Snail text Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠾⠋⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⠶⠶⣶⣧⣀
⠀⠀⠀⠀⠀⢀⣠⡶⠟⠛⠉⠉⠉⠉⠉⠉⠉⠛⠳⢶⣤⡀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠙⠻⣦
⠀⠀⠀⢀⣴⠟⠁⠀⠀⣀⡤⠴⠶⠖⠶⠦⢤⣄⡀⠀⠈⠙⢷⣄⠀⠀⠀⣾⠃⠀⡤⢤⡀⠀⢀⡤⢤⡀⠹⣧
⠀⠀⣰⡟⠁⠀⢀⡴⢋⡁⢲⡀⠘⠆⠀⠀⠀⠀⠉⠓⢦⡀⠀⠙⢷⣄⢰⡟⠀⠘⠁⠀⠛⠀⠘⠀⠈⠃⠀⣿
⠀⣼⠏⠀⠀⢠⠏⠀⠀⠳⠀⢀⣤⠤⠤⠤⠤⣄⡀⠀⠀⠈⢦⡀⠀⠻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⢸⡏⠀⠀⠀⡟⠀⠀⠀⢀⠞⠉⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢳⠀⠀⢹⣿⠀⠀⠀⢦⣀⡀⢀⡴⠀⠀⣸⡇
⣿⠀⠀⠀⢰⡇⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⢷⠀⠀⠈⣇⠀⠀⣿⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣿
⣿⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠠⠎⠉⠙⢦⠑⠋⠀⠸⡇⠀⠀⢿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⣿⡄⠀⠀⠀⣇⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣸⠀⠒⠂⢀⡇⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠸⣇⠀⠀⠀⠹⡄⠀⠀⠀⠉⠓⠲⠶⠒⠛⠁⠀⠀⠀⣸⠁⠀⠀⡿⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⢻⡄⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⢠⠃⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⢻⣄⠀⢀⡤⠈⠓⠦⣄⣀⠀⠀⣀⣠⡤⠖⠋⠀⠀⠀⢠⠏⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⣹⣷⣍⠚⢀⡤⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⡾⠁⠀⠀⠀⠒⠶⢤⠀⠀⣼⠏
⠀⠀⢸⣏⠉⠙⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢋⣠⣴⠟⠋⠀⠀⠀⢀⣀⠓⠦⠀⢀⡾⠃
⠀⠀⠀⠙⢷⣤⡀⠀⠉⠙⠛⠷⠶⠶⣶⣶⡿⠿⠷⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠋⠉⠛⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠒⠛⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠰⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⣸⣧⣀
⠀⠀⠀⠀⣀⠀⠲⢌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡔⠀⠀⠀⠀⠀⢠⠚⠁⠀⣹⠧⣄
⠀⠀⠀⠠⣈⡳⣄⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⡒⠀⠀⠀⠱⡁⢹
⠀⠀⠀⠀⠈⠉⠂⠙⠦⣄⠀⠈⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡥⠀⠀⠑⢦⣭⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⣼⠟⠋⠉⠉⠒⠒⠒⠶⠒⠒⠚⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⢆⣀⣀⣀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠌⠙⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠉⡿⠁
⠀⠀⠀⠀⠀⠀⠰⣭⡤⠬⢿⡄⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⣀⣀⣀⣀⡄⠐⠶⠆⠀⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠰⢥⡥⠭⠿⠶⠶⠟⠳⢦⣄⣀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠦⣤⣀⡀⠀⠀⢀⣀⡤⠾⠳⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡈⠉⠉⠉⠉⠀⠀⠀⠀⣀⣠⣬⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠶⠶⠶⠟⠛⠋⠉⠉⠉⠉⠛⠓⠒⠒⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⠿⠿⠿⠿⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣿⡇⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⣤⣴⣶⠿⠿⠟⠛⠛⠛⣻⣿⢿⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣤⡀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⢀⣾⡟⠉⠀⠀⠉⠙⢿⣦⡀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠹⣷⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠘⣿⣆⡀⠀⠀⠀⠀⠀⠀⢿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠈⠛⠿⠂⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⢀⣀⣤⣤⣶⣶⡿⠿⠛⠉⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⢀⣴⡿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣶⣶⣶⣶⡾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏
⢿⣿⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠋
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠿⠿⠿⠿⢿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⡿⠿⠿⠛⠋⠉
⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠀⠉⠉⠉⠉⠉⠁⠐⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⡔⢁⠤⡉⠆⠀⠀⠀⢀⠄⠠⢄
⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠀⠉⠉⠉⠁⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠣⣀⣠⠆⠸⠀⠀⢠⠁⡔⠐
⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢀⡠⠄⠒⠀⠉⠐⠂⠬⡀⠑⠤⠔
⠀⠀⠰⠁⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠰⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⡠⠊⠁⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⡇⡘⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⠀⠀⠰⡀⠀⠐⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⢺⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢣⡀⠀⠀⣠⠃⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠱⢄⡀⠀⠀⣀⠴⠒⠀⢠
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠈⠁⠉⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠈⠢⡄⠀⠀⠀⠈⠀⠀⠀⢀⡴⠁
⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⡘⠀⠀⠀⡰⠁⠀⠀⠀⡔⠒⠒⠈⠁
⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⡰⠁⠀⠀⡰⠁⠀⠀⠀⠰
⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⢀⠜⠀⠀⠀⠠⠁⠀⠀⠀⠀⠇
⣀⠤⠤⠤⠀⣀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⢠⠃⠀⠀⠀⡰⠁⠀⠀⠀⠀⠘
⢣⠀⠀⠀⠀⠀⠈⠑⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⣠⡆⠀⠠⠔⠊⠀⠀⠀⠀⠀⢠⠃
⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠠⠤⠄⠀⣠⣤⣐⣈⣁⠀⠤⠤⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⢶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⣿⣿⣮⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠚⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣱⣿⣿⣶⡹⣿⣿⣿⣿⣿⡟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣝⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣇⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣜⠻⢿⣿⡿⢟⣼⣿⣿⣿⣿⣿⣣⣿⣿⠀⣀⣀⣀⣀⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣷⣤⣬⠗⠒⠒⠀⠁⠒⠲⠆
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⣷⡝⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠂
⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣷⣦⣭⣭⣭⣭⣿⣭⣵⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠛⠛⠿⠿⢿⡿⠿⠿⠿⠿⠛⠛⠋⠉⠉⠉⠋⠁







⣿⣿⣿⣿⣛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣿⣟⣻⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠸⠀⠀⡸⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠹⠢⣀⠑⡄⠈⠌⠀⡦⠊⢸⢀⡠⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡤⢙⣅⠓⠈⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣇⡤⢔⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢖⠈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⣀⡠⣤⠄
⠀⠀⠀⠀⠀⠀⠤⢀⡀⠀⠀⠙⠂⡀⠓⠂⠀⠀⠀⡀⠀⣤⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢪⣠⠀⠘⠂⠀⠀⣀⠀⡏⠲⠁⠓⠁⠧⠔⡇⠀⠀⠀⠀⠈⠑⢒⣲⠦
⠀⠀⠀⠀⠁⠀⠁⠀⠒⢴⠋⠈⠀⠀⢱⠀⠀⢙⣄⠀⠀⠀⠀⠀⠀⠘⣢⠤⠀⠀⠀⠐⠻⢍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠐⠘⠃⠀⢸⠀⠙⢣⡄⠀⠀⠀⢻⣀⠀⣤⣧⠀⠀⠀⠀⠰⢖⡒⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⡀⠀⠀⠎⠀⠘⢣⡤⠀⠀⠀⠈⠀⠛⠁⠀⠀⠀⠀⠐⢶⡒⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠢⡀⠀⠀⠉⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣖⠒⠛⠂
⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠚⠁⠀⠀⠀⠑⠢⠤⢤⣘⣹⠲⠶⠤⠤⠴⠖⠞⠺⠉⠛⣂⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠐⠋⠙⠙⠋⠋⠛⠙⠃⠀⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒

⣟⣿⣻⣻⣛⣛⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣟⣟⣿⣟⣟⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡦⣤⣄⣤⣤⣤⣀⠀⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠁⠀⠀⠀⠀⠉⠉⠓⠪⢽⣦⡑⢂⡀
⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⢠⡀⠀⡀⠀⣀⠀⠀⠀⠙⠻⣆⡐⠆
⠀⠀⠀⢰⠃⡠⠀⠀⢠⠐⠄⠀⢃⣀⡇⡴⢋⡴⠂⠀⠀⠀⠙⣧⠀⢣
⠀⠀⠀⣇⡼⠀⢠⡀⠈⣠⡴⠟⠛⡛⠛⠻⢿⣦⣞⠁⠀⢀⠀⠘⡥⠈⣇
⠀⠀⢐⡇⠁⠀⠀⠁⣼⠏⣀⣘⣶⣷⣶⣧⡒⠈⢿⣿⣃⡀⠘⠆⠐⢃⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⢸⣇⠀⢀⠄⢐⡏⢠⢤⣿⣡⣶⣦⡘⣿⣥⠘⣿⣿⠶⠀⠳⠄⢜⣴⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉
⠀⠀⠀⣿⣄⠈⡀⣘⣿⡠⠎⢻⣽⣾⣾⠃⣽⠿⠂⣿⣿⡟⠋⠀⢀⣾⣿⡏⠝⣲⣤⣤⣀⣀⣀⣤⣤⣶⣿⢀⣀
⠀⠀⠀⣸⣿⣧⡉⠐⠎⢷⣶⣉⣉⣻⣬⣾⣏⠄⣸⣿⣿⡇⠰⣠⣾⣿⡟⣠⡚⠫⣹⣿⣿⣟⣿⣛⢿⣿⣿⠋⠉
⣠⣴⣾⣿⣿⣿⣷⣦⣌⣀⠰⠋⠉⠉⠗⠛⣫⣶⣿⣿⣿⣾⣿⣿⡿⠋⣐⣇⡀⠀⡷⣷⢢⡉⢛⠀⠸⢹⣿⣷⣄
⠀⠀⠉⠉⠉⠉⠉⠉⠻⠿⣿⣿⡿⠿⠿⣿⣿⣿⡿⠿⠿⠛⠉⠛⠶⣴⣩⠵⠶⠶⠧⣌⣷⡼⠛⠛⠓⠚⠻⠷⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⠿⠟⠻⠿⢿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⢀⣤⣴⣶⣿⣿⣶⣦⣄⠀⠀⠈⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⢠⣶⣿⣿⣿⡿⠿⠛⠻⢿⣿⣷⡀⠀⠀⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⢰⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⢹⣿⣇⣤⡀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡄⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⢹⣿⣿⡄⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⠟⠉⠀⢀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠙⢿⣿⣷⣶⣶⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠀⠀⠈⢹⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⣠⣾⣿⡟⠀⠀⠀⢸⣿⣿⠀⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄⠀⠀⠀⠻⣿⣿⣷⣤⣤⣤⣤⣶⣿⣿⡿⠋⠀⠀⠀⣠⡾⠉⢁⣠⡿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠟⠛⠁⠀⠀⢀⣀⣴⡏⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⠛⢿⣿⣯
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡆
⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⣉⠉⢂⠀⠀⠀⢰⢟⣉⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠛⢀⠜⠀⠀⠀⢳⠈⢛⣡⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠘⣧⠀⠀⠀⠸⠀⡜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠶⠒⠒⠒⠂⠀⢄⣀⠀⠀⠀⠀⠈⣷⠀⣿⡀⠀⢀⡇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢹⡆⢸⣇⣀⣼⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢀⠀⣀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠘⣷⠀⠉⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢠⠁⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠒⠤⡀⠀⠘⣧⠀⠀⣿⠀⠄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⢀⠇⠀⠠⠚⠉⠀⠀⠀⠀⠀⠀⠠⠀⠀⠱⠀⠀⠘⣷⣾⠟⠀⡀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠈⠋⠹⠿⠀⠓⠀⡜
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠤⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣀⠀⢀⠀⠠⡄⢀⡴⢦⠀⠐⢄⠀⠀⠀⡆⠀⢠⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡔⠁⠀⠈⢆⣀⠇⠈⠁⡸⠀⠀⢀⠇⠀⢀⡇⠀⠻⣄⣠⡼⠁⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⣤⠨⠗⠂⠀⠒⠒⠛⠒⠒⠊⠁⠰⠉⠀⠀⢀⠞⠀⠀⠀⠠⠎⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡀⠤⣤⣤⡤⠶⠛⢀⡤⠀⠐⠀⠀⡠⠂⠀⠀⠀⡠⠴⠄⠭⠅⠠⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⢳⣄⡀⠀⠀⣀⠀⠈⠲⠄⢀⡀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠃
⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠗⠺⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠿⠿⠿⠟⠛⠛⠋⠉

⠀⠀⠀⢀⣀⠀⠀⠀⢀⣤⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀
⠀⠀⣴⢯⡝⣷⡀⠀⢾⡗⠗⣸⡇⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠻⠿⣿⣿⣷⣦⣄
⠀⠀⠙⠷⡴⣿⡇⠀⠈⠛⣿⡏⠀⠀⠀⠀⣠⣶⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⢿⡇⠀⠀⢸⣿⠀⠀⠀⣠⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆
⠀⠀⠀⠀⠀⣸⣿⣤⣤⣼⣏⠀⢀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀
⠀⠀⢀⣴⣿⣿⣿⣿⢿⣿⣿⣷⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠈⢿⣿⣷
⠀⢰⡏⢾⠋⢹⣿⠃⡿⠁⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠉⠀⠀⠀⠀⠉⠙⠻⢿⣿⣷⣄⠀⠀⠈⣿⣿⣇
⠀⢸⣧⣀⣤⣿⣿⣷⣤⣤⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧⠀⠀⢸⣿⣿⡀
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣦⣄⠀⠀⠘⣿⣿⣇⠀⠀⣿⣿⡇
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢀⣿⣿⠟⠉⠉⠙⣿⣿⡆⠀⠀⢸⣿⣿⠀⠀⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⣸⣿⣿⠀⠀⢸⣿⣿⠀⠀⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣆⠀⠀⠀⠻⣿⣿⣶⣶⣶⣿⣿⠇⠀⠀⣸⣿⣿⠀⠀⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⣰⣿⣿⡇⠀⣰⣿⣿⠁
