Sunny cloud Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠸⢆⠀⠜⡄⢀⣤
⠀⠀⠀⠀⠀⢸⠢⢀⠀⠑⠇⠈⠊⠀⠳⠃⢸⡠⢒⠃
⠀⠀⠀⠹⡒⠰⠆⢀⠤⠒⠂⠉⠉⠉⠒⠢⢄⠀⠸⠐⢺⠃
⠀⠐⢖⠒⠓⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀⠓⠒⡶
⢠⡤⠤⠓⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠔⠉⠉⠒⡄
⠀⣈⠱⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡔⠈⠉⠀⠀⠀⠀⠘⠒⢄
⠉⠒⣠⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠑⢆⠀⠀⣀⠠⠤⢄⡀
⠰⠮⠥⣀⠘⡀⠀⠀⠀⠀⢀⡠⠤⢤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠀⠀⠀⠀⠈⠱
⠀⢀⣔⣁⣀⠑⢄⠀⠀⢠⠃
⠀⠀⠀⢠⣃⢠⡤⠓⠂⠉
⠀⠀⠀⠉⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣀⣀⣀⣀⣀⣀⣑⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣔⣁
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⣆⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣸⠀⠀⠀⠀⠀⣰⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠈⠹⡄⠀⠀⠀⠀⠈⢳⣀⡏⠀⠀⠀⠀⠀⣿⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢻⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢻⠞⠁⠀⠀⠀⠀⠀⣠⠴⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠾⠛⠛⠛⠛⠻⠶⣦⣄⡀⠀⠀⠀⠀⢸⠧⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠙⢦⡀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠃⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀⣀⡀⠀⢠⡟⠀⠀⠀⠀⣠⡴⢶⣄⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠸⣧⠀⠀⠀⢀⣴⡋⠀⠀⢀⣨
⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠉⠉⠉⠉⠉⠉⠙⠻⢿⣇⠀⠀⠀⠀⡿⠀⠀⠿⠀⠀⠀⠀⠿⠁⠈⣿⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣴⠟⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡤⢀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⣼⠏⠀⠀⠠⣄⠙⢦⠀⠀⠀⠀⠀⠀⠚⠰⠃⡼⠀⠀⠈⣿⣤⠶⠶⣦⣄⠻⣦⣴⠖⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢾⡋⠉⠉⠙⢲
⠀⣸⡏⠀⠀⠓⢦⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠁⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠉⠓⠦⠤⠴
⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣤⣄⠀⠀⠀⢀⣴⠟⠁
⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⣧⣤⣶⣟⡁⠀⠀⠀⢠⡤⣄⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⠀⡀⠀⠀⠈⠛⠉⠉⠉⠛⢷⣄⠀⠀⢳⡀⠈⠙⣦
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠁⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠳⢤⣀⡼
⠛⠛⠛⠛⠛⠛⠛⠻⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⢧⠀⠀⠀⠀⠀⢠⡞⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠈⢷⡀⠀⠀⣰⠏⠀⢻⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣟⠳⢦⣀⠀⠀⠀⠀⢻⠀⠀⠈⢷⡀⢰⠏⠀⠀⢸⠀⠀⠀⢀⣠⠶⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠙⠢⣄⠀⢸⠀⠀⠀⠈⢧⡟⠀⠀⠀⣸⠀⣠⠶⠋⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⢙⡾⠶⠒⠒⠋⠙⠓⠒⠶⢤⣿⠞⠁⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⢀⡞
⠀⠘⠻⣍⠉⠉⠉⠉⠉⠉⠉⢉⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡞⠒⠚⠛⠋⠉⠉⠉⣛⡿⠂
⠀⠀⠀⠈⠙⠢⢄⡀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢀⣠⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣙⣳⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⠖⠋⠁
⠀⠀⠀⢀⣠⠤⠒⠋⠉⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠛⠒⠶⣤⣀
⠠⣶⣟⡉⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠶⠖⠿⠶⢤⣄⠀⢀⣀⣈⣹⣶
⠀⠀⠈⠉⠉⠉⠉⠛⠉⣻⠟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⢀⣀⡀⠀⠈⢻⡟⠛⠉⠉⠉⠙⠓⠲⠦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⡇⠀⠀⠀⠀⢰⠁⢀⡹⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡠⠔⡿⠢⣄⢀⠴⠊⠉⠀⠀⠈⠉⠃⠀⠀⠀⠀⠈⠦⣀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇
⠀⠀⠀⠠⣾⡥⠴⠶⠒⠋⠁⠀⢀⠇⠀⢨⠃⠀⢀⠤⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠉⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄⠒⢺⡀⠀⠘⠤⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣀⡀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠙⠲⠶⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠘⠁⠙⡆⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠤⠤⠞⠁⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠦⠄⣀⣀⣀⣀⣠⣤⠞⠉⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⠉⠐⠛⠓⠒⠛⠉⠉⠁⠀⠀⠀⠀⠉⠛⠒⠒⠒⠒⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠂⠲⠀⠂⠐⠰⠐⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠘⠘⠀⠂⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔
⠀⠀⠀⠀⠀⠐⠟⢍⣉⡱⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠀⠈⢀⠤⠒⠂⠀⠒⠢⢄⠀⠀⠀⢀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠉⢲⡤⠤⡀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠑⡄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠊⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠠⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠁⢀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠲⡀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣠⠽⠉⠡⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠐⢴⠀⠐⣀⠀⠀⠀⠀⠀⠠⠐⠋⠙⠒⢄⠀⠀⠀⠀⠈⠒⠒
⢠⠎⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠖⢄⠐⠀⠀⠀⠀⠀⠀⠀⠉⠉⢢⡀⣀
⠀⠓⢰⠒⠦⣄⣀⣀⣠⠴⠦⣀⣀⡠⠄⠲⢄⣀⣀⣀⣀⠤⢀⣀⣀⣀⣀⠀⠄⢀⣀⣀⡤⢦⣄⣤⠤⠊⠀⣀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠦⣀⣀⣀⣀⠤⢤⣤⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠐⠂⠉⠉⠀⠀⠉⠉⠉⠀⠙⠚⢏⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡤⢤⣤⡤⠤⣄⣀⣀⣀⡤⢄⣀⠔⠀⠄⠁⠀⠀⠈⠢⠔⠂⠂⣀⣀⡠⠔⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢢
⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠒⠠⡀⠀⠀⠀⠙⠤⢤⡠⠤⢤⡀⣀⠤⠖⠤⢀⣀⣀⡠⠤⣀⡠⠔⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠢⠤⠤⠔⠓⠢⠤⠤⠒⠊⡑⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠑⠁⠉⠀⠈⠁⠉⠑⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠉⠉⠙⠛⠉⠑⠚⠻⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⢀⣀⣀⠤⡠
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⡏⠈⠉⠲⣴
⠀⠀⠀⠀⣀⣀⠀⣲⣾⠇⠙⣷⠀⠀⠒⠛⢃⢠⣿⠉⠀⠀⠀⠀⠀⢴⠯⠁⠀⠄⡍⠻⡧⠀⠀⠇⣸
⠀⠀⠀⢈⣍⠻⠷⠼⠟⠁⣠⡿⢿⡶⠒⠒⠀⠀⠀⠀⠀⠀⣀⡄⣺⣔⠀⠀⠀⠀⠙⠀⠑⠙⠉⠙⢋⡄⠀⣠
⠀⠀⠐⣚⣛⠿⣥⣰⣶⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠰⠴⢶⣬⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠸⣟⣠⠉⡟
⠀⠀⠀⠀⠀⠀⠙⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣶⣤⣤⣀⡄⣠⠀⡂⡰⡖⠳⠤⣴⡖⢱⢜⡞⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⣽⡛⣿⢦⡝⠻⣷⣀⣷⣏⡘⢠⡧⣾⣿⠧⡆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠰⠦⠭⠉⠁⠌⡻⠛⠑⠀⠈⢋⡽⢋⠀⠛⠉⠁


⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠀⠄⠀⠀⣀
⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠄⠀⠀⠀⠀⠀⠉⠀⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡀⢀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣴⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣙⡇
⠀⠀⠀⠀⠀⣤⣈⠄⣇⠀⠀⠙⢦⣤⡈⢳⣤⡀⠀⠀⠀⠀⠀⢀⠈⠀⢉⡀⢄⠀⠀⠸⣄⣀⠀⠀⢰⠤⠌⠀⠸
⠀⠀⠀⢠⡄⠀⠀⠈⠁⠐⠀⢤⠈⠿⠛⠈⠁⠠⠀⠃⠀⠀⠀⠈⠡⣄⣰⡿⣶⡷⣶⡆⠀⢥⡅⢀⠀⠠⠀⠀⡀
⠀⠀⠀⣄⣀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠈⠄⠀⠈⠐⠆
⠀⠀⠠⣼⣯⣀⡀⠒⠘⢦⡀⠀⠀⠠⢰⡄⠀⢐⠂
⠀⠀⠀⠀⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣄⡀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⣀⣤⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠆⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⠉⠉⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣇⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⣿⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡿⠛⠋⠉⠉⠉⠙⠛⢷⣤⡀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⢸⣿⡟⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢾⡿⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⣾⣏⠀⠀⠀⠉⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠈⠙⢷⣄⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠉⠛⣷⡀
⠀⠀⠀⠀⢀⣴⠟⠋⠉⠉⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢻⣆
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⣿
⠀⠀⠀⠀⠘⠷⣦⣤⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢶⣤⣤⣤⣤⣤⣤⣴⠶⠟⠻⣦⣀⠀⠀⠀⠀⠀⠀⠘⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⠷⢦⣤⣤⣀⣠⣤⣴⠾⠟⠻⠶⠶⠶⠶⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣩⠇⠀⠀⠀⠀⠀⣠⠖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠘⣮⣇⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣣⠞⠁⠀⠀⠀⠀⢀⡞⢁⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠘⢧⠘⢦⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⣧⣼⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⢀⡴⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⢧⡀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⣠⣾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠈⠷⠀⠀⢀⣀⣀⣤⣬⣄⣀⣀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠈⠻⡄⠀⣠⠴⠚⠋⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠴⠟⠁⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠛⠦⣝⣦⡀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢚⣉⡟
⠀⠀⠀⠀⠀⠀⠙⠻⢦⡄⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠠⠶⠟⠛⠋⠉⠁
⠀⠀⠀⢀⣠⠤⠴⠶⠶⠶⠾⢤⣀⡀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠉⠙⠲⢤⡀⠀⠀⢀⡤⠶⠚⠛⠉⠉⠛⠓⠦⣄
⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠴⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⠀⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠁⢀⣀⠀⠙⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⢀⣤⣾⣿⣿⣿⣿⣷⣦⣀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⣿⣿⣿⣿⣿⠿⠛⠉⢉⣉⠉⠁⢀⣤⣶⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡄⠈⢿⣿⣿⡟⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⡿⠿⠿⣿⣿⡿⠿⣿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣴⣼⣼⣧⣥⣥⣡⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣻⠿⠿⠿⠛⢿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣟⣻⣿⣿⡿⢁⡀⡈⠉⠀⡄⡙⣿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣅⣀⠁⠐⠀⢠⠀⠴⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠿⠉⠁⠀⠀⠀⠐⠂⠀⢀⣿⣭⣻⣿⠿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⠉⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⣿⣿⡿⠃⠀⠀⠀⠀⠹⢿⣿
⠛⠻⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢹⣿⣿⣿⣷⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⣄⣠⣾⣶⣾⠁
⠀⠀⠀⠀⠹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡶⠖⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠻⣿⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⠿⠿⠛⠛⠛⠛⠉⠛⠛⠛⠛⠿⠿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛⠛⠛⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄
⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦
⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣼⣿⠀⠀⠀⠘⣷⣄⣀⣀⣠⣾⡿⠁⢀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇
⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠉⠉⠉⠛⠿⡇⠀⠀⠀⠈⠛⠻⠛⠛⠋⠀⠚⠛⠉⠉⠉⠙⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇
⠀⠀⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡆⠀⠀⠀⠤⠀⠰⢶⣷⢰⠦⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿
⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⣿⡇⠀⠀⠀⢀⣬⠻⠷⣿⠴⠶⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃
⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢀⣿⡇⠀⠀⠀⣀⠩⢿⣋⣴⣘⡿⠌⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣴⣾⠟⠀⠀⠀⠀⠉⠀⠘⠋⠙⠈⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣷⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣿⡿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⣆⠀⠀⣴⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣸⠷⣤⡾⠙⠳⠞⠉⠷⠴⠿⣇⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠒⠋⠀⠀⣀⣀⣤⣤⣄⣀⡀⠀⠙⠛⢹⡇⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡶⠚⣁⣀⣤⡶⠿⠛⠛⠛⠛⠛⠿⢿⣿⣦⣄⠀⠉⢉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠞⣛⣉⣉⣉⣙⠓⠶⣤⡀⠀⠀⠀⠀⠀⠉⠻⣿⣷⡄⠀⠛⢲⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢚⣛⣉⣉⣛⡓⠶⣤⠞⣡⡶⠟⠛⠛⠛⠛⠿⣿⣷⣤⡙⢦⡀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⢺⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⠾⠛⠛⠛⠛⠻⢿⠗⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣌⠳⢤⣤⣀⡀⠀⠀⠈⣿⣿⠀⠀⣼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡞⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠾⠿⠿⠿⣶⣦⣄⠙⢿⣿⣶⣶⣬⡙⠳⣄⠀⢸⣿⠀⠀⠛⣦⣄
⠀⠀⠀⠀⠀⢀⣀⡾⠀⢀⣤⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⠀⠈⠙⠻⣿⣦⣬⣿⣛⡛⠶⣤⣟⠁
⠀⠀⢀⣤⢞⣫⣵⣦⡾⠛⠉⠁⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠈⠉⠙⠛⠻⢿⣷⣦⡙⢷⡄
⠀⣠⠟⡵⠋⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠹⣆
⢰⠏⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⢹
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸
⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡟
⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠈⠙⠓⠶⠶⠶⠶⠒⠛⠁⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣤⣤⣤⣤⠴⠞⠋⠀⠈⠙⠛⠒⠒⠒⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⣠⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣿⣆⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆
⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣳⠀⠀⠀⠀⢠⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢀⠙⣧⠀⠀⠀⠀⣀⣼⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⡶⠀⠀⠀⠀⠀⣿⣿⣿⣣⣿⡆⠀⠀⠀⣾⣿⣿⣿⡏⢷⣄⠀⠀⠀⠀⣸⣿⣿⣿⠿⠿⠿⠇⠀⢀⣾⣿⠸⣿⣿⡟⡆
⠀⠀⠀⠸⣿⣿⡻⠇⠀⠀⠀⠀⣾⣿⡟⠿⣿⡿⣿⡄⠀⢀⣿⣿⣿⣿⣀⣨⣿⡆⠀⠀⠀⣿⡿⠉⠛⠀⠀⠀⠀⢰⣿⠋⠈⠀⠛⠟⠃⣿
⠀⠀⠀⠀⠠⣿⣿⣿⣤⡀⠀⠀⠈⢿⣷⣤⣾⡇⠘⠛⠀⠘⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⢻⡷⣾⣿⡇⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠘⣿⡀
⠀⠀⠀⢠⣿⣷⣶⣶⣿⣿⣦⠀⠀⠀⠈⠛⠟⠀⠀⠀⠀⠀⢻⡛⠿⠟⠀⠀⠀⢀⣄⢀⣴⣿⣧⠀⢉⣀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⣹⡇
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⡀⠀⠀⠀⢠⠀⠀⠈⢿⣷⣶⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⣼⣿⣄⢀⣼⣿⡇
⠀⠀⠀⠈⠉⠉⠉⠉⠉⢻⣿⡀⠀⠀⠘⠛⠂⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⠻⠿⠛⠋⠉⠉⠉⠛⠛⠛⠉⠁⠀⠀⠸⠿⠿⠟⠺⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣻⣻⣟⣙⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠙⠙⠿⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⡄
⠀⠀⠀⠀⠀⢀⡜⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣁⣤⣤⣄⠀⠠
⠀⠀⠀⠀⠠⣿⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⣦⡀
⠀⠀⠀⠀⠀⡤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢿⣷⡄
⠀⠀⠀⠀⠘⠓⢻⣿⣿⣿⣿⣿⣿⣼⣿⢿⣿⣿⣿⠀⠀⠀⢸⣿⣿⡄⠀⠑⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⢸⡟⠉⠀⠀⠀⠀⠀⠀⠀⢁⠠⢻
⠀⠀⠀⠀⠀⠠⠜⣬⣿⣿⣿⣿⣿⣿⣿⣇⠛⢿⣿⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡾
⠀⠀⠀⠀⠀⠀⠐⠹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⡇
⠀⠀⠀⠀⠀⠀⡄⢠⣯⣹⣿⣿⣿⣿⣿⣿⣧⠀⣿⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣟⣡⣾⡿⠁
⠀⠀⠀⠀⠀⠈⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⠀⠀⠀⣿⠀⠀⠀⢀⣠⣴⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠀⠀⠀⣿⣧⣴⣾⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠘⠿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠠⣾⡄⡰⣿⣿⣿⣿⣿⣿⣿⠃⢸⣧⠀⠀⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⣤⣿⣴⣿⣿⢿⡿⠋⠀⠸⣿⣿⣾⠿⠛⢹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⡻⣿⠻⣿⣦⣀⠁⠠⠩⠉⠵⠄⠀⠀⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢋⠻⠃⠀⠀⠄⢠⠄⡀⢀⠄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠗⠀⠀⠀⠀⡀⠈⢉⡀⠁⠈⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⣼⣿⣿⣮⠷⠀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣶⣆⠀⠀⠀⡀⢀⣀⣉⣰⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣄⠀⠀⢀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⡄⠘⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠲⣄⠀⠀⠀⣰⠁⠀⠈⢇⠀⠀⠀⢀⣠⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠞⠁⠀⠀⠀⠈⠦⡤⠞⠋⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⡤⠶⠖⠒⠛⠛⠛⠒⠲⠶⢤⣄⡀⠀⠀⠈
⠀⠀⠀⠚⠓⠒⠲⠶⠖⣫⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡠⣄⣀⢀⣀⣀⡀
⠀⠀⠀⠑⢄⡀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠉⢉⣭⠿⠛⠛⠛⠛⠷⢦⡀
⠀⠀⠀⠀⠀⡷⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⠋⠀⠀⠐⠀⠀⠀⠀⢀⠙⢂
⠀⣠⡤⠴⠚⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⡞⢁⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⣇
⢎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⠋⠀⠀⠀⠐⢁⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⣽⠲⣄
⠈⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣠⠞⠁⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠇⠀⢹⣤⣤⣤⡀
⠀⠀⠀⠈⣧⠸⡀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⢙⠷⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠄⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠘⠀⠀⠀⠙
⠀⠀⢀⡴⠋⠀⡇⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡐⠀⠃⠀⠠⠀⠀⠠⢡⠂⠄⡐⠀⠀⠀⠀⢠
⢀⡾⠋⠀⠀⠀⠹⡄⠀⠀⠀⠀⡸⢧⡀⠀⠀⢀⠀⠀⡠⠁⠀⠄⠀⢀⠎⠀⡐⢀⠂⡀⠠⠁⠈⠠⢁⠃⡐⡰⠀⠀⠌⢠⣀⣂⣠⣠⡾
⠿⣤⣄⣀⣀⣀⠀⠻⣆⠀⠴⠚⠁⠀⠙⠳⠶⣆⡔⠜⠁⠀⡘⠀⠀⠈⡆⡰⢀⠂⡐⠠⠁⡌⢠⠃⠌⡐⢠⠇⠀⡘⢰⡏⠉⠉⠉⠁
⠀⠀⠀⠀⠈⠉⢣⠀⠙⠿⣤⣀⠂⠀⠀⠀⠀⡘⠻⢶⣶⡶⢧⣀⠀⠌⡹⣄⡂⡐⠡⢁⠜⠠⠃⠀⣠⡤⠻⠶⠶⠟⠋
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠙⠛⠷⠷⢶⣶⣶⣶⣶⡶⠿⠟⠛⠛⠿⢿⡿⠛⠷⠷⠾⠶⠷⠟⠛⠉
⠀⠀⠀⠀⠀⠀⣇⠀⢀⣠⡴⠖⠻⢶⡀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⢻⡄⠀⢠⡞⠁⠀⠉⠳⢦⣄⣼⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣶⣋⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⢶⣄⠀⠀⠀⠀⣰⠏⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠙⣷⣄⣀⣰⣏⡀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠷⠛⠋⠉⠉⠉⠉⠉⠉⠛⠻⢤⣀⣤⣤⠶⠶⢶⠄
⠀⠀⠐⣿⡲⠶⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢠⡟
⠀⠀⠀⠈⠻⣦⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠟⠛⠛⠛⠛⠛⠛⠲⢦⣄⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⣸⡃⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⢦⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⢀⣤⠴⠞⠛⠹⣇⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠛⠳⠶⠶⣤⣤⡿⠶⠶⠶⠶⢤⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠛⠶⣄
⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠉⠛⠓⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠶⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠤⠒⠛⠛⢙⡞⠀⠤⠠
⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀⠀⠀⠈⠁⠸⠆⠈⢢⠀⡀⠀⠄
⠀⠀⠐⠀⠀⠀⢀⣀⡠⠖⠂⠐⠲⣤⢀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠈⠁⠀⠀⠛⠿⢷⢤⣀⡀⠀⣀⣀⡨⠊
⠀⠀⠒⠉⠒⣤⣼⡉⠀⠰⣶⡀⠀⠀⠀⠀⠀⣾⢹⢹⡱⣅⠠⣀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⢤⠀⠀⠦⠈⠀⠁⠀⠆⠀⠛⣤⡠⠔⠁⠀⠪⡢⢕⡛⠦⠭⠒
⠀⠈⠷⢬⡁⠀⠈⢀⠀⣠⠔⢈⠄⠀⠀⠀⠀⠀⠀⠁⣀⠁
⠀⠀⠀⠀⠉⠁⠀⠐⠒⠭⠒⠁⠀⠀⣠⣴⡶⠶⠒⠒⠓⠀⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠠⠀⢀⡖⢂⣰⠄⠀⣄⡀⢆⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢣⡘⢦⣀⠀⠀⠀⠀⠀⠈⠔⠀⠀⡞⠀⢀⣠⡤⠄⠠⣄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠁⠉⠑⠏⠉⠉⠉⠀⠀⠈⠀⠀⠀⠉⠁⠀⣀⣤⡴⠙⠀⡆⢀⠐⠲⢄
⠀⠀⢀⣤⣴⣤⡤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⠄⠁
⠀⠠⡜⢜⠎⢯⡳⠽⣶⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣄⠀⠀⠰⠂⠀⠰⠀⠠⠃
⠀⠀⠈⠒⠅⠊⠭⠓⢒⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢍⠫⠝⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠃⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠙⠻⣶⣦⣤⣀⣀⣤⣤⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠓⠲⢄⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣀⣀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠹⡶⠤⠤⠤⠴⠚⢻⡀
⠀⠀⠀⢀⠖⠉⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠒⠒⠒⠒⠤⣄⠑⢄⡀
⢀⠴⠒⡎⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⣄⠀⠀⠀⠀⠙⢦⠉⠙⣲⠂
⡏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⢳⠀⡇⠀⠀⣀⣀⣀⣀⡀
⠙⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠞⠀⠀⠀⠀⠀⠀⠈⣇⠷⠊⠉⠀⠀⠀⠀⠉⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡘⣆⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠲⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⠣⣀⠀⠀⢠⠞⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⣈⡵⢶⡏⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠎⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣯⣤
⣿⣿⣤⣴⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠚⠉⢉⠉⠙⠒⠢⠤⣀
⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⢀⠟⡆⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⡜⠀⢹⡀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⢀⠇⠲⣖⠒⠒⠒⠖⠒⢲⡗⠒⠒⠒⠚⡖⠖⠒⠒⠲⠖⢲⠶⠈⡆
⠀⠀⢸⠀⠀⠈⠑⠦⡀⠀⠀⡼⠀⠀⠀⠀⠀⢱⠀⠀⢀⡤⠚⠁⠀⠀⢳
⠀⠀⢸⠀⠀⠀⠀⠀⠈⠓⢴⡃⠀⠀⠀⠀⠀⠀⣧⠖⠉⠀⠀⠀⠀⠀⡸
⠀⠀⠘⡄⠀⠀⠀⠀⠀⢀⡎⠈⠲⢄⠀⣠⠔⠋⠘⡄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠱⡀⠀⠀⠀⠀⡼⠀⠀⢀⠴⠋⠣⣄⠀⠀⢱⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠱⡄⠀⠀⢰⢃⡤⠚⠁⠀⠀⠀⠀⠑⠦⣀⢇⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠈⠢⣄⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠤⣀⣀⡀⠀⢀⣀⣀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⣿⢿⠿⡿⡿⠿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣻⣿⣻⣿⣟⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠳⢦⠀⠀⠀⠀⠋⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠶⢶⣶⣶⣤⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣵⣶⣿⣿⣿⣿⣿⣿⣷⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣛⣛⡛⢿⣿⣿⣿⣿⣿⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⣿⣿⣿⠇⠀⠀⣠⡤⠿⠂
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣭⣅
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠖⠲⡄⠀⠸⣄⠀⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣠⠏⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⠳⡄⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⣸⣿⠀⠀⢻⠀⠀⠀⣄⡀⠀⢀⣿⣿⠤⠀⠐⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⢀⣿⡇⠀⠀⡾⠀⠀⠀⠈⠉⠉⢩⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢸⣿⡇⠀⢠⠇⠀⣴⠖⢦⡀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣼⣿⠁⣰⠋⠀⣸⣿⠀⠀⢷⠀⢸⣿⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣀⣀⣠⣿⣿⠋⠁⠀⠀⣿⣿⣦⣀⣸⡤⢾⣿⡇⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣿⣿⠁⠀⠀⣿⣿⠀⠀⠀⠀⢿⣿⠁⢩⡏⠀⠘⣿⣷⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣿⣿⠀⠀⠀⢻⣿⡀⠀⠀⠀⡟⠛⠓⠋⠀⠀⠀⢻⣿⡀⠀⠾⠀⠀⠀⠀⣠⣶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⣿⠇⠀⠀⠀⠸⣿⡇⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⢀⣙⠃⠀⠛⠛⣿⣦⣾⣿⣿⣿⣿⠿⠿⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠲⢦⣷⣤⠾⠋⠀⠀⠀⠀⠀⢻⣷⡀⢀⡞⠀⠀⠀⠀⠀⢀⣴⡿⠉⢛⣴⡾⠿⣿⣿⣿⣿⣿⣿⠿⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⢀⣾⡿⠁⠐⣯⠁⠀⣴⡿⠛⠛⢿⡋⠛⢷⡄⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⣠⡶⠲⡄⠀⠀⠀⠀⠀⣾⣿⠇⠀⢠⡇⠀⠼⠋⠀⠀⠀⠸⡇⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⡇⠀⠀⠀⠀⢰⣿⣿⠀⠀⡾⠀⠀⣠⣖⣀⣠⡀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣤⣤⠀⣿⣿⡀⡸⠀⢀⣤⣄⠀⣸⣿⡇⢠⠄⢳⣶⣾⣿⣿⣏⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠐⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⡇⠀⢸⣿⣿⠀⠹⣿⣷⣁⣠⣾⣿⡏⠀⣿⣿⡟⠉⣴⠟⢻⡿⠿⣯⠈⠉⠁⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⡴⢹⣿⣿⠀⢸⣿⣿⠀⠀⢸⠏⠉⢸⣿⣿⠃⠀⣿⣿⡇⠘⠁⠀⠺⡁⠀⠈⢷⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⢀⣠⠞⠁⢸⣿⡟⢀⢼⣿⣿⠀⠀⡟⠀⠀⢸⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⢀⠃⠀⠀⠈⣧⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⣀⣠⣼⣿⡟⠁⠀⠻⣿⣄⡼⠃⠀⠀⢸⣿⡇⠀⢠⡿⣿⣿⠀⠀⢀⡟⠀⠀⠀⠀⢹⡆⣰⣿
⠀⠀⠀⠀⠀⠀⣠⡶⠒⠲⣄⣴⠟⠉⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣀⡞⠀⠙⢿⣧⣤⠞⠁⠀⠀⠀⣦⣼⣿⣿⣿⣿⠿⠷
⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⢸⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠉⠉⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⣫⠤⠀⠁
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣦⡀⠼⠿⠁⠀⠀⠀⠀⠀⠀⠎⣿⡆⢀⣀⠀⠀⠀⠀⢀⠋⣿⡆⢀⣀⠀⠀⠀⣀⣤⣄⣸⡟⠀⠃
⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⣸⣿⠀⠀⣾⡇⠀⣿⡇⡘⠀⣿⣧⠏⣿⡇⠀⣿⡇⡌⠀⣿⣧⠃⣿⡆⠀⣼⣿⠁⣼⢻⣷⡌⣠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⣀⣿⣿⠀⣸⣿⠇⠀⣿⣷⠁⠀⢿⡿⠀⣿⡇⠀⣿⣷⠀⠀⣿⡏⠀⣿⡇⢰⣿⡟⠊⠁⠀⡟⠉⢹⣿⠁⢀⠆
⠀⠀⠀⠀⠀⠀⣠⠤⠒⠻⣿⡅⠘⢿⡴⢻⣿⠀⢠⠿⡿⠀⠀⠈⠁⠀⣿⡇⢀⠿⡟⠀⠀⠈⠁⠀⣿⡇⢸⣿⣧⠀⢀⡜⠁⠀⢸⣿⠀⣸
⠀⠀⠀⠀⠀⢰⡏⠀⠀⢀⣿⡇⠀⠀⠀⠘⣿⣄⡾⠀⠀⠀⠀⠀⠀⠀⠹⣧⡸⠀⠀⠀⠀⠀⠀⠀⢻⣇⡜⠈⠉⠋⠉⠀⠀⠀⠘⣿⣰⠃
⠀⠀⠀⠀⠀⠸⣇⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠉⠀⠛⠻⢶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠶⢆⣤⣤⣴⣶⣶⣶⣆⣸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣵⣿⣯⣿⣿⣿⣿⡿⢋⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⢟⣛⣛⣀⡀⠀⠐⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡷⠙⢿⣿⣿⣿⣷⣦⡿⣿⣿⣿⢿⣽⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠉⠁⠁⠀⠀⠙⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⡿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣐⣤⣰⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣷⣹⣯⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡶⠶⠟⠃⠀⢸⣿⣿⣿⣿⠙⢿⣯⢰⡟⠙⢋⣝⣿⣽⣿⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣇⣀⡥⠐⢐⣥⣿⣿⣷⣬⣿⣷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣋⠀⠀⠀⠀⠀⢀⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⣀⣀⡀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⢀⣾⠟⠛⣿⡆⠛⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣿⠈⢿⣧⣤⣿⠇⠀⣿⡇⠀⠀⠀⢀⠤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠈⠉⣠⡄⠀⢈⣠⣤⠞⠟⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠙⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡄⠟⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠁⠤⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠂⣰⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⡘⠁⠻⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣠⣎⣀⣼⠃⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠁⠀⠀⠈⠂⠻⣿⣿⣤⠇⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠙⠻⢿⡆⣀⣀⣈⣢⣄⠀⡩⠟⠿⠿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠠⠤⠀⠀⠤⠔⠒⠉⠉⠉⠛⠓⠒⠒⠛⠛⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠦



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⢦⡀⠀⠀⠀⠀⠀⣼⠏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠙⢦⡀⠀⠀⣼⠏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠶⠶⠛⠛⠛⠛⠛⠛⠶⠶⣧⣀⠀⠀⣀⣀⣤⣤⣤
⠀⠀⠀⣤⣤⣄⣀⡀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡉⠉⠀⣰⠏
⠀⠀⠀⠙⢷⣌⠉⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣦⣴⣿⠴⠶⠶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠙⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⢀⣀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⣠⡶⠞⠛⠉⠀⢻⡄⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠉⠛⠛⠳⣶⣶⠾⠿⠞⠛⠛⠳⠶⢾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀
⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⢶⣄
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠙⠛⠶⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠶⠶⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠛⠛⠉⠉

⣾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣷
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢻⡟⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⣴⠋
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠙⠳⣄⡀⠀⠀⠀⣸⠁⠀⠀⢸⡆⠀⠀⠀⢀⣠⠞⠋⠀⢀⡞⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠈⠙⠦⣄⣀⣿⣤⣤⣤⣼⣧⣀⣠⠴⠋⠁⠀⠀⣰⠏
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢀⡴⠟⠋⠁⠀⠀⠀⠀⠈⠉⠻⢦⡀⠀⢀⡾⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠏
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣼⠃⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⢀⣴⠾⠛⠛⠛⠛⠷⣦⡀
⣿⠀⠀⠀⢀⣀⣀⣠⣤⡤⠤⠶⠶⠒⠛⠛⠉⠉⠉⠁⠀⣿⠀⠀⢀⣴⠾⠛⠉⠉⠉⠉⠙⠻⣶⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣶⠶⠶⠤⣤⣤⣀⣀⣀⡀
⣿⠀⠀⠀⠈⠉⠉⠉⠛⠓⠒⠶⠶⠤⣤⣤⣄⣀⣀⣀⢀⣷⣠⣀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⠛⠛⠛⠿⣿⡛⠉⠉⠉
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⡿⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡧
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠀⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠶⠶⠶⠶⠶⠶⠾⠃
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⣿
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣭⣓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠘⠇⠀⢠⣾⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⣀⣤⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⣰⣿⣿⣿⣿⣿⣿⣦⣍⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇⠀⠚⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣮⣭⣛⣛⣛⠛⠉⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⣿⣿⣿⣿⡿⠛⠛⠉⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠦⣄⡀⠀⠀⠀⠀⠰⠋⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⠁⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣠⠶⠚⠋⠉⠉⠉⠙⠓⠦⣄⠀⠀⠐⠒⠒⠛⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀⣀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⢉⣀⣀⠀⠈⠉⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠙⢶⡀⠀⠀⠀⠀⢸⠃⠀⠀⠈⠛⣦
⠀⠀⠀⠀⣠⠴⠊⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⡀⣠⠇⠀⠀⠔⠚⠛⠉
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⣄
⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠈⠓⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠚⠁



⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠧⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻
⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⠀⡀⢀⠀⡠⠀⡀⠀⡀⡀⡀⠀⣀⠄⠀⣀⠄⢠⡀⢀⢄⡀⡠⢄⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠒⢸⠀⡸⢸⠀⡇⡸⠽⡀⡗⡧⡇⠀⣗⠂⠀⠙⢢⠀⡇⢸⠲⡹⡅⢀⠇⠿⡄⠗⠂
⣷⣷⠾⠾⠾⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡤⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⢀⠇⣠⠞⠠⠤⠉⡉⠉⠁⠒⡄
⠀⠀⠀⠀⠀⠀⢐⡘⠀⠂⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⡔⠀⢇⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⡞⠀⠀⠀⠀⢀⠣⠤⡾⠊
⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠀⠸⠀⠀⠀⠀⡠⠊⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢡⠀⠀⡠⠊⠀⡀⠀⠀⠀⠈⠑⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠄⠀⠈⢣⠀⡇⠀⡄⠑⢄⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⡇⠘⢆⠱⡄⠀⠙⠢⣄⡀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⢀⠇⠀⠀⢣⠸⠀⠀⠀⠀⠈⢉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡘⠀⠀⢀⠜⡸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⢳⠠⠔⢊⠞⠀⠀⠀⠀⠀⠀⢱⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠠⠎⠤⠄⠬⠭⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠈⠉⠢⡄
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⡄⠀⠀⠈⠉⠉⠉⠁⠒⠒⠉⠁⠀⣀⣁⣀⣀⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠐⠐⠀⠂⠀⠀⠀⠀⠧⠔⠒⠊⠉⠉⠉⠉⠑⠒⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⢛⣠⣤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣠⣴⣶⣶⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣍⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠉⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⣠⣴⣾⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣾⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣰⣿⣿⣿⣿⣿⣿⣿⣶⣭⣉⣉⣉⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠀⠀⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⣝⡛⠿⢿⣿⡿⠿⠿⠛⠉⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡶⠖⠀⠀⠠⡄⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠼⣿⣿⣿⠟⠁⠀⢠⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃





⡟⠉⢻⡟⠿⠿⠿⠻⢿⠛⠟⠻⠿⠿⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⠿⠿⡿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢠⡀

⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⡀⠀⠀⢸⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⢛⡍⠁⠀⠉⠻⠻⢿⣶⣦⣄
⠀⠀⠁⠠⠀⠘⢀⣀⣉⠁⠀⠀⠀⠀⣁⠤⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⣒⣂⠀⠀⡶⡒⠊⠩⢔⣣⣄⡀⡀⠀⠈⢑⠀⠀⠀⠈
⠀⠀⠀⠀⢀⣄⣿⡏⠉⠉⠀⠒⠖⠊⠁⠐⠂⠀⢦⡴⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠖⡉⠥⠒⢒⣒⡺⡂⠀⠀⠀⠉⠻⣟⢮⠒⡀⠀⠈⠔⠀⢀
⠀⠐⠒⠚⡳⠛⠹⢿⢦⡀⡀⠀⠀⠠⡄⠀⢀⡠⣠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠈⠀⠑⠆⠀⠀⢠⠀⠈⠈⢧⢑⣀⠀⠀⠀⠡⠚
⠀⠀⠀⠈⠀⢀⠀⠀⠁⠀⢨⠀⠀⠘⠂⠈⠁⠘⣯⠠⠀⠀⠀⠀⠀⠀⢀⢇⠀⠀⠀⣀⠁⡀⠀⠀⠀⠀⢀⠀⠀⠸⢀⠆⠀⢀⡰⠂⠀⠐⠒
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠐⠂⠀⠀⠀⠀⠣⡂⠀⠀⠙⠂⠀⠉⠉⠉⢭⠄⠀⠀⠔⠋⣠⠄⠀⠁⡔⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢀⠀⣀⣀⣀⣠⣤⡤⠤⠶⣛⠵⠂⣠⠞⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠴⠒⢋⣡⡴⠚⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡤⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠌⢛⠩⠅⣀⣀⠀⢡⡎⠀⠐⠠⢤⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢈⠔⠉⠀⠠⣤⣤⠍⢡⣌⣉⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⢄⠀⠀⠀⢠⣤⠿⠋⠀⠀⠈⢳⡄⠀⡈⠄⠀⠐⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⢦⡜⢾⣦⡈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠀⠀⡼⢃⡠⠏⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠲⢝⣛⠷⢦⣤⣀⣀⢀⡄⢀⣂⣀⡤⢔⡒⠍⠐⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠀⠀⡀⠀⠈⣐⣂⠉⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠛⠛⠶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⢦⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⡞⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠛⠻⢦⣀
⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⡾⠛⠉⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⢀⣤⠿⠶⠶⢾⠏⠀⠀⠀⠀⠀⠀⠹⡷⠶⠶⠶⣤⡀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⠋⠉⠉⠉⠙⢷⡄⠀⠀⠀⠀⠹⣆
⠀⢠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠻⠞⠛⠛⠷⣦⣿⡄
⠀⣠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡅
⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠉⠛⢻⡛⠛⠛⠛⠛⠛⠛⠛⠻⣟⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⣠⣴⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⠋
⢠⡾⠋⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣏⠉⠁
⠘⣧⣀⣀⣼⠃⠀⠀⠀⠀⠀⣴⠟⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣆⠀⠀⠀⣠⡴⠟⢻⡄
⠀⠈⠉⠉⠁⠀⠀⠀⣤⠀⠸⣏⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⣿⠀⠀⣾⠋⠀⠀⣾⠁
⠀⠀⠀⠀⠀⢀⣤⡾⢻⡇⠀⠙⠛⠛⠋⠀⠀⠀⢀⣼⣧⠀⢸⡏⠀⠀⣸⡏⠀⠀⢻⣤⣤⣼⠏
⠀⠀⠀⠀⣰⡟⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⣿⠀⠈⠻⠶⠾⠋⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠹⣦⣀⣠⡿⠁⠀⠀⠀⠀⠀⠰⣟⠀⠀⢠⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠋⠉⠉⠁⠀⠀⠀⠈⠉⠉⠛⠻⢿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣤⡀
⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦
⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⢲⣄⠀⢠⣇⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⣰⣿⠋⠀⠀⣀⠀⠘⣏⣷⠾⠿⢶⣋⡏⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⢠⣿⠇⠀⠀⠀⠈⠻⣿⠋⠀⠀⠀⠀⣹⡿⠟⠛⠛⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀
⠀⠀⣾⡟⠀⠀⠠⠴⣖⣛⡇⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⢀⣿⠇⠀⠀⠀⠀⠀⣸⣷⣄⣀⣀⣀⣿⡇⠀⠀⢦⣀⠀⠀⣠⣿⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠋⣩⣾⠟⠛⠉⠛⠻⢧⠀⠀⠈⠛⠿⠟⠛⠁⠚⠛⠋⠙⠛⢿⣦⡀⠀⠀⠀⠀⢸⣿
⠀⠸⣿⡄⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⢸⣿
⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣸⡿
⠀⠀⠸⣿⡀⠀⠀⠀⠀⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⣀⣴⡿⠃⠀⠀⠀⢠⣿⠇
⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⢀⣿⠏
⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢷⣶⣶⣶⣶⣶⡿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠛⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠁⠈⠀⠀⠀⠈⠁⠁⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢧⠀⠀⠼⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⢀⣀⠤⠤⣀⡀⠁⠀⢀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣄⠀⢀⡔⠉⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠘⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠚⠒⠒⠒⠦⣄⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⡠⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠙⠒⠪⣄⠀⠈⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣘⣤⣿⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣼⣿

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


⣇⡱⠠⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠤⠤⠤⠤⠤⠴⣃
⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⡀⢀⢀⢀⠀⡀⡀⡀⡀
⠀⠀⠀⠀⠀⠀⢃⡀⣇⡸⢀⠀⠀⠆⠃⣘⡢⢀⡀⣇⡀⢈⣱⠀⡇⢘⢢⢨⣀⠅⡟⢄⣇
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠙⣩⣒⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⢡⠐⠀⠀⠀⠙⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠁⠀⠀⠈⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⣊⢀⡍⠀⠀⠔⠀⠀⠈⠛⠁⠀⠀⢀⠀⠀⠀⠀⢠⡀⠆⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠠⠀⠀⠀⣀⡠⠆⠀⠃⢀⠀⠐⠀⢀⠀⠜⠸⠁⠀⠡⠈⠀⡀⠀⠀⠀⠤⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠂⢀⠀⠀⠀⠢
⠀⠀⠖⠀⠀⡀⠀⠀⠀⠄⠈⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠇⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⡄⠀⠀⠀⠀⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⡄⠀⠀⠁⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠃⢀
⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⢀⠴⠂⢄⠈⠑
⠀⠀⠀⠀⡠⠀⢠⠀⠀⠠⠀⠠⠂⠀⠀⠀⠀⠂⢀⡄⢠⠀⠄⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⠀⠀⠀⠀⠀⡢⠀⠀⠂
⠀⠀⠀⠀⠁⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤⠈⠁⠀⠀⡀⠀⠰⠂⢀⠆⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠁⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠁⠀⠰
⠀⠀⠄⠁⠈⠀⠀⠀⢀⡀⠀⠂⠀⠁⠀⡄⠀⠀⠀⠀⢠⠂⠀⠀⠀⠠⠀⠀⠀⠠⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠦⠃
⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡐⠀⠀⠐⠀⠀⠀⠀⡰⣶⠀⠠⠀⡖⠂⠲⢠⣀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠖⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠺⠂⠀⠈⠋⠠⣾⡓⣲⠾⢿⣴⣻⡖⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⠀⠀⠀⢺⡾⢋⣿⠻⡶⡾⠃⠀⠈⠐⠒⢮⣀⠀⠀⣰⡴⠤⠴
⠀⠀⠀⡀⠀⠀⢄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠉⠀⠀⠀⠀⠀⠈⠉⠩⠈⠀⠉⠉⠀⠀⠀⠀⠀⢀⣼⢋⡞⠻⠅⢀
⡄⢀⠜⡛⠋⢅⣀⣀⣁⣈⡂⠄⠀⠀⢰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡋⠋⠹⡢⠊
⠀⠀⢐⠉⠉⠀⠀⢤⣆⠠⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠇⠖⣄⡀⠰⠃⠀⠈⢀⡴⠋
⠀⠀⠸⠛⠴⢖⠤⠄⠀⠂⢀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠰⠀⡼⠀⠣⠀⠐⠀⠀⠀⠀⠀⣨⠚⠀⠡⠞⠃⠈⡄
⠀⠀⠀⠀⢓⠳⠒⠈⠥⠥⠏⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠃⢀⡏⠁⠠⠄⠐⠆
⠀⠀⠀⠀⠈⠰⠊⡠⣀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⢋⠀⢀⣠⠇⠀⠀⠀⠀⠀⡠⠋⠀⠀⠈⠁⢀⠎⠁
⠀⠀⠀⠀⠀⠀⠈⣯⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠂⠹⡀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⣰⠃⠀⠁⠀⠳⡀⠀⠀⠀⡰⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠼⠀⠀⠀⠀⠀⡴⠁⡐⠀⠀⠀⠀⠹⣄⠀⠀⠳⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⠄⢄⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠃⠀⠀⢀⡴⠋⠀⠀⢀⠂⠀⠀⠀⠀⢠⠀⠀⠙⢦⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠙⡆⠀⠀⠀⣠⠞⠀⠀⠀⠀⠘⣀⢀⡐⠀⢠⠊⢦⠀⠀⠀⠳⣄⠀⠀⠀⡸⠳⡀
⠀⠀⠀⠀⠀⢀⠷⠀⠀⠙⠒⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⢦⡀⠀⠳⠴⠃
⠀⠀⠀⠀⠀⠘⠴⠃⠀⠀⠀⢀⡼⠁⠀⠀⣠⣴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠞⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡉⠙⠳⣄⠀⢻⡀⠀⠀⢠⡀⠀⠁
⠀⠀⠀⢠⠋⡀⠀⠀⠀⢰⠃⠀⠀⢀⣴⣿⠛⠙⣿⣿⣦⡀⠀⠀⠀⠀⢠⣾⠟⠙⢿⣿⣷⣄⠈⠀⠀⢳⠀⠀⡜⢣
⠀⠀⠀⠀⠉⠀⠀⠀⢠⡏⠀⠀⠀⡜⣿⣿⣤⣤⣿⣿⣿⢣⠀⠀⠀⢀⢿⣿⣦⣠⣾⣿⣿⡏⡆⠀⠀⠘⡇⠀⠓⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⠀⢇⠹⣿⣼⣿⣿⣿⠇⡼⠀⠀⠀⠘⡘⢿⣭⣿⣿⣿⡿⢁⡇⠀⠀⠀⣷
⠀⠀⠀⠀⠠⠆⠀⢀⣿⠀⠀⢀⠤⠼⢆⡈⠛⠛⠋⢁⡴⠃⠀⠀⠀⠀⠱⣄⠙⠛⠛⠉⣀⠾⠤⢤⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⢠⠞⢸⡄⠀⠠⠊⠉⢢⠉⠑⠒⠚⠉⠀⠀⠀⠰⠔⠀⠀⠈⠉⠒⠒⠋⢡⠊⠈⠑⡄⠀⡏⢳⡀⠀⠀⣜⠄
⠀⠀⠀⠀⠀⠀⢸⡀⢀⣧⠀⠘⠄⡠⠜⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣄⠀⠀⠀⠀⠀⠀⠘⠤⠀⠴⠁⣸⣃⣠⠇
⠀⠀⠀⠀⠀⠀⠀⢸⠋⠈⢧⡀⠀⠀⠐⠀⢢⠀⠀⠀⠀⠀⢺⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠎⢳⡀⠀⠱⢤⡀⠈⠒⠁⠀⠀⠀⠄⠠⠈⠙⠒⠋⠀⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⠻⣄
⠀⠀⠀⠀⠀⠀⡎⠀⠀⢱⠀⠀⠀⠙⠲⢤⣄⣀⡀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠖⠋⢿⠀⠀⠀⠀⣇⠀⣸
⠀⠀⠀⠀⠀⠀⠙⠦⠴⠋⠀⠀⠀⠀⠀⠀⢸⠉⢹⠋⠛⠓⠒⠒⠒⠛⠛⠋⠉⠉⠀⠸⣄⣀⡞⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄
⠀⠀⢂⣬⣄⠂⠀⠠⠔⣥⣤⡕⠤⠀⢀⣴⠂⠀⡔⢩⣿⣦⠀⠀⢠⡀⡇⣤⠀⠀⣦⣴⣴⢰⠀⠀⢸⡇
⠀⠈⡘⠿⠟⡈⠀⠨⢅⠻⠿⢇⠬⠀⠘⢿⣦⡀⢧⣈⣻⡟⠀⠀⠰⢊⡏⠶⠀⠀⢠⣤⣄⡄⠀⠀⢸⣇⠀⢀⣶
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠘⠛

⠀⠀⠀⠀⠀⣀⣀⠢⣀⣀⠰⠀⠀⠀⠀⠀⢀⣀⡠⢀⣃⡠⠀⠀⠀⠀⠀⢀⣀⠀⣠⡤⠀⠀⠀⠀⠀⢀⣀⠀⢀⣤
⠀⠀⢠⣶⣶⣿⣿⣿⣿⡿⠇⠂⠀⢀⣴⣶⣿⣿⣿⣿⣿⠗⠒⠀⢠⣴⣴⣿⣿⣷⣿⣧⡀⠀⢀⣤⣴⣿⣿⣷⣾⣿⣀
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠎⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠸⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠭⡭⠭⠍⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⢹⢩⢉⡉⡏⠉

⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣀⣠⣶⣶⣿⣿⣶⣦⠀⠀⠀⠀⢀⣠⣶⣶⣿⣿⣶⣦⠀⠀⠀⢀⣀⣴⣶⣦⣀⡀⠀⠀⠀⣀⣀⣶⣶⣄⣀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢰⣿⣿⣿⣿⣿⣿⣿⡄⠀⣼⣿⣿⣿⢿⣿⣿⣧⡀
⠀⠀⠈⠛⠛⣿⣿⡛⠛⠛⠁⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠟⠀⠀⠀⠈⠛⢛⢛⠛⡛⡛⠛⠃⠀⠈⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡄⡅⡅⠅⠅⠀⠀⠀⠀⠀⠘⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠲⢄⡀
⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀
⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⡀
⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡠⠃⠀⠀⠸⡀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⢠⠋⡝⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠧⠴⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠘⣆⠀⠀⠀⠀⠀⠀⣀⡠⠖⠢⠤⢤⣄⣤⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠓⠒⠚⠉⠉⡡⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢁⡇⠀⠀⠀⠀⠀⡼⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢲⠀⠀⠀⠸⣄⠜⠀⠀⠀⠀⠀⠀⠣⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡦⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣖⣚⣉⣉⣁⣀⣀⣸⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣀⣤⠤⠴⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢰⠚⢻⡏⠁⠀⠀⡆⢠⡄⡤⠄⠐⡖⠂⠀⠀⣠⠶⠀⣤⢰⠤⡀⡄⠀⠸⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠘⡆⢸⡇⠀⠀⠀⡧⢸⣿⡇⢸⠀⡇⠀⠀⢰⡏⠘⡇⣿⢸⣠⠏⡇⠀⠀⢷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢷⢸⡇⠀⠀⠀⠇⠸⠏⠧⠎⠘⠇⠀⠀⠈⠧⠴⠁⠟⠸⠍⠂⠓⠀⠀⠸⣾⠅
⠀⠀⠀⠀⠀⠀⠀⠸⣄⡇⠀⠀⠀⣴⠦⣤⠀⣄⣴⡀⢀⣶⢰⡄⠀⣶⢠⡄⠀⣦⢤⡀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢻⡀⣿⢀⡏⡿⣇⡸⣿⢸⣧⢸⣿⢸⡇⠀⣿⡸⠃⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠐⠾⠇⠹⠞⠇⠇⠹⠇⠿⠸⠸⠇⠿⠸⠧⠀⠿⠑⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣠⡄⢰⣶⠀⠀⠀⣴⢦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⣼⠃⠁⡸⠛⣦⠀⢸⣿⠋⢠⣾⠃⣰⡆⢿⡤⠊⠀⠀⠀⢸⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡇⠀⠀⣿⢀⡼⠁⢸⡟⣰⠋⠿⠤⠃⢻⡴⢻⡇⣸⠀⠀⠀⠀⠀⢸⠆⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⠀⠀⠈⠉⠀⠀⠘⠓⠁⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⠀⠀⠀⠀⢸⡁⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⢾⡗⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣭⣭⣥⣤⣤⣤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣤⠤⠶⠖⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣿⣆⠀⠀⠀⠀⢰⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⡄⠀⠀⢰⣿⣿⣿⣧⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⣠
⣿⠟⠀⠀⠀⠀⠘⠿⣿⠿⠃⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⠿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⢠⣾⡆⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⠀⠀⠰⣿⣷⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⣿⡄⠀⠀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣾⣷
⠀⢠⣾⣿⡆⠀⠀⠈⠀⠀⠀⢀⣼⣷⡀⠀⠀⠸⣿⣿⡗⠀⠀⠀⢠⣾⣿⣿⣷⠀⠀⠀⠀⢠⣿⣷⠀⠀⠀⢻⣿⣿⠇
⠀⠘⠻⠿⠋⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢿⣿⣿⠿⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀
⡄⠀⠀⠀⢰⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⠀⣠⣾⣿⡆⠀⠀⠀⠀⡀⠀⠀⢀
⠟⠀⠀⠀⠀⠉⠁⠀⠀⢠⣶⡀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⣾⣿⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⠀⠀⠀⠀⠀⠉⠉⠀⠀⣠⣾⣧⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠈⠁
⠀⠀⢀⣴⡄⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿
⠀⠀⣾⣿⣷⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧
⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⢠⣾⣿⣿⣇⠀⠀⠀⠀⣠⣆⠀⠀⢾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠇⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠀⠀⠀⠘⠿⠿⠀⠀⠀⠉⠉

⢀⣴⣿⣿⠶⡀⠀⠀⠀⢀⣀⣀⠀⢀⣀⠀⡀
⢸⣿⣿⡟⣃⡿⠀⠀⠀⠈⠁⠈⠈⠉⠁⠀⠁
⠈⠻⠿⠿⠿⠃


⠈⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠂⠂⠘⠀⠁⠁



⠀⠀⠀⠀⠀⢠⠀⠀⡀⣤⠀⢀⣀⠀⢀⠀⣀⣀⡀⢀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠁⠈⠐⠀⠈⠁⠁⠀⠀⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠖⠧⡀⠆⠆⠂⠄⠆⡆⠂⡔⠠⠖⠢⠒⠄⠰⠀⢴⢴⠰⣀⠆⠂⠰⡂⠆⠠⠴⠃⠶
⠀⠀⠀⠀⡄⡀⢀⣀⣀⢀⣀⡀⣀⠀⣀⢀⠀⠀⡀⣀⣀⡀⠀⣀⡀⣀⣀⡀
⠀⠀⠀⠀⠁⠀⠉⠉⠈⠁⠀⠁⠀⠉⠃⠈⠁⠈⠉⠀⠀⠀⠀⠀⠈⠁⠁⠁
⠀⠀⠀⠀⠀⠀⠢⡀⠀⠐⠢⣀⢄⡇⡆⠆
⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⡀⢀⡀⠀⠀⡀⠀⡀⢀⢀⠀⢀⢀⡀⠀⠀⠀⠀⢀⢀⢀⢀⢠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠘⠂⠁⠁⠃⠃⠘⠀⠁⠀⠁⠂⠁⠉⠈⠁⠁⠈⠀⠘⠀⠈⠐⠁⠈⠘⠉⠈⠀⠉⠀⠀⠋
⠀⠀⠀⠀⡖⠄⡆⡂⠢⠄⠢⢔⡄⢐⠄⡀⠖
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠘⠂⠑⠁⠃⠃⠘⠋⠃⠉⠐⠘⠛⠀⠐⠈⠑⠈⠑⠘⠀⠛⠘
⠀⠀⠀⠀⠠⠒⠀⣤⠤⠂⡔⡆⠆⠖⡄⡄⠤⡄⠠⢤⠰⠲⠢⠀⡤⡄⠢⠄⠦⠤⠤⠢⠀⣤⠔⠂⡔⠀⣠⡄⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⡀⡀⠀⢀⠀⢀⠀⢀⠀⠀⡀⢀⠀⢀⠀⡀⢀⠀⣀⠀⡀⠀⣀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠋⠀⠈⠊⠁⠉⠊⠐⠛⠂⠉⠛⠀⠃⠋⠚⠙⠈⠓⠘⠀⠚⠋⠘⠚⠀⠀⠀⠂⠃⠁⠀⠑⠑⠀⠂⠃
⠀⠀⠀⠀⡤⡤⢰⡔⡂⠠⣤⢤⢠⣤⠄⠴⠀⡄⡄⡤⣄⠐⠀⡂⣤⠄⡤⠀⡄⠤⢰⠀⣄⣤⠴⠰⢠⠀⢠⡠⢀⡤
⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⡉⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠛⠐⠁⠃⠈⠀⠀⠀⠃⠀⠂⠃⠈⠈⠙⠙⠉⠐⠀⠁⠀⠑⠀⠉⠁⠙⠉⠃⠁⠃⠀⠃⠇
⠀⠀⠀⠀⠄⡤⢀⣀⢠⣄⠄⠀⡶⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠈

⣿⡆⠀⠀⠀⠀⣴⣿⣿⣷⠀⠀⠀⠀⢰⣿⡇⠀⠀⢠⣿⣿⣿⣷⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⢀
⠿⠟⠀⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⣠⣿⡄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢀
⠀⠀⢀⣤⠀⠀⠸⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⣠⣿⣇⠀⠀⠀⠀⢀⣴⣿⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣴⣿⣆
⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⣴⣿⣧⠀⠀⠀⠿⣿⠿⠀⠀⠀⢀⣾⣿⣿⣿⡀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠿⡿⠟
⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠙⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⣄
⣆⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠰⣿⡷⠀⠀⠀⣴⣿⣿⡆⠀⠀⠀⣠⡄⠀⢀
⠋⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⠀⠀⠀⠀⠀⢾⣿⠆⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠸⢿⠗⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠙⠉
⠀⠀⣠⣿⡆⠀⠀⠘⠿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡀⠀⠀⠀⠀⢀⠀⠀⠀⣴⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⢠⣾⣧⠀⠀⠻⠿⠟
⡀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠙⠋⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠉⠁
⣿⡀⠀⠀⢠⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡿⠃⠀⠀⠈⠻⠿⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⣰⡄⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣾⣿⣿⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣴⣿⡄⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣾⣿⡄⠀⠀⠀⠘⢿⣿⡿⠃⠀⢰⣿⡧
⠀⢠⣶⡄⠀⠀⠈⠉⠀⠀⠀⠘⠻⠿⠟⠃⠀⠀⠀⠀⣾⣷⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⢀⠀⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣴⣿⡄⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⣼⣿⣿⡀

