Black and white stars Emojis & Symbols

⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⢤⡤⠀⠀⠀⡀
⠀⠀⠀⠀⠘⠃⠀⠀⠄⠀⠀⢰⣾⠄⠀⠀⠴⠀⠀⠀⡀⠀⠀⠀⠀⢴⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠘⠻
⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄
⠀⠀⡀⠀⠀⠠⠦⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⡄⠀⠀⠤⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠁⠀⠐⠂⠀⠘⠀⢀⠀⠀⢸⢿⠂
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠂⠀⠀⠐⠓⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢹⠿⡇⠀⠀⠀⣴⡆⠀⠀⠀⣀⠀⠀⠀⠘⠋⠀⠀⠀⠐⠀⠀⠀⠀⠘⠃
⠀⣤⡄⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢾⠆⠀⠀⠀⠀⠐⠂
⠀⠰⠀⠀⠀⠀⠄⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠
⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⡀⠀⠁⠀⠀⠤
⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⢤⣆⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⣀⠀⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠐⠿
⠐⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠻⠁⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣤⣆⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡱⣿⠄
⠀⠀⠉⠀⡀⠀⠀⠰⠀⠀⠀⠠⣶⡆⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠺⠀⠀⠀⠀⣀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠁
⢀⡀⠀⠀⠁⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠄⠀⠀⢀⣄⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⣠⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠺⠏⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠹⠛⠂⠀⠀⠆⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢶⡆⠀⠀⠀⢠⠀⠀⠀⠀⢠⡄
⠀⠠⣷⡖⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠉⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⠀⠀⠀⠈⠁⠀⡀
⠀⢀⠀⠀⠀⠀⣠⡄⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢰⣾⡄⠀⠀⠀⣠⡄⠀⠀⠀⠀⠐⠂⠀⠀⣶⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠁⠀⠀⠰⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠙⠁
⣠⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⣦⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠛⠀⠀⠀⣠⡀
⠉⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⠙⠀⠀⠀⠠⡤⠀⠀⠀⢀⣶⡄⠀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂

⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠐⢶⡾⣿⣶⠖⠀⠀⠲⣾⣿⡶⠖⠀⠀⠲⣶⣿⣶⠆⠀⠀⠒⢶⣿⣿⡖⠂⠀⠐⢶⣾⣿⣶⠖
⠀⠀⠀⣸⠟⠻⣧⠀⠀⠀⢠⠟⠛⠷⠀⠀⠀⠀⠟⠛⠳⠀⠀⠀⠀⡸⠟⠻⡆⠀⠀⠀⢠⠿⠛⢧

⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠈⠛⣺⣿⡿⠂⠀⠀⠲⣈⠁⢀⠟⠁⠀⠲⣶⣿⣷⠖⠂⠀⠒⢶⣿⣷⠶⠂⠀⠘⠳⣾⣿⠿⠛
⠀⠀⠀⠼⠋⠙⠃⠀⠀⠀⠀⡿⠚⠺⡆⠀⠀⠀⡾⠛⠻⡄⠀⠀⠀⠼⠛⠻⡆⠀⠀⠀⠠⠟⠁⠲

⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠘⢷⣿⣿⡶⠒⠀⠀⠛⣿⣿⡿⠃⠀⠀⠲⣶⣿⣷⠶⠂⠀⠐⢶⡃⠙⡶⠂⠀⠐⢶⣾⣿⡶⠒
⠀⠀⠀⠸⠋⠙⠧⠀⠀⠀⠠⠛⠉⠳⠀⠀⠀⠀⡾⠛⠻⡄⠀⠀⠀⡼⠗⠻⢇⠀⠀⠀⢰⠟⠛⢧

⠀⠀⠀⠀⠀⢰⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠦
⠀⠀⠀⠶⠶⣿⣿⡷⠖⠀⠀⠀⠀⠀⠀⠐⢚⠑⢹⠞⠁⠀⠀⠀⠀⠰⣂⡂⠀⠀⢠⡴⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠠⣠⣶⣤⡲⠂
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠀⠳⠀⠀⠀⠀⠀⠀⢈⣥⠴⢶⣬⠀⠀⠀⠀⠀⢠⠀⠀⠆⠀⢠⠀⠀⠀⠀⠀⠀⢠⢼⠛⣇⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢠⣤⠈⢁⡀⠀⠀⠀⠀⠀⢀⠂⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡀⠈⠿⣢⡤
⠀⠀⠀⠀⢈⠀⠠⠁⠀⠀⠀⠀⠀⠀⠙⠃⠀⠈⠁⣠⡀⠀⠀⠀⠀⠈⠠⠀⢶⠖⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣥⢌⡉⠁
⠀⠀⠀⠀⠈⢂⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠀⢀⠀⢤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠈⠴⠈⠋⠛
⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠐⠂⢀⡀⠛⠁⣴⠀⠀⠀⠀⠀⠀⠀⠂⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⣴
⠀⠀⠈⠀⠙⠁⢂⢀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠁⠒⠂⠀⠀⠀⠀⠀⠀⡤⢠⡟⢶⡶⠦⠀⠀⠀⠐⢾⣿⣿⣟⣤⣤⡴⠚⠀⠀⠀⠀⠆⢐⠈⢃⡖⠃
⠀⠀⠀⢠⠀⠙⠤⠂⣠⡄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⡿⣤⡜⢯⠀⠀⠀⠀⠀⡾⠛⠻⠧⠈⠀⠀⠀⠀⠀⠀⠀⣀⠀⠢⢈⡀
⠀⠀⠀⠓⠃⠈⠀⠀⠉⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠁⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⢀⣄⠀⠈⠀⠠⠄⠀⠄⠀⠀⢀⣀⢀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⢀⣚⣳⣀⣠⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⣤⡴
⠀⠀⠶⣾⣿⡶⠂⠀⠐⠀⠐⠀⠀⠀⠈⠉⠀⠀⠈⡅⠉⠀⠀⠀⠀⠈⠉⠭⣭⠥⢎⠀⠀⠀⠀⠠⠤⣦⣄⣤⠐⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣏
⠀⠀⢠⠟⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡕⠀⠀⠀⠀⠀⠀⠰⠗⠀⠈⠙⠂⠀⠀⠀⠀⡀⠓⠒⢇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠉⠉⠻⠄

⠀⠀⠀⠀⠄⠀⡐⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠆⠀⠄⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠄⡠
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⣀⠀⠁⠐⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⠀⠤⠶⣄⣿⣣⡴⠖⠀⠀⠀⢀⣀⠀⠈
⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡠⠄⠰⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢿⣄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⢄⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠈⠆⢀⡀⠀⠀⠀⠀⢀⡤⠞⠈⢓⣶⠄
⠀⠀⠠⡀⠘⡠⠛⡂⢀⠐⠀⠀⠀⠀⠈⠳⡇⡁⠘⣥⠞⠁⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⡗⡠⠤⣄⣣⡀
⠀⠀⠂⠠⠍⠀⠈⠋⠁⢠⠁⠀⠀⠀⠀⢠⣠⠖⠣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠐⠱⠀⠀⠀⠀⠀⠙⠋⠀⠀⠈⠛⠁

⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠁
⡀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡤⠀⠀⢀⣠⡀⠀⠀⠀⠀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡤⠀⠀⢀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘
⠀⠀⠀⠼⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠰⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⠄⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⠄⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠟⠛⠂⠀⢀⣀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠟⠛⠂⠀⢀⣀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠈⡿⠿⠀⠀⠀⠀⠠⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠈⡿⠿
⡆⠀⠀⠨⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠠⠙⠃
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⢤⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢤⣾⣄
⣾⠄⠀⠀⢸⠿⡇⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠉⠙⠀⠀⠀⢀⣶⠄⠀⠀⢸⠿⡏⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠄
⠐⠿⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⢴⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠘⠋⠂⠀⢴⣦⠄
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀
⡶⠀⠀⠀⠀⠉⠁⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠛⠏⠀⠀⢰⣾⡖⠀⠀⠀⠀⠉⠁⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠙⠏⠀⠀⢐
⠁⠀⠀⢠⣦⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣦⡀⠀⠀⠀⠉
⠀⠀⠀⠉⠙⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡖⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡖
⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠶⠀⠀⠠⣼⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠶⠀⠀⠠⣼⣶⠂
⡀⠀⠀⠠⣷⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⡀⠀⠀⠠⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉
⠃⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠘⠃⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠
⣠⡀⠀⠀⢠⣶⡤⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⠽⢿⠃⠀⠀⠀⣠⡀⠀⠀⢠⣶⡤⠀⠀⠀⠀⠀⠐⢾⠀⠀⠀⠽⢿⠃
⠛⠃⠀⠀⠘⠉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠘⠉⠁⠀⠀⠀⡄
⢀⣤⡀⠀⢀⡀⣀⡀⠀⣺⣿⣁⠀⢀⣄⠀⠀⠀⠀⣀⢀⡀⠀⢀⣤⡀⠀⢀⠀⣀⡀⠀⣺⣿⡁⠀⢀⡀⠀⠀⠀⢀⡀⢀⡀
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⢠⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡀⠀⠀⡀⠀⠀⢀⡀
⠀⣀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣠⡇⣀⣀⠀⠀⠒⠤⠤⠒
⠀⠈⠂⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⣿⣿⡟⠁⢠⣤⠀⠁⠈
⠀⠀⠠⠐⠀⠀⠄⠀⡤⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢑⣯⡟⠁⠀⠀⠀⠀⠀⠀⡸⣇⠀⠁⠀⠈⠁⠀⠙⠀⠈
⠀⠀⢀⡼⢆⠀⠀⠀⠘⠙⠀⠀⠀⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⠈⠀⠈⠀⠄⠀⠀⠐⢶⡒⠃⠘⢒⡶⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠈⢳⢀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠂⠀⠀⡟⣠⣄⢸⠀⠀⠀⠉⢀⣷⡀
⠀⠀⠚⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣴⠀⠀⠠⠠⠀⠀⠀⠀⠀⠋⠁⠀⠙⠃⠀⠀⠙⣿⣿⡟⠉
⠀⠄⠘⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣷⣃⣤⣤⡀⠀⠠⣴⡄⠀⠀⠀⢀⡆⠀⠀⠀⠰⠋⠉⠛⠀⠀⠐⡆
⠀⠀⠀⠂⠀⣰⢏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢿⣿⣿⣿⣿⠟⠁⠀⠀⢀⠁⠀⢤⡀⠈⠀⠐⠤⠄⠀⠀⠀⠀⠚⠻⣦⣯⣤⠖
⠀⠀⠲⡶⠚⣱⠟⣻⣾⣧⠖⠀⠀⠀⠀⠀⠘⠆⢀⠀⣼⡿⠿⢿⣿⡀⠀⢠⣤⣾⣤⡤⠀⠉⢀⠀⢠⡀⠀⠐⣶⡦⠀⠀⡟⠁⢷⡀
⠀⢀⡀⠘⡿⢣⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠁⠀⠀⠀⠈⠁⠀⠀⣸⠟⢿⠀⠀⠛⠁⠀⠈⠃⠀⠀⠁⠈
⠀⠈⠁⢀⡟⠟⠙⠛⢿⡄⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠶⠀⠀⠀⠀⠀⠀⠈⠿⠿⠀⠰⣖⠃⠙⣲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠏⠘⢆⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣸⠴⠤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⣤⣤⣼⣿⣧⣤⣤⠀⠀⡀⠈⠳⡄⠠⣴⣧⠄⣠⠜⠁⢀⡀⠀⢈⣀⣠⣿⡆⠀⠀⠀⠀⠀⢠⡄⠀⠀⠘⠃⠀⠀⠀⠀⠀⡰⠣⡀
⠀⠀⢹⣿⣿⣿⡏⠀⠀⠀⠀⠰⠀⢸⠀⢋⣙⠀⣇⠀⠦⣾⣷⠖⠀⠉⢻⣵⣴⡊⢀⠀⠀⠘⣿⣿⡋⠀⠀⠀⠀⠀⠀⠘⢣⠀⠀⡤⠋
⠀⠀⠸⠋⠉⠙⠧⠀⠀⠂⠐⠂⠀⠾⠚⠉⠈⠓⠾⠀⠐⠋⠙⠀⠀⠀⠋⠁⠙⠃⠈⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠼⠒⠓⠶