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⠃⣠⣿⣿⠇
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠠⠤⠤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣀⣤⣶⣶⣶⣦⣶⣾⣤⣤⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⣠⣾⠿⠛⣋⡉⣉⡉⠉⠛⠿⣿⣿⣿⣆⡀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢠⣿⡟⠁⣤⡾⠛⠛⠛⢶⣆⢄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢻⣿⠀⣰⠋⡖⣋⡙⢶⠀⠸⣯⠈⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⣿⣿⡀⠘⣦⡓⠤⢎⡜⠀⠀⣿⡄⠀⣹⣿⢿⣿⡟⢛⣿⣿⣿⡟⢯⠴⣴⣶⣤⢤⣤⣴⣇⢠⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢻⣿⣷⣄⠈⠛⠛⠛⠁⢀⣸⣿⠅⠀⣽⣿⣾⣿⣿⣾⣟⢻⢶⣾⣯⣽⣆⢼⢍⣿⣾⣿⣿⣾⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢹⢿⣿⣿⣷⣶⣤⣤⣶⠟⠃⢀⣴⣾⣿⠟⣿⣿⡿⠛⣿⣿⣿⣾⣿⣯⣿⣿⣿⣷⣗⣪⣉⣿⣾⣟⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢼⣼⢿⢿⣿⡿⠟⢋⣤⣴⣶⣿⣿⡿⢋⣼⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣽⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⡀⣔⢾⣿⣿⣿⣓⣲⡉⣧⣴⣿⣿⣿⠿⠛⣁⣵⡿⢿⢿⣿⣿⡿⣯⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⡟
⠀⠀⠀⠀⢀⡠⣀⢀⡔⢭⠌⣼⣝⣴⠿⠿⠿⠿⠿⠿⠷⠿⠷⠿⠶⠶⠿⠿⣿⣏⡔⠦⠮⠬⠼⠷⠿⠟⠺⠓⠏⠚⠋⠉⠉⠉⠈⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠁⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⡾⠿⠿⠿⠿⠿⠿⠿⠷⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠉⣀⣤⠴⠒⠉⠉⠉⠉⠉⠉⠋⢒⠶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⢀⡴⠞⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠴⡏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣴⣿⠋⠀⢀⡞⠀⠀⠀⠀⢀⣠⣹⣄⣠⣤⣆⣸⣀⢀⣆⠀⡠⠁⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠤⠃
⠀⠀⠀⣼⣿⠃⠀⢀⠟⢧⡀⠀⢰⣤⡴⠛⠻⠋⠁⠉⠉⠙⠻⢿⣄⣼⡅⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⢀⠆
⠀⠀⢰⣿⠇⠀⠀⡒⠀⠠⣙⢶⣴⠋⠀⠀⠠⡀⠀⠀⠀⠄⠀⠠⠜⢻⡖⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠈
⠀⠀⣾⡿⠀⠀⠀⡇⠀⠀⢈⣽⠀⠀⣦⠼⠖⠉⠟⢻⣌⣠⠀⠀⠀⠀⢿⡿⣀⠀⠀⢀⠀⠁⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⡖
⠀⠀⣿⡇⠀⠀⠀⣍⡤⠴⣾⡏⠀⣴⠏⢠⡞⠒⢶⡀⠈⢧⠄⠀⠀⠀⠠⣟⡵⠋⠀⠀⠀⠀⢀⣠⣴⣿⣆⠀⠀⠀⠀⠀⠀⠀⠠⠈⡿
⠀⠀⣿⡇⠀⠀⠀⢷⠀⠚⠹⣷⡀⠸⣧⡈⠃⠀⣨⠁⠀⡼⢀⠀⣀⠀⡀⣿⣡⣀⣀⡠⢇⣸⡦⢛⣉⣵⣶⡇⠀⠀⠀⠀⠀⠠⠀⡀⠃⡆
⠀⠀⣿⣷⠀⠀⠀⠘⡡⡀⠀⠛⢷⣤⢠⠟⠒⠚⠁⢀⣽⠇⠀⠀⠀⢀⢤⣿⣿⣵⣭⢞⣩⣵⣾⠯⡿⢿⡞⢹⣻⢖⣶⣶⣶⠇⠀⢇⡔⠁
⠀⠀⠸⣿⡆⠀⠀⠀⠹⣷⡀⠀⠀⠙⠿⢶⣶⡶⠾⠛⠋⠀⠀⣠⣤⣤⣶⣿⣿⣧⣴⡿⡫⡯⢝⢁⠼⢛⠤⣟⠰⣛⡥⣌⡿⣤⣴⢿⢇⢠
⠀⠀⠀⢻⣿⡄⠀⠀⠀⢹⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣭⣭⣟⣿⣿⣿⢿⣿⣿⣷⣿⣮⣧⣾⣴⣮⣝⠇⡣⢫⡗⣻⡿⣃⣓⣯⣷
⠀⠀⠀⣀⣻⠿⠄⡰⠃⠍⠿⢿⣷⣶⣤⡄⠀⣀⢦⡠⡠⣄⣠⣿⣿⣿⢿⣿⣟⣷⠟⣴⣳⢤⣭⣉⣙⢛⠙⠻⢛⡿⢷⣵⣯⣿⣦⣓⣞⣿⡿⠂⠤
⠆⠈⠉⠉⠁⠀⢀⣀⣀⣀⣤⣁⣛⣛⠿⠿⢶⣿⣿⣿⡿⠿⠟⠛⢉⣁⣀⣀⠀⠀⠈⠀⠈⠀⠘⠉⠏⠉⠙⠙⠛⠛⠛⠿⠿⠛⠍⣗⡀⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⢀⣤⣿⠟⠀⠀⠈⠹⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢷⣶⣶⣶⣶⣶⣶⣶⡶⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠛⠛⠛⠋⠛⠛⠛⠓⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⣾⠉⢹⡆⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠹⡆⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣷⠀⠘⢧⡀⠀⠀⠠⠿⠟⠛⠛⠀⠀⠀⠀⣶⣶⣆⠀⠀⣠⡟⠀⢰⡇⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⣼⠷⣄⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠙⠳⣤⠤⠶⠶⢤⡀⠀⠀⠀⠀⠉⠉⣩⡴⠛⠁⠀⣠⠞⠀⠀⠀⠀⠀⠀⢀⡴⢿⡄
⠀⠀⣼⠃⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠞⠁⠀⠀⠀⠀⠘⢦⠀⢀⠴⠚⠛⠳⣄⠀⣴⠞⠁⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢻⡀
⠀⢰⠏⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠈⣷⠋⠀⠀⠀⠀⠈⢿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠈⣷
⠀⣿⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠰⠆⠀⣿⠀⠰⠆⠀⠀⠀⢸⣆⡀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢸⡇
⢰⣇⣤⣄⠀⠀⠀⠀⣧⠀⠀⢀⣠⠶⠛⠉⢻⡀⠀⠀⠀⠀⠀⠀⢠⢿⡀⠀⠀⠀⠀⠀⣸⠉⠙⠳⢦⣀⠀⠀⢠⡇⠀⠀⠀⢀⣤⣄⣷
⣸⡟⠀⠘⣇⠀⠀⠀⢻⣀⡴⠋⠁⠀⠀⠀⠀⠳⣄⡀⠀⠀⣀⡴⠋⠈⢷⣄⠀⠀⢀⣴⠋⠀⠀⠀⠀⠉⠳⣄⢸⠃⠀⠀⢀⡟⠀⠘⣿
⣿⠁⠀⠀⢹⡀⠀⠀⣸⠟⠀⠀⠀⠲⡀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⡰⠂⠀⠀⠙⢿⡀⠀⠀⣸⠁⠀⠀⢹
⣿⠀⠀⠀⢸⡇⠀⣰⠏⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠈⢷⡀⠀⣿⠀⠀⠀⢸
⣿⠀⠀⠀⠈⡇⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⣀⣀⣀⣀⠀⠀⣀⣀⣀⡀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⡏⠀⠀⠀⢸
⣿⠀⡆⠀⢰⣇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣿⠀⠀⡄⢸
⢸⡄⣧⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⢀⡇⣼
⠘⡇⠘⠳⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠳⠚⢀⡟
⠀⢹⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⠁
⠀⠀⢷⡀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⠇
⠀⠀⠈⢳⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣰⠋
⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⡇⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡇
⠀⠀⠀⠀⢻⡀⣸⠿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢿⡀⣸⠃
⠀⠀⠀⠀⠀⠙⣟⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢈⡟⠁
⠀⠀⠀⠀⠀⠀⠻⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡤⠤⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠁⠈⠀⠉⠑⠄⠀⠀⢀⠀⠈⠙⠓⠶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠉⠁⠀⢀⠀⠀⠀⠀⢀⣀⠀⣤⣬⠀⣀⠄⠀⠀⠀⢉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡆⠁⠀⠀⠀⠀⠀⣠⠞⠉⠀⠈⠁⠀⢀⠀⠀⠈⣦⣤⣾⠿⠛⠉⠀⠀⠈⠀⠈⠀⠑⠢⢄⡁⠀⢈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⠸⠀⠀⠀⠀⢀⣴⠋⣒⠚⠒⠤⣀⠀⠈⠓⣠⣾⠟⠉⠀⠀⣠⡤⢛⣰⣦⠴⠤⣴⣄⡀⠀⠙⢿⡅⢀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⡆⡂⠀⠀⠀⢀⡾⠁⢠⡧⢀⣀⡄⠀⠑⢤⣾⣿⠃⢀⣀⡶⠞⣡⠾⠋⠁⠀⠀⡀⠀⠀⠙⠳⣄⠀⠙⠆⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡧⠐⠀⠀⣀⡜⢠⡇⠀⠀⢠⡟⠀⠂⠀⠀⠀⠈⠑⠶⣴⣿⡟⠀⠠⣼⣿⠚⢹⠋⠀⣀⣶⠟⠁⠀⠈⠰⡄⠀⠸⣧⠀⠸⡆⠋⢷
⠀⠀⠀⠀⠀⠀⣴⠏⠁⠀⠀⠀⠀⠉⢀⣸⠁⠀⠀⣸⡀⠰⡷⠤⠀⠀⢀⡀⠀⣿⣿⠄⠀⢰⣿⣇⣶⠃⠠⣼⣿⠁⣰⠖⣀⠐⡄⢹⡄⠀⣿⡇⠀⣷⡤⢾
⠀⠀⠀⠀⣠⣼⣿⠂⠀⠀⣀⠐⡀⠀⠈⢻⠀⠀⢠⡿⢀⠀⠁⠀⢠⣯⠉⠛⠃⠘⣿⠁⠀⢸⣽⣿⣇⠐⠀⣿⡇⠈⡇⠺⣄⣤⠃⣸⠁⠀⣿⡇⠀⣯⠀⣼
⠀⠀⠀⠀⠁⣿⣽⡆⠀⠀⣿⣆⢠⡄⠀⠀⢆⠀⣸⡇⠈⠀⠀⠀⢠⣤⣀⢓⠀⠀⣼⡆⠀⢘⡽⣿⣿⠀⢀⢹⣿⡀⠙⣦⣤⣤⡾⠯⠀⣸⣿⠅⢰⠏⢘⡟
