Sweat Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡽⡥⢤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⣀⣾⡑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠻⠀⡔⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠗⠟⡠⠐⠉⢁⣀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠱⢆⡅⠀⠀⢐⡁⢊⣉⡴⠒⠐⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣁⢺⡏⠀⠀⠘⠁⠀⡨⣧⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠑⠊⠀⠁⠀⠐⠐⠉⠀⠀⠈⠑⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠉⢀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⠠⡀⠤⠤⠚⠟⠉⠉⠀⠈⠀⡄⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠈⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢎⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⣠⡀⠀⠀⠀⢀⠳⣄⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⣿⢠⡅⣠⠈⠲⠄⠄⢸⠀⠈⠉⠐⠒⠈⠀⢀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠘⠿⠘⠂⠀⠀⠀⠀⠀⠀⠉⢂⡀⠀⢀⠀⠠⠒⠲⡦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⡆⠀⠀⠀⠈⢌⢆⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠈⠁⠀⡷⠷⠘⠲⠉⠢⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠈⠸⢢⡀⠀⠀⠀⠙⠃⠀⢀⠱⠀⠀⣀⡀⠀⠤⠀⠖⠈⠉⠒⠄⡀⠠⢴⣷⠦⣀⠰⠂⢀
⠀⣠⠔⠀⠒⡒⠒⠒⠄⢄⣺⣂⡗⠂⠧⢄⡀⠑⠄⠀⠀⠠⠀⠀⠰⡀⣳⡜⣣⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠁
⠀⢏⠀⠀⠀⠑⢘⣿⣹⠁⣿⠃⠻⡀⠀⠀⠀⠑⢦⢢⠀⠃⠀⠀⠀⣇⣰⡍⢠⣀⣀⣤⣄⣀⣀⡀
⠀⠀⠂⣀⣤⣥⣜⣻⣷⣷⣿⣧⣀⠈⠀⠀⠀⠀⢘⣮⣼⣄⠀⣀⣀⣬⡷⠶⠒⠻⢍⠋⠳⠶⠿⢪
⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⡟⠛⠚⠚⠋⡀⠉⡆⢈⣾⣶⣶⣤⣤⣤⣤⣤⣤⣼⣿⣶⠄
⠀⠈⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⠾⠿⠿⠿⠿⠿⠿⢷⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄
⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆
⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠉⣼⣷⡀⠀⣀⠙⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⠛⠋⠁⠀⠀⠀⢿⡿⠃⣸⣿⡇⠀⠈⠛⢿⣶⣄⡀⠀⠀⠀⠀⠀⠸⣿⡀
⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⠀⠀⠈⠙⠻⢷⣦⣤⣀⣀⡀⣻⣇
⢸⣿⣀⣀⣠⣤⣤⣤⣶⣶⡶⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⣿
⣿⡟⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡾⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠶⣶⡆⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⣿
⣿⡇⠀⠀⢀⣿⣷⠀⠀⠀⠀⠈⠁⣀⣠⣤⣶⡾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⣿
⣿⡇⠀⠀⣸⡟⣿⡇⠀⠀⠀⠀⣾⡟⠋⠉⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠉⠙⣿⠆⠀⠀⠀⠀⠀⢿⣷⣿⠀⠀⣿
⢸⣷⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠘⢿⣦⣀⣀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⣀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢰⣿
⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⢠⣶⠀⠀⠀⢰⡆⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣼⡏
⠀⢻⣷⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⢰⣿⠁
⠀⠈⢿⣆⠀⠀⠀⠀⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠃⠀⢀⣿⠇
⠀⠀⠈⢿⣆⠀⠀⠀⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣷⣦⣾⠿⣷⣦⣴⡿⣷⣤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠈⠉⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠷⣶⣶⣶⣶⣶⣶⣶⡶⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠻⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠦⠀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⣠⠁⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡏⠀⠠⣤⣜⡓⠘⠰⣶⣂⣀⣀⠀⢠⠋⡄⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣰⠃⠀⠈⠉⠉⠀⠀⠀⠉⠉⠛⠋⠁⢸⠀⣇⣠⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⣀⠀⠀⢀⠀⢀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠄⠒⠋⠉⠒⠶⠮⠜⠉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠢⠤⠚⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡦⡠⠖⠋⠙⠶⠊⡇⠀⠀⠀⠀⠀⠀⠀⡶⢄⠜⠲⢄⡉⠙⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠒⠂⠤⠤⠤⠤⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡼⠉⠉⠉⢹⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⢤⡇⠀⠀⠀⠀⣇⡸⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠀⠀⠀⠀⠀⠓⠒⠚

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡖⠛⠉⢿⣦⣶⣿⣿⣿⣿⣿⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⢀⣖⣾⣧⠀⢸⣿⣟⡿⠟⠻⣿⣿⢿⣿⣿⣿⣿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⢀⠀⡀⢾⣿⣿⠄⣠⣾⠏⠻⣷⣷⣶⣂⠙⠲⠄⠘⠻⣗⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠁⢀⣠⡴⠋⠀⣘⠲⢀⣴⣾⡋⢽⠂⠀⢰⣿⣿⡇⠑⠂⠀⠀⠁⡻⣆⠀⠀⣄⢄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢉⣁⣤⣤⠴⠾⠛⠁⠀⠀⢰⡏⠀⢸⢉⣉⣵⣿⠀⠀⠈⢿⣉⡝⠀⠀⢇⢲⠀⠀⢘⣶⣦⡙⠾⠇
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢻⡏⠁⠀⢰⣧⣤⣤⠾⠛⢿⡏⠓⠻⣿⢿⣿⠇⠀⠀⠀⢸⡟⣍⠁⠀⠈⠉⠀⠀⠿⣧⣻⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣗⠛⠉⢷⡀⠀⠈⢳⣭⠅⠀⢀⡀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⣧⠈⠑⠀⠀⠀⠀⠀⠀⣄⣙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣀⣠⣷⠄⠀⣸⡇⠀⢰⣯⠗⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠉⠈⢷⣬⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠙⢿⣟⠳⣤⡀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⣠⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠈⠻⣆⠀⠉⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠞⠋⠁⣠⡞⠁⠀⠈⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠉⢙⡷⢄⠀⣼⢿⡛⠋⠉⠁⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⣴⣏⣦⡘⣾⡁⢈⣿⣄⠀⠀⢀⣴⠞⠉⠀⠀⠀⢠⣆⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⠃⠈⠛⡿⢺⣿⡭⠔⠻⣧⣰⠟⠁⠀⠀⠀⠀⠀⠀⢹⡄⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣾⡏⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠶⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠴⡾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡞⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⠞⢿⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⡇⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠶⠻⡏⠁⠐⣦⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⣿⣇⡏⠀⠀⠀⠀⠀⠀⢠⣾⣿⣅⣀⣤⣴⡇⠀⠀⢹⡀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣶⣦⣄⣀⠀⠀⠀⠀⢸⣇⡿⠙⠛⠃⠀⠀⠀⠀⠀⠀⠘⠛⠛⣿⠟⡏⠀⣿⠀⠀⢸⡅⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⣶⣤⣬⣭⣁⣠⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣾⠿⢻⠇⠀⢿⠀⠀⠘⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠘⣦⠀⣾⠀⠀⠀⡇⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠘⠛⠓⠏⠀⠀⠀⡿⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠈⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠒⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢸⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⡒⠩⠅⠒⠛⠁⠘⠛⠛⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠛⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⠀⢻⡇⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⣼⡟⣁⣀⣠⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠉⠛⠻⢿⣿⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠘⠿⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⣾⠟⠛⠻⣷⣄⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣀⣤⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠻⣧⣤⣤⣤⣿⠿⠂⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠐⢿⣿⣍⡀⠀⣈⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣄⣀⡀⠀⠀⠀⣀⣠⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉


⣶⡶⣶⠶⡶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⣶⣶⣶⢶⣶⠶⢶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠕⣄⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠉⠁⠉⠉⠉⠉⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⣀⡄⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⡀⢀⡀⡄⠰⠇⠸⡀⠰⣠⡀⢠⣤⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠘⠀⠀⣝⢤⠑⡌⠹⠘⠃⢴⠃⠱⠀⠋⠓⠁⢡⠘⢃
⠀⠀⠀⠀⠈⠄⠊⠉⠀⠀⠀⠀⡆⠀⠰⠀⠀⢫⠀⠀⢀⣀⣀⡴⠀⡤⠀⠠⣄⠀⠀⢸⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠓⢤⡀⠀⡌⠰⣠⡎⠥⠒⠉⠱⡄⠧⠀⡠⠊⠻⢍⣮⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠔⠒⠵⣤⡃⠀⡇⠀⠀⠀⠀⣷⡁⠀⠸⠁⠀⠀⣾⠈⣿⡓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠐⢊⡇⠀⠀⢠⠀⠐⢄⡀⠀⢀⠵⠁⠀⠈⡣⢄⣀⡠⠚⡝⢫⡃⠀⠀⠛⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣐⡃⠀⠀⠉⠀⠀⠀⠈⠉⢡⠀⠀⠈⠉⠃⠀⠀⠀⢀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⢀⠀⠔⠀⠀⠀⠀⠈⡄⠀⠀⠋⠀⠀⡄⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⡇
⠀⠀⠀⠀⠐⠕⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢠⠃⠀⠀⠛⢀⠔⠊⠉⢢⠀⠀⠀⠐⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠼⠦⣄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡀⠀⠀⠠⡏⠒⠢⠤⠤⣄⣀⣀⣀⣀⣀⡤⢤⡒⠉⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⡴⠀⢀⠀⠀⠙⢄⠀⡠⠒⠲⣥⠟⢦⠀⢀⠇⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⡀⠈⠁⢀⠃⠀⠀⠂⠀⠉⠀⠀⠀⠁⠀⢀⠖⢱⠀⠀⠀⢸⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠈⠉⠒⠖⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣧⠠⠤⠚⡇⠀⠀⠨⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢡⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣀⣤⣴⡶⠶⠿⠟⠛⠛⠻⠿⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⠾⠛⠉⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣈⠙⠻⣶⣄
⠀⠀⠀⠀⠀⢀⣴⣾⡏⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠋⣽⣿⠁⠀⠀⠀⠀⠀⠀⠘⢁⡴⠀⣠⠂⠀⠈⢳⣄⠀⠘⠋⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡾⢠⣾⠙⡆⠀⠀⡏⢹⣧⡘⡀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⢀⡆⠀⠀⠸⣷⣿⣿⠀⡇⠀⠀⡇⢸⣿⣿⣷⠀⠀⠀⠀⠘⡇⢀⣠⡀
⠀⠀⠀⠀⠀⢸⣿⣇⠉⠀⠀⣼⡇⠀⢠⣾⠛⠟⠃⢀⡇⠀⠀⢇⠀⠛⠟⢻⠷⠀⠀⢀⠀⣿⡏⣠⢼⡆
⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⢸⢻⡇⠀⠀⠘⣧⠀⠀⣼⠃⠀⢸⡜⣦⡀⢀⡜⠀⠀⠀⣾⠀⢿⣷⣏⢸⠃
⠀⠀⠀⠀⣾⠋⢀⠙⢧⡀⠙⠛⠀⠀⠀⠳⣌⣙⠋⠁⠀⠀⠀⠹⣮⠙⢩⡴⠃⠀⠀⢻⠇⠸⣧⠉⡟⠀⠀⠀⢀⡤⠴
⠀⠀⠀⠀⢿⣠⡎⢳⡄⠀⠀⠀⢸⡇⠀⠰⠬⠉⠀⠐⠋⠀⠀⠀⠈⠳⣤⡘⠁⠀⠀⢸⡆⠀⢻⣷⠇⠀⠀⠀⠉⠠⠒⠋⣉⣉⡁
⠀⠀⠀⠀⠈⢿⡁⠸⣿⡄⠀⠀⣼⣿⠀⠀⠀⠀⡤⠀⠛⠛⠷⠶⣤⣀⠈⠙⢦⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⡴⠚⠉⠉⠉⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠙⢦⡈⠁⡀⠀⡆⡟⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈⠉⠐⢋⠀⠀⠀⠀⠀⢸⣿⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠸⣴⠇⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⣾⡏⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⢾⠃⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠸⡇⠀⠀⣼⡿⢁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣷⡀⠀⠀⠀⢸⣤⠞⠋⠉⠁⣤⣤⣤⠀⠉⠙⢶⣄⡇⢀⣾⡿⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠙⢿⣄⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣵⡿⠋⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠙⠷⣦⣄⣘⣦⣄⡀⠀⠀⠀⠀⠀⣀⣠⡾⠋⠁⠀⠀⠀⠀⠈⠳⢤⡤⡀⠀⠀⠀⠀⣠⠾⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠰⣿⠓⣄⠀⣉⠽⠛⢿⠿⢷⣶⣾⣿⣿⠋⠀⠀⠀⠀⠀⣠⠤⣄⣠⣎⡼⣿⠦⠤⠖⠋⠁⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡴⠛⠉⣀⡤⣶⢿⣦⣠⣴⣮⠀⡾⠛⣦⡀⠀⠀⣰⢧⡀⠈⠻⣏⢰⡏⠀⠀⠠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣾⣧⠀⠀⠀⠀⢫⡴⢾⠟⣿⠶⣌⠡⠞⠁⠘⡎⢷⡀⠀⣷⣄⢙⡏⠁⠈⠹⣷⡀⠀⠐⠚⠉
⠀⠀⠀⠀⠀⠀⢀⣴⣯⡤⠴⠾⠃⠀⠀⠀⠀⠈⢀⡿⠀⣷⠀⠀⠀⠀⠀⣠⣿⡇⣹⠶⢿⠆⢺⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⣠⣤⣤⣤⣶⡏⠀⣼⣿⡆⠀⠀⠀⠀⠈⢷⡾⠁⣠⠼⢷⡀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⢀⣠⠞⠁⠀⠀⠀⢺⣤⣴⣿⣿⣿⣀⣀⣀⣀⣀⣸⣇⠀⡏⠀⠀⠉⢠⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⣀⣄⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣻⣤⣤⣴⣾⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣏⣀⣠⣤⣤⣤⣤⣤⣄⠻⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣿⢿⣿⣿⡇⢹⣿⠁⠀⠀⠈⣿⡇⠀⢿⡿⣿⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠖⠚⠯⠤⠝⢻⡄⠸⡿⠀⠀⠀⠀⣿⡇⣠⠾⠤⠼⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣄⣉⣀⡤⠖⠲⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣤⣤⣀⠈⠿⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠸⠐⢠⢆⡠
⠀⠀⠀⠀⠀⠀⠀⡈⠂⠀⡠⠤⠦⢄⡀⠉⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⡜⠀⠀⠀⠀⢱⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠈⢁⠀⠱⡀⠀⠀⢀⡜⠀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⢡⠔⢂⡈⠉⠉⠉⠀⢄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢠⠃⠸⠄⠈⠀⠀⠀⠀⢠⠞⠉⠉⢢⠀⠀⠀⠠⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢦⠀⠀⠀⢃⡜⠛⠲⣄⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣲⡿⣗⡇⠀⢀⠞⠍⠳⢤⠈⢹⡆⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠣⡀⠉⠉⣏⢰⠄⠩⣈⡇⣸⠃⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠤⠬⣉⠁⠈⠓⠒⠒⢟⠲⠋⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⡁⠈⡆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢅⠈⠉⠉⠉⠉⠉⢉⣉⡏⠉⠙⢄⡀⠐⢀⡜⢱⠄⡇⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠲⠤⠝⠒⠒⠊⠉⠉⡁⠀⠈⢢⠀⠀⠉⢲⠎⠀⠀⡇⢱
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠬⠤⢄⣀⣀⣀⣁⣀⣀⣀⣀⠤⠧⠤⠔⠋⠀⠀⠀⠱⢌⣻⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠎⠀⠀⠉⠁⠈⠓⠒⠓⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⢲⡀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣵⡾⣿⣶⣄⢷⠀⣰⠇⣠⠞⠙⢦⡲⣄⠀⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠫⢎⡥⠖⢺⡽⡏⠁⢧⠀⠀⠀⠀⠀⢩⡄⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠈⢠⣞⣉⡤⣇⠀⠀⣶⠀⢤⣀⡀⠈⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢀⡟⠉⠈⢉⡁⠀⠀⠀⠀⣀⠈⠀⠀⠛⠻⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⡴⢿⠉⠀⠀⠀⠘⠋⠀⢀⡀⠈⠙⠀⠀⠀⣠⡴⠃
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⡞⠁⠈⠙⢲⡀⣦⠀⢀⡤⣤⡤⢤⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢸⠁⠀⠀⠀⠈⢳⡀⠀⠈⠓⠚⠓⠚⠁⠸⢆⡞⠀⠀⠀⡐⡆
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠙⢲⡤⣤⡄⠀⠀⠤⢶⠋⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠙⡾⠲⢤⣀⡤⢼⡁⠀⠀⠀⠀⠀⢈⡧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⡼⠁⠀⠀⢻⣀⣠⡽⣆⠀⠀⢀⡴⣫⣀⣀⡟⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡞⠁⠀⠀⠀⠈⠁⠀⠓⠮⣷⣤⡮⠴⠏⠀⠉⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⠉⠁⠀⣇⣀⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡏⠉⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠭⡓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠈⠈⢳⡀
⠀⣀⡤⠤⣤⣀⠀⠀⠀⠉⠓⠦⣄⠈⣇
⡞⠁⠒⠒⠂⠉⠓⢦⡀⠀⠀⠀⠈⢧⣿
⢧⡀⠀⠀⠀⣀⡀⠀⠙⣆⠀⠀⠀⠸⡏⠀⠀⠀⢀⣠⣀⣠⣤⣤⣀⡀
⠀⠉⠙⠋⠉⠉⠉⠙⠲⣌⣧⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⢠⡏⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠙⣆
⠀⠀⣠⢚⣛⠛⠒⠶⢤⡀⠀⠀⠀⠀⠀⢸⡇⣠⠴⠛⠉⠀⠈⠳⣤⣀⠀⠀⣹
⠀⠘⣇⠁⠀⢀⣤⠴⠦⢭⣷⡄⠀⠀⠀⣼⠛⠃⠀⠈⠓⠚⡁⠀⠀⢉⠛⢶⠏
⠀⠀⠈⠓⠛⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠹⣦⠀⠀⠀⠉⠉⠀⠀⠘⠬⢶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠶⠦⣄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣟⠻⢦⣀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠉⠁⠀⠉⠙⠛⠛⠛⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⡛⠶⠦⢤⣤⣀⡀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣾⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠉⣻⠋⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠘⣧⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀⡀⣠⡏⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⢸⠿⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⡿⣋⡴⠳⠦⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⣀⠀⠀⠀⠈⢷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⢀⣤⣄⣉⣙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢲⡏⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠓⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠉⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣴⣾⠛⠃⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢪⣾⣿⣿⡁⠀⡄⢉⠸⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⣿⣿⣧⠀⠁⡠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢿⣿⣿⡟⢀⣴⡅⠰⢐⠖⠁⣹⣖⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠑⢾⣻⣧⠀⡚⠚⠉⡽⢌⣁⣁⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠛⠟⠀⠈⠲⠊⠀⠀⠀⠉⠀⠀⠀⠀⠐⠒⠒⠒⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠋⠁⠀⠀⡄⠀⠀⠀⠀⠀⠘⠀⠀⢀⠀⠀⠀⠀⠆⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢩⠀⠀⠀⠀⠄⠀⢢⣄⠀⠀⠀⠈⠀⢰⠀⠀⠀⠀⡀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡄⠀⠀⠀⠀⠠⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠁⠠⠄⠀⠃⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⠀⠀⡀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡰⠁⠔⠚⠈⠈⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠧⣀⠀⢆⣀⡠⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠉⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠖⠒⠚⢱⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠹⠉⡗⠒⠂⠀⠀⠀⠀⠀⠀⠀⠤⣴⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⠃⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠄⡀⡌⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠚⠁⠘⠧⢔⡒⠠⠤⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠀⢠⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣁⠉⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠰⡚⣃⡭⠳⡤⠋⡆⢹⠀⠀⠒⡖⠆⠀⢀⡠⠊⠓⢄⡠⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⢐⡇⠑⢄⠀⠀⡇⠀⢣⠀⢀⠀⠀⢠⠁⠀⢥⠂⡄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⠁⠹⣯⡧⢠⠇⠀⢸⡆⠉⣀⠀⣸⡀⣀⠈⠘⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢒⠞⠀⠀⢀⣙⣞⣡⣴⠲⣻⠙⣯⣽⣼⢛⠋⣫⢀⣉⢠⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠹⠀⠀⠙⠛⠿⠿⠿⣯⠴⣷⣾⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⠿⠿⠿⠿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠍⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣀⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⠏⠀⠀⠀⠀⠈⣿⠇⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡄⢠⣿⣿⣿⣿⣿⡀⢸⣿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢋⣤⠀⡟⠀⠀⠀⠀⠀⠀⢻⠆⣤⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠞⣿⠁⣿⣿⣿⣿⣿⣿⣧⢸⡟⢶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢳⡄⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣆⢹⣿⣿⣿⣿⣿⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⣀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠿⠿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠛⠀⠀⠉⠉⠀⠀⠛⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⢛⠉⢡⣿⣿⣿⣶⣿⣿⣧⡍⠙⡛⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⡞⠉⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠉⢳⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢋⣴⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣷⣎⢻⣿⣿⣿⣿
⠀⠀⠀⠀⢸⠁⠀⠀⢸⣿⣿⣦⣀⣀⣀⣀⣤⣿⣿⡇⠀⠀⠀⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⢸⣿⣿⣿⠀⠀⠙⠿⠿⠿⠿⠟⠁⠀⢸⣿⣿⣿⡆⣿⣿⣿⣿
⠀⠀⠀⠀⢸⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿
⠀⠀⠀⠀⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡤⠀⡀⠐⡈⡉⠤⠄⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠭⢑⡑⠧⠘⢀⠞⠁⠀⢀⣤⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣁⣀⡀⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⢡⠔⠂⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⠔⠊⢉⡀⠀⢀⠠⠐⢈⡁⠄⠤⠤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢔⢞⡉⢠⠖⢁⠤⠊⠁⠠⠐⢀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠁⠀⢀⠷⢅⡐⠀⢸⡇⠴⠊⠙⠒⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠨⠑⠀⠀⠀⠁⠤⡴⠙⠂⠉⠉⠀⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠘⠀⡇⠀⠀⠀⡀⣈⠀⢀⣀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠠⡀⡃⠀⢀⡾⠉⠉⢀⠎⠀⠈⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡤⣾⡿⡀⠨⠃⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠰⠉⣴⠋⠀⠙⠢⠄⠊⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠈⠉⠈⠉⢀⡄⢀⠄⠀⠐⠒⠃⠀⠘⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆⢀⠄⠂⠉⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡘⢷⣤⣀⠌⠀⠀⠒⠂⢤⠆
⠀⠀⠀⠀⠀⠀⢠⠤⣀⡱⡆⠹⣉⠒⠠⠤⠄⣤⠜
⠀⠀⠀⠀⠀⠀⠎⢠⠏⢩⢧⡀⠘⠝⠁⣎⠉⢽⠋
⠀⠀⠀⠀⠀⣸⢦⣴⣀⠔⠋⠳⠄⢈⠀⠈⠁⠁
⠀⠀⠀⠀⣴⠉⢈⡾⠍⡲⡶⢶⣤⢷⣄
⠀⠀⢀⣤⣴⣿⣷⣷⣶⣿⣶⣚⣋⣅⡀⢙⣿⣿⣷⣶⣶⣤⣤
⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣦⣤⣤⣀⠛⠿⢿⣷⣤⡀⠀⠀⣿⡏⠀⣰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⣉⣉⣉⠉⠉⠛⠛⠿⢿⣶⣤⡈⠻⣷⡄⠀⣿⣧⣼⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⠿⠿⠿⠿⠿⠿⠿⣷⣶⣦⣄⡉⠻⣿⣦⣼⣿⣿⡿⠟⠛⠛⠿⢿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠉⠙⣿⣷⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣤⡀
⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠿⣿⡿⠛⠛⠻⢿⣷⣾⡿⠟⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣦⡀
⠀⠀⢰⣿⣋⣩⣽⣿⡿⠿⠃⠀⣠⣴⡿⠛⠉⢀⣴⣿⠟⠁⠀⠀⢀⣿⡿⠉⠀⠀⠀⠀⠀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⢀⣾⠟⠁⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⣤⡀⣤⣄⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⣶⠶⠾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⢹⣿⠃⠀⠀⠲⣮⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡿⠛⠛⠋⠀⠀⠀⢀⣴⣾⣷⠘⣿⣆⠀⠀⠀⠀⠈⠀⠀⣶⣶⣌⠻⣯⡙⢿⣿⣷⣄⠀⠀⠀⠙⠿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⢰⣟⣡⣾⠇⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠙⢷⣄⠻⣿⣿⣷⣄⠀⠀⠀⠀⠉⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠀⣼⣿⠃⢀⣠⣄⡀⠀⠀⠘⠻⠿⠋⠀⠀⠀⠀⠻⣿⣦⣄⣀⠀⠀⠀⠹⣿⣿⣦⠈⠻⣧⠈⠋⢹⣿⡆⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⣠⣤⡶⢾⣿⣿⡿⠁⢠⣿⡿⠀⠉⠉⠙⠿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣶⣄⠘⣿⣿⠃⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣾⣿⠃
⠀⠀⣾⣿⣁⣤⣾⡿⠋⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⡶⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣶⡀⠈⢹⣿⠀⠘⣿⡀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣸⣿⡏
⠀⠀⠻⠿⠿⠟⠋⠀⠀⠀⠀⣼⣿⠁⣀⣀⡀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⠀⠀⢹⣷⠀⠀⠀⠀⢸⣿⣧⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠻⣿⡿⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⡀⠀⠈⣿⡄⠀⠀⠀⢸⣿⣿⣀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢸⣿⣇⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⠀⠀⠀⠀⠀⠉⢫⣥⣄⡀⣹⣯⡀⠀⠀⢸⣿⣿⣿⠟⠋
⠀⠀⠀⠀⣠⣴⣾⣿⡿⠀⠀⠀⣿⣿⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣇⠀⠀⠈⣿⣿⠁
⠀⠀⣰⣿⣋⣰⣿⠟⠀⠀⠀⠀⠘⣿⣧⠀⣰⣿⠏⠀⠀⣀⣤⣶⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡹⣿⡄⠀⠀⢻⣿⡀
⠀⠀⠙⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⣏⣠⣶⡿⠟⠛⠉⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣿⣿⣆⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠟⠋⠁⠀⢴⣤⣤⣀⡀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡿⠛⣿⣦⠀⠀⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣄⠀⠀⠉⠙⠻⢷⣶⡄⠘⢿⠄⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠋⠀⠀⠈⢿⣧⠀⠀⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣤⣀⣀⠀⠈⠁⠀⠀⠀⠀⢀⣠⣤⣶⣿⠿⠛⠁⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣶⣶⣶⣿⣿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⡿⠋⢙⣻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣛⣻⠭⠡⢔⣭⡿⢉⣼⡧⣲⡀
⠀⠀⠀⠀⠀⠀⠀⣎⣴⣯⠉⠁⡀⣶⣶⠴⠀⢿⣿⣋⣻⣧⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣤⠙⠀⠀⣀⠀⠠⠐⣖⣺⣿⡄⠀⠐
⠀⠀⠀⠀⠀⢲⣮⣿⣿⣿⣿⠟⣀⡐⠮⢀⣤⣤⠀⠉⣿⣿⠕⡀⠀⠀⠀⠄
⠀⠀⠂⢠⡖⢩⠒⠚⡿⣿⣯⣤⣿⠱⣟⢿⡵⠖⠀⠐⠉⠸⠆⡃⠀⠁
⠀⠀⠀⢀⠉⡇⢀⠤⡆⠹⣷⠺⢿⣧⠀⠘⠓⠀⠀⣰⠂⢱⣖
⠀⠀⠀⠀⠘⢲⡧⢶⠃⠰⣿⡀⠀⣿⠁⢀⡖⢤⡀⠈⠀⡀⠹⢷⡄
⠀⠀⠀⠀⢀⡸⢧⡉⠲⡀⠈⢻⣦⣿⣿⣃⣤⡤⠍⠀⡰⠁⢸⠀⢷⠈⠲⠤⣀⡀
⠀⠀⠀⠀⠈⢑⡮⣻⣆⠘⢆⣀⡙⣧⡉⢠⠿⠂⠀⡠⠁⢠⡆⠀⢸⣇⡘⠀⠀⠉⠲⣄⡀
⠀⠀⠀⠀⠀⣾⡇⠈⢿⡄⠀⢰⢹⣿⠻⣦⣤⠤⠚⠁⠀⡾⡀⠀⢨⡥⡍⠂⠤⡄⠀⢈⣹⣦⡀
⠀⠀⠀⠀⢰⣿⡇⢀⡿⠀⠀⢠⠋⣇⠀⠹⣿⣦⡄⠀⣜⣡⡁⠀⢸⠛⠀⢀⠆⢠⠞⣉⢁⠀⠙⣆
⠀⠀⠀⢀⡿⡏⢧⣾⠁⠀⠀⡜⢀⠹⣧⡀⠘⣿⣿⣼⢀⢹⣷⡄⢸⠀⢀⠏⣰⣣⠊⢁⠎⠀⠀⣌⣆
⠀⠀⢀⡾⠁⢡⣾⠃⠀⠀⢠⢃⠘⡆⠈⢷⣇⣿⣿⡇⢸⣿⣿⡿⡞⢀⡞⢠⠓⠁⢠⠎⠀⠀⠀⣼⠸⡄
⠀⠀⣼⣤⣤⣿⠇⠀⠀⠀⡞⠈⣇⠸⡄⠈⠻⣿⣿⢡⠟⢿⡿⠀⠀⣼⠀⡞⢀⡴⢃⠀⠀⠀⢠⡏⠀⢷
⠀⢸⣇⣰⣿⡏⠀⠀⠀⢰⠁⣆⠹⡄⠹⣄⠀⢻⡏⣼⡇⣸⠃⠀⡇⡟⢀⡵⢋⡴⠁⠀⠀⠀⠉⠀⡾⠸⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⠋⠐⢢⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⠀⠘⠀⠉⢽⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠈⠀⠀⠊⠁⠀⠈⠁⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠒⠲⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠂⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⣄⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠠⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⡶⠄⠲⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠢⡀⠀⠀⠈⠃⠀⠀⢁⠀⣀⡀⠀⠀⠀⠆⠈⠙⠂⠀⠠⢼⡶⢄⡠⠂
⠀⢠⠖⠀⠀⠀⣀⣀⡠⢰⡬⡂⠘⠰⠀⠙⠀⠀⠀⠁⠀⠐⠀⢶⡋⠤
⠀⠘⡀⠀⠀⠌⣭⣿⣃⢸⡀⠁⠀⠀⠀⠀⢓⠀⡌⠀⠀⠀⢠⣼⠀⣦⡤⣶⠂⢄⣤
⢀⣠⣤⣤⣶⣷⣶⣾⣿⣿⣿⣦⣀⡀⢀⣀⣼⣿⣿⡄⠐⣢⠞⠻⠁⠀⣁⣀⣀⠉⠁⠃⠀⠀⢀⣄⣀
⠈⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣶⣶⣆⣼⣶⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠚⠋⠉⠉⠉⠛⠛⠒⠒⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠉⠛⠲⠦⠤⠤⠤⠴⠺⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢀⡏⢰⢷⢀⡤⠄⠀⠀⠀⠀⠀⠀⠤⢤⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢸⢁⡘⠛⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⣠⠖⠛⢲⡘⣿⡷⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⠁⠀⠀⠀⣷⡇⠀⣤⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠘⢦⣀⣀⠀⠉⠀⠐⢯⠇⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠈⣧⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⢀⡟⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⠦⣤⣀⣀⣀⣀⣀⣀⣤⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠦⣄⠀⠈⠹⡯⢭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠻⢤⣀⠀⠈⠙⠲⣄⣻⣼⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠈⢻⡓⠶⢦⣠⡽⢿⡀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢠⢳⡀⠀⠀⠀⢸⡇⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢠⡏⠀⢹⠀⠀⠀⠀⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠤⠤⠤⠤⠼⠤⠤⠾⠤⠤⠤⠴⠧⠤⠼⠿⠆