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡇⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢸⡇⠀⠀⣰⡟⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⣠⣤⣤⣀⡉⠁⠀⣠⡾⠋
⠀⣀⡀⠀⠀⠈⢀⡄⠘⠉⠀⠀⠀⠈⠉⠻⢷⣄⠈⠀⠀⠀⢀
⠀⠈⠛⠳⠆⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄
⠀⠀⢀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣷⣄
⠉⠛⠛⠋⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠈⠁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⢀⣠⡄⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀
⠀⠿⠛⠉⠀⠀⠻⣷⣄⡀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣠⡾⠃⠀⠙⠛⠷⠶⠶⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠘⠋⠀⠀⢀⣾⠃⠀⢰⡆⠀⠀⠙⠛⠛⠻⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢸⡇⠀⠀⠈⠿⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⠟⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡟⠙⣛⣁⣈⣛⠋⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢡⣦⠥⠾⠷⢬⣶⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣟⠉⡵⢋⡵⠶⠀⠉⠳⣌⠉⡷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠡⣶⢟⡵⢚⣩⣿⣷⣬⠳⣶⢨⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⠟⢸⢱⡏⠀⠀⢀⣠⡤⠼⣦⣳⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⣡⡏⡞⣸⣿⣿⣿⠿⣛⣃⡻⠌⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⣦⠸⣄⣀⣀⣰⠋⠴⠚⠛⠲⠍⢧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡙⣇⢿⠿⠿⠟⣴⣋⣭⣬⣍⣳⡜⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢯⡴⢫⠵⠆⠏⠀⠀⠀⠀⠀⢀⣸⣧⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣘⢋⡴⣛⣽⣸⣿⣿⣿⣿⣿⡿⠗⠘⠿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣇⡋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠦⡙⣆⠀⠀⠀⣿⣿⣿⣿⡿⠸⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣭⣝⢦⠹⣿⣿
⠀⠀⠀⡼⠉⠉⠙⢀⣀⡀⠛⣛⣛⣀⣀⠀⠀⠀⠀⠛⣸⠀⠀⠀⣿⣿⣿⢋⣶⣿⣦⡿⠿⢿⣤⠤⠤⠿⠿⣿⣿⣿⣿⣼⠇⣿⣿
⠀⠀⠀⢳⣀⣐⢒⣒⣒⡒⢂⣀⡒⠒⣒⢒⣒⣂⣀⡴⠋⠀⠀⠀⣿⣿⣿⣜⠿⣯⣭⣭⣭⣭⣽⣿⣭⣭⣭⣭⣭⣿⠿⢋⣼⣿⣿
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⠰⣰⠀⠃⠃⠐⠄⠀⣉⠀⡌⠁⠐⠂⠠⠂⠸⡸⠰⣉⠀⢁⠀⠐⠀⠀⠤⠀⢇⠅⢐⢙⠈⠂⠘⠊⠀⣡
⡠⡀⢀⠆⠰⠙⠀⡰⡄⢀⢄⠈⣥⢠⢱⢀⠛⠀⣤⠀⣀⠀⡰⠀⡜⢃⢀⢢⠀⡰⡀⢀⠅⢠⢉⠀⣎⠀⠄
⠄⠅⠈⠂⠈⡉⠀⠒⠃⠣⠜⠐⠤⠀⡁⠀⢉⠀⠤⠰⣁⠇⠑⡁⠁⢁⠈⠊⠀⠤⠂⠘⠜⠀⡁⠀⡰⠀⡜
⡰⠀⠜⡄⢘⡡⢰⠡⠀⠶⠀⢠⡀⢈⡱⢠⠉⡆⢰⠂⠀⠆⠀⢙⠀⡊⡆⡌⡂⠴⠀⡐⠂⠸⡰⠀⠂⠁⢈
⠃⠃⢁⠁⠀⢤⠈⢁⠀⠒⡀⠀⠂⠀⣠⠀⡤⠀⢈⡁⠈⡊⠀⣄⠀⢀⠀⢈⡀⠒⠁⠑⡂⠀⣤⠀⠜⠀⢆
⡜⡀⢆⡇⠨⠠⠀⠧⠂⡎⣱⢀⠳⠰⡀⠂⠠⠀⢈⡁⢐⠡⠘⠬⠀⠍⠀⣂⡡⢀⢳⠠⡱⠀⠠⠀⠑⠁⡄
⠁⠁⠀⡰⡀⠠⠄⠀⡄⠀⢀⠈⠈⠀⠀⡴⠀⢢⠀⢀⠀⢠⡀⢠⠄⠀⡠⠀⢠⠀⠁⡀⠀⡴⡀⡔⢃⠘⠜
⡄⠋⠀⠂⠃⠐⠔⠐⠜⠀⢆⡇⢰⠉⠀⠒⠀⠉⠀⣎⡃⠣⠆⠀⠄⠀⠠⠂⠑⠃⢘⡰⠀⡁⠁⠈⠁⣤
⡀⠉⡀⠀⣖⠀⠔⠄⢠⡀⠀⣤⠀⣩⠀⡘⠂⡊⡆⣀⠀⢀⡄⠰⠆⢠⠒⠀⡰⡀⢀⢄⢠⢙⠀⡰⠀⠤⠂
⡁⠘⢙⠀⢉⠀⠒⠁⠂⠅⠸⠠⠂⠥⠃⠑⠁⠈⠀⣉⠄⠇⠸⠈⠁⠈⠒⠀⠓⠃⠣⠜⢀⠁⠀⠂⠃⠰⡆
⡀⠀⡄⠀⣉⠀⡔⠀⢠⠀⠠⠄⠀⢆⠀⠚⡄⡐⠆⢀⡀⢠⠀⠘⠃⢠⢣⢀⠒⠀⣄⢠⠊⡆⠰⢂⠀⢈⡁
⠄⠸⡰⠀⡀⠀⠓⠁⠇⠇⠀⠀⠀⠉⠀⠉⠁⠂⠂⠨⠅⠠⠄⠈⠁⠈⠊⠈⠊⠸⠨⠀⠉⣁⠐⠊⠀⣆⡇
⠄⢀⠆⠸⡸⠀⡔⠆⠀⡄⢠⠚⡄⠜⡀⠔⠃⢠⡀⢀⡄⠀⢄⠀⡴⠀⢈⡄⡠⠂⢠⠄⠀⣉⠀⡌⠆⢀
⠜⠘⠜⠀⡄⠀⠓⠂⠐⠔⠈⠀⠀⠁⠁⠁⠀⠣⠄⠠⠔⠘⠬⠀⠒⠀⢀⠀⠁⠂⠐⠂⠀⢀⠀⠈⠁⢈⠂
⡄⢀⢆⠨⡸⠀⠐⠃⠀⣄⠀⢦⠀⠎⠃⢠⠆⠀⣤⠀⢤⠀⠴⠀⡴⠀⡌⡂⢀⠆⠀⠚⡀⣃⡃⡜⡃⠀⡀
⠄⠘⠘⠀⢀⠄⠈⠁⠀⠊⠈⠚⠀⠉⡁⠈⡁⠀⠒⠘⠤⠀⠒⠀⠒⠀⠈⡀⠈⠊⠀⠉⠁⢀⡀⠈⡀⢐⢡
⠆⠀⠊⠆⠘⠂⡔⢡⢀⢢⠀⠎⡆⢰⢱⢰⢱⢀⠓⠀⡴⠀⠎⠂⠠⠄⡎⡡⠠⠂⢠⠊⡆⢆⠄⢰⢡⠀⠁
⠂⠀⢉⠁⠐⡄⠈⠁⠈⠚⠀⠁⢁⡀⠁⡀⠁⡀⠉⠀⠒⠁⠁⠁⠐⠂⡈⠀⠘⠊⠀⠉⠀⣤⠀⢀⠁⠰⢣
⠞⠀⡎⡄⠑⠃⡎⡄⡜⡆⢠⢂⠨⠅⢘⡁⠐⢙⠀⢶⠀⢦⠀⠛⡀⢐⢱⠀⠞⠀⡐⠆⠨⠠⠀⣎⡆⠈⡁
⡍⠀⡈⠀⡰⡀⠈⡀⠈⣁⠐⠂⠀⠠⡀⢠⡀⠁⡄⠉⡀⠉⣀⠉⢀⢆⠀⣠⠉⢠⠑⠂⡀⢀⠆⢀⡄⠐⢡