⠀⠀⠀⠀⠀⠹⣯⣷⣤⡄⢈⡠⣾⣿⠂⠀⠈⢿⣿⣴⣛⣠⣤⣤⣈⣛⣻⢷⣄⣠⡏⣷⡀⠀⠝⢻⣿⡆⠀⠈⠻⣷⡄⠀⠀⠁⠀⣀⣼⣿⠇⢠⡟⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⡔⢹⣿⣿⣆⠀⠘⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⣷⠹⣧⠀⠀⠀⠙⢿⣦⡀⠀⢩⠟⢷⣶⣾⡟⢿⠏⢉⡴⠋⢀⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⣧⠉⣿⣿⡟⢦⣆⣀⠉⠹⠛⠻⢿⣿⣯⣽⣛⢿⣿⣿⣧⡹⣿⣤⠀⠀⠲⣝⣿⣶⣤⣄⣁⣈⣀⣥⣴⠞⠋⠀⣼⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣹⣿⣿⣦⢻⣿⡵⢺⡙⠿⠿⢾⡿⣾⣾⣶⡷⡟⢯⢿⣿⣿⣿⣷⣬⡻⢿⣦⣀⠀⠙⠓⠶⠉⠩⠉⡉⠉⠀⢐⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⣿⣿⣷⡨⣿⣦⢥⣌⠳⠠⡄⢦⡄⡄⣠⠠⠤⠤⢠⡌⢿⣹⢿⣿⣿⣶⣤⣍⣛⠶⢶⣤⣠⣤⣡⡡⡴⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡸⣿⣿⣧⠚⠷⣾⣷⣯⣷⣴⢲⡰⢠⡀⡤⣆⢄⢀⡀⢀⠈⠈⠙⠿⢿⣿⣿⣽⣟⣓⣲⣶⣶⣶⣦⣭⡵⠶⠖⠖⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡿⣿⣿⣧⠀⠉⠿⡿⡶⡶⡷⠟⣟⠛⢻⢻⢻⠶⡿⣿⣻⣬⣹⣤⣲⣴⡿⡿⠿⡽⣿⢽⣿⡿⢶⢶⣿⣛⣛⣛⣛⠛⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣷⣄⡀⠀⠀⢡⠁⣀⣼⣬⣿⣿⣘⠘⠦⠇⡏⡏⣯⣯⣇⣧⣶⣿⣷⣦⣭⠬⠤⠶⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠂⠉⠉⠉⠉⠁

⣿⣿⡿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⢀⣠⡤⠤⠐⢶⠂⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⢀⡠⠔⠊⠁⠀⢀⠀⠘⠀⠀⠀⠀⠀⠈⡆⠀⠐⠀⠄⠈⠀⡀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠘⠡⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠁⠓⢄⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⡠⣆⠐⠂⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢴⠈⠀⠀⠀⠀⠀⠀⠘⡆⠀⠑⠄⠀⠀⠀⠢
⠀⠀⠀⠀⣠⠋⠀⠀⢠⠞⠀⢇⠀⠀⠀⠀⠀⠀⠠⠰⡀⠀⠀⠀⠀⠀⢀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠢⠀⠀⠀⢡
⠀⠀⠀⢠⠃⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠂⢄⣀⣀⡠⠔⠊⠀⠑⢀⠀⠀⠀⠀⡀⠁⠄⠀⠀⠰⠤⣀⠀⠀⠀⠡
⠀⠀⢠⠃⠀⠀⠰⠁⡠⠴⠒⡄⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠲⠆⠀⠈⠉⡀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⡎⠀⠀⢠⠗⠉⠁⠘⠀⢰⠀⠀⠂⠄⠀⡴⠦⠤⠀⢀⠀⠀⠀⢠⠊⠀⠀⢠⠰⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠰
⠀⢰⠁⠀⠀⠎⠀⠀⣀⣀⠀⠀⡀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⣀⢀⣀⠘⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡆
⠀⡌⠀⠀⠀⠁⠀⠠⠀⠀⠁⠳⡇⠀⢠⠁⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠈⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢸⠀⠀⠀⡇
⠀⡇⠀⠀⢀⠤⢀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⢀⠀⠀⠀⢱⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⢀⢣⠊⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡈⠀⢠⢀⡤⡀⠀⠠⠄⣀⡜⠀⠐⠀⠂⠀⡀⠀⠠⠀⠒⠒⠂⢀⠀⠀⠀⠀⢀⠁
⠀⢡⠀⠀⠀⡗⠲⠎⠀⢀⡀⠜⠁⠀⠀⠣⣀⠀⠀⢇⠀⠘⠄⣠⠖⠊⠉⠉⠛⢇⠀⠀⠀⡠⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡘
⠀⠸⡀⠀⠀⢳⠀⠀⠀⠀⢀⠔⠊⠉⠉⢂⡈⢧⡐⠊⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠅⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⢀⠇
⠀⠀⢇⠀⠀⠈⢆⠀⠀⡀⢨⠀⠈⠀⠁⢠⠃⠀⠐⠄⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡞⠀⠀⠀⡎
⠀⠀⠀⠄⠀⠀⠘⢆⠀⠀⠀⠁⠠⠐⠊⠀⠀⠀⠀⠘⡀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⡀⠀⢀⡠⠊⠔⠀⠀⠀⡜
⠀⠀⠀⠘⣆⠀⠀⠈⢶⡀⠀⠀⠀⠀⠀⠀⣠⠤⠤⡤⠇⠀⠖⠂⠄⠁⠂⠤⠀⠶⠄⠊⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⢀⠎
⠀⠀⠀⠀⠈⢦⠀⠀⠀⠙⢶⠄⠀⠀⠀⠁⠁⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠀⠀⠘⡀⠀⠀⠀⢀⠤⠊⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠈⠑⠢⢤⣀⠀⠠⣀⠀⠀⠀⣀⡴⠃⠠⠄⢀⣀⠠⠐⠊⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠉⠁⠘⠛⠚⠛⠁⠘⠓⠀⠈⠁⠀⠀⠀⠀⣀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣈⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣙⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣟⣋⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣼⣿⣿⣿⠛⠉⠉⠉⠉⠛⣿⣿⣿⣧⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⡇⠀⢾⣿⣿⡷⠀⢸⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣄⡀⠉⠉⢀⣠⣾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⢉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡉⠉⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠿⠟⠛⠋⣉⠉⠉⠉⠉⣉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠛⠉⠀⠀⠀⢸⣿⣿⠁⠀⠀⠈⣿⣿⡇⠀⠀⠀⠉⠛⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⠙⠛⠛⠛⠛⠛⠛⠛⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⣀⣀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⣀⣀⣀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⡿⠿⠃⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠘⠿⣿⣿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣷⡦⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠛⠋⠁⠀⠀⠈⠙⠛⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢀⣤⣾⣿⣿⡿⠿⠿⠿⠿⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣠⣿⣿⣿⡿⢉⣤⣶⣶⣶⣦⣄⡈⠛⢿⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣷⣄⣀⣴⠏⠀⠀⠀⠀⠀⢰⣿⣿⣿⣏⣵⣿⣿⣿⠟⠛⠛⠿⣿⣆⠀⢹⣧
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⡟⢀⣴⣊⡑⡄⢸⣿⡆⠀⣿
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⣦⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣟⠓⣡⣾⡟⠁⣸⡿
⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠘⠉⠟⠛⠉⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣦⣙⢿⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣶⠶⠶⠾⣿⣿⣦⡀⠛⢾⠦⣤⣆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣧⣍⣟⣿⠿⢿⢷⠟⡾⠿⠿⣿⣿⣿⣒⣛⣷⣿⣿⣷⣾⣿⣿⠦⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠓⠋⠀⠂⠀⠃⠘⠐⠙⠑⠘⠚⠉⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠁

⡠⠊⠉⠑⠦⣀
⣇⠀⠀⠀⠀⠈⠳⢤⣀
⠈⠓⠶⠤⠤⣤⣤⣀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠶⠖⠛⠉⠁⠀⠀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠁⣀⣠⣤⣤⣤⣀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡤⠖⠋⠉⠀⠀⠀⠀⠈⠉⠙⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡇⠀⠀⠀⠀⠀⠀⡼⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢡⠀⠀⠀⠀⢀⡞⠁⡰⠋⠀⠀⠀⣀⣤⣤⠴⠶⠶⠶⠶⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣼⠀⠈⠶⠠⠤⣤⠎⠀⠼⠁⢀⣠⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣡⠤⠌⠀⠀⠀⠀⠀⠣⠀⠠⠛⠲⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣡⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⣴⠃⡰⠉⠀⠀⢻⠀⠀⠀⠀⠀⣠⡴⠶⢤⡀⠙⢧⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣥⣄⡀⠸⡆
⠀⠀⠀⠀⠀⣼⠃⠘⠀⣰⣾⠶⠘⠀⠀⠀⢀⠜⠁⠀⠀⠀⠙⠄⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠈⠉⠳⣿