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀
⠀⠀⠀⠀⢠⠏⠓⡾⠁⠀⢹⡀⠀⠀⠀⡀⠀⠀⢀⡤⠶⠒⠲⣤⡀
⣠⣤⢠⣄⡾⠀⣰⡁⢸⣡⠀⣧⠀⢀⡴⠁⢀⡔⠁⠀⠀⠀⠀⠈⢷
⠷⢫⢩⣄⠀⠀⠀⠈⠳⡄⣔⣿⡆⢉⡤⠲⢾⢀⡀⠀⠀⠀⠀⠀⣸
⠀⠈⠁⠘⣆⢀⡴⠲⢤⡝⢮⠁⢹⡏⠀⠀⢨⡿⠟⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡀
⠀⠀⠀⠀⠈⠉⠀⠀⣀⣙⣭⡇⠈⠳⢤⡤⣾⠦⣄⣀⣀⣀⣴⣏⣀⣠⣤⡤⠤⠤⠤⠤⣤⣀⠀⠀⠀⠀⠀⡖⠲⢤⡀⡀⣄
⠀⠀⠀⠀⠀⠀⢰⠋⣭⣾⢭⠳⠀⡀⠀⠔⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢳⡀⣸⠳⠷⡏
⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣤⡄⠰⠵⠀⡠⢆⠀⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣏⣹⣿⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢀⠀⠙⠋⠀⣍⡆⠀⠀⠙⠲⢤⣀⠐⠠⠄⣄⢀⡀⣀⣠⠟⠀⠀⣠⢴⡁⠈⣯⡞⡫⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢨⣱⢀⠴⡀⢀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡖⠚⠒⢻⣹⠁⠀⠀⠀⠙⠀⣉⣽⣩⠧⡄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠶⡇⠀⠀⠈⠛⠁⠧⠇⠀⠀⠀⣀⣀⣀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣄⡷⠴⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡛⠤⣿⡀⠀⠀⠀⠀⢀⡤⠶⡎⠙⠍⠳⡄⠀⠀⢸⣄⠀⠀⠀⠀⢀⣀⡤⠔⠊⠁⣹⠲⢲⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣌⣐⠈⠉⠒⠒⠾⠭⠄⣀⣙⣦⣶⣚⣁⣀⠀⠈⣧⠿⠍⠉⠉⢧⠀⠀⣠⠞⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠙⠓⠶⢤⣀⣀⠀⠀⠀⠀⠀⠀⢠⠀⠙⣶⣿⠀⢤⡀⠀⣸⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠉⠉⠓⠲⠤⢤⣀⡾⠀⠀⠀⠘⠀⠀⠳⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣧⡠⠤⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢴⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠸⡄⠀⢸⡀⠀⠀⠀⢀⣀⣀⣀⣤⡤⢤⡖⣲⠋⠉⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠻⡀⠈⡏⠉⠉⠉⠉⠉⠀⠀⠀⠀⡜⢠⠇⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣎⠓⠀⢱⡀⠀⠀⠀⣀⣀⣀⣠⣎⣠⣋⣀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⢥⡄⣀⡜⠁⠀⠀⠀⠀⠊⠉⣿⣉⣉⡥⠤⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣶⣶⡒⠒⠒⠚⠹⣏⠉⠉⠉⠉⢉⡩⠕⠛⠧⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡽⠛⠛⠻⣝⢦⣀⣀⡼⡆⠀⠀⠀⡯⣀⣀⣠⠴⣒⡿⠿⢍⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢼⣒⣛⣛⣩⠬⠭⠖⠊⠁⠀⠀⠀⠑⠲⠤⣉⣉⡓⠒⠶⠤⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⣤⣤⠶⠶⠶⠛⠛⠛⠛⠛⠛⠷⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢻⣧⣤⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠙⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣰⠋⠉⠛⠓⠶⠶⠦⣤⣤⣬⣙⣛⣛⣛⣛⣂⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⡏⠀⠀⢀⠀⢤⣄⣈⠙⠯⡷⠀⠿⠀⣖⣲⠶⠆⠀⠀⠀⠀⠀⠀⠀⢠⡏⢹⡰⠃⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⣴⠟⠉⢻⠁⠀⠀⠈⣭⣭⣭⣿⡿⠶⠀⠀⠀⠀⠠⢴⣶⣶⣿⡿⢿⣯⣥⠀⠀⣸⠀⠀⣧⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⣿⣀⣘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠄⠀⠀⣏⠀⠀⣿⠀⡰⢚⠋⠻
⠀⠀⠀⠀⠀⠀⠈⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⠶⠛⠚⠙⠏⠀⣠
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡿⠟⢿⣄⣠⣄⢀⣼⠗⠒⣲⠟⠻⢯⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠓⠒⠛⠋⠁⠀⠀⠀⠀⠉⠛⠛⠿⠶⠶⠚⠉⠀⠀⠀⠈⠙⠳⢦⣄⡀
⠀⠀⠀⣀⡀⠀⠀⢀⣸⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⡦
⢀⡤⣤⣯⠹⠶⠞⠋⠁⢘⣇⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡼⠓⢦⡀⠀⢀⣀
⣹⡶⠄⠀⠀⠀⣀⣤⠶⠛⢻⣆⣀⣤⡴⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⡼⣧⡀⠀⠉⠲⠋⢽⠦
⠛⢲⡾⢃⡶⠛⠉⠀⠀⠀⠀⠉⠉⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠳⣤⠾⠁⠀⠙⠳⢤⡀⠀⠀⠴
⠀⠈⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠘⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⡶⠤⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⢀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣠⣀⣀⣈⣉⣉⣉⣉⡉⠉⠙⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢰⡏⠈⠉⠉⠉⠉⠉⠙⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠉⠉⠉⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠚⠋⠉⢹⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣾⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠰⠆⢠⠄⠠⠄⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡒⠀⠀⢇⠀⠄⡌⡀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢁⠉⠀⢀⠏⢀⡀⠊⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢨⡤⠀⠸⠀⠀⢱⠰⠆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠤⠄⠤⠈⠀⠀⠘⢄⠀⢻⠃⠒⠠⠤⠤⠤⠤⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⡖⠀⠨⠀⠀⠉⠛⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠠⠀⢀⠂⠀⠀⠀⠀⠀⡨⠒⠤⢀⠀⠀⠀⢀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡦⠀⠀⢀⠤⠖⠀⠰⠀⠠⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠋⠀⠀⠀⡀⠈⢑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠘⡄⣤⣴⠂⡞⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠜⡴⠁⢀⢿⡟⠈⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⡜⠈⢈⠱⠀⠐⡖⠀⣀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠰⠂⠀⣌⠅⠀⠀⠀⠀⠁⠓⡈⠀⠸⠁⠉⣈⠠⡃
⠀⠀⠀⠐⢚⠁⠈⠃⠀⠠⠆⠀⢠⠀⠸⠀⠀⠀⠂⠉⠁⠀⠁
⠀⠀⠀⠀⠠⠀⠀⠀⢠⠀⢀⣐⠆⠀⡆⠀⠀⠘⢠
⠀⠀⠀⠀⠀⠀⢰⠀⡎⠀⠈⠉⢢⠤⠦⡜⠀⡧⠆
⠀⠀⠀⠀⠀⠁⠏⠆⠀⠀⠁⠀⠘⠀⠀⠉⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⠋⠙⠁⠀⢀⡤⠁⠈⠙⠿⠛⡲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣁⡤⠖⠂⠀⠀⠙⠒⠀⠀⠀⠰⠬⠭⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⣻⣿⣁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⣠⣹⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⢡⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣾⣼⣷⣿⣿⣿⢿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡧⠋⠀⠀⠚⠀⠀⠀⠀⠀⠘⠀⠀⣴⢠⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢋⣾⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣋⣽⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⠿⠟⣻⠟⢫⣽⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢠⡏⢽⡿⡏⠉⢀⡖⢼⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣿⣿⣿⣿⣿⠑⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⡀⢰⣿⣤⣿⢰⠁⠀⠘⠃⣿⣿⣸⣿⣿⣿⣿⣿⠴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣹⣿⠇⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⠋⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣼⣿⣿⣸⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣤⢻⣿⣿⣿⣿⣿⣿⡿⢿⣿⣇⣀⡀⠀⠀⠀⠀⣼⡿⢟⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠐⣹⣿⣿⣿⣷⡟⣿⣿⣿⣶⣾⣿⡷⠿⠟⣋⣁⣀⠀⠀⢠⣭⣽⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠂⢉⢿⣿⣿⣿⣷⣿⡿⣿⣿⣿⠛⠔⠖⢀⣘⠡⠏⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡂⠐⠒⡀⠙⢧⡤⠨⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠐⠐⢺⣿⣿⣿⣿⡽⣿⣿⣇⣻⣿⣯⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠻⠟⠛⡛⠛⠿⠿⠿⠿⠶⠮⠉⠉⡁⠡⢬⣅⣤⣾⣿⣿⡿⣯⢿⢽⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣻⣾⣿⣿⣿⣿⠦⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠲⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⣀⡴⠛⠉⡠⠒⢁⡞⣠⡴⠶⠛⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢧⠞⠁⠀⣠⠊⠀⣀⠾⠋⠁⢀⣀⣀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⡼⢁⣀⣴⣯⣤⡴⠛⠉⠉⠉⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⡄⠀⣀⡤⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⢠⡎⠈⠑⠦⡀⠀⠀⢰⣦⣟⠀⢸⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⡠⠚⠁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠛⠀⢀⡾⠁⢈⡷⠋⠀⠀⠀⢠⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠛⠓⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⣤⠒⠒⣲⠄⠀⠀⣼⡀⢀⡜⠁⠀⠀⠀⠀⠻⢋⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀⢻⠀⠀⠀⠠⣔⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠹⠴⠛⠁⠀⠀⠀⡿⠌⢸⡇⠀⠀⠀⠀⣠⠞⠋⠉⠉⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡁⠀⠘⣇⠀⠀⠀⠈⠛⠦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠞⠹⡇⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⡆⠀⠀⣴⠉⠀⠙⣆⠀⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡤⢿⠀⠀⠀⢿⣤⡤⠶⠶⠶⠟⢋⡇⠀⠀⠀⡄⠀⠀⢹⡙⠛⢻⠏⠀⢸⡍⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠘⢇⠀⠀⠘⢧⡀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢳⡄⠀⠀⠉⠈⠁⠀⠀⢸⣇⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠷⣤⣘⡄⠀⠀⠀⠙⠛⠚⠛⠁⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⠶⠺⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣤⣴⠾⠋⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⣰⣿⣿⣷⣭⣿⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢠⣇⡘⠻⣿⣿⡏⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⢰⠋⢙⡷⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠁⠉⠙⠻⠿⠀⠀⠀⢠⡾⠋⠀⠀⠀⢠⡞⠙⠓⢾⠁⢀⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⣛⡭⠿⠿⢷⣶⡦⠤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢸⡆⠂⢴⡿⠤⡎⣀⡾⠁
⠀⠀⠀⣠⠶⠚⠛⠛⠉⢁⡴⠚⠁⠀⠀⠀⠀⠸⣤⣤⣬⠿⣤⣀⠀⠀⠀⠀⢀⣠⡴⣏⠀⠀⠀⠀⠀⠀⠀⢀⡽⠀⢀⡀⠠⠘⠁
⠀⠀⣾⠁⡀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠈⡼⠉⠛⠛⠛⠛⠋⣹⣦⢘⣷⠀⠀⠀⠀⢀⣤⠞⣡⡴⠋
⠀⠀⠉⢶⠁⢀⡀⢀⣀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⡇⠀⢀⠀⠀⠀⠀⠌⢿⠟⠙⠻⢶⣶⣾⡯⠶⠚⠁
⠀⠀⠀⠈⠛⣿⡀⣸⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢠⠀⠀⣹⠗⢐⣶⠀⡄⢸⡇
⠀⠀⠀⠀⠀⠈⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣘⠀⠙⠃⠀⠾⠏⢀⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⣦⠀⠀⠀⠀⠀⢀⣿⣤⣀⣀⠈⠛⠛⠶⠶⠶⠶⠖⠀⢸⡇
⠀⠀⠀⠀⠀⢀⣼⠏⡰⠃⢸⣇⠀⠀⠀⠀⢸⡗⠀⠉⠉⠙⠛⠓⠶⠤⣤⣄⣀⣀⣼⠁
⠀⠀⠀⠀⣠⡿⢡⠞⣀⣴⣏⣹⡄⠀⢀⣴⠞⢻⣇⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⣹⠏
⠀⠀⢀⣾⠋⡴⠃⠰⣿⡟⢿⡀⢻⣄⣼⣿⣄⠀⢙⡷⣴⣆⡀⠀⠀⠈⠙⠛⣺⡧
⠀⣰⠟⣡⠞⢦⢀⣴⠋⠀⠈⢷⣀⣩⡼⠋⠙⠛⠉⠀⠀⠈⠙⠳⠶⣤⡶⠿⣿⣟⡳⠶⣤⡀
⣼⣋⣴⣁⣠⡾⠟⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠆⢀⡿
⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣥⣼⣿⣶⣶⢦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠧⣄⣀⣀⣙⠉⠁⠀⠀⡔⠋⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⣶⣦⣭⣤⣭⣉⣉⣛⡓⠶⠶⡤⢿⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣙⣛⣛⣿⣷⣿⣇⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⣐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⣿⣿⣿⡿⠟⠿⣿⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡸⣿⣿⣿⣿⢱⣿⣿⡞⣡⢨⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠌⡛⠿⣿⣿⣿⣿⣿⡿⠟⣫⣴⣿⡇⣿⣿⣿⣿⢸⣿⣿⢻⣿⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⣉⢸⣿⣷⣶⣶⣤⣤⡰⢶⣿⣿⣿⡿⢰⣿⣿⣿⣿⢸⣿⣿⢸⣿⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⣶⢰⣿⡆⣿⣿⣿⣿⣿⣿⣿⣶⡆⢠⣬⣄⢻⣿⣿⣿⣿⢸⣿⣿⠸⣿⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⣿⣮⣭⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⠟⣵⣾⡿⢿⣷⣌⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠈⠉⢡⣿⣿⣿⢸⣿⠣⣶⣶⢹⣿⡆⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⡘⢿⣷⣭⣥⣾⡿⢡⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢸⣿⣿⣿⣿⣦⣝⣛⣛⣩⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠟⠋⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣦⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡀⢶⣿⣿⣿⣿⣿⣿⣷⡆⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⠟⣫⣾⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⢿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⢠⣾⣿⠋⠀⣀⣀⣀⣀⣠⣤⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣷⣦⣤⣀⣀⣀⣀⣀⠀⠙⣿⣷⡄
⠀⠀⠀⣰⣿⡟⠁⠀⠘⠛⠿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠃⠀⠈⢻⣿⣆
⠀⠀⣼⣿⠟⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠻⣿⣧
⠀⣰⣿⡟⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⢻⣿⣆
⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣛⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣛⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠰⠿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⡆⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠟⠛⠛⠉⠉⠉⠉⠛⠛⠻⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏
⠀⠀⢻⣿⣦⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣴⣿⡟
⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠋⣁⣀⣤⣤⣀⣈⠙⠻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣼⣿⠏
⠀⠀⠀⠀⠘⢿⣿⣄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⣶⡿⠿⠛⠛⠛⠛⠿⣿⣶⣼⣿⣿⣿⣿⣿⠃⠀⠀⠀⣠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠘⠻⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⡿⠟⠁⠀⢀⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡔⢆
⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⡇⣿⠇⠐⠒⠒⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⢀⡀⠀⠾⢿⣿⣿⣿⣿⣿⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢻⣿⣿⣿⣿⣰⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⠿⠛⠈⠻⣷⣔⣄⠀⠀⠀⠀⠀⠀⣠⣴⣶⣄⠀⠀⣤⠋⢀⣼⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠦⣄⠀⠀⠀⠀⣿⣿⣿⣿⡇⠈⠁⠐⠋⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣌⡂⢰⣤⣠⣿⣿⣿⣿⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣹⣿⣿⣿⣧⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣒⠈⠙⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⡿⣋⣽⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠛⠛⠛⠛⠛⠋⢉⣼⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⠿⠿⠿⠿⠿⠿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⣀⣤⣶⡿⠿⠟⠛⠁⠀⠀⠀⠀⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⢀⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⣠⣿⠏⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⠆⠀⣾⣿⣥⣤⡄⠀⠐⢒⡶⠂⠀⠀⠀⠀⠀⠘⢿⣧⡀
⠀⠀⣰⣿⠋⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⡄⠀⠀⠀⠀⠀⠀⠀⠰⢿⢤⠄⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⢠⣿⠇⠀⠀⠀⢼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡿⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣤⣤⣤⣄⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⠋⠉⠉⢛⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟
⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⠿⠟⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⢶⣄
⠀⠀⠀⠀⠀⠀⣾⣻⣭⣥⠴⠶⣦⣹⣦⣄
⠀⠀⠀⠀⠀⢰⡿⢃⡀⠠⠤⠶⠾⣿⠇⣹⡀
⠀⠀⠀⠀⠀⣸⠃⢏⣀⠀⠤⠤⣤⣾⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠶⠒⠒⠒⠒⠀⠀⣀⡤
⠀⠀⠀⠀⠀⣿⠀⠈⠁⠐⣦⣤⡤⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠁⠀⠀⠐⠦⣤⣤⣤⠶⠟⠉
⠀⠀⠀⠀⠀⡿⠀⠀⠀⠈⠙⣧⣴⢟⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⣷⠀⣶⠀⠀⠀⢸⣧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⣿⠀⠛⠶⠶⠶⢋⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⡴⢒⡦⠖⣻⠓⠆
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠙⠻⡻⣌⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣿⣤⣘⣵⣋⡉⠉
⠀⠀⠀⠀⠀⠀⢻⡀⢢⡀⠀⠀⠙⣦⠙⣧⡀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠈⠉⠛⢿⣟⢷⣄⠐⢶⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢷⡀⠀⠀⠈⠃⠈⢷⣄⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠹⣆⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢷⠀⠀⠀⠀⠀⠀⠙⢷⣄⣾⠃⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⣧⣄⠈⠻⣦⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣸⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠉⠛⠦⣌⠙⠻⠷⢶⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⢠⡿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⢸⠀⢠⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣷⠸⣄⠀⣿⣿⢧⣀⣀⡀⠀⠀⠀⠀⠀⣿⡀⣿⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⢸⡇⣸⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢹⡎⠒⠀⢹⡄⠑⠚⠒⠊⠀⠀⠀⠀⠀⣿⣿⢯⠐⠦⣤⣤⣤⣴⠾⠋⠀⡠⣞⠄⠀⢸⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠸⣧⡀⠀⠀⠀⠀⠀⢠⣤⠾⠃⢹⡄⠀⠀⠀⠀⠀⠀⢄⠀⡼⡼⠁⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠈⠛⠷⠶⢶⣤⡤⠤⠄⠀⠀⠸⠃⢰⡄⠀⠀⠀⠉⠢⣭⣥⣷⠄⠀⢀⣾⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⣾⠋⠀⠙⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠙⠦⣤⣤⠤⠀⠈⠁⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⠶⠟⠋⠀⠀⠀⠀⠀⠉⠛⠛⠿⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄⡀⣀⣠⣴⠾⠛⠛⠋⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀⣠⣤⡴⠶⠶⠶⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠞⠋⠉⠀⢀⣠⡄⠀⠀⠀⠠⣌⡙⠷⣄
⠀⠀⠀⠀⠀⠀⠠⢾⣿⠁⠀⠀⠀⠀⠿⢋⠀⡠⠀⢠⡀⠘⠷⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⢰⢃⣞⢣⠀⢰⢻⣦⣂⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠆⠀⢰⠄⠀⣸⣿⡏⢸⠀⢸⠘⣿⣿⣄⠀⠀⠸⣦⠔⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢠⢿⠀⠈⢳⡀⠀⡞⠀⢾⣆⠀⢰⠋⠀⢰⠀⣿⣞⣽
⠀⠀⠀⠀⠀⠀⡞⠡⡙⠦⠘⠋⠀⠈⠣⣭⠉⢀⡀⠈⢧⡉⠵⡋⠀⢸⠃⢹⣍⡇⠀⠀⡤⠖⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢻⡿⢹⣆⠀⠀⣿⠀⠉⠁⡀⢨⣤⣄⣀⠙⠲⣄⠀⠘⠃⠘⣿⠁⠀⠀⢀⡩⠴⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⣀⢰⣿⠀⠀⣰⠃⠀⠀⠀⠈⠙⠒⢚⠀⠀⠀⠀⣿⠀⢀⡴⠋⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠘⠛⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣸⡏⣰⠋⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⣧⡴⠖⢒⣒⣀⠒⠲⢤⣸⠀⣴⡟⢰⠃⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠹⣧⡀⠘⢁⠀⠀⠀⠀⠀⠀⠀⢀⣬⠾⠋⠀⢸⡀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣠⣝⡓⠲⣿⣦⣤⣤⣤⣤⡶⠋⠀⠀⠀⢀⡀⢉⢾⣤⣀⣀⠴⠋⣡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡜⡴⠓⣋⡤⣾⣧⢭⣽⣍⡗⢦⠀⠀⡰⣇⢙⢿⣁⡏⠀⠠⠔⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣿⠆⠀⠀⠸⢞⡟⣿⠓⠄⠋⠀⣯⡳⣄⣷⢈⠏⠀⠈⢳⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠉⠁⢀⣀⣀⣠⡞⢁⣿⠀⠀⠀⠐⢿⡵⢉⡹⣌⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠠⣇⡀⣀⡴⠋⠀⠀⢸⣤⣾⣿⣧⣥⣤⣄⣸⡇⢾⠀⠈⢡⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢠⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⣤⡶⠶⠶⣶⡌⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢿⣙⢿⡃⢻⡇⠀⠀⣿⠁⣼⣋⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠭⠤⠖⠒⠚⠃⠀⠀⠀⠀⠈⠈⠷⠤⠤⣈⡓⠂⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠰⠂⠀⠀⠀⠀⠀⠀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⢒⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣶⢰⠀⠀⠀⢰⠀⠀⢠⠐⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⢀⠐⣀⡸⠁⠀⠀⡘⠃⠀⠀⠀⣀⠀⠀⠈⠷⠀⠀⢠⢸⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡉⠀⠆⠀⠀⢸⣀⢁⠁⠀⠀⠀⠁⠄⠀⠀⠀⡽⡇⠀⠀⢠⠀⠀⠀⠸⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠝⢆⡇⠀⠀⢸⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⢎⡵⠋⠀⠀⠀⠀⢀⠞⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠈⠃⢈⠀⠀⠀⠸⠀⡄⠀⠀⠀⠀⠀⠀⠀⡸⠔⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠈⠄⠀⠀⠀⢄⠻⠀⠀⠀⠀⠴⠀⠀⠀⢆⡀⠀⠀⠀⠀⣀⠀⢠⡄⠀⠀⠀⠀⠀⠇⡇⠀⠀⠀⡇⠀⣷⡀
⠀⠀⠰⠘⡀⠀⠀⡸⠅⠘⠀⠀⠀⠈⣧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢀⣴⡧⠧⡖⠴⠆⠀⠀⢰⡇⠀⠀⠀⢤⠁⣸⣅⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠤⣀⡀⣠⠀⢀⡄⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡬⣿⠀⠀⠀⢸⡉⠋
⠀⠀⠀⠀⡱⢿⣿⠷⣴⠮⡇⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡝⣿⡗⠀⠀⠈⡏
⠀⠀⠀⠀⠀⠀⡉⠲⣈⣱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣿⡇⠀⠀⠀⡇⠀⠀⠀⢀⣀⠤
⠀⠀⠀⠀⠀⠀⢈⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢤⠐⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠁⠄⠀⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠔⢩⠘⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⢱⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⢧⠀⠀⠀⡐⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⣇⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⡁⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠤⠟⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠣⠌⠀⢤⢙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠐⣉⠁⠄⠀⠀⠀⠀⠀⠀⠀⠠⠰⠗⣼⣧⡀⠊⠀⢀⡒⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣇⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠙⢫⡋⠛⠃⠀⡤⠈⠁⡗⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠓⢀⠀⠀⠀⠷⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠤⠤⠈⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⡄⠠⢦⠀⠀⠈⠈⢹⡄⠀⠀⠀⠀⠀⠀⠀⣴⣄⢆⠀⠀⠀⠢⠀⠰⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡄⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⢣⠐⡇⠀⠀⣀⡀⠀⢀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⢢⢰⠀⠖⠀⢸⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠁⡨⠐⠂⠀⠀⠩⢣⣄⠈⣷⡘⢧⠀⠀⠀⠀⠀⠘⢧⡤⠌⠰⢷⣄⠠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡌⠀⠀⠀⠄⠀⠀⠈⠉⠷⣬⣷⣈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡂⢀⠄⠀⢿⣳⣴⠀⠀⠈⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠠⢊⠤⠀⠻⢿⠞⠄⠀⠀⠒⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⠶⠛⠛⣷⣦⣶⣿⣷⣶⣶⡶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⢠⡶⣿⣁⠀⢻⣿⡿⠿⠿⢿⣿⣿⣿⣞⣶⣶⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⢀⢠⣿⣿⣯⠁⣠⣿⠛⢿⣶⣶⣦⠌⠙⢦⠉⠘⠿⣧⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠛⠁⠀⣠⡴⠃⠈⠳⠤⢈⣴⣞⡛⣷⠀⠀⣬⣿⣿⠏⠐⠄⠀⠀⠂⢿⡆⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⣁⣀⣠⣴⡶⠛⠉⠀⠀⣸⠃⠀⡟⠋⢛⣱⡏⠀⠀⠘⣿⠛⡳⠀⠀⡗⢦⠀⠁⠘⣦⣤⡹⣮⡧
⠀⠀⠀⠀⠀⠀⠘⣏⠀⠀⢺⡟⠛⠉⠀⣼⣀⣀⣠⡾⢶⣿⠲⠴⢿⣿⣿⣿⠃⠀⠀⠀⢸⣿⡓⠀⠀⠘⠛⠀⠀⢾⣏⢻⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣦⠴⠞⢳⡀⠀⠈⢻⣝⡛⠁⠀⠀⠉⠀⠀⠈⠁⣿⡟⠀⠀⠀⠀⢸⡇⠙⠢⠀⠀⠀⠀⠀⠀⠉⠹⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⣳⡄⠀⠀⣿⠁⠀⣴⣻⠄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⠛⠛⢧⡀⣾⣟⠀⠀⠙⠉⠀⠀⠀⠀⠀⠙⢷⣤⣤⣤⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠙⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⢿⣦⠉⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠁⣠⠞⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠘⢧⠀⠀⠈⠙⠷⢦⣄⠀⠀⣠⣤⣤⠶⠶⠛⠛⠋⠁⠀⣠⡞⠉⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⣠⢾⡉⢧⣰⠏⠹⣆⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⡀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣸⠛⢷⣿⣮⣿⣤⠖⣛⣷⡄⢀⣴⠟⠁⠀⠀⠀⠀⠀⢿⡀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⢸⠁⣸⠟⠋⠁⠘⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⣧⢀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠙⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡞⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣛⣭⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⣇⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠾⠟⣋⢹⣧⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣸⢹⡇⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠁⣷⠀⠀⢻⡄⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⣤⣶⠾⣿⠀⠀⠸⡇⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣦⣄⣀⠀⠀⠀⣿⣵⠏⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⢉⣿⣋⡾⠀⢹⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣴⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⡿⠛⢹⡇⠀⢸⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⢈⣷⡀⣸⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⡿⢿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠘⠉⠉⡏⠀⠀⣀⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡏⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⣿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠖⠋⠉⠐⠛⠋⠀⠙⠛⠛⠻⢶⣤⣄

⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢂⣠⣴⣾⣷⣾⣷⣿⣿⣿⣿⣿⣿⠿⢷⣶⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⣠⣶⣿⣟⣯⣿⣿⠟⣿⣿⣯⣀⠘⠻⠿⢦⣌⡙⠿⣦⡈⠻⣿⡟⠻⣶⣦⣄⡀
⠀⠀⠀⠀⠁⠀⠐⠁⢠⣾⡿⣫⣾⣿⢿⣿⣧⣤⣤⣭⣭⣭⣭⣝⣒⣒⠮⢭⣓⠦⣍⡲⢌⠻⢦⠙⢿⡏⢻
⠀⠀⠀⠀⠀⠈⠀⣰⠟⣩⣾⣿⣿⡃⢀⣉⣭⠤⠶⡒⠒⠒⠀⠀⢒⣈⡉⠑⠚⠭⣲⢝⡲⣕⢤⡑⢌⠻⡄
⠀⠀⠀⠀⠀⠀⠐⠁⣴⣿⣿⠻⠿⠟⣋⡥⣖⠯⣓⠠⠨⠅⣀⡭⠤⣤⣊⠉⠒⠤⡈⢑⢯⡪⣷⣝⢮⠳⡘
⠀⠀⠀⠀⠀⠀⠀⣸⢹⣿⣿⣤⡴⢞⡥⣾⢗⠍⠀⣐⠶⠋⠉⠉⠛⠛⠳⢖⡤⡀⠀⠀⠑⢌⢪⡪⡳⡱⡝
⠀⠀⠀⠀⡄⠀⢠⡇⡜⡏⠛⠋⣠⢞⢞⢝⢕⠕⡩⡢⢕⣠⠭⠭⠥⠴⢦⣔⣤⣄⠀⠀⠀⠀⠑⡑⡙⡝⡜
⠀⠀⠀⠀⡇⠀⢸⠀⠀⣷⣤⡾⢡⢎⣾⢣⢫⢊⢎⡔⢩⡶⠋⣩⡬⠭⢵⣾⣝⢿⣷⡄⠀⠀⠀⠘⡄⠘⡜
⠀⠀⠀⠀⡇⠀⢸⠀⠰⡘⠋⢀⡞⣸⣹⡎⡎⣾⢸⣇⠘⢷⡀⢻⡇⢠⣶⠮⣟⣷⣝⣿⡆⠀⠀⠀⠘⡀⠱
⠀⠠⠀⠀⢃⠀⠸⡇⢢⡻⣦⣾⠃⣿⢸⢷⢳⡹⣦⣉⡛⠦⡙⣄⢷⢸⡇⢀⣈⡻⣿⠻⡇⠀⠀⠀⠀⠁
⡇⠀⡀⠀⠘⡀⠀⣷⣾⣷⣌⡁⢠⣿⠘⣆⠳⡙⠦⣭⡉⢳⡽⡸⣾⢾⡇⣾⠟⠻⡜⠄⣷⠀⠀⠀⠀⠐
⡰⡀⠰⠀⠀⠐⠈⢿⣯⡻⣿⣟⡛⠛⠀⣿⡆⠹⣦⠈⣿⢸⢃⢧⢿⢸⢠⠇⣠⣤⡙⠀⢸⠀⠀⠀⢀
⢣⢣⠠⠣⠀⠀⠀⠀⠙⢿⣮⣝⡿⢟⣚⣋⣡⠴⢋⡴⡣⢫⢎⢎⠎⢃⠏⡼⠛⠙⡇⡀⣸⠀⠀⡀⠐
⢣⣳⡳⡱⡑⠀⠀⠀⢄⠀⢉⡛⠙⠻⠒⠒⠒⠩⠕⠪⣒⠕⠃⠀⡠⣫⠞⣠⣴⣆⣧⢆⡏⠀⠀⠁
⢳⡳⡝⣝⢎⢦⡢⠀⢐⠵⡢⢌⣑⠒⠤⠤⣤⣤⠶⣙⠢⣀⢤⣪⢞⡥⠞⠉⢹⣿⣿⡼⠁⠀⡌
⢧⡙⢌⢮⡳⣕⢯⡢⣄⠉⠚⠥⣊⡉⠛⠒⠒⠘⣐⠦⣽⡾⠿⣚⣩⣴⣶⣷⣾⣿⡿⢁⡔⡘
⡄⠳⣌⠳⣍⠢⣑⠮⣓⠭⣒⡤⢄⣂⣉⠀⠄⠤⠤⠴⠒⣚⣋⣉⣀⢀⣿⣿⣿⢏⣤⢞⠝
⢿⣤⣿⣧⡈⢳⣌⠓⢬⣙⠲⢭⣑⡒⠮⠭⢭⣍⣉⣉⣉⠉⢙⣿⣿⣿⡿⣻⣵⣿⡿⠃⠀⠀⢀⠄
⠀⠉⠛⠻⠷⣤⣿⣿⣆⠙⣿⣦⣌⠙⢻⣶⣦⠀⣩⣿⣿⣷⣿⣿⣿⣽⣿⣿⠟⣪⠂⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠾⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠛⠩⠠⠕⠉⠀⠠⠞⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣾⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠇⢀⣬⣙⣿⣇⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⢋⣶⠘⢿⣿⣿⣿⢰⡏⠀⠈⠙⠏⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⣿⡏⣠⡀⣼⣿⡇⠀⠙⢿⡇⠸⣇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠈⢰⣿⡇⣈⡉⠀⠀⠀⠀⠛⠦⣌⣳⣦⡀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠉⠁⠀⠀⣤⠀⠀⠠⡦⠉⠁⣿⣆⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣸⢣⡿⡇⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⣰⠿⠛⢀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣷⣄⠀⠲⠿⠿⣷⣦⠀⠀⢀⣴⡿⣶⣿⡟⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣿⣷⣤⣄⣀⣀⣀⣤⣶⣿⣿⣿⣿⠋⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⣯⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠾⠷⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣹⣿⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⠒⠢⠤⡀
⠀⠀⠀⠀⡠⠐⠂⠉⠀⢀⠤⢀⠁⠢⡀⠈⠉⠓⠁⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⡌⠀⠉⠭⠁⠤⠐⡊⡡⢔⠱⡈⢢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⡀⠀⠀⣀⣠⠤⠒⢤⡀⢳⠊⢲⡀
⠀⠀⠠⢀⠒⠒⠒⠒⠀⠈⠇⠀⠄⢆⠑⢬⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡏⠈⡉⠉⠤⠄⠒⠀⠆⡿⢉⡆⠈⠉⡆
⠀⠀⠀⠦⠀⠂⠀⠀⠀⠒⠀⠄⠁⠀⠩⣬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⡎⠀⠀⠀⣀⡤⠤⠀⡌⢰⠋⠀⣏⠁
⠀⠀⠀⠸⠙⠛⠀⠀⠘⠛⠚⠀⡄⢠⠒⡣⠰⢑⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⡞⠇⢀⠀⢁⠤⣀⠁⡜⠉⠉⠁
⠀⠀⠀⠈⠢⡀⢀⡠⠀⠀⠀⠀⡠⠃⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠑⣄⡀⡔⣁⡠⠜⡋⠒⠤⡀
⠀⠀⠀⠀⠀⠈⠁⠀⠒⢰⣛⠅⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠀⠈⡱⢿⠒⠊⠁⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠌⡀⠁⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⠁⡰⠁⠸⡆⠀⢸⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⠀⠘⡀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢲⠀⢹⡄⢸⠀⠀⠀⠀⡞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⠻⡌⢲⠒⡦⠰⠃⢧⡀
⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⢰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⢾⠀⡀⠀⡀⠼⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠨⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⠀⢿⣁⡠⠆⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠤⠄⠂⠁

