Plate tectonics Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⣤⠤⠴⠶⠖⠖⠶⠶⠤⠤⣄⣀⡀⠀⠀⠀⣀⣠⠤⠖⠒⠛⠛⠉⣉⠉⠉⠉⠉⠉⠉⠉⠙⠓⠒⠦⠤⡄
⠀⠀⠀⣧⠤⠤⠤⠶⠶⠦⠤⠤⣤⣀⡈⠉⠑⠚⠋⣁⡤⠶⠒⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠒⠲⠦⠤⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⢀⣤⣶⡴⠒⠒⠛⠉⠉⠉⠉⠉⠋⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡗⠛⠉⠉⠉⠉⠉⠛⠲⢤⡀⠀⠙⣆⠀⠀⠀⠸⣄⣠⠤⠖⠒⠛⠉⠉⠉⠉⠉⠉⠛⠓⠒⠦⢤⣀⡀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢘⣦⡀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠙⠷⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠑⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⢠⠶⠖⠒⠒⠛⠛⠛⠒⠒⠲⠶⠤⣄⣀⡀⠀⠀⣀⣠⡤⠶⠒⠛⠉⠉⣁⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠉⠉⠉⠛⠒⠶⡄
⠀⠀⢸⣤⠤⠤⠶⠶⠶⠶⠦⠤⢤⣄⣀⡀⠈⠉⠓⠋⠉⣀⡤⠶⠒⠛⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠙⠛⠒⠲⠦⢤⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⣠⣆⣠⠤⠴⠶⠒⠒⠒⠒⠒⠒⠶⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⣄⠀⠀⠀⠀⠈⢳⡀⠐⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⣀⣤⡤⠤⠤⠤⠤⣤⣀⡀⠀⠀⠈⠳⡄⠀⠀⠀⠀⢷⠀⠀⠀⠀⣀⣀⣤⡤⠤⠤⠤⠤⠤⠤⣤⣀⣀⡀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠹⡄⠀⠀⠀⠈⢧⡴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⢤⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⣽⣶⡀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠙⠷⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠠⠀⠤⠀⠄⠤


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠄
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⢤⣀⣀⣤⠖⠓⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⣷⠀⠀⠠⠂
⠀⠀⠀⡴⠤⢤⣀⠀⠀⠀⠀⠀⠀⢀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣀⣀⣄⣀⢀
⠀⠀⡰⠁⠀⠀⠉⣯⠀⠀⠀⠀⡴⠋⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠉⠀⠉⠉⠉⠛⠛⠲⣞⠓⢦⣀⡀
⠀⠀⡅⠀⠀⠀⠀⢻⡀⠀⠀⠘⣇⡠⢶⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡤⠶⣶⣶⣶⣤⡤⣼⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣬⣍⡁
⠀⠀⠈⢦⠀⠀⠀⠈⠳⣄⡀⢠⠟⠛⠛⠟⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠙⢛⡟⠁⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢱⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠙⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⠳⠤⣀⡀⣸⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣀⣀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⢀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠉⡏⠀⠀⢀⣠⣤⣀⠈⢧⡀⠀⠀⠀⠀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣎⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡶⠚⠁⢀⣀⣼⣠⡤⠿⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠋⠉⠉⠁

⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠢⠄⠠⠌⠀⠀⠀⠀⠀⠀⠀⠈⠃⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⣤⣤⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠈⠁⠀⠀⣀⡁⠀⢀
⠀⠀⠀⠀⠀⠀⡘⠀⢀⠄⠀⠀⢀⡠⠄⠊⠈⢢⡀⢗⣒⡒⠓⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣀⣤⠉
⠀⠀⠀⠀⠀⠀⣇⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢨⢻⡙⠉⠋⠀⠂⣀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡄⠈⠴⠀⠄
⠀⠀⠀⠀⢠⠔⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠉⠑⠒⠶⠆⠒⠚⠢⢲⠞⢶⡀⠀⣠⢤⡀
⠀⠀⠀⠀⠂⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣆⣀⣠⠤⡤⢤⠤⠤⡎⠀⠀⠀⠀⠀⠀⠐⢖⣖⡘⡅⠖⡈⠙⠛⠛⠙⠛⡇
⣀⠀⠀⠈⢆⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡇⠈⢙⢶⢒⣖⠀⠀⠑⠲⡀⠀⠀⠁⠀⠀⠈⠉⠀⠈⠉⠉⠣⡀⠈⠁⡜
⠈⠒⠠⠤⠜⠉⠙⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠈⠁⠻⣷⣾⣥⣤⠀⠀⠀⠉⢹⠀⠀⠀⠦⢤⡄⠀⠀⠀⠀⢰⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠁⠈⠀⠀⠀⠀⠀⠀⠀⠅⠀⠁⡀⠀⢹⠿⢲⡖⠒⠀⠀⠀⠘⠄⠀⠀⢤⠦⠔⠀⠀⠀⠀⣘⡀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠢⢄⠀⠀⡌⠀⠋⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠀⠈⡆
⠀⡀⠀⣀⣀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠈⠲⡇⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠈⠁⠀⠉⢦⠀⠎⠀⠀⠀⠀⠀⠀⢀⡔⠒⠒⠁⠀⠀⠀⠀⠀⠑⢤⡤⠔⠔⠒⠂⠤⠀⢀⠗⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠒⠷⠒⠢⢄⢀⡠⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠰⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⢈⣀⣀⣀⠀⡀⠀⡰⠊⠀⠀⠀⡀⢧⣀⣦⡀⡈⠠⡄⢆⠀⡆
⠀⠀⠀⠀⠀⠤⠐⠀⠀⠠⣀⠀⠀⠀⡀⠴⠐⠀⠀⠀⡀⢀⠀⠂⠀⠀⠐⠉⠈⠹⢿⡧⠀⠀⠁⢀⢸⡄⠀⠀⡀⠉⠙⣿⣷⡇⠁⠀⢰⠀⢰⠃
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣀⡐⠈⠀⢰⠀⠀⢘⢀⣴⠀⠀⠈⡉⠁⠀⠀⢀⡆⢀⣨⣀⣤⡁⣦⢸⣼⣷⣴⣾⠛⠛⠓⠛⡿⣇⠄⣀⡾⣁⣾
⠀⠀⠀⠀⠀⠄⢀⠘⠂⠀⣻⡇⠀⠔⠞⢀⠠⠞⠊⡟⠁⢠⣀⠃⢀⠂⣀⡊⠹⠦⠠⡘⠾⣻⣿⣿⣿⠟⠋⠀⢁⠀⠀⠄⠀⠘⣼⡿⠖⣾⠷⡄
⠀⠀⠀⠐⠀⠀⠘⠂⡂⡇⢴⣄⡀⣰⠖⠉⠣⣀⠠⠤⣀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠐⠂⠐⢟⣩⡿⠋⠀⠀⠀⠄⠀⠈⠂⠀⠀⠘⠻⠷⡔⠈
⠀⠀⢠⣁⠠⠤⠰⣿⠁⣷⢼⣰⡟⠁⠀⠀⠀⠄⠀⠀⠈⠀⠀⠐⠠⠀⠀⠀⠀⠂⡀⠉⠀⠈⠀⠀⠀⠀⠀⠀⣰⢿⡆
⠀⠀⠀⢉⠀⠀⣰⣿⣽⣷⠞⠁⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁
⠀⠀⠀⠐⠃⠈⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠚⠙⠃⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠶⠶⠶⠶⠶⠶⠶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢀⡾⠛⠶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣅⡀⠀⠀⠈⠙⠓⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠙⠳⠦⣄⣀⠀⠀⠀⠉⠙⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣿⣤⣄⡀⠀⠀⠀⠀⢀⡟⠛⠶⢤⣄⡀⠀⠀⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⠏⠛⢻⣍⡿⠋⠉⠀⠈⠉⠙⠛⠿⢷⣦⣀⢀⡞⠀⠀⠀⠀⠈⠙⠓⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⣿⡿⣿⡿⣇⣀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠛⠛⣷⣏⢷⡄⡤⣄⠙⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠙⢿⡾⠛⠓⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⠉⠉⠛⠋⠉⠁⠀⣔⣦⣏⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣼⠃⠀⠀⠀⠀⠈⠉⠛⠲⠦⣤⣀⡀
⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡆
⠀⠀⠀⠀⣸⣿⠟⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠁⠐⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠷⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⢀⣿⡿⠁⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠸⣿⢻⠳⠶⣤⣀⡀⠀⠀⢠⡏
⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠈⠉⠛⠲⠛
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣦⠄
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠈⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠠
⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⢽⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣀⣤⡤⠶⠟⠋⠁⠀⠀⠀⣾
⠀⠀⠀⠀⢿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡤⠬⠉⡉⠛⠛⠛⠛⠛⠛⠉⠙⢧⠀⠀⠀⣡⣤⡴⠶⠶⣄⡏
⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⢠⡀⠀⠀⠀⢀⣠⣬⠷⠞⠛⠉⠁⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠷⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⣀⣠⣴⣶⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠘⢦⡴⠞⠛⠉⣁⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡀⠀⠀⠀⠀⠀⡆⠀⠀⡔⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠢⠤⠧⠤⠯⠔⠐⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠐⠦⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠂⠀⠀⠀⠀⠀⠀⠀⢈⡷⣀⠀⠀⠀⢀⡀⢀⠀⢀⠀⢀⡀⠀⠀⣠⠀⠚⢸⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠗⠀⠀⣈⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⢟⡀⠀⠇⢈⣿⢽⡂⠀⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠇⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣅⠀⠶⠋⢉⢻⠵⢦⡀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⡑⠀⠀⣁⠤⠤⠿⠈⢎⡛⠂
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢺⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⡈⡥⣤⡠⢴⡖⠒⢿⣄⣀⠀⠀⠀⠀⠀⠀⠂
⠀⢠⣀⣀⡤⠤⠤⠄⠄⠤⠔⠤⠤⠴⡏⠔⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⢀⠤⠂⡀⠋⢘⠰⠀⠹⡖⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢸⠀⠀⠀⠁⠀⠁⠀⠴⢄⡀⠀⠀⠙⡆⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠄⠥⠰⠀⡰⠚⠐⢥⣸⢸⠀⠀⠈⡑⠂⠊⠉⠉⠉⠉⡒⢺
⠀⢸⠀⢠⠒⠒⠓⠀⠃⠁⠀⠉⠢⣄⠀⠸⠄⡀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠁⠀⠀⠈⢯⢸⠀⠀⠐⡀⢶⠀⠀⠀⠠⠀⠀⠸
⠀⠘⡂⠈⠤⠀⠖⠒⠒⠢⣀⡤⠐⠁⠀⠁⠀⠁⠉⠉⠀⠈⠉⠉⠀⠃⠒⠂⠒⠂⠒⠒⠦⢄⡀⠀⠀⠒⠁⠀⠀⠀⢘⢨⣾⢡⠌⠁⠈⠉⠉⠉⠉⣳⠈⢸
⠀⠀⠓⠒⠒⠐⠒⠂⠂⠂⠒⠂⠊⠂⠒⠠⣀⣀⡀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢶⡀⠀⠀⠀⠀⢸⢸⠁⠀⠑⢄⣴⠶⠤⠸⢰⠗⠀⠼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠑⠐⠤⢤⣀⠀⠀⠙⢶⣤⣄⣀⢘⢸⣀⣀⣠⣌⣉⣀⣖⣔⡁⠀⠀⣒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠠⠱⣽⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢾⠟⠛⠋⣻⣯⣾⣶⣖⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⡿⠖⠈⠀⠀⢰⣿⣿⣿⣤⣽⣻⣇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⣤⣀⠀⠀⠛⢻⣾⡿⠁⠙⠈⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⠉⠀⠀⠈⣿⠆⠀⠀⠀⢈⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠠⠴⠤⠤⠤⠴⠒⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠀⡀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠝⠙⠈⠠⣴⠂⠶⠿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⢽⣿⡛⠆⠀⠠⠌⣅⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡸⣦⡴⡀⠲⣤⣙⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠰⠈⠀⠀⡘⠀⠀⠀⠀⠈⠻⠄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣛⣀⠀⠁⡜⠿⠃⠠⠟⠀⠂⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠰⢐⠃⡗⡶⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠹⠋⠀⠀⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠁⡄⠀⠀⠁⡀⠀⠀⠀⢀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠁⣈⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣡⡀⢶⣿⠳⣶⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⡝⣶⣀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⣴⢏⡁⠈⠓⠤⠙⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⣷⡟⠿⠟⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡽⠿⣬⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⣨⡞⢈⠀⠀⢀⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⡠⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠻⢲⡀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣛⣃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢈⣷⠀⣸⠟⣆⣠⢴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠀⠘⠛⠟⠒⠛⠋⠉



⣀⣀⣀⢀⡀⣀⣀⣀⣀⣀⣀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢻⣄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢻⠛⢻⣧⣀⡙⣟⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⡀⣜⡁⠈⢳⡕⠈⠻⢿⣧⣀⡨⣵⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠄⠀⠐⠉⠖⠐⠘⠏⠻⡦⢮⣁⠺⢿⣄⠀⠐⣦⣝⠬⣀⣌⠻⠶⡯⠢⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠘⠛⣁⡙⢲⠠⣤⣀⠛⣏⣀⣨⠯⠀⠙⢿⢧⣌⡙⠟⠶⢈⡓⠒⠲⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠱⠆⠓⠂⠀⣌⠉⢈⠙⣿⠁⠀⢀⠘⢷⡓⢆⣦⣀⠑⢤⠀⣈⡀⠀⠙⠶⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⢀⠒⢂⣀⣀⢠⣥⡄⠀⠀⡀⠀⠀⠀⠈⠁⠹⣝⡳⠤⣁⡁⠘⢷⣒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠙⠓⠀⠀⡀⢻⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠹⣤⣤⣙⠂⠀⠙⠶⠤
⠀⠀⠀⣀⣀⣀⡀⡠⠠⠂⠲⠶⣶⢀⠀⢄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⢿⡁⠒⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠛⠋⠁⠀⠙⠐⠙⠋⡹⠋⢈⠋⠫⡄
⠀⠀⠀⡇⠀⢠⠤⠤⠤⠤⠠⠀⠖⠈⠲⢤⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢚⠁⠀⠀⠀⠀⠀⠀⠀⢠⠍⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡂⠀⢼⡐⣀⡀⡀⡀⡀⡀⠀⠀⣠⠙⠀⠀⠀⠀⢉⠙⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⢪⠀⠀⠈⠉⠉⠈⠉⠉⢉⢱⠀⠀⠀⠀⠀⠀⠀⠊⡇
⠀⠀⠀⠸⣀⡀⠀⠀⠀⠀⠀⠀⠰⠔⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠙⠻⠶⣦⣤⣥⣀⠀⠀⠙⢄⡰⠀⠐⠒⠐⠦⠖⠎⠀⠀⠀⠀⠄⠀⠀⢌⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠉⠉⠉⠉⠉⠁⠂⠂⠂⠂⠀⠂⠂⠒⠒⠤⠤⣀⣀⠉⠉⠻⢿⣦⡤⣦⣭⣤⣠⡀⠀⠀⠁⠀⠀⠀⣀⡀⣀⣀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠢⠬⣉⠓⠴⢄⡈⠙⢌⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠪⢕⡢⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠶⠄

⠀⠀⠀⠀⠀⠀⢀⠄⠀⣠⠈⡀⠀⢀
⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠐⠛⠇
⠀⠀⠀⠀⢀⠋⠀⠀⡄⠀⡀
⢰⣤⣤⡔⠂⠀⠀⠀⠀⠀⠀⠀⡀