⣆⠀⠀⠉⠀⠀⢠⣀⡀⠀⠀⠛⠃⠀⠀⠀⠀⠀⢤⡄⠀⢠⡄⠀⠀⠘⠋⠀⠀⠀⠀⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠁⠀⠀⠀⠀⠈⠽⠻⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠐⡾⡆⠀⠀⣴⠀⠀⠈
⣀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠛⠁⠀⠐⠷⠀⠀⠴⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠃
⠛⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠨⠿⡗⠀⠀⠀⠀⠀⢀⡀⠀⠀⠛⠀⠀⠀⢀⣀
⠀⠀⠶⠆⠀⠀⠀⠐⠆⠀⠀⢠⣴⡀⠀⠀⠀⣶⡦⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠃⠀⠀⠀⢠⠄⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠁⠀⠀⠀⢺⢿⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣤
⠀⠀⠤⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠐⠖⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⢼⣶
⠀⠀⠀⣤⠀⠀⠺⠇⠀⠀⠀⠛⠉⠀⠀⠘⠃⠀⠀⠛⠁⠀⠀⢹⠿⡏⠀⠀⠀⠀⠀⣀⠀⠀⣶⠄⠀⠀⠀⠈⠈⠀⠀⢈⣿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠁⠀⠀⠀⠀⠀⢠⡄⠀⠀⢠
⠀⠀⠉⠀⠀⠉⠀⠀⣤⣆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠙⠃⠀⠀⠰⠇⠀⠀⠀⠀⡤⠀⠘⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⣀⣄
⠀⠲⠀⠀⠶⠀⠀⠀⠉⠁⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⣠⠀⠀⠀⡄⠀⠀⢠⠀⠀⠀⠀⣸⣶⣇⠀⠀⢀⣀⠀⠀⠀⠈⠋⠀⠀⠀⠰⡶⠀⠀⠀⠀⢰⣶
⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠀⠘⠟⠂⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠴⠀⠀⣀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠛⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠛⠀⠀⠙
⡀⠀⠀⠈⠋⠀⠀⠀⠀⡶⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣷⠆⠀⠀⠆⠀⠀⠀⠀⠀⠠⠀⠀⣤⠀⠀⣤⡆
⠉⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⡀⠀⠠⣠⡀⠀⠀⠀⠿⠁⠀⠠⠆⠀⠈⠈⠀⢀⡀⠀⠀⠼⡿⠄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠂⠀⠰
⠀⠀⠀⠚⠂⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠸⠷⠀⠀⠀⠘⠂⠀⠀⠀⢠⡀⠀⠀⠀⠀⠈⠁⠀⡀⠀⠀⣀⡄
⠀⡀⠀⠀⠀⢀⣠⠀⠀⠀⡄⠀⠀⢼⣷⡁⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠘⠁⠀⠀⣤⡄⠀⠀⠀⠁⠀⠀⠛⠏⠁
⠀⢿⠧⠀⠀⠸⠻⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠰⡦⠀⠀⠚⠀⠀⠁⠁⠀⢀⡀⠀⠀⠀⢀⣰⣤⠀⠀⠀⠶⠀⠀⠀⠽⣷⠂

⠁⠀⠀⠀⠀⠺⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣹⠿⣇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⢸⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠐⠁⠘⠁⠀⠈⠂
⠀⠁⡇⠁⡀⠀⠀⠀⠀⠤⣤⣤⣼⡶⠚⠉⠀⠀⠀⠀⠀⣼⡧⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠘
⠒⣾⣿⠋⠁⠀⠀⠀⢀⡀⢀⡼⠉⢻⡄⠐⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠐⠀⠀⠀⠀⠀⠀⢄⠀⢠
⠐⢁⠈⠇⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣾⡞⠁⠈⠀⠀⠀⠀⢀⠀⠀⣿⠀⠂
⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⠀⠀⣼⠄⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⢀⡀⠈⢙⣿⣿⠛⠉
⠀⢀⠀⠀⠀⠰⠆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠹⠀⠈⠂
⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾
⡄⠀⠀⠀⠀⠀⠀⣆⡠⢀⠀⠀⠀⠀⠀⠀⣀⣀⣰⡇⣈⡀⠀⠀⠀⠠⠶⠶⢶⣿⡞⠉⠀⠀⠀⠀⠀⠀⠠⡷
⠀⠀⠀⠀⠀⠈⡹⠻⠀⠀⠀⠀⠀⠀⠠⠀⢀⣽⠿⡟⠉⡀⠀⠀⠀⠠⠄⣠⠋⠈⢷⠀⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠓⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖
⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⡄
⡏⢀⣁⠀⠀⠀⠀⠀⠀⠀⠠⡧⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⠀⠀⠀⡄⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⣀
⣟⠉⠁⠀⠀⠘⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡽⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠠⠀⠀⣩
⠹⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣴⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈
⠠⠆⠀⠀⠀⠀⢶⠀⠀⠀⠀⠰⢤⣤⣧⣤⠄⠀⠀⠀⠀⠀⠀⢀⡆⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⡴⠋⢿⠀⠤⠀⠀⠀⠀⠐⠶⣾⣷⠚⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⣸⠀⢐⣀
⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠉⠙⠄⠂⠀⠀⠀⠀⠀⢠⡄⠀⠀⠶⠶⢶⣿⡟⠋
⣸⣇⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠠⠄⢠⠞⠈⠻⡄⠉⠀⠀⠀⠀⠀⢀
⠟⢯⠀⡀⠀⠀⠀⠀⢼⡄⠀⠀⠀⠀⠴⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢾
⠄⠈⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢀⣰⡀⠀⠀⠀⠀⠀⢤⣤⣼⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢸⠀⢀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠁⠀⠀⠀⠀⠀⠀⠴⠛⢧⠠⠀⠀⠀⠀⠀⠀⢺⠂⠀⠀⠀⢀⠀⣿⣠⡴⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⢀⣦⡀⢀⠀⠀⠀⠀⣀⡀⠀⠀⣠⣾⣿⠀⠀⠀⠀⠀⢠⣼⣿⣿⡀
⠀⠀⠀⠠⢶⣾⣿⣿⡟⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣀⡀⠀⠀⢰⣾⣄
⠀⠀⠀⠀⠀⢹⡿⠛⠷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⠁⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⣿⣿⠿⠷
⠀⠀⠀⢠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠻⣿⠀⠀⠀⠀⣲⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⠠⣴⣿⣦
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠟⠂⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣼⣿⣆⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢤⣤⣴⣶⣿⣿⣿⣶⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣶⣿⡟⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠻⠿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⢀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠀⠙⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⡟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⢤⣾⣦⡀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣦⣤⣠⡀
⠀⠘⠛⠟⠀⠀⠀⠀⠐⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⣠⣾⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⠿⠿⣿⡀⠀⠀⠘⣿⣿⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠿⠛⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠟⠷⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠃
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⣸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡄
⠀⠀⠀⠀⢀⣿⣿⣿⣷⣶⣶⣶⡶⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⡄
⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠋⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⣷⣿⣿⣤
⠀⠀⠀⠀⢸⣿⣿⣿⠿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⣠⡄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⣿⣿⣿⡄⠀⠐⠟⠻⣿
⠀⠀⠀⠀⢸⡿⠋⠁⠀⠀⠈⠉⠁⠀⢀⣦⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣇⠀⠀⠘⠻⠿⠀⠀⠀⠀⠀⣿⠟⠉⠀⠀⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣿⣿⡆⠀⠀⠀⠀⠚⠛⢿⣿⡿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣶⠶⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣧⣤⣤⣤⠀⠀⢀⣶⡆
⠀⠀⠀⠀⠀⣀⣠⣷⣀⡀⠀⢈⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⠙⠁
⠀⠀⠀⠀⠀⢘⣿⣿⡟⠁⠀⣼⡿⠟⠛⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣿⣄⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⠋⠀⠀⠀⠀⠠⠟⠋⠀⠈⠉⠓⠀⠀⢶⣶⣿⣿⣶⡦
⠀⠀⠀⠀⠀⢤⣼⣦⡄⠀⠀⠀⠀⣄⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠃⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠟⠻⠂⠀⠀⠀⠀⣼⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⢀⣀⡄⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⣠⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⡄⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠘⢿⠓⠀⠀⠀⢀⠀⠀⠈⠁⠀⣀⣠⠀⠀⠀⠚⡟⠂⠀⠀⠀⠀⠀⠀⠉⠀⢀⣀⡄⠀⠀⠐⠻⡟⠂⠀⠀⠀⠀⠀⠈⠁⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠟⡿⠃⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠰⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠀⠀⠀⠀⠼⢿⠓
⠀⠰⠆⠀⠀⠤⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠐⠶⠀⠀⠠⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠠⣴⣆⡀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡀⠀⠀⠘⠃
⠀⢀⣼⣶⡃⠀⠀⠐⠛⠃⠀⢀⠀⠀⠀⠒⠀⠀⢠⣿⣾⠀⠀⠀⠘⠙⠀⠀⡀⠀⠀⠀⠆⠀⠀⣠⣷⣆⠀⠀⠀⠛⠛⠀⠀⡀⠀⠀⠐
⠀⠀⠈⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠈⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠋⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⢠⠄⠀⠀⠀⠛⠃⠀⠀⠆⠀⠀⠹⠟⠇⠀⠀⢤⠀⠀⠀⠘⠛⠀⠀⠰⠆⠀⠈⠹⠻⠀⠀⠠⡄⠀⠀⠀⠙⠋⠀⠀⠶⠀⠀⠈⠟⠧
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣸⣿⠧⠀⠀⠉⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⣽⣿⠄⠀⠈⠁⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⢀⣿⡷⠄⠀⠉⠀⠀⠀⠐⠆
⠀⠀⠈⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⣷⣿⠄⠀⠀⠀⠁⠀⠀⠀⢠⣶⠀⠀⠀⠀⢈⣶⡧⠄⠀⠀⠀⠁⠀⠀⠀⢤⡦⠀⠀⠀⠀⣸⣾⡦
⠀⢠⡄⠀⠀⣀⠀⠀⠀⠀⠤⠀⠀⠀⠁⠀⠀⠀⣤⡀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠈⠁⠀⠀⢀⣤⠀⠀⢀⠀⠀⠀⠀⠠⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠰⠆
⠀⠀⣰⣤⠄⠀⠀⠨⠿⠟⠀⠀⠀⠀⠀⣀⠀⠀⠀⣦⣤⠀⠀⠀⠸⠿⠋⠀⠀⠀⠀⠀⡄⠀⠀⢀⣦⡄⠀⠀⠀⠿⠿⠁⠀⠀⠀⠀⢀
⠀⠀⠹⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠈⠹⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠉⠟⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⢀⡀⠀⠀⠀⠾⠆⠀⠀⣄⠀⠀⢲⣿⡇⠀⠀⣀⠀⠀⠀⠰⠷⠀⠀⢠⡀⠀⠐⢾⣿⠁⠀⠀⡀⠀⠀⠀⠺⡗⠀⠀⣠⠀⠀⠐⣿⣟
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢰⣴⡆⠀⠀⠖⠀⠀⠀⢠⡀⠀⠀⠀⠂⠀⠀⢶⣴⡀⠀⠐⠆⠀⠀⠀⣄⠀⠀⠀⠘⠀⠀⠀⣦⣆⠀⠀⠐⠀⠀⠀⢀⡄⠀⠀⠀⠂
⠀⠈⠙⠉⠀⠀⠀⣠⡀⠀⠀⠀⠀⣤⣴⡀⠀⠀⠉⠋⠁⠀⠀⢀⣄⡀⠀⠀⠀⠠⣤⣆⠀⠀⠈⠙⠏⠁⠀⠀⣀⣀⠀⠀⠀⠀⢠⣴⣆
⠀⢀⡀⠀⠀⠀⠀⠛⠁⠀⣀⠀⠀⠉⠋⠁⠀⠀⣀⠀⠀⠀⠀⠈⠙⠀⠀⡀⠀⠘⠙⠋⠀⠀⠀⣀⠀⠀⠀⠀⠈⠃⠀⢀⡀⠀⠈⠹⠁
⠀⠙⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⠁⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⣀⠀⠀⠀⠈⠛⠀⠀⠘⠀⠀⠀⡀⠀⠀⠀⢀⡀
⠀⠀⢀⣀⡀⠀⠀⢐⣾⡷⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⢲⣿⠦⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣶⣷⠆
⠀⠐⢺⡿⠆⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠉⠀⠀⠐⢻⠿⠄⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠁⠀⠀⠚⡿⠧⠀⠀⠀⠁⠈⠀⠀⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⢤⣷⡄⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠠⣼⣦⠄⠀⠀⠀⠀⠀⠀⢤⡦⠀⠀⠀⠀⠀⢠⣼⡤
⠀⠛⠂⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠘⠉⠃⠀⠀⠒⠀⠀⠀⠈⠉⠀⠀⠈⠁⠀⠀⠘⠙⠀⠀⠐⠃⠀⠀⠀⠈⠁⠀⠀⠙⠀⠀⠀⠋⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢽⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣶⡧
⠀⠀⠀⠈⠛⢶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠤⠴⠿⣶⡀⠀⠀⠀⢸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠤⢠⣭⣥⡄⠀⠀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣈⠉⠙⢿⣆⠀⣿⡿⠁⠀⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣭⡗⣩⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠟⠛⠉⠁⢀⣾⣧⡙⣯⣙⠛⠻⠿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠈⠻⣟⣛⡁⠀⠈⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣏⡀⠀⠉⣿⣭⣤⣀⡈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣯⣤⠄⠀⠈⢿⣦⣶⣤⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡿⠿⣽⣖⠄⠀⠀⠀⠹⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠟⠁⠀⠀⠈⠙⠶⣶⡄⠀⠀⠘⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣀⢠⢳⢀⡀⠀⠀⣀⠠⠃⣀⡀⠀⠀⣀⣐⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⢀⣀⠀⠀⠀⣀⣴⠀⣀⠀⠀⢀⣀⣴
⠈⣆⣄⣊⠁⠀⠀⠈⣀⢀⡎⠀⠀⠀⠈⡽⠻⡋⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⡀⢠⠀⠀⠀⠀⢹⡖⣟⠀⠀⠀⠀⢹⠆⠄
⠀⠁⠀⠁⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡠⡀
⠀⢖⣽⡆⠀⠀⠀⠐⣞⣙⡶⠀⠀⠀⠲⠀⠀⠒⠀⠀⠀⢯⠁⠈⡽⠀⠀⠀⠲⡈⠱⠂⠀⠀⠐⠶⠈⠐⠒⠀⠀⠘⢍⠀⢨
⠀⠈⠉⠀⠀⠀⠀⠀⠋⠙⠂⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⠘⠚⠓⠃⠀⠀⠀⠘⠁⠙⠀⠀⠀⠀⠘⠃⠙⠀⠀⠀⠀⠊⠁

⠀⣠⠦⣀⠀⠀⠀⢠⣴⣧⣠⠀⠀⠀⠀⠊⠐⠀⠀⠀⠀⡀⠘⠀⠠⠀⠀⠀⢀⡰⣄⡀⠀⠀⠀⣠⠞⢦⡀⠀⠀⢠⡀⠋⠠
⠀⠘⠛⠇⠀⠀⠀⠀⡿⠿⡇⠀⠀⠀⠘⠠⠄⠃⠀⠀⠀⢈⡠⠀⡄⠀⠀⠀⢀⠗⠺⠀⠀⠀⠀⠸⠦⢼⠀⠀⠀⠀⢠⠄⢰

⠀⠀⠄⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⣠⢆⠀⠀⠀⠀⣠⡶⢶⣄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣠
⠘⢆⣀⡞⠁⠀⠀⠃⠀⠀⠀⠁⠀⠀⠙⠄⠀⡜⠀⠀⠀⣿⢀⡀⣿⠀⠀⠀⠐⡀⢈⠃⠀⠀⠈⠀⢠⣦⡌⠀⠀⠈⢋⠀⠘
⠀⠉⠈⠁⠀⠀⠀⠈⠃⠀⠋⠀⠀⠀⠈⠉⠉⠃⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⢠⣤⠀⠀⠀⠀⠠⡔⠣⡤⠀⠀⠀⠤⠊⠑⠠⠀⠀⠀⢤⣴⡄⠀⠀⠀⠀⡒⠁⠘⣲⠀⠀⠠⣀⠃⠲⠤⠀⠀⢀⠉⠀⠈
⠀⠈⠉⠀⠀⠀⠀⠀⠞⠘⠆⠀⠀⠀⠈⠄⠀⠇⠀⠀⠀⠰⠟⠛⠀⠀⠀⠀⠘⠤⠤⠃⠀⠀⠀⠨⠔⠸⠀⠀⠀⠈⠁⠤⠄

⣀⡤⠲⣄⡀⠀⠀⢀⣀⢆⣀⠀⠀⠀⢀⣠⣆⣀⠀⠀⠀⣀⡔⢢⣀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⡀⠖⠀⢀⠀⠀⠀⠀⡴⣀
⠑⠆⣀⠰⠁⠀⠀⠈⣇⣀⡏⠀⠀⠀⠘⣿⣽⡏⠀⠀⠀⢱⢀⡀⡎⠀⠀⠀⢙⡄⢬⠉⠀⠀⠈⢳⣀⣀⡋⠀⠀⠀⢙⡭⢯
⠀⠉⠈⠁⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣠⡀
⠀⡘⠈⡂⠀⠀⠀⡀⢶⣷⠂⡀⠀⠀⢀⠁⠈⡐⠀⠀⠀⠲⠈⠑⠖⠀⠀⠀⠰⣾⣷⠆⠀⠀⠐⠂⠀⠀⠐⠀⠀⠰⣎⣥⢕

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠙⣳⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⢚⡽⢂⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⣠⠞⠉⠓⢛⣦⡤⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠏⠀⣠⠞⠁⢀⡤⠞⣯⠀⣻⣦⣼⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠚⠋⠀⠀⢰⠋⣠⠞⠛⢷⡤⢾⠋⣁⠼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢁⡤⠞⠉⠀⢸⡏⢁⣀⡉⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⠀⠀⣀⣤⠶⣲⡿⠻⣏⠉⠀⠀⠀⠀⠀⢷⡏⠀⠙⢷⣀⡴⠒⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠚⣋⡥⠶⠛⠁⠀⢀⣨⡷⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠹⡅⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⡥⡶⠋⠁⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠈⣧⠀⠖⠀⠀⣿⠉⠀⣸⠁
⠀⢀⣀⣤⠴⠾⠟⠛⠋⠉⠀⠀⢧⣀⢄⣶⠀⢀⣀⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢸⠶⠞⠋
⣾⡋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⣼⢻⠞⠉⢀⣹⣆⣀⣹⠀⠀⢀⣠⣤⠀⠀⠈⢧⣀⣀⡼⢦⠀⢀⡤⠖⠒⠲⡄
⠀⠉⠛⠒⠒⠒⠒⠛⠛⠉⠉⠀⠀⠀⠉⠀⢀⠖⠋⠁⣀⡈⠉⠀⠀⠸⠻⡄⠀⠀⠀⠀⠀⠀⠀⠈⢷⡞⠀⠀⠀⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠐⠛⠛⠛⠂⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣀⣤⠖⠻⡄⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠉⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠛⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⣼⠉⡿⢉⡿⠶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⣀⣠⡴⠃⠀⢀⣀⣀⣳⣀⡇⢸⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢰⡀⠀⠈⠉⠛⠛⠛⠛⠉⢉⠁⠙⠳⢴⠋⠀⣀⡉⠛⠛⠾⢦⡤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠀⠀⠀⠈⣇⠀⠀⢠⡄⠚⠥⡸⠁⢤⢳⡀⠀⠈⢛⣿⡷⠙⢦⣤⠀⢀⣠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⣀⣸⣄⠐⢦⠌⠀⢀⡷⣄⠀⠙⠻⣆⡴⣿⣿⣧⣄⠀⡿⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⢹⣿⣿⠀⠈⠋⠉⠀⣤⡞⠁⠈⣩⠟⠀⠈⢷⠉⠙⠧⣌⠛⠃⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠘⡟⢻⡄⠀⠀⠀⠀⠀⢻⣰⠖⠾⠇⠀⠀⠈⢳⡄⠀⠈⠙⠶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣀⡀⣧⠀⢧⣀⣀⣀⣀⣀⣨⣥⣤⠤⠶⠒⠚⢻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡟⠉⢙⣆⣸⡿⠋⠉⠁⠀⢰⡇⢸⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣯⠗⠂⣿⣿⡇⠀⡍⠉⠁⠀⠀⠀⠀⠀⣸⠃⡿⠀⠀⢀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣱⣏⠠⣶⢤⡏⡟⣧⠀⠘⠦⠀⠀⠀⠀⠀⢠⡏⢠⠇⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⠃⠈⠓⠛⣎⢻⣹⡘⠆⠀⠀⠀⠀⠤⠶⣶⣿⣶⡾⠤⠤⠀⠺⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⣀⡽⠞⠻⣧⡀⠀⠀⠀⣀⣴⡞⠉⠑⠦⠁⠀⠀⠀⣀⣼⣧⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠙⢮⣝⡳⠶⣶⣒⠛⠛⠯⠞⠣⡄⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠾⠭⣭⣕⣒⣚⠳⢶⣶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢤⠀⠀⢿⣸⠆⠀⠀⣦⣼⠀⠀⢸⣅⡷⠀⢀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡞⣉⢷⣦⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⠁⣀⣤⣿⢺⣿⣿⡇⢸⣽⣿⡟⣿⣤⡀⢘⡶⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣽⣿⣿⣿⣿⡟⣉⠔⡉⠳⣈⢻⣿⣿⣿⣿⣯⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣽⣾⣿⣏⠻⠟⠀⠈⠿⠟⠁⣿⣷⣿⡿⣄⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⣁⣴⢂⠀⠞⡅⠙⡅⣽⢶⠊⣠⠾⠆⢷⣬⡍⣉⣿⠟⠁
⠀⠀⠀⠀⠀⢀⣀⠤⠾⠿⠿⢿⣿⣯⣵⣶⣠⣄⡀⠒⠀⣠⡽⠿⠿⢿⣮⣳⡄⠀⠀⠀⠀⠀⠀⢈⠛⢛⢃⡋⠀⠸⡅⠘⡱⢀⣠⠀⣟⠡⠆⣾⣡⣼⡟⡁
⠀⠀⠀⠀⡴⠉⢀⣤⡶⢊⠀⢰⠟⡵⢨⠟⡵⢸⣷⢶⠞⠁⣠⣾⣿⠂⣿⣷⣹⡄⠀⠀⠀⠀⡴⠎⠟⢁⡾⢠⣇⣨⡅⢘⣵⡟⢩⣵⠌⠃⠼⠡⠆⠀⢉⡟⣦
⠀⠀⠀⠀⣧⣴⣿⡟⢱⡿⢀⠏⣸⢃⠀⣼⢃⡚⠃⠘⡀⢰⣿⠕⠁⡰⢡⣿⣷⣿⠀⠀⠀⠀⠘⠶⠶⣿⠛⡾⠿⢶⣶⠶⢦⣽⠶⠶⢾⡳⠶⢶⠶⣦⣬⠶⠋
⠀⠀⠀⣔⠁⣀⡤⢠⡶⠀⡈⠀⢣⡞⠀⢣⡾⠡⣄⣾⡄⠸⡷⠒⠚⠀⢿⡿⢿⢿⣧⣀⣤⡀⠀⠀⢸⡟⠰⣓⣫⣥⣴⣶⣿⣿⣿⣶⣦⣬⣍⣚⠆⢻⣇
⠀⣴⢦⣈⠿⠋⢀⣾⠁⢰⡇⠐⣫⡆⠐⣋⣥⣾⡏⣀⣬⣷⡌⠻⠁⣼⠃⣴⠃⡜⡤⢀⣼⠳⣄⠀⣾⠷⠿⠛⠛⠉⠀⠈⠉⠉⠉⠁⠀⠉⠙⠛⠻⠾⣷
⠀⠹⣄⣀⣀⣴⣿⣿⣄⣸⣟⣛⣉⣉⣈⣉⡉⢹⣧⣉⣉⣉⣠⣶⣀⣡⣀⣁⣀⡄⠀⠾⢋⣴⡟⠀⡀⠤⠒⠒⠒⣤⠴⣤⠴⣤⣤⡴⠒⣒⢦⣀⣠⡀⣀⡄⢀⡀
⠀⠀⠈⠛⠛⠉⢻⡽⣿⡟⣿⣿⣍⠉⠉⠉⠛⠿⠋⠙⠛⠛⠉⣸⣿⡟⣻⣿⢿⠿⠶⠾⠛⠉⠀⢸⣁⣴⢏⡴⠰⢱⠁⣱⠡⠟⠋⢠⣿⠏⠘⣿⠃⠧⢻⣠⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣝⣿⣟⣽⠿⣷⣦⣄⣀⣀⣀⣀⣠⣴⣿⢿⣝⣿⡿⣳⠏⠀⠀⠀⠀⠀⣀⣬⣠⠄⡴⢠⡁⡱⠃⣱⢃⣤⠧⡘⢆⡚⣸⢗⠤⠤⠼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢷⣿⣛⡿⢻⡿⢿⠿⣟⠛⣏⢿⣶⡿⣫⠞⠁⠀⠀⠀⠀⠀⠐⣏⠋⢁⣼⣇⢸⠦⠞⠂⠐⠻⣇⠒⠛⣈⠀⡇⠚⢐⠀⠼⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢯⣟⣻⠿⠷⣾⣶⡿⣶⣟⣿⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠙⠛⠛⠛⠛⠙⠻⠟⠛⠛⠋⠛⠛⠛⠛⠓⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠉⠉
⣿⣿⡿⠿⣿⠿⢿⢿⣿⡿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣷⣮⣶⣷⣶⣿⣶⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠈⢩⣿⡿⠁⠀⠀⠀⠉⠛⠿⣿⣶⣤⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣄⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠻⢿⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣧⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⠇
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢠⣶⣆⠙⢿⣿⠇⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠉⠛⠻⠟
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⡿⠟⠋⠀⠀⠀⣰⣿⣧⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⣀⣤⣤
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢰⣶⣦⠀⢀⡀⠈⠻⠋⠀⠀⠀⠀⠀⢠⣿⡟⠀⣀⣤⣴⣾⣿⣿⣿⡏
⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠰⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⠀⣾⣿⡿⠋⠀⠀⠀⠀⠀⣰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⣿⣿⣿⠟⠀⠀⠀⠁⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠈⠀⠂⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠠⠀⢀⣾⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠸⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢱⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣶⣯⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢁⣿⠇⠀⠀⢀⡀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⣴⢾⡵⠛⠉⠁⠋⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣼⡿⠀⠀⢀⣾⡇⠀⢠⣿⡇⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⠀⠀⣀⣴⣦⠀⣰⣷⣶⣷⡄⠀⠰⢳
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢠⣿⡇⠀⢀⣾⣿⠃⢠⡿⣿⠁⠀⠀⠀⠀⠀⢀⣇⣀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠃⣠⣾⡿⣿⣿⠠⣿⡿⣿⡟⢁⡌⠀⢸⠀⠀⡠⣀
⠀⠀⠀⠀⠀⡀⠀⡰⢁⣤⣼⣿⣶⠂⣾⢷⡏⠀⣿⣻⠏⠀⣀⣀⣀⣤⠀⠀⠙⠉⠛⠛⠲⣶⡀⢀⣿⠇⠀⣰⡿⠋⣰⣿⠃⢠⡏⢰⣿⢀⣾⡇⢀⠊⢀⠈⠀⢻⣆
⠀⠀⠀⠀⢠⢷⣞⣵⣜⣿⣿⣿⡏⣸⣿⡿⠁⣸⣿⡟⠀⠸⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⣿⣧⣾⣿⠀⣰⣿⣁⣼⢻⣿⣴⠟⠀⢺⣿⡿⠙⠫⣽⠖⠁⠀⠀⢸⣿
⠀⠀⠀⣠⣿⣿⠿⠾⠚⢻⣿⠛⠁⣿⡿⠁⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣼⣿⠃⣾⣿⡾⠃⠘⠿⠃⠸⠿⠋⠀⠀⠈⠉⠀⠀⢀⢀⣀⣤⡤⣴⣿⣿
⠀⠀⠀⠈⣀⠃⠀⠀⠀⣷⠁⠀⢸⣿⠁⠀⣰⣿⠀⢀⣼⠃⠀⠀⠀⠀⣰⣴⣖⡲⣿⣱⠿⠁⠀⠘⠋⠀⠀⠀⢀⣀⣀⣤⣤⣶⢶⣾⣿⣛⣎⠁⠀⠋⡹⢹⣿⣿⡿
⠀⠀⠀⣰⣿⠀⠀⠀⠐⡏⠀⠀⠈⠿⣀⣴⠛⣿⣷⣾⠃⠀⠀⠀⠀⠀⠓⠛⠚⠋⠀⠀⠀⠀⣀⣀⣤⠴⢿⠿⣿⣿⣿⣿⣯⠉⠘⠋⣹⠾⣫⣠⡤⠸⠚⠛⠋⠉
⠀⠀⣼⡿⠁⠀⠀⠀⢸⣽⠂⠀⠀⠻⠛⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣀⣀⣤⣠⣶⣿⡏⢹⡿⢿⣛⣧⡈⠁⠀⠈⠉⣹⢽⣃⣤⣄⡈⠞⠛⠉⠁
⠀⢸⣿⠃⠀⠀⠀⠀⢷⠃⠀⠀⠀⠀⠀⠀⣀⣀⡀⢤⡴⡖⡲⠉⢯⢟⣭⣾⣿⣟⡛⠁⠀⢉⣙⠷⣻⠎⢀⣀⠀⢿⠽⠟⠓⠉⠁
⠀⣿⠋⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣴⢚⣹⣏⣟⣌⣿⣉⠉⠁⠀⠘⠛⢻⣿⣿⣿⢃⣤⡀⢿⣿⣷⣶⣬⠟⠋⠉
⠀⠶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇⠈⢿⣿⣿⣿⣿⣿⡗⠀⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉
⠀⠀⠀⠙⠻⢿⠻⢿⡿⢻⢿⣦⡀⠀⠀⠀⢀⣶⣿⣿⣿⣷⣿⣿⣶⣽⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣿⡿⠀⣠⣄⡀⢻⣿⣿⢿⣿⠿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡯⣸⣿⣷⠸⠿⠟⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⡻⣿⠟⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠤⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠁⠀⠀⢀⣠⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⣿⣿⠟⢁⣀⣀⠀⣀⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣻⣿⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⠟⢁⣤⣶⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣤⣤⣴⣿⣿⣿⡿⠃⠀⣿⣿⣿⣿⣿⣿⣿⡇⣰⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠛⣿⠟⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⡟⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⠉⠀⠀⢀⣤⣾⡿⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠙⣻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠻⢿⣿⣧⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢀⣠⣶⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣤⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣥⣇⣠⣁⣭⣴⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢄⢲⠬⠅⠓⠐⠐⠒⠚⠩⠡⡒⡠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣚⠅⠊⠀⢠⡄⠰⡆⣾⠀⢲⣒⠆⠀⣤⣈⠑⠬⣂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡪⠂⢀⡀⠘⣿⠦⣷⠀⠻⠟⠀⠾⣥⠆⣠⠿⡼⠃⢀⣈⠐⢕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⠒⠀⢰⠋⠉⡧⠘⠃⠈⠀⠀⢀⣿⡀⠀⠀⠉⠘⠃⣤⢻⡽⠇⠀⠲⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠂⣠⠶⠈⡙⠚⠁⠀⠀⠀⠀⠀⣼⣿⣧⠀⠀⠀⠀⠀⠈⠛⣁⣤⡾⣆⠱⡑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠌⠀⠻⣤⣼⠇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠙⠶⠁⠁⠀⢡⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢑⠀⠀⠀⠀⠀⠰⢶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⡶⠖⠀⠀⠀⠀⠀⡊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢃⠀⠀⢠⠖⣶⡾⠁⠀⣠⠎⢹⣿⣿⣿⣿⣿⣿⣿⡏⢁⢒⣋⠀⣀⣴⣀⡀⠀⠀⡘⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡼⡀⠀⠻⠔⠻⠿⠷⠽⠿⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠋⠛⣿⠛⠛⠋⠀⠀⠀⢧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢣⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠉⣀⠉⠻⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡼⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢂⠀⣤⢴⣾⡷⢀⠠⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⠄⢠⡞⣲⡀⠀⠀⡰⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡳⡀⠠⡟⢀⡼⠓⢠⣀⠀⠀⠀⠀⠀⠀⣀⣀⢴⣶⣀⠙⣧⠙⢁⢞⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⡲⣀⠛⠦⠄⣰⠃⠀⠀⠰⣏⣻⠘⠹⡍⠘⣏⠙⠓⣀⢔⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢝⡢⢌⣉⠛⠁⠀⠰⠦⠼⠃⠀⠛⢀⡡⢴⡪⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠭⠯⢶⣲⣒⣒⣶⠬⠍⠓⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣸⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢁⣿⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣼⣿⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢰⣿⣿⠀⠀⠀⢻⡆
⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⠁⣿⣿⣿⠀⠀⠀⠈⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠉⠻⣯⣍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢸⣿⣿⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⣾⠟⠉
⠀⠀⠀⠈⠙⢷⣦⡈⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢊⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⡙⠳⣦⡠⢄⡀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⣀⣴⢚⡵⢋⣡⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⠙⢳⣝⠷⣤⡀⠀⢉⡀⠀⠤⢶⣵⠿⠋⠒⣡⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡗⠀⠈⠅⠒⠀⣠⣿⣷⣄⠀⠀⠀⠀⠀⢾⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠬⠅⢀⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢀⡒⠄⣴⣿⣿⡿⠟⠃⢿⣿⣿⣄⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠐⣠⣾⣿⠟⣉⣴⠿⠿⣦⣘⠻⣿⣷⡀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢌⣶⠟⣋⣴⡾⠋⠁⠀⠀⠈⠙⢷⣦⣙⠿⣆⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠰⢛⣵⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣬⡓⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣥⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣬⣿⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣼⣟⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣄⣀⣀⣀⣀⣠⣉⣻⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠁⠁⠀⠉⠁⠁⠉⠁⠉⠈⠉⠈⠈⠈⠈⠀⠁⠁⠁⠉⠈⠈⠈⠀⠉

⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⣾⡇⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠰⡀
⠀⠉⠻⣭⣍⡉⢻⡇⠈⣉⣭⡽⠋⠁⠀⠙⠯⣍⠉⠉⠃⠀⠉⠉⣩⠽⠋⠀⠈⠙⢯⣉⣉⣉⣿⣆⣉⣉⣩⠝⠉
⠀⠀⠀⠀⢹⠛⣡⣦⡙⢻⠁⠀⠀⠀⠀⠀⠀⠈⠻⠉⠀⡀⠉⡟⠁⠀⠀⠀⠀⠀⠀⠈⡋⢹⣿⣿⠉⡋⠁
⠀⠀⠀⠀⣎⣴⠟⠛⢷⣌⡆⠀⠀⠀⠀⠀⠀⢠⢃⡴⠞⠳⣆⡸⡀⠀⠀⠀⠀⠀⠀⢠⣱⡿⠛⠻⣷⣠
⠀⠀⠀⠼⠋⠠⠤⠄⠀⠈⠻⠀⠀⠀⠀⠀⠀⠾⠩⠤⠤⠤⠠⠙⠧⠀⠀⠀⠀⠀⠀⠾⠉⠠⠀⠀⠀⠙⠧

⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠤⠀⠃⠈⠂⠠⠄⠀⠀⠀⠤⠀⠀⠀⠀⠀⢠⠄⠀⠀⠠⠀⣀⣼⣧⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣧⣤⣤⠄
⠀⠀⠀⠘⠄⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏
⠀⠀⠀⠀⠄⠒⠀⠀⠄⠀⠀⠀⠀⠀⠤⠀⠀⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠰⠛⠁⠈⠳

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⢀⣀⣠⣾⣿⣀⣀⡀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠁⠱⢀⣀⡀
⠀⠀⠀⠉⢿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠉⢈⡕⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠠⠊⠁
⠀⠀⠀⠀⠿⠛⠛⠿⡄⠀⠀⠀⠀⠀⠀⠔⠀⠀⠆⠀⠀⠀⠀⠀⠀⠘⠚⠉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⠀⠠⣼

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡼⠁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⣀⣀⣜⡡⡀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠈⠳⡄⠀⠀⢈⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠻⠄⠀⠀⠀⠀⠋⠀⠀⠀⠀⠃⠀⠀⠀⠠⠃
⠀⠀⠀⠀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⠤⢄⢸⠀⠀⠀⠀⠀⠀⣿⠿⠿⣿⡀⠀⠀⠀⠀⠀⣀⡠⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠
⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⡼⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡀
⠀⠀⠘⢿⡉⠁⠀⢉⡹⠗⠀⠀⠀⠂⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⠗⠀⠀⠀⠲⣄⠈⠀⠀⠉⡙⠃
⠀⠀⠀⢀⡟⣠⣄⣸⡄⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢁⣀⡀⢸⡀
⠀⠀⠀⠘⠋⠁⠀⠉⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠘⠉⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠰⣆⠀⠁⠀⠁⢀⠆⠀⠀⠀⢴⣶⣌⠿⣣⣶⡦⠀⠀⠀⠰⣶⠒⠃⠈⠓⣶⠆⠀⠀⠀⢖⠒⠁⠀⠑⢂⠖⠀⠀⠀⠠⣤⣴⣿⣷⣶⣤⠄
⠀⠀⠀⠈⡇⢀⡀⢰⠃⠀⠀⠀⠀⠀⢩⣵⡆⣮⡍⠀⠀⠀⠀⠀⠈⡗⢀⣀⢸⠁⠀⠀⠀⠀⠀⠱⠀⣀⠀⡏⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠓⠉⠉⠛⠃⠀⠀⠀⠀⠀⠘⠋⠀⠙⠓⠀⠀⠀⠀⠀⠐⠛⠉⠈⠙⠃⠀⠀⠀⠀⠀⠖⠉⠉⠑⠂⠀⠀⠀⠀⠀⠘⠋⠁⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣾⣿⣿⣿⡿⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⡆⢸⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡟⢉⣴⣶⣿⣿⣦⠈⠀⣠⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡤⢉⣩⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣭⣭⣽⣿⣿⣿⣿⣿⣿⡿⠋⣠⢊⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣬⣍⣿⣿⣿⣿⣻⡿⠋⣠⢞⡁⠾⠿⠿⢷⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣉⣹⣿⣿⣽⡿⠋⣠⠞⣡⣾⡱⠿⠖⠀⠴⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣂⣉⣹⣿⣿⣿⣿⠋⢠⠞⠁⠀⢸⣟⣱⣶⠂⠐⠒⣀⣈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣉⣙⣿⣿⣿⠟⠁⣠⠋⠀⢸⡆⢸⣿⣟⣵⢚⣁⡴⠀⡤⠎⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⣿⣿⣿⡿⠋⠁⠀⠔⠁⠀⠀⣿⣷⣿⣿⣿⣷⣿⣩⡴⠖⢀⡛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣯⣿⣻⣿⣿⣿⣴⣟⣥⣶⣾⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠊⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡒⠦⢤⣈⡉⠛⠿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣑⢄⠀⠉⠉⠉⠉⠀⠀⠀⠀⠛⠛⣛⣉⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠿⢿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠉⠁⠀⠈⠉⠙⢧⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⢶⣦⣤⣤⣤⣤⣤⣤⣤⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇

⠀⠀⢼⡿⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡿⠃
⢀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀
⠻⠂⠀⠀⠀⠀⣲⣿⡥⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠐⢿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠁⠀⠀⠀⣄⣠⠀⠀⠐⠀⠠⣴⣄⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠐⢻⠟⠂⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠠⣶
⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢿⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟
⠀⢠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡧⠀⠀⠀⠀⠀⣺⣷⡥⠀⠀⠀⠀⢀⣠⡄
⣶⡇⠀⠀⠀⠀⠀⠀⠄⢠⣷⣇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠄⠀⠀⠘⠻⠋
⠛⠉⠀⠀⠀⠀⠀⠃⠀⠉⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠆⠀⠀⠀⠀⣽⣯⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠋
⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣄⠄⠀⠀⠀⠀⠀⠀⢀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠜⡿⠏⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢀⢀⠀⠐⠂⠀⠁⠀⢀⣄⠀⠀⠀⠀⠀⠚⠟⠃⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⢠⣀⠄

⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⣄⣠⣆⣠⡄⠀⠀⠀⠀⢤⣰⣤⣆⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢸⠀⣠
⠀⠀⠀⠀⠀⠲⣶⣿⣿⣿⡶⠂⠀⠀⠀⢤⣼⣿⣿⣿⡦⠄⠀⠀⢐⣺⣿⣿⣿⣗⠂⠀⠀⠀⠀⢼⣿⣷⠀⠀⠀⠀⠠⠤⢽⣿⣿⠥⠤
⠀⠀⠀⠀⠀⠀⣸⡿⠿⣿⠀⠀⠀⠀⠀⠀⠼⠻⣿⠻⠆⠀⠀⠀⠈⠽⢻⢿⡟⠏⠁⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠠⠞⢹⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠢⢄⣧⣞⡀⠀⠀⠀⠀⠀⣼⣶⡦⠀⠀⠀⠀⠀⠈⠳⣄⡴⠋⠀⠀⠀⠀⠀⣠⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⢉⠟⡟⠢⠄⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⢀⡴⠛⠳⣄⠀⠀⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⣠⣧⣀⠀⠀⠀⠀⠀⢀⣀⣀⣇⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣤⠆⠀⠀⠀⠀⠀⢀⣴⣄
⠀⠀⠀⠀⠀⠀⠈⠙⡟⠉⠀⠀⠀⠀⠀⠈⠉⠉⡏⠉⠉⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⢰⠿⠿⡄⠀⠀⠀⠀⠀⠙⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⣿⣿⡗⠃⠀⣀⣠⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⢀⣀⣤⡴⠀⢲⣦⣀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇
⠀⠙⢠⡄⠀⠈⠉⢻⣿⠿⠛⠛⠀⠀⠳⣶⣶⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⢻⣿⣷⣤⡀⠀⠀⢠⣾⣿⣿⠃
⠀⠀⢸⣿⡀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⢻⣿⣿⣿⣶⣶⣿⣿⣿⡏
⣀⣀⣿⣿⣇⣠⣴⡾⠀⠀⠀⠀⡄⠀⠀⠀⢸⣿⠟⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣤⣤
⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢲⣼⣧⣤⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠸⠛⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⠿⠛⠉
⠟⠋⠁⠙⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣾⣷⡖⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁










⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠴⢿⡿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⣀⣠
⠀⣀⣤⣶⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⡄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⣤⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠛⢻⡟⠧⠀⠀⢀⣼⣿⣿⣿⣿⣿
⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣴⣿⡇⠀⠀⠀⠘⠀⠀⠀⠀⡾⠟⠋⢹⣿⣿⠉
⠀⠆⣸⣿⣿⣿⡿⠿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠈⣿⡇
⠀⢠⣿⣿⡿⠃⠀⠀⠈⠛⢿⣿⣧⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠿⠿⢦⠀⠀⣠⣤⣶⣿⣧⣀⡀⠀⠘⠃⣄
⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠉⠻⠧⠀⠺⠛⠉⠁⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠋⠉⠀⢠⢴⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⢁⠔⠀⠀⠀⠤⠀⠀⠀⠀⠠⡀⢀⠐⡠
⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠄⠂⠠⠀⠀⠀⠀⢠⡳⡀⠀⠀⠀⡤⠀⠂⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠊⢐⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡙⡄⠀⠀⠀⠀⠀⢠⠀⠀⠡⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠄⠀⠄⡂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢦⠀⠀⠁⠀⠀⠑⠠⠄⣈⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠢⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⢆⢣⡀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⢄⠐⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠤⠀⠐⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠈⢆⠁⠀⠀⠀⠠⠄⠀⠀⠀⢀⡀⠀⠀⠀⠭⠈⡀
⠀⠀⠀⠀⠀⠀⠃⠀⠤⠠⠋⠀⠀⠀⢜⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡴⠁⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠁⠒⠀⠀⠀⠀⠀⠱⢕⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠂⠀⢂⠠⠀⠀⠊⠄⢀⡠⣪⠖⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠠⠀⠀⠑⢕⢤⡀⠀⠀⠀⠀⠀⠠⠂⠡⢀⠅⢊⠀⠀⢀⢔⠭⠊⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠢⢀⡀⠀⠀⠀⠀⠀⡉⠂⠀⠀⠠⢀⠁⠀⠄⠂⠀⠀⠔⠀⠚⠗⠁⠀⠀⠀⠢⡀⢀⡈⢀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠄⢂⠄⠀⠀⡈⠀⠀⠠⠀⠀⠀⠀⢀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠄⠈⣀⠄⠦⡀⠀⠀⠀⠅⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⡩⠔⠊⠙⠪⡓⢄⠀⠈⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⢔⡊⠅⠊⠁⠀⠀⠀⠀⠀⠈⠂⢝⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⡓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠹⠗⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁

⠀⠀⠀⠀⠀⣀⠀⠀⡄⡀⠀⣄⡄⠀⡀⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣄
⠀⠀⠀⠀⠀⠳⢆⣠⣿⢲⣾⡏⣿⣶⢿⣥⣀⡷⠃⠀⠀⠀⢀⣀⣠⡶⠿⢿⡟⡡⡊⢌⡻⢿⣿⣶⣄⣀⡀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣏⠛⠀⠈⠋⢘⣿⣿⣷⡄⠀⠀⠀⠈⠻⡧⠶⠷⠈⠇⠑⠚⠋⣴⠋⣸⢖⣴⠟⠁
⠀⠀⡰⠊⣡⡄⡀⡸⢫⠹⢫⢹⣦⡖⢉⣴⡆⢹⣿⣆⠀⠀⠀⡄⠖⣰⢱⣀⡇⠺⡞⣱⠝⠢⠫⠉⢁⣶⡀
⠀⠀⡱⠚⠛⡘⠡⢡⢣⠠⢣⠌⢠⠄⣾⣋⡠⣰⣿⣿⡀⠀⠀⠙⢻⡏⣟⠻⢛⣓⣾⣟⣛⠟⣻⡻⡖⠋
⢠⢌⡷⠋⣸⠃⣖⢐⣋⠐⣫⣼⢋⣱⣌⠲⢠⠎⡭⠩⠉⣹⢧⡀⣾⠴⠞⠛⠉⠙⠛⠋⠉⠛⠳⠶⣿
⠘⢦⣤⢾⣿⣤⣯⣭⠥⠤⣤⣹⣮⣭⡤⢶⣤⣤⣤⣴⣀⣫⠾⢁⠀⣠⠀⠲⡲⡖⣶⠖⣢⡔⣦⠆⣠⠀⡄
⠀⠀⠀⠀⠻⣿⣾⣿⣶⣄⣀⡈⣀⣀⣴⣾⣿⣾⡿⠃⠉⠀⠀⢸⣋⢡⢁⢨⠄⡕⣤⠄⢏⢀⠿⠠⠬⡟
⠀⠀⠀⠀⠀⠙⠿⣷⣯⣟⣿⣻⣻⣛⣿⣶⡿⠟⠁⠀⠀⠀⠸⣍⡵⢧⣼⣾⣤⣙⣧⣛⣥⣬⣨⣄⣸⡽
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣦⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄
⠀⠀⠀⠀⣰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡿⠃
⠀⠀⠀⠀⠚⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣬⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄
⠀⠀⠀⠀⠀⠐⠛⡏⠃⠀⠀⠀⠀⠀⠀⠀⣠⣧⡀⠛⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠉⠻⡿⠋⠉⡀⠀⠀⠀⠀⠀⠐⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣯⣀⣽⣿⣿⣿⣿⣿⣿⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠻⠇⠀⠀⠀⠀⡀⠀⠀⠀⠈⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠸
⠀⠀⠀⢀⣀⣼⣷⣀⣀⡀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⢠⣴⣦⠄⠀⠀⠀⠈⠁⠀⠀⣠
⠀⠀⠀⠙⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠿⠿⠁⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⠋⠙⠃⠀⠀⠀⠋⠃⠀⠀⠀⠀⠀⠀⠀⢹⠿⡏
⡄⠀⠀⠀⡿⠟⠻⢿⡄⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⢠⣼⣦⠄⠀⠀⠀⠀⣠⠀⠸⠂⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⣤⡄⠀⠀⠋⠛⠀⠀⠀⣀⣰⣿⣧⣀⠀⠀⠈⡿⢿⠁
⠀⠀⠰⣾⡷⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢹⡿⡟⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠶⠀⠀⠀⣽⣿⣿⣿⣿⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⠀⠀⠐⢶⣶⣿⣿⣿⣷⣶⡶⠂⠀⠀⠀⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠉⠛⠇⠀⠀⢻⣿⡟
⣷⠆⠠⣴⣿⣦⡤⠀⠀⢹⣿⣿⣿⣿⡏⠀⠀⠀⠀⣻⣿⡃⠀⠰⣶⣿⣶⠆⠀⠀⠀⢠⣴⣦⠄⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐
⠉⠀⠀⡽⠿⢿⠀⠀⠀⣸⠟⠋⠙⠿⣇⠀⠀⠶⠀⠀⠀⠀⠀⠀⠿⠛⠿⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠨⠿⠏⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠰⠆⠀⠀⠀⢴⡦⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⣠⡀⠀⠀⠀⠰⣶⣶⣿⣿⣶⡶⠀⠀⠀⠀⠛
⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣶⣀⠀⠀⠀⠀⡀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣦⡀
⠀⠀⢶⣷⠖⠀⠀⠀⠲⣿⣿⡶⠂⠀⠀⠀⢤⣾⣷⡤⠀⠀⠸⠛⠇⠀⠀⠀⢶⣷⠖⠀⠐⠋⠁⠈⠙⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠉⠉⠁⠀⠀⠀⠐⠛⠛⠇⠀⠀⠀⠀⢸⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⡀⠀⠀⠀⠀⠀⠀⠠⣼⣧⠄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢤⣿⡤⠀⠀⠀⠶⠀⠀⠀⠀⠐⣾⣷⠆⠀⠀⠀⠀⠀⠀⢀
⠯⠀⠀⠰⠂⠀⠀⠀⠋⠙⠀⠀⠀⠀⣀⣀⣴⣿⣧⣀⣀⠀⠀⠘⠉⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⣀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⣰⣿⡀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡟⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⠀⠀⢠⣴⣤⠀⠀⠀⠀⠈⠛
⠀⠀⠀⢶⣶⣶⣿⣿⣿⣶⣶⠆⠀⠘⠂⠸⠟⠋⠛⠧⠀⠀⠘⣿⣿⠁⠀⠚⠀⠀⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠀⠀⢴⣿⡦
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠀⠈⠉⠁
⠀⠀⠀⠀⢠⡿⠟⠛⠻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠀⠀⣀⣤⡀⠀⠀⠀⠀⣀⣦⣀⠀⠀⠀⠀⠀⠙⣿⣿⡟⠁
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠇⠀⠀⠀⠀⠹⠻⠇⠀⠀⠀⠀⠀⢀⡉⠈⠉
⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠁⠀⠀⠀⠀⠀⢶
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⣀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⡯⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⡇⢀⣀⠀⠀⠒⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣾⣿⡟⠁⢠⣤⠀⠁⠈
⠀⠀⠠⠐⠀⠀⠄⠀⡤⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢑⣯⡟⠁⠀⠀⠀⠀⠀⠀⡸⣇⠀⠀⠀⠈⠁⠀⠙⠀⠈
⠀⠀⢀⡼⢆⠀⠀⠀⠘⠙⠀⠀⠀⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⠈⠀⠈⠀⠄⠀⠀⠐⢶⡒⠁⠘⢒⡶⠂⠀⣀
⠀⠈⢳⢀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠂⠀⠀⡟⣠⣄⢸⠀⠀⠀⠉⢀⣷
⠀⠀⠚⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣴⠀⠀⠠⠀⠀⠀⠀⠀⠀⠋⠁⠀⠙⠃⠀⠀⠙⣿⣿⡟⠉
⠀⠄⠈⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣷⢁⣄⣄⡀⠀⠠⣴⡄⠀⠀⠀⢀⡆⠀⠀⠀⠰⠋⠈⠛⠀⠀⠐⡆
⠀⠀⠀⠂⠀⣰⢏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢿⣿⣿⣿⣿⠟⠁⠀⠀⢀⠁⠀⢤⡀⠘⠀⠐⠤⠄⠀⠀⠀⠀⠒⠛⣦⣯⣤⠖
⠀⠀⠲⡶⠚⣱⠟⣩⣾⣧⠒⠀⠀⠀⠀⠀⠘⠆⢀⠀⣸⡿⠿⠿⣿⡀⠀⢠⣤⣾⣤⡄⠀⠉⢀⠀⢠⡀⠀⠀⢖⡤⠀⠀⡟⠁⢷⡀
⠀⢀⡀⠘⡿⣣⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⡀⢰⠁⠀⠁⠀⠀⠀⠈⠁⠀⠀⣸⠟⣿⠀⠀⠚⣁⠀⠀⠃⢠⠀⠁⠈⠀⢀⡀⠀⠀⢀⢄
⠀⠈⠁⢀⠞⠛⠙⠛⢿⡄⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢠⠄⠀⠂⠀⢠⠤⠋⠣⢤⣀⠈⡧⣼⠁⣀⡐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠶⠀⠀⠀⠀⠀⠀⠈⠿⠯⠀⠰⣖⠋⠙⣲⠆⠀⠈⠂⠀⠀⠈⠁⠀⠀⠀⢂⡉⠉⠓
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠏⠘⢆⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣸⠴⠤⡇
⠀⣤⣤⣼⣿⣧⣤⣤⠀⠀⡀⠈⠳⡄⠠⣴⣧⠄⣠⠜⠁⢀⡀⠀⢀⣀⣠⣿⡆⠀⠀⠀⠀⠀⢠⡄⠀⠀⠘⠁⠀⠀⠀⠀⠀⡰⠣⡀
⠀⠀⢹⣿⣿⣿⡏⠀⠀⠀⠀⠠⠀⢸⠀⢋⣙⠀⣇⠀⠦⣾⣷⠄⠀⠉⢛⣕⣵⡋⢀⠀⠀⠘⣿⣿⡋⠀⠀⠀⠀⠀⠀⠘⢣⠀⠀⡤⠋
⠀⠀⠸⠋⠉⠙⠧⠀⠀⠂⠐⠂⠀⠾⠚⠉⠈⠓⠾⠀⠐⠋⠙⠀⠀⠀⠋⠁⠙⠃⠈⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠼⠒⠒⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⡼⢹⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⣾⣿⠿⢻⠏⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⡼⢁⣿⠀⠀⣼⡇⢀⣾⡇⠀⠀⠀⠀⣿⠋⠀⠀⠁⠀⣠⣾⣷⠀⢀⣤⡦⢀⣾⣶⡆⢀⠼⣧
⠀⠀⠀⠀⠀⡼⠁⣸⣏⡀⣼⣿⠀⡾⣿⠀⠀⠀⠀⠀⢿⣶⣤⣤⡀⠀⣻⠟⠁⣴⠟⣻⡗⢸⠟⣿⢁⡜⠀⡏⢠⠻⣄
⠀⠀⢀⣾⣼⣿⣿⣿⣿⢰⣿⠇⢸⣿⠃⢰⣾⠿⠇⠀⠀⠀⠀⠉⣿⣰⣿⢀⣼⣏⡼⣿⣠⠏⢸⣷⠞⢿⣾⡶⠃⠀⣿
⠀⠀⣾⣿⠿⠟⢿⡟⠃⣾⠏⠀⣿⠃⠀⠀⠀⠀⠀⣀⠀⣀⣤⣾⡟⢸⣿⠞⠈⠛⠁⠿⠃⠀⠀⣉⣀⣠⣤⣤⣴⣶⣿
⠀⠀⣰⠇⠀⠀⣿⢀⠀⣿⠀⣰⣿⣀⡜⠁⠀⠀⢰⣿⣿⡿⠟⠋⠀⠀⢀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⣰⡟⠀⠀⢸⣿⠎⠀⢿⠟⠁⠻⠟⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁
⢰⡟⠀⠀⠀⠘⠋⠀⠀⣀⣀⣤⣤⠴⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉
⢛⣁⣤⣤⣶⣶⣿⣿⣿⣿⡿⣋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉
⠀⠉⠻⣿⣿⣿⣿⣿⣿⡿⠃⠁⠀⠀⠀⠀⠀⢀⡾⠛⡿⠟⠋⠉
⠀⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠈⠛⠉⠁⠀⠑⠄⣀⠀⠀⠈⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡒⣦⠡⣖⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢔⣶⡲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡈⢀⠉⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⢣⡅⣴⡄⡵⢃⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠘⣃⠶⠀⡘⢂⣛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣊⠍⠸⡛⢛⠈⢪⣵⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⢍⠀⡀⢷⠖⣄⠀⡮⡅⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⣈⠦⠀⢀⣀⣀⠀⢰⢴⠀⠀⣀⡀⠀⢰⢉⠀⠀⢀⣀⠀⠀⠴⣌⢛⡰⠖⠃⠈⡳⢃⡙⢤⣻⠀⠤⠰⣦⡰⣌⠷⢡⡞⠌⠻⠬⣷⡜⣃⡛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠴⠟⣈⠃⣮⡱⠋⠓⠾⠆⣛⠴⡩⠊⠑⠎⠷⢙⡡⠌⣥⡛⠾⠵⠛⡴⡅⠂⣥⢘⣋⣉⡈⣉⢩⠘⠣⣴⠆⠂⢐⡫⠇⠱⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠁⠛⣱⣀⣀⡻⢇⠅⣲⠖⢤⡔⢂⠒⢨⠐⠞⠃⡿⢀⢀⡀⣄⣉⠏⡔⠎⠃⠨⣾⢁⡼⠆⠲⣐⠯⠧⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⡣⡌⣤⡙⠒⢸⡛⡄⠠⢦⡀⠀⠨⢇⠁⠂⠉⠀⠀⠀⠡⣘⡄⣟⠆⠀⢠⢎⠃⠹⢑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠱⠁⠑⢬⡦⠤⣍⢓⡙⣣⢄⢤⡒⠌⠀⠂⠀⠀⢠⠐⣖⡮⠰⠀⠾⠉⠜⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣉⢦⡱⠎⣟⡤⠃⠃⠴⣠⠤⠚⠈⠂⠽⢈⡃⠿⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⡔⣃⢴⡲⢤⠀⠰⣉⠵⠀⡴⣚⠝⣨⡕⢞⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠺⠰⣏⠂⠈⢓⠓⣘⢩⠛⣜⢊⣥⢀⣗⡇⢈⡰⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢨⣟⠁⡠⠺⠷⠘⠛⣡⡅⡖⡦⠱⣌⠃⠘⣏⠘⣣⠱⠞⣠⢆⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠷⢩⣜⠳⡅⠊⣬⣤⣅⠂⠈⠁⠘⢬⣄⠶⣌⠚⡁⢐⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⡘⢢⡦⠰⢂⡛⠀⠊⠀⠀⠀⠀⠀⠀⠈⠘⡩⡌⣡⡙⠇⠙⢪⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢏⠀⠀⡴⠩⠈⠎⣥⠀⠀⠀⠀⠀⠀⠀⠀⠸⠔⠁⠹⣸⣄⢀⣷⡰⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠⡙⢾⣶⡐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⣊⡕⢻⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⡅⢶⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠡⠃⠸⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡥⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠡


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣼⣁⣧⣀⣀⣄
⠀⠀⠀⠀⠀⠐⢶⣖⣮⠟⠃⠀⠛⠛⣻⣿⠖⠀⠀⠀⠀⠀⠀⠶⣚⡿⣛⠵⣫⣵⠟⣫⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢰⠇⠀⠸⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠉⢳⢑⠀⠀⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣵⡿⣋⠴⣫⢖⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣯⣀⣠⠞⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣐⣶⣤⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⢞⣵⣎⡴⣫⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡴⠛⠳⣄⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠁⠀⠈⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠔⠋⠁⠀⠙⠶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠈⠙⠷


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠹⡄
⠀⠀⠀⠀⠀⢀⣀⣤⠤⠞⢡⣷⠙⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣌⠀⣿⡷⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⢳⢧⠳⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠈⠳⣄⠚⢷⣿⣿⣿⠿⣢⠖⠁⠀⠀⠀⠀⠀⠀⠈⠫⡉⠛⢛⣷⣿⣶⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠑⢦⡐⠾⡍⢈⡽⢃⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⣷⣼⠟⠙⢿⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⡟⠁⣿⣄⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢⠟⠛⠧⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣧⠴⠖⠒⠦⣄⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⠠⠔⠻⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡴⠋⠉⠓⠦⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠯⡼⣆
⠀⠀⠀⠀⠀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠲⡘⠀⠁⠀⠀⠀⠈⠁⠁⢂⠒⠀⠀⠀⠀⠀⠀⠶⣞⠛⠉⠁⠈⡄⠈⠩⠋⣿⠗
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡆⢂⠌⡀⠀⠠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣐⡀⠁⡉⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠀⠑⠂⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠋⠉⠉⠓⠶⠷

⣹⣿⡟⠉⠀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁⠀⠀⠀⠀⣹⣿⡟⠉⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠠⣤⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄⠀⠀⠀⠀⠠⣤⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄
⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁⠀⠀⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣤⣼⣧⣤⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣤⣼⣧⣄⠀⠀⠀⠀⢠⣤
⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⠿⠁⠀⠀⠀⠀⠀⡿⣿⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⠿⠁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀
⣴⣦⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀⠀⠀⠀⢠⣴⣦⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀
⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠋⠁⠀⠀⠀⠚⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠋⠁
⠀⠀⠀⡀⠀⠀⠀⠰⠿⣿⠷⠆⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⠷⠆⠀⠀⠀⠀⣤
⠀⢤⣾⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶⠀⠀⠀⠀⢤⣾⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶
⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠰⠿⣿⠃⠀⠀⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠘⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠁⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠁⠀⠀⠀⢀⣄
⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⢿⣿⡃⠀⠀⠀⠠⣤⣦⣀⠀⠀⠀⢀⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⠀⣤⣦⣀
⣹⣿⡟⠉⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁⠀⠀⠀⠀⣽⣿⡟⠋⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠿⠛⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠠⣤⣴⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄⠀⠀⠀⠀⠠⣤⣴⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡼⢿⣿⠁⠀⠀⠀⢠⣴⣦⡄
⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁⠀⠀⠀⠀⠴⠿⣿⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣠⣴⣷⣄⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⠀⠀⣠⣴⣧⣀⠀⠀⠀⠀⢠⣠
⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠿⠁⠀⠀⠀⠀⠀⡿⣿⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠿⠁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠆⠀⠀⠀⠀⢠⣴⣦⡀
⣶⣦⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀⠀⠀⠀⢰⣶⣦⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠰⠟⠻⠁⠀⠀⠀⠀⣤⣼⣇⡀
⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠛⠁⠀⠀⠀⠚⠛⠏⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠿⡿⠷⠆⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠿⡿⠷⠆⠀⠀⠀⠀⣤
⠀⢤⣾⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶⠀⠀⠀⠀⢤⣾⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡷⠂⠀⠀⠀⢠⣤⣶
⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠁⠉⠀⠀⠀⠀⠰⠿⣿⠃⠀⠀⠀⠀⠿⠛⠓⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠐⠿⣿⠓
⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⢀⣄
⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⠠⣤⣦⣀⠀⠀⠀⢀⣀⣴⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⠠⣤⣦⣀