⠀⠀⠀⢰⠋⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢱
⠀⢠⠒⢺⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡗⠒
⠀⢼⠀⠸⡇⠀⢸⠀⠀⠀⠀⠀⢀⣠⢤⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡤⢤⢄⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⡶
⣤⢸⡀⠀⡇⠀⠸⣒⡒⢒⣒⣒⣇⢠⡠⠀⢗⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠀⠂⡤⢠⡁⠀⠀⠀⢈⡇⠀⢸⡇⠀⡇
⠛⠀⡇⠀⡇⠀⠀⠁⠀⠀⠀⠀⠙⣆⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⣴⠋⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⡇
⠀⠒⡇⠀⡇⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⣀⡤⢤⣤⡄⠀⢀⢤⡖⠲⠤⣀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠘⡇⠀⠉
⠀⠀⠣⠤⡇⠀⠀⡇⠀⠀⠀⠀⠀⢸⡴⠋⠀⠀⠘⠉⠀⠈⢑⠈⠉⠀⠀⠈⠳⣼⠃⠀⠀⠀⠀⠀⠀⡇⠀⠈⠓⠒
⠀⠀⠀⠀⠣⠄⠤⠃⠀⠀⠀⠀⠀⡸⣇⠀⠀⠀⠀⠀⣀⠀⠎⣤⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⠀⠓⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠈⠀⠀⠀⡄⠘⠛⠀⡆⠉⠁⢀⠃⠀⠀⠈⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠂⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⠀⡠⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡀⠀⠀⠀⠑⠠⣀⡀⠀⠀⠀⡀⡀⠐⠀⠀⠀⠀⠀⡀⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠂⠀⠀⠀⠀⠀⠀⠖⠂⠀⠃⠠⠃⠀⠔⠀⠀⠀⠀⠀⠀⠼⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⣀⡉⠦⠀⠀⠀⠐⠤⠀⠀⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⣀⢀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⡤⡀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠑⠒⠒⠒⠉⣿⠀⢹⡏⠉⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⠀⢸⣇⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⢂⠀⢀⡹⠂⢎⡀⠈⡐⠉⠈⠲⡀

⠀⠀⠀⠀⢈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢁
⠀⠀⠀⢤⣌⣠⣤⣉⣳⢤⣀⡀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠁⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠁⠀⠁⣀⣀⣀
⠄⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣷⣦⣤⣀⣀⣀⣀⣀⣀⣠⣤⣴⣿⠿⠟⠀⠀⠚⠻⢷⣦⣄⡀⣀⠀⠱⣦⣤⣄⣀⠀⣀⣠⣴⡿⢻⣿⠿⣿⢿⣿⣿⣿
⣤⣀⠀⠒⠂⠀⠀⠀⠐⠶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠐⢒⣢⣤⣦⣤⣤⣭⣽⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣾⣿⣵⣿⠿⢻⣌⡱⣶
⣿⣿⣿⣷⣶⣶⣶⣤⣤⣴⣶⣿⣿⣿⣿⡿⠿⠛⠛⠁⠀⠀⠀⣀⣀⣹⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⡼⠻⣧⣉⢳⣤
⠈⠉⠉⠛⠛⠻⢿⣿⣷⣤⣤⣭⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠉⠁⠄⠛⠛⠉⠉⠻⠛⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⣷⣌⠻⣧⣄
⠀⠀⠀⠀⠀⠂⣀⣀⣈⡉⠛⠛⠿⠿⢿⣿⣷⣶⣶⣦⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠋⢉⣉⠁⠤⠤
⣦⡔⠛⠓⣦⣤⣯⣭⣭⣤⡤⢶⣶⣆⣀⣭⣭⣥⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠉⡀⠀⠠⢤⠄⠒⠒⠢⢤⣭⡉⠒⠲
⠛⠛⠒⠛⠿⠣⠤⠤⠬⣴⣶⣮⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠉⠉⠉⢁⣀⡀⠀⠐⠒⠒⠀⠉⢉⣁⣀⠐⠲⢤⣈⣉⠒⠶⢶⣬⣿⣷
⠛⠓⠲⠶⠶⠦⠤⢄⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⡀⠀⠠⠤⠶⠶⠶⠒⠀⠉⠉⠉⢁⣀⣀⠠⠤⠶⠂⣈⣉⡀⠒⠆⣈⣉⣱⣶⣶⡿⣿⣷⣾⣿⣿⣿
⠤⠶⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠤⠤⠤⠤⠤⠀⠒⠛⠋⣉⣀⡀⠤⠤⠄⣘⡃⠤⢤⣄⣿⣷⣾⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⢀⣀⣀⣀⣀⣤⠤⠤⠖⠒⢛⣉⣠⡤⠤⢒⡒⠢⣬⣽⣶⣿⣿⣿⣿⣭⣒⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠉⠉⠉⣉⣉⣡⣤⣤⠖⠒⠒⠋⣉⣡⣤⡔⣲⣮⣽⣿⣿⣿⣿⣿⣿⣟⣻⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⠶⠶⠶⠶⠛⠉⠉⠉⠀⢀⣤⣤⠶⠖⢊⣩⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣴⠶⠶⠛⠛⣉⣠⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠛⠛⠉⠁⣀⣠⡤⠖⣛⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠻⠿⣿⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣴⠶⠾⠟⠛⠋⠉⠁⢀⣀⣤⣤⠞⠛⢉⣡⣴⣾⣿⣿⣿⣟⠿⣭⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡀⣠⣤⡴⠶⠏⠉⠁⣠⣤⣶⣿⣿⣿⣿⣿⣿⣷⠻⢧⡝⢷⣹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⠶⠶⠾⠟⠛⠉⠀⠀⢀⣤⠶⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣤⠶⢛⣫⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⡴⠾⠛⢛⣩⡴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢛⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣤⣴⠶⠛⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣶⡘⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣩⣤⣴⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠛⠛⠛⠛⠛⠛⣤⡿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⡿⠿⣿⣿⣿⡿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣛⠛⠛⠛⠿⠿⠿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⡀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠷⠶⠿⠿⠿⣿⡿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡛⢻⣿⣷⣦⣀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿⠿⢿⣭⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⣥⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠿⢿⠟⣉⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢡⡦⠀⢉⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠖⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣴⠛⢳⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠙⠶⠃⠀⠘⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠶⠦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡆⠀⠀⣇⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣇⠀⠀⠀⢸⡇⠀⠀⡿⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠐⣦⡀⣳⢄⣀⠼⠉⣲⣤⣤⣴⣋⡷⠤⠤⠾⢽⣶⣴⠋⠒⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⣀⣀⠀⠀⠀⢸⠉⠉⢰⡤⠒⠉⢠⡄⠀⠀⠀⡂⠀⠀⣤⠀⠀⠈⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠸⣁⠺⢧⡀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠠⠃⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⠉⠉⢹⠒⠋⠀⠀⠀⠢⠐⠤⠀⠀⠤⠒⠀⠀⠒⠠⠤⠄⢂⡠⠊⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣠⠄⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠸⠥⣤⠽⠶⠃⠀⠀⠀⠀⠀⣠⠞⠁⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⠓⠦⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠋⠁⣦⣀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣠⡾⠋⣇⠀⠀⢀⣴⣧⣀⡤⠖⢉⣀⡀⢈⣉⣩⢭⣭⣍⡙⢅⣠⣀⣀⣠⣤⠞⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠉⠛⠉⠁⠀⡾⢡⡞⣉⠔⠋⠉⠀⠀⣀⡬⠗⠛⠂⢹⡌⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠉⠀⣀⣠⠴⠒⠉⠙⠢⣤⣀⣀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⠃⠀⠀⠀⠀⠀⠀⢿⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣶⠶⢶⡶⠶⠶⣶⠶⠶⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠒⣾⠁⠀⠀⠘⣶⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡇⠀⠀⠀⠀⠘⣇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⣡⡼⠀⠀⠀⠀⠀⠀⠸⣄⣹⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠉⠉⠉⠁⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢞⠁⠀⠀⠀⠀⢀⡀⢤⡀⠀⠀⠈⠂⠠⢄⠀⠀⠀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠄⠀⠐⠖⢋⠉⠈⠑⠂⠀⠀⠀⠀⠑⣶⠋⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢒⢶⠦⢸⡀⢸⠀⠀⠀⠀⠀⠀⠟⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣋⢀⡠⡄⠀⡄⠸⡀⢀⣤⠄⠒⠊⡐⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠈⠁⠘⠊⠀⠀⠉⠐⠊⠂⠀⢠⡇⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⣠⠀⠀⠀⠀⠀⠀⡈⠁⠒⠁⠀⠀⠁⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠤⡄⠘⢄⠀⠨⠭⠹⠦⠤⠃⠠⠁⠀⠐⠀⠀⡄⠘⠤⠤⠌⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠡⣴⣃⠓⢄⠀⠑⠤⡀⠀⠢⢂⡔⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⢠⠄⠠⢤⠤⠤⠤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣉⠔⠂⠀⠀⠀⠈⠁⠈⡟⣇
⠀⠀⠀⠀⠀⠘⠤⡀⡶⢗⠒⠒⠒⠚⣧⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢂⢂⠀⢀⡠⠄⢒⣟⠼⠋⠀⠀⢸⠀⠤⠬⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⠨⣓⠊⡉⠑⢬⡑⠄⡀⠀⠀⠀⠀⠀⠀⠈⠂⠒⠀⢇⢠⡁⠀⣔⠖⠒⠤⠄⠀⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⢑⠠⣀⣷⡮⣑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠁⠀⡈⠀⠀⠀⠀⠀⡠⠔⠀⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢘⠢⣝⡣⢌⠓⢌⠂⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠣⣀⠀⠀⠀⠀⠱⠂⠀⠀⣌⣚⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠆⠇⠈⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⡌⠁⠉⢓⠀⠀⠀⠀⠑⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⢱⠜⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⡇⠀⠀⠀⠀⠀⠀⢀⠔⠁⡀⢴⣿⣆⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠁⠀⠀⠀⠀⢀⠔⠡⠒⠀⠀⠀⠫⡈⢂⠀⠀⠀⠤⢸⣌⠙⠑⡆⠀⠲⢀⡠⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠄⠣⡀⠀⠀⠀⠀⠙⢌⠢⠔⠉⢉⡏⠩⠷⠺⠟⠟⠓⠦⠤⠤⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⡛⠂⠄⡀⠀⠰⡺⣀⡇⠀⠀⠀⠀⠀⠀⠡⠌⠀⠈⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄⢴⠈⡞⠳⣤⡋⢛⡖⢷⡯⢀⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠄⠠⠤⠸⠷⢃⠖⠐⠀⠀⠀⠈⠓⢧⣁⣉⠛⣟
⠀⠀⠀⠀⠀⠀⡠⠴⠶⠀⠙⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢢
⠀⠀⡠⠖⠒⠲⠦⠴⠶⠤⠧⠤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⢀⡅⠠⣤⣄⡁
⠀⠀⠉⠉⠁⠀⠐⠒⠒⠂⠀⠠⠤⠤⠄⠱⠬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣑⣄⡀⠀⠘⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠠


⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⣹⠳⡀
⠀⠀⠀⠀⠀⢀⡞⠁⡟⠀⢠⠃⠀⡇
⠀⠀⠀⠀⠀⡼⠀⢸⠃⠀⡎⠀⠀⠃
⠀⠀⠀⠀⢰⠇⠀⡟⠀⢰⠃⢀⢰
⠀⠀⠀⠀⣸⠀⢰⡇⠀⡾⠀⣾⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢦⠤⣀
⠀⠘⠀⠠⡿⠀⣸⠀⢀⡇⢠⡿⠧⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡸⠀⢸
⠀⠀⠀⠀⡇⠀⡿⠀⢸⠁⢸⣿⠃⠐⠂⠀⠨⢍⠋⣰⠀⠠⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢠⡇⠀⣸⠑⣆
⠀⠀⠀⠀⡇⠀⡟⠀⢸⠀⢸⢋⠀⠀⠀⠀⠀⢐⠀⠀⠀⠉⠐⠚⠀⠬⢐⡂⠀⠄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠜⡤⠀⡼⠀⢠⡇⠀⡏
⠀⠀⠀⠀⡇⠀⡇⠀⣾⠀⠀⠆⠀⠀⠀⠀⠀⠸⡄⠀⠀⠤⣤⡉⣿⠆⠀⠀⠀⠁⠒⠇⡀⡐⠀⠄⠀⠀⡜⣼⠇⢰⠃⠀⡾⠀⢰⠃
⠀⠀⠀⠀⢃⠀⡇⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⢄⡉⠈⠛⠑⠀⠈⠑⡄⠀⠀⢀⡴⠀⠀⠈⠑⠂⠨⣙⡟⢀⠏⠀⣸⠃⢀⡟
⠀⠀⠀⠀⠈⠉⢧⠀⢧⢠⠃⠀⠀⠀⠀⠀⠠⡀⠀⠀⠙⢄⠀⠀⠀⠀⠠⣼⡤⠔⠋⠀⠀⠀⠀⠀⢀⢱⡿⢀⡞⠀⢰⠏⠀⡼⢀
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠙⢶⠢⢲⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠞⠁⡜⠀⢠⠏⠀⡼⠁⠂⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠖⠉⠉⣽⣦⣄⣀⣠⣴⣄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡼⠁⢠⠏⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠻⠿⣿⣿⠿⡇⠑⣄⠀⠀⡀⠈⠀⡎⠀⡜⠀⣠⠋⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡿⣿⣦⣤⣀⣀⣴⡇⠀⠈⡠⠊⠀⠀⠀⣇⠎⢀⡴⢇⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡈⠙⠻⠿⢻⠏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠙⠷⠶⠞⠁⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠁⠀⠀⠀⠀⠀⠁⠀⠐⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⣠⠴⠒⠲⣄⠙⡄⠀⠀⣠⠖⠛⠋⢉⣉⣍⣈⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⣠⠶⠶⢶⣇⡜⠀⢰⠇⠀⢀⣼⠫⠤⣤⡈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⠑⠒⠠⠔⠛⠁⠀⣾⠀⠰⣏⠙⠦⠄⠚⣁⣤⠴⠚⠊⠐⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢒⣦⡤⠀⠀⠀⠀⠀⣿⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⢹⡃⠀⠀⣠⠞⠋⠉⠉⠛⠷⣦⡀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠈⠙⠓⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⢸⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠹⡀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⣾⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣠⠶⠶⠤⢧⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡏⢸
⠀⠀⠀⠀⠀⠀⠀⣠⣸⠇⣿⣠⠶⠶⣾⡉⣧⠀⠀⣀⣤⣿⣄⣀⠀⠀⠀⢸⠇⢸⡇⢠⠔⣒⡶⠶⢶⣖⠒⠲⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⢰⠉⠟⠀⣿⠈⠓⠒⠋⠃⡿⠀⢰⡏⠀⠹⣷⣌⣷⣀⣰⠟⠀⢸⡇⢸⡼⡁⠀⢀⡤⠈⠑⢦⠀⠀⠀⢉⣷⡤⣀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡆⠀⠀⠀⡰⠇⠀⣾⠀⠀⠀⠀⢹⡟⠋⠁⠀⠀⡼⠀⠈⢷⣿⡾⠟⠀⠀⠀⠈⡇⠀⡴⠋⣽⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢷⣿⠀⠀⣷⠀⠀⠀⢷⣄⣴⠏⠀⠀⠀⠀⢸⡇⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠘⢷⠾⠃⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠘⡄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢀⡀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⢾⠋⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠘⣄⡀⢀⣀⣀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⣍⣉⠭⠟⠉⠉⠉⠓⢢⣄⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢸⡿⠀⠀⢀⡴⠏⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⣤⣤⣀⡀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⣯⠴⠚⠁⠀⢠⡾⠋⠉⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠈⠉⠓⣾⣏⠀⠀⠀⠀⠀⠀⠀⠘⢤⡤⠶⠚⠉⣿⠀⠀⠀⢠⠟⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣨⠷⣶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡞⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡞⠁⣀⣈⡇⠈⡇⠀⠀⢀⡴⠶⣤⡀⠀⢸⡆⠀⠀⡇⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⢀⡾⠃⢸⠀⢸⡏⠙⢶⡄⢩⠀⢀⠟⣠⣤⣌⣷⠀⢸⡇⠀⠀⡇⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⢠⡾⠁⠀⢸⠀⢸⠛⠛⠛⠁⡆⠀⢸⠛⠧⠍⠿⠛⠻⢾⠷⠶⠾⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⠟⠀⠀⠀⢸⠀⢸⡆⠀⠀⢠⠃⠀⣿⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣧⠀⠀⠸⢦⣤⡇⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠈⣧⠀⠸⣆⣀⣀⣀⣀⣤⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠈⢻⡄⠀⠀⠸⡆⠀⠈⠉⠉⡩⠟⠁⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠹⣆⡠⠖⠉⠀⠀⠀⣠⠟⠁⢀⣄⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⠀⠀⠀⣀⣀⣽⢦⡖⠋⠉⠳⢦⣤⣤⣤⠞⠁⣠⠔⠋⠉⠛⢶⣄⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠉⠁⠀⠀⠙⠲⣄⡀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠛⠶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢚⠏⣀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠙⠚⢁⠔⢁⠞⣉⠤⢤⡁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⡜⠀⢀⠤⠚⠂⠉⠉⠀⠀⠀⠘⢦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⠀⠆⢠⠟⢡⠞⠁⢠⣤⡄⠀⠀⠀⠀⠀⠀⠈⣇⠀⠐⠠⠘
⠀⠀⠀⠐⠡⠒⠀⣼⢰⠁⠀⠀⡨⠕⠤⡀⠀⠀⠀⠀⠚⠂⢸⡀⠀⠢⠌
⠀⠀⠀⠀⠀⠀⠀⢹⠙⡄⠀⣜⢀⣀⣀⢽⠀⠀⠀⠰⠥⣽⠄⡧⢤
⠀⠀⠀⠀⠀⠀⠀⢈⣇⠱⠀⠘⢄⣀⡠⠎⠀⠀⢇⠀⠀⠀⠀⡧⠞
⠀⠀⠀⠀⠀⠀⠰⡏⠉⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡀⠀⠀⠀⠀⠐⠦⣄⡤⠋⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣠⣶⣤⡀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠰⠭⢿⣿⠁⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡤⢀⡀
⠀⠀⠀⣀⣀⠤⣒⠶⠶⢦⠤⢷⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠈⢳⡀
⠀⡔⠉⠀⠀⢸⠁⠀⠀⠈⢉⡏⠙⠲⠶⠖⢺⣱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠈⢧⡄⡴⠊⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡏⢷⣄⡀⠀⠀⠀⠀⢀⡖⠄⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠉⢠⣄⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⡇⠀⠑⢭⠒⠒⠢⡤⣞⣈⣂⡀⢀⣀⣀⡠⠔⠊⠀⠀⢀
⠀⠀⢀⡴⡃⢈⣆⠀⠀⣻⠉⠉⠒⠒⠦⠤⣤⠇⠀⠀⢠⠤⠓⢎⣳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷
⠀⣠⢞⠈⢴⠿⡙⣦⣿⡉⡳⢤⣀⠀⠐⣲⣏⠀⠀⠀⠘⠂⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁
⣴⣃⣉⠶⠃⠀⠙⠒⠁⠈⠀⠀⠀⠉⠉⠉⢛⡍⣳
⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣴⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣃⣠⡍⠁⠠⢌⡑⣦
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣿⣿⣶⣾⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣠⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢦⡀⠀⠀⠀⠀⠀⠀⠈⡋⠀⠀⠀⠀⠀⠀⣴⣴⠀⠀⠀⠀⢠⣤⣄
⠀⠀⣠⣿⣿⣄⣄⣼⣿⣧⡄⠀⠀⠀⣰⠛⢻⣷⣶⣾⡇⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⡏⠁
⠀⠀⠀⠿⣿⠁⠀⢸⡿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠉⠉⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠚⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣶⣄⣀⣀⣰⣶⠀⠀⠀⠀⡷⠶⠶⠶⠶⠶⡇⠀⠀⠀⠀⠀⠀⢠⣥⡄⠀⠀⠀⠀⠀⢰⣿⣿⡆
⠀⠀⣤⡄⠿⠏⢉⣯⡹⠿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⢀⣹⣏⣀⣀⣀⣀⣀⣀
⠀⠀⣿⡟⠛⠛⠻⣿⠅⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠈⢹⡏⠉⠉⠉⠉⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠘⢷⠂⠀⠀⢠⡾⠏⠀⠀⠀⠀⣀⠀⣴⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⣀⠄⢀⠤⣀⢰⣄
⠀⠀⣤⣾⣶⣶⣶⠾⢧⡀⠀⠀⠀⠈⣿⠀⠉⠉⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⣈⡀⠀⠀⠀⠀⠀⢈⡁
⠀⠀⢿⣯⣼⣿⣿⣄⣠⠇⠀⠀⠀⠸⠿⠸⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⡇⠀⠀⠙⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠙⠋
⠀⠀⠀⠉⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⢠⣄⢀⣤⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣠⣤⣤⣤⣤⣿⣇⠀⠀⠀⠀⣿⣿⣤⣄⣾⣿⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣄⠀⠀⠀⠀⠙⢻⠉⢹⣿⡍⠉⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣄⣅⣸⣿⠀⠀⠀⠀⠀⢸⠀⢸⣿⡇⠀⡇
⠀⠀⢶⣶⣶⡶⡶⣶⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣍⠀⠀⠀⠀⠀⠼⠄⠨⠿⠄⠤⠧

⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣠⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣀⣠⣾⣿⣿⣷⣤⣾⣿⣿⣷⣄⠀⣠⣾⣿⣿⣤⣴⣆
⠀⠀⢀⣤⠶⢾⣿⣿⡟⠛⠒⢦⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⣰⠟⣡⡴⠾⠿⠿⠿⠶⣤⡀⠙⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢀⡏⣰⠃⠀⠀⠀⠀⠀⠀⠀⠻⡄⢸⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⢹⣿⣿⣿⡄
⠈⣧⠙⢦⣴⢦⡴⢦⣴⢶⡞⢾⠇⣸⠇⠀⠀⢠⣿⣿⠀⡄⣄⠀⠀⠉⢉⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣷⠗⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠰⢿⡉⠛⢶⡄
⠀⠘⢷⣼⡷⠞⠷⠞⢳⡞⠛⢻⣶⠋⠀⠀⠀⢸⣿⡇⠀⠿⠋⠀⠀⠀⠸⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠙⠶⡴⠇
⠀⠀⠀⢈⡙⣷⠶⠴⣏⠉⠻⠏⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠰⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⡀⢹⣿⣿⡀
⠀⠀⢠⣿⡇⠹⢦⡀⠈⡷⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⠛⠶⡄⢰⠶⠀⠰⠟⠋⠀⠀⠀⠀⠀⠀⠘⣷⠇⠈⣿⣿⣇⡀
⠀⠀⠀⠉⠀⠀⢀⣹⣆⣀⣠⣤⣧⡀⠀⢀⡤⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠀⠹⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⣧⢰⡏⠀⠀⡗⠀⠀⠀⠀⠙⠲⣶⣤⡀⠀⠀⠀⠀⠰⠾⣿⣭⣥⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠘⣧⣤⣤⠤⠴⠖⢿⡀⠳⣄⣀⡇⠀⡄⢠⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠈⣧⠴⠟⠁⠀⠠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠈⣧⠀⠈⠙⡇⠀⠛⠋⠀⠀⠀⠀⠠⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠘⣧⣙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠹⣆⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⢹⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠙⢦⣀⣿⠀⢠⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣸
⠀⠀⠀⠀⢀⣠⣴⠖⠀⠀⠻⣆⠀⠀⠀⠀⠀⠉⠹⣆⠈⠛⠀⠀⠰⠞⢦⣠⠴⢦⣤⠶⠶⠴⠟⠓⠛⠛⠂⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠰⣏⣴⠏⠀⠀⠀⠀⠘⢦⡀⠀⢺⣴⣦⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠁⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠠⣄⡤⠀⠀⠀⠀⠀⠀⠀⠘⠛⢀⣠⠾⠋⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣄⣀⠀⠀⠀⠙⠓⠶⢤⣤⣉⣀⣀⣀⣀⣀⣀⣤⡴⠶⠛⠉⠀⠀⠀⠀⠘⢧⠀⠀⠀⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠙⠳⣦⡀⠀⠀⠀⣿⣤⢼⣿⣿⣭⣉⢈⡇⠀⠀⠀⠀⠀⠐⣦⣤⠀⠘⣧⠀⠀⠀⠻⣌⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠘⣿⣿⡏⠈⠉⠁⠀⠀⠀⠀⢰⡀⠈⠁⠀⠀⢸⡆⠀⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢰⣿⣿⣷⠀⠀⣄⢀⡀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣸⣿⣿⣿⡄⠀⠙⠞⠻⣤⡖⠀⢸⣇⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢈⣿⡀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⡦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⡇⢻⠖⠛⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣇⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠆⢸⡷⠶⠶⠒⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣟⣠⡄⠀⠀⠀⢸⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡷⡴⠶⠶⠋⢹⣿⣷⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣧⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⠃⢈⣿⣿⣿⣿⣿⣿⡟⠉⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣴⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠟⠋⠁⠀⠸⣿⣿⣿⣿⣿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⠟⠻⠧⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠊⢉⢀⠀⠐⠒⣘⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠞⡵⣇⣴⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠆⠀⠀⢀⣀⠀⢲⢋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣽⣇⡆⠀⠀⠀⢣⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣆⠀⢠⠀⠉⠉⡤⢾⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⣿⣿⡃⠀⠀⠀⠀⣽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢫⣿⡅⠈⠀⠀⠀⡁⠦⣸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⢀⣀⠤⠠⠄⠀⠀⠀⡀⠀⠠⣼⡏⠸⠙⢫⠀⠀⠀⠀⠔⠁⢀⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠿⠀⠀⠀⠀⡤⠤⢒⡉⠀⠈⠉⠛⠘⣀⠠⢤⡀⠁⠂⠄⠈⠙⣇⢀⠈⠀⠀⠀⠰⢸⡄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠀⠀⠀⠀⠊⢀⠀⢊⠐⠶⢀⣾⠧⠚⠉⠀⠂⠙⢀⡁⠠⠀⠐⠀⠰⠀⠀⢀⠀⠂⠀⠈⡓⠴⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠢⢀⡸⠣⠀⣩⡗⣶⢴⠀⢀⣤⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⣠⣴⣿⣶⣤⠈⣀⣫⣿⣶⠆⢈⣼⣿⣮⣽⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠐⢇⠀⠀⠀⢀⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣿⣿⠿⡛⣋⣽⣿⣿⣐⡀⠻⣿⣿⣿⠛⣿⠿⣿⣷⣄⣆⠀⠀⠀⠀⠈⢳⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣶⡿⢋⣠⣿⡿⣿⣿⣿⣿⣿⣿⣶⣌⣹⣿⣿⣿⣷⡿⣸⣿⡏⠀⠀⠀⠀⠀⢸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣟⣼⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣾⠟⡋⠀⠀⠀⢀⠀⠰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣼⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣯⣴⠃⠀⠀⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡄⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⢰⠃⢈⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡆⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢃⣿⣿⣿⠵⡀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⡿⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣻⡿⢷⣾⠃⠊⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡇⢶⠀⠘⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⣲⣾⣿⡿⢀⣿⠇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠁⠀⠀⠓⠀⣤⠀⠀⢽⣛⢿⣶⣿⣿⣟⠛⣋⠀⠈⠀⠈⠁⠉⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠢⠀⠀⠈⢀⣴⠋⠀⠀⠀⠙⢆⣙⣿⣿⣽⠶⠇⠀⠀⠀⠀⠀⠀⠀⢴⡦⠀⠰⡆⠢⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⣤⡵⠇⠀⠀⠀⠀⠘⣿⣿⠟⢁⣷⠜⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⢬⣿⡄⠐⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣿⡃⠉⠀⠁⠀⠀⠀⠀⣠⠄⠆⠀⠠⠠⠌⢸⣿⠟⠈⠀⢨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⢨⣦⡄⠀⠀⠀⠀⠀⠀⣤⠀⠀⢸⣿⡧⠄⠀⣠⢦⣤⢶⠘⠈⢲⡄⠀⠀⠒⠃⠈⠛⠀⢀⢀⣬⡿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢱⡀⠀⠀⠀⠀⠀⠀⢀⣔⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⣀⣀⠀⢀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠔⡿⠋⠐⠁⠖⠂⠒⠀⠀⠀⠴⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢰⠋⠀⡠⠖⡛⣤⠊⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⠀⠀⣀⡽⠻⣶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢠⠀⠀⠀⠀⠀⢶⡤⠤⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣠⠤⠶⣄⠀⠀⠀⠀⠀⠀⢀⣀⡸⠋⠀⣤⣖⣺⠟⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢿⠛⠋⠉⠁⠀⣠⣀⠈⠻⠶⢤⣤⡔⠛⣯⠙⣧⣤⡟⢯⡩⣄⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣻⠖⠂⠳⣤⣄⡴⠋⠙⠙⢦⡀⠀⠀⢹⣧⠀⣹⢾⣟⡟⢳⣼⢧⠀⠉⢳⡀⠀⠀⡷⡀⠀⠀⠀⢀⡴⣤⠴⣄
⠀⠀⠀⠀⠀⠀⠘⢷⣟⣤⡞⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⣾⢻⠀⠛⢠⡷⡇⠈⣿⡼⣶⣄⠀⠳⡀⠀⠑⠃⢀⣠⣶⠏⢰⣱⣋⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣼⠃⢠⢀⣦⡆⢸⠇⢰⡏⣧⢸⡿⣦⡚⠛⠓⠒⠒⠋⢹⣙⣷⢀⣝⣓⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⣤⠾⢯⠻⡅⠀⣾⠟⣿⣧⠎⠀⣼⠃⣿⠛⡇⠘⣧⡀⠀⢀⣀⣤⠼⠋
⠀⠀⢀⡀⠀⢀⣀⣠⡤⠞⠉⣿⠀⠀⠻⣏⠀⠀⠀⠑⠈⣰⢿⣀⡼⠋⢀⣼⣡⡾⠃⠀⡇⠀⠈⠉⠋⠉
⠀⠀⠸⣍⠛⢻⡍⢻⣿⣀⡰⠛⣧⠀⠀⠙⣦⡀⠀⣠⡾⣧⢶⣶⣶⣛⣿⣿⡿⢶⣤⣶⣛⣀
⠀⠀⠀⠈⠙⠻⠟⠋⢉⡟⠀⠀⠘⣆⠀⠀⠈⣛⢾⡯⠚⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠈⡿⠘⠞⠉⠁⠀⠀⢀⠴⠿⠿⠚⠛⠛⠛⠛⠛⢲⣾⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣀⣀⣸⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠋⠉⢨⢟⢟⠟⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⣀⣠⡭⠭⠴⠖⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⡶⡿⢟⣛⣻⣟⣛⡻⠿⣿⣷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣟⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⣽⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢅⣈⣢⡀⢿⣿⣿⣿⣿⣿⠟⠋⠉⠁⣀⡈⠛⠛⠙⠋⠉⠉⠉⠻⣿⣿⣿⠀⠀⢠⢊⡀⠅
⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡀⠀⢺⣿⣿⣿⡿⠁⢀⠀⠀⠾⠛⠋⠀⠀⠀⠀⠀⠀⣠⣄⠹⣿⣿⠀⠀⠀⢠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠀⠀⠘⣿⣿⣿⠁⠀⠀⣱⠖⠋⠑⢢⡀⠀⠀⠀⠀⠀⣀⣈⠀⢿⣿⠀⠀⠀⠀⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⡇⣀⣀⣀⡠⡷⠀⠀⠀⠀⠾⠤⣬⡗⢸⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⣿⣿⠀⠀⠀⢫⡉⠁⠈⡠⠃⠀⠀⠀⠀⠈⠒⠊⠀⢸⣇⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠛⠛⠃⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣄⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣠⠗⠀⠀⠀⠀⣼⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⣰⣿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⢹⡄⠀⠀⠀⢀⣾⣷⣻⡄⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⣏⡻⣿⣿⠁⠀⠀⣠⠎⠀⠀⣰⡋⡳⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡆⠀⠀⠀⠀⠉⠋⠀⣠⠞⠁⠀⠀⢸⠁⣨⣇⡐⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣲⠟⠛⠧⢭⡽⢤⣀⠀⠀⢀⣠⢾⡁⠀⠀⠀⠀⢸⠆⣈⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡼⠁⠀⠀⠀⣼⠁⠀⠉⠉⠹⠩⠰⣮⢷⣄⣀⣠⣖⡡⠞⠁
⣞⣒⡖⠦⠤⢤⣀⣀⠀⢀⠶⠋⠀⠳⡄⠀⠀⢰⠇⠀⠀⠀⠀⠀⠇⠀⡇⠀⠈⠉⠉⠁
⠀⠈⠉⠉⠒⠒⠤⠤⢬⡏⠀⠀⠀⣠⠵⣤⣠⣟⡀⠀⠀⠀⢀⣤⣴⣤⣷⣤⣴⡶⠶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⢺⠤⣧⣽⠒⠒⢤⡬⣉⣟⡑⠋⢩⣟⣹⣩⡟⠉⠉⠙⢦⡶⠟⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡞⡁⢡⣴⡹⣆⠀⣴⠚⢧⡀⠀⠉⠲⣼⣍⣉⡿⠃⠀⠀⠀⢸⣧⣄⣹⡇
⠀⠀⠀⠀⠀⠀⡴⢋⠎⠀⡽⠋⢣⡘⢚⡿⢦⠴⠛⠓⠦⣤⣈⣻⣿⣷⣦⣀⣄⣤⣟⠀⢩⣿⠃
⠀⠀⠀⠀⠀⣾⣕⣁⡼⠋⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡟⢿⣷⣦⣽⣷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣴⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⣉⡙⠛⠉⢉⠝⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠲⠶⠶⠤⣭⣭⣰⣚⡧
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣠⢀⣆⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠀⠀⠀⠀⠀⠀⠀⣰⣀⣀⣀⣀⣀⣶⡀
⠀⠀⠀⠀⠀⠙⠶⣾⣷⡶⠞⠁⠀⠀⠀⠀⠀⢰⣿⠻⠦⠄⣴⠂⠀⠀⠀⠀⠀⠠⠞⣿⢦⣠⢀⡿⠀⠀⠀⠀⠘⠐⣆⡶⣠⠆⠛
⠀⠀⠀⠀⠀⠀⣀⣼⣿⣄⡀⠀⠀⠀⠀⠀⠀⢶⣭⣷⡀⢠⠃⠀⠀⠀⠀⠀⠀⠀⣸⠟⢶⡀⣸⠇⠀⠀⠀⠀⠀⠀⢘⣿⡏
⠀⠀⠀⠀⠀⠀⢻⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢹⠶⠿⠻⣗⠀⠀⠀⠀⠀⠀⢠⣭⣥⣴⣾⣶⡿⠀⠀⠀⠀⠀⠀⠀⣼⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢉⡳⢄⠀⠀⠀⠀⠀⠀⠀⠐⢲⡂⢶⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣸⣃⣀⡽⠂⠀⠀⠀⠀⠀⠀⠀⠹⣶⣦⡄⠀⠀⠀⠀⠀⠀⢈⣭⣀⣠⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣥⡀
⠀⠀⠀⠀⠀⠀⢹⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠟⠂⠀⠀⠀⠀⠀⠀⠻⣿⣥⣄⠈⣻⡇⠀⠀⠀⠀⠀⣠⠿⣿⣿⢷⣄
⠀⠀⠀⠀⠀⣤⣬⣿⣏⣿⣤⣄⠀⠀⠀⠀⠀⠀⣾⠁⢻⡀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣷⡟⣷⣿⡇⠀⠀⠀⠀⠀⠘⣿⠿⢿⣿⠃
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⠀⡀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⢠⡴⣿⣿⠦⡄⠀⠀⠀⠀⠀⠀⠀⢠⢾⣷⣆⠀⠀⠀⠀⠀⠀⠠⡾⣿⢧⡀⢀⡾⠃⠀⠀⠀⠀⢶⠎⣷⣦⣤⣄
⠀⠀⠀⠀⠀⢰⠀⣿⣿⠀⡰⠀⠀⠀⠀⠀⠀⠀⠘⣼⣿⣮⡅⠀⠀⠀⠀⠀⠀⢹⡟⢳⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣮⡙⣷
⠀⠀⠀⠀⠀⠈⠢⡌⣿⠴⠁⠀⠀⠀⠀⠀⠠⠴⠚⠉⠀⠸⠁⠀⠀⠀⠀⠀⠀⢸⠃⠼⢤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠃⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠹⣄⡀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣪⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⣰⠛⣿⡇⠀⠀⠀⠀⠀⠀⠰⡶⣻⠄⢀⣄⡀⠀⠀⠀⠀⠀⠀⠈⢉⣹⣷⡘⠟
⠀⠀⠀⠀⠀⠀⠸⢿⣟⢻⠆⠀⠀⠀⠀⠀⠀⠀⠸⡶⢛⡇⠀⠀⠀⠀⠀⠀⠀⠐⠿⣷⣾⡿⢻⡄⠀⠀⠀⠀⠠⣔⣛⡯⠽⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠒⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁

⠀⠀⠀⠀⢠⡖⠒⠒⠢⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⣀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠉⠈⠐⠲⢤⣠⡀⣀⠔⠊⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠁⠈⣀⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠈⡝⠁⠀⠀⢀⣀⣀⠀⠀⠀⠀⠱⡀⠔⠀⠈⣀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣠⣴⡾⠟⡋⠛⠇⠀⠀⠀⠀⣧⠀⡶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠋⣥⠀⠀⠂⠀⠀⣠⣀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⠀⠀⠀⠀⠀⠈⠈⢹⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⢊⡡⠔⠋⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠏⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⡀⡤⣖⠋⠈⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠈⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣦⡀⠀⠀⠀⠺⣿⣿⣿⣶⣶⣾⣿⣿⡷⠀⠀⠀⠀⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡆⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣤⠂⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠆⠀⠀⠀⡿⠿⠿⠿⠿⠛⠿⠿⠛⢀⣼⣿⣿⡆⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣇⡀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠈⣳⣿⣿⣿⠟⠃⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⡁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣤⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⠿⠟⢋⠑⠊⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡠⡉⢉⠉⡉⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠙⠛⠿⠿⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠐⠆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠊⠉⠉⠉⠉⠉⠓⠒⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢀⠠⠄⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⣾⠀⠸⠀⢀⢆⣠⠀⢀⣤⣠⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠰⡀⠀⠀⡷⢀⠛⣄⡌⣶⠁⠾⠀⣄⢆⢠⡆⠈⠟⣧⠎⠘⡃⠱⢟
⠀⠀⠀⠀⠀⢠⠐⢀⡠⠶⠂⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠘⠀⠘⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢰
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠀⠀⡘⠸⠀⠀⣠⠤⠤⣤⣔⠁⠀⠛⠀⠀⠙⣆⣀⣀⡐⣼⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⠛⠳⢤⡀⠀⢠⢁⠐⣠⡮⠤⠖⠊⠀⠈⢳⠀⠓⠁⢠⠞⠁⠙⠦⣽⣆⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠠⠒⢢⠹⣤⡸⢀⠀⣏⠀⠀⠀⠀⠀⣾⠆⡇⠀⠀⡇⠀⠀⠀⢸⡇⢸⣸⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡧⠒⡆⠀⠉⠛⡘⠀⠹⡀⠀⠀⠀⠀⠙⡱⠀⠀⠀⢣⣀⠀⠀⠈⢁⠜⠳⣟⡮⠀⠀⠤⠤⢄⢒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⢀⣺⡄⠀⠀⢀⠷⠀⠀⠙⠲⠤⠤⠴⠊⠀⠀⢠⠤⢶⠈⠛⠒⠚⠁⢠⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⠄⠀⠀⡎⠐⠀⠀⠀⠃⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⡀⢄⠖⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠁⠀⠀⢰⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣎⠔⠂⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠺⠀⢀⡠⠒⠉⠲⡀⠀⠀⠀⠀⠶⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠘⠖⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠋⠉⠉⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠋⠀⠀⠀⠀⠀⠘⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⢀⠀⠀⠀⠀⠸⡀⠉⠉⠒⠒⠶⠦⣤⣤⣀⣤⣄⠠⠤⡔⠲⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢠⠆⠀⢀⠀⠀⠀⠙⢄⠀⢀⠔⠚⠳⣧⡰⠗⢦⡀⠀⣠⠃⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠋⠀⢀⠃⠀⠀⠀⠀⠈⠓⠁⠀⠀⠀⠸⠁⠀⠈⡧⠚⡅⠀⠀⠀⠈⣇⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠲⠦⢄⣀⡘⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⢱⠀⠀⠀⠀⣸⡀⠀⠀⠀⡵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢈⠃⠀⠀⢠⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁⠀⠀⡗⠒⠈⠉⠁⢇⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠰⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢱⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⢰⣴⣀⣀⣀⣐⣀⢐⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢺⣟⣭⣿⣿⣿⣿⣿⣽⣿⣿⣗⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠀⢱⣼⣤⣶⣾⣿⣿⡿⢿⣿⣟⣛⣻⣿⣟⣛⣿⣿⢿⣿⣿⣿⣿⣶⡠
⠀⠀⠀⠀⠀⠀⠀⢀⠰⡜⢄⡳⣦⣷⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠈⠉⠻⡿⠿⣷⣿⣿⣿⣿⣿⣦⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠈⣲⣤⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠠⡀⢠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠊⢀⣴⣿⣷⣾⣿⣿⣿⣿⣧⠙⢦⡀
⠀⠀⠀⠀⠀⠛⢚⣶⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⡀⠓⠤⠤⠤⠤⠔⠒⠋⠁⣀⣠⠔⢹⣿⣿⣿⣿⠋⠁⠀⠀⢙⡷⠀⠙⣄
⠀⠀⠀⠀⠀⠉⠈⠟⠋⠀⢀⠀⠈⣿⣿⣿⣷⣿⣿⣦⡤⠤⠤⠤⠔⠒⠚⠉⠁⠀⢀⣼⣿⣿⣿⡇⠀⢀⣠⣴⠾⢃⠄⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⠿⠟⡛⠫⠁⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠉⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠈⠢⠀⠐⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⡤⢄⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠛⡈⠀⠀⠀⠃⡄⢈⠙⠋⡄⠀⠀⠀⠀⠡⣀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠁⠀⠀⠂⣈⠉⠦⠠⢤⡀⠀⠀⠀⠀⠀⠀⡉⠉⠉⡁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⡱⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠈⠀⠀⠠⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠀⡆⠈⠂
⠀⡀⠀⢀⠐⢄⡀⠲⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢣⢆
⠀⠀⠈⡹⠁⠀⠀⠐⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⡀⠁⠆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠙⠋⠀⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠅⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⡤⠆
⠀⠀⠠⠀⠀⠀⠀⠀⡠⢆⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠶⡵⠠⠀⠈⠂⠀⠀⡀⠀⢀⠀⢀
⠀⠀⠀⢠⠀⡀⠂⠀⠁⡨⢄⠀⠀⠀⠰⠐⠂⠀⠀⠀⠀⠀⠀⠚⠈⠀⠀⠒⠎⠂⠀⠂⠀⠀⠀⠈⠁⠘⠁
⠀⠀⠀⠀⠐⠀⢠⡜⠂⠡⣌⡀⠀⡀⠢⡀⢀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠒
⠀⠀⠀⠠⠀⠀⠛⠁⠰⠄⠃⠀⠀⡽⠀⠀⠀⠀⠘⢀⠄⠀⠀⡉⠁⠀⡀⠀⠀⠂⠁
⠀⠀⠀⠐⠂⠀⡀⠀⠀⠁⠀⡰⠊⢀⠀⠁⠀⠀⠘⠡⠤⠀⠀⠠⠀⠀⠘⠂⡀⠀⠀⠛⠡⠀⠡⣀⠒⠄
⠀⠀⠀⠀⠀⢉⠇⠲⣆⡶⠚⠁⠖⠁⠀⠀⠀⠀⠀⠛⠂⠀⠀⠰⠡⡄⠀⡀⠐⡀⠀⠀⠀⢈⠀⠀⠡⠄⠨
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⠀⠀⣠⡦⠀⠀⠒⠂⠀⠀⠐⣀⡬⠀⠆⠀⠀⠀⠁
⠀⠀⠀⠀⠂⠤⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠅⠤⠷⡶⡂⡂⡐⡋⠉
⠀⠀⠀⠀⠀⠂⠂⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⡀⠀⠄⣀⡀⠀⠀⠀⠐⠠⣰⣤⠄⠑
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠀⠀⠀⡤⣠⣠⣿⣿⣷⣄⠀⠀⠀⠙⠋⣴⣃⠀⣤⡤⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠔⣋⣼⢀⣀⣶⣷⣶⡟⠿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⡇⢠⡴⠇⠀⠀⠉⠳⡀
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣾⣿⣿⣿⣿⣧⣄⠈⠿⣻⣿⣷⠀⠀⢠⣿⣿⣴⠟⢀⣀⣀⣤⣄⣀⡀
⠀⠀⡔⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠽⠿⢿⡄⠰⠿⣿⠿⠶⠿⣯⣥⣤⡄⠀⣈⣉⣻⡄
⠀⠀⠁⢰⣿⣿⣿⡃⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠄⠀⠉⣍⡙⠄
⠀⠀⠀⢸⣿⣿⣏⠀⢴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡇
⠀⠀⠀⢺⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃
⠀⠀⠀⠸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀
⠀⠀⢴⠞⢻⣿⢂⣴⣶⣧⣤⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣤⣤⣴⣶⣶⣤⣄⠀⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⣸⣿⣿⡿⡿⣿⣿⣿⣿⣿⣦⡐⡄⠀⠀⠀⠀⣤⣽⣿⣿⡛⠛⠳⠤⢉⣿⠳⠀⠀⢸⣿⠋⢹
⠀⠀⢸⡇⠀⣿⣿⠇⠓⣻⣿⣟⡛⠿⢿⣿⣿⠗⠒⠒⠈⠁⣿⣿⣭⣭⣿⣿⠦⡀⠉⢂⣠⡴⢻⣿⡄⣾
⠀⠀⢸⡧⣀⢸⡄⠀⢀⡙⠿⠟⠁⠀⣼⣿⡟⠀⠀⠀⠀⠀⠛⠋⠙⠿⠿⠉⠁⣿⣾⣬⠄⢀⣸⡿⠁⠏
⠀⠀⠈⢧⣸⣿⡇⠀⠈⠙⠓⠂⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⠉⠀⠀⣼⣿⠴⢃⠄
⠀⠀⠀⠀⢩⣿⡟⣿⡤⣤⠀⠀⠀⠀⠀⣿⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⢾⣿⡷⠖⠋
⠀⠀⠀⠀⠀⠹⣇⢸⡇⢱⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠸⢻⡇
⠀⠀⠀⠀⠀⠀⣿⢻⣧⢸⠀⠀⠀⢰⣾⣇⣀⡀⠲⠶⠶⠃⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⢹⠈⠿⢺⡄⢀⠀⢸⡇⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠈⡄⠈⢸⡇⣼⠀⠸⣷⣿⣧⣤⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠
⠀⠀⠀⠀⠀⠀⠀⡿⣦⠘⠇⣿⣧⣴⡿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⣿⣼⡿
⠀⠀⠀⠀⠀⠀⠀⢸⠸⣷⠀⣿⣻⣇⣷⣦⣴⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢧⢹⢻⣿⢾⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣌⡟⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⡙⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⣷⣶⣶⣷⣶⣿⣷⣿⡿⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠋⠙⠛⠛⠿⠿⠶

⣿⣿⡿⠻⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⡀⠀⢀⠀⢀⡀⠀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⡙⣿⣿⣾⠏⣿⡃⢸⣿⠈⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣼⡇⣿⣿⣿⠠⣿⡁⣿⣿⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠀⠁⠀⠉⠁⠈⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⢀⡀⣀⢀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣝⢸⣿⣼⡇⣿⢸⡧⠀⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⢺⡿⢻⡇⣿⠸⣷⡄⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢀⣄⣠⢀⣤⣄⣠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠾⠟⠿⢘⡿⠟⠙⠟⠛⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⣾⠏⠹⣿⠿⣿⣿⣿⣷⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⠿⣿⡆⠀⠀⠀⢠⣤⣄⢠⣦⠄⣴⣤⣠⣴⠄⣬⡝⢻⣧⡄⠀⣿⡇⣠⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣻⣿⣿⡇⠀⠀⠀⢸⣷⡟⢸⡷⠄⣿⠿⢹⡷⢀⣿⣷⠀⣿⠀⠀⠘⣿⣿⣿⡿⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠘⠟⣻⣼⣿⡊⠟⠀⠸⠿⠺⠟⠛⠀⠟⠀⠀⢾⣿⣿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⢿⣿⣿⣿⣷⡀⢀⣴⣾⣿⡿⢿⣿⣷⣦⣄⣀⣠⣴⡿⠀⠀⠀⠀⠘⢿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠉⠉⠛⢿⣿⡟⠁⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣤⣶⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠛⢦⡀⠀⠀⠀⠹⡄⢲⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣙⢶⣄⠀⠀⠹⡌⢧⠀⠘⠇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣭⡳⡄⠀⢁⣤⣴⣶⣾⡿⠻⣦⣦⣀
⠀⠀⠒⠶⠤⣤⣄⣀⡀⠀⠀⠶⠤⣤⣀⣀⠀⠀⠁⠀⣴⣿⣿⣿⢏⡿⠿⠶⠿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠶⠤⣬⣍⣙⡛⠂⢸⣿⡿⠛⠛⢿⣇⡀⠀⠀⠀⠙⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣠⣿⡧⡔⠉⠩⠂⠒⠒⠒⠂⠀⢽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⣷⣶⢶⡜⠀⢺⣟⣛⠂⠈⡿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢫⠾⢤⡀⠀⢠⢟⣻⠿⢸⠘⠢⠉⠙⠁⠀⣵⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣠⣞⡒⢌⣂⠸⣄⠀⠀⣼⡀⢀⣄⠀⠀⡴⡆⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣉⠦⢤⢹⡀⠀⠀⢹⡄⠚⠁⣁⣀⣈⠁⣇⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢸⡄⠈⠓⠅⡖⠀⠀⣿⡀⠉⣓⣂⣉⠀⡟⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⣀⡴⡏⢷⠀⠀⣼⢻⡆⠀⢻⣅⠀⠈⠋⠀⢀⡾⠁⡏⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⣷⠖⡇⠘⠆⠘⠁⠘⣷⠀⠸⡿⡷⣶⠶⠶⠋⢀⡼⣥⡈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢷⡶⠦⢤⡀⠀⠈⢧⠀⢳⣷⠈⢷⡄⣰⠋⢀⣾⠟⢮⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠛⠲⠶⠶⠶⠿⢷⣄⣿⠁⢠⡾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣾⣿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣠⣾⣿⣫⡾⠃⠀⠈⠙⣦⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠐⠙⠋⣠⣦⣤⡀⠀⠀⠀⠀⢀⠀⣀⡴⠚⠙⠐⡄⠈⠁⣀⠀⠀⠀⠀⠈⠙⢶⠜⠉⣠⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⢠⡾⠛⠁⠀⠻⢶⡄⠠⣀⠋⡽⢁⡀⠠⠃⠀⣀⠀⢀⣿⣧⠀⠀⠀⣀⣶⡤⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠈⠙⢦⡈⠁⣉⡁⠈⢀⠀⢸⣿⡆⢸⣿⣿⣀⡤⢊⠝⠉⠐⢀⣴⠰⣿⣏
⠀⠀⠀⠀⢀⡀⠀⠀⠀⡴⢁⡴⠀⠀⠀⠀⠀⠀⠀⣤⣿⡷⠉⠀⠔⠉⠀⢰⣿⣷⣿⣿⣿⣇⠀⠀⠀⠀⠔⢉⣴⠾⠟⠉
⠀⠀⠀⠀⠺⢷⣦⣤⡈⣠⢋⡀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠄⠀⣠⣿⣿⣿⣿⣿⣿⣿⠃⣀⠀⠔⠚⠛⣡⣄⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣾⠿⠶⢤⣀⠀⠀⣠⣾⡿⠃⠀⣠⡀⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣟⣿⡇⣾⣷⣤⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠑⢦⣌⠁⠀⠀⠈⠹⣶⣷⣿⠋⡀⢀⣸⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟⠋⢉⠀⠔
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠙⠓⣤⡄⠀⠀⠈⠉⠉⠙⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⢀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢶⡿⠧⣄⠀⠀⠈⠓⠤⣄⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠠⢶⡿⠛⠁⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠓⢆⣠⡀⣈⠻⣤⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠻⣿⡶⣷⣿⣿⣿⣿⣿⠿⠛⠛⠉⠋⠉⠁⠀⢀⣠⣆⣠⡴⠀⠀⢀⠴⠋⠉⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢡⣾⣿⡿⠟⠛⠛⠁⠀⠀⠀⠀⠂⠀⠴⠛⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠄⠰⡐⢀⠈⠀⠁⡀⢡⢆⡐⠳⢣⡦
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠀⠀⠀⠀⠢⠐⠈⠃⠁⠀⠀⠃⠀⠁⠀⠈⠀⢨⠀⠠
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⠀⠈⠀⠀⢘⠀⡠⠄⠲⠴⡁⠀⠁⠀⠱⢤⠤⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠌⠢⠀⠀⠀⠞⠀⠁⠀⢠⡜⡀⠁⠀⠀⠀⢩⡜⣶⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠀⠛⠃⠀⢃⠀⠀⠀⠘⡣⠀⠀⠠⡀⠀⠈⡡⠻⢖⡄⠀⠀⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠠⠵⠀⠀⠘⠀⠀⠁⠒⠂⠊⠀⠀⠀⠒⠈⠁⠈⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠉⡊⠀⠀⠄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠃⠀⠀⠇⢀⠠⠒⠢⡀⠀⠀⠠⠄⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⢤⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠈⠓⠢⠤⠄⣀⣀⠀⠀⡀⠀⣀⢠⡄⠂⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⢀⠀⠀⠑⢄⠀⠀⠒⢬⡨⠩⡁⠀⡘⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠰⠊⠆⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠲⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⠄⠤⠐⢃⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢰⣿⣿⣿⣿⡆⠠⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣭⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢻⣷⣿⣿⠇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣋⢀⣀⣀⡀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⣴⡾⢺⣿⣃⣤⣄⣾⠀⣠⣴⡦⠀⠀⠀⠀⠀⢀⣴⡞⣿⣿⣿⢹⡿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣼⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣷⣦⣄⠀⠀⠀⢸⣿⣇⢘⣿⡟⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⣿⣻⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠈⢿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣷⣾⡆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⠀⠀⠀⠀⢹⣷⣶⣶⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⠀⠀⠀⢀⣾⣾⡿⢹⣿⡿⠀⠀⠀⠀⣿⣿⣿⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⠏⠘⣿⢿⠀⠀⠀⢸⣿⡏⠀⢸⣿⡇⠀⠀⠀⠀⢻⣿⡏⠀⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⡀⠀⢸⡏⠀⠀⠀⠈⣿⣿⠀⢸⣿⡇⠀⠀⣀⡀⢸⣿⡇⠀⢸⣿⡇⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠘⣧⠀⢸⡇⠀⠀⠀⠀⢹⣿⡄⢸⣿⠃⠀⠀⠈⠁⢸⣿⡇⠀⢸⣿⡇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣆⢸⠁⠀⠀⠀⠀⠀⣿⡇⢈⣿⠀⠀⠀⠀⠀⠀⠿⠃⠀⠈⠿⠁⠀⠀⠀⣠⡄⠀⣤⡀
⠀⠀⠀⠀⠀⣠⡤⣤⡀⠉⠀⠀⠀⠀⠀⠾⠋⠘⠷⠀⠀⠀⠀⠘⠋⠁⠉⠉⠀⠀⠀⠀⠀⠀⢶⣦⡀⠀⢶⣦⡄⠀⠸⣿⡷⠒⣿⡿
⠀⠀⠀⠀⠀⠢⣤⠤⠎⠈⠓⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠁⠀⠀⠉⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠈⠳⣄