⢸⡿⢻⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢂
⢸⣳⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡄⢼⢂⡀
⠀⠀⠀⡀⠀⢠⣠⣄⡄⠀⠀⠀⠀⠀⠀⢀⣤⡶⢣⢋⠎⣠⣷⡡⡤⡄⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⢀⡀
⣿⢸⡇⠑⠀⣺⡇⡈⣿⠀⠋⣾⢸⠰⠶⠦⠟⠱⠋⠊⠀⠷⠂⠻⠞⠲⠾⠷⠶⠀⠀⠀⡇⣻⡀⡅⣼⣿⣏⡇⠠⠸⢁⡂
⠀⢘⣀⣀⣀⣥⠇⠻⣦⣤⣄⣘⣀⢠⣤⣤⣤⣤⣤⣤⡀⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠁⠀⠁⠀⠈⠿⠋⠁
⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠸⣿⢿⡿⡿⠛⠉⠀⠉⠙⠻⢿⡿⣿⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠰⠞⠛⠶
⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠘⡄
⣀⣀⣀⣾⣿⣿⣦⣤⣤⣄⣀⣀⣀⠞⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠰⠆⠀⠀⠀⠄⠀⠀⠀⠄⢤⣀⠀⠀⠀⠛
⠉⠉⠉⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠰⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠂⠀⠀⠀⠀⡀⠀⠐⠈⠀⠀⠀⢈⣀⣀⣀⠀⡀⢀⠲⠊⠀⠀⠀⡀⢧⣀⣦⡀⣈⠠⡄⢆⠀⡇
⠀⠀⠀⠀⠀⠤⠐⠀⠀⠠⣀⠀⠁⠀⡀⠴⠐⠀⠀⠀⡀⢀⠀⠂⠀⠀⠐⠉⠉⠹⣿⡧⠀⢈⠋⢀⢸⡄⠀⠁⡀⠉⠹⣿⣷⡇⠁⠀⢠⠀⢰⠃
⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⣤⡐⠀⠀⢰⠀⠀⢐⢀⣴⠀⠀⠘⡉⠁⠀⠀⢐⣆⢀⣨⣀⣤⡃⣦⢸⣼⣷⣴⡾⡛⠛⠛⠛⡿⣇⠄⣀⡾⣉⣿
⠀⠀⠀⠀⠀⠆⢀⠘⠂⠀⣻⡇⠀⠔⠞⢀⠠⠞⠊⡟⠁⢠⣀⠃⢀⠲⣄⡎⠻⠦⠠⡘⠾⣿⣿⣿⣿⠟⠉⠀⢁⠀⠀⠄⠀⠘⣾⡿⠗⣾⠷⡄
⠀⠀⠀⠐⠀⠀⠘⠂⡂⡧⢼⣄⡀⣴⠖⠉⠣⣀⠠⠤⣀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠐⠂⠘⢟⣫⡿⠋⠀⠀⠀⠔⠀⠉⠂⠀⠀⠘⠿⢷⡜⠈
⠀⠀⢠⣁⠠⡤⠸⣿⡁⣿⢾⣰⡟⠁⠀⠀⠀⠄⠀⠀⠈⠀⠀⠐⡠⠀⠀⠀⠀⠂⡀⠉⠀⠈⠄⠀⠀⠀⠀⠀⣰⢿⡆⠀⠀⠀⠀⠃⢀
⠀⠀⠀⢛⢂⠘⣰⣿⣽⣿⠞⠃⠀⠀⠀⠀⠀⣠⡦⠀⠀⠀⠀⢀⠀⠀⠆⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠐⠛⠊⠁⠀⠄⠀⠀⠀⠀⠀⠀⠠⠚⠛⠃⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠴⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡕⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡰⣄⠉⡰⢤⡀
⠀⠀⠆⠤⠄⠄⠀⠀⠀⠀⠒⠒⠂⠂⠒⠒⠂⠉⠈⠐⠸⣿⠀⠀⠈⠑⠒⠠⠠⠄⠤⠄⠤⠄⠤⠤⡤⠤⠤⠤
⠀⠀⡄⠀⠀⠀⠀⡴⠚⣀⡀⣀⡀⡀⡀⠀⠀⠀⢀⠄⢊⣿⠀⠀⠀⡀⣀⣀⣀⣀⣰⠠⡀⠀⠀⠈⠀⠀⠀⢸
⠀⠀⡆⠀⠀⡀⠦⡀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠘⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠈⠀⠄⢨
⠀⠀⣇⠀⠁⠀⠀⠈⢢⡅⠈⠉⠉⠉⠀⠀⠀⠀⠀⡠⠔⠹⢄⠀⠈⠉⠈⠘⢋⠛⢆⢠⠖⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠉⠁⠉⠁⠀⠀⠀⠀⠀⠈⠁⠁⠑⠒⠐⠒⠚⠛⠒⠒⠒⠒⠂⠀⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⡀⡀⠀⠀⡀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⡷⠀⠈⠀⠀⡄⠀⢀⠉⠹⢶⡦⠀⠀⡄⢀⠂
⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⠀⣈⠀⢀⢀⣦⠀⠀⠀⠀⠀⢠⣆⠠⠆⠠⣰⣦⣦⣷⠶⠋⠉⠁⠀⠠⡀⣴⢣⡾
⠀⠀⠀⠀⠀⠀⠀⡀⡉⠀⢉⡡⢦⠀⠀⡁⠀⠒⠀⠀⠐⠀⠈⠀⠀⠉⡾⢿⡿⠁⠀⠀⠀⠀⠀⠀⠸⣯⡘⠉⠂
⠀⠀⡀⠀⠀⢴⠀⣧⠟⡵⠊⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠈
⠀⠀⠈⠀⢀⠈⠬⠷⠊⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠦⢤⣤⣄⣀⣀
⠀⠀⠀⡞⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠲⠶⢤⣄⣀⠀⢀⣠⡤⠶⠚⠋⠉⠉⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠉⠉⠙⢳
⠀⠀⠀⣧⡤⠴⠶⠶⠶⠖⠒⠶⠶⠶⠦⢤⣤⣀⡀⠀⠀⠉⠙⠉⠁⢀⣠⠴⠖⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠒⠶⠦⣼
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢀⣴⣾⣿⣟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣧⠤⠶⠶⠖⠒⠒⠒⠶⠶⠦⣤⣀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢀⣀⣠⣤⠴⠶⠶⠒⠒⠒⠒⠒⠲⠶⠶⠤⣤⣄⣀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⢳⡀⠀⠀⠀⠀⠈⢷⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢤⣼
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢀⣳⣶⡀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠙⠻⣧⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈


⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠦⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡚⣗⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢱⠇⢙⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣄⠈⢀⠣⣦⣀⠀⠀⠀⠀⠀⠄
⠀⠀⢰⠡⠤⠤⠤⠠⠄⠄⠤⡠⠀⠖⠤⠰⠠⠂⠖⠒⠖⠀⠊⠅⠁⠂⢹⣾⡅⢀⠀⡉⠓⠖⠦⠤⠠⠤⢄⣄⡀⡠⢤⢤⣄⣄⢀⣠⡤⣄⣀⡄
⠀⠀⢐⠀⠀⢀⠀⠀⠀⢀⡨⠦⠀⠀⠀⠀⠀⠀⡂⠀⢀⠨⠂⢀⠁⣈⠴⣿⡃⠔⠀⡂⢀⢀⠈⠂⡀⠀⠁⣤⠀⠀⠀⠀⡀⡐⡋⡀⠂⠀⢀⡆
⠀⠀⠸⡀⠀⠀⢀⠢⠀⠋⠀⠘⠆⠂⠒⠐⠐⠂⢦⠄⠠⡪⠂⠀⠊⠀⢐⣿⡆⢁⠀⠨⡾⠙⠉⠉⠻⠿⠛⠋⠙⢿⣿⣿⡯⣾⣫⣾⣯⣿⣿⡇
⠀⠀⢸⠀⠀⢁⡀⠆⠓⢄⠀⠀⠀⢀⢀⡀⣀⣐⡲⠀⠀⠀⠠⠂⠀⠁⢐⡯⡇⠀⠠⢐⣷⣀⣀⣀⣀⠀⠀⠀⠀⠀⢈⣩⣸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢘⠀⠂⠁⠀⠀⠄⠈⠣⣼⠀⠀⠀⠀⠁⠁⠨⠀⠄⠀⠪⠀⠀⢠⠕⠑⢇⡀⠀⠀⠀⠅⠉⠘⢉⡉⠉⠇⢀⠴⠁⠀⠀⠀⠀⠨⠂⠈⠡⡆
⠀⠀⠈⠉⠋⠊⠘⠁⠁⠈⠘⠘⠐⠂⠂⠐⠁⠃⠚⠐⠐⠃⠊⠈⠁⠀⠀⠀⠀⠉⠚⠊⠂⠐⠤⠴⠡⠤⠤⠭⠼⠤⠄⠄⠅⠄⢄⢠⣈⣈⣨⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢀⣤⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠁⡋⠋⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠍⢰⠁⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢸⠀⢠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⠀⢲⠀⠀⠄⠀⡇⣠⡄⣶⠐⣄⣤⣤⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡎⠁⢀⠀⠀⠂⠀⠉⣀⢿⣧⡟⣤⢿⣾⠟⠋⢀⣀⣯⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠋⠋⠠⠀⠀⠠⠀⠈⠀⠀⠐⠢⠱⠚⣇⣟⡳⣴⠺⡍⠟⢻⣿⠘⣄⡴⠒⠠⣁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⢀⠀⠀⠃⠀⠀⠋⡀⠀⠉⡄⠂⠁⢂⠔⠓⠚⠙⣁⣷⣫⣠⡙⢛⠛⣿⠗⢸⡀⣶⠈⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⠀⠀⠀⡄⠀⠀⠄⠀⠀⠃⡄⢡⠀⠀⠀⣠⠝⢮⠟⡿⠙⠒⣦⣻⠾⣦⠐⣍⠰⣎⠁⡀⠤⠁
⠀⠀⠀⠀⠀⠀⠘⡟⠀⡄⠀⠀⠀⠄⠀⠀⠲⠀⠀⠈⠠⠀⠀⠁⢦⠀⣠⠈⠸⠰⣽⠃⣶⣻⣷⠋⠀⠋⣇⡱⢀⡅⠂⠉⠀⠠⠄⠁
⠀⠀⠀⠀⠀⠀⣼⡠⠀⠀⠀⡄⠀⠀⠐⠀⠀⠈⠀⠄⠠⣜⢣⠄⢸⠄⠈⢀⠃⡆⣯⡻⡟⢿⢺⡓⣄⢠⠛⠁⠂⢠⡀⠒⠈⠠⠤⠄⠚⠂⡀
⠀⠀⠀⠀⠀⢠⠘⣧⢀⠀⠀⠀⠠⠀⠀⠀⠁⢠⠀⠀⠌⣲⣿⣤⠂⠀⠁⡴⢔⠀⢠⣆⠙⡌⠉⢓⠜⠻⠀⠋⠈⡀⢀⠀⠂⠘⠀⠀⠢⠀⠁
⠀⠀⠀⠀⠀⣎⢰⣿⠀⠀⠀⡀⠀⢀⠐⠀⣠⠂⠀⠘⠀⠅⢊⠞⠒⠃⠰⠤⡼⠶⠀⠚⠂⢉⠗⠪⢦⠀⡄⢼⢊⢙⡀⢄⣠⠒⡋⢃⢀⠑
⠀⠀⠀⠀⠀⠩⣿⢸⠀⠀⠀⠀⠀⠆⠀⠀⠁⠀⠂⠀⡀⠀⡈⢠⡞⣬⣡⠤⣶⠞⠛⠛⠷⣧⣀⠃⣴⠂⠀⠸⠆⢈⡝⠀⠙⠃⡀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⣀⠐⡁⠢⡤⠀⣠⠀⡠⢗⣺⡁⠁⠀⠤⠀⠀⠂⢄⡄⠀⠙⠉⣫⠐
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠋⠀⠀⠈⠀⠀⠀⠛⣤⠮⠁⠀⠀⠂⠀⠀⠁⢠⠀⠀⠘⠀⡀⠁⣠⠂
⠀⠀⠀⠀⠀⠀⢀⣀⠴⢲⡤⢀⡀⠀⣀⠂⠀⠀⠀⠀⠛⡻⡁⠀⠐⠀⢀⠈⠀⠠⡀⠀⠘⠀⣄⠀⠐⠓⠳⠉⢳⣄
⠀⠀⠀⠀⠀⠀⡜⡇⠀⠚⠁⠈⠉⡏⠉⠐⡥⠀⠄⠀⣴⣿⠀⠚⠀⠀⠈⠀⠴⠀⠀⠉⠀⡄⠀⠈⠁⠠⠁⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⢂⠀⠂⠀⡀⣀⠀⠀⠤⠀⠀⠇⠈⠙⠉⠐⡙⠳⣀⡐⠁⠀⠆⠀⠀⠉⠀⠄⠀⠈⠁⢠⠄⠀⠈⠀⠰⠀⢰
⠀⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠀⢀⡀⠀⢠⠀⠀⠇⠰⢦⠖⠐⡌⠓⢾⢦⣄⠁⠀⠌⠀⡀⠁⠠⠆⠀⡈⠀⠰⠀⢀⢻⡄
⠀⠀⠀⠀⣰⠇⢀⠀⠤⠀⠐⠃⠀⠀⠁⠀⠈⡀⡀⠰⠄⠀⡂⠂⢁⠀⠉⡀⢛⣧⠆⢀⡀⠁⠀⠆⣀⠈⠀⠰⠀⢀⠀⠘⠇
⠀⠀⠀⠀⣟⡀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠀⠁⢁⠀⠀⡄⠀⠤⠀⠘⠀⠉⢁⣼⠃⠀⡐⠁⠐⠦⢀⡈⠁⢰⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⢁⢡⡀⠀⠀⠃⠀⠀⢁⠀⠀⢠⠀⠘⠂⠀⠠⠀⣀⡄⠀⠃⠀⠹⣿⠀⡀⠁⠀⠆⢀⡀⠀⠠⠀⡀⠈⠀⠀⠆⢸⣄⡀
⠀⠀⠀⠀⠈⠳⠂⠀⠀⠀⡀⠀⠈⠁⠀⠀⡄⠀⠰⠂⠈⠃⠀⢐⡀⠈⡖⢀⣿⡀⠈⠐⠂⢀⡀⠁⠰⠁⠀⠈⠀⠠⠀⠀⡀⠈⢁⡿⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠐⠺⢄⡀⠀⠀⠀⠆⠀⠘⡀⠀⢠⠀⠘⠀⠀⢃⡠⢋⠞⡋⠀⠐⠢⢀⡀⠀⠰⠃⢀⠈⠀⠠⢀⡀⠴⠥⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠺⣄⠀⠘⠀⠀⢢⠀⠚⠀⠈⣵⡇⡀⠀⠀⠂⢀⡈⠈⠰⠂⢀⠈⠁⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠘⠀⠀⢢⠀⠐⡀⢹⡿⠁⠀⠃⢀⡌⠀⠐⠁⢀⠊⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠘⢎⠀⢢⡤⡊⣼⠀⢁⠂⢠⡄⠀⡙⠂⣤⡤⠤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣅⢀⠀⠂⠀⡰⠀⣥⡅⠂⢠⠆⠀⠙⣠⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠢⡀⠓⣧⠀⢸⣉⣢⠤⠤⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡄⢀⠼⢀⠈⠛⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⡐⢼⡀⠈⡻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠾⠿⠟

⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⠃⣠⣄⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣶⠒⠒⢲⣲⠦⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣿⡷⠾⠷⢶⣓⣵⣖⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⠯⠷⣒⣶⡿⣷⠴⠿⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠸⠟⠚⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣻⡾⢶⣗⠚⠯⣽⡟⠀⠀⠀⠀⠀⠉⠄
⠀⠀⢀⠀⠠⣖⣞⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢀⠀⠀⠀⠀⠀⢸⣻⣭⣁⡀⠄⠀⠛⠋⠹⡀⠀⠀⠈⠁⠐
⠀⠀⣿⣷⣴⠓⠀⠀⠉⠉⠙⠲⠀⠀⠀⠀⠀⠈⢫⣿⡆⠀⠀⠀⠀⣻⠟⠉⠛⠿⠻⢟⡉⢉⣉⠥⡤⠤⠴⡆
⠀⠀⢹⣫⣯⡄⠀⠀⠀⠀⠀⢰⠂⠀⠁⠀⣠⣶⣷⣿⠃⠀⠀⠀⠀⠘⠀⢀⡀⠀⠀⢐⠩⠤⣤⣄⣤⣴⣿⡇
⠀⠀⠀⢻⣿⣿⣥⢄⡀⠀⠀⡆⠀⠀⢠⣾⣶⣿⣿⡟⠀⠀⠀⠀⠀⠀⢢⣀⠀⠀⠀⡄⠀⠠⣥⡘⡲⠝⢻⡃⠀⠀⠄
⠀⠀⠀⠀⠻⣻⣿⣟⢳⣄⠀⠰⠶⣊⣽⣿⣿⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠸⣥⣤⣼⠗⡧⠽⠒⡈⠥⡠⠈
⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣶⣶⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣿⣿⣛⣛⣛⣫⡥⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠦⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢒⣤⣄⡀⠀⠀⡀⠒⣷⣾⣧⣏⣶⣦⡀⣤⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣟⠃⣦⠛⠻⠶⢮⣤⣃⣿⣿⣻⣛⣷⡿⢿⣷⣦⣽⣳⣦⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣤⢀⣶⠿⣿⣿⣜⣥⣭⣿⣿⣥⣤⣀⡩⡧⠹⠽⠅⣡⡭⠩⠉⠛⠳⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠾⣟⣿⣻⣾⠻⢟⣿⣻⣽⠿⠟⣠⣔⣄⡦⢾⣻⣿⣿⣫⣶⡤⠒⠤
⠀⠀⠀⠀⠀⠀⣠⢠⠄⠀⢀⠇⠀⠀⠀⠀⢣⣌⠸⢿⠅⠋⠙⠿⠓⠾⣭⣿⣟⣂⠐⣊⡙⣝⠈⠓⠀⠓⠙⣃⠂⠛⢉⡮⠛⠁
⠀⠀⠀⠀⠆⢀⣭⢼⠅⠀⠸⠇⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠑⠓⠈⠀⠚⠉⠛⠁⠉⠀⠐⠦⠄⠠⠽⠒
⠀⠀⠀⢖⣧⠤⠼⠴⣤⣤⡤⠄⠘⢣⣠⣀⣀⣀⣀⠀⠛⠛⠀⠀⠀⠐⠂⠀⠀⠀⠘⠻⠀⠀⡀⠰⠟⠆⠀⠀⠀⠀⠀⢀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠉⠙⠻⡄⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣖⡀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⠖⠋⠁⠀⠀⢠⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠍⠙⠓⠀⢠⠐⠚⠣⢤⡤⠄⠀⠀⠤⠬⠿⠧⣤⢄⡄⣀⠀⠀⠰⢊⡥⠖⠋⠀⣠⡾⠖⡋⠰
⠀⠀⠀⠀⠀⠐⠶⠤⠤⢀⡤⠦⣠⣤⣄⡀⢀⢀⣀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⠁⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠤⣤⣠⣤⣀⣀⣀⣀⠀⡀⠀⠀⠀⠉⠉⠁⠀⣠⣥⣴⣅⡀⡀⠀⠀⠀⠀⠀⣠⡦⠖⠋⠁
⠀⠀⠀⡀⢤⡤⠤⠬⠤⠜⠻⣿⢟⣻⣛⣛⡓⠂⠀⣰⡦⠷⠾⢿⡿⠿⢷⢾⢿⣧⣤⣠⣄⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠮⢉⣷⠦⠴⠿⠛⠃⠀⠉⠀⠀⠘⠛⠂⠈⠋⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣽⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣭⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣄⣤⡔⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠛⠋⣠⡀⠀⠀⠀⠀⠀⠠⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣴⠞⢱⠀⡰⠈⣹⡁⠀⠀⠀⠀⠀⠀⠀⠰⠗⠀⠀⠀⠘⠓⠛⠉⠠⡆⠀⠀⠀⠈⠙⠛⣷⣤⣤⡀
⠀⠀⠀⠀⠀⢀⣠⢞⣻⣽⠂⢁⡄⠀⠀⠀⠦⣹⡄⠀⠀⠀⠀⠈⠁⠠⠐⢇⠀⢠⣀⠚⠓⠀⠀⠀⠀⠀⠀⠀⠤⠤⣄⣨⢿⣷⣌⣳⣤⡀
⠀⠀⠀⠀⡀⠈⠙⠋⠉⠈⠻⠞⠓⠒⠒⠀⠒⠘⢷⠀⠀⢰⠀⠀⠄⠠⠁⠀⠀⠀⠉⠉⠄⠀⠠⠀⠀⠀⠀⠢⠄⠀⠀⠿⢈⣿⣉⢧⠾⣿⣦⡀
⠀⠀⠀⡜⢡⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰⠀⡄⠀⠉⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⠁⢈⣻⡛⢟⡓
⠀⠀⢘⣷⡞⣿⣃⠀⠀⠀⠀⢀⠀⣉⠀⠀⢀⣐⡃⠀⡀⠀⠀⠀⠙⢂⡤⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⢀⣄⠂⢠⣉⣯⣿⣟⣿⣿⣿⠁⡆
⠀⠀⠸⡏⣷⣿⣯⣹⠀⢰⡤⠀⠀⣸⡧⠀⠈⠉⠁⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⡀⠐⣿⣿⣯⡀⠀⣽⠟⢿⠋⣿⠟⣉⡽⠃
⠀⠀⠀⠹⣿⠻⣿⣿⠀⠸⣦⠀⣴⠀⢰⠴⠆⠀⠛⠀⠀⢣⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠛⠛⠊⢉⠿⣆⠙⠂⠉⠀⠈⢂⣤⢺⣿⠃
⠀⠀⠀⠀⠉⢨⣿⣿⣦⠆⣸⢴⣾⠐⠻⡗⠐⠛⠛⠂⠀⠂⠙⡛⠛⣦⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⣤⣾⣶⢯⣴⣶⡤⢒⣤⢛⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠙⠳⣌⣹⣧⣤⠋⢳⣦⡉⠲⣦⡀⠙⣦⡀⠀⠠⠀⢈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣉⣆⡁⣠⣄⢂⣉⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠾⣏⣹⣓⣶⣿⢿⣿⡏⠻⠶⠐⠻⠋⠻⠿⣀⠀⠀⣠⣤⣴⣟⠿⢯⣡⡔⢻⣷⠳⢟⠻⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠶⢷⣤⣦⣴⣯⣄⣉⣀⣀⣈⢛⣋⣩⣁⣠⡤⠴⠂⠙⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢉⣉⣉⣉⠉⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠚⠛⠛⠛⠉⠉⠙⡿⠋⠉⢻⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣦⣿⠟⠛⡷⠶⢶⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣅⠀⠀⠀⠀⠚⠓⠂⡀⠀⠀⠀⠀⠉⢶⣤⣀
⠀⠀⠀⠀⠀⢀⣠⣖⣫⣿⠿⢁⡰⠞⡉⢱⠘⡟⠀⠀⠀⠀⠀⣠⡄⠖⣻⣏⣁⣄⠀⣤⡌⢷⡠⠀⠛⠀⠀⠀⠀⠀⠀⢹⣯⡙⠂⣀
⠀⠀⠀⢀⣴⣿⣻⣿⠿⢷⣶⡿⢷⣤⣽⣦⡄⢳⡄⠀⣰⣶⣾⣧⢀⣴⠛⠉⠁⢿⡶⣆⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⢿⡾⣷⣦⡀
⠀⠀⢠⣾⣻⣿⡿⠿⣧⣀⡀⠀⠀⢀⣀⡀⠠⢀⡿⢤⡈⢛⣿⣿⡎⠁⠀⠀⠀⠀⠀⠉⠁⠀⠈⣢⡀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⢻⣯⣉⣷⡄
⠀⠀⣾⣿⣿⣿⣷⣶⣼⣿⡇⣠⣤⣼⣧⣄⣶⣮⣵⣠⣹⡿⠟⠛⠳⢄⣀⣀⡀⠀⠀⠀⠀⠀⣿⠯⠁⠀⠀⠀⠀⠀⠀⠻⣿⣧⣌⡣⢉⣼⣿⣿
⠀⠀⣿⣿⣿⣿⢿⢿⣿⣿⠿⣿⣿⣿⣿⢿⡿⢿⡏⢿⣿⡃⠀⠀⠀⠀⠉⠙⣧⠀⠀⠀⠀⣼⡏⠀⡂⢠⡴⠶⠾⢿⣔⣐⢋⣼⡿⠓⣾⣿⣿⣿⠃
⠀⠀⠸⣷⣿⣿⣿⠀⠻⢤⡔⢾⠉⣽⣿⠿⠁⠸⣷⢀⠘⠧⣄⠀⠀⠀⠀⢰⡏⠀⠀⠀⡰⢿⣀⡠⠟⠋⠀⢠⣶⡛⠍⠙⠛⠉⣀⣾⣿⣿⣿⡿
⠀⠀⠀⠈⠻⣶⣿⣶⣧⢌⣷⣿⣤⠾⢷⣴⠦⠦⢿⡾⠷⢴⡿⡧⠀⠀⠰⡇⢹⡄⣀⡼⠿⠀⠿⠗⠀⠀⣠⣿⣥⣥⣶⣦⣀⠀⣷⡾⢻⣿⠟⠁
⠀⠀⠀⠀⠀⠙⠻⣯⡙⢣⣜⠻⠿⣆⠀⠹⠶⠀⠀⠀⡀⢈⠀⢿⡀⠀⠸⡇⠀⠀⢩⡤⠄⠤⢠⣀⠠⠊⠉⠉⠀⢀⣿⣿⣿⠾⣻⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠧⣤⣭⡳⢶⣴⠀⢠⣤⣀⣌⡄⣘⠳⢦⠰⢧⣤⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣤⣿⣼⣿⠿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠽⠷⢤⣼⣿⣤⣄⣀⠐⠤⠇⠀⠀⠀⢀⣀⣀⣀⡠⠶⠿⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠚⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣀⡤⠶⠠⠶⠿⢿⡟⠛⡿⠶⠶⣖⠒⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠠⠀⠤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⠿⠀⠀⢠⡄⠙⣴⢃⣠⠟⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⢶⣤⣀
⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠈⢀⣰⣿⢹⡁⠈⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣝⡶⣄
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣇⠀⢀⣀⡀⣠⢶⣿⠋⣉⡮⠀⠒⠶⣤⣭⡅⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠛⣿⡿⢿⣶⣄
⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⡗⠋⣻⠀⠏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢠⠁⣦⣿⡿⣦
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻⡿⣿⠛⠛⠛⢷⣤⡛⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣿⡇⠀⣀⣤⣄⠀⢠⣿⣿⡤⢛⢿⣿⠿⣾⣷
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠉⠙⢻⡿⡓⠚⠻⡄⠀⠀⠀⠀⣴⡻⣼⢷⣶⡟⢧⡿⢷⣀⠁⢘⣷⠛⠾⢿⣶⣿⣿
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣶⡄⠀⠀⠀⢠⡆⠀⠀⠘⢀⡇⠀⠀⠀⣨⡗⣛⣿⣿⣋⠳⢿⣷⠚⢿⢛⡻⡿⢿⣶⣴⣿⣿⣿
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢠⣿⠀⠀⠀⣈⣀⣷⠀⢀⣴⣿⣉⣿⣿⣉⣩⣀⣿⢻⣇⣼⡿⠟⠳⣾⡿⣯⣿⡿⠁
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⣿⣿⣿⡿⣿⣉⣥⡉⣷⡀⠘⢃⡀⠀⠀⠀⠦⢈⠛⠿⢭⠉⣉⣙⣹⠍⣡⠞⠋⠁⠀⠀⢠⣾⡿⢿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡿⢿⣌⠛⢀⡐⣈⢷⣶⡾⣷⡄⠀⣤⡉⣠⡤⠗⠚⠿⢿⣿⣷⠾⠈⣳⠀⠀⣀⣴⣾⣿⡿⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢾⣿⣿⣿⣟⣋⣈⡉⢛⠤⠁⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⣹⢶⣾⣯⡶⠿⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠘⠛⠛⠛⠶⠷⡄⠀⠀⠀⠤⠶⠶⠶⠒⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄


⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠤⠤⠔⠒⠒⠒⠒⡲⠒⠒⠐⠒⠲⢒⠒⠂⠠⠤⢠⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠦⣀⠀⠀⠉⠐⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠉⢑⠆⠈⠉⡘⠀⠀⠀⠀⠠⠄⠀⠠⠀⠈⠳⡀⠀⠀⠀⠀⠀⠉⠒⠤⡀
⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠂⠀⠈⠈⠁⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠝⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠲⠒⠐⠐⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃
⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣅⠀⠀⠀⠀⠀⠀⠀⠸⢴⠲⠦⠤⠒⠂⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠐⠹⣵⡌⠀⠀⠀⠀⠀⠑⠂⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠈⠑⠀⣀⠀⠠⠀⠀⠀⠀⠄⠑⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠰⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⢶⣯⠕⠀⠄⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠟⠁⠀⠀⡰⢀⠴⠒⠈⠀⠀⠈⠂⠀⠀⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⢄⡀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⡠⠀⠀⢀⡰⠂⠇⠐⠀⠒⠛⠚⡁⠀⠈⠀⣀⠀⣈⡨⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠠⠤⢀⣀⡀⠑⠄⡉⠿⠚⠉⠀⠀⠀⠀⠀⢀⣠⣮⠥⡴⠬⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣋⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⣄⡀⠀⠀⠀⢸⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⣶⣾⣿⣿⡦⠀⠀⢸⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡝⢿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⣎⢿⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠈⢿⣦⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⢻⣧⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠻⣷⡹⣷⡀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠹⣷⡙⣿⡄⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠙⣿⡜⣿⣄⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣏⣉⣉⣉⣉⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣷⣀⣀⣀⣀⣘⣿⣌⣿⣆⣀⣀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠶⠶⠶⠶⠶⠶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠄⠠⠀⠤⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠤⢤⣶⠖⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠉⢀⡠⣄⡀⠀⠀⠀⠀⠐⢶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⣰⠖⠈⠋⠀⠂⢡⣯⠀⠀⠀⠀⠀⢀⠀⠀⢺⡃⠀⠀⡀⢈⠙⠋⠂⠰⠆⠀⠀⠀⠀⠉⠹⣿⣶⠶⣀
⠀⠀⠀⠀⠀⢠⠴⣫⡽⢿⣉⠀⠖⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢠⡈⠧⠀⢢⣄⣈⠁⠀⠀⠀⠀⠀⠀⠀⠒⠲⢦⡜⢿⣿⣦⣵⣦⡀
⠀⠀⠀⢀⠐⠀⠔⠋⠀⠈⠉⠛⠀⠀⠉⠉⠁⠈⠷⠀⠀⢒⡀⠀⣀⠂⠀⠀⠀⠀⠀⠙⠆⠀⠢⡄⠀⠀⠈⠑⠒⠂⠚⠓⣸⡷⡞⢪⣹⣿⣦
⠀⠀⢀⡎⣠⣦⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠀⠀⠆⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠻⣿⢿⣠⣼⣏⣩⣿⡇
⠀⠀⢸⣾⡏⣽⣤⣤⠀⡀⠀⠤⠠⠤⢀⠀⠀⣴⠀⠀⡁⠀⠀⠀⠉⠶⠂⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⢠⣄⣴⣤⠀⢤⣼⣵⣿⣯⣿⣿⢧⣼
⠀⠀⠸⣍⣷⣿⣾⡏⠀⢻⠖⠀⠰⠒⠛⠀⠈⢘⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⣆⡀⢙⣿⡟⡆⡀⣸⢻⠘⡋⠹⣟⡉⣰⡏
⠀⠀⠀⠙⡿⢇⣻⣰⠀⠛⠷⠀⢃⠘⣧⠚⡀⢈⣆⠀⠀⢳⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠈⠉⠉⠉⡩⢻⡀⠈⠈⠃⠀⠀⣰⣈⣻⡏
⠀⠀⠀⠀⠀⠺⣾⡿⢷⡊⠐⢿⣟⠃⠙⣃⠘⠋⠉⣥⠀⠈⠈⠁⠉⢧⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣷⠻⢋⣶⠧⠤⣴⣾⣭⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠓⢤⣟⢳⣤⡙⠳⣦⡈⠳⣶⡄⠈⣶⡄⠀⠳⢀⠨⣄⡀⠀⠀⠀⠀⠀⢀⣀⣀⣤⢬⢿⡷⣶⣌⣁⣾⣃⣡⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣳⣾⣛⣷⢯⠿⢿⡁⠛⠛⡁⠋⠑⠛⠛⣄⣀⣠⣤⣴⠿⠭⢻⡤⣶⣬⣿⣿⡫⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠶⠶⠬⣿⣤⣤⣀⣠⣭⣩⣥⡤⠤⠴⠶⠒⠚⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⢙⠏⠁⠀⠻⡎⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠽⠋⡭⢿⡿⣽⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⠋⠁⢢⡀⠀⠀⠀⠀⠙⢳⣤⠄⡀
⠀⠀⠀⠀⠀⣠⣴⣯⣵⡿⠛⠁⠶⠧⠉⠤⠚⡇⠀⠀⠀⠀⢀⡴⠂⢹⣟⣦⢀⡂⠠⠶⠌⢳⡔⠀⠋⠀⠀⠀⠀⠀⠀⢻⡶⠙⠁⣤⡀
⠀⠀⠀⢀⣾⡿⢿⡿⢏⣿⣟⠛⠛⢓⠾⠦⠄⢷⡄⠀⣼⣿⣿⡧⣴⠞⠉⠀⠈⠿⠶⣦⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠸⢿⣯⡿⢦
⠀⠀⢠⣿⣶⣿⣯⠿⠏⣤⡄⠀⠀⣴⡄⠀⠀⢠⠟⠦⣌⣩⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣧⠀⠀⠀⠀⠀⠀⠀⣰⣿⠶⠆⣿⡎⣿⣷⡀
⠀⠀⣿⣿⣾⣿⣿⣷⣿⣿⣇⣠⣤⣿⣤⣰⣿⣿⡦⢤⣽⠟⠋⠙⠛⢦⣤⣤⡄⠀⠀⠀⠀⢸⡟⠋⠀⠀⠀⠀⣀⡀⠈⠛⣿⣶⣶⠈⣷⣿⣿⡇
⠀⠀⢿⣿⣿⣿⣿⣿⡿⣿⠏⣿⢿⣿⣾⣿⠯⠿⠟⣣⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣿⠁⠘⣀⡴⠞⠛⡛⣷⣮⣉⣼⡿⠛⢻⣿⣿⣿⡏
⠀⠀⠘⣿⡻⣿⣿⠟⠠⢿⣶⠙⠲⢾⡟⠛⠀⢸⡒⠍⠉⠳⣄⠀⠀⠀⢀⡜⡇⠀⠀⢠⣞⢃⣤⠖⠋⠁⠀⣴⡟⠄⠉⠉⠁⠠⠞⣿⡿⣿⣿⠃
⠀⠀⠀⠈⠻⣟⡻⣷⣤⡄⠻⣿⣿⠟⠳⣶⠶⠶⢻⠖⠋⠒⠿⡇⠀⠀⣾⠁⠳⣤⡴⠟⠣⠒⠟⠓⠀⣀⣾⡯⠤⢶⣿⣦⣄⣲⣿⣛⣷⡿⠁
⠀⠀⠀⠀⠀⠈⠛⠦⣝⣶⣶⠛⠻⢦⠁⠙⣇⠀⠀⠢⡀⠘⠀⢿⡀⠀⢻⡄⠀⢀⠐⠶⠒⠶⠆⣠⠊⠁⠀⠀⠀⣴⣿⣣⣿⣻⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠐⣲⣶⡟⣻⣥⣐⠢⣤⡘⠶⠀⠉⠙⢳⠘⠧⠶⠁⠀⠀⠀⠀⠀⢀⣤⣀⣀⣤⣾⣑⡎⠹⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠯⠷⢾⣿⣦⣴⣂⣼⣀⣃⢀⣀⣀⣠⠤⢤⣤⠚⠛⠍⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣉⡉⣉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣄⡤⠖⠚⠛⢛⡛⢻⡋⢩⡟⠛⠛⢏⠉⠓⠂⠀⠀⠀⠀⠀⣀⡀⠐⠆⠐⠒⠰⠂⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣯⣽⣿⡿⠋⠀⠀⢴⡁⠰⣎⢠⡾⢁⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣷⣦⣀
⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣽⣿⣿⡿⠁⠀⠀⠀⠀⢀⣀⣾⡿⣣⠃⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⢷⣟⣷⣄⡀
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠀⣠⣤⣀⣶⣫⣿⠑⣤⠇⠀⠋⠻⠶⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡟⡻⣮⠟⣦⡄
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠙⣿⣿⡞⣁⣛⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣄⠀⠀⠀⠀⠀⠀⢸⣿⠈⡡⢙⣿⣙⢟⣄
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⡿⠉⠉⠉⠳⣮⣕⡣⣄⠀⡀⠀⠀⠀⠀⠀⠀⠐⡿⢿⡀⢀⣴⡶⣄⠀⢺⡿⣿⣋⣭⣿⣿⣻⣿⡆
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠉⡻⠟⢉⣙⠻⡄⠀⠀⠀⢠⣾⣛⣿⣷⣿⠛⣿⢻⣧⣨⠀⢛⣛⡒⠸⣿⣿⣿⡟
⠀⠀⠻⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣰⠃⠀⠀⣉⢸⡇⠀⠀⢀⣬⡷⣿⣿⣟⡉⢿⣼⡇⢀⣩⣛⣟⢛⣻⣾⣿⣿⣿⠇
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣭⣿⣽⣿⣿⣿⣿⣿⡿⢷⡀⠀⢸⡧⠄⠀⠀⡴⢈⣷⠀⣠⣾⣷⢿⣿⣧⣬⣅⣈⣯⣭⡴⠿⠛⠉⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠈⠙⢯⣿⣿⣿⡿⣿⣿⣿⡹⣿⣶⠀⢠⢷⡀⠘⢣⡄⠀⠀⢡⠈⠘⠹⢋⣼⣁⣦⣉⡥⢞⣈⠉⠀⠀⠀⠀⣸⣿⣟⣻⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣾⣟⢻⣄⣉⣳⣤⣘⢻⣿⣿⢷⡄⠀⣶⣤⠴⠖⠋⠉⠻⠟⢿⡔⠃⣨⠇⢀⣀⣴⣾⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣿⣷⡞⣥⣲⣀⠙⠎⠀⠂⠋⠀⠀⠀⠀⠀⠀⠀⣠⠛⣿⣿⡿⠯⠟⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠓⠀⠠⠄⠒⠒⠛⠛⠉⠉⠉⠉

⡏⠉⠉⠉⠉⡉⠉⢉⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣍⢩⣭⣩⣭⣭⣩⣭⢉⡋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣫⠉⢉⡉⠉⠉⠉⠉
⡇⠀⠐⠲⢦⡬⢿⣾⡗⠄⠀⣀⠀⡑⠀⠀⠀⣀⡀⠀⠸⣾⡿⠭⠀⢀⠀⠨⢹⣿⡾⠀⠀⣀⡠⠀⠀⠁⠁⢤⡀⠀⠈⣿⣿⠥⠶⠒⠉
⡇⠀⠀⠀⠠⠖⣸⠿⣇⢦⡐⠁⠀⢀⠬⠓⡠⠬⠐⢠⠊⠉⢿⠀⡄⠹⠁⡄⠸⠛⠈⢢⠐⠀⠔⠀⠁⢄⡀⠀⠙⡤⢚⠝⡻⣌⠲⠄
⡗⠁⠀⠀⢀⠞⢁⠃⠈⠆⠀⠀⠀⠁⢀⠜⠁⠀⠀⠁⢶⠀⠐⠰⠀⠂⠀⢰⠀⠀⢰⠆⠁⠀⠀⠈⣦⡀⠑⠀⠢⢀⠲⠀⢃⠈⢧⠀⠀⠀⡀
⡇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⣠⠂⠀⠀⠀⡄⠀⠀⡄⠀⠀⠀⠢⣀⠄⠂⠀⠀⢣⠀⠀⠀⠀⠁⠀⠀⠂⠀⠑⠀⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⣤⠀⠀⠀⠏⢼⡄⢣⠀⠀⢠⡄⠉⠀⠀⠀⠀⠀⡀⢀⠀⠃⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠠⠋⠓⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⡅⠈⠀⠀⠀⠠⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠈⠀⠄⢠
⡇⠀⢸⠀⠀⠀⠀⠠⠀⠁⡌⠀⠠⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠦⠀⠀⠀⠀⠀⠀⢸⠁
⡇⠀⠀⢠⠀⠃⠀⠸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢻⡀
⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠦
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠲⣄
⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⢀⢻⠸⢀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⡀
⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠒⠀⣣⠀⠄⠀⠁⠀⠀⠀⠀⠀⠑⠦⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀
⡇⠀⠀⠀⠀⠀⠀⡠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀
⡇⠀⠀⠀⢀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡆⠀⠀⠀⠠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠠⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠔
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠲⣶⣦⠀⠐⠄⠀⣆⠀⠂⠉⠚⢷⣼⣄⠃⠁⠘⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠀⠈⡰⠀⠀⠀⣠⠁⠀⢒⠐⠀⠀⠠⡄⢀⡃⢀⣂⡄⣄⣿⣤⣴⠷⠗⠾⢿⣏⡀⣀⡗⣲⡇
⠀⠀⠀⠀⠀⢀⠐⠠⠘⡇⠀⠔⠏⡀⠔⠋⠿⠁⢄⡘⠀⡠⢀⡎⠓⠀⠄⠻⣿⣷⣿⡿⠋⠀⢁⠀⠠⠀⠈⢶⡿⠲⡿⠄
⠀⠀⢀⠀⠀⠘⣀⢼⡲⡧⣄⡴⠊⠙⠂⠄⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢻⠽⠋⠀⠀⠀⠀⡀⠁⠀⠀⠈⠛⠳⠁
⠀⠀⢢⡄⢒⢈⡧⣬⣗⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⢠⠾⠻
⠀⠀⠀⠢⠠⠞⠛⠛⠋⠀⠀⠀⠀⢀⠴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡀

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣗⣾⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠁⠀⠀⠠


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠂⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣴⣾⣿⠿⢙⡿⠟⠿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠛⠟⠣⠓⣿⣿⣤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡋⠐⠠⠁⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡁⣴⣷⣀⠀⠀⠀⠀⠛⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⢣⣶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⣿⠟⠛⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⣿⣿⣿⠿⠂



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣿⣛⠟⠷⠶⠟⢻⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠁⠉⣠⣶⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠉⠀⣀⠀⠀⠀⠈⠙⢿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⠁⠀⠀⢠⣿⣯⣿⣿⡿⢿⡿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠸⠿⢱⣶⡄⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⣄⠀⠘⠛⢿⣿⡟⠀⠀⠀⠨⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠀⣿⡿⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠏⠀⠀⠀⠸⠟⠑⠀⠀⠀⢠⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠛⠁⠉⡀⣠⣶⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠛⠛⠛⠛⠁


⣿⡟⡙⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⡀⠉⠂⠀⠀⣀⣴⣾⣿⣶⣤⡄⣀⡀⣀⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢾⣿⣿⡛⠛⢷⣤⠀⠀⢠⣿⣿⣿⣿⣿⡿⡏⠙⢿⣿⠿⣿⠻⢦⡀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⣤⢴⣷⠋⣿⣯⠉⠀⣠⣿⣷⣿⡿⣫⣿⣿⣿⣿⣗⠀⠀⢈⠿⣄⠙⢦⣰⣷⣾⣦⣧⡀
⠀⠀⠀⠀⠀⠀⠠⣿⠚⠁⠀⠈⣿⡧⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⠁⢎⢷⡜⠛⣿⡟⠛⠛⢧⣀
⠀⠀⠀⠀⠀⢀⣾⡟⠀⢱⣤⡀⠈⢻⣦⡀⠹⣿⣿⣟⣿⣿⣿⣿⣿⣷⡀⠐⠀⠰⣤⢨⡻⢦⣈⣿⡂⠀⠘⡟⣇
⠀⠀⠀⠀⠀⣿⡛⠳⠶⠏⠉⠻⣦⡈⢻⡀⠀⡙⠛⢿⣿⣿⣿⣿⠿⣿⡟⢆⠀⠀⠘⢷⡮⣕⡫⠻⣷⣶⠂⢧⠸⣆
⠀⠀⠀⠀⢸⣿⣧⣤⣀⠀⠀⠀⠈⠻⠦⠭⣰⣅⠀⠀⠙⣿⣿⣿⣿⣿⣷⣤⣢⡀⠀⠈⢿⡠⣙⣄⠙⢿⡄⠀⢣⣿
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⡄⣀⠈⢳⣄⣰⣾⠃⠣⠛⢿⣿⡿⣿⣿⡟⠳⢤⡀⠑⢌⠪⣓⠄⢳⡀⠀⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣫⠛⢦⣽⣿⣿⡄⠀⠀⠈⠛⢴⣿⣿⣿⣶⣤⠙⢦⡀⠃⠘⣮⣀⡹⣄⠸
⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠟⠙⠋⠘⠹⠛⠊⠈⠝⠻⠏⠑⠀⠀⠀⠢⠙⠟⠙⠉⠋⠓⠖⠁⠀⠀⠀⠀⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⢶⠿⢛⡿⠋⠉⠉⠉⠉⠀⠁⠈⠹⣿⡏⢀⡀⠀⠀⠀⠀⠀⠀⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣶⣾⣛⣿⠿⢿⣿⡿⠿⠛⠉⠀⠀⠀⠀⢀⣤⣶⣄⣀⣠⡽⠿⠿⠿⠶⣶⣤⡀⠀⠀⠀⠙⠻⣿⣶⡆⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⡛⣣⣿⣋⣻⣟⠛⢣⣼⣿⡇⢀⡀⠛⣴⡶⡾⠆⢉⠐⣿⣄⢹⣟⣡⡴⢦⡰⠆⠁⣀⠉⠒⠂⢀⣤⣀⣠⣿⣿⢋⣸⣷⣦⡀
⠀⠀⠀⠀⢀⣌⢳⣿⠟⠋⠻⣤⣿⣏⣩⣿⣿⣏⣻⣇⠈⠻⣿⣄⣁⡁⠀⣾⡟⢸⣿⣤⣿⢿⣶⣦⠑⣤⠀⠀⣴⣦⣤⣄⣀⣈⠉⣿⣿⡿⠋⠖⠉⠙⢂⡄
⠀⠀⠀⣴⡧⢡⣆⠀⠀⢀⠛⠀⣀⣀⣽⣿⣿⡿⢯⣿⢧⣀⣿⣿⠟⢱⣾⠟⠁⠉⠁⠀⠀⠀⠈⠁⠀⠀⠑⢢⠈⠁⠈⠹⣯⠐⣤⠾⣿⣷⠀⠀⣶⣶⣿⣿⡄
⠀⠀⣾⡟⣶⣿⣏⠀⣰⣿⣷⣤⣾⣿⣿⣿⠏⣱⣎⣱⣿⢻⠋⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠀⠀⠀⢀⡀⣾⡶⣙⣿⣿⠀⠀⣙⣿⣿⣹⣧
⠀⠠⣿⣴⣿⣴⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⡿⢿⣿⣿⣿⣿⡄⠀⠀⠀⠈⡿⠛⠃⠁⠀⠀⠀⠀⠀⠀⣴⢣⠤⢾⡤⢴⣾⣿⣿⡿⢿⣿⡟⠈⠙⠛⠛⣛⠛⣛
⠀⠀⢿⡏⢻⣿⣿⣿⣿⣿⣦⠼⣿⣿⣿⣿⣷⣾⣿⣿⣤⣽⣷⡤⣴⡄⡈⠷⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢰⢴⡄⣈⣡⣾⢿⣿⣿⡿⠷⠔⠀⢰⣿⣿⣿⡿
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠷⣶⠿⢿⣿⣏⣉⣷⣾⣇⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣟⣯⣽⠙⣷⣀⣠⠷⠀⢀⣴⡿⣿⣿⡟⠁
⠀⠀⠀⠈⠙⢿⣉⣻⣿⣹⣷⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣏⢉⣿⡏⢻⠛⣿⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⣟⣉⠹⠛⠛⣛⣿⡛⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠙⠧⣼⡿⢳⣿⣿⣿⣿⣿⣽⣿⣿⣦⣾⡿⢿⠟⢃⠻⣿⣿⣳⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣧⣸⠟⣁⣌⣉⣀⠾⠿⣯⡵⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡷⣿⣟⣿⣿⣣⣼⣧⡀⠀⢀⣤⣴⣶⣿⡿⠿⣧⣭⣴⣏⣤⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣿⣿⣿⣶⡿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠛⠋⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠿⠟⠛⠛⠻⡿⠟⠛⢻⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠁⠀⠀⠀⠉⠹⣿⠶⣄⠀⠀⠀⠀⠀⠀⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣾⣛⣇⣼⠀⠀⠀⠀⠀⠠⠀⠀⣤⣼⠚⢳⡀⢢⣀⣀⠤⢠⣤⠘⢶⠀⠀⠀⠀⠀⠀⠘⢷⣸⡇⢠⣄
⠀⠀⠀⠀⠀⢀⣤⣶⣻⣿⣿⣋⣹⣿⣿⣿⣶⣻⣿⡿⠀⠀⠀⣠⣄⣀⠶⡉⢸⣥⡿⢧⣽⣠⣝⠛⢣⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠘⣤⡼⢿⣄⡀
⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⠟⢷⣦⠀⢸⡷⣾⣿⣶⡟⠋⠀⠀⠖⡿⠋⠛⠷⠀⠰⠦⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠋⠿⡆⠉⢳⡄
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⠋⣶⣾⠻⣷⠤⣄⣱⣿⡕⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢴⠷⠐⢀⡀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠛⡀⠀⠃
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣙⣃⣌⣻⣆⣼⣿⣿⢟⠃⠉⠋⠤⣤⣤⣶⠀⠀⠀⠀⠀⠀⣤⠘⡀⠈⠁⢀⣀⣤⣦⣀⣀⣽⠁⣰⡜⣠⣿⡀⠶
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⣏⣿⣯⣭⣿⣿⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢺⠀⠀⢡⣴⠟⠛⠉⠿⠿⢿⣿⣷⣿⠏⠁⢻⣟⣻⣶
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⠀⣿⡿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⢀⣾⡀⠀⠀⢀⡜⢀⣀⣴⠊⠁⠀⠄⠘⠗⠀⠠⠄⠀⠄⣤⡴⠛⢛⣿⠏
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣻⣿⣁⣾⣿⢧⣠⣶⣾⣿⣿⣤⢡⡜⣿⠃⠀⠀⠀⣿⠀⠇⡀⣠⡞⠳⡌⢡⡞⠀⠀⣀⠼⠷⠦⠶⣾⣶⢤⣶⣶⣄⣀⣻⠏
⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣯⣍⣩⣿⣿⣀⠺⣿⣯⣉⠉⠻⣦⡀⠸⢿⣿⠀⠀⠀⢻⠀⠾⢉⡡⠶⠦⠬⠥⠀⡠⠊⠁⠀⠀⠀⢰⢿⠟⣤⣧⣽⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣦⣀⣿⣷⣤⡀⠴⣤⠶⠈⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣤⣼⣧⠶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣾⣿⣿⣿⣿⣋⣹⣿⣿⣿⢇⡹⢄⣷⠀⠀⠀⠀⠀⣀⣀⣀⣀⡴⣿⣿⡻⠿⠝⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠻⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠿⠛⠛⠋⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⡤⣤⣤⣤⣤⣤⡤⣄⣤⠤⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣶⣶⣿⣶⡖⠋⠁⠈⠩⣝⠉⡏⠀⢸⡛⠙⠻⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢤⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⡶⣿⣿⠏⠁⠀⠀⠺⡗⠋⣻⢧⡶⢯⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢿⡿⡴⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣏⡹⠛⣫⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣤⣼⠟⢻⠃⠀⣀⣀⠀⢠⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢻⣶⣍⣻⣦⣄
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣋⢻⣿⣿⣿⣿⣯⣿⠆⢀⣠⣤⣀⣴⣛⣭⣥⣀⡿⠁⠈⠉⠛⠛⠛⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠻⢛⠻⢏⣉⠷⡄
⠀⠀⠀⢀⣾⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⡿⢦⣀⠙⢿⣿⣯⠟⢿⣉⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⠚⠛⢿⣷⡶⢷
⠀⠀⠀⣾⢿⣿⣿⣿⣇⣤⣿⡇⣠⣿⣿⣿⣯⣘⣿⡯⠙⠋⠙⠳⣦⣤⠘⠃⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠙⠃⢛⡀⠀⣄⣻⢗⣤⢊⡿⠳⠾⠷⠂⠺⣿⢀⣾
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠉⠛⠉⡟⠛⠻⡀⠀⠀⠀⠀⢀⠚⠃⢼⠛⠿⠟⢩⡟⣿⣷⣴⣐⣾⣿⣅⡘⢿⡟⣿
⠀⠀⠀⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⢿⣶⡀⠀⠀⠀⠀⣸⢇⠀⠁⡄⢰⡇⠀⠀⠀⢀⣼⠠⠀⡌⠀⠀⠸⠿⣿⡟⢻⡟⢹⣏⣛⠹⣷⣿⣃⣽
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⢛⣯⣟⣿⡄⠀⠀⣴⡇⠀⠠⠀⣴⡄⢱⡄⠀⢀⣾⠇⠀⠀⠇⠁⢠⣦⣴⡛⠷⠾⠿⠟⢉⣉⠰⠿⣿⣽⠇
⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⠿⢷⠿⣿⣿⣿⣻⣿⣿⣿⣉⣿⣿⡀⠰⡿⢱⡄⠂⣠⢧⡄⠊⡳⠶⠌⠁⣤⠇⠠⠼⠀⣻⡝⠉⠀⠀⠀⠀⣸⣯⡍⢲⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢾⡿⣷⣦⣉⣙⣻⣼⣿⣿⣿⣿⣿⢻⣆⣴⣾⣧⡀⢁⡀⠒⣄⠩⠤⠐⠒⠦⠌⠲⢀⠘⣽⣴⠆⠀⢀⣤⡾⣿⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡟⠙⣯⡭⠋⠉⠀⠀⠀⠀⠀⠀⠀⠱⣶⢾⣿⣐⠶⠾⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠿⠿⠿⢿⣿⣿⣤⣽⣤⡀⠀⠀⢀⣠⣤⣤⣤⠤⠴⠞⠛⠋⠉⠉⠁

⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿
⢸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠀⠀⠀⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⢸⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣿⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⢸⣿⣧⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⢸⣿⣿⣷⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠀⠀⠀⣴⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣤⣤⣶⣿
⢸⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⠀⠀⠀⣿⣧⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢁⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣀⣴⣾⣶⣿⣿⣿⠀⠀⠀⣿⣿⣿⣷⡄⠀⣿⣿⣷⣦⣤⣤⣴⣖⠀⣀⣴⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣷⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢀⣤⣤⢤⣶⠠⠰⠂⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⠠⠀⠄⠒⠀⠐⠀⠀⠖⠂⠐⠂⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⡀⡀⡀⠀⠈⢤⠀⠄⠀⡀⠒⠑⠙⣿⣄⢆⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰⡂⢤⡉⠠⢤⠤⠄⠁⠠⠂⠀⠀⠀⢄⠀⠈⠁⠘⠟⠀⠑⠀⠀⠛⠃⠂
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠬⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⡄⠀⠀⠀⠀⠀⠀⣥⠤⠀⠀⡀⡀⡀
⠀⠀⢀⡤⠀⠀⠀⠀⠒⠂⠈⠁⠀⠀⠀⠄⠐⠂⠄⠀⠀⠀⠀⠆⠀⠸⠀⠀⡠⠀⠁⡀⠀⠀⠤⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⡀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣷⡄⠀⠀⠀⠀⠀⢰⣿⣏⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋⠙⣿⣿⡄⠀⠀⢀⣾⣿⡟⠙⠛⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁⠀⠀⠀⣸⣿⣿⣿⣶⣿⣿⣿⣇⠀⠀⠀⠈⠻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠹⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠁⠀⠀⠀⠉⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠶⢄⡀⠶⢤⡞⠀⠀⠀⠀⠀⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢶⣾⡇⣤⣾⠀⠀⠀⠀⠀⠀⠀⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⡟⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠾⠆⣰⣄⣠⡀⠀⠀⠀⠀⢀⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⢀⣼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⠿⠛⠛⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⡄⠀⡈⠁⠀⠐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⢾⠛⠛⠀⢀⣤⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣀⣀⡀⢶⣴⣦⣉⣹⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣤⣼⣷⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣽⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⣻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⢀⣼⡟⢻⣿⣿⣿⣯⡍⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠈⣿⣟⣿⣿⣿⣿⣿⠃⠀⢠⣄⠀⣠⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⣤⣤⠀⠀⢻⣿⣧⣼⣿⣿⣿⣦⣀⣼⣿⣶⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⡴⠶⠶⠶⠶⢶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⣶⢾⣿⣿⣿⡡⠉⠀⠀⠀⢀⣄⠀⢀⣿⣶⣶⢤⣀⠀⠀⠀⠈⠻⣦⣤⣀
⠀⠀⠀⠀⠀⠀⣴⣾⢫⣿⣿⣍⠛⣷⣿⡗⠀⢡⢄⣰⠶⠔⠉⢛⣉⣿⣡⣤⣤⠶⠉⠉⠐⠤⠀⣀⣀⡉⠁⠈⠁
⠀⠀⠀⣀⢦⡸⠟⠙⢧⣼⠥⣤⣼⣿⣿⣯⠈⢟⣤⣥⣀⣮⡿⠺⣥⠿⠿⠷⠦⠔⣂⠤⣶⢦⣤⣄⠈⢧⣴⡄⠀⢀⡀⠀⡀
⠀⠀⣤⣧⣴⡇⢀⣦⠀⢲⣶⣾⣿⣿⣧⣿⢷⣮⠛⠋⠻⠟⠀⠁⠀⠀⠀⠀⠀⠀⠈⡻⠠⠇⠙⣻⣿⡛⣿⡇⠀⢸⣯⠹⢷
⠀⢰⣯⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠀⠀⠘⢷⣤⡤⠀⠀⠀⠀⠀⢀⡜⢡⡴⢢⣴⣿⣿⣷⣿⡇⠦⠰⣿⡿⣾
⠀⢨⡽⣭⣿⣽⣿⣿⣿⣟⣿⣿⣿⠃⢹⣿⣿⣿⣄⣤⠀⢻⠀⠀⠀⠀⠀⠀⢠⠏⠈⡄⢙⣋⣬⣿⣿⣷⡟⠃⠀⣠⣾⣧⣿
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣷⣾⣿⣿⣹⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣹⠶⣩⡜⠁⣴⣿⣷⣿⠋
⠀⠀⠀⠘⠣⣽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣼⣧⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠉⠴⢋⣩⣿⣛⠿⠛
⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣯⣿⣿⣿⣟⣉⣿⣿⣿⣿⣶⡤⠀⠀⣀⣀⣤⣶⣿⢟⣭⣝⣿⣶⡼⠟⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣹⣿⣿⡇⢘⣙⣿⣿⣿⣿⣿⣯⣼⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡤⢤⣤⣦⡤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠒⠂⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡆⢀⣀⠀⠀⠈⠁⠀⠀⠀⣀⡸⠁⠀⠈⠛⢷⣤⠀⠀⠀⠀⠀⠲⣤⣀
⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣯⡿⠀⠀⠀⠀⠀⢀⣠⣿⣉⡖⠐⢀⣴⢤⣤⠰⠆⠀⠀⠀⠀⠈⢻⡟⠠⣄⡀
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣱⣿⣿⣿⣿⠿⣏⠀⠀⣴⣦⣼⣦⡹⠟⠋⣿⣿⣿⡉⢌⢁⣀⠀⠀⠀⠀⠀⠀⠀⠿⣾⣿⡛⢦⡀
⠀⠀⢀⣾⣿⣿⣿⢉⣿⣿⣿⣿⣿⣿⠛⢯⣷⣄⡛⣻⡟⠘⠁⠀⠐⠀⠀⠈⠁⠈⣉⡷⠀⠀⠀⠀⠀⠀⣰⣟⠀⠠⣏⠈⣉
⠀⠀⣾⣿⣇⢈⣿⣼⣿⣉⣻⣿⣟⣋⣵⣾⡛⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡷⠈⠁⢀⣀⣤⡀⢙⣿⢀⣠⣉⣷⣤
⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⣸⠁⠈⣦⡖⠛⢩⡿⠛⠿⡿⠟⣃⡸⢿⣿
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣯⡉⣽⣟⠻⢿⢻⣿⡿⢿⣶⣤⠀⠀⠀⣼⠃⠀⠀⣴⣏⣶⡼⠃⠀⢰⠟⢀⣭⡔⣉⠨⣭⠃⣸⠟
⠀⠀⠀⠈⠻⣿⣿⣿⣭⢿⣿⣿⡟⠷⣾⡿⠿⣿⣜⢻⣿⡀⠀⠐⢧⠼⢶⡾⣉⠅⣹⠁⠠⠞⠉⠉⢁⣽⡿⣋⣿⣯⠾⠋
⠀⠀⠀⠀⠀⠀⠙⠻⣽⣿⣿⡿⣿⣄⣸⣿⣆⣻⣿⣟⣘⣷⣤⡀⢶⣤⠞⠁⠀⠀⠀⠀⢀⠀⠀⣠⣴⣧⡾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣟⣻⡟⠁⣧⠀⠀⠀⣀⣀⣠⣤⣾⣿⠛⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣶⣿⣶⠋⠉⢉⣽⣋⣽⠀⣿⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠒⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡠⢶⣾⣿⣿⣿⡿⣿⠟⠃⠀⠀⠛⠁⣽⣿⣟⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⣶⠦⣄
⠀⠀⠀⠀⢠⣴⣿⣿⣿⣥⣽⣿⣿⣿⠏⠀⢀⡀⣠⡴⢞⠋⢹⠄⠰⠶⣦⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠶⣾⡻⢦⡀
⠀⠀⠀⣴⣿⣿⣿⢧⣿⡿⢿⣿⣿⣇⣤⠘⢻⣿⡟⢴⠟⣯⠁⠀⠀⠀⠀⠀⠀⠀⠉⢁⡀⠀⠀⠀⠀⠀⢸⣷⡴⠿⣿⣭⣹
⠀⠀⢸⣿⣿⣿⣿⣴⣿⣧⣴⣿⣿⣿⣩⡟⠉⠉⠙⢦⣍⣡⠄⣀⣀⡀⠀⠀⠀⠀⢠⡏⣧⣀⣰⣶⣶⡶⡟⠻⣿⣀⣙⣟⣼
⠀⠀⢹⣿⣟⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣇⡀⠀⠀⠀⠀⡘⡈⠹⠏⣣⠀⠀⠀⢠⠃⡜⠡⠟⠋⣿⡿⢿⣷⠶⣷⣾⢾⡯⢽
⠀⠀⠘⢿⡟⢻⣿⣿⣿⡟⣿⣿⣿⣿⣿⣹⣿⣄⠀⠀⣰⠇⠀⠐⣃⢠⠀⠀⢠⡾⠀⡉⠙⢠⣔⣛⣻⣭⣴⡶⠓⢠⣾⢷⣾
⠀⠀⠀⠈⠡⣼⣿⣿⣷⢾⣿⣿⡿⢿⣿⡟⢿⣿⡄⠰⣿⡷⢀⡀⡇⠈⠳⣶⠟⠁⠖⢙⡖⢸⡿⠋⠉⠀⠈⣳⡦⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣯⣹⣿⣯⣽⣿⣿⣿⣿⣤⣼⣷⣄⣠⣄⣸⠶⠖⠂⠒⠂⠤⡌⢙⣿⠂⣀⣤⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⡟⣿⡉⠛⠋⠀⠀⠀⠀⠀⢀⣀⣼⠿⠿⠎⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠂⠀⠀⠒⠚⠋⠉⠉⠁
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣃⣀⣀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠂⠘⢀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⢀⠐
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠀⠀⠀⠀⠀⡠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠄⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⠀⠦⠶⠄⠀⠀⢀⠔⠀⠂
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠤⠤⠤⠄⠀⡘⡡
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠁⠀⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠠⡀⠀⠈⠰⠠⠉⠨⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠚⢗⡀⡀⣀⠠⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⢀⣀⢀⡀

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠴⣂⠠⠂⢀⠠⠀⠀⠀⠀⢠
⠀⠀⠀⠄⠈⠀⠀⠀⠢⠔⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⠀⠀⠠⠖⠀⠀⢰⢞⣁⠀⠀⠀⠂⠀⠀⠐⣦
⠀⠀⢀⠀⠠⠐⠀⠂⠀⠴⠦⡀⢀⠀⠀⠀⠀⠀⠨⠁⠀⠀⠀⡂⡀⠂⠀⠀⠀⠀⠀⠉⠀⠈⢢⡀⠤⢀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠒⠒⠑⠂⠀⠀⠠⠀⠀⢙⠂⠀⢀⠀⠀⠀⠀⠔⠒⠐⠙⠃⠀⠘⠀⣿⢨⡂
⠀⠀⠀⠠⡐⠒⠂⠀⠀⠀⠈⠉⢠⠬⠀⠀⢒⠖⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠁⠀⠍⠂
⠀⠀⠀⠀⠈⢀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⢈⠉⢂
⠀⠀⠀⠀⠀⠀⠑⠀⡆⠀⡀⠤⠀⠀⠀⠐⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡀⠀⣀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠂⠀⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