⠀⠀⠀⠀⠾⠀⠀⠀⠀⢸⡇⠀⣿⠂⠀⢀⠀⠘⠃⠀⠰⡀⡆⠀⣠⠀⢰⠀⠀⠀⠀⢠⡄⠀⢠⠀⠀⠀⠈
⢠⡳⠀⠀⠀⠀⣶⠀⠀⠈⠁⠀⠀⠀⠀⢎⡆⠀⢀⡄⠀⠉⠁⠀⣿⠇⠀⠀⢠⡄⠀⠘⠃⠀⠧⠃⠀⠀⣾
⠀⠀⠀⢰⣆⠀⠀⠀⢠⢃⠀⠀⣷⠀⠀⠀⠀⡀⠘⠃⠀⠀⠀⠀⠀⡀⠀⠀⠙⠃⢀⣄⠀⠀⠀⠀⠀⠀⠉
⠀⣶⠀⠘⠃⠀⣴⠀⢇⡜⠀⠀⠉⠀⠀⠀⠘⠃⠀⠀⠀⢌⡆⠀⠀⣿⠀⠀⡄⠀⠘⠟⠀⠀⣿⠀⢸⣇
⡀⠉⢀⠀⠀⠸⠿⠀⠀⠀⢠⡄⠀⠀⣿⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⡄⠀⢸⢸⠀⠀⢰⠀⠀⢀⠀⠈⠁⢀
⠇⠀⣾⡇⠀⠀⠀⠀⢀⠀⠘⠃⠀⡀⠀⠀⢀⡀⠀⠁⠀⣾⠀⠀⢸⣿⠀⠈⠁⠀⢠⠀⠀⠀⠸⠇
⠀⠀⠉⠁⠀⡴⠀⠀⠿⠂⠀⠀⠀⠻⠀⠀⢈⢱⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠘⠂⢀⠀⠀⠀⢰⡇
⣦⠀⢠⡄⠀⠛⠁⠀⠀⠀⢠⣳⠀⠀⢠⠀⠈⠚⠀⠀⡎⡄⠀⢠⡆⠀⠀⣿⠀⠀⠀⠀⠸⠂⢠⡆
⠛⠀⠸⠇⢀⢆⠀⠀⢰⣧⠀⠉⠀⠀⠺⠂⠀⠀⠀⠀⠓⠁⠀⠘⠃⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⢀⣤
⠀⠀⣄⠀⠸⣈⡆⠀⠈⠁⠀⠀⠾⠀⠀⠀⠀⢰⡆⠀⣶⠀⠀⠀⡰⠀⠀⠀⣓⠀⠈⠀⢀⡄⠀⠀⠘⠛
⠀⠀⠛⠀⠀⠈⠀⠀⡠⢻⠀⠀⣄⠀⢰⡷⠀⠈⠁⠀⠛⠁⠀⠰⣀⠇⠀⠀⠉⠀⠀⠀⡇⡇⠀⢀
⠀⠰⡀⠀⠀⣾⠀⠀⠧⠎⠀⢸⣿⡄⠀⠀⠀⢠⡆⠀⢠⠀⢀⠀⠀⠀⣾⠀⠀⢀⡆⠀⠉⠁⠀⣎⡁⠀⡀
⠠⣇⡇⠀⡄⠀⠀⢀⠀⠀⣀⠀⠉⠀⡌⡇⠀⠘⠃⠀⠙⠀⡌⢂⠀⠀⠀⠀⡀⠈⠃⠀⠀⡀⠀⠀⠀⢠⣿
⠀⠈⠀⠘⠃⠀⠀⠘⠁⠀⠿⠀⠀⠀⠙⠁⠀⣰⠀⠀⠀⠀⠑⠞⠀⣾⡀⠘⠃⠀⠀⠀⠀⠼⠀⢸⣇⠀⠉
⢸⡇⠀⠀⠀⢰⡄⠀⠀⣀⠀⠀⣾⡆⠀⠀⠀⠛⠀⠀⣾⠀⠀⠀⠀⠛⠃⠀⠀⠰⡹⠀⠀⠀⠀⠀⠁⠀⢶
⠀⠀⠀⡖⡄⠀⠀⠀⠐⠽⠀⠀⠀⠀⣾⠀⠀⠀⢠⠀⠀⠀⠀⣰⡄⠀⠀⢰⣇⠀⠀⢠⣷⠀⣰⣷⠀⠈⠋
⢰⣆⠀⠉⠀⠀⠎⡆⠀⠀⠀⣾⠀⠀⠉⠀⡘⢆⠈⠀⢀⡄⠀⠙⠃⢸⣇⠀⠁⠀⠀⠀⠉⠀⠹⠟⠀⢠⡆
⠘⠃⢀⡄⠀⠀⠶⠃⠀⢀⡀⠉⠀⠺⠀⠀⠱⡼⠀⠀⠘⠟⠀⣤⠀⠈⠁⠀⣾⠀⠀⡠⡆⠀⠀⠀⠀⠈⠁
⠀⢀⣾⡇⠀⠀⢠⡀⠀⢸⣧⠀⠸⡰⠁⢰⡀⠀⠀⢾⡆⠀⠀⠿⠀⢀⠀⠀⠀⠀⠐⣄⠇⠀⡴⡀⠸⡧
⠀⠈⠛⠀⢀⠀⠘⠃⠀⠈⠁⠀⢀⠀⠀⠘⠁⢀⠀⠀⠀⣄⠀⠀⠀⠯⠀⠀⢼⠆⠀⠀⠀⠐⠶⠃⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣤⣴⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠰⣿⡿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢛⣯⣟⢥⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣄⠀⢾⣿⣽⣬⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⡣⡿⠚⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⣿⣿⣿⡆⢘⡟⣻⣟⣧⢀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⢸⣿⣿⣷⢿⡗⡿⣷⡟⣸⣏⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⡈⠛⣿⣿⢾⠁⠉⠋⠀⢿⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢷⢳⠋⠀⠀⠀⠀⠀⠈⣷⣹⡇
⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡄⠀⠀⢀⣤⣠⣤⣀⣀⣴⣶⣶⣇⣀⣾⣃⣀⢀⣤⡴⣶⡶⢶⡻⣾⠃⠐⡀
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠈⣺⣶⡷⣄⣀⠘⠼⣶⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣾⣿⣿⡿⠋⠉⠉⠉⠁⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⣭⣭⣼⣌⣻⣓⣻⡿⣿⣿⣿⣿⣧⡤⣄⣭⠉⠩⠁⠀⠀⡄⠀⢀⠂⢀⡀⠀⢀⣀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠉⠭⠭⠛⠒⠂⢌⣉⣿⣿⣿⣶⡩⢿⣿⣿⣻⡺⡍⠐⢄⢧⡅⣰⣗⣾⣿⣷⣤⣶⣤⣀⡀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣥⣿⣧⠗⣗⣿⠤⠬⢤⣏⣿⣿⡿⣿⢿⣞⣷⣾⣮⣽⣦⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⢿⡿⠿⠿⠿⠿⢻⡿⡸⡄⣿⣀⣀⣀⣄⣽⣿⣏⢾⣿⣿⠟⠛⠋⠁⠀⠀⠀⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢸⡇⢱⠀⣿⠉⠉⠉⡇⢸⡟⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡻⡆⣿⠀⠀⠀⣷⢸⡇⠻⣿⣧⣿⡇⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⡘⣧⢱⣿⢤⣤⣤⣾⣾⣷⣦⣿⣿⣸⣷⣶⣴⣿⠏⣠⠷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡄⠰⣾⣿⣷⣾⣿⣿⣴⣇⢸⣿⣿⣿⣿⣿⣿⡿⡾⣻⡟⠻⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠙⠚⠈⠛⠛⠛⠛⠛⠉⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠒⠆


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⡿⣿⣛⣿⣕⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣠⣶⣿⣿⣿⣿⡿⠋⠀⣡⣿⣿⣿⣷⡀⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠐⣪⣿⣿⣿⣿⣿⡟⠁⠉⠬⠧⠼⢿⣿⣿⣿⣄⠀⠀⠱⢦⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠠⠀⣤⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠠⢿⣿⠿⢿⣿⣿⣿⡆⠀⠀⠀⢙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣁⣾⣿⣿⣿⣿⣿⣿⠯⠤⠤⠤⠤⠤⠴⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣾⣿⠿⣿⣿⣿⣿⠏⠀⠀⣀⣀⣠⣀⣀⣂⣛⣿⣻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣿⣾⣶⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⡶⣶⣶⣶⣤⣬⣅⡀
⠀⠀⠀⠀⠀⠀⢰⠿⠿⡿⢿⢿⣿⠹⣿⠏⣿⣿⣿⣿⡧⣿⢿⣿⣿⢻⣿⣿⣿⡿⣿⣿⣿⡿⣿⢻⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠁⠀⠀⠈⠀⠀⠀⠙⠛⢻⠛⠇⠈⠘⠓⡿⠚⠩⠷⣿⠀⠟⡿⢿⡇⣿⢸⣿⣿⡿⠿⠿⡿⣿⢸⡟⠛⠾⣿⠃
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⢀⡄⠀⠀⠀⣯⠀⠀⠈⣿⠀⠀⠀⠀⠀⡏⢸⡇⡇⠀⠀⠀⠀⠘⠀⢡⡆⠀⣿⠠⡇
⠀⠀⠀⠀⠀⠀⠸⠀⢸⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢹⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠈⠀⢠
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⡟⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡈⠁⠀⢀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣴⣤⢄⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠛⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⢶⣄
⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⣠⡶⠟⠛⠛⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⣀⣿⣦⣤⣤⣾⠋⠀⠀⠀⠀⠀⠈⢻⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⢠⡾⠋⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⢻⣦⡶⠛⠛⠛⠻⢦⣄⠀⠀⠀⠀⠙⢷⡄
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⢻⣦⣤⠶⣤⣤⡈⣿
⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠻⣿
⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷
⠀⠙⠷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⢀⣴⠾⠋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣙⡳⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠛⠁
⢠⡟⠁⠀⠀⣿⠁⠀⠀⠀⠀⠀⢀⣠⣴⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦
⠈⢿⣤⣤⡾⠋⠀⠀⠀⠀⠀⣰⡟⠉⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⠀⠀⠀⣠⡶⠟⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢻⣆⡀⣀⣾⠃⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠁⣿⠃⠀⢸⡏⠀⠀⢠⡿
⠀⠀⠀⠀⠀⢀⣤⡾⠛⣿⠀⠀⠉⠛⠋⠁⠀⠀⠀⣀⣼⣷⠀⢸⣏⠀⠀⢠⡿⠀⠀⠘⢷⣤⣴⠿⠁
⠀⠀⠀⠀⢰⡟⠁⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣴⠾⠋⠁⣿⠀⠀⠙⠷⠾⠛⠁
⠀⠀⠀⠀⠘⣧⣄⣠⡾⠃⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⢠⡿

⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⣿⣟⣠⣾⣿⣿⡉⣻⣄⢿⣿⡇⠀⠀⢸⣿⣿⡟⠁⠀⣼⣿⣿⡟⠛⠿
⠀⠀⢸⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢉⣱⣿⣿⣿⣿⣿⣿⣿⡈⠛⠁⠀⠀⢸⡿⠋⠁⠀⢰⣿⣿⣿⠛⠛⠋
⠀⠀⠘⠋⠀⠀⠀⢾⣿⣿⣿⣿⣷⣻⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁
⠀⠀⢸⡷⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡻⡇⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣿⣿⣿⣇
⠀⠀⢸⣷⣶⣿⠄⢠⣼⣿⣿⣿⣿⣿⠂⠀⠀⢸⣿⣿⣿⣿⣿⡿⠋⢻⣷⠁⠀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣿⣿⣿⣼⣦⣆
⠀⠀⢈⡥⠀⠀⣴⣿⣿⣿⣿⣿⡿⣛⠀⠀⠀⠈⣿⣿⣧⣹⣿⣀⣀⣚⣿⣧⠀⠀⠀⠀⢙⣛⣻⣿⣿⣿⣿⣿⣿⣛⣛⡛
⠀⠀⠈⠶⠶⣴⢿⣷⣿⠿⢿⠏⠦⠿⠀⠀⠀⠀⠹⢿⠿⠇⠀⠈⠛⠫⠸⠿⠷⠀⠀⠀⠰⠿⠗⠹⣿⣿⢿⣿⣿⣿⠿⠿
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⢀⣀⣀⠀⣀⣀⢀⡀
⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣛⣿⣷⣿⣿⣿⣿⣶⣍⢸⡇
⠀⠀⠀⠀⣿⣿⣿⡿⠿⢿⠃⠻⣿⣿⣿⡇⠀⠀⠀⢀⣩⣿⣿⡿⠿⣿⣿⣿⣿⡇⠁
⠀⠀⠀⠀⣿⣿⣿⣿⣶⣿⣿⣾⣿⣿⣿⡇⠀⠀⠀⠈⠉⢰⣿⣷⣶⣿⣿⣿⣿⣃⡀⠀⠀⠀⣀⢠⡤⠀⠀⠀⢀⣀⢀⠀⢀⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⣿⢼⣷⣶⣾⠃⣿⢭⣿⣶⢺⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡇⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣴⡛⠈⠉⠉⠈⠁⠨⠟⠉⠉⠈⠁
⠀⠀⠀⠀⣿⣿⣿⠟⠛⢻⣿⣿⠛⢻⣿⡇⠀⠀⠀⣶⠀⢻⣿⣿⣿⣿⣿⣽⣿⣿⣿⠀⢈⢳⣼⣿⣿⣿⣿⣿⣿⣷⣟⣿⠃⢻⡆
⠀⠀⠀⠀⢿⣿⣿⣿⣾⣾⣿⣷⣶⣼⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢻⣿⣿⣿⣿⣿⣿⣿⡿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⢿⣿⣿⣿⡿⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⡿⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣟⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣭⣶⣿⣿⣿⣶⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠾⠿⠿⠿⠿⠿⠿⠿⠷⠽⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