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣞⣛⣿⣿⣿⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣹⠉⡁⠀⣿⣿⣤⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⣿⣿⠏⣿⣿⣿⢽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢹⢿⣿⣿⣓⣿⣷⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢸⠟⣿⡏⠁⠉⠹⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠹⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣀⠄⡇⡀⠀⣠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣶⣾⣷⣶⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠒
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⣸⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠛⠿⠿⠟⡩⣿⣿⣿⣿⣷⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⢀⣿⡟⣿⣿⣷⡀⣿⣿⣿⡛⠀⠻⣿⣿⠟⠁⠈⠀⠀⠀⠀⠀⠀⠘⠿⣿⡿⠏⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⡀
⢸⣿⠁⣿⣿⣿⣷⣼⣿⣿⡷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄
⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⢸⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿
⢸⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣿⣿⣿⣿⣿⡟⣿⣿⠟⠁
⠘⣷⣄⡘⣿⣿⣿⣿⣿⣿⣿⣿⣟⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⣰⣿⣿⡿⠟⢋⣼⠿⠃
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⣿⠃⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠁⠈⠁
⠀⠀⠀⠉⠛⠛⠛⠿⠿⠛⠉⠉⠉⠉⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣤⣀
⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣄⣀⣀⡀
⠐⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣿⣷⡀⣸⣿⡿⠟⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⣿⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡠⠀⢈⣧⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠰⠀⣠⠋⠈⠷⣄⠀⠀⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⢠⡎⠉⠑⠦⡀⠀⢀⣿⠀⠐⠃⠀⠉⠀⠁⣠⠟⠷⣤⣀⠀⠀⠉⠒⠢⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⢸⡇⠀⣠⠔⠈⠉⢱
⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠛⠂⢸⡇⠀⠀⠀⠀⠀⠁⣼⠏⠀⠀⠈⣹⣿⣿⣷⣦⣄⣀⣀⡉⠉⠐⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⢸⡇⠐⠛⠒⠒⠒⠊
⠀⠀⠀⠀⠀⣠⠤⠤⢤⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⠏⠀⣄⠀⠀⠛⠋⠁⠀⠀⠈⠉⠉⠛⠛⠛⠛⠓⠶⢦⣤⣤⣄⠀⠀⢁⢸⡇⠀⠀⣠⡤⠤⠤⣄
⠀⠀⠀⠀⠀⠧⡠⠶⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⠇⠀⠀⠈⣳⡶⠛⠛⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⣄⠈⣼⡇⠀⠀⠈⠙⠶⢄⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⢠⡿⠀⠀⠉⣹⠏⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠓⣶⡁⢹⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢸⡇⠀⠀⠀⣿⢀⣀⣀⣠⣤⣤⠶⣿⠃⠀⠀⠀⠀⠀⠀⢻⠖⠶⣤⣼⠃⠈⣿⠛⢲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡄⠀⣿⠀⠀⠀⠀⢻⡋⠉⠉⠀⠈⠉⢠⡟⠀⠀⠀⠀⣶⠀⠀⠈⠲⠤⠔⠋⠀⠀⣿⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣠⣿⠀⠀⠀⠀⠀⠛⠦⣄⣀⣠⠴⠋⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⠉⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣿⠋⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠟⠋⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⢼⣗⢙⠆⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢁⠀⢠⠀⢿⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⣭⣿⠀⠀⠀⠀⠀⠀⣠⠞⠁⢿⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣏⣠⣌⣀⣈⠀⠘⣧⠀⠀⠀⠀⢀⣟⠈⠿⣿⣿⣿⠃⠀⠀⠀⠀⢀⡾⠋⠀⠀⢸⡇⣾⠉⢙⡷⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⢻⡄⠀⠀⠀⠀⠉⠙⠛⠻⢿⡏⠀⠀⠀⢀⣴⠋⢀⠂⠀⢀⣸⠛⠛⠶⣿⠀⢀⡿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⣛⣭⣷⣶⣦⣤⣤⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠉⠙⠛⠛⠛⠾⣷⠀⢠⣴⡿⣠⡞⠁⣸⠇
⠀⠀⠀⠀⣠⡤⠞⠛⠒⠛⠉⣠⡶⠋⠉⠀⠀⠀⠉⣇⣀⣀⣙⣧⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡛⠁⠀⠀⠀⠀⠀⠀⠀⢘⡦⠀⠘⠁⢈⠿⠛⠁
⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡯⠌⣹⠛⠶⠶⠤⠴⠶⠻⢋⡉⣻⣆⠀⠀⠀⠀⠀⠀⣠⠞⢁⣴⠟⠀⠈
⠀⠀⠸⢦⡜⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠏⠀⠀⢀⠀⠀⠀⢘⣿⣷⡾⢿⣦⣤⣤⣤⣶⣛⣡⠶⠋
⠀⠀⠀⠸⣧⣤⡞⠀⣴⠷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠰⣦⠀⣤⡀⠀⠀⣿⠀⠀⠈⠉⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠘⢷⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠸⠀⣤⣾⠋⢀⣾⠏⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⢤⣤⣀⣀⡀⠉⠉⠀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⡽⣷⡀⠀⠀⠀⠀⠀⣿⣻⠶⣤⣤⣀⣀⣉⠉⠉⠛⠛⠋⠁⠀⣿
⠀⠀⠀⠀⠀⢀⣴⠟⣡⠞⠀⣸⣧⠀⠀⠀⠀⠀⣿⣅⠀⠀⠀⠉⠉⠙⠛⠛⠷⠶⢦⣤⣰⡟
⠀⠀⠀⠀⣠⡾⢃⡜⢁⣤⣾⣇⠾⣧⠀⠀⣴⠿⠋⢿⣄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣠⡿⠁
⠀⠀⢀⣼⠏⣠⠋⠀⢺⣿⠏⢿⡀⠹⣦⣴⣿⣧⡀⢀⣹⠷⣾⣅⣀⠀⠀⠀⠀⠙⣻⣿⡆
⠀⣠⡿⢁⡞⢹⡄⢠⡾⠉⠀⠈⢿⣄⣈⡴⠟⠁⠛⠋⠁⠀⠀⠈⠙⠛⠶⣦⡶⠿⢿⣯⣟⠳⢶⣤⡀
⣼⣏⣰⢋⣀⣰⠿⠋⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠀⢨⡿
⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⣉⣾⣯⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⠁⠀⠉⠉⠿⠻⠃⠈⠉⣉⠿⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣤⣭⣏⣉⣛⡒⠒⠶⠒⢴⡧⣤⣤⣀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠿⠷⠾⠶⣶⣤⣯⣬⣿⠆
⣾⣶⣶⣷⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣿⣿⣶⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣷⣾⣷⣶⣾⣷⣶⣶⣶⣾
⣿⣿⣿⡇⠀⠉⠈⠀⠈⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣶⡶⠟⠉⢻⣿⡇⠀⠀⠀⣿⡇⠀⢀⠀⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⣿⣿⣿⣿⣿⣿⣿⣿
⣧⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⡇⠀⠀⢀⡧⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⢰⣿⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⡏⣿⣿⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⡇⠀⢠⠀⣿⣿⣿⡇⠀⠀⣀⣀⣰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠀⠀⢻⣿⡇⠀⠀⠀⣿⡇⡀⡰⠀⣿⣿⣿⡇⠸⣿⣟⠛⠉⠻⣿⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠀⠀⢀⢸⣿⡇⠀⠀⠀⣿⣧⠇⠳⠀⣿⣿⣿⣧⠄⠈⠛⠿⣿⣶⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣤⣀⣸⣄⣿⣧⠀⠀⠀⣿⣿⣶⣦⣤⣿⣿⣿⣿⣤⡤⣀⢀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠉⢹⣿⣿⣿⣿⣶⣶⣿⣿⣷⣶⣬⣿⣿⣿⣿⣿⣷⣿⣿⡆⢿⣿⣿⣿⡟⠿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣥⡉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣷⣿⣿⣿⣿⣠⣶⣷⠀⣶⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠀⠀⠀⠙⣛⣿⣿⣿⣿⡿⠿⠿⠛⠛⠃⠀⠀⣤⣤⣀⢀⡘⠿⠿⣿⣶⣿⣿⣿⡟⢀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⡤⠀⠀⠴⠿⢿⡿⢿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⡂⢀⡀⣯⠙⢛⣿⠿⠇⠋⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣅⣀⣠⣤⣴⣾⣿⣿⡷⢆⣀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠀⡖⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣴⣯⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣷⡤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⡍⠈⠀⠻⠿⠛⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⣀⡠⠔⠒⠿⠟⠣⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠀⠠⣄⠀⣀⢀⡒⠢⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠃⠀⢨⡍⠉⢉⠀⡼⠀⠀⠉⠉⡁⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢀⣀⠀⣣⠀⠒⢰⢡⠆⠀⠀⠀⠉⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡇⠁⢠⡄⠸⠀⢄⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠐⠀⠀⠀⠀⠑⠀⢰⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⢀⣙⣓⠢⢟⠃⠀⠀⠀⠀⠀⠤⡤⢤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡉⠑⠚⠙⠀⠀⠀⠄⠀⠠⢤⠴⡃⠀⢀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠐⠒⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⢀⠟⠒⠤⣀⡐⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢄⢀⠞⠁⠀⠀⢀⡀⢀⠀⣀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⢸⡼⠃⠀⠀⠠⠂⠈⠀⠈⠈⠁⠈⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠘⠀⠀⣠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣀⡐⠀⠘⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡀⠀⠀⣃⣤⠃⡀⠀⠈⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠚⠡⠮⡀⠀⠈⣉⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠈⠁⠀⠀⡏⢰⠰⡶⠒⠶⡤⢀⡤⢄⠀⢀
⠀⠀⠀⠀⡎⡇⠀⣰⡑⢩⠁⠀⠀⠀⢠⠁⡌⢰⠀⠀⠰⢁⢄⢀⣴⠀⢎
⠀⠀⣖⡂⠘⠀⠀⠡⠀⡘⢀⠔⣄⠀⢸⠀⠁⠃⠀⠀⠀⡈⠈⠀⠢⠁⠉
⠀⠀⠀⠠⣂⠄⠀⠀⠀⢶⠁⠀⡟⣤⡇⠀⠒⠀⢀⠀⢠⠃⡆
⠀⠀⠀⠀⠀⠀⠀⡄⢀⡞⠀⠰⠶⢶⡀⠀⢰⠀⡜⠀⡌⢰
⠀⠀⠀⠀⠀⡄⢰⠇⠘⠇⠀⢠⠂⠀⢸⠓⠋⠐⣇⣀⡏⠁
⠀⠀⠀⠀⠀⠀⢸⠺⡤⢤⡔⠁⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠈⠂⠇⠀⠙⠓⠢⠼⢃⣐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠲⣼⠃⠀⠿⠞⠛⠛⠉⠉⠙⠛⠛⠛⠳⠶⠦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡆⠀⠀⢸⡀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢀⡀⠀⣄⠀⠀⢸⠧⣄⠀⠀⢀⡿⢄⡀⠀⢠⡷⣄⣀⣸⢧⣠⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⣟⠦⠟⢑⠒⡩⠤⠚⠛⠋⠉⠓⠎⠉⠉⠉⠉⠙⠛⢧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡵⠒⢦⡀⠀⠀⢸⠀⠀⠘⠋⠀⠀⠐⠗⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢈⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠙⠦⠭⠷⣄⣀⡼⠀⠀⢀⡠⠀⠀⠀⠀⠀⢀⠀⠣⣀⠀⠀⠀⠀⠠⢂⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠍⠊⠑⠂⠐⠂⠁⠀⠀⠀⠉⠁⠈⠠⠖⠫⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢯⡛⣦⠀⠀⠀⠀⠀⠀⠀⣴⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠛⠁⠀⠀⠀⠀⣀⡴⠚⠁⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⣾⠁⠀⠀⠀⢀⡀⣰⠿⣄⣀⠀⠠⠤⠤⣄⣀⣀⣤⣤⡤⠤⠶⠖⠋⠁⠀⣸⢦⣤⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣤⠞⠋⠸⣦⣀⣀⣠⠞⡾⠁⠀⠀⠉⠙⠓⠒⠲⠶⢾⣄⣀⣀⣀⣤⠦⢤⣤⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣼⠃⠀⠀⠀⢀⣀⡤⠤⡄⢀⣼⡇⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠈⢸⡋⠀⠀⠀⢣⢸⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢳⠀⠀⠀⢸⡾⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⣷⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠸⡄⠘⠧⢤⡄⠀⠀⣀⡀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣀⠠⠼⢷⣀⠐⠛⢲⡖⠒⠛⠶⣾⢻⡟⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⣠⠖⠋⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠃⢸⣁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠓⠒⠲⠶⠶⠶⠶⠶⠶⠦⠤⣤⠾⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠞⠁⠀⠀⠀⠈⢳⡄⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠻⡴⠋⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡠⠄⠒⠈⠁⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⣀⡀⡀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠼⠅⡀⠤⠤⠐⠂⠉⢀⠠⠀⠐⠘⠉⠉⠉⠉⠁⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⡁⠤⠀⠀⠀⠀⠀⠀⠒⠒⠒⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠁⠀⠀⠀⢠⠀⢄⣀⣤⠴⠚⢋⡥⠂⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠛⣦⠀⠀⣌⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣀⣀⣀⣤⡤⠶⠟⠋⠉⠀⢀⡴⠚⠁⠀⡠⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢬⠉⠢⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡰⠀⠀⢸⠗⠀⢀⠜⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⠀⠀⠀⠀⡐⠉⠑⠀⠀⠀⠀⡈⠉⠆⠀⡿⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⠀⠀⠀⠀⠙⠄⠔⠀⠀⠀⠀⠣⠠⠂⢀⡇⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⢹⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⡟⢠⠤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡄⠀⠀⠀⠀⠀⠀⠟⠛⠋⠉⠁⠀⠀⡰⠀⠅⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣈⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠉⠓⠿⣦⣤⣀⣀⣀⣀⣀⣀⠤⠤⣎⠀⠀⣠⠃⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠾⡈⢳⡴⠚⠳⢄⡀⠀⠙⠦⠤⠤⠤⠴⡉⠢⠒⣧⠀⠀⣀⣀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢀⣸⠋⠀⠀⠀⠀⢙⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣀⠀⠀⠀⠀⠀⡓⠀⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠻⣄⠀⠀⠀⠀⣿⠙⠛⠟⠿⠿⠿⠿⣁⡀⢋⡷⠶⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢉⡀⠀⠘⢦⡀⣠⠞⠁⠀⠀⣠⣀⣀⣀⣀⣤⣶⣟⣀⠀⠀⠀⠀⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣄⡴⠞⠻⡋⠀⢀⡴⠞⠁⠉⠉⠉⠁⠀⠀⠈⠉⣹⠿⣆⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⣀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠤⠀⠠⠀⠀⠄⠄⠄⠀⠆⠄⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠂⠀⠀⠂⠔⠀⠦⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⢾⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢯⣉⠳⡄⠀⣰⣿⣿⣿⣿⣿⠟⠋⠉⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢠⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣖⠛⣛⡶⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣿⣿⣿⡇⠀⠀⠀⠀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢰⣿⡿⠀⣤⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠐⠲⠌⠻⠟⠀⠀⠀⠀⠀⢿⣤⠏⠀⠀⠀⠀⠀⠀⠀⢀⠈⠙⠀⢸⣿⠃⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡲⠀⣾⡏⠀⢻⡓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠛⠁⠀⠂⣿⠀⠀⠙⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⠀⢰⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣦⠀⠀⠀⠀⠀⠀⠀⢞⠙⠛⢿⡇⠀⠀⠀⠀⠀⢀⣼⣁⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉⠉⠉⣻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠙⢿⠶⣄
⠀⠀⠀⣠⠶⠋⠉⠋⠁⠀⢀⣠⢤⣴⣇⠀⠙⢷⣶⣤⣀⣀⡀⠀⠀⠀⣀⣀⡤⠞⢻⡃⠲⣶⠋⢀⡼⢳⡄
⠀⠀⠸⣇⡀⠀⠀⠀⠀⢺⡋⠀⠀⢀⡿⠉⠀⠀⠈⠛⠶⠭⠽⠿⠛⠉⠙⢧⡀⢀⡼⠃⠀⠈⠑⢯⣠⡾⠁
⠀⠀⠀⠹⣄⡀⠀⢀⠀⣼⠁⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⡾⠛⠋⠀⠀⣠⠞⠲⠚⠉
⠀⠀⠀⠀⠈⠳⠦⠟⠛⠁⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⠳⠚⠋
⠀⠀⠀⠀⠀⣠⢦⣄⠀⠀⠀⣷⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣠⡞⡡⠊⠙⣧⡀⠀⢻⡄⠀⠉⠉⠛⠳⠶⢦⣤⣄⣀⠀⠀⡾
⠀⢀⡼⢋⠞⡠⣤⡾⠁⠙⠳⣤⡟⢦⣀⠀⠀⠀⠀⠀⠀⢨⡟⠻⣿⡁
⣴⢋⠔⢳⣪⣹⠜⢧⡀⠀⠀⠈⠉⠳⢬⡿⠓⠶⢦⣤⣤⡟⠀⠀⠈⣷
⠙⠻⠶⠚⠋⠀⠀⠀⠙⠶⣄⣀⣀⡴⠛⠀⠀⠀⠀⠀⣼⠃⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⣼⣅⡀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠯⣀⠈⢹⣛⡧⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣑⠢⢌⡲⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣍⡒⢼⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠟⠻⣿⠛⠻⣿⡟⠛⣿⠟⣿⠛⢻⡟⠛⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⡷⣾⣷⣷⣾⣿⢻⣞⣷⣶⣶⡟⢿⡞⢻⣦⣿⣟⣶⡿⣿⣟⢳⣟⢻⡟⢣⡼⢶⡾⠃⠛⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣧⣾⣤⣿⣤⣿⣴⣯⣼⣧⣼⣧⡿⢇⣿⣦⣧⡜⢿⣧⣼⣯⡜⢫⣼⣿⣼⣧⣾⠷⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠀⠄⠘⠀⠈⠀⡀⠀⢠⣤⢀⣤⡄⠈⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿
⣿⣿⣿⣿⣿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠋⣸⡛⣻⡏⣹⡟⣻⡛⣿⣌⣿⣙⣿⡽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠙⠛⠛⠉⠛⠋⠛⠉⠙⠋⠈⠋⣉⣤⣤⣤⣤⡀
⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⣤⣀⠀⠀⠀⠀⠀⣴⡿⠋⢩⣽⣟⠉⠙⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⣦⡌⠙⣧⣀⣤⣤⣼⡟⠁⠀⠛⠉⠉⠛⢧⣀⡀⠀⠀⢀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠉⠁⠀⠈⠉⠀⠛⠋⠁⠉⠉⠛⢦⣀⠀⠀⠀⠀⠀⠉⠉⠓⠊⠉⢁⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢟⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠘⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣤⣤⡀⢀⡀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⢨⡑⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡇⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⢠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠃⢀⣾⢿⣼⣄⠀⠀⠀⠀⣇⢀⣵⣤⠀⠀⢄⠀⠀⠀⠀⠀⠀⡘⠃⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⣿⠜⣋⣀⣀⣉⣿⣷⡀⠀⠀⠹⣏⣉⡙⣧⣄⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠲⣤⠞⠋⣠⣤⣾⠆⠀⠀⣹⠾⠋⠉⠉⠉⠻⠟⠛⠀⠀⠾⠟⠉⠉⠙⠻⡿⡇⠀⠀⢴⣤⣔⣠⡞⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡙⢃⣻⠆⣼⣧⠈⡄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠟⣀⠀⠆⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡟⠉⠀⢿⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠆⢻⡧⠀⢀⡾⠋⢻⡆⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀⠻⢆⡠⣾⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣮⡀⢀⡜⠁⠀⣸⣇⠋⠀⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣥⣼⠋⣠⣶⡄⠀⠘⢷⡀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⢀⣼⣿⠁⡈⠃⠀⠀⠛⠁⠀⢀⣼⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠏⠉⠉⡀⣤⠖⣲⠄⠛⢦⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠸⣷⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣍⡰⠶⠞⠋⡠⢶⡄⠉⠳⣶⣡⣄⣀⡀⠀⠀⠀⠁⠀⠀⢸⡿⣄⠀⠀⠁⠠⣄⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⡄⠀⠀⢸⡥⢾⡁⠀⠰⠇⢛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⣃⢾⣄⡘⠃⢀⣠⠾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠻⣦⠀⠀⠀⠀⠀⠀⠀⣠⡶⢶⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢋⣽⠶⠋⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠀⠈⢷⡄⠀⠀⠀⠀⠀⠉⠀⠈⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠉⠳⠶⠶⠶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡍⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⢦⣀⠀⠀⠀⠀⠀⣠
⣄⡀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠛⢷⣶⣤⣤⣶⡿
⣿⣧⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣠⡿⠉⠉⠁
⣿⣿⡆⠀⠀⠀⠘⢰⣿⠃⠀⠀⠀⠹⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⣰⡟⠁
⣿⣿⣿⣶⣦⢢⠄⣼⣿⠀⠀⠀⠀⠀⠹⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡟⠃⡀
⣿⣿⣿⣿⣿⣇⠰⣿⣿⣤⣄⠀⠀⠀⠀⠸⣿⣧⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣾⠿⠿⠋⣁⠰⠂⠀⠀⣀⣴⣾
⣿⣿⣿⣿⣿⣟⣻⣍⣙⣻⠿⠿⠿⣷⣶⣶⣶⡿⣧⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣶⣶⡶⠿⠛⠛⢋⣁⡀⠠⡤⠆⣀⠴⢶⣉⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣂⣈⣉⡉⣥⣈⣉⡉⠙⠿⠛⠛⠛⠛⠛⠛⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⣺⡀⢈⣉⣴⣶⣷⣶⣿⣶⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣍⠛⣛⣛⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣷⣶⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡟⠉⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠀⠀⠈⠉⠀⠙⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⣽⣿⡄⢳⠜⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⠏⠀⠀⢰⡸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠄⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣿⣿⣿⣿⣤⡀⢀⢾⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣶⣿⣿⣿⣿⣿⣿⡅⢸⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⣿⣿⣿⣿⣿⣿⣿⣷⣾⣦⣴⣄⡀
⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠉⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣿⡿⢏⣿⢀⢿⣿⣿⣿⣿⣿⡿⠛⠶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢉⠁⢸⡏⡸⠀⠙⣽⣿⣿⡿⣿⣿⠶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢐⣇⠔⣿⡿⣁⠀⢀⣿⣿⡿⠀⠀⠉
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⡏⢉⣿⡁⡀⢹⠛⣿⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢌⠋⡀⠜⠉⠁⣸⣧⣿⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠁
⣿⣿⡿⢿⣿⠿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣷⣷⣾⣶⣾⣶⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠛⠉⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠁⠙⠆⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢀⣠⠞⠙⠛⠓⢦⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⢠⠆⠀⢀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠈⠙⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⣸⣀⡴⢋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠛⠛⠳⢤⠞⡹⢯⡀⣾⠀⠀⠀⠀⠀⠀⠀⠸⡇⣀⣀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⢀⡴⠶⢦⠏⠀⠀⣙⣿⡀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠈⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⠀⠀⢀⠋⠀⠀⠣⣀⠀⠀⠙⢦⣷⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣿⠀⠀⢸⡤⠤⢄⣠⠏⣿⠲⣄⣀⣿⠁⠀⠀⠀⠀⠀⡀⠀⠑⣤⣤⣤⣄⣀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⠀⠀⣼⠀⠀⠀⣟⢰⣷⢀⡼⠛⢿⡆⠀⠀⠀⠀⠰⠀⠀⢠⡇⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣿⠀⠀⢾⠀⠀⠀⠈⠉⠉⢁⣀⣀⣿⠀⠀⠀⠀⠀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠘⠷⠤⠤⠶⡖⠊⠉⠀⢀⣏⣀⣤⣤⣄⣀⣃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢈⡟⠉⠁⠀⠈⠉⠉⠙⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⣷⡆⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠛⠛⠓⠒⠶⠶⠶⠖⢃⠀⠀⠀⠈⣯⣷⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢈⡟⠀⠀⠀⠀⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠱⡄⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣼⠃⠀⠀⠀⠀⠀⢀⡏⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⢷⠀⠀⠀⠀⡀⠀⠈⣇⠀⢰⡃⠀⢀⡀⠀⠀⢀⣾⡴⠶⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⡧⣴⠚⠛⠙⢺⣏⣁⣀⡼⠉⠑⠛⠤⣄⣠⡟⠀⠀⠀⢸
⠀⠀⢀⣤⢤⣀⣀⠀⢀⣀⣠⡤⠶⠶⠾⠧⠘⣦⡶⠛⠉⠉⠀⠀⠀⠀⠀⠀⢠⡾⠁⢻⡄⠀⠀⣸
⠀⠀⢸⠃⢸⠀⣼⠁⢹⣏⣀⣠⢄⣀⣠⡴⠟⠁⠀⠀⠀⢀⣀⣀⡠⠤⠤⠴⠋⠀⠀⢸⠇⠀⠀⡏
⠀⠀⢸⣧⡏⠀⢸⠗⠉⢩⢿⡇⣾⠉⠁⣀⣠⠤⢖⡖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢧
⠀⠀⢸⢿⢁⡜⠁⠀⠀⢸⣾⠃⢈⠓⡏⠁⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⡆
⠀⠀⢸⣾⡟⠀⠀⠀⠀⢸⣿⠀⣾⣻⠁⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠸⡇
⠀⠀⠀⠙⠁⠀⠀⠀⠀⠘⡿⢠⣿⡗⠤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣯⣤⠼⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⣧⣄⣀⣀⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⠒⠦⣤⣀⣉⣉⣲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠋⠈⢉⣀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣴⡾⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⠿⠿⠟⠛⡛⡟⠻⠿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⣛⣫⣡⣴⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠰⣏⠀⠙⢦⡀⢰⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢀⡔⠁⢀⣹
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠸⣿⣿⣿⣿⠏⠀⠀⠀⠀⣼⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻⡀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⢞⢉⡩⠟⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⣉⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠀⠘⣇⠀⠀⠘⠫⣉⠉
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⢀⡞⠁⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⣠⠖⠲⣄⠀⢿⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⠀⢸⣀⣀⣀⣤⣤⡴⢾⠀⠀⠀⠀⠀⠀⠷⠲⢤⣼⠀⢸⡇⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠘⣏⠉⠀⠀⠈⣠⠎⠀⠀⠀⠀⠀⠀⠈⠲⠖⠃⠀⢸⣇⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⢿⣿⣧⠀⠀⠈⠓⠶⠶⠚⠁⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢸⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠴⠖⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠞⠁⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢀⣤⣶⠤⣄⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢠⡾⣿⣿⣷⣾⠃⠀⠀⠀⠀⣠⠟⠀⠀⠀⣠⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠺⠤⠭⣿⣿⡏⠀⠀⠀⣠⠞⠁⠀⠀⢀⡴⣅⣠⠟⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠚⠛⠒⠶⠦⣤⣀⢻⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡼⠋⠀⠀⠀⠀⡇⠀⣀⣽⢀⡴⠁⡵
⠀⠀⠀⣀⣤⠶⠶⠾⢧⣄⣀⣤⠶⠶⠦⢤⣤⣉⡛⢧⡀⠀⢀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⣹⡄⠈⠁⣈⡷⠊⠁
⠀⠀⡾⠋⠀⠀⠀⠀⠀⡟⠋⠀⠀⠀⠀⠀⠀⠉⣿⠀⡙⣷⣿⣷⣾⣷⣿⢉⠻⣦⣀⠀⠀⢀⣠⠞⠉⠻⣾⡃
⠀⠀⠓⡞⠀⠀⠀⢀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠘⣏⠠⢙⠟⡀⢸⡷⢤⣉⡛⠛⠋⠁⣀⣤⠶⠋
⠀⠀⠀⠛⢾⣇⣈⠏⠉⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠈⠠⠘⠶⠋⠈⠀⠀⡇⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠉⠁⠀⣀⠀⠀⠀⠀⠀⠀⢀⡿⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣠⣾⣿⢷⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⣴⣿⡟⠁⣸⣧⠀⠀⠀⠀⢻⣿⣿⣶⣶⣤⣴⣷⣀⠀⠀⠀⢸⠃
⠀⠀⠀⣠⣾⣿⠋⣰⣾⣿⣿⣆⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠏
⠀⢀⣼⣿⡿⠁⢀⣿⠏⠸⣿⣿⣶⣿⠟⠋⠀⠈⠛⠻⠿⠿⠿⢿⣿⣿⣥⣄⣀
⣠⣿⡿⠋⢀⣧⠞⠁⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣦
⠙⠛⠷⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣥⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣁⣀⣉⠙⠛⠃⠀⢀⠝⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣤⣽⣆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣷⣾⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⢤⣤⡤⣤⣤⣤⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣺⣴⡉⠿⣬⠟⠛⠓⠋⠉⠀⢴⣾⡏⢳⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡟⠶⣋⢛⣽⠟⠉⠀⠀⠀⠀⠂⡠⠀⠐⠙⠙⠟⠗⢿⢿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡭⣝⠟⣷⡏⠔⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠈⠛⢢⢙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡈⣷⣦⡔⣀⠉⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢃⠈⠀⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣻⣏⢻⠙⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡋⠀⣴⠉⣋⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣧⠀⠈⠉⠁⠉⢁⠀⠢⣀⠀⠀⡀⢀⠀⠀⠀⣴⠂⠀⠀⠐⠀⡀⢀⣹⣽⣃⣼⢿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠛⠛⣿⣿⡷⣟⣤⣐⣀⣐⣾⣛⡀⠀⠁⠀⣈⠳⡦⣮⣁⣀⣻⣆⡀⠙⣿⣿⢍⣬⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣟⣿⣿⣯⣿⡯⠦⣾⣟⣲⣶⣾⣭⡇⣽⣿⣿⣿⣿⣯⣥⣤⣼⣥⣶⣾⣯⢥⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣿⣼⣷⣉⣉⡈⠉⠛⠋⠉⠉⠹⠿⠿⠾⠛⢷⣭⠿⢿⣿⡛⠛⣿⣟⣛⣿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⡿⣿⢿⠿⡿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠉⠀⠀⠀⠀⠁⣼⡿⣟⣭⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡟⣻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⣀⣸⣟⣻⣿⣽⣿⣿⣿⣿⣿⣿⣿⠟⣗⣦⣠⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠄⠉⡙⠛⠻⠒⠿⠗⠿⠿⠟⠛⠛⠻⠛⠛⠛⠋⢉⣁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⠀⠀⠄⠠⠀⠀⣀⡀⠀⠀⣀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠷⢦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠤⣒⠼⠟⠛⠛⠻⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠈⠉⠛⠅⠢⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⣀⣀⣠⣤⣤⣷⣵⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠶⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⡾⠛⢿⣿⣿⣿⠇⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠸⣿⣯⠀⢟⠙⠿⠿⠟⠉⠛⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠱⣄⡀⠉⣀⣞⡤⣺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⡕⠾⣦⣤⣠⣤⣒⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠛⠛⠋⣁⢼⣿⠙⠉⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡶⣄⡈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢉⣴⠿⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⢀⠞⠟⢷⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠩⠀⠘⡀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⠀⢀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣀⣀⣀⣤⣤⣤⣤⣄⠤⠤⠀⠐⠀⠂⠀⠀⠀⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠋⠉⠉⠉⠀⠀⠀⠀⠀⠒⠲⠬⣵⣒⡢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠒⠊⠉⠀⠀⠀⠀⢀⣀⡠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠮⠍⣀⠀⠀⠀⠈⠉⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠴⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣴⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡡⠤⠤⠄⡀⠀⠀⠀⡀⠀⠀⠒⠒⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢔⢴⡲⠂⡨⡳⡄⠉⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠁⠀⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠍⠀⠉⡽⠪⠬⠕⠂⠀⠀⠀⠀⠒⠒⠂⠤⠄⣀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⡀⠊⡀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢄⠠⠤⠀⢀⢀⠀⠀⠌⠀⠀⠀⠀⢤⣭⠤⣠⣐⡄⠉⠓⠲⣂⠁⠀⠐⣈⠄⠊⠀⡊⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠁⠀⠉⠁⡆⡤⣤⡔⢉⠔⠖⠲⢤⠍⠛⡼⡛⠋⣨⡻⢟⢛⠢⠦⣀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡠⠊⡦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠶⣽⠐⢁⠌⢠⠆⢘⡌⠀⠀⣤⠞⢁⣄⠀⠳⣄⠁⠀⠉⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠠⡁⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠠⠚⠒⠴⣁⠴⣋⢠⣾⡯⠉⠰⠃⠀⠰⢨⠉⠙⠻⠖⡀⠀⠀⠳⠤⡄
⠀⠀⠀⠀⠀⠀⢀⠱⠄⠀⠀⠈⠁⠀⠂⠀⠀⠀⠀⢀⠠⢀⣨⢞⡡⢛⢟⡠⠂⠀⠠⢀⠃⡐⠀⠀⡆⣰⠀⡇⠀⢸⠀⠁
⠀⠀⠀⠀⠀⠀⢨⠀⠀⠑⠢⠤⢀⣀⣀⣀⣂⠨⠤⠀⠊⠁⠀⡀⡙⢂⠊⠀⢀⡄⠠⠂⡔⢀⠌⣰⢧⠀⠀⠠⠂⠘⠄
⠀⠀⠀⠀⠀⠀⠈⢄⢆⠀⠀⠀⢀⣀⡠⢄⠒⠢⠬⠀⠀⠀⢈⠔⢠⠧⠤⢤⡤⢴⣱⡾⣶⣁⡴⢉⡟⡤⢊⠵
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢄⡀⢨⠀⠁⠀⠀⠀⠀⠀⡠⠐⠁⢠⠁⠀⠀⡘⠀⠁⠆⢈⡶⠉⡳⢿⣫⢿⡁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣉⠒⠤⠀⠀⠀⠀⠐⠉⠀⠀⠀⠂⠀⠀⢰⠀⠀⠀⡰⣉⣦⣦⠟⠿⠮⢅⡱⡈⠢⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠠⠤⠼⢦⡒⠗⠙⠽⡀⠂⡀⠈⠀⠀⠈⡹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠤⣀⡈⠂⢄⠀⣆⠀⡀⡀⣘⠶⢽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⢀⠜⡉⡟⠻⠳⡮⢧⡸⢀⡧⢄⡠⡿⠉⠒⢤⣉⠀⢁⠤⠂⠁
⠀⠀⠀⠀⡠⢒⠀⣶⡷⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣠⠔⢡⡆⠵⣡⡄⢉⡾⠊⠀⠠⢐⠨⢷⣆⠄⢠⣤⠴⠛⡧⢄
⠀⠀⠀⡞⠳⣿⠧⠄⠠⠀⠤⡖⢣⠀⢀⣀⠀⠠⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠈⠲⠏⠃⣞⣈⣹⠞⠃⣈⠢⣤⣀⠻⠿⠓⡸⢁⣀⠀⣀⣰⠶⣄⠀⠂
⠀⠀⠀⡇⠈⠁⠀⡤⠨⠢⣠⠁⡰⠠⢀⠀⠄⠀⠀⠁⣀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠰⠎⣨⡞⡉⠜⡡⠀⠁⠁⠈⠑⠠⢎⡠⠋⢉⡭⠛⣲⡾⠋
⠀⠀⠀⠀⠰⣾⣒⠀⠀⢁⣁⠐⠕⠁⠂⠤⠀⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠌⡩⠙⡩⢀⠀⠀⠀⠂⠀⠂⠄⠐⠂⠀⠐⠐⢀⠢⠀⠤⠖⠀⠤⠒⠂⠀⠐⠂⠐⠀⡀⠂⢀⠤⠖⠀⡐⠈⡡⠔⠤⠖⠠⠒⠠⠂⠠⠄

⠀⠀⠀⠀⢀⢰⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣆⣀⡆⠃⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠐⢻⡟⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⣦⡀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⢾⡷⡴⠂
⠀⠀⠀⠀⠀⣞⡷⠀⠀⠀⠀⠀⢀⣯⣍⠁⠀⣻⣇⠀⠀⠀⠀⠀⢰⢿⠀⠀⠀⠀⠀⠀⢀⣀⡿⣇⢣
⠀⠀⠀⠀⡀⠘⠃⢀⠀⠀⠀⠀⠘⢿⡿⠃⠀⢏⠉⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⢠⡄⢠⣼⣼⣦⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⣻⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡟⠀⠀⠀⠀⠀⠀⡞⣿⡦⠓⠀⠀⠀⠀⠀⠀⣠⡾⣷⡄
⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⣰⠿⣬⠁⠀⠀⠀⠀⠀⠀⠓⣿⡄⠀⠀⠀⠀⠀⢀⡼⢻⡄⠸⣿⡀
⠀⠀⠀⠀⠰⠁⢸⠀⠀⠀⠀⠀⠀⠞⠁⠀⠈⠳⡄⠀⠀⠀⠀⠀⠰⠁⡇⠀⠀⠀⠀⠀⠏⠀⠞⠀⠀⠻⠇

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣶⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢈⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⠐⣿⠂⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⣤⣾⣿⡇⠀⠀⠀⠀⠀⣀⣤⠟⠻⢿⠀⠀⠀⠀⠀⠀⠼⣿⠄⠀⠀⠀⠀⠀⣶⣾⣷⣶⣶⣦
⠀⠀⠀⠀⠘⠿⠿⠁⠀⠀⠀⠀⠾⠉⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢶⠠⢠⡄⡄⡦⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠙⢾⡗⠋⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠀⠀⠁
⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⢀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡄⠀⠀⠀⠀⠀⠀⠀⡎⠋⡇
⠀⠀⠀⠀⠀⡃⠃⠀⠀⠀⠀⠀⠀⣸⠀⠀⠓⠂⡄⠀⠀⠀⠀⠀⡞⠀⣇⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀

⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿
⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢉⣉⡑⠢⡀⠀⠀⣀⣤⠴⠶⠖⠲⣆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠈⢁⣤⣬⣥⡰⠀⢰⠁⠀⣰⣚⣉⡙⠻
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠙⠒⠀⠚⠁⠀⡇⠀⣎⡑⠀⢚⣃⡤⠖⠂⠐⠢⢄⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠷⠂⠀⠀⠀⠀⣇⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠀⠀⠀⠀⠀⠀⠻⢤⣤⠤⣤⠀⠀⢀⡤⠶⠶⣤⣀⠀⠀⠀⠙⡄
⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠉⠲⠦⢤⣄⠀⠀⠀⠀⠀⠀⡾⢀⡴⠋⠀⠀⠀⠀⠈⠳⣄⠀⠀⡇
⣿⠀⠀⠀⠀⠀⠀⢀⡞⠁⠈⢳⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⡇⡎⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠊
⣿⠀⠀⠀⠀⠀⠀⢸⢡⡖⢁⠘⠧⡀⠀⠀⠀⣿⠀⠀⠀⠀⢰⠃⡄⠀⢀⡀⠀⠀⢀
⣿⠀⠀⠀⠀⠀⠶⡞⢸⡗⢍⣙⠧⠸⠀⢠⠖⢻⣖⢢⡀⢀⡾⠀⡇⢰⣡⠚⠋⠙⠫⣍⠉⠙⠒⢄⡀
⣿⠀⠀⠀⠀⠸⠇⠀⠈⣇⠀⠀⢀⡖⠀⡾⠀⠀⠙⣿⠓⠋⠁⢀⠇⠈⢿⣦⡾⠃⠀⠈⠇⠀⡴⢚⠃⠑⡄
⣿⠀⠀⠀⠀⠀⠳⡇⠀⢹⠀⠀⠸⢤⣼⠃⠀⠀⠀⣿⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⠷⠏⠀⢠⠃
⣿⠀⠀⠀⠀⠀⠀⠸⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠓⣦⠀⠀⠀⠀⠀⠀⢠⠞⠀⢠⣄⢀⡰⠃
⣿⠀⠀⠀⠀⠀⠀⠀⠳⡀⢱⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣰⠏⠀⠀⢹
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢝⡒⣚⠿⠛⠛⠢⢤⡀⠀⠀⠀⠘⡇⠀⠀⠀⢀⡟⠀⠀⣠⠞⠀⣀⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⣀⡀⠀⣼⠃⠀⠀⠀⠀⢡⠀⠀⠀⢈⣧⠐⠋⠀⣠⠞⠉⠙⣧
⣿⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⡽⠧⣀⡀⠀⠀⠀⠈⠓⠒⠊⠁⢧⠀⠀⢠⠃⠀⠀⠀⣸
⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡼⢡⠞⠙⢏⠳⡄⠀⠀⣀⣀⠀⠀⢸⠀⠀⡎⠀⠀⠀⢠⠏
⣿⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢀⡾⠁⠃⢰⠶⠮⡀⠃⠀⡸⢁⣌⣳⡄⠘⠀⠀⡇⠀⣀⠴⠃
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢀⡞⠀⢸⠀⢸⠛⠛⠁⡆⢀⡟⠫⠭⠟⠛⢾⠶⠖⡟⠋⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠋⠀⠀⠈⡄⠸⡀⠀⢠⠁⢸⠃⠀⠀⠀⠀⡜⠀⠀⠃
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣇⠀⢧⠀⠈⠙⠋⠀⠀⠀⢀⠜⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠙⢷⡀⠀⠸⡀⠈⠛⠛⣻⠟⠁⠀⡴⠋⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠈⢳⡀⠀⢹⣤⠔⠋⠀⠀⣠⠞⢀⣠⣄⠀⠀⠀⢸⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣄⣀⣤⠤⠴⠛⢮⡁⠈⠛⠶⠶⠚⢁⡴⠋⠀⠈⠑⢦⣀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠤⠖⠉⠀⠀⠀⠀⠀⠀⠈⠉
⣿
⣿

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