠀⠀⠀⢉⠷⢶⡀⠀⠺⣀⠁⢑⣼⣿⣙⣛⢿⠆⠌⠄⡀⢀⡀⢀⡶⠞⡉⠀⠀⠀⠀⣠⡄⠐⠂
⠀⠀⠀⠀⠈⢁⣩⠰⠆⠰⠀⡹⢢⠞⠁⠀⠀⠙⠓⠀⣀⡀⣀⣣⢈⠉⠛⠋⢂⡀⢈⣀⠀⠚⠋⠀⠀⠈⠳⡜⢏⠀⠆⠰⠄⢍⡈⠁
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⣡⣞⠛⢛⣥⢼⢃⣼⡀⢀⣷⣘⡧⣬⠛⠛⢳⣌⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠂⠀⠠⢀⡾⣥⡴⠺⢃⣴⠏⠧⣒⠍⠩⣂⢼⠹⣦⡙⠟⢦⣬⢷⡀⠄⠀⠐⠂⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⣎⣞⡽⠴⠛⠋⠁⠀⠘⢽⠁⠀⡯⠃⠀⠈⠙⠛⠦⢯⣣⣱⠀⠀⠀⠐⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀⠀⠁

⠀⠀⣠⣾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣷⣄⠀⠀⠀⣠⣶
⠀⠀⣿⡇⠀⠀⢀⠀⠀⢀⣀⡀⠀⣀⣀⡀⠀⣀⣀⡀⠀⠀⣀⡀⠀⡀⠀⠀⡀⣀⣀⣀⠀⣀⣀⠀⠀⢸⣿⠀⠀⢠⣿⡇
⠀⠀⣿⡇⠀⢠⡟⣧⠀⣿⣉⣹⠆⣿⣉⣿⢈⣯⣉⡿⢠⡟⠉⠹⡆⢻⡄⣼⠃⣿⣭⣍⠀⡏⠉⢻⡄⠸⢿⠀⢀⣿⣿⠁
⠀⠀⣿⡇⠀⡾⠛⠻⡇⢿⠁⠀⠀⠿⠀⠀⠨⡇⠈⢷⠈⠳⣤⡼⠃⠀⢿⠏⠀⢿⣤⣤⠀⣷⡤⠾⢡⣶⣦⣀⣼⣿⡇
⠀⠀⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠿⣿⣿⡿
⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⠈⠻⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣼⠥⠀⠀⠀⠈⠑⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣿⠾⠃⠀⠀⠀⠀⠀⢀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⣴⣶⣶⡶⠶⢶⢶⡏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠀⠀⣼⢸⡇⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡼⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠃⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠺⠛⠛⠛⠻⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠇⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⣴⠶⠿⠛⠷⠶⣦⣀⡏⠈⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⢰⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠞⠛⢧⣄⣀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢀⡴⠞⠛⠒⠒⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠺⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣾⣿⣿⡿⠟⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣶⡿⠿⠟⠿⠿⠛⠋⠉⠁⠀⠀⠈⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣦⣾⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣼⣿⣿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠶⠀⢻⣏⠉⠙⣿⡄⠀⢽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣿⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⣀⣀⡀⠠⣦⡀⠀⣿⡇⢸⣧⣤⣴⠆⠈⣿⡀⠀⣸⡇⠀⠘⣿⣿
⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⠿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⠀⢰⡟⠋⠙⢿⣆⠙⣷⡄⣿⠀⠈⣿⣀⣀⣤⡄⠹⠟⠛⠋⠀⠀⠀⢻⣿⡇
⠀⠀⠀⣴⣿⡿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⢶⣄⠸⣿⠉⣈⡽⠇⢹⣇⠀⠀⢸⣿⠀⠈⢿⡿⠀⠀⠙⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⠃
⠀⠀⠰⣿⣿⠀⠀⠀⠀⢀⡀⠀⠀⢶⡾⠛⢻⣦⠸⣷⣀⣤⠿⠀⢿⡟⠙⢷⣦⡀⠛⠷⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣿⣿⡿⠿⠛⠁
⠀⠀⠀⢻⣿⡆⠀⠀⠀⣿⢿⣆⠀⠘⣷⡶⠾⠃⠀⢻⡏⠀⠀⠀⠘⠟⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠐⣿⣷⠀⠀⢀⣿⣤⠿⣷⡀⢻⡇⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣿⡿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⢿⣿⡆⠀⠸⠏⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣿⣿⠿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⡿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠻⣿⣷⣦⣔⣶⣿⣿⣿⡿⠿⠛⠛⠉⠁