⠀⠀⠀⢀⡔⠃⠀⠀⠀⣿⣿⣶⡇⠀⠀⠀⡎⠀⣠⣶⡿⠂⠀⢐⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⢰⠏⠀⠀⠐⠢⠀⠈⠉⡹⠀⠀⠀⢰⠀⠀⣿⣿⣷⡆⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⢀⡟⠀⠀⠀⠀⠀⠈⠒⠈⠁⠀⠀⠀⠈⢆⠀⠈⣛⣩⠤⠴⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣰⣋⠀⠨⡆
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⡏⠈⠉⠙⢇
⠀⠈⣧⠀⠀⠰⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢸
⠀⠀⠸⣆⠀⠀⢻⡉⠙⠓⠶⠶⢤⣤⣤⣤⣤⡤⢤⡾⠆⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢀⡞
⠀⠀⠀⠙⢦⠀⠈⢷⡀⠀⡶⠤⠤⠀⠀⠀⢀⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠛⠲⠖⣻
⠀⠀⠀⠀⠈⢳⡄⠀⠙⢶⣄⣀⣀⣀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⡦⣤⣤⣤⣤⡤⠴⠚⠁⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⣠⣴⠋⠀⠀⠀⢠⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⡤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠋⢡⡟⠀⠀⠀⠀⡿⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠈⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣁⣀⣀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣦⣄⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠈⠙⠶⣦⣤⣤⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠿⠟⠛⠛⠉⠁
⣿⣿⣿⠟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣶⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⣠⣾⣿⣿⡿⠿⠛⠛⠛⠿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢠⣾⣿⣿⡿⢃⣤⣶⣷⣿⣶⣦⣀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⣸⣷⣤⣤⡞⠁⠀⠀⠀⠀⢀⣿⣿⣿⣷⣼⣿⣿⡿⠟⠉⠉⠻⢿⣆⠀⢹⣧
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣼⣿⣿⣿⣾⣿⣿⡟⢀⣾⣥⡌⡆⢸⣿⠀⢘⣿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⢻⣯⣍⣴⣿⠏⢀⣼⡏
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠉⠉⣠⣴⣿⠏⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣷⣬⣽⠿⣿⣿⣿⣿⣿⢻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣌⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠷⢾⠾⢏⣹⢻⣛⢺⠛⢉⢿⠿⢿⠿⠿⢻⡿⣛⣛⠿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠈⠀⠀⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠈⠁⠤⠄⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠎⢇⠀⠀⠀⠀⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⠀⠈⠉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠂⠀⠇⠜⠀⠐⠀⠂⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡁⢀⠀⠀⠀⠀⠀⡀⢈
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠋⠀⠀⠀⠀⠠⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠀⠒⠀⠀⢸
⢠⠀⡄⠰⡀⢠⠀⢆⠀⠀⠀⡆⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠊⠀⠘⠀⠑⠘⠀⠈⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠓⠤⠤⠤⠄⠁⠀⠁⠚⠀⠤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠘⡆⢸⠀⢠⠀⡇⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⢀⠀⡄⠀⡄⢀⢄⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠆⠘⠄⠇⠘⠊⠀⠀⠘⢄⣀⣀⣀⣀⣀⣀⣀⣀⠀⠇⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠘⠒⠃⠐⠓⠢⢤⡄⢀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⢀⡼⢁⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢣⡤⠀⡠⠀⠀⠘⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠓⠆⢀⣾⠁
⠀⠀⠀⠀⠀⡾⢠⠟⠀⠄⡀⢂⠀⠀⠀⠈⢂⠀⠀⠀⠹⣞⠅⢀⠀⠀⠀⡻⢳⡀⠀⠀⠀⠀⠀⠀⠀⡠⣠⠔⠀⠀⠀⠘⣇⣤⡆
⠀⠀⠀⠀⢸⡧⣺⡅⢸⡆⢿⣄⠄⠀⡄⠀⠘⡄⠀⠀⠀⣷⠞⡁⠀⠀⠀⠀⡼⣷⢆⠀⠀⠀⠀⣠⠊⠊⠁⠀⠀⢰⡶⡣⠞
⠀⠀⠀⠀⢺⠎⡼⣿⠀⠻⢦⣤⠠⠜⠁⣀⢠⠇⠀⠀⠀⣸⠭⢖⡁⠀⠀⢈⢔⣿⠀⣧⣀⣤⠞⠁⠀⠀⠀⠀⢐⡿⠞
⠀⠀⠀⠀⢸⣾⡘⣟⢿⣤⡀⡀⠀⠠⣈⣡⠟⠉⠀⠒⠁⣿⣿⣅⠂⠀⢐⠅⢂⠌⠀⣿⣿⠕⠀⠀⠀⠠⣢⡴⠊⠁
⠀⠀⠀⠀⠀⢿⣇⡎⡓⢯⣿⣿⣶⡿⠾⣛⣒⣒⡀⠄⣸⣿⣿⣾⠵⢚⡡⣖⠅⠀⢸⣾⣾⠕⠀⢀⡤⣠⠋
⠀⠀⠀⠀⠀⠈⢻⣿⣱⡐⣄⢀⢄⡨⢔⣶⣾⡖⢊⣼⣿⣿⣿⠗⠪⠽⠚⣁⠀⣠⣾⡯⣒⠁⣒⡭⠚⠁
⠀⠀⠀⠓⠲⣶⡦⢿⣿⣿⣾⣶⣵⣮⣵⣶⣶⣾⣿⡯⠥⠤⠀⠀⢀⡐⢬⣣⣾⡿⠗⣊⠔⢩⣥⣤⣄
⠀⠀⠀⠈⠲⠤⠤⠤⢄⣀⣭⠭⠽⠋⠉⠩⣶⣾⣭⡛⠳⠶⠶⠿⠗⠺⠭⠭⠿⣟⣉⠷⠾⠙⠛⠛⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⡀⠑⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡋⠀⢠⣤⠈⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢘⢈⡏⠒⢉⠅⢺⣿⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠁⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠸⣿⠁⠀⠁
⠀⠀⠀⠀⠀⠸⣿⣿⣋⠕⠄⠹⣿⣧⡶⡉⠀⠀⠛⠉⠀⠀⠀⠀⠐⠀⠲⡿⣅⡀⢸⠀⠑⢔⡒⠡⠀⢀⠆⠀⠀⠀⠀⠅⢀⣀⣜⣿⣶⣦⡴⠃⠀⠀⠐
⠀⠀⠀⠀⠀⠑⠢⠽⣿⠿⣶⣿⣿⣿⢆⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠁⠀⣀⡭⠹⣾⣄⠀⠈⠁⠀⣀⡾⠀⠀⠀⠴⠖⠛⠛⠋⣉⣀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠪⠬⠭⠭⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆⠉⠛⠖⠛⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠺⠛⠳⣦⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⡐⢠⠀⠀⠀⢀⢠⡀⠀⢸⢶⣀⣀⡀⠀⢃⡠⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⡀⠀⠀⠀⠀⢀⡀⠘⠁⠀⢰⠀⠀⣀⡀⠽⣿⣦⣤⣠⡤⠈⠒⠒⠁
⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢸⣇⣀⡤⠊⠃⠜⣋⡉⢁⣀⡠⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⠦⠀⠀⠐⠻⢅⡀⣄⣔⠸⣧⠀⠀⠐⠆⠠⢉⣇⣠⡴⠟
⠀⠀⠀⠀⠀⠁⣀⣀⡀⢀⣀⠼⠯⠥⣤⠤⠚⠂⠌⠁⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠾⠿⠿⢥⣴⠶⠛⠁⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠈⡀⠘⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡤⣄⡤⢿⣿⣥⠀⠀⠀⠀⠀⡀⠀⢐⢂⣒⠢⢄⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣀⠤
⠀⠀⠀⠀⠀⠄⢠⠀⠈⢷⣤⠀⠀⠙⣄⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⡎⠁⠀⢀⡂⡈⠀⠀⠀⠀⡰⢠⠆⠀⠀⠈⠑⠄⠰⡄⠀⠀⢀⡀⠀⠃⠄⠈
⠀⠀⠀⠀⠀⡀⡆⠀⢀⡀⣀⣠⣄⡬⢿⠷⠌⠀⠀⡀⠀⠀⠀⠀⠉⠐⠸⢇⢀⠀⠀⠉⠉⠀⠀⠀⠀⣧⠙⣄⠈⠃⠀⠀⣹⠀⢷⡶⠚⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠙⢤⣐⣪⠿⠋⠁⠉⢀⠁⠀⣁⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⣀⣀⡼⣧⣄⣀⣈⣠⣼⡿⠶⠈⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠂⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠛⠛⠛⠁⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⠖⢁⡈⣂⠀⠀⠀⣀⠤⠒⠊⠉⠉⠉⠉⠉⠉⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠊⡠⠀⠂⠭⠀⠁⠀⠈⢆⡠⠊⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⢀⠆⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⢠⠊⠀⠀⠀⠳⡰⠄⡠⢶⠀⠄⠐⠪⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠲⠤⣀⠀⠀⠀⠀⢱
⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠯⠤⠔⠊⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⡇
⠀⠀⠀⠈⡄⠀⠀⠀⣤⣤⣤⣤⣤⣴⣖⢺⡁⠀⣀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢀⡤⢄⠀⠀⠀⡇⠀⠀⠀⢠
⠀⠀⠀⠀⠙⢄⠀⠀⠙⠯⣉⣉⠉⣛⣿⠷⠋⢁⠄⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢠⠇⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠥⢀⣈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⡤⠏⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⠑⢄⢇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡃
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡙⠲⢄⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡉⢳⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⠀⠀⠀⠐⢄⠀⠀⠀⠀⠈⠣⡀⠈⠲⢤⣀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠴⠞⠋⣠⠞⠐⠒⢁⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠈⠓⠦⢄⣀⣀⡉⠉⠉⠉⣉⣀⣠⣤⣴⣒⣉⠠⠤⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣨⠭⠚⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠺⣤⠤⠼⠲⠤⢄⣀⡤⠬⠶⢳⠀⠀⡠⠞⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣾⣿⣿⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⢿⡛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣯⣵⣶⣃⡀⢀⡴⢂⡀⠀⡀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣉⢟⣿⣿⣿⣦
⠀⠀⠀⠀⠀⣰⣿⣿⢿⣟⣋⡙⠻⣿⣿⣿⣿⣰⣿⣷⣿⣏⣤⡦⠀⠙⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⡤⠆
⠀⠀⠀⠀⢠⣿⡿⠿⢿⣿⣿⣷⣷⣾⣽⣿⣿⣿⣿⣿⣿⣻⣽⣶⣒⣤⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣠⠖⠉
⠀⠀⠀⠀⣾⣏⣲⠁⣼⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡴⠋⠁
⠀⠀⠀⢠⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣯⡻⣷⣾⡏
⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠍⠉⠻⣿⣿⣇⢹⣿⡇
⠀⠀⠀⠸⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠞⠓⣩⣵⣤⠘⣿⣿⣿⣿⣻⡇
⠀⠀⠀⠀⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣶⣿⣿⣿⣷⡉⢙⣿⣿⠉⣿⣇
⠀⠀⠀⠀⠸⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⢿⡿⣻⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠃⠀⣫⣾⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣋⣏⣻⣤⣴⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢫⡏⠀⠀⢠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⡇⠀⣰⢟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠳⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠁⣾⣀⡾⢃⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠈⠉⢀⣾⠁
⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢀⣄⠙⢧⡀
⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠙⠛⠀⠘⡇
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃
⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠰⡀⠀⠀⢀⣼⠷⠶⠚⠲⠾⢧⣄⡀⠀⠀⢀⣀⣠⠤⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⢦⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣠⡤⠤⣤⣀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⢸⡇⠀⠀⠀⠀⠠⣄⣀⣸⠃⠀⠀⡾⠃⠀⠀⠀⠙⣦⠀⠀⠀⠀⢹⡶⠶⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢀⣠⡤⢿⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠶⠛⠁⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⣴⠛⠁⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠹⣦⡀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠙⠳⢦⣄⡀⠀⠀⠉⠛⠶⣤⣤⣀⣀⣀⣀⣀⣤⡴⠞⠋⠀⠀⠈⠉⠉⠛⠛⠛⠲⠶⠶⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠈⠙⠓⠶⣤⣄⣀⡀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠚⠛⠛⠛⠉⠉⠉

⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣐⡶⢖⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠈⠓⠠⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠰⠾⢓⡄⠀⠀⠀⠀⠘⢿⣿⣿⠑⠀⠹⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠶⠟⣦⠀⠀⠀⠀⠀⠻
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠰⣿⡇⠀⠰⣶⣿⣿⣦⡀⣀⣶⣝⠃⠀⠀⠀⢀⡀⠀⠈⠁⠂⠀⠀⢀⣀⡀⠀⠀⠀⠀⣿⣷⠀⠀⢶⣾⣟⣷⣄⢀⣰⣯⡓⠀⠀⠀⠀⡀
⠀⠐⠛⣉⣉⠁⠀⠀⠀⢤⡟⢇⠀⠀⠀⠈⠉⠉⠀⠉⠛⢿⠷⠀⠀⠀⠉⡉⠛⠓⠀⠀⠐⠛⢋⣉⡉⠀⠀⠀⢢⣽⠻⠀⠀⠀⠈⠉⠉⠁⠈⠙⠻⡿⠆⠀⠀⠈⠉
⠀⠀⠘⠛⠛⠋⠀⠀⠀⠸⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠽⠟⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⢅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣴⣦⡄⠀⠀⠀⠀⢠⣦⣠⡄⠀⠀⠀⢂⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣧⣶⡄⠀⠀⠀⠀⠀⣴⣤⣄⠀⠀⠀⢒⡸⠆
⣀⣀⠀⢀⣠⣶⣷⠄⠀⠀⣀⣈⣥⣤⠄⠀⠀⢤⣌⣉⣉⡀⠀⠀⠀⢻⣴⡆⠀⠀⠀⣀⣀⡀⠀⣀⣴⣾⡆⠀⠀⢀⣀⣡⣤⡄⠀⠀⠠⣤⣉⣉⡀⠀⠀⠰⠘⣧⡖
⣯⡿⠃⠈⠽⢻⡅⠀⠀⠀⠀⠉⠀⠀⣀⠄⠀⠀⠀⠉⠉⠀⠀⠀⠀⢸⣿⠀⠀⢼⢿⣿⣽⠛⠈⠩⠟⣭⠀⠀⠁⠀⠉⠀⠀⣀⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣿⡇
⠉⠀⠠⢶⡮⠟⠀⠀⠀⠀⢀⣴⣿⣿⣇⠀⢰⡄⠂⠀⠀⠀⠀⠀⠀⠈⠉⢀⠀⠀⠀⠈⠁⠀⠦⣶⠽⠁⠀⠀⠀⠀⣰⣾⣿⣏⡀⢀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡
⡀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⣷⡶⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⢽⡶⠭⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠈⠄⢀⣀⠀⠀⠀⠀⠀⠀⣶⣶⣤⣭⠛⢼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡀⠀⠀⠀⠀⠀⣴⣶⣦⣭⡙⠬⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣤⡀⠈⠙⠃⢷⡀⠀⠀⠀⠀⠙⠻⠿⣆⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⢀⢀⣠⣄⠀⠉⠙⠸⣆⠀⠀⠀⠀⠈⠛⠿⢧⡀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⣤⡄
⣯⣿⠆⢤⣽⣾⣅⠀⠰⠀⣠⣤⣄⣀⠀⠁⠀⣀⣠⣤⠤⠀⠀⠀⠀⢸⣿⡀⠀⠙⠿⣿⣽⡷⠠⣼⣷⣯⡀⠀⠆⢀⣤⣤⣀⡀⠈⠀⢀⣀⣤⡤⠄⠀⠀⠀⠐⣿⡇
⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⢀⣤⣄⡉⠁⠀⠀⠉⢠⣤⣤⡀⠀⠀⠉⢾⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⣠⣤⡈⠁⠀⠀⠈⠁⣤⣤⣄⠀⠀⠈⠱⡏⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠙⠉⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠋⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠠⢾⣷⠆⠀⠀⠀⢸⡸⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠳⠿⠶⠀⠀⠀⠀⠀⠾⣾⡶⠀⠀⠀⢀⣄⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠾
⠀⠐⠶⢦⣤⠄⠀⠀⠀⢉⣷⡇⠀⠀⣀⣤⣴⣦⡀⢤⣶⣿⠟⠀⠀⠀⠤⠶⠶⠒⠀⠀⠐⠲⠶⣤⡤⠀⠀⠀⠃⣽⣿⠀⠀⢀⣠⣴⣦⣄⢠⣴⣿⡿⠃⠀⠀⠢⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠘⠛⠿⡿⠋⠀⠐⢋⣵⠂⠀⠀⠀⠀⢀⣀⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠛⠛⣻⠟⠁⠀⠚⣽⠗⠀⠀⠀⠀⢀
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⠻⠒⠁⠀⠀⠀⠀⢰⣿⣿⣿⠆⡠⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠛⠗⠂⠀⠀⠀⠀⠀⣾
⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄
⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⡀
⠑⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠤⡀⠀⠀⠀⠀⠸⣿⣿⣿⠦⠐⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠢⣠⡦⡄⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡆⠀⢠⣤⣶⣶⣄⠈⠀⣙⠳⡄⠀⠀⠀⠀⠈⠙⠛⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⣤⣴⣾⣆⠀⠀⢁⡛⣆⠀⠀⠀⠀⠈
⠀⢠⠴⠖⠛⠂⠀⠀⢀⡈⣿⡇⠀⠀⠉⠿⠿⠟⠁⠺⢿⣿⣦⠀⠀⠠⠶⠶⠦⣤⠀⠀⠀⡤⠶⠚⠓⠀⠀⠀⡀⣻⣿⠀⠀⠉⠹⠿⠿⠋⠐⠿⣿⣶⡄⠀⠀⠴⠶
⠀⠀⠠⣶⡾⠦⠀⠀⠀⢸⢡⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣴⣶⡶⠀⠀⠀⠀⠀⢴⣾⠶⠀⠀⠀⠈⠋⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠨⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠤⢝⡀
⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠉⠛⠛⣁⡀⠀⠀⣀⠘⠛⠛⠁⠀⠀⢀⢶⣈⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠈⠙⠛⢃⡀⠀⠀⢀⡀⠛⠛⠋⠀⠀⢀⠰⣎⣤
⣿⣿⠆⠒⢻⡿⡋⠀⠠⠀⠙⠛⠛⠉⠁⠀⠀⠉⠛⠓⠖⠀⠀⠀⠀⢸⣿⠁⠀⣠⣤⣿⣿⡷⠐⢺⣿⢟⠁⠀⠄⠈⠛⠛⠋⠁⠀⠀⠈⠙⠛⠶⠂⠀⠀⠀⢠⣿⡇
⠛⠁⢀⣀⡄⠾⠁⠀⠀⠀⠀⣠⣤⣶⡏⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⠈⠙⠋⠀⣄⣀⢰⠏⠀⠀⠀⠀⢀⣤⣶⡞⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⣿⣾⣾⣿⣿⡷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣷⣾⣾⣿⣿⣿⣶⣷⣿⣾⣿⣷⣿⣿⣿⣶⣾⣶⣿⣷⣿⣿⣿⣿⡿⡿⠿⢿⡿⠿⣶⡿⠶⠾⡶⠷⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⣀⣯⢴⠟⢠⡴⠂
⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠙⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⠿⡁⠛⢨⢅
⠀⠀⠀⠀⢀⠐⠅⠀⠀⢀⠠⠀⠀⠢⠀⠀⠀⠄⠀⠀⠀⠈⢰⣴⠖⡒⢶⡶⡶⠤⢤⢀⣼⡯⣿⠠⢃⠀⡀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⠀⠀⠀⣸⣿⣽⠧⠍⢰⣀⢨⠋⢀⡝⠃⡄⠀⢈⠀⠁
⠀⠀⠀⢀⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢣⢂⢀⣿⣿⣿⣸⡂⠍⡦⠀⢮⠁⡂⠔⢙⡱⢫⡞
⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠈⡀⠁⣾⠻⠿⣿⠿⠷⡤⠠⡭⡦⡽⢤⢿⡛⠕⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢈⠀⠀⠀⠀⠀⠈⣸⣿⢿⢎⠔⠁⠁⠉⠁⠀⠉⠀⠈
⠀⠀⠐⡎⡄⠀⠂⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⢨⣿⣿⡏⡌
⠀⠀⠀⠙⡍⣳⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠠⠄⣼⣿⣿⠙
⠀⠀⠀⠀⠈⠛⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣾⣿⣿⠇⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠴⠀⢃⢀⢒⢄⣤⣽⣾⢿⣟⡛⡏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣿⣿⠿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠻⡘⡏⠮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⡀
⠀⠀⣤⡀⠀⠀⠀⠀⠀⢀⣴⡿⣿⣿⣿⣿⣿⣿⡿⠋⣦
⠀⢰⣯⣷⣷⣆⡀⢀⣼⣿⣿⣿⠆⢻⣿⣿⣿⣿⣷⠄⠩⢧⡀
⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣿⣿⠂⠀⠈⢀
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⣬⡆
⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣧⠀⠀⠈⠋⠉
⠀⠀⠀⠙⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠀⠀⢀⣠⢂⣤⡀⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠟⠿⣿⣿⣿⣿⣿⣿⣒⡶⣾⣿⣿⣿⣰⣒⣯⡉⠸⡄⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠭⢾⡭⠿⣒⡦⢿⢟⡿⣿⣿⣿⣷⣶⣿⣄⣘⠧⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠊⠃⠋⠛⢛⣿⣿⣿⠿⠎⠹⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠨⠐⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠋⠉⠉⠉⠛⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⣠⠴⠚⠉⠉⠀⠀⠉⠉⠓⠦⣀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠛⠀⠀⠀⠀⢠⠏⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡾⠀⠀⣰⠃⠀⠀⠀⠀⠀⣠⠴⠒⠲⢤⡀⠀⠀⠀⢳⡀⠀⠀⢸⡄
⣤⣤⠤⣤⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⢠⠇⠀⠀⠀⠀⠀⡞⠁⢠⠄⠀⠀⢹⡄⠀⠀⢘⡇⠀⠀⠈⡇
⠉⠁⠀⠀⠈⠳⣄⡠⠖⠋⠉⠉⠑⢦⡀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⢻⡀⠀⠀⣸⠃⠀⠀⢸⠃⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⢀⣀⠙⢆⣷⠀⢸⠀⠀⠀⠀⠀⠀⢧⡀⠀⠉⠛⠋⠁⠀⠀⣠⠋⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⠀⠀⠘⠛⠀⠀⠹⣦⠘⡆⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣠⠤⠚⠁⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⢧⠘⠿⠃⠠⠤⠃⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⣀⣀⣀⣀⣀⣀⣠⡤⠤⠖⠚⠉⠁⠈⠙⠒⠲⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠛⠉⠉⠉⠉⠉⠙⠓⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀
⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⡰⠋⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡈⠳⡀
⠀⠀⢀⣞⠁⠀⢇⠘⢤⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⠜⢀⠇⠀⢙⣆
⠀⢀⡞⠈⠱⣄⠀⠑⡄⣹⠤⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠦⢼⡁⡔⠁⢀⡴⠁⠘⣆
⠀⡞⠀⠀⠀⠸⣆⡤⠋⠁⣀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢄⡀⠉⠣⣄⡼⠀⠀⠀⠘⡆
⢸⣡⢤⡀⠀⢠⠏⠀⢀⠎⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠈⢆⠀⠈⢧⠀⠀⣠⢤⣹
⣿⠁⠀⢳⢀⠏⠀⠀⢸⠀⠀⠰⠆⠀⠀⢘⠀⠀⠀⠈⠀⠀⠀⢘⠀⠀⠐⠶⠀⠀⢸⠀⠀⠈⢇⢰⠃⠀⢹
⡇⠀⠀⠸⡿⠀⠀⠀⠈⢦⡀⠀⠀⠀⣀⠎⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⣠⠎⠀⠀⠀⠸⡿
⣇⢀⠀⢀⡇⠀⠀⠀⠀⠀⠈⠁⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠉⠀⠀⠀⠀⠀⠀⣇⠀⢀⢀
⢻⠸⣄⣸⡇⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣿⣀⡼⢸
⠈⣇⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢀⡏
⠀⠘⢆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠞
⠀⠀⠈⣳⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⡋
⠀⠀⠀⣿⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢸⡇
⠀⠀⠀⠈⠳⢼⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠴⠋
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣤⣤⣤⣤⣤⣽⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣥⣤⣤⣤⣤
⣿⣧⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠟⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠑⢜⣦⡀⠀⠀⠀⠀⠀⢀⢔⠕⠊