⠀⠀⠀⠀⣿⡡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢻⣇⣾⠿⠛⠁⠠
⣦⡤⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⢿⡇⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⣿⡻⣶⣶⣶⣦⣤⣤
⠀⠀⠀⠈⣷⡀⠀⠀⣀⠀⠀⢀⣠⣴⣿⡿⠿⣾⢿⣏⡉⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⣾⠿⠋⠁⠀⣼⣿⡇⠈⠛⠛⠉⠉⠁
⣀⣤⣤⣦⣸⣏⣤⡞⠁⠀⠈⠛⠉⠀⠀⠀⣾⣿⠈⢻⠿⢿⣶⣤⣄⠀⠀⠹⣦⡀⠀⠐⠋⠐⠂⠈⠀⠀⠘⣿⣿⠀⠆
⠀⠀⠀⣴⡟⢷⣄⡀⠀⠀⠀⠀⡄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄⠀⠀⠀⣠⡞⠀⠀⠀⠈⢿⡄
⠀⠀⠀⣿⠀⠀⠉⠙⣂⣀⠀⠀⣿⠀⠀⠀⠈⣏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡈⣿⡏⢀⣴⣾⠏⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⢙⣷⣯⣤⠶⠋⠀⠉⠀⠀⠀⠀⠴⠾⠛⠛⠛⠛⢻⣾⣟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠿⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⠃⢻⣿⣦⣄⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠸⣄⠀⠀⠈⢀⡀⠀⠈⠂⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠈⠉⠛⠳⠶⠀⠀⠀⠘⣷⣄
⣰⡾⠁⠀⠀⠀⠹⣷⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦
⠏⠀⠠⠴⠾⠟⢳⣿⣟⠋⠀⠲⠶⢶⣶⣶⣴⡀⢸⣿⠆⠀⠀⠀⣀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢿⣿⠇⢀⣠⣶
⠀⠀⠀⠀⠀⠀⣿⠁⠛⠛⠶⠤⠀⠀⠈⠉⢛⣷⣾⣥⣴⣶⣶⠟⠋⠁⠀⠀⢸⣆⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣷⣬⣿⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠋⣿⣎⠉⠋⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⢀⣀⠀⠀⠀⠀⣀⣴⣿⢹⣷⣤⡀⠐
⣑⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠁⠀⠻⢿⣧⠀⠀⠐⠒⠺⠿⢿⣦⣿⣡⣤⡶⠛⠁⠀⠀⠀⠀⢸⣿⠇⠀⠿⠿⣿⣶
⠙⠛⠂⠀⡟⣿⣆⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⣶⡞⢻⣯⠉⠀⠀⠀⠀⠀⠀⠀⢻⡟⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡇⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠄⠀⠀⠀⢀⠀⠀⠀⢰⡟⠀⠈⠛⠷⣄⠀⠀⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠀⡇⠈⣿⣿⣷⣄⡀⠄⠀⠂⣉⣴⡿⠃⠀⠀⠀⠀⢸⣇⠀⠀⠚⠀⠀⠀⠀⠀⠈⠁⠐⣦⡀⠀⠀⠈⢀⡄
⠀⠀⠀⢀⡀⠀⠸⣿⣿⡏⠀⢀⣤⣾⣿⠟⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⣴⡏
⣶⣶⣿⣿⣿⣷⣤⣻⣿⣠⣶⣿⣿⡿⠋⠀⠈⠛⠛⠻⠿⢿⣤⣟⣡⣤⣶⠟⠁⠀⠀⠀⢀⣠⣴⣷⢮⣷⡞⠛⠀⠀⠀⠀⠀⣀⣠
⠛⠛⠛⠛⠛⠛⣻⣿⣿⣯⡉⠉⠉⠣⡀⠀⠀⠀⠀⠀⢰⣶⠟⣿⣍⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣾⠋⠿⠷⠦⣤⡀⠙⠛⠟⢛
⠈⠁⠒⠂⣴⣿⣿⡇⠘⣿⣿⣶⣄⡀⠑⢄⠀⠀⠀⠀⣿⠃⠀⠛⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣿⣿⡿⠀⠀⡿⠿⢿⣿⣿⣦⣌⢢⠀⠀⠸⠃⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⢀⣀⠀⠀⠘⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⣿⣿⠃⢀⠌⠀⠀⠀⠀⠉⠙⠛⠷⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣀⠀⢀⠄⢡⣿⡟
⠀⠀⠀⠀⣿⡟⢠⠊⠀⠀⠀⠀⠀⠀⢹⣦⡀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⠻⣿⣿⡇⢀⣿⣿⡇
⣿⣿⣿⣻⣟⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣻⣿⣿⣛⣟⣻⣛⣿⣻

⠀⢀⡀⣀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡀⣠⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠃⠀⠀⠀⢀⠀⠀⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠇⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄
⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠀⠀⠈⠉⠏⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⠀⠀⠈⠉⠋
⠀⠈⠛⠂⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠚⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣤⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣾⣤⡀⠀⠀⠀⠉
⠀⠀⣀⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴⠀⠀⠀⣠⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴
⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⢀⣀⠀⠀⠐⢾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⢀⣀⠀⠀⠐⢾⣿⡟
⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠀⠁⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠀⠁
⠀⢀⡀⣀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡀⣠⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠃⠀⠀⠀⢀⠀⠀⠀⢠⣿⡿⠦⠀⠀⠈⠀⠀⠀⠀⠸⠇⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄⠀⠀⠀⠀⠃⠀⠀⠀⠀⢤⣦⠄⠀⠀⠀⠀⢘⣶⣿⡄
⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⠀⠀⠈⠉⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⠀⠀⠈⠉⠋
⠀⠈⠛⠂⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣾⣤⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣾⣤⡀⠀⠀⠀⠉
⠀⠀⣀⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴⠀⠀⠀⣀⣷⣶⠁⠀⠀⠀⠚⠛⠇⠀⠀⡀⠀⠀⠀⠴
⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⠀⣀⠀⠀⠐⢾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⠀⣀⠀⠀⠐⢾⣿⡟
⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠀⠁⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⢲⠐⠣⣄⠀⠀⠠⠈⠁⠃⡄⠀⠀⢀⡀⠀⠀⣼⣗⣿⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠠⣤⣾⣇⣀
⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠖⢄⠀⠚⠒⠌⠀⠀⠀⠈⢀⠀⣠⠐⠀⢀⣾⣇⠀⠀⠀⠘⠁⠀⠀⠄⠐⠀⠈⡁⠂⠀⠀⠀⣀⣀⣾⣿⣦⠶⠒⠀⠠⠟⠻⡏⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⡘⠀⠄⢣⣀⡀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⣾⣁⣿⡄⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠠⠀⠀⠀⠀⠉⠉⢹⡟⢿⡀
⠀⠀⠀⠀⠀⡤⠀⠀⠐⠃⣀⡀⠀⢡⠀⢐⡣⠀⠀⠀⠀⠉⠠⣠⡿⠉⠉⠙⣻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⡆⠀⠀⠸⠀⠀⠃⠀⠀⣠⠜⢐⡀
⠀⠀⣶⣶⡂⠈⠢⢀⠐⠀⠈⠁⠀⠀⢔⠉⠀⠀⠀⠀⠀⠀⢀⡞⠑⣤⣤⠾⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠗⣷⡦⠄⠀⠀⠀⡀⠀⢘⢁⠀⠀⢠⠁
⠀⠐⠛⠿⠋⠁⠀⠀⠉⠀⠀⢐⡂⠉⢀⡱⡀⠀⣀⠀⠀⠀⣼⡷⠟⠉⠉⠲⣼⣇⠀⠐⢦⢤⠎⠄⠀⡀⠀⠀⠚⠋⠹⣏⠀⠀⠄⠰⠆⡀⠀⠀⠸⠴⠕⠂
⠀⠀⠀⣀⠀⠀⠀⠀⠀⣈⠔⠁⠈⠁⠊⠡⠅⠀⣾⣷⣄⣀⣡⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⣪⠄⠐⠂⠉⠀⠠⠶⢠⣤⠀⠀⠀⠀⠀⠀⣀⣨⡄
⠀⠀⢸⠁⢻⢃⡖⡤⣀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⠛⣿⣿⡃⠀⠀⢻⣶⠶⣾⡃⠀⠐⠁⠀⠀⠂⠀⠀⣶⣦⠀⡀⠀⠀⢀⡀⠀⣠⣞⣿⣿⡇⠀⢤⡤⠘⠃
⠀⠸⡼⢠⠏⡟⡼⢱⡟⡰⣰⠂⠀⠀⠀⠀⠈⠙⣿⣿⠿⠿⠷⠄⠘⠋⢻⡿⠋⠉⠁⠀⣶⡀⠀⠀⠀⠀⠉⠁⠀⠘⢶⣿⡿⠥⣼⠿⢛⣭⠴⣧⡀⠀⠀⠴
⠀⣠⠀⠀⠈⠑⠣⠏⣿⢡⠓⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠻⣄⣤⣤⠀⠀⠀⡀⠀⠀⠻⡄⢊⣡⣶⣿⣿⣯⡵⢞⣻⢦⣄⡀
⠀⠀⠚⠐⠀⠄⠀⠀⠅⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⣏⡁⠁⠠⠁⣴⠃⠀⢘⣆⢡⠄⠀⣠⣞⣩⣶⣿⣿⣿⡷⢟⣿⠿⠟⠛⠋
⠀⠀⠀⠆⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣄⣀⣠⠀⠀⠈⡇⣠⠷⣤⣹⡀⠀⠈⠀⠙⠀⣰⣿⠿⢿⡿⢟⣫⣵⣾⣿⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣤⡰⠚⣇⠀⠀⠀⠀⢀⣠⣾⣿⣿⣦⡄⠀⡿⠁⠀⠀⠉⠃⠀⠀⠁⠀⡐⠋⠀⠀⠈⠀⠈⠻⣿⣿⡏⠀⣌⡩
⠀⠀⠠⠀⠀⠀⠀⠀⣿⣦⣴⡞⠀⠀⠀⢱⠀⠀⠈⠽⠂⠀⠀⠈⠀⠀⠹⡟⠀⠀⠀⠀⣠⡄⠀⠀⠀⡀⢀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠘⢧⡅⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⠶⣿⣿⣿⣷⣄⠀⠀⠓⠊⠳⡜⠀⠀⢀⡄⠀⠀⠀⠀⠃⢀⡴⡆⢸⡌⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠶⣬⠃⠀⠀⠀⢉⡜⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡨⢤⢀⣤⡤⠀⠀⠳⣁⠐⡄⠿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠘⠛⠋⠐⠂⠀⡀⣾⠄⣐⣤⣠⠄
⠀⠀⠠⠀⠀⠃⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡁⢺⡇⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⡀⢠⠀⠊⠀⠀⠀⠀⠀⠃⠀⠀⠀⠰⠋⠁⠋⠁⠈⠉
⠀⠀⠀⠀⢠⢾⠀⠀⠀⠀⠑⠀⣀⡄⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⢀⡀⠀⠀⠀⠀⠁⡀⠈⠓⠀⠁⠁⢛⡀⠀⠀⠀⠰⣶⣾⣧⣀
⠀⠙⢆⠐⠁⠸⢄⣀⠀⠠⠀⡐⠙⠉⡐⠀⠀⢻⠦⣄⠀⠀⢀⢠⠄⠠⠺⣿⣿⡄⠀⠀⠈⣀⢠⠀⢠⣶⡄⠀⠍⠐⠂⠀⠀⠠⠿⢻⡟⠁
⠀⠀⠜⠀⡀⢠⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡀⠈⠓⠂⠀⡞⠀⠀⠈⠻⢅⣹⠀⠀⡨⢁⠊⠀⢀⠀⠀⢠⣄⢊⡀⠀⠀⢀⡀⠀⠁
⠀⠈⠀⠀⠙⢾⠀⠀⠀⣤⠀⣀⠀⠀⠀⠀⠀⣠⠜⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⢿⠀⢀⠀⠈⠴⠀⣶⠐⢄⠠⡘⠃⠀⠀⠀⢈⠱⣄⠀⠀⠀⠀⠀⢀
⠀⠀⣀⠀⣦⠀⢠⡀⠀⡏⢰⠋⣠⠀⠀⠀⠾⠥⠆⢠⡀⢠⠀⠀⠀⠙⠀⠀⢀⡀⢀⣿⡀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢀⣠⠤⣾⠒⠉⢣⡀⠀⠀⣀⢟⡢⣤
⠀⠀⡉⠳⢌⠃⢸⣷⣆⠀⠀⠛⡉⠀⠀⠀⠀⠀⠀⠈⣧⣧⠀⠀⠀⠀⠀⠀⠈⢻⣿⡛⣍⠓⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠐⡷⠀⣠⣈⠠⡀⠈⠙⣾⠿⠳⠄
⠀⠈⠛⠛⡃⣠⣿⣿⣟⣿⣾⡿⠁⣀⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠞⠋⠉⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠀⡇⠀⠀⠀⠈⠉⠀⠀⠁
⠀⠀⠀⠘⠻⠽⣿⣿⣿⡽⣿⠀⣙⠷⣤⠄⠀⠀⢠⡄⠈⠄⠂⠀⠀⠀⠀⠀⢀⡤⢀⡆⠀⠀⠀⠀⠀⠴⣄⡁⠀⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⡶⠖⣢⠀⣻⡿⠋⡁⠻⠇⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠀⠀⠀⠘⢆⠉⡇⣶⢶⠸⡆⠀⠀⠈⣥⠛⠓⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⣻⣦⡀
⠀⠀⠀⠺⠃⠀⠈⠁⣾⠸⡦⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⡀⠂⠀⢰⣨⠇⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⠛⠛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣻⣾⣻⣟⣿⣟⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻⣟⣷⣟⣿⣟
⣛⠾⣻⢞⡳⢎⣱⢟⡷⣟⠿⣋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠵⣛⠞⠉⠚⡻⢞⡳⢟⡷⣛
⣉⠖⡡⠎⡱⢎⡱⢊⠱⢉⠶⡉⠦⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢉⠶⣉⠆⡀⢄⡱⢎⡱⢎⠴⢉
⡁⠂⡁⠂⡑⢊⠐⢀⠐⢈⠐⡉⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠒⡀⠂⡁⠂⡑⢂⠐⢈⠐⢀
⡀⠂⡀⠂⡐⠀⠐⢀⠐⠀⠐⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠂⠀⠂⡀⠂⠐⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠁⠖⠐⠂⠑⠊⠀⠀⠀⠀⠀⠀⠀⠁⠊⠑⠂⠰⠀⠬⠙⠷


⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⡂⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣷
⠀⠀⠀⢤⣖⠒⠈⠁⠀⠓⠐⣲⠶⠀⠀⠀⠀⠀⢠⠶⠆⢋⡹⠆⣴⣦⡤⠄⠀⠀⠀⠀⠖⠒⢲⡟⠒⠻⣷⣶⡶⠂
⠀⠀⠀⠀⠈⢡⠆⠀⠀⠀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠠⢔⠍⠪⠞⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⢄⣀⡴⢿⡏
⠀⠀⠀⠀⠀⣾⡴⠋⠀⠄⢹⡀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠊⠉⠺⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣴⠞⠉⠳⢬⣷
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠰⡀
⠀⠀⠠⠶⠶⠖⢶⠷⠆⠺⡖⠀⠀⠀⠀⠀⠀⠰⣶⣶⣿⣿⣿⣿⣿⣶⣶⠖⠀⠀⠀⠀⢫⡉⠉⠀⠀⠀⠈⠉⡩⠂
⠀⠀⠀⠀⠐⢲⡯⠀⠀⢀⣽⠊⠁⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⡆
⠀⠀⠀⠀⢀⡞⠀⠰⠲⢅⡀⢇⠀⠀⠀⠀⠀⠀⢀⣿⡿⠛⠙⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⡀⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠚⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡜⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢇
⠀⠀⠀⣠⡤⠠⠀⠀⠀⠐⠒⠒⣠⠄⠀⠀⠀⢤⣤⠠⠶⠚⠀⠹⠶⠶⣦⠤⠀⠀⠀⠠⢤⣶⠶⢟⣷⣿⣿⣷⡶⠖
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⢰⠊⠀⠀⠀⠀⠀⠀⠀⠁⣤⣻⣿⣿⣿⡏
⠀⠀⠀⠀⠀⡏⠀⠀⠰⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠤⢤⡘⣆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠻⠋⠺⣿⠇
⠀⠀⠀⠀⠐⠃⠁⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⢀⠀⡀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⢰⣓⡄⠀⢳⣇⣤⣬⡷⣧⣤⣸⣾⠃⠀⣞⡆⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⠾⡣⢜⠷⣦⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢉⣦⣾⣿⣿⢿⡿⠁⢻⣿⠫⣿⣷⣶⡋⠀⠀⠀⠀⠀⠠⣶⡶⠛⣋⠉⢹⠇⠾⠐⣄⡵⢈⣭⢻⣛⠻⢶⣶⠆
⠀⠀⠀⠀⢀⣀⡴⠿⠿⢿⣿⣯⣤⣤⣤⠤⠤⣠⡿⠿⢿⣿⣦⡀⠀⠀⠀⠀⠈⡷⠚⢃⠃⠀⡃⢘⡌⣁⡀⡟⠡⢰⣏⣵⡟⠁
⠀⠀⠀⡴⠁⣠⣴⢂⡀⡸⢫⠂⠏⡅⣸⣷⡞⠁⣴⢿⠇⡹⣿⣷⠀⠀⠀⠀⡖⠛⣡⡏⢸⡨⠇⠨⢾⡫⠵⢎⠃⠏⠆⠀⣡⢳⡄
⠀⠀⠀⡹⠞⠛⠃⠟⠠⢁⢏⡄⡼⣡⠉⢀⡅⢸⡟⣁⡔⣰⣿⣿⡇⠀⠀⠀⠙⠛⣿⢹⣛⠻⠟⣛⣲⣟⣛⠻⠿⣙⡟⢷⡖⠋
⠀⣠⡘⢶⡶⢁⡾⠁⡆⠠⢞⠀⠼⢃⣼⠞⠳⣌⠣⡤⢠⠝⣩⠉⠟⠒⣻⣆⠀⢸⣧⣼⠶⠿⠛⠛⠛⠛⠛⠛⠻⠶⣧⣼⣇
⠀⢧⡉⢁⣠⣾⣇⣸⡷⣒⣛⣂⣘⠛⢻⣘⠛⢋⣡⡆⣘⡀⣃⣈⠈⠸⢏⣼⠇⢉⠁⠤⠤⢤⣤⣤⢤⣄⡤⠤⡤⣄⣀⡀⣉
⠀⠀⠉⠋⠉⢻⣿⣟⣻⣿⣍⠉⠉⠛⠟⠉⠛⠋⢉⣿⣟⣻⣿⡿⠳⠞⠛⠁⠀⣧⡶⢫⠆⢩⠂⡵⡘⠛⢠⡿⠃⢹⠏⠲⢻⣴⠋
⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⣻⣷⣶⣤⣤⣤⣴⣾⣟⢻⣿⣿⡟⠁⠀⠀⠀⢠⣼⡶⢢⡆⡄⢰⡁⢞⣴⢚⣬⠣⢡⢟⡄⠒⣻⢇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣼⣏⣿⣹⣭⣷⣿⣿⠟⠋⠀⠀⠀⠀⠀⠘⠦⠴⠛⠦⠯⠽⢶⢤⣽⣮⣤⠶⠴⠦⠴⣤⡽⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⢀⣴⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣴⣿⠟⠁⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢦⡀⠀⠀⠀⠀⠈⠉⠛⠛⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣴⠶⣄⠀⠀⠀⠀⠀⠈⣷⣹⠂⠀⠀⠀⠀⢠⡶⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡀⠀⠀⠀⠀⠹⠶⠟⠀⠀⠀⠀⠀⣼⣟⣡⣴⠶⠛⠶⣤⡀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠈⠙⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢳⠇⠀⠈⢷⡀
⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣿⠏⠀⠀⠀⠈⢷⣄⣀⣤⣤⣤⣤⠴⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡄
⠀⠀⠻⣟⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢀⡴⣦⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠈⠷⣌⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠘⠓⠋⢠⣶⣄
⠀⠀⠀⠀⠀⠈⠻⣦⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠈⠳⣄⣀⣠⡴⢾⡷
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣀⡴⢤⡀⠀⠀⠀⠈⣧⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣸⣼⠇⠀⠈⠋⠁⠀⣼⠃
⠀⠀⠀⠀⠀⢠⠏⠀⠀⣠⠴⣛⣥⠶⠶⣬⣗⣦⣄⠀⠸⣆⠀⠻⠾⠃⠀⠀⢠⣶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠰⣇⡀
⠀⠀⠀⠀⢠⠏⣠⣴⣿⠿⠛⠉⠀⠀⠀⠀⠈⠉⠛⠻⢦⣽⡀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⠀⠀⠀⣰⠶⠛⠛⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⣷⠀⠀⠀⠀⠀⢠⣟⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⣿⣿⠛⢿⠛⠿⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣡⡿⠁
⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟
⠀⠀⠀⠀⠀⠘⣿⣟⠻⢷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣷⣶⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⢀⣀⣀⣤⣤⣶⣶⠿⠿⠟⠛⠛⢋⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⣀⣀⣀⣤⣤⣤⣴⡶⠾⠿⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁
⢺⣿⣿⡛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣛⣉⣤⣤⣴⡀⠀⠀⠀⠀⠀⢠⣾⠟⠁
⠀⠙⠻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡶⠾⢿⣿⡶⠀⠀⠀⠀⠀⠺⣿⣟⡛⠉⠉⠁⠀⠀⠀⠀⠀⢀⣴⣿⠋
⠀⠀⠀⠀⠉⠻⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠆⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣄⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⢰⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣶⠀⠀⠀⠀⢸⣦⣤⣤⣤⣤⣶⡶⠾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢸⣿⠉⠉⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠹⣿⣍⣹⣿
⠀⠀⠀⠀⢀⣀⣠⣴⡆⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠈⠛⠛⠉
⠀⠀⣶⣿⠛⣫⣽⣿⠃⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄
⠀⠀⠙⠿⠿⠿⠋⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠉⠀⠀⠀⠈⠙⠻⠿⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣷⣶⣦⣤⣤⣹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⣀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣀⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⣧⡄⠀⠀⠀⠀⠀⠀⠀⣐⢆⠠⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠠⡣⠀⣀
⠀⠀⠈⠉⠻⡿⠋⠉⠀⠀⠀⠀⠀⠈⣛⡄⣏⠀⠀⠀⠀⠀⠓⠄⢀⡀⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣲⣷⡛⠁
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠟⠉⠙⠃⠀⠀⠀⠀⠘⠀⠈⠀⠸⠀⠀⠀⠀⠀⠰⠋⠈⠓
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡌⠀⣠⠀⢃⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠈⠷⣠⡄
⠀⠀⠀⠀⡅⠠⠁⠀⠀⠀⠀⠀⠙⠁⠀⠉⢠⣄⠀⠀⠀⠀⠁⠄⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡷⣈⡉
⠀⠀⠀⠀⠁⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠊⠈⠉⠃
⠀⠀⣀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠂⠰⡆⠄⠈⠋⠀⠀⠀⠀⠀⠀⠰⢢⡄⠀⠀⠀⠀⠀⢀⢀⣼⣤⣀⠀⠀⠀⢠⣴⣿⣤⠄⠀⣀⡔⠁⠀⠀⡀⠠⠳⢀⠤
⠀⠀⠀⡀⠲⣈⠂⣀⡀⠀⠀⠈⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠉⡾⣁⡼⡇⠀⠀⠀⠀⣿⠿⣷⠙⠋⠁⠀⠀⠀⠀⠀⠀⠄⢊
⠀⠀⠸⠟⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠉⠙⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉
⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀
⠀⠀⠀⣴⡀⡀⠀⠐⠀⠐⠀⠀⢠⡤⠄⠀⠦⣀⠀⠀⠀⠀⣀⣠⡭⠧⠤⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣿⣷⠶⠂
⠀⠀⢻⣿⣿⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⣞⠚⠻⣅⠀⠀⠀⠈⢘⡺⢚⠈⠀⠀⠀⠀⠀⠀⢀⣿⠿⢿⡆
⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⡀⠀⠀⢂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠤⢤⣸⣗⣤⠆⠀⠀⠀⢀
⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠹⢧⡀⠀⠀⠀⠀⠀⠠⠀⠄⠠
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⣀⡀
⠀⠀⠀⠀⠄⠦⠀⠀⠀⠂⠀⠀⠠⣤⠄⠘⢇⡴⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠀⠐⠃⠀⠀⠀⠐⣯⠁⣀⠺⠋
⠀⠠⠈⢐⠀⠀⠗⠂⡐⠀⠀⠀⠀⢈⣫⠶⣻⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢂⠀⠀⠀⠀⠘⠗⠀⠈⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⡀
⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⣿⠀⠀⠀⣀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⠋⣹⠛⠀⠀⠀⣰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢀⣿⡇⠀⠀⣰⣿⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠁⠀⠀⣠⣶⣿⣿⠀⠀⣀⣴⣶⠄⢠⣾⣶⣾⡆⠀⣰⢿⣷
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣸⡿⠀⠀⣰⣿⡟⠀⣰⣟⡿⠀⠀⠀⠀⠀⠀⢸⣷⣤⣀⡀⠀⠀⠀⠰⢿⣿⠟⠃⢠⣾⡿⢿⣿⠀⢾⡿⢻⡿⠃⣰⠃⢨⡿⠀⣠⣶⡀
⠀⠀⠀⠀⢀⠔⢠⣟⣠⣤⣿⣷⡖⢠⡿⣼⠃⢠⡿⣼⠃⢀⣀⣀⣤⣄⠀⠈⠛⠛⠛⠿⢿⣷⡄⢀⣾⠇⠀⢠⣿⠋⣠⣿⠏⢀⡾⠁⣾⠃⣰⣷⣄⣼⢃⣴⠃⠈⣿
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠁⣾⣷⠏⠀⣾⣿⠇⠀⠸⠿⠿⠟⠓⠀⠀⠀⠀⠀⠀⠀⣽⡧⣾⣿⠀⣠⣿⡇⣰⠟⣿⣤⡾⠁⠸⣿⡿⠋⠹⢿⣿⠟⠁⠀⠀⣻
⠀⠀⢠⣿⣿⣿⣿⠿⢿⣿⡟⠋⢰⣿⠏⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣤⣾⣿⠃⢸⣿⣾⠋⠘⠿⠃⠀⠿⠋⠀⠀⠀⠉⠁⠀⣀⣀⣠⣤⣤⣶⣾⣿
⠀⠀⠀⢉⣿⠁⠀⠀⢸⣿⠀⠀⢸⡏⠀⠀⣼⣿⠀⢀⡼⠀⠀⠀⠀⢀⣾⣶⣾⣿⣿⣿⠿⠁⠀⠈⠋⠁⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣾⠃⠀⠀⠀⣿⡏⣰⠀⢸⣇⣀⡾⢻⣿⣶⡾⠁⠀⠀⠀⠀⠘⠿⠿⠟⠛⠉⠀⠀⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁
⠀⢠⣾⠏⠀⠀⠀⢸⣿⣿⠃⠀⠸⣿⠟⠁⠀⠛⠋⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉
⢀⣿⡟⠀⠀⠀⠀⠸⡿⠃⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉
⢸⡟⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁
⠠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠀⡄⠀⠄⠀⠀⠄⠀⠠⠀⠠⠀⠄⠄⠀⠀⠀⠀⠀⠰⠠⠆⠀⠀⠂⠶⠀⠂

⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠁⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶
⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿
⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣤⣤⣄⣀⣀⣀⣸⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣷⣾⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⣴⣾⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢶⣶⣿⣤⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠨⠿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠋⠑⠂⠀⠀⠀⠱⠀⡀⠀⠀⠀⢸⠿⢿⡏⠀⠀⠀⠸⡶⢀⣤⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠒⣶⣷⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠤⡔⠀⠟⠁⠀⠀⠀⠀⠐⣶⡌
⠀⠀⠜⠋⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠞⠙⠆⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠰⣾⣿⡖⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠲⣾⣷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣾⣿⡷⠂⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠛⠙⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠋⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠃⠀⠀⠀⠀⠀⠘⠁