⠀⠂⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠶⠶⠶⠦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢞⡫⠽⠒⢋⣭⡉⠉⣭⡍⠉⣝⠒⠯⢝⡳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⡽⣊⡁⠐⣿⣆⠈⣿⠇⠀⠿⠇⢰⣟⠀⣰⣷⠈⠑⢯⡳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⠕⣁⡀⠹⣇⠀⣹⠭⠒⠚⠉⠉⠉⠉⠓⠒⠤⣝⠃⠀⠀⣀⡈⠪⡻⣆
⠀⠀⠀⠀⠀⠀⢀⡾⡳⠋⠈⠻⣇⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠙⠢⡀⠛⠃⠀⠙⢞⢷⡀
⠀⠀⠀⠀⠀⢀⡾⡱⠁⠻⣷⠆⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠈⢢⠀⠀⣀⠈⢎⢷⡀
⠀⠀⠀⠀⠀⣼⢳⠃⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⠀⠀⠀⢳⠘⠛⠃⠘⡞⣧
⠀⠀⠀⠀⢀⡟⡏⠰⠿⠆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢹⢻⡀
⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣶⡆⢸⢸⡇
⠀⠀⠀⠀⢸⡇⡇⢠⣤⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠈⣇⣇⠈⠉⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⣤⠀⣸⣼⠁
⠀⠀⠀⠀⠀⢻⡼⡄⠀⢀⠀⢧⠀⠀⠀⠀⢿⣷⣶⣤⣄⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠈⠋⢠⢧⡟
⠀⠀⠀⠀⠀⠈⢷⡱⡀⠻⠇⠀⠳⡀⠀⠀⠈⠛⠛⠻⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣴⣤⡀⢀⢎⡾⠁
⠀⠀⠀⠀⠀⠀⠈⢷⡵⣄⠀⠀⣀⡈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢡⣄⠈⠛⢣⢮⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⡢⡀⠛⠃⠀⢀⣝⠒⠤⢤⣀⣀⣀⣀⡤⠤⢒⠋⢤⣷⡀⠙⢒⢔⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣳⢄⡠⢾⡏⢀⣿⡆⢰⣶⠀⢶⣦⠀⢿⣧⠀⢙⡣⣞⡵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢮⣕⣲⠼⣅⣀⣸⣋⣀⣸⣛⣠⠬⣗⣪⡵⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠲⠶⠶⠶⠶⠖⠛⠛⠉⠁

⠀⠀⣤⣤⣀⠀⣀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⢀⣀⣀⡠⠀⢤⣤⣤
⠀⠀⢹⣿⠋⠀⠹⣿⡏⠀⠹⣿⡯⠉⢽⣿⡷⠀⠲⣿⡶⠂⠰⣾⡶⠂⠰⣟⡶⠃⠈⢻⡿⠏⠈⢻⡿⠇⠀⠛⣿⠇⠀⠐⢿⠏
⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⠀⠛⠀⠀⠈⠛⠀⠀⠀⠻⠃⠀⠀⠸⠃⠀⠀⠸⠇⠀⠀⠈⠏⠀⠀⠀⠛⠀⠀⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⢀⣀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⡀⠀⠀⠈⠛⠀⠀⠀⠀⠀⣀⡴⠄
⠀⠀⠀⠀⢛⣼⡺⠀⠀⠀⠀⠀⣻⣿⣿⠋⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⣿⣿⡟⠁⠀⠀⠀⠀⢠⣆⣀⠀⢿⣿⡘
⠀⠀⠀⠀⠀⠉⠁⠐⣶⣾⣇⠀⠈⠀⠉⠀⣾⣿⣿⠀⠀⠀⠀⠀⢴⣿⣿⡃⠈⠁⠈⠁⠀⠀⣀⠀⠘⢻⣿⣿
⠀⠀⠰⠖⠀⠀⠀⠰⠿⢿⡏⠁⠀⠀⠀⠀⠈⠉⠉⠀⢠⣾⣷⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⡞⡹⠇⠀⠈⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠘⠿⠾⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠐⠒⠀⠀⠀⠀⠀⢀⠀⠁⠁
⠀⠀⠀⢀⡾⠿⠞⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣦⡀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⠖⠄⠉⠃
⠀⠀⠀⣿⣧⠀⠀⢈⣿⡇⠀⠀⣀⣀⡀⠀⠀⡀⠀⡀⠀⣀⡀⢘⢋⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⡀⢀⡀⣀
⠀⠀⠀⠻⣿⠀⠔⢺⡿⠃⠀⠨⢛⣧⣧⠀⠀⡟⠶⢻⠀⡧⠄⢸⢴⠃⣯⢼⠁⢱⠎⠀⠀⠈⠁⠁⠀⠀⢛⠋⣉⣡⣟⡃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠈⢀⠃⠃⠈⠀⡁⠁⠈⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠊⠀⠀⠀⠀⠙⠁⠘⠃⠑⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠀⠈⣠⣤⡀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣂⠀⠈
⠀⠀⠀⠰⣾⣷⣾⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡄⠀⠀⠐⠽⠿⠯⠛⠄
⠀⠀⠀⢀⣝⣛⡿⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢀⡖⠀⠀⠠⣄⣀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠉⠹⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠠⡾⠃⠀⠀⠀⡞⠛⠆⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣠⠤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⣀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠤⠄⠀⠀⠠⠤⠀⠄⠀⠀⠀⠀⠿⠿⠶⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⣀⡀⢮⣷⡄⠀⠀⠀⠀⢀⡴⣆⣠⣄⣤⣀⡄⠀⠀⠀⠀⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢮⠅⠘⠛⠀⠀⠀⠈⠀⠠⢤⣀⠀⢠⣀⣈⡀⠀⠁⠠⠄⢀⣠⡼⠛⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣸⣿⣇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠈⠀⠀⠀⠁
⠀⠐⠀⠀⠄⠤⠀⠀⠀⢀⣠⡝⠁⡈⣿⠇⠀⠀⠀⠀⠀⠀⢠⣦⣴⣦⣴⣦⣤⠀⠀⠀⠀⢿⡏⠋⠁⠀⠀⠀⠀⠒⠒⠲⠆⠐
⠀⠀⠀⠀⡀⠀⠙⠿⠛⠛⣿⣇⠀⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠒⠒⠒⠘⠋⠙⠀⠀⠀⠀⠀⠐⠋⠋⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢄⠀⠀⣠⠖⠲⡄
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣾⠀⠀⠀⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⣠⠞⠛⠉⠉⠛⠛⠾⣿⠤⠤⠚⠀⣾⠃⠀⠀⠆⠀⠀⠀⠀⠀⢠⠋⠁⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠈
⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⣿⡄⠀⡘⠀⠀⠀⠀⠀⠀⢹⣀⠀⡠⠀⠀⠀⠀⠹⡄⠀⠀⢠⣾⠟⠁⠀⠀⠀⡸
⠀⠀⠈⣇⠀⠀⠠⢄⠀⠀⠀⢹⣿⡀⠀⠀⢻⣇⠈⠀⠀⠀⠀⢠⡾⠓⡄⠈⠉⢁⢤⡀⠀⠀⠀⠈⠢⣴⡿⠃⠀⠀⣀⡠⠊
⠀⠀⠀⠈⠢⠄⠠⠜⠀⠀⠀⠀⢻⣷⡀⠀⢸⣿⠐⠙⣿⠀⢠⣿⠁⠀⢸⠀⡰⢁⣾⣣⠔⣶⡄⢀⣼⠟⣉⣉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠈⣿⡆⠀⣿⡀⢸⡏⠀⣴⠆⡰⢁⣾⠟⠁⢠⣿⢃⣾⡟⠉⠀⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⢹⣷⠀⢿⣆⠼⣧⠞⢿⠔⠁⢾⠏⠀⢀⣾⠇⣾⡟⠉⣯⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠈⢿⡀⠀⢿⠇⠈⠉⡠⠤⣄⠀⠀⠀⠀⠀⠀⠘⠿⠺⠿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⠈⡆⠀⢸⠇⠀⠈⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠃⠀⠘⠀⠀⠀⠀⠀⠘⢆⠀⢸⡇⠀⣰⡆⠀⣾⠓⠀⠀⠀⠀⠸⣇⠀⠈⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣴⠋⠈⠀⠀⠀⠀⠀⠘⣧⡴⣿⡇⣤⡜⢧⠠⣾⠂⣴⠆⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⣠⡄⠀⠀⠀⢀⢾⡇⣿⠁⡜⠀⣿⡠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠄⢠⡖⡄⢷⣇⡀⠀⢀⠂⢸⡇⠈⠋⠀⠀⠀⠀⠙⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠰⣿⠛⠖⢡⣿⠃⠀⢸⣀⣼⠃⠀⠀⢰⡟⢹⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠻⡤⠃⢸⡇⠀⠀⠀⠉⠁⠀⠀⢀⣿⢃⢦⡾⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠈⠓⠒⠁⠀⣠⣶⠒⠀⣸⣿⢁⣿⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⡀⣿⡇⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⢿⣇⣾⠀⣿⡇⣾⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⠓⠹⠦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠚⠁

⠀⠀⠀⠀⢀⣀⠀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣩⠶⡀⠰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠆⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⡴⠀⠈⠐⣀⣧⢞⠁⢠⠀⠀⢀⠠⠀⠀⠄⠚⢢⡄⠊⠉⠹⡄
⠀⡲⠐⠄⡀⠀⢀⣼⣗⠇⠈⠀⠀⠈⠀⠀⢧⠀⢀⢸⠏⠜⢈⣶⡋⠈⠓⠀⠀⣠⠞⠀⠀⠀⡁⠀⠀⢠⢃⠄
⠀⠸⡂⠬⣟⣴⡯⠦⠯⠋⠀⠀⠀⠀⠀⠂⠈⠿⣿⣴⣮⠜⠉⠜⢁⠠⠀⠀⠀⠘⢄⡢⣀⠢⠁⣀⣀⡜⠁
⠀⠀⠄⠀⡐⡿⠗⠀⠀⠤⠀⠀⠀⠀⠀⢀⡴⠚⢹⠋⠟⣛⣿⢣⡀⠀⠀⠀⠀⠀⠀⣉⡻⠛⢻⠛⠓⡀
⠀⠀⠀⠈⠁⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠜⠀⠀⠀⠈⡆⠀⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⡶⢿⣭⣿⣽⡿⢶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⡓⠀⢼⣿⠿⠿⠿⠟⠛⢶⣿⣻⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠶⢀⠇⠃⠀⠀⠛⠀⠀⠀⣀⣀⠀⠻⣯⣿⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⢿⡄⠚⠙⢶⠤⠐⡿⠟⢿⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠍⠀⠀⠀⠀⠀⢐⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣘⣃⠀⠀⠀⠀⣻⣦⣿⠁
⠀⠀⠀⠀⡄⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣀⣤⠞⣿⢇⡽⣿⣦
⠀⠀⠀⡈⠀⠀⠀⢠⡇⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⡀⠀⠙⣾⠿⠋⠀⠀⠸⣼⣛⣯⡟
⠀⠀⠀⡧⠀⠀⠐⠀⠉⠉⠉⠉⠉⠉⠉⠛⠻⣝⣟⠁⠈⢹⣷⣾⣿⣄⠀⠀⠀⠀⠙⣿⢯
⠀⠀⠀⣧⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⡆⠀⠈⠻⠿⠉⠛⢦⠀⠀⢀⡴⠃⣰⠷⣄
⠀⠀⠀⠀⠉⠙⠲⠤⣄⣀⣀⠀⠀⠀⢠⣴⣾⡟⡼⠁⠀⠀⠠⣤⠴⢻⡞⣷⣞⣉⡀⢰⡇⠀⠈⠙⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⣷⣶⣿⣿⣦⡆⣸⠇⠀⠀⠀⠀⠘⢻⡿⠁⠀⠳⣸⠁⡠⠂⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠻⠛⠿⢾⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠇⠀⠘⠟⠒⠒⣤⠶⣦⣶⣶⣿⣷⢔⠤⣄⣄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡄⠀⢚⠃⠀⠀⠀⠀⠀⠐⠟⣿⢛⣻⣿⣿⣯⣗⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠙⠄⢻⡅⠀⠀⠀⠀⠉⠉⣼⢣⣏⣭⣵⣾⣯⣟⠭⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠠⡄⠸⡘⡇⠀⠀⠀⠀⠀⢸⣧⠜⠋⠁⠀⠀⠀⠙⢷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡈⠣⠐⢧⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠉⢂⣀⡨⠤⠖⠋⠁⠀⠀⠀⠀⢀⣠⡴⠖⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⣀⠀⠤⠤⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⣠⠆⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠛⠛⠻⣿⣏⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⠋⢀⠀⢀⣀⡈⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⡄⠁⠀⠀⢀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣻⠿⢏⠙⣆⢀⡠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠁⠀⣛⣀⢤⣀⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡡⢋⡁⠐⣎⠛⠶⠤⠜⠛⢆⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣅⠘⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣱⡏⠀⠀⠀⠀⠀⠀⠀⠗⢸⠀⡅
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⣠⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⢀⠀⠀⠀⢸⠀⢨⠑⢹⣿⡇⡴⣿⣤⠀⣆⢸⠀⠁
⡉⠢⣀⠀⠀⠉⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠠⣀⡀⢀⠎⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠅⠔⢉⡀⠀⠀⡼⠀⡶⠀⠀⠐⠅⠃⠙⠉⠲⠁⠇⠄
⢈⡓⠦⠟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⡦⣬⠁⠀⢦⡬⢥⡄⢀⠀⠀⠀⠀⠀⡆⠈⠁⠀⠈⡠⢠⠀⢀⡼⢁⠃⠁⠀⠀⠐⠀⠀⠀⡀⢁⠰⠠