⠀⠀⠀⠀⠀⠀⠀⣰⠟⣋⣴⡾⣿⣿⣿⣿⣶⣬⡙⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⠙⡢⠤⠠⠤⢔⠕⠁
⠀⠀⠀⠀⠀⠀⢰⠏⡜⣩⣶⣶⣶⣬⠻⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⡐⠀⠀⠀⢅⡠⠠
⠀⠀⠀⠀⠀⠀⡏⠸⣼⣿⣿⣿⢻⣿⣧⢹⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡇⢠⢻⣿⣿⡿⣼⣿⡿⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠐⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢿⡌⢷⣭⣭⣿⣿⡿⢃⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠘⣿⣦⣙⣛⣛⣋⣴⣿⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣾⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⢀⡄⠀⠀⠉⠛⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠈⠧⠤⠐⠒⠒⠒⠒⠢⠤⠤⠤⠔⠒⠒⠒⠒⠤⠤⠤⠤⠒⠒⠒⠒⠢⠤⠤⠤⠞




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠘⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣁⡱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢿⣿⣫⣟⡀⢀⠀⠀⠀⠀⠀⠀⢀⣉⡁⢐⡢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣐⣄⣀⣀⣀⠀⠀⠹⣿⣟⠀⢡⣀⣄⣐⣻⣶⣶⣾⡿⠿⠿⠾⢮⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢰⠞⠁⠉⠙⠛⠿⣿⣶⣴⣿⣿⡄⡀⠹⠿⣯⣻⣿⡟⠁⣰⣮⣾⣶⣶⡝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠋⡀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⢧⣄⠈⢸⣿⡟⠀⠭⣿⣿⠋⢵⣨⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡹⣧⣾⣿⡇⠀⣠⣿⣿⣄⡘⣉⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠻⣿⣿⣧⡈⠻⢛⡿⣿⣿⡿⣿⠏
⠀⠀⠀⠀⠀⠀⣠⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡉⣿⣿⣷⣤⣉⣈⣃⡬⠞⠁
⠀⠀⠀⠤⠄⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠛⢿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⡙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣎⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠯⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄






⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣡⣉⣬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠚⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⠀⢀⣠⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠄⢐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⢀⠔⠋⠁⠀⠀⠀⠉⠙⢷⣀⠀⠀⠀⠀⠘⣌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⠃⠀⠀⢀⣀⣄⡀⠀⢀⠀⠹⣆⠀⠀⠀⣼⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡴⠡⠀⢉⠛⣆⠀⠀⣀⢹⣷⠀⠀⣿⣿⣦⡀⠂⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠳⡘⠛⣸⣿⡿⢠⢾⠻⠈⣿⣦⣄⣥⣾⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢀⠀⠀⠘⠻⣶⣷⣾⠟⠀⣾⣦⣤⢢⣿⣿⡟⠋⠉⠛⣫⡶⣢⣴⡶⠖⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡹⣄⣀⣈⡀⢀⣀⣠⣴⣿⣿⣿⠇⣘⣿⣿⣶⣶⣿⣻⡟⡛⢿⡿⢛⠄⣄⣪⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣼⣿⢿⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⡿⠛⠻⠟⣟⡷⢛⠿⠵⡉⠔⠉⡿⢟⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠛⠟⠛⠛⠉⠷⠿⠿⠟⠛⠷⠞⠓⠈⠛⠉⠡⠤⠍⠘⠁⠴⢧⡴



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢭⣟⣛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⡉⠀⠉⠻⣿⣯⡻⣿⣷⡂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡂⠈⠙⣿⣷⡀⠀⠀⠘⢿⣿⡈⢿⣿⡦⣕⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣍⠛⣿⡆⠀⢸⣿⣅⠀⠀⠀⢸⣯⡄⠈⣿⣿⣄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢰⣿⡃⠀⣾⣿⣯⣀⡀⠀⠨⣿⣧⡀⢻⣿⣿⠂⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣠⣴⣀⡘⣿⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣾⣋⠀⢠⣾⣿⡷⠖⠀⠀⠸⣿⣽⠄⠸⣿⡿⡤⠀⠀⠀⠆⠀⠀⠀⠀⣠⡟⣿⢽⣥⡙⢿⠷⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠃⠀⠁⣠⣾⡿⠿⠉⠀⠀⠀⢸⣿⡗⠀⠀⣿⣅⣀⠀⠀⠀⠈⢀⠀⣀⣺⣫⣽⣫⣩⡤⠛⣠⣷⠟⠟⠳⠤⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⣴⣿⣟⠿⡟⠃⠀⠀⠀⢠⣿⡿⠞⠱⣾⣟⠿⠓⠀⠂⢰⠶⣾⡫⣭⣏⣧⣠⠶⠛⠛⠋⠀⠹⣖⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠟⠛⠻⠛⠁⠀⠀⠀⢀⡴⢋⣁⣀⠀⠀⣸⣿⣷⣤⣶⣾⣿⣶⣍⣷⣦⣤⣹⣟⠀⠀⠀⠀⠀⠀⠈⠵
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣷⣤⣄⣀⣤⣤⣴⢶⣟⣿⣹⣿⣟⣟⣿⣏⠙⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢀⣤⣾⢿⣿⣿⣟⣿⣻⣿⠾⠿⣯⣿⣾⣽⣿⣮⣴⣷⣿⣶⣿⣂⣟⣹⢮⠌⣿⢼⣿⣷⠷⠃
⠀⠀⠀⠀⠘⠋⠉⠉⠉⠉⠀⠙⠛⠛⠻⠿⠻⠇⣟⣿⡾⢿⡟⡻⠿⠿⠻⠃⠛⠉⠉⠉⠉⠉⠉⠉⠉








⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⠖⠒⠆⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠉⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⢀⠀⠙⢷⡀⠀⠨⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠂⠀⡔⠀⠀⠀⠀⢄⠸⢧⠀⠀⢹⡄⠀⢘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢰⠆⠀⡃⠀⠀⠀⢸⡆⡧⢈⡇⠀⠰⣿⠀⠈⣼⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣯⣄⣠⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠸⣧⡀⢀⡀⠀⠒⣛⡴⠃⣸⠇⠀⠀⣿⡄⠀⣸⣿⣿⣟⡀⣀⠀⠀⠀⠀⢀⣀⣠⣤⡾⠿⠛⠻⡟⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢹⡁⠀⠀⠘⢿⣄⡉⠉⠉⢉⣀⡴⠋⠀⠀⣴⣿⣿⣿⡿⠻⣿⣿⣿⠿⠿⠿⠿⠿⠟⠟⠋⠁⠀⠀⢀⠀⣀⠩⠛⠃
⠀⠀⠀⠀⢀⣀⣠⡤⣵⣄⠀⠀⠀⠙⠛⠛⠛⠛⠉⠀⢀⣲⣼⡿⠟⠋⢁⣠⣾⣿⡷⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠐⣿⠝⠁
⠴⣶⣶⣟⡋⠉⠏⠘⠀⢛⣿⣶⣷⣄⣦⣀⠀⣀⣀⣤⣶⣿⣫⣤⣶⣾⣿⣿⣿⣳⣀⣆⠀⢡⠄⠤⣀⣊⣤⡽⠃⠀⠀⠀⠀⣀⣀⣀⣤⣴⣶⣶⡿⠓
⠀⠀⠉⠉⠛⠛⠿⠷⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣭⣭⡍⣭⣭⣵⣶⣷⣾⣛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠓⠓⠛⠛⠛⠓⠷⠾⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣟⣛⣛⣛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠗⣤⢄⡛⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣭⣍⡉⢭⣭⣭⣭⡭⠁⣾⡷⢋⣥⣬⣭⣭⣍⡙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢿⣿⣿⣿⣿⣦⡙⠟⣡⣶⣿⣿⡇⢹⣿⣿⣿⣿⣿⡇⢸⣿⡇
⠀⠀⠀⠀⠀⢰⣿⡟⣡⠶⢶⣦⡙⣿⣿⣿⣧⢸⣿⣿⣿⢛⣡⣾⣿⣿⣿⣿⣿⡇⢸⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡄⢧⣼⡆⣹⡇⢹⣿⣿⡿⢸⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⠇⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣾⠿⢡⣿⣛⣩⣴⣿⣿⣿⢁⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣠⣦⣬⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⠏⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠠⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠁