RAINBOW Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠋⠈⠉⠉⠉⠉⠉⠙⠒⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⠀⣀⡀⠤⠀⠐⠂⠒⠒⠒⠂⠤⢄⣀⠀⠀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⢀⡤⠒⠉⠀⠀⢀⡀⠤⠤⠤⠤⠤⠀⣀⠀⠀⠈⠐⠤⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣠⠞⠁⠀⠀⠀⠈⠀⠀⢀⣀⡀⠀⢀⣀⣀⡀⠀⠉⠒⠤⡀⠀⠑⢄⡀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⡠⠊⠀⡠⠂⠁⠀⠀⠐⠈⠀⢀⣀⡀⠀⢀⣀⣀⠉⠉⠒⠤⡀⠈⠑⢀⠀⠉⢦⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡔⠁⡠⠊⢀⠤⠊⢀⡠⠔⠊⠉⠁⠀⣀⣀⣀⠀⠀⠉⠑⠂⢄⡀⠑⢄⡀⠑⢄⠀⠱⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡜⠀⡔⠁⡠⠁⣀⠔⠁⢀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠉⠐⠠⠀⠀⠈⠢⡀⠑⢄⠀⠳⡀⠱⡀⠈⡆
⠀⠀⠀⠀⠀⠀⣀⠼⠤⠴⣀⡜⢀⣎⣀⡔⠁⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠈⠢⠀⠣⠀⠱⡀⢱⠀⢰
⠀⠀⠀⠀⣀⠎⠁⠀⠀⠀⠈⠖⠋⠁⠀⠈⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⢱⣀⠷⠤⠷⡀⣦⠚⠁⠒⠒⠒⠐⠢⡀
⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠊⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⡄
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⢄⠀⠀⠀⠀⠀⠀⡠⠒⠠⠔⠚⠁
⠀⠀⠈⠒⠢⠤⠒⠉⠑⠤⠀⣀⣀⣀⡠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⢶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙⠓⠶⢤⣀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠀⠀⠀⠈⠉⠙⠓⠦⣄⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢀⣠⣶⠾⠿⠿⠿⠿⢶⣦⣄⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⣿⠇⠀⢀⣀⣠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠘⣆⠀⠀⢀⣠⣤⣷⣤⣄⡀⠀⢹⣧
⠀⠀⠀⠀⠀⢰⣿⣠⡾⠟⠛⠛⠿⣶⣄⣤⣤⣼⣧⣤⣀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⢸⣤⣾⠟⠉⠁⠀⠈⠙⠻⣦⡘⣿
⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠈⠛⠉⠁⠰⠶⢭⣙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣀⣠⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⢀⣴⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢷⣤⡀
⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠘⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠙⠻⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣌⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣮⣭⣋⣠⣤⣶⣧⡀⠀⠀⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣤⣤⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉⠻⠷⠶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠉⠐⢄⡀⠀⠂⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⡘⠀⢀⣀⡀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⣀⣀⠘
⠀⠀⠀⠀⣀⡷⠛⠋⠉⠙⢠⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢀⠀⡠⠊⠉⠙⠛⢷⣀
⠀⡰⠖⠛⠉⠉⠀⠀⢀⣄⡐⠋⠙⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠙⢂⣤⡀⠀⠀⠉⠉⠛⠲⢆
⠀⠁⠀⠀⠀⠀⢠⡞⠉⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠉⣳⠄⠀⠂⠀⠀⠈
⠀⠀⢳⡄⠀⠀⠀⢻⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡀⢀⣠⠏⠀⠀⠀⢠⡟
⠀⠀⠀⠷⣤⣤⣤⣤⠟⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠋⠳⣤⣤⣤⣤⠾




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⣀⣠⣤⣶⣶⣶⣿⣿⣿⣷⣶⣶⣤⣤⣀⡀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠿⠿⠛⠛⠛⠋⠙⠛⠛⠛⠿⢿⣿⣿⣶⣤⡀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠋⠉⢠⣤⠀⠀⠀⢰⣿⠄⠀⠀⢀⣤⡀⠈⠙⠻⣿⣿⣷⣄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⣠⣾⣿⡿⠋⢁⡀⠀⠀⠈⠋⠀⠀⢀⣀⣀⣀⠀⠀⠈⠛⠁⠀⠀⣀⠈⠙⣿⣿⣧⡀⠀⠀⢠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠻⠟⠀⢀⣤⠶⠛⠋⠉⠉⠉⠉⠉⠛⠲⢤⣀⠀⠘⠿⠃⠀⠈⠻⣿⣿⣄⠀⠈⠁
⠀⠀⠀⠀⢀⡀⠀⠀⢠⣿⣿⡟⢁⣤⡀⠀⠀⣠⠞⠉⠀⣀⣤⣶⣶⣿⣿⣶⣶⣦⣄⡀⠈⠳⣦⡀⠀⠀⣤⡄⠹⣿⣿⣆⠀⠀⣀⡀
⠀⠀⠀⠀⠈⠁⠀⢠⣿⣿⡏⠀⠀⠛⠁⢠⡞⠁⢀⣴⣾⠟⠋⠁⠀⠀⠀⠀⠈⠉⠻⢿⣦⡀⠈⠳⣄⠀⠛⠁⠀⠸⣿⣿⡄⠀⠉
⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⣤⡄⠀⣠⠏⠀⢠⣾⡟⠁⠀⣀⣤⠶⠞⠳⠶⢦⣄⠀⠀⠙⣿⣆⠀⠹⣆⠀⣠⣤⠀⢹⣿⣿⡀⠀⢀⡀
⠀⠀⠀⠻⠀⠀⢸⣿⣿⠁⠀⠙⠁⢠⡏⠀⢠⣿⠏⠀⢀⡼⠋⠀⠀⠀⢀⡀⠀⠙⢷⡄⠀⠘⣿⣇⠀⢹⡄⠘⠋⠀⠈⣿⣿⡇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣿⣿⡇⢀⣀⠀⠀⣾⠀⠀⣿⡏⠀⠀⣾⠁⠀⠀⢺⣷⣿⡗⠀⠀⠀⢻⡄⠀⢸⣿⡀⠀⢷⠀⢀⣀⠀⢹⣿⣿
⠀⠀⠰⠖⠀⢀⣿⣿⡇⠘⠛⠃⢠⡇⠀⢸⣿⠁⠀⢸⡇⠀⠀⠀⠈⠿⠟⠁⠀⠀⠀⢸⡇⠀⠀⣿⡇⠀⢸⡄⠘⠟⠀⢸⣿⣿⡀⠀⠲⠆
⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠈⠁⠀⠘⠛⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠛⠃⠀⠈⠁⠀⠀⠀⠀⠛⠛






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡶⠶⠶⠶⠶⢦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⢀⣀⡤⠤⠤⠶⠶⠤⠤⢄⣀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⣀⣠⡤⢤⣄⣀⡀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⡴⠁⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠙⣆⠀⠀⠈⢿⡄
⠀⠀⠀⠀⢠⡿⠀⠀⠀⡼⠁⠀⠀⠀⡴⠃⠀⠀⣀⣤⠶⠶⠶⢦⣤⣀⠀⠀⠙⢆⠀⠀⠀⠈⣆⠀⠀⠈⣷
⠀⠀⠀⠀⣸⠇⣀⣤⣴⣁⠀⠀⠀⡜⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠈⠙⢷⡄⠀⠈⢇⠀⣠⣴⠾⠶⣤⡀⢸⡇
⠀⠀⠀⠀⣿⡾⠋⠁⠈⠙⠷⠞⠛⣛⡳⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣸⡾⠉⠀⠀⠀⠈⠹⣮⣷
⠀⠀⣰⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠻⠿⣤⡀
⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠸⣇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠈⠛⢷⡆⠀⠀⠀⠀⠀⠀⣤⣤⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣜⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠟⠁
⠀⠀⠀⠀⠈⠻⣄⡀⠀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⠷⠶⠞⢷⣄⣀⣠⡴⠏
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣶⣤⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣠⣾⣿⣿⡿⠟⠉⢀⣤⡀⠀⠀⠀⣴⣶⠀⠀⠀⠀⣠⡀⠀⠉⠻⢿⣿⣿⣦⣄⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⢀⣴⣿⣿⡿⠟⠁⠀⠀⠀⠘⠿⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠙⠻⣿⣿⣦⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣾⣿⡿⠋⠀⠠⣿⡦⠀⠀⢀⣠⡤⠶⠶⠚⠛⠛⠓⠶⠶⣤⣀⠀⠀⠀⢰⣿⠆⠀⠙⢿⣿⣿⣄⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⣀⣀⣤⣤⣤⣤⣀⡀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠶⠆⠀⠀⣾⣿⣿⠋⠀⢾⡷⠀⠀⣰⠟⠁⠀⣠⣶⣿⠿⠟⠛⠛⠛⠛⠻⠿⣿⣦⣄⠀⠈⠳⣄⠀⠀⣿⡷⠀⠹⣿⣿⣇⠀⠀⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⢀⡾⠁⠀⣠⣾⡿⠋⠁⠀⠀⣀⣀⣀⡀⠀⠀⠈⠙⢿⣷⣄⠀⠙⣦⠀⠀⠀⠀⠀⢹⣿⣿⡆
⠀⠀⠀⢀⡀⠀⠀⢰⣿⣿⠇⠀⣴⣶⠀⢠⡟⠀⠀⣼⣿⠏⠀⠀⣠⡶⠟⠋⠉⠉⠛⠻⢦⣄⠀⠀⠹⣿⣆⠀⠘⣧⠀⢰⣶⡄⠀⢿⣿⣿⠀⠀⢠⣦
⠀⠀⠀⠘⠃⠀⠀⣿⣿⡿⠀⠀⠈⠁⠀⡾⠀⠀⣼⣿⠃⠀⢀⣾⠋⠀⠀⣀⠀⣀⡀⠀⠀⠹⣦⠀⠀⠹⣿⡆⠀⠸⡆⠀⠉⠀⠀⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢀⣠⡀⠀⢸⠇⠀⢠⣿⡇⠀⠀⣾⠃⠀⠀⠀⣿⣿⣿⡗⠀⠀⠀⢹⣇⠀⠀⢿⣿⠀⠀⢿⠀⢀⣠⡀⠀⣿⣿⣷
⠀⠀⠀⠶⠀⠀⢸⣿⣿⠃⠘⠻⠃⠀⣾⠀⠀⣾⣿⠀⠀⢸⡏⠀⠀⠀⠀⠙⢿⠟⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⡇⠀⢸⡆⠘⠻⠃⠀⢿⣿⣿⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠉⠀⠀⠛⠛⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠛⠃⠀⠈⠃⠀⠀⠀⠀⠘⠿⠟






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⣿⠛⡿⠿⣿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠸⠀⠀⢸⠀⢀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⠂⢀⡠⠅⠰⠒⠀⠐⠆⠤⣈⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠓⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠈⠁⣀⡔⠊⠑⠢⠤⣀⡠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⢆⠈⡰⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⠀⠀⠈⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡁⠀⠀⠏⠙⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⢱⠒⡛⠤⣀⠴⠒⠚
⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠒⠒⠒⠒⠒⠾⢄⡉
⠀⠀⠀⠀⠀⠀⠀⢀⣐⣒⡀⣈⢆⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀
⠀⠀⠀⠀⠀⡖⠉⠉⠀⠀⠀⠀⢫⠳⡀⢀⡜⠁⠀⠀⠀⣀⠤⠖⠒⠒⠒⠒⠤⢄⡀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢰⢊⡄⣨⠟⠁⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠈⢣⠀⡀⠄⣀
⠀⠀⠀⠀⠈⠒⠲⣀⢀⡤⠤⠊⠉⣰⡏⠀⠀⡰⠋⠀⠀⣀⠴⠒⠋⠉⠙⠒⠦⣄⠀⠀⠈⢆⠀⠀⠀⢏⠀⠀⠈⠓⠒⠖⠂⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⡸⠁⠀⢀⠞⠁⣀⡠⢤⠤⠤⢄⠀⠈⠳⡀⠀⠹⣇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢰⠁⠀⢠⠃⠀⡶⠋⠀⠀⠀⠀⠀⠑⡄⠀⠱⠀⠀⢻⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠌⠀⠀⡌⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⡇⠀⠀⠠⠀⠀⡀⣀⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠚⠢⠴⠣⠤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⠧⣀⡰⢇⣀⡠⠛⠒⠊⠁





⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠘⠄⠀⠃⠀⠂⠠⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢀⠔⠂⠈⠀⠀⠀⠈⠀⠢⡈⠠⠆⠀⡠⠠⢄⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠠⡀⡹⠀⠀⠀⠀⠉⠀⢑
⠀⠀⠀⠀⠠⠤⣀⠁⢠⠀⢀⣄⡀⠀⠀⠀⠀⠀⠉⠈⠀⠀⡽⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠈⠀⠀⠀⠀⠄⠀⠆⠀⠀⠀⠀⢣⡀⢄⠀⢀⣀⠜⠉
⠀⠀⠀⠀⠐⠤⠤⠀⠰⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠀⠠⠤⣀⠂⠉⠁
⠀⠀⠀⠀⢀⣀⠤⠭⠤⣣⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⢀⠅⠀⠀⠀⠀⡸⠑⢠⠞⠀⠀⡠⠔⠊⠉⠉⠉⠉⠒⠤⡀⠀⠈⢢
⠀⠀⠀⠘⠤⡄⠀⣀⡠⠒⢡⠋⠀⢠⠊⠀⢀⡠⠤⠒⠦⠤⡀⠀⠈⣦⠀⠀⢱⠊⠉⠢⠤⠤⠠⠄
⠀⠀⠀⠀⠀⠈⠉⠀⠀⢠⠃⠀⠰⠁⠀⡔⢁⣠⠤⠄⠤⣀⠈⠢⡀⠘⣇⠀⠀⡆⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠇⠀⡌⠀⡞⠁⠀⠀⠀⠀⢣⠀⢡⠀⠸⡀⠀⢰⠀⠀⠀⢀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡨⢄⣀⣇⡰⠀⠀⠀⠀⠀⠀⠀⡀⢨⡀⢀⡀⠀⡼⠤⠔⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡶⠶⠶⠶⠶⢦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⢀⣀⡤⠤⠤⠶⠶⠤⠤⢄⣀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⣀⣠⡤⢤⣄⣀⡀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⡴⠁⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠙⣆⠀⠀⠈⢿⡄
⠀⠀⠀⠀⢠⡿⠀⠀⠀⡼⠁⠀⠀⠀⡴⠃⠀⠀⣀⣤⠶⠶⠶⢦⣤⣀⠀⠀⠙⢆⠀⠀⠀⠈⣆⠀⠀⠈⣷
⠀⠀⠀⠀⣸⠇⣀⣤⣴⣁⠀⠀⠀⡜⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠈⠙⢷⡄⠀⠈⢇⠀⣠⣴⠾⠶⣤⡀⢸⡇
⠀⠀⠀⠀⣿⡾⠋⠁⠈⠙⠷⠞⠛⣛⡳⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣸⡾⠉⠀⠀⠀⠈⠹⣮⣷
⠀⠀⣰⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠻⠿⣤⡀
⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠸⣇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠈⠛⢷⡆⠀⠀⠀⠀⠀⠀⣤⣤⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣜⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠟⠁
⠀⠀⠀⠀⠈⠻⣄⡀⠀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⠷⠶⠞⢷⣄⣀⣠⡴⠏
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⠀⠀⢀⡆⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⡀⠀⠀⠹⠄⠀⠈⠀⠀⠘⠃⠀⡄⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠉⢀⡤⠔⠂⠉⠉⠉⠉⠉⠑⠲⢄⡀⠚⠁⢀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠈⣣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠉⢀⡄⡔⠉⠀⠉⠲⠤⢤⠤⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⢦⠀⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠃⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠁⠀⠀⠀⣵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠀⠀⡌⠀⠀⠸⠋⠓⠀⠀⠀⠀⠀⡀⡀⢀⠠⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠉⠁⠀⠀⠀⠀⠀⠀⢳⡤⠶⢆⡀⢀⡤⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⠤⢄⣸⠀⠒⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠄⠘⡆⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⡠⠤⠔⠒⠒⠂⠒⢜⢆⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢨⠀⠑⢤⣾⠃⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠈⠉⠓⠦⣀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠘⣅⠔⢠⡞⠁⠀⠀⡠⠊⠁⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠈⠳⡀⠀⠀⠀⢳⣀⠔⠒⠦⣀
⠀⠀⠀⠀⠀⠈⠉⠳⣄⡠⠖⠒⠋⠀⢠⠻⠁⠀⢀⠞⠁⠀⠀⣠⠖⠋⠉⠁⠀⠉⠉⠓⢦⡀⠀⠀⢜⣆⠀⠀⠀⢣⠀⠀⠀⠈⠉⠙⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠎⠀⠀⢠⠞⠁⣠⣤⠦⠶⠒⠢⢄⡀⠀⠙⢄⠀⠀⢿⡄⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡼⠀⠀⢠⠏⠀⢮⠎⠀⠀⠀⠀⠀⠀⠙⣆⠀⠈⡆⠀⠈⣱⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⡟⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⠀⠀⢸⠀⠀⠀⢰⠀⠀⠀⠀⣠⠎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠷⣄⡠⢧⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⣸⡀⠀⣸⡀⠀⣀⠗⠢⠖⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠀⠉⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠚⠉⠉⠉⠉⠉⠉⠐⠒⠒⠢⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠁⠀⢀⡀⠤⠐⠒⠒⠒⠒⠒⠂⠒⠒⠂⠤⢄⣀⠈⠙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠔⠊⠀⠀⠀⠀⢀⡠⠤⠒⠂⠈⠉⠉⠉⠉⠉⠀⠀⠐⠒⠠⠄⡀⠀⠀⠈⠓⢤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢀⠔⠀⠀⠀⣀⠔⠁⠀⠀⠀⢀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⠀⠀⠈⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠠⠃⠀⠀⢀⠎⠀⠀⠀⢀⠔⠊⠀⠀⠀⢀⡀⠤⠄⠀⠀⠤⠄⣀⡀⠀⠀⠀⠀⠀⠑⠢⣀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡰⠁⠀⠀⡐⠁⠀⠀⠀⠘⠁⠀⢀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⢄⡀⠀⠀⠀⠀⣱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢠⠁⠀⠀⡔⠀⠀⠀⠐⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡤⠖⠁
⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠇⠀⠀⠀⠀⠀⣤⣀⣄⣀⡀⠀⠀⡔⠁
⠀⠀⡴⠋⠀⠀⠀⠀⠈⠙⠢⣀⠔⠂⠁⠀⠀⠀⠀⠀⠈⢓⣬⠀⠄⣀⡀
⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡗⠀⠀⠀⠈⠳⡄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠡⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⢤⠁
⠀⠀⠈⡾⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠢⢀⡀⠀⢀⣂⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⣀⣀⡠⠤⠚⠀⠙⠢⢤⣀⡀⠀⠀⣀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣚⣛⣛⣛⣛⣳⠶⣤⣀
⠀⠀⠀⠀⠀⢀⣴⢞⣭⢞⣫⡭⠷⠶⠶⠾⣭⣟⡷⣭⡳⣤
⠀⠀⠀⠀⣠⢟⣵⢫⡶⣫⡵⠞⠛⠉⠉⠛⠳⢮⣟⢮⡻⣮⢳⡄
⠀⠀⠀⣰⣏⡾⣱⢏⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡹⣞⢷⢻⡄
⠀⠀⢀⣟⣼⢱⢇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣹⡞⣧⣿
⠀⠀⠘⠋⠀⠉⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠋⠉⠀⠙⠃⡀
⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣷⣦⣄
⠀⠂⠄⠠⠤⠀⠠⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠄⠀⠤⠀⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⣠⡄⡄⠠⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⠿⣗⢮⣟⢮⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⡄⠈⢳⡝⣮⢳⡝⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠐⡲⠂⠒⠐⠂⠒⠐⠀⠲⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠿⠛⠛⠁⠀⠀⢿⣸⡏⣿⡹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢸⣇⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣛⣘⣿⢸⣧⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠈⠀⠀⠀⠀⠁⠀⠑⢤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣮⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⣄⣀⣤⣀⣠⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣤⣶⣺⣿⣿⣿⣿⣲⢤⣀
⠀⠀⠀⢀⡴⣯⣾⣽⣺⡿⠭⠽⣿⡾⣝⢯⡳⡄
⠀⠀⢠⣞⣞⣿⡵⠋⠀⠀⠀⠀⠀⠉⢻⡷⡽⣿⣆
⠀⠀⣾⢾⣾⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⡽⢽⡄
⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷

⠀⠀⠀⠀⢀⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠈⣉⡉⢉⡉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⠈⠻⡿⡽⣟⣆
⠀⠀⠀⠀⠀⠀⠁⠁⠁⠁⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠁⠀⠀⣿⢻⢹⡼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠸⡟⣇⣿⠀⠀⠀⠀⠀⠠⡠⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣷⣾⡁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈
⣦⣴⣦⣴⣤⣶⣤⣶⣶⣶⣶⣶⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢢⠀⠘⠂⠀⠇⢀⠀⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢁⠤⠐⠀⠁⠀⠈⠐⠂⢄⠘⠀⡄⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⢒⠁⠀⠀⠉⠐⠈⠑⡄
⠀⠀⠀⠀⠀⡀⠀⠐⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠑⠀⠀⢱⠇⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠀⠚⠙⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⠀⠀⢀⣀⣀⡁⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣀⣀⡀⢀⠋⠍⠂⠐⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠤⠀⢡⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⠈⠁⠂⢄
⠀⠀⠀⠀⡔⠒⠋⠉⠉⠑⡗⠀⢀⡔⠁⠀⠀⣀⠠⠄⠀⠀⠤⢀⡀⠀⠀⠑⢄
⠀⠀⠀⢠⠁⠀⠀⠀⠀⢐⡡⢠⠏⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢣⣀⠤⢄
⠀⠀⠀⠀⠁⠡⠤⠔⠒⠁⠠⠋⠀⢠⠊⠀⢀⠔⠊⠉⠀⠉⠙⠢⡄⠀⠘⣆⠀⠀⢃⠀⠀⠉⠙⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠃⠀⡰⠁⣠⠖⠉⠉⠉⠒⡄⠈⢆⠀⠹⡀⠀⠸⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⢠⠁⢠⠁⠀⠀⠀⠀⠀⠈⡄⠈⡄⠀⠇⠀⠀⠄⠀⠀⢀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠚⠠⠘⠤⠎⠀⠀⠀⠀⠀⠀⠀⠢⡠⢆⡠⠇⣀⠔⠓⠂⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠤⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠉⢀⣀⡀⠤⠤⠤⠤⠤⢀⣀⡀⠉⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⣀⠤⠒⠉⠁⣀⣀⣤⠠⠤⠤⣄⣀⣀⠈⠉⠲⢤⡀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡠⠚⠁⣀⠤⠒⠉⠁⣀⣀⠠⡤⠄⣀⣀⠈⠉⠒⠤⣀⠈⠓⢄⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡠⠊⠀⡠⠊⠁⣠⠔⠊⠉⠀⣀⣀⣀⣀⣀⠀⠉⠑⠢⣀⠈⠑⢄⠀⠑⣄⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡜⠁⣠⠎⠀⡠⠊⠀⡠⠔⠊⠉⢀⣀⣀⣀⠀⠉⠑⠢⣄⠈⠑⢄⠀⠱⡄⠈⢦⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢀⣜⡀⣰⠃⢀⠞⠀⡠⠊⠀⡠⠖⠋⠁⢀⣀⡀⠈⠙⠲⣄⠀⠑⣄⠈⠣⡀⠘⣄⠀⣧⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠚⠉⠉⠉⠉⠓⢮⡀⡼⠁⢠⠎⠀⡠⠚⠉⠁⠀⠈⠉⠲⢄⠀⠳⡀⠈⢆⠀⡱⠖⠋⠉⠉⠉⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⣁⢀⠇⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠱⡀⣈⡞⠁⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⢀⡤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡦⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢤⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠈⠣⣄⣀⡤⠤⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⣀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⡴⢤⣀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠓⠲⠤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠴⠚⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠒⠛⠛⠛⠛⠛⠛⠛⠛⠒⠶⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠋⠉⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠉⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⢀⣠⠤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⢤⣀⠀⠀⠈⠙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡠⠞⠋⠀⠀⠀⣀⣤⠴⠖⠒⠛⠛⠛⠛⠛⠛⠒⠶⢤⣄⡀⠀⠈⠙⠶⣄⠀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢀⠴⠋⠀⠀⢀⡤⠖⠋⠁⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⠙⠳⢦⡀⠀⠈⠛⢦⡀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢁⡴⠃⠀⠀⣠⠞⠉⠀⢀⣤⠶⠚⠋⠉⠉⠀⠀⠀⠀⠉⠉⠙⠓⠶⣤⣀⠀⠀⠙⠷⣄⠀⠀⠙⢷⣄⠀⠀⠻⣆
⠀⠀⠀⠀⠀⢠⠞⢀⠀⣰⠋⠀⠀⣠⠞⠁⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠈⢷⣄⠀⠀⠙⣦⡀⠀⠙⣧
⠀⠀⠀⠀⢠⡏⠀⢀⡼⠁⠀⢀⡼⠃⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠙⢦⡀⠀⠈⢻⡄⠀⠘⣧
⠀⠀⠀⠀⡞⠀⢀⡞⠁⠀⢠⠞⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⢳⡄⠀⠀⠻⣆⠀⠘⣧
⠀⠀⠀⣸⠁⢀⡾⠀⠀⣰⠋⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠹⣆⠀⠀⢹⡆⠀⠹⡆
⠀⠀⢀⡏⠀⣼⠁⠀⡴⠃⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠘⣦⠀⠀⢻⡄⠀⢿⡀
⠀⠀⢸⠃⣰⣇⣀⣼⠁⢠⠏⢀⣤⠖⠒⠒⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣷⡀⠘⣧⢀⡬⠷⠒⠺⢧⣄
⠀⠀⣸⠋⠉⠀⠀⠉⠓⢯⡴⠏⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠈⠉⠳⢤⡼⠋⠀⠀⠚⠉⠀⠙⣆
⢠⡴⠟⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠙⠲⠶⠞⢻⡄⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠞⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⢰
⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣀⣰⢦⣀⣀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⣀⣀⣀⣴⣤⣀⡀⣀⣀⡴⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣿⣿⣿⣷⣶⣶
⣿⣿⣇⣤⣍⣤⣮⣬⣧⣥⣾⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠋⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠒⠒⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⢀⡀⠤⠐⠂⠉⠈⠉⠉⠉⠉⠉⠉⠁⠒⠢⠤⣀⡈⠙⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⡀⠄⠊⠁⠀⠀⠀⠀⠀⣀⡀⠀⠠⠄⠀⠀⢀⡀⠀⠀⠀⠈⠑⠢⢄⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⠀⠊⠀⠀⠀⢀⡠⠔⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠤⢀⠀⠀⠉⠢⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠐⠁⠀⠀⢀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡠⠂⠀⠀⢀⠔⠁⠀⠀⢀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠀⠀⢑⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⡐⠀⠀⠀⠔⠁⠀⠀⡠⠒⠁⠀⠀⡀⠤⠒⠈⠉⠀⠀⠉⠁⠒⠢⠄⣀⠀⠀⠀⠀⠉⠢⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡜⠀⠀⢀⠊⠀⠀⠀⠊⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⢠⠔⠈⠉⠉⠑⠂⢦⡀⢀⡤⠀⠒⠈⠉⠉⠑⠒⢄⡀⠁
⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡠⠚⡏⠉⠉⠉⠒⢄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠔⠁⠀⠀⠀⠀⠈⠇
⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⣀⡸
⠀⠀⠁⡴⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠙⢆
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢄⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⢀⣀⣀⠤⠖⠁⠙⠢⢄⣀⠀⠀⠀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⠀⠀⠀⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⢉⡠⠄⠒⠒⠀⣀⡀⠐⠒⠀⠤⢈⠑⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢁⠔⠊⡠⠔⠂⣉⡉⠤⠤⠤⠈⠁⡁⠂⠤⡈⠒⢄⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⠔⢁⠔⢁⠄⢊⡡⠄⢒⣂⣀⣀⢒⠂⠄⢁⠂⢄⠑⢄⠑⢄⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡰⢁⠔⢡⠞⡡⢊⠥⢒⠩⠄⠐⠒⠒⠀⠬⢁⠢⢁⠢⡈⠀⠐⠄⠑⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡐⢀⠊⡰⢁⢎⠔⡡⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡑⠌⢀⠁⡀⠂⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⣰⣁⡎⣐⢠⣃⣎⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣂⣀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠉⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠁⠀⠀⠀⠉⢂
⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠑⠤⠄⠀⢄⡀⠀⠀⠀⢀⡠⠀⠠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⠠⡀⠀⠀⠀⠀⢀⠄⠀⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠈⣁⡠⠤⠤⠤⠤⠤⠄⢀⡉⠐⠢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⡠⠔⠊⣁⠠⠄⠒⠒⠒⠒⠂⠀⠤⢀⡉⠒⠤⡈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⢁⠔⠉⡠⠒⢉⠠⠐⠒⣀⣉⠉⣉⣁⡐⠒⠤⢈⠑⠢⡀⠐⢄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡔⢁⡴⢋⡠⠊⡡⠔⣊⠥⠤⠐⠒⠒⠠⠤⢉⡒⠤⡉⠢⡈⠐⠀⠑⡄⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠎⢠⠊⡠⠊⡴⢋⠔⣉⠄⠒⠉⠉⠁⠉⠉⠑⠂⢌⡐⢌⠐⠈⠢⡈⠢⠈⢀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠎⢰⠁⡜⢠⠊⡔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⠌⢂⠐⡀⠁⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣁⠼⠤⢇⣘⡠⠧⠮⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡌⠄⠤⢀⡀⠤⠨⠄⣀
⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀
⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠑⠤⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠐⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠉⠀⠉⠉⠉⠉⠁⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⣀⠠⠐⠂⠀⠈⠀⣈⡉⠁⠀⠂⠀⢀⠈⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢁⠰⠊⠁⠀⠀⠀⠉⢀⠀⠀⣀⠈⠀⠐⠠⠀⠁⠀⡀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠁⠀⠂⠀⠀⠀⣁⠀⠠⠀⠀⠀⠀⣈⠀⠀⠀⠁⠀⠈⠢⡀⠱⡀
⠀⠀⠀⠀⠀⠀⡘⢀⠎⠀⠊⠀⠈⡠⠒⠁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠑⢄⠀⢄⠐⡀⠱
⠀⠀⠀⠀⢀⡠⠅⠌⡠⢀⣊⡠⠂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠑⠀⠁⡀⢂⠘⡀⢀
⠀⠀⠀⠠⠁⠀⠀⠀⠑⠉⠀⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⠑⠐⠂⡵⠊⠀⠂⠁⠐⢀
⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠑⠄⣀⣀⠠⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠢⠤⡀⠀⠠⠒⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠛⠉⠉⢉⣀⣀⣀⣀⣀⡉⠉⠉⠛⠛⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉⢁⣠⣤⠶⠖⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠳⠶⣤⣄⡀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⣀⡴⠞⠋⠁⣀⣤⡴⠶⠖⠛⠛⠛⠛⠛⠛⠛⠓⠶⢦⣤⣀⡈⠙⠳⢦⣄⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣴⠞⠉⢀⣤⠶⠛⠉⣀⣠⣤⠴⠶⠶⠶⠛⠶⠶⠶⠶⣤⣄⣀⠉⠙⠳⣦⣀⠈⠻⢦⡀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢀⣴⠟⠁⣠⡾⠋⢀⣠⡶⠛⠉⢁⣀⣤⣤⠴⠶⠶⠶⠦⣤⣤⣀⡈⠉⠛⠶⣤⡀⠙⠳⣄⡀⠙⢦⡀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⣠⡟⠁⣠⠟⠁⣠⡾⠃⢀⡴⠛⠁⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣄⠈⠙⢶⣄⠈⠻⣄⠀⠻⣆⠀⠹⣆
⠀⠀⠀⠀⠀⣰⠏⠀⣴⠏⠀⣴⠋⢀⣴⠋⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠙⢷⡀⠘⢷⡀⠘⣧⡀⠹⣦
⠀⠀⠀⠀⢠⡟⠀⣸⠇⢀⡾⠁⢠⡾⠁⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⢻⣄⠈⢷⡀⠘⣷⠀⠹⣆
⠀⠀⠀⠀⣿⠀⢰⡏⠀⣼⠃⢀⡿⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢻⡄⠈⣷⠀⠸⣇⠀⢻⡄
⠀⠀⠀⢸⡇⠀⣾⠀⢰⡏⠀⣼⠁⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣿⠀⠸⣇⠀⢿⡀⠘⣇
⠀⠀⠀⣼⠁⢠⣯⣤⣼⣁⣀⣟⣀⣼⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⣧⣤⣿⣤⣼⡇⠀⣿
⠀⣠⣤⠿⣶⠋⠁⠀⠀⠉⠛⠟⠉⠀⠀⠀⠉⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡾⠛⠛⠛⠋⠁⠀⠀⠀⠈⠙⢷⣿
⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣄
⠹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠈⠙⠛⢷⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⡷⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠞
⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⣤⠾⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⣤⡶⠶⠋⠛⠲⠶⠶⠞⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⢈⣁⠀⠤⠤⠤⠀⣀⡉⠐⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⡠⠔⠈⣁⠤⠀⠀⠀⠀⠀⠤⢀⡉⠂⢄⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡠⠊⡠⠒⢁⡠⠐⠒⠀⠉⠀⠐⠂⠄⡈⠒⢄⠉⢢⠈⢢
⠀⠀⠀⠀⠀⠀⠀⡜⢀⠌⢀⠎⢀⠔⢁⠤⠒⢉⣁⣀⣈⡉⠐⠠⡈⠑⢄⠑⡄⠑⡀⠡
⠀⠀⠀⠀⠀⠀⣐⡠⠮⠤⣇⡠⠁⡐⠁⡠⠊⣁⠤⠤⠤⢀⠑⠢⡈⠢⠈⢢⣈⡤⠴⢄⣡
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠙⣞⠀⠎⢀⠊⠀⠀⠀⠀⠀⠑⠄⠑⡀⢡⠞⠁⠀⠀⠀⠈⢣
⠀⠀⢀⠴⠒⠃⠀⠀⠀⠀⠀⠀⠈⠙⠢⢦⡀⠀⠀⠀⠀⠀⠀⡸⠤⠋⠉⠀⠀⠀⠀⠀⠀⠀⠓⠢⡄
⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡼
⠀⠀⠀⠈⠉⠉⠉⠒⠒⠒⠢⢤⡠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⢤⡠⠴⠒⠒⠒⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠋⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠒⠒⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⢀⡀⠤⠐⠂⠉⠈⠉⠉⠉⠉⠉⠉⠁⠒⠢⠤⣀⡈⠙⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⡀⠄⠊⠁⠀⠀⠀⠀⠀⣀⡀⠀⠠⠄⠀⠀⢀⡀⠀⠀⠀⠈⠑⠢⢄⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⠀⠊⠀⠀⠀⢀⡠⠔⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠤⢀⠀⠀⠉⠢⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠐⠁⠀⠀⢀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡠⠂⠀⠀⢀⠔⠁⠀⠀⢀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠀⠀⢑⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⡐⠀⠀⠀⠔⠁⠀⠀⡠⠒⠁⠀⠀⡀⠤⠒⠈⠉⠀⠀⠉⠁⠒⠢⠄⣀⠀⠀⠀⠀⠉⠢⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡜⠀⠀⢀⠊⠀⠀⠀⠊⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⢠⠔⠈⠉⠉⠑⠂⢦⡀⢀⡤⠀⠒⠈⠉⠉⠑⠒⢄⡀⠁
⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡠⠚⡏⠉⠉⠉⠒⢄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠔⠁⠀⠀⠀⠀⠈⠇
⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⣀⡸
⠀⠀⠁⡴⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠙⢆
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢄⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⢀⣀⣀⠤⠖⠁⠙⠢⢄⣀⠀⠀⠀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠤⠤⠤⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠁⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠈⠉⠐⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⢀⡠⠄⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠢⢄⡀⠀⠈⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⢀⠤⠊⠁⠀⠀⣀⠤⠤⠄⠒⠒⠒⠒⠒⠒⠀⠤⠤⢀⡀⠀⠀⠑⠢⢀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⡠⠚⠁⠀⣀⠔⠊⠁⠀⠀⢀⣀⢀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠈⠑⠢⢄⠀⠀⠑⢤⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢠⠎⠀⠀⡤⠊⠀⠀⣀⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢄⠀⠀⠉⠢⡀⠀⠙⢆⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡰⠁⠀⡠⠊⠀⢀⡴⠊⠀⠀⣀⠤⠒⠈⠉⠉⠉⠈⠉⠈⠁⠒⠤⣄⠀⠀⠉⠢⡀⠀⠈⢢⠀⠀⠱⡀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡜⠀⠀⡔⠁⠀⡠⠋⠀⢀⠔⠈⠀⠀⣀⠠⠄⠐⠒⠒⠒⠠⠤⣀⠀⠀⠉⠢⡀⠀⠈⢢⠀⠀⠱⡀⠀⠘⡄⠀⠘⡀
⠀⠀⠀⠀⠀⠀⢰⠁⠀⡘⠀⠀⡘⠀⠀⡔⠁⠀⡰⠁⠀⢀⠔⠉⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⠉⠢⡀⠀⠈⢢⠀⠀⠱⡀⠀⠑⡀⠀⠘⡀⠀⢱
⠀⠀⠀⠀⠀⠀⠆⠀⢠⠃⠀⢰⠁⠀⡐⠀⠀⡜⠀⠀⡐⠁⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠉⠑⢄⠀⠈⠢⡀⠀⠱⡀⠀⠱⡀⠀⠱⠀⠀⢡⠀⠀⡄
⠀⠀⠀⠀⠀⢰⠀⠀⡌⠀⢀⡧⠤⠴⢅⠀⠰⠀⠀⡜⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠱⠀⢀⠵⠒⠂⠓⢄⠀⠇⠀⠈⡄⠀⢰
⠀⠀⠀⠀⠀⣠⠤⠐⠃⠴⠋⠀⠀⠀⠀⠑⡆⢀⡠⣁⡀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠳⠁⠀⠀⠀⠀⠀⠱⣰⠀⠀⡇⠀⢘
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠈⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⡿⠒⠠⣄⠀⢸
⠀⠀⠀⢀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠒⠒⠂⠠⣀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⡄⢸
⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⡠⠊⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠐⠢⡀
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠡⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⡀⠤⠚⠁⠀⠀⠣⡀⠀⠀⠀⣀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠠⠔⠋
⠀⠀⠀⠈⠐⠒⠀⠒⠚⠣⡀⠀⠀⠀⠀⡠⠧⣀⠀⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠈⠉⠀⠈⠐⠠⠄⣀⣀⠠⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠛⠉⠉⠉⠉⠉⠛⠓⠲⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠁⠀⣀⠤⠴⠒⠒⠛⠛⠛⠓⠒⠲⠤⢄⣀⠈⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢀⡤⠚⠉⠀⣀⡤⠤⠒⠒⠒⠒⠒⠒⠦⢤⣀⠈⠙⠢⣄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢠⠎⠀⢀⠔⠁⠀⡠⠖⠋⢁⣀⡤⠤⠤⠤⠤⠤⢤⣀⡀⠈⠙⠢⣀⠈⠙⢦⡀⠈⠳⣄
⠀⠀⠀⠀⡰⠃⢀⡴⠁⠀⡰⠊⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠈⠳⣄⠀⠙⢦⠀⠙⣦
⠀⠀⠀⡰⠁⢠⠎⠀⢠⠎⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠈⢧⡀⠈⢳⡀⠈⢧
⠀⠀⢠⠃⢠⠏⠀⡰⠃⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠱⡄⠀⠹⡄⠘⣇
⠀⠀⡞⢀⡏⠀⡼⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠙⣆⠀⢻⡀⢸⡄
⠀⢀⣇⡼⠤⢜⣀⠞⣠⠖⠚⠓⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢼⣆⠘⣆⡴⠓⣚⡳⣄
⢀⣸⠁⠠⠀⠀⠉⠛⠁⠀⠤⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡎⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⢸⡆
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠳⣄⣀⣠⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⢀⣄
⠀⠀⠉⠁⠳⣄⡀⠀⠀⣀⡀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⢦⡀⠀⠀⢀⣀⠀⠀⢁⡼
⣶⣶⣶⣶⢶⣶⣿⣿⣿⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣷⣾⣿⣿⣷⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠐⠒⠉⠉⢉⣉⡉⠉⠉⠁⠒⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢁⡠⠤⠒⠉⢉⣉⠀⠀⠀⢀⣉⠉⠐⠢⠄⣀⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⡠⠒⢁⡠⠔⠊⣉⣀⠠⠤⠤⠤⠤⠀⣈⡁⠐⠤⣀⠑⠢⡀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⡴⠋⡠⠒⢁⡤⠒⢉⡠⠤⠒⠒⠒⠒⠒⠂⠤⣈⠑⠢⣀⠑⠢⡈⠢⡀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢠⠊⣠⠎⢠⠔⢁⠔⢊⡥⠐⣊⡉⠤⠤⠤⠌⣉⡒⠠⢈⠒⢄⠑⢄⠈⢢⠈⠢⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡰⠁⡰⠁⡔⢁⠔⣡⠞⡡⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡑⠂⠑⢄⠑⠄⠑⡀⠡⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢠⠁⡸⢀⡜⢠⠋⡔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠑⠄⢢⠈⠄⠐⡀⠡⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠤⠧⠴⠧⣼⠤⠧⠾⠴⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠼⠄⠧⠨⠄⠵⠠⠦⢨⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠈⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⠢⠤⠤⠤⠔⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠂⠤⠤⠤⠤⠒⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠈⣉⠉⠉⠉⣉⠉⠐⠒⠦⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⡁⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⡉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⡀⠀⢁⠄⠀⢈⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢈⠀⠠⢀⠀⠀⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⡠⠊⡠⠂⠀⠀⢈⠀⠀⢀⠉⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⢀⠁⠀⠈⠢⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠊⠠⠊⡠⠊⠀⠊⠠⠀⠈⠄⠀⠀⠂⠀⠀⠀⠀⠀⢈⠀⠀⡁⠠⠈⠠⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠠⠀⠐⠀⠈⠀⠂⠐⢁⠄⠈⡠⠔⠒⠉⠉⠉⠉⠉⠑⠒⢤⡈⠂⠈⠢⡈⠀⠐⠄⠀⡀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⢀⠀⠐⠀⠀⡐⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠠⠈⠀⠀⡀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⢸⢀⣂⣴⢤⣆⡀⢀⠂⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠐⡀⠄⠀⠈⣤⡦⣴⣄⣰
⠀⠀⠀⠀⢀⣀⡿⠋⠙⠀⠀⠀⠁⣄⣀⡀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢀⣀⣀⠊⠀⠀⠀⠋⠙⢷⣀⡀
⠀⢠⡶⠛⠟⠁⠈⠀⠀⠀⢀⣤⡀⠾⡉⠛⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠛⢉⠷⣀⣤⡀⠀⠀⠀⠁⠈⠛⠛⢶⡄
⠀⠈⠀⢀⠀⠀⠐⠀⢢⡶⠚⠋⠉⠡⡔⠄⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠠⠢⠈⠀⠙⠛⢳⡔⠀⠂⠄⠀⡀⠀⠁
⠀⠀⢱⡇⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⢸⡞
⠀⠀⠀⢻⡆⠀⠀⠀⠀⠸⢦⣤⣤⣄⣤⡜⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢳⣤⣤⣤⣤⡾⠃⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠈⠻⠶⣶⢶⣦⡶⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠙⢶⣴⡶⣶⠶⠟⠁






⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠤⠤⠤⠠⠤⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠁⠀⢀⡀⠀⠀⠄⠀⠄⠀⢀⡀⠀⠀⠉⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⣀⠤⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⢀⠀⠈⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⢀⠔⠊⠀⠀⡀⠤⠐⠂⠁⠈⠉⠁⠈⠉⠉⠈⠀⠒⠠⢄⡀⠀⠉⠢⢄⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⠔⠁⠀⡠⠂⠁⠀⢀⡠⠤⠀⠒⠒⠀⠀⠐⠒⠂⠤⠄⡀⠀⠈⠑⠤⡀⠀⠑⢄⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠔⠁⠀⡰⠋⠀⢀⠔⠊⠁⠀⢀⡀⠤⠤⠄⠠⠄⠠⢀⡀⠀⠀⠁⠢⣀⠀⠈⠢⡀⠀⠑⡄⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⡔⠀⢀⠎⠀⢀⠊⠀⢀⠔⠁⠀⡠⠔⠉⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠉⠒⢄⠀⠈⠱⡄⠀⠘⢄⠀⠈⢄⠀⠘⡄
⠀⠀⠀⠀⠀⠀⡐⠀⠀⠎⠀⢠⠃⠀⡠⠃⠀⡠⠊⠀⢀⠤⠂⠉⠀⠀⠀⠀⠀⠀⠉⠐⠤⡀⠀⠑⢄⠀⠈⢂⠀⠈⢆⠀⠈⠆⠀⠐
⠀⠀⠀⠀⠀⢠⠁⠀⡌⠀⠀⠇⠀⠠⠁⠀⡐⠁⠀⡔⠁⠀⢀⠤⠒⠈⠀⠉⠈⠁⠒⢄⠀⠈⠢⡀⠀⠣⠀⠀⢣⠀⠈⠆⠀⠈⡄⠀⢃
⠀⠀⠀⠀⠀⡀⠀⢠⠁⠀⣘⣀⣠⡃⠀⡰⠀⠀⠌⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠱⡀⠀⡣⠄⠀⠦⡀⠘⡀⠀⢃⠀⠈
⠀⠀⠀⠀⠀⣆⠤⠸⢤⠔⠁⠀⠀⠈⠲⡁⢀⣘⡀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠎⠀⠀⠀⠀⠈⢂⡅⠀⠘
⠀⠀⠀⠀⠐⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠏⠀⠀⠈⠱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠓⠐⠂⠀⠀⠀⠀⠀⠀⠈⠗⠀⢬⠀⠀⠃
⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠐⠒⠂⠠⢄⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⢀⠔⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁⠒⢄
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠑⢄⡀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠆⠤⠤⠀⠒⠉⠀⠀⠀⠁⢄⡀⠀⠠⠤⠀⠬⠢⡀⠀⠀⠀⠀⠀⠀⢀⠔⠓⠂⠐⠂⠁
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠢⢄⡀⣀⡠⠚⠑⠠⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠒⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⠠⠤⠀⠤⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⣀⠤⠔⠒⠈⠉⠉⠈⠁⠀⠈⠉⠉⠉⠐⠂⠤⣀⡀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⢀⠤⠂⠉⠀⠀⢀⣀⠤⠤⠄⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠀⠈⠑⠢⣀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡠⠚⠁⠀⢀⠤⠒⠉⠁⠀⠀⠀⢀⣀⢀⡀⢀⣀⠀⠀⠀⠀⠉⠒⠠⣀⠀⠀⠑⠦⡀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣠⠊⠀⠀⡠⠊⠁⠀⢀⡠⠄⠒⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⠤⡀⠀⠀⠑⠢⡀⠀⠈⢢⡀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⢀⠔⠁⠀⡠⠊⠀⠀⡠⠊⠁⠀⢀⣀⠤⠐⠒⠒⠒⠐⠒⠐⠂⠤⢀⡀⠀⠈⠑⢦⡀⠀⠈⢢⡀⠀⠙⢄⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⠎⠀⠀⡜⠁⠀⡠⠊⠀⠀⡠⠒⠉⠀⠀⢀⣀⠠⠄⠀⠄⢀⣀⠀⠀⠈⠑⢤⡀⠀⠉⢢⠀⠀⠑⡄⠀⠈⢆⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⠎⠀⠀⡎⠀⠀⡜⠁⠀⡠⠊⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠙⢦⠀⠀⠑⡀⠀⠘⠄⠀⠈⢇⠀⠈⠆
⠀⠀⠀⠀⠀⠀⡘⠀⠀⡜⠀⠀⡜⠀⠀⡜⠀⠀⡔⠁⠀⡠⠊⠀⠀⢀⠤⠒⠉⠈⠉⠁⠁⠒⠤⡀⠀⠙⢦⠀⠀⠱⡀⠀⠘⡄⠀⠘⡄⠀⠈⡄⠀⠸⡀
⠀⠀⠀⠀⠀⠀⡇⠀⢰⠃⠀⢰⠀⠀⡸⠀⠀⡜⠀⠀⡔⠁⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⢣⠀⠀⢱⣀⠠⢰⡀⠀⠰⠀⠀⢰⠀⠀⠃
⠀⠀⠀⠀⠀⢠⠀⣀⣼⡀⡠⠊⠉⠉⠉⠢⣠⠃⠀⠰⠁⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢡⡰⠋⠀⠀⠀⠈⠑⡄⡆⠀⠘⠀⠀⢠
⠀⠀⠀⠀⠀⡜⠁⠀⠀⢸⠁⠀⠀⠀⠀⠀⠘⡄⠒⠉⠒⠤⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡤⠠⣸⠁⠀⠀⠀⠀⠀⠀⠸⣅⣀⠀⡆⠀⢰
⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢑⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⢣⠀⠸
⠀⠀⢀⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⣀⠤⠤⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠧⠤⢀
⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠈⠦⣀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀⠔⠠⠤⠤⠐⠊⠁⠀⠀⠀⠘⠤⣀⣀⢀⠤⠤⠀⠤⠣⣀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃⠒⠒⠒⠉
⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠢⣀⠀⠀⢀⡠⠊⠒⠤⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠄⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⠈⠀⠁⠀⡀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠌⡐⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠂⠀⡈⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠁⠀⡌⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠈⡄⠀⠡
⠀⠀⠀⡠⠄⠠⠚⠉⠀⠈⠁⠣⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠃⠉⠀⠈⠙⠢⠀⠤⡀
⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄
⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠂
⠀⠀⠀⠉⠂⠤⠄⠢⠄⣀⣀⠠⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢀⣀⡀⠤⠂⠤⠄⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠶⠶⠶⠶⠶⠶⠶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⣉⣠⣤⠤⠶⠶⠶⠶⠶⠶⠶⢤⣤⣀⡉⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⢁⣤⠶⠛⢉⣁⣤⡤⠶⠶⠶⠶⠶⠶⠦⢤⣄⣈⠉⠛⠶⣤⡈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⢁⣠⠞⠉⣠⡴⠞⠋⣁⣠⡤⠴⠶⠶⠶⠶⠶⠦⣤⣄⡉⠙⠳⢦⣀⠙⠳⣄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣠⠞⠁⣴⠟⢁⣴⠞⢁⣠⠶⠛⢉⣀⣤⠴⠶⠶⠶⠶⠶⠤⣤⣀⠉⠛⢦⣄⠉⠳⣄⠈⠳⣄⠈⢷⡀
⠀⠀⠀⠀⠀⣰⠋⢠⡞⠁⣰⠟⢁⡴⠋⢁⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡈⠳⣦⠈⠳⣄⠘⢷⡀⠹⣆
⠀⠀⠀⠀⣸⠃⢠⠟⢀⡼⠁⣠⠟⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠈⢳⡄⠘⣦⠀⢳⡀⠹⣆
⠀⠀⠀⢰⡇⢠⡟⠀⡾⠁⣰⠃⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠹⡆⠘⣧⠀⢷⠀⢹⡄
⠀⠀⠀⣾⠀⣼⠁⢸⠃⢰⡏⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⢻⡀⢸⡆⠘⣇⠈⣧
⠀⠀⢠⡇⢀⣿⣤⣿⣀⣼⣀⣼⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢘⣧⣤⣧⣤⣿⠀⢿
⢀⣤⠾⠷⠏⠁⠀⠀⠉⠛⠉⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡞⠋⠙⠋⠁⠀⠀⠀⠈⠛⣾⡀
⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣦
⠘⠷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠘⢷⣄⡀⠀⣀⣠⡶⠦⠤⠴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣠⡴⠦⣤⣄⣤⡴⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠉⠈⠉⠉⠉⠉⠉⠒⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⢀⡠⠤⠐⠀⠀⠀⠀⠐⠒⠒⠢⠤⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠴⠊⠁⠀⠠⠐⠂⠐⠒⠒⠒⠂⠂⠠⢀⡀⠈⠒⠀⠀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠠⠖⠁⡠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠒⠂⠤⢀⠀⠁⠠⠀⠀⠢⡀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⠔⠁⡀⠈⡀⠐⠀⣀⠄⠐⠂⠀⠀⠀⠀⠀⠒⠠⢀⠈⠀⢄⠀⠠⡀⠘⠄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⡌⢀⠎⢀⠊⠀⠊⢀⠔⠉⢀⠀⠐⠀⠀⠉⠉⠁⠐⠂⠀⠀⠈⠀⢄⠑⢄⠈⢦⠈⢆⠈⠇
⠀⠀⠀⠀⠀⣀⠼⠤⠌⣠⠂⣐⣁⡔⠁⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠡⡀⠣⠀⢣⠈⡆⠀⡀
⠀⠀⠀⠀⠜⠁⠀⠀⠀⠙⠊⠀⠀⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢐⠤⠓⠒⠢⣰⠊⠁⠑⠊⠉⠐
⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉
⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⢤⡀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠊
⠀⠀⠑⠂⠤⠄⠊⠂⠄⢀⣀⣀⡀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⡇⠀⢀⡄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢠⡀⠀⠹⠀⢀⣁⣀⠘⠀⠰⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⡠⠔⠂⠉⠀⠀⠀⠈⠉⠒⠤⡈⠀⠤⠀⠀⡀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠐⣺⠀⠀⠀⠉⠑⠊⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠓⠀⠀⠱⣼⠁⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠈⠙⠒⠂⠀⡇⠀⠀⠞⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⡇⠀⠀⠀⠀⠐⠀⠀⠚⠀⠍⠀⠀⠀⠀⠀⠈⢲⠐⢦⣀⣠⠤⠔⠃
⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⢃⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠒⠢⠦⣈⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣚⣃⣈⢆⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀
⠀⠀⠀⠀⢰⠋⠉⠀⠀⠀⠀⢹⠱⣄⣠⠎⠀⠀⠀⣀⠤⠒⠒⠒⠒⠒⠢⢄⡀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢰⣣⠄⣼⠋⠀⠀⡴⠊⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⠢⡀⠀⠀⠱⣀⠤⠤⢄
⠀⠀⠀⠀⠈⠉⠣⠤⠔⠒⠊⠀⡼⠃⠀⢠⠎⠀⠀⡠⠖⠉⠉⠉⠉⠉⠒⢄⠀⠀⢻⡄⠀⠀⢹⠀⠀⠀⠉⠑⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢠⠃⠀⢀⠞⢀⣤⠖⠲⠋⠐⠢⡀⠀⠳⡀⠀⢻⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡜⠀⠀⡎⠀⡽⠁⠀⠀⠀⠀⠀⠈⡆⠀⢡⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⢀⣧⠀⢸⡀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⡇⠀⠀⣧⣀⡠⠂⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠑⠚⠙⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠒⠛⠉⠉⠉⠉⠉⠛⠓⠲⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⣀⡤⠤⠖⠒⠒⠒⠒⠒⠒⠶⠤⣄⡀⠈⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⡤⠒⠉⠀⢀⣠⠤⠤⠖⠒⠒⠶⠦⠤⣄⡀⠉⠑⠦⣄⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⡴⠁⠀⣠⠞⠁⠀⣠⠔⠊⠉⢀⣀⣠⣤⢤⣤⣄⣀⡀⠀⠉⠓⠦⡀⠈⠙⢦⡀⠀⠙⣆
⠀⠀⠀⠀⢀⠞⠀⢀⠞⠁⢀⡴⠋⢀⡠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⡀⠈⠳⣄⠀⠙⢦⡀⠈⢳⡀
⠀⠀⠀⢀⠎⠀⡰⠃⠀⣠⠊⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⢧⡀⠀⠹⣄⠀⢻⡄
⠀⠀⠀⡎⠀⡴⠁⢀⡴⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠹⣄⠀⠘⣆⠀⢻⡀
⠀⠀⢸⠀⣰⠁⢀⠞⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠘⢦⠀⠘⣆⠀⢧
⠀⠀⡇⢠⡃⢀⠎⢠⠏⢀⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠈⢧⠀⣸⡤⢼⣆
⠀⢀⡗⠉⠉⠉⠲⢯⠔⠁⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠙⠧⣬⠟⠁⠐⠒⠈⢳
⡴⠚⠀⠘⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠈⠲⠤⠴⢆⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠴⡆⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀
⠀⠀⠀⠀⠈⠳⢤⣄⣠⡴⢦⣤⣠⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣠⡴⢤⣀⣠⡴⠊
⣿⣿⠛⠿⢛⠿⡿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢖⣛⣛⣛⣛⣛⡶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⣠⡾⣫⡵⢟⣫⡭⠿⠿⠿⢭⣽⣛⢾⣝⢷⣄
⠀⠀⠀⠀⢀⡾⣫⠞⣩⢞⣫⡷⠞⠛⠛⠛⠓⠶⣽⡳⣮⡳⣜⢷⡄
⠀⠀⠀⢠⡟⣵⢫⡾⣱⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⢳⡝⣧⢻⡄
⠀⠀⠀⣾⢱⢇⡿⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢻⡼⣇⣿
⠀⠀⠰⠟⠉⠚⠓⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠞⠓⠉⠹⠇
⠀⠔⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣴⣤⣀
⠀⠄⡀⣀⣀⠀⠀⡀⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⢀⠀⠀⣀⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠉⠍⠟⠹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣗⢮⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠂⠀⠀⠀⢐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠘⠙⠙⠀⠑⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣍⠉⠛⢮⡳⣜⢷⡹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠅⢈⠂⢀
⠀⠀⠀⠀⡀⣀⢀⡀⣀⢈⠀⡀⢀⡀⡀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⠇⠀⠈⢿⡹⣎⢿⡼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠁⠀⠀⠀⠀⢸⣇⢿⡜⣷⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⣿⡎⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⠀⠀⠀⠀⠐⢄⠀⢠⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣻⣼⣶⣾⣃⣻⡇⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠁
⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣶⣶⣤⣴⣴⣤
⣿⣿⣇⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢀⣤⣾⣿⣿⠿⠛⠋⠉⠁⠀⢀⣄⠀⠀⠈⠉⠙⠛⠿⣿⣿⣦⣄⠀⠀⠲⠆
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠀⠀⠸⡿⠀⠀⠀⠙⠋⠀⠀⠀⢾⡷⠀⠀⠈⠙⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣴⣿⣿⠟⠁⢰⣦⠀⠀⠀⣀⣤⠤⠶⠶⠶⠶⠤⣤⣀⠀⠀⠀⣴⡦⠀⠙⢿⣿⣦⡀⠀⠺⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠁⣠⠖⠋⠁⢀⣀⣤⣤⣤⣤⣀⡀⠉⠙⢦⣄⠈⠁⠀⢀⠈⢻⣿⣷⡀
⠀⠀⠀⠀⠸⠃⠀⢠⣿⣿⠏⠀⠺⠗⠀⣠⠞⠁⢀⣴⣾⠿⠛⠋⠉⠉⠙⠛⠿⣷⣦⡀⠈⢳⡀⠀⠿⠇⠀⢻⣿⣷⠀⠀⠛
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⡀⠀⠀⡼⠃⠀⣴⣿⠋⠁⠀⣀⣤⣤⣤⣤⣀⠀⠈⠻⣿⣆⠀⠹⣄⠀⠀⣀⠀⢿⣿⣧
⠀⠀⠀⡶⠀⠀⣼⣿⡟⠀⠸⠟⠀⣼⠁⠀⣼⡿⠁⠀⣴⠟⠉⠀⠀⠀⠀⠙⢳⣄⠀⠘⣿⣧⠀⠹⡄⠘⠟⠀⠸⣿⣿⡄⠀⠚⠃
⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⢰⠇⠀⣸⣿⠁⠀⣼⠃⠀⠀⣾⣦⣾⡆⠀⠀⠹⡆⠀⠘⣿⡆⠀⢷⠀⠀⠀⠀⢿⣿⣇
⠀⠀⢠⡆⠀⢸⣿⣿⠀⠻⠟⠀⣾⠀⢀⣿⡇⠀⢰⡇⠀⠀⠀⠸⣿⠟⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⢸⡄⠸⠿⠀⢸⣿⣿⠀⠀⣤
⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠋⠀⠘⠟⠁⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠙⠋⠀⠈⠃⠀⠀⠀⠈⠿⠟





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠋⠉⣁⣀⣠⣤⣤⣤⣤⣤⣄⣀⣈⠉⠙⠛⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⣀⣤⠶⠚⠋⠉⣉⣀⣀⣀⣠⣀⣀⣀⣈⠉⠙⠛⠶⢤⣄⡈⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣠⡴⠛⠉⣀⣤⠶⠚⠋⠉⢉⣁⣀⣀⣀⣀⣉⠉⠙⠛⠶⢤⣄⡈⠙⠶⣄⡈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢀⣴⠞⠁⣠⡴⠛⠉⣀⣤⠶⠚⠛⠉⢉⣉⣉⣉⡉⠉⠙⠛⠶⢦⣄⡈⠙⠶⣄⠈⠛⢦⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢠⡞⠁⣠⠞⠁⣠⠞⠉⣠⡴⠛⠉⣀⣤⠶⠚⠛⠉⠉⠉⠉⠉⠙⠛⠶⢦⣄⡈⠙⠶⣄⠈⠻⣦⡀⠹⣦⠀⠻⣆
⠀⠀⠀⠀⠀⣰⠏⠀⣼⠋⢀⡾⠃⢠⡾⠋⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠈⠳⣄⠈⠳⣄⠈⢷⡀⠙⣧
⠀⠀⠀⠀⢰⠏⠀⡾⠁⢠⡟⠀⣴⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠘⢧⡀⠹⣆⠀⢻⡄⠘⣧
⠀⠀⠀⢀⡟⠀⣼⠃⢠⡟⠀⣼⠃⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⢷⡀⠹⣆⠈⢷⠀⢹⡆
⠀⠀⠀⣸⠃⢠⡏⠀⣾⠀⢰⠇⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠘⣧⠀⢻⡀⠸⡇⠀⣷
⠀⠀⠀⣿⠀⣸⣇⣠⣇⡀⣿⣀⣸⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣻⣄⣼⣧⣄⣿⠀⢹
⠀⣠⣤⣿⡾⠋⠁⠀⠉⠙⠟⠋⠁⠀⠈⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⠛⠛⠟⠋⠁⠀⠀⠈⠉⠳⣾⡇
⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⣤
⠹⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠉⠙⣧⡀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣼⠟⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⢀⣴⠦⠶⠞
⠀⠀⠀⠀⠈⠙⠲⠶⠶⠶⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠶⠚⠋⠉⠉⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⢈⡁⠡⠠⠤⠤⠀⠉⣉⡑⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢈⡠⠒⢈⡠⠄⠐⠒⠒⠒⠒⠒⠠⢌⡁⠂⢄⡑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⣡⠔⢁⠔⢊⡠⠔⠂⣉⡁⠀⠀⢉⣁⠐⠢⢄⡑⠢⡈⠢⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⠔⢁⠜⡡⠒⣁⠔⢊⡡⠤⠐⠒⠒⠀⠤⢈⡐⠢⡈⠢⣌⠢⡈⠢⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⠊⡰⢁⠔⢡⠊⡠⠂⣁⠄⠂⠀⠈⠉⠀⠒⠠⡈⠒⢄⠱⡈⠢⡈⢆⠱⡈⢂
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠆⣰⠡⠬⢤⠁⠜⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⢣⠈⠄⠱⠈⠆⠱⠈⡄
⠀⠀⠀⠀⠀⢀⡠⠦⠴⡔⠁⠀⠀⠀⠙⡤⠇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠼⡀⢣⠘⡀⢃⢸⠀⡆⢰⠄⢀
⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⡀⠤⠊⠀⠀⠁⠈⠀⠃⢰⠀⠀⠀⠘⠀⠀⠘⡄
⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⡄⢠⠀⡆⠘⠀⠀⡀⢠⠀⠀⢀⡇
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠆⠀⠀⠀⠀⠃⠚⠐⠂⠒⠘⠒⠓⠊⠀⠀⠀⠙⠄
⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠉⠙⢄⡀⣀⠔⢄⡀⠀⠀⡠⠂⠀⠒⠁⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⣀⠀⣀⠠⢄⣀⠀⢀⡠⠊





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠐⠒⠀⠢⠄⡀
⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡄
⠀⠀⠀⣠⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠔⠈⠁⠀⠉⠒⢄⠀⠀⠈⠆
⠀⠀⣰⠿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠹⡿⠿⠿⠦⠀⠀⠀⠀⠀⣈⠤⠤⣀⠃⠀⠀⠀⠀⠀⠀⡀⣣⠤⠤⠼⠄⡀
⠀⠐⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⡇⠀⠀⡜⠀⠀⠀⠀⢑⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡁
⠀⠈⠑⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠂⠐⠂⠀⠊⠀⠀⠀⠈⠑⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠢⠀⠂⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠉⠉⠉⠉⠉⠉⠙⠒⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⢀⡠⠤⠐⠒⠀⠒⠚⠒⠒⠒⠠⠤⡀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠴⠊⠁⠀⠠⠄⠒⠒⠒⠒⠒⠒⠂⠤⢄⡀⠀⠂⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢠⠖⠁⡠⠀⠀⢀⠀⠀⠀⠒⠀⠀⠐⠒⠂⠤⣀⠈⠁⠀⠀⠀⢠⡀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⠔⠁⡀⠈⡀⠐⠀⣀⠤⠐⠂⠈⠀⠀⠈⠐⠒⠠⢀⠈⠂⢄⠈⠢⡀⠙⢄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⡜⢀⠎⢀⠊⢀⠈⢀⠔⠉⢀⠠⠐⠀⠀⠉⠉⠉⠐⠂⠀⠀⠈⠂⢄⠑⢄⠈⢆⠈⢆⠈⠇
⠀⠀⠀⠀⠀⣀⠼⠤⠎⣠⠃⣐⣁⡔⠁⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠠⡀⢢⠀⢣⠘⡆⠘⡀
⠀⠀⣀⠠⠜⠁⠀⠀⠀⠙⠊⠁⠀⠀⠉⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⢰⡤⠓⠒⠦⣹⠞⠉⠑⠂⠁⠒⢤
⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⢤⡀⠀⠀⠀⠀⠀⣠⠤⠠⠤⠊
⠀⠀⠑⠂⠠⠐⠊⠒⠤⣀⣀⣀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠒⠊

⠀⣤⣄⠀⠀⣠⣴⣶⣦⣄⡀⠀⠀⠀⠀⢀⡤⢖⣒⣒⠶⣄⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⣀⢤⣒⣒⢤⡀⠀⣤⡄
⠀⠉⠃⣠⣾⢟⣭⣭⡙⢿⣿⣄⠀⠀⣠⢫⣾⣿⣿⣿⣿⣮⡳⡄⠀⠴⣿⣯⢿⡻⣯⡳⠀⣔⣵⣿⢭⢍⢳⡝⡄⠙⠁
⠀⠀⢠⣿⢣⡟⣵⣾⡽⣆⢿⣿⡄⢀⡇⣿⣿⡟⠉⠉⠻⣿⣷⢻⡀⠀⠈⠀⠀⠉⠀⠀⢸⣼⣿⣿⠿⢷⣷⣿⣸
⠀⠀⣼⡿⣼⢻⡣⣪⣿⡹⣎⣿⡇⠘⠛⠛⠛⠀⡀⠀⠀⠉⠉⢁⣥⣶⣶⣤⡀⠀⢀⣤⣾⣿⣿⣏⠀⢈⣿⣿⣿⣤⡀
⠀⠀⠉⠉⠉⠀⠀⠁⠈⠁⠉⠉⡡⠂⠀⠀⠀⠘⠋⠀⠀⠀⣰⣟⣥⠶⠶⣮⣻⣆⠻⠿⡿⠿⠿⠟⠀⠘⠿⠿⠿⠿⠿
⠀⠀⣠⣶⣾⣷⣦⣄⠀⠀⢀⣔⡒⠀⠀⠀⠀⠀⠀⡀⠀⢀⣿⣾⡵⢋⡙⣎⢿⢿⠀⠃⠄⢃⠘⠀⠀⠀⠀⠃⠐⢨
⠀⣼⣿⢋⣥⣤⡉⢿⣧⠀⢻⡿⠧⠀⠂⠀⠀⢈⢉⡁⠀⠀⣁⡁⠁⠀⠀⠈⠈⢈⠀⠀⠈⠀⢀⣀⣀⡀⠀⠈⠈
⠀⣿⠇⣾⣫⢬⣻⡆⢿⡇⠀⠀⠀⠀⢸⣡⢀⣿⢨⡇⡷⣸⣿⡨⡼⢁⣾⣤⠘⠯⡀⠀⢀⡴⢛⣭⢭⣝⠳⣤⠸⣾⠇
⠀⣿⡄⡿⠿⠟⠟⠛⠈⠋⠀⠀⣀⣀⡘⠣⠜⠸⠸⠇⠃⠙⠯⠇⠑⠊⠹⠚⠃⠠⠇⠀⣾⢡⢏⡴⠶⣌⠳⡌⢷⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣴⠟⣋⣉⣛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⣾⣼⣟⣭⠻⣷⡹⠜⠇
⠀⠰⠆⠆⡉⠘⠃⠀⢀⡾⣱⢟⣭⣭⣝⢷⡹⡆⠀⢠⣿⣮⡀⠀⣠⢞⡯⠿⠭⣗⢦⠀⠓⠛⠙⠁⠀⠀⢀⡀
⠀⠀⠛⠰⠀⠛⠀⢀⣼⣷⣯⡟⠀⠀⣸⣷⣿⣷⣤⠀⠈⠀⠀⣼⡵⣻⣞⣭⣟⢮⣿⣧⠀⠀⠀⠻⠃⠀⠚⠇⠀⣀⡀
⠀⠀⠀⣀⣀⣄⡀⢿⣿⣿⣿⡷⠆⠘⠿⠿⠿⠿⠟⠁⠀⠀⢠⣿⢿⣷⢁⢂⢈⣿⡿⣿⡆⢀⣤⡶⠾⠷⣶⣄⠀⠛⠃
⠀⢠⡾⢋⣡⣭⡙⣦⡀⠀⠀⠀⠀⠀⣄⣠⠀⢀⡶⢛⣯⣛⢦⡀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡾⢉⣴⡶⢶⣦⡙⣷⡀
⠀⣿⢣⡿⣩⣍⢻⡜⣧⠀⠀⣀⣶⡄⠛⠁⢠⣟⣾⠟⠉⠹⣧⣷⠀⠀⠶⠰⢎⡁⠄⢀⡿⢰⡿⣡⡶⣦⡙⣷⣸⣇
⠀⣿⢸⡷⣿⠽⠿⠿⠻⠀⠀⠙⠻⠃⠀⠀⣿⣾⢃⡾⢻⣇⣿⣾⠀⠦⣉⠰⠂⠁⢀⣼⣿⣿⣷⣯⠀⢸⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠉⠙⠀⠛⠀⠀⠀⠀⠈⠻⠿⠻⠿⠋⠀⠀⠙⠋⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠚⠛⠛⠉⠉⠛⠛⠓⠲⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⣁⣤⠴⠖⠛⠛⠉⠉⠉⠉⠛⠛⠲⠦⣤⣈⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⣠⠴⠛⢉⣠⠴⠖⠛⠛⠉⠉⠉⠉⠛⠛⠲⠦⣄⡉⠛⠦⣄⠙⠳⣄
⠀⠀⠀⠀⠀⢠⡞⠁⣴⠞⢁⣤⠞⠉⢀⣠⠴⠖⠚⠛⠛⠛⠛⠓⠲⠦⣄⡀⠙⠳⣤⡈⠳⣦⠈⢳⡄
⠀⠀⠀⠀⣰⠋⣠⠞⢁⡴⠋⢀⣤⠞⠉⢀⣠⡤⠶⠖⠒⠒⠲⠶⢤⣄⡀⠉⠳⣤⡀⠙⢦⡈⠳⣄⠙⣆
⠀⠀⠀⣼⠃⣰⠋⢠⠞⠁⣰⠏⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠻⣆⠈⠳⡄⠙⣆⠘⣧
⠀⠀⣸⠃⢰⠇⢠⠏⠀⡼⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠈⢧⠀⠹⡄⠸⡆⠘⣇
⠀⢀⡟⢀⡿⠚⠛⠛⠺⡅⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⣧⣠⠿⠦⢿⡀⢻⡀
⣠⠞⠉⠉⠁⠀⠀⠀⠀⠙⠛⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠶⠞⠁⠀⠀⠀⠛⠚⠳
⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸
⠀⢷⣀⡀⣀⡴⣤⣀⣀⡴⠛⠶⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠛⠦⠤⠞⠶⣤⡤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠒⠒⠒⠒⠢⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⣀⠤⠒⠋⠉⠉⠉⠉⠉⠙⠒⠦⣀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⡜⠁⠀⠀⠀⢀⡠⠖⠚⠉⠉⠉⠉⠙⠒⢤⡀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢀⡞⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⠀⠀⠹⡄⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣼⠁⠀⠀⣠⠋⠀⠀⢀⡠⠖⠒⠒⠒⠲⢤⡀⠀⠀⠀⢳⡀⠀⠀⠀⢳⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢰⠇⠀⠀⢠⠃⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢳⠀⠀⠀⠘⡆⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡼⠀⠀⠀⡞⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠈⢇⠀⠀⠀⢣⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢀⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠸⡄⠀⠀⠸⡀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠃⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢧⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠼⠦⣄⣸⠀⠀⣀⣸⣄⣀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀⠀⠀⣣⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠙⣦⠊⠁⠀⠀⠀⠑⣾⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣧⣀⣘⡇⡴⠋⠉⠑⢦⣸⣤⠴⠒⠓⠒⢦⡀
⠀⠀⠀⠀⠀⠀⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠉⠉⠉⠳⡄⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠉⠻⠃⠀⠀⠀⠀⠉⠀⠀⠐⠆⣠⠀⢱
⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠃⠀⡹⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢠⠀⠀⠀⡼
⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠦⢀⡴⠃⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘⢧
⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠙⠦⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠉⠉⠁⢳⡀⠀⠀⠀⠀⠀⠀⡼⢆⡀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣼⡏⠓⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠦⣀⣀⣀⣤⠚⠀⠀⠉⢲⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⡤⠤⡖⠋⠙⠦⣄⣀⣀⡤⠞⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⡏⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⠳⡄⠀⠀⣿⠀⠀⡴⠋⠛⠋⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢦⠀⠀⠀⡇⠀⠀⡞⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣠⠇⠀⠀⣽⠀⠀⠱⡀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⢈⡇⠀⠀⡇⠀⠀⠣⣄⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢠⠾⡄⠀⠀⠙⠦⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣠⠏⠀⣀⣀⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⢀⣴⠾⣿⣲⣄⠀⠀⠀⢀⣴⠶⠶⢶⣤⡀⠀⠀⢀⣤⠶⠶⢦⣄⠀⠀⢀⡴⠒⠙⠑⢦⡀⠀⠀⣠⢴⣲⣶⢦⡀
⠀⠀⠀⢀⣿⣷⡫⠻⣿⣿⡆⠀⢰⣟⣵⢿⣻⣷⡜⣷⠀⢠⣿⢺⠵⡶⣕⣽⡆⠀⡞⢀⡴⣛⢲⡀⢳⠀⢰⣷⢏⣥⣌⢳⣷⡀
⠀⠀⠀⠘⠁⠛⠛⠛⠙⠛⠻⠀⠿⠿⠿⠏⠈⠿⠿⠿⠇⠸⠋⠟⠏⠹⠿⠸⠿⠀⠇⠸⠗⠿⠿⠇⠸⠀⠿⠿⠞⠶⠞⠞⠿⠇

⠀⠀⠀⠀⣠⢴⣲⡤⣀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⡠⢆⣂⠆⡀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⣸⣵⡽⠒⢿⣞⡆⠀⠀⠀⣸⣿⣟⣿⣿⡀⠀⠀⡰⣰⣵⣲⣷⡜⡀⠀⠀⠀⠾⠟⠭⣭⣻⣆⠀⠀⣠⢠⣶⢤⣶⣦
⠀⠀⢠⣿⣿⡆⠀⣼⣿⣿⠀⠀⠀⣿⣿⡏⣿⣿⡇⠀⠀⠅⣿⡟⠀⣿⠁⣂⠀⠀⣺⣛⣳⡛⣏⣻⣛⡀⠀⢃⣯⠃⣄⣯⣿⡄
⠀⠀⠀⠉⢉⠁⠀⠀⠉⠀⠀⠀⢀⡉⡉⠀⠉⣉⢁⠀⠀⠃⠛⠃⠀⠛⠈⠐⠀⠀⠛⠙⠛⠃⠛⠛⠛⠀⠀⠀⠀⠘⠛⠀⠈

⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠉⠉⠉⠐⠢⢄⠀⠀⠀⠀⢸
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠑⢄⠀⠀⢸
⠀⠀⣰⣿⣿⣿⡿⠟⠛⠛⠛⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⡔⠉⠀⠀⠀⠀⠑⢄⠀⠀⠈⠆⠀⢸
⠀⠰⠟⠛⢿⡏⠀⠀⠀⠀⠀⠀⠈⠿⠛⠛⠛⠂⢄⠀⠀⠀⡠⠥⠒⠢⣜⠀⠀⠀⠀⠀⠀⢀⠄⠖⠒⠖⠚⠢⣸
⢎⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡸⠀⠀⠰⡁⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠒⠒⠛⠛⠛⠛⠓⠒⠢⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⡞⠈⠓⢄⡀⠀⠀⠀⢀⡴⠚⠁⢫⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⡸⠀⠀⠀⣀⣙⣦⣤⣞⣁⣀⡀⠀⠘⡆⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣁⡀⠀⠀⠀⢰⣣⠴⡞⠉⠁⠀⡇⠀⠀⠀⢸⠉⠙⠒⢷⣤⠤⠤⠤⠤⠽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⡅⠀⠈⠉⢉⠝⠋⠀⢀⣇⠀⠀⠀⡿⠀⠀⠀⢿⠀⠀⠀⠀⠈⠲⣄⠀⠀⢸⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢧⠀⢀⠔⠁⠀⠀⠀⠠⡧⠀⠀⠀⣛⣀⣀⠀⠛⠀⠀⠀⠀⠀⠀⠈⠳⡀⡏⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⢸⡴⠋⠀⠀⠀⠀⢀⣠⢴⣎⠛⠋⠿⠙⡋⢹⠏⠶⢦⣄⡀⠀⠀⠀⠀⠘⣧⠤⢄⣀⡈⢆
⠀⠀⠀⠀⠀⢀⡮⠤⠖⠒⠚⡿⠁⠀⠀⠀⣠⡶⣭⠩⡦⢡⡜⠃⢶⢈⠋⢶⠘⢃⠘⡑⠟⢦⡀⠀⠀⠀⠈⣆⠀⠀⠉⡹⡆
⠀⠀⠀⠀⠀⡼⠱⡀⠀⠀⡸⠁⠀⠀⢀⡴⣭⢡⡄⠰⣆⠴⠚⠉⠉⠉⠉⠑⠲⢍⠉⣉⠘⡃⣷⡄⠀⠀⠀⠸⡄⠀⡸⠁⠸⡄
⠀⠀⠀⠀⢠⠇⠀⢱⡀⢰⠃⠀⠀⢀⡾⠄⣤⠲⢦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⠈⡃⠰⠞⡄⠀⠀⠀⢹⡴⠁⠀⠀⢳
⠀⠀⠀⠀⢸⠀⠀⠀⢣⡞⠀⠀⠀⡞⠺⠀⠶⡰⠃⠀⠀⠀⡔⠒⣄⢠⠖⠓⡆⠀⠀⠈⣎⠋⢴⠜⠻⡀⠀⠀⠀⡷⠦⣀⠀⠈⡆
⠀⠀⠀⠀⢸⠀⠀⣠⠴⡇⠀⠀⢸⢥⡜⣣⣰⠃⠀⠀⣀⣀⣧⠀⣸⣇⡀⣠⣇⣀⡀⠀⠘⡴⠆⠘⠃⢣⠀⠀⠀⢸⠀⠀⠙⠲⣷
⠀⠀⠀⠀⢼⡠⠚⠁⢠⡇⠀⠀⣾⡄⠶⢀⡼⠀⠀⣞⠁⠀⠉⡏⠀⠀⠈⡏⠁⠀⢸⠆⠀⣧⣄⠙⢁⣼⡀⠀⠀⠈⣆⡠⠖⠋⢸⡄
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠁⠀⠀⠈⠉⠉⠙⠛⠒⠚⠛⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠈⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠿⠛⠛⣉⣉⣉⣉⣉⣉⡙⠛⠻⠿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡉⠛⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⣡⣴⣿⣿⠿⠛⢉⣁⣤⣤⣤⣤⣤⣤⣄⣉⠙⠻⢿⣿⣷⣤⡉⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⢠⣾⣿⡿⠋⣡⣴⣾⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣶⣤⡈⠻⣿⣿⣦⡈⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⣴⣿⡿⠋⣠⣾⣿⣿⠟⢋⣁⣤⣴⣶⣶⣶⣤⣄⣉⠛⠿⣿⣿⣦⡈⠻⣿⣷⡄⠹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⣼⣿⡿⢁⣼⣿⣿⠋⣠⣶⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣷⣦⡈⠻⣿⣿⣆⠙⣿⣿⡄⢹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⢸⣿⡿⠁⣾⣿⡿⢁⣼⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣄⠙⣿⣿⡆⠸⣿⣿⡀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⡇⢸⣿⣿⠁⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆⢸⣿⣿⡀⢿⣿⡇⠸⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠐⠟⠛⢀⡉⠛⠃⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠀⠛⢉⡁⠘⠻⠿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠛⠃⣤⣾⣿⣿⣿⣿⣷⣄⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣠⣶⣿⣿⣿⣿⣷⣤⡀⠛⠛
⠀⠀⠀⣠⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠙⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠟⠉⠉⠁⠀⠀⠀⠀⠀⠂⠀⠒⠀⠄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣿⣶⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⢀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠈⠉⠉⠛⢿⣿⣿
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⡿⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⣿⣿⣿⣶⣦⣤⣤⣀⡀⠀⢀⣠⣄⣀⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⢀⣀⣠⡀⠀⠀⠀⢀⣤⣀⣤⣴⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⣷⡄⠀⠀⠀⠀⠀⣠⣲⠯⠭⣖⣦⠀⠀⠀⠀⢀⣤⣶⣾⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣏⣀⠀⣈⣿⣿⣀⠀⠀⠀⠘⡟⠣⠀⠀⠀⠍⠁⠀⠀⠀⣿⣿⠟⠉⠙⢿⣿⡇
⠀⠀⠐⢄⣄⠀⠀⢀⣄⠜⠀⠀⠘⠛⠛⠛⠛⠀⠛⠛⠛⠛⠁⠀⠀⠀⠁⠀⠈


⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠁⠢⡀⠀⠀⠀⠀⢀⣴⣶⣿⣶⡶⣄⡀
⠀⠀⢀⣤⣾⠟⠛⠛⢿⣦⣄⠀⠀⠀⡂⡐⠁⠀⠈⠂⠀⠀⠀⠀⣰⣻⣫⠗⠛⠳⣿⣿⣿⡆
⠀⠺⠿⠿⠿⠂⠀⠀⠈⠉⠉⠁⠀⠀⢱⡔⠊⠀⠱⣦⠂⠀⠀⢰⣿⣿⣿⣶⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠐⠐⠁⠀⠀⠀⠈⠉⠉⠁


⠀⠀⠀⡠⠐⡀⠀⡐⠠⡀⠀⠀⠀⠀⢀⡤⢖⣒⡶⢤⡀⠀⠀⠀⠀⢀⡠⠖⣒⡲⢤⡀⠀⠀⠀⠀⢀⡤⣖⣒⣒⠢⣄
⠀⠀⡌⠠⠁⠀⠒⠠⠱⠈⡄⠀⠀⢰⢫⡾⠛⠉⠛⣷⡽⡄⠀⠀⢠⢋⣾⠟⠛⠻⣷⡜⡆⠀⠀⢠⢏⣾⠟⠛⠛⣿⣎⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠁⠁⠀⠀⠈⠈⠁⠀⠀⠀⠈⠁⠈⠀⠀⠈⠈⠋⠀⠀⠀⠈⠋⠈


⠀⠀⠀⣴⣛⣛⠷⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢤⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⡿⣿⣶⣄
⠀⠀⠸⠟⠉⠻⣷⡜⣷⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢻⣦⢻⣿⣦⡀⠀⠀⠀⢰⡿⢫⣴⣶⣶⣬⠻⣧
⠀⠀⠀⠀⠀⠀⠸⠗⠈⠃⠀⠀⠀⣼⣿⡿⠉⠉⠙⣿⣿⡇⠀⠀⠀⠀⠀⣿⡆⢿⣿⣿⡀⠀⠀⢸⡇⣿⡿⠛⠻⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠁⠀⠀⠀⠳⠻⠇⠀⠀⠿⠱⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠀⠀⢀⣀⡤⠤⠖⠒⠒⠚⠛⠓⠒⠒⠶⠤⣤⣀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⢀⣠⠶⠚⠉⠀⢀⣀⣠⡤⠤⠤⠤⠤⠤⣤⣀⣀⠀⠈⠉⠓⢦⣄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⣠⠖⠋⠀⢀⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣀⠀⠈⠓⢤⡀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣠⠞⠁⠀⣠⠞⠉⠀⠀⣀⡤⠖⠚⠋⠉⠉⠉⠉⠉⠛⠲⠦⣄⠀⠀⠈⠓⢄⠀⠀⠙⣄⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⡞⠁⠀⣠⠞⠁⠀⢀⡴⠊⠁⠀⣀⣠⡤⠤⠶⠶⠶⠤⢤⣀⠀⠈⠙⢦⡀⠀⠀⠳⣄⠀⠈⢧⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢠⠏⠀⢀⡜⠁⠀⠀⡴⠋⠀⣠⠴⠋⠁⠀⣀⣀⣀⣀⣀⣀⠀⠈⠙⠲⣄⠀⠙⢦⠀⠀⠘⣆⠀⠈⢧⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢠⡏⠀⢀⡞⠀⠀⢀⡞⠁⢠⠞⠁⠀⣠⠖⠋⠉⠀⠀⠀⠀⠈⠙⠲⣄⠀⠈⠳⡄⠈⢧⠀⠀⠘⣆⠀⠘⣇⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⡞⠀⠀⡾⠀⠀⢀⡟⠀⢠⠏⠀⢠⠞⠁⢀⡤⠖⠋⠉⠉⠙⠲⣄⠀⠈⠳⡄⠀⠹⡄⠈⣧⠀⠀⠸⡄⠀⢹⡀⠀⢻
⠀⠀⠀⠀⠀⠀⢠⡇⠀⣸⣧⡤⠼⠧⣄⣀⡾⠀⢠⠇⠀⢠⠏⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠹⡄⠀⢹⡀⠸⡆⢀⣀⣧⣤⣬⣇⡀⠘⡇
⠀⠀⠀⠀⠀⠀⣸⠖⠋⠁⠀⠀⠉⠙⠶⠍⠳⣄⣾⣠⣀⡟⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⣳⣀⣈⣇⡤⠟⢭⡗⠒⠂⠀⠀⠉⠓⢧⡀
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣈⣁⡀⠀⠙⣆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡞⠁⠀⣀⣋⡤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠹⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠿⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠘⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠞
⠀⠀⠀⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠁
⠀⠀⠀⠀⠀⠈⠧⣄⡀⠀⣀⣠⣄⠀⠀⠀⠀⠰⢋⡞⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣏⠫⠀⠀⠀⠀⢀⣤⣀⡀⠀⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠈⠓⠶⠶⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠶⠒⠋⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠚⣉⣉⣉⣉⣉⡉⠉⠒⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⣉⠤⢒⣊⠭⠭⠥⠤⠤⠤⠤⢍⣉⡙⠒⠦⢄⡈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⡡⣒⠭⢒⡩⠥⣖⣒⣒⣈⣉⣑⣒⡒⠲⠤⣈⡙⠒⢤⡈⠑⠦⡀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⣠⢎⡴⡫⢊⢵⡪⢕⣪⠭⣕⣒⣒⣒⣒⣒⠦⠭⣉⡒⠦⣌⠓⢤⡈⠓⢄⠈⠢⡀⠈⢢⡀
⠀⠀⠀⠀⠀⡰⠡⠫⠊⣾⣗⣵⣮⣓⠯⠟⠒⠒⠒⠒⠒⠢⠭⣑⠢⢍⡓⢤⡙⢦⡈⠢⡀⠑⣄⠈⢦⠀⠑⠄
⠀⠀⠀⠀⡼⣱⡵⣴⣷⣽⣿⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣍⠢⡘⢦⠙⢆⠘⢆⠈⢆⠀⢣⠀⠘⡄
⠀⠀⠀⢰⢳⣻⣽⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡙⡄⢳⡈⢧⠈⣆⠈⣆⣀⣧⡀⢹⡀
⠀⠀⣀⠼⢮⡷⠟⠋⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⡤⠷⠬⣆⡼⠊⠁⠀⠀⠈⠙⢧
⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑
⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠣⠀⢀⣄⠀⠀⡀⠀⢀⡤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠚
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣈⣲⣤⣴⣋⣳⣤⣴⣊⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢊⣉⣉⠑⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⢈⠤⠀⠀⠌⠐⠄⠱
⠀⠀⠀⠀⢀⡤⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠔⠀⠀⠢⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣮⡉⠛⠉⠄⠂
⠀⠀⢀⡴⢋⡴⢛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡾⣬⠄
⠀⠀⡞⢠⠏⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋
⠀⠀⠃⠛⠘⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢐⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠐⠀⡀⠀⠀⠀⠀⢀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⢸
⠀⣰⣿⣿⣷⣶⣦⠀⠀⠀⠘
⠚⠛⠛⠛⠛⠛⠛⠃⣠⣶⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⠿⠿⠟



⠀⠀⠀⠀⡠⠄⠒⠒⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⣒⣒⣲⡦⣄
⠀⠀⡐⠁⠠⠔⠈⡉⠉⣑⡢⣝⢆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣫⢞⢽⣚⣷⣒⢭⡲⡵⣄
⠀⠐⠀⠐⠁⠀⠀⠀⠀⠀⠙⢮⣾⡆⠀⠀⠀⠀⠀⠀⣀⡛⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢳⣳⣳⣫⠞⠛⠲⡵⡽⡽⣼
⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠀⠀⠸⠿⡿⠷⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠘⠻⠛⠉⠃⠀⠀⠀⠛⠁⠃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⣴⡿⣫⠽⣾⣽⣆⠀⠀⠀⣰⡾⢛⣉⣉⡛⢷⡄⠀⠀⢀⡴⣛⠭⠭⣙⢷⡄⠀⠀⣰⠋⠀⣀⡀⠈⢳⡀⠀⠀⣴⣫⡽⠿⢯⡳⣄
⠀⠀⠀⠀⣸⢹⡟⣕⣉⢪⣿⣿⡆⠀⣼⣟⣾⣟⡭⣝⣿⣎⣿⡄⠀⣾⡕⣵⣛⣛⣮⢣⣿⡀⢰⠇⢠⡞⣩⡙⣧⠀⣧⠀⣸⣳⡏⡬⠶⣄⢿⣽⡄
⠀⠀⠀⠀⠛⠂⠛⠋⠛⠙⠛⠛⠃⠀⠿⠻⠿⠟⠀⠘⠿⠿⠻⠇⠸⠟⠺⠳⠇⠸⠿⠇⠿⠇⠘⠇⠘⠇⠿⠇⠿⠀⠞⠀⠿⠿⠸⠱⠿⠸⠘⠟⠇

⠀⠀⠀⠀⠀⢀⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠠⠄⡄
⠀⠀⠀⠀⡼⡵⣚⣿⡓⣝⣦⠀⠀⠀⠀⢠⣾⣻⢿⣮⣆⠀⠀⠀⢀⡘⡰⣪⣭⣢⡱⠄⠀⠀⠀⠀⣠⡾⢛⡛⠷⣦
⠀⠀⠀⢸⣿⣷⡁⠀⢘⣿⣼⡄⠀⠀⠀⣾⣿⣱⢲⣿⣿⡆⠀⠀⠰⢸⣿⡗⠱⣿⢣⢃⠀⠀⠀⣼⣯⣞⣩⣍⢳⣹⣇
⠀⠀⠀⠻⣿⣿⠇⠀⠻⠿⠿⠇⠀⠀⠐⠿⠿⡟⠸⠿⢿⠇⠀⠀⡁⢺⣿⠁⠈⣿⠘⢰⠀⠀⠀⣿⢹⣾⡏⢹⡎⡟⣿⠀⠀⠀⠀⠀⣰⣦
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠠⠄⠀⢠⣤⠰⠀⠀⠁⠈⠉⠀⠀⠉⠀⠈⠀⠀⠀⠉⠈⠉⠁⠈⠉⠁⠉⠀⠀⠀⠀⠀⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣶⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⣉⣤⣶⣾⠿⠿⠿⠿⠿⢿⣶⣶⣤⣉⠛⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⢁⣴⣿⠟⣋⣥⣶⡶⠿⠿⠿⠷⣶⣦⣭⡙⠿⣷⣤⡙⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢃⣴⡿⢋⣴⡾⢛⣭⣶⣶⠿⠿⠿⢿⣶⣮⣝⡻⣷⣌⠻⣿⣆⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢁⣾⡟⣡⣿⢋⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⢿⣮⡻⣷⡌⢿⣧⠘⣿⣿⣄
⠀⠀⠀⠀⠀⣰⠋⠉⠉⠑⢾⠿⣰⡿⢱⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡘⣿⣌⢿⣧⠊⠉⠉⠑⣆
⠀⠀⠀⠀⣠⡇⠀⠀⢀⠇⠀⠀⠈⢧⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠹⠁⠀⠘⣅⠀⠀⠀⠸⣄
⠀⠀⠀⡼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⢧
⠀⠀⠀⢧⠀⠀⠉⠑⠦⠄⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠤⠊⠉⠁⠀⠀⡼
⠀⠀⠀⠀⠑⠲⠶⠶⠶⠶⠶⠶⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠶⠶⠶⠶⠶⠶⠶⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠊⠀⠉⠉⠉⠉⠉⠘⠒⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⢀⡠⠠⠄⠐⠒⠐⠒⠒⠂⠠⠤⢄⡀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⡠⠔⠈⠀⠀⠀⠤⠠⠤⠤⠤⠤⠄⠄⢀⠀⠀⠀⠢⢄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠔⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⠤⠄⣀⠀⠈⠁⠢⢀⠀⠀⠠⡀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⠔⠁⠀⠐⠁⠀⠀⠀⠀⢀⣀⠀⠤⠀⠠⠀⠀⣀⠈⠁⠂⢄⠀⠀⠢⡀⠈⠢⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⠂⢀⠔⠀⡠⠊⢀⡠⠒⠉⠁⠀⠀⠀⠤⠄⢀⡀⠀⠈⠁⠠⢀⠈⠢⡀⠈⠢⠀⠑⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠠⠁⠠⠂⡠⠂⢀⠔⠁⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠑⢄⠈⠢⡀⠱⡀⠘⡄⠈⠄
⠀⠀⠀⠀⠀⢀⠄⠚⠒⠃⣠⠃⣰⠥⠴⢁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠱⡀⠱⡀⠰⡀⢱⠀⢠⡀
⠀⠀⡀⠀⠠⠁⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢰⠄⠛⠒⠓⢄⡗⠁⠀⠉⠁⠀⠈⠂⡀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡠⠊
⠀⠈⠢⣀⠀⠀⣀⠤⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⢀⡀⠴⠊⠀⠉

⣉⡇⣿⠷⠆⠂⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠠⠠⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⡆⠾⣿⢸
⢙⡇⣿⣶⠄⠀⡈⠢⡈⢀⠀⠄⠁⠬⢀⣀⠤⢒⠈⠅⠀⢀⡀⠀⠉⠁⠀⢐⡀⠀⠌⢑⠂⢄⡀⠀⠀⢰⠀⠀⠀⠀⠀⢈⠆⡇⢴⣾⢀
⠉⠁⠉⠀⠀⠀⡈⢀⠔⠁⠀⠀⢀⠔⡊⠔⢈⠡⠐⢀⠉⠀⠀⠀⠀⠀⠀⠀⠠⢉⠀⠂⠌⡐⠌⡑⢄⡀⠁⢐⠀⠐⠂⡂⠀⡇⠀⠉
⠶⣦⣶⣄⡀⠀⠀⠂⠀⠀⢀⠔⡡⠊⠠⢊⠠⠐⡁⠄⢐⡀⠁⠠⠀⠠⠀⠉⣐⠀⠄⣁⠂⢌⠐⢌⠢⡉⢢⡈⠈⠂⠆⠁⠀⡇⣀⣴⣤
⣶⡟⣿⣋⠁⠀⡀⠀⠀⡔⠡⠊⡐⢁⠔⠁⠔⡁⠐⣈⠥⠐⠂⠁⠀⠀⠁⠒⠢⠍⡀⠠⡁⠢⡑⠠⡑⢌⠢⡑⠄⠃⠀⠆⠀⡇⢙⣿⢻
⡴⠇⡿⠛⠃⠀⠄⢡⠜⡐⢁⠊⡐⢁⠄⡠⢊⠔⠉⡄⠠⠀⢀⡀⠀⢀⠀⠄⠀⣜⢂⠑⢤⡑⠌⠢⡑⢄⠠⠑⡈⢆⠀⠀⠀⡏⠛⢿⠸
⠀⠀⠀⠀⠀⠀⠊⡌⠐⢀⠂⠌⠠⢁⠎⡔⠁⠀⠈⡔⡀⠀⠀⠀⠍⠀⠀⢀⠨⠁⠀⢂⠀⠙⢄⠢⠐⡈⢂⠡⠐⡈⠆⠀⠀⡇
⢉⡇⣿⡶⠄⠀⢰⠠⠁⠀⡘⠀⢁⠂⡌⠀⠀⠀⡐⠀⡠⠀⢀⠊⠀⠀⡠⡑⡠⠤⢄⠡⢂⠀⠈⢆⠡⠐⡀⡄⢃⢀⠘⡀⠀⡇⠶⣾
⠀⠀⠀⠀⠀⠀⡆⣰⠈⠁⠒⠉⠘⢼⡀⠀⠠⠡⢻⢹⢁⢡⠂⠀⠀⡐⠌⠀⠣⠤⠞⠀⠡⢂⠀⢈⠤⠏⠉⠉⠈⠈⠑⠦⡀⡇⠀⠈
⠶⡆⣦⣄⡀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢈⠀⠢⢆⠈⢉⠀⣃⣀⡀⢺⢊⠠⢄⠀⢰⠤⠄⡄⠛⠀⢅⠀⠀⠀⠀⠀⠀⠀⢀⠄⣇⣠⣴⢠
⢾⡇⣿⣉⠀⠀⠡⡀⡠⡀⠀⠠⣀⡠⠁⠀⠀⢸⠀⢨⠀⡇⠀⠁⢸⠨⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠠⠠⠤⣀⠠⠤⠄⠂⠀⡇⢉⣻⢘
⠴⠇⠿⠛⠁⠀⠀⠀⣀⠀⠀⠀⠠⠤⠀⠀⠐⠘⠤⠼⠀⠧⠤⠄⢸⢀⠀⠈⠀⠸⠀⠀⠇⡆⠀⡀⠤⠤⣀⠀⠀⢀⡀⠀⠀⡇⠙⠻⠈
⣀⡀⣀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠠⣀⠄⠀⠀⠁⠀⠀⠒⠂⠀⠀⠸⠸⠀⠀⠓⠒⠀⠀⠀⠁⢈⣈⠀⠀⣀⠀⠀⠀⠀⠈⠉⡇⠀⢀
⣩⣿⣿⡷⠆⠄⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠼⠁⠀⠀⠀⠀⠀⠇⠾⣿⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⡿⠿⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠟⠋⠉⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣶⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠋⠁⠀⢀⣠⣤⣶⣿⣿⣿⡿⠿⠟⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠋⠁⠀⣀⣤⣾⣿⣿⠿⠛⠋⠁⠀⠀⢀⣀⣀⣠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⢀⣤⣾⣿⡿⠟⠉⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⢀⣴⣿⣿⠟⠉⠀⢀⣠⣴⣿⣿⡿⠿⠛⠉⠉⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⢀⣴⣿⡿⠋⠁⠀⣠⣴⣿⣿⠿⠋⠁⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⠀⠀⣴⣿⣿⠏⠀⠀⣠⣾⣿⡿⠋⠁⠀⣀⣤⣾⣿⣿⠿⠟⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⢀⣾⣿⡟⠁⠀⣠⣾⣿⡿⠋⠀⢀⣤⣾⣿⡿⠟⠉⠀⠀⢀⣀⣤⣤⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⢠⣿⣿⠏⠀⠀⣴⣿⡿⠋⠀⢀⣴⣿⣿⠟⠉⠀⢀⣠⣴⣾⣿⣿⠿⠿⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠁⠀⣠⣿⣿⠋⠀⢀⣾⣿⡟⠁⠀⣠⣾⣿⠟⠁⠀⢀⣴⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⢀⣤⣿⣿⣿⣶⣶⣾⣿⡟⠀⠀⣴⣿⡿⠃⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣾⣿⠿⠛⠉⠉⠉⠉⠛⠿⣿⣷⣼⣿⡿⠁⠀⣠⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠁⠀⣰⣿⣿⠋
⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠁⠀⠈⠉⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⢰⣿⣿⠃
⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣧⣿⣿⡏
⠀⠀⠀⢀⣼⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⡅
⠀⠀⣴⣿⡿⠋⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⢻⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠃
⠀⠀⠀⠙⠿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠐⠒⠂⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⢠⣁⣤⠶⠦⡄⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠰⠶⢶⣨⡀
⠀⢀⣤⡴⠚⠅⠀⠀⠀⢀⡦⠦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠴⣄⠀⠀⠀⠀⠝⠲⣤⣄
⠀⠋⠀⠀⠀⠀⢠⠤⠟⠓⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠙⠷⢦⠀⠀⠀⠀⠈⠃
⠀⠀⣆⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⡆
⠀⠀⠸⣧⣀⣀⣀⣙⠶⠶⠶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠶⠶⢏⣀⣀⣀⣠⡿
⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉




⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⠄⠀⠀⡀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠐⡀⠀⠀⠀⠀⠀⠐⠁⠀⠄⡈⠤⠒⢀⠩⠀⠀⠀⠀⠉⠁⠒⠀⠈⠀⠀⠄⡀⠁⠀⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡠⢊⠠⢂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠐⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⠋⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢀⠁⠄⠁⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠄⠑⢄⠀⠈⢪⢂
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⠆⠀⠁⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠌⢂⠀⠀⢡⠡⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢊⢣⠐⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⢃⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠌⠆⠀⢐⢠⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⣀⡀⠤⠄⠦⠤⠬⣠⠀⢁⢘⠀⡄⠀⠘⣐⡀⠀⢀⣀⡤⠄
⠀⠀⠀⠀⠀⠀⠓⠀⠄⠔⠘⠀⢀⢀⣀⣀⣀⠄⠀⠁⠈⠀⠀⠀⠀⠐⠀⠘⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠤⠤⠤⠀⡂⡄⠀⠀⠀⠓⠚⠁
⠀⠀⠀⠀⠀⠀⡀⠐⠀⣀⣐⣀⡀⠠⠄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠀⠀⠀⢈⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠆⠀⠀⠁⠀⠀⠀⠈⠉⠉⠒⠢⠤⣄⣀⣀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠈⠀⠀⠀⠠⠀⠄⠄⠄⠀⠠⠀⠠⠀⠠⢄⡀⣀⡀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠤⠄⠀⡀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠁⠐⠤⠠⠂⠀⠀⡀⡀⠀⠀⠀⠉⠉⠐⠐⠂⠠⠀⠤⠄⠤⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⣋⣉⡥⠤⠤⠤⠤⠤⣬⣉⣙⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⡤⠖⢋⣩⠤⠶⠒⠒⠒⠒⠒⠶⠤⣍⡙⠲⢤⡙⠲⣄
⠀⠀⠀⠀⠀⠀⣠⠞⣡⠞⢉⡴⠚⣉⡤⠖⢚⣉⣉⣉⣉⣙⡓⠲⢤⣉⠓⢦⡉⠲⣌⠳⣄
⠀⠀⠀⠀⠀⡼⢁⡼⢁⡴⢋⡴⠋⣡⠖⠋⠉⠁⠀⠀⠀⠈⠉⠓⠦⣌⠑⢦⡙⢦⡈⢦⡘⢦
⠀⠀⠀⠀⡼⢁⡞⢠⠏⣰⠋⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠹⣄⠱⡄⢳⡈⢧
⠀⠀⠀⢸⠁⡾⢠⡏⢰⠃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠘⡆⢹⡀⢧⠘⡆
⠀⠀⠀⡟⢰⣇⣼⣀⡏⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣄⣻⢈⣇⣸⡀⣷
⠀⠀⣀⡿⠋⠀⠀⠀⠉⠋⠙⣦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⠁⠀⠈⠙⠉⠀⠀⠙⠛⠦⡄
⢠⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠓⠲⠦⣄⣀⣀⡤⣄⣀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢦⣄⡤⣄⠀⠀⢀⡴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