⠀⠙⠚⢉⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⣼⠉⠳⢄⡐⠦⣀⢮⣶⣯⠜⢻⠀⠀⠀⠀⠀⣃⠀⢀⠀⠀⠈⠉⠀⠈⠂⠛⠛⠛⠃⠀⢀⣀⠀⠐⠖⠲⠤⠠
⠀⠀⠀⠀⠀⠈⠀⠰⣮⠗⢄⠀⠀⠀⢠⡇⠀⠀⠈⠳⣞⢛⡻⠋⠀⠀⠀⡇⠀⠀⠀⣰⠯⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡈⢳⡀⠀⠘⡇⠘⢇⠀⠀⠘⣿⡁⠀⠀⠀⡄⢿⠀⠀⢀⡏⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⡇⠀⢠⣀⡴⠀⢠⡙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠹⢆⣸⠀⡇⢸⡆⠀⠈⣿⠁⠀⠀⣼⢇⠸⡆⠀⡈⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡏⠀⢤⠙⡄⠀⡎⣷⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠉⢰⠇⠀⣿⠀⠀⢸⠀⠀⠀⣿⠘⡄⢃⡜⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠘⣆⠀⠉⠀⢰⠁⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⢿⠀⠀⢷⡆⠀⢠⡇⠀⢷⣈⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⢿⠀⠀⠀⢸⠀⠸⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠸⡇⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⢸⡄⠀⠀⢸⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⢠⡅⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⢸⠁⠀⠀⢸⡇⠀⢠⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣤⡀⠰⡟⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠀⢸⠀⠀⠀⠀⡇⠀⠘⡄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡼⠁⠀⣇⠀⢹⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⠀⠀⠀⠀⢳⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣀⠀⣟⠀⠀⣉⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇⢀⡟⠀⠀⠀⠀⠘⣇⠀⠸⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠙⣛⠛⠛⠻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢙⠁⢸⠇⠀⠀⠀⠀⠀⢻⡀⠀⠁⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡿⠉⢳⡀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⠷⢢⠄⠁⠀⡟⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠈⠁⠛⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⣾⠇⠀⠸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠁⠀⠁⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⣿⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⢀⡟⠀⠀⠀⠸⡇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⡇⠀⠀⠀⠀⣧⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⡆⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⢸⡇⠀⠀⠀⣸⠃⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⡇⠀⠀⠀⣭⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠸⠁⠀⠀⣘⡇⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢾⡆⠀⠀⣿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⡇⠀⢸⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡆⠀⣈⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢼⡇⠀⡿⠃⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣽⠟⠛⠉⠉⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢸⡇⠀⣷⣄⢀⡀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⣼⡇⠀⠙⠿⠿⣿⡿⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⢦⠀⠀⡠⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡿⠽⠗⠀⠀⠀⠀⠈⠳⣄⡉⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠒⠀⢀⢀⠄⢐⡀⠄⠊⠀⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡈⢲⡄⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠀⠀⠘⠷⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⣄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⣏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢦⡘⢶⡿⢈⣷⣫⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⣿⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⣾⣆⠃⠋
⠀⠀⠀⢠⣴⣶⣶⣶⣾⣶⣦⣸⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠀⠀⠀⠀⠀⠀⠀⣀⠛⠶⠟⠀⠀⠀⠀⠀⠀⢲⣤⡀⠀⣥⣭⣿⡆⠺⠟⠁
⠀⠀⠀⢼⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⠘⠻⢋⢻⣷⣶⠆
⠀⠀⠀⢾⣿⣸⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⢰⣿⣿⣿⠟
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠙⢿⡿⡾⠿⠛⠁
⠀⠀⢰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠓⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⣿⣿⣆⠀⠘⢀⣐⣒⢢⣄⡀
⠀⠀⠀⠙⠺⣬⣿⣿⣿⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⡟⢿⣿⣠⣴⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣦⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣭⣿⡟⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⣏⡿⣿⣿⣿⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⠃⣴⠀⠀⠀⢀⣴⣤⣄⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⡜⢿⣿⠟
⠀⠀⠀⠀⠠⣤⡀⠀⢀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠓⠀⢸⡿⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⢿⣿⣷⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⠁⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠻⠿⢧⠄⠀⠀⠀⣾⣤⠀⠁⠀⠀⠀⠀⢀⣿⣿⠿⠃⢸⣿⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄
⠀⠀⠀⠀⠀⢤⣤⣶⡚⣠⣶⠀⣠⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣾⣿⣿⣿
⠀⠀⠀⢴⣦⡈⢻⣿⣿⡟⠁⠈⠁⢠⡜⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣿⣿⣿⡿⠀⠀⠀⢠⣼
⠀⠀⠀⠸⣿⣿⡄⠈⠛⢿⠟⠃⢤⣜⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡟⣿⣿⣿⣿⠇⢠⢀⣴⠿⡟
⠀⠀⠀⠈⢻⣿⣿⡏⢀⣰⣾⣆⡰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠈⣿⣿⣿⣿⠟⢀⣼⣿⡿⠞
⠀⠀⠀⣀⣼⣿⣿⣷⡀⠈⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⢄⠹⣌⠛⢃⣴⣤⣤⣤
⠀⠀⠀⠉⠻⢿⣿⣿⣇⠀⢀⣴⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂⠉⠁⠈⢉⣥⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠠⠼⠿⠂⢸⣿⣿⣿⣿⡿⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠻⠛⠀⠠⠀⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠿⠿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⣠⡶⠆⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⡉⠉⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠈⠀⠘⢿⡇