Frozencore Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣀
⠀⠀⠉⠀⠀⠀⢰⠹⡓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠀⠀⠐⠂
⠀⠀⠀⣀⠀⠀⡀⡀⢰⡀⠢⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠶⠶⠆⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢇⢄⠀⢀⡀
⠀⠀⠈⢉⠒⡄⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣨⠉⠀⠀⠀⠀⢠⡀⠄
⠀⠀⠠⠿⠄⡀⠀⠀⣀⠀⠤⠄⣾⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠠⢤⠀⠐⠡⠬⠵⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠼⣟⠀⠀⢠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠰⡂⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠆⡿⠠⣶⠦⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠁⠀⠀⠀⠀⠀⠀⠠⣄⠀⠻⠿⠇⣣⣤⣄⠀⣀⡤⠤
⠀⠀⠈⢿⣿⣧⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠰⡿⠇⠀⠀⠉
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠟⢀⣁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢰⣴⡤⠄⣦⣤⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⣷⢸⡀⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠤⠘⠜⠀⠉⠐⠃⠘⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠆⠰⠐⣀⢰⠈⢰⢐⠀⣈⡇⢐⡄⠁⢂⣰⠈⠤⠐⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡤
⠀⠨⠘⠜⠀⠘⠘⠁⠘⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡈⠃⠀⠀⠐⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⡀⡀⡀⣀⠀⡀⢀⢀⣀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠐⠱⠈⠀⠀⠀⠁⠈⠀⠀⠀⡀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⢘⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠁⠳⠡⠊⠀⠘⠘⠀⠈⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⢤⣤⣤⣤⣤⡤⠶⠚⠋⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣧⠐⣰⡂⡢⡆⠦⠂⠂⡀⡂⠀⠒⢂⠀⢰⠀⠨⠀⠐⠀⠀⠀⠠
⠃⠉⠁⠃⠀⡏⠓⡅⠐⠐⠐⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⣿⣿⠀⢀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠙⢿⣿⣦⣿⣿⣴⣿⡿⠋⠀⢠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣿⣧⠀⠀⠀⠙⢿⣿⣿⡿⠋⠀⠀⠀⣼⣿⡇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣦⣿⣿⡄⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢠⣿⣿⣴⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣽⣿⣿⣿⣷⣄⡀⠀⠀⣿⣿⠀⠀⢀⣠⣾⣿⣿⣿⣯⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠛⠋⠉⠛⢿⣿⣷⣦⣿⣿⣴⣾⣿⡿⠛⠉⠙⠛⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣿⣿⣿⣿⣏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣤⣄⣀⣤⣾⣿⡿⠟⣿⣿⠻⢿⣿⣷⣤⣀⣠⣤⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣻⣿⣿⣿⡿⠋⠁⠀⠀⣿⣿⠀⠀⠈⠙⢿⣿⣿⣿⣟⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠟⣿⣿⠃⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠘⣿⣿⠻⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⡟⠀⠀⠀⣠⣾⣿⣿⣷⣄⠀⠀⠀⢻⣿⡇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⣠⣾⣿⠟⣿⣿⠻⣿⣷⣄⠀⠘⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠁⠀⣿⣿⠀⠈⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠋⠉⠉⠉⠉⠉⠛⠛⠷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⡤⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⠎⠀⠀⠈⠛⢷⣤⣤⣤⣤⣠⣤⠀⢤⢴⡒⠲⠤⣄⢀⠀⠀⠀⠀⠠⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⠀⠀⠀⡤⠠⡀⠈⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠀⠈⠇⠑⠠⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢸⣀⣠⣤⢤⡀⠀⠀⠀⠀⠀⠀⢀⠐⣉⠉⠉⠛⠀⠀⠐⡆⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠟⠋⠀⣶⣄⠀⠀⠀⠀⠀⠀⠈⠀⡙⣃⠠⠂⠀⠀⠀⠁⠀⠀⠰⠆⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⢀⠉⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠳⣤⡀⠀⠀⢀⡠⠖⠋⠁⠠⢄⠀⠀⠀⢀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣿⠙⠛⠁⠀⠀⠀⡈⠀⠀⠃⠀⠀⢘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠲⠀⢸⡄⢀⠄⠁⠀⠀⠘⠢⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⢸⠀⠀⡧⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠛⠶⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠘⠄⠀⠀⠠⠂⠀⠀⠀⠉⠻⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢰⠎⠐⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄⠀⠀⠂⠄⠀⠀⠀⠀⠠⠐⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠠⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠱⠀⠀⡐⠀⠀⠀⠀⠀⡀⠄⠒⠰⠀⠐⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡠⠊⠁⠀⠀⠀⠀⠁⠐⠒⠒⠠⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠊⠀⡀⠀⣦⠀⠐⠁⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢤⡠⠊⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠁⡄⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⣰⣇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠤⠠⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⡀⠀⡄⡆⡄⡄⣠⢰⠀⡤⣠⠄⠦⣠⠴⢀⡄⡦⡀
⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠁⠉⠈⠀⠉⠈⠀⠉⠈⠈⠈⠁⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⢤⡠⢰⠄⢤⣠⡤⡀⣠⢄⡄⡦⣄⠠⠄⢤⢀⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠁⠈⠁⠁⠀⠈⠁⠁⠉⠁⠀⠉⠉⠀⠈
⠀⠀⠀⠀⠉⠛⠩⠁⠀⠀⠀⠀⠃

⠀⠀⠀⠀⢀⣀⣄
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠠⠆⠗⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠙⠘⠏⠃⠻⠙⠐⠏⠈⠙⠣⠘⠏⠀⠭⠚⠜⠢⠄⠧⠓⠱⠆
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⢀⡀⠀⡀⠀⢀
⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠛⠄⠅⠠⠆⠧⠛⠚⠍⠣⠃⠘⠜⠋⠸⠌⠂⠇⠺⠓⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠒⠖⠛⠂
⠀⠀⠀⠀⠀⡀⣠⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⠠⢠⢠⢠⢤⠤⡤⠄⢠⠀⡄⣤⢄⡤⠀⡤⢄⡄⡆⣤⡴⢀⣄⡆
⠀⠀⠀⠀⠀⠋⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠁⠈⠀⠀⠁⠀⠈⠀⠀⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠤⡤⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠒⠒⠒⠒⠒⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢛⡿⠿⠛⠛⠿⢿⣟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠠⣶⠀⠀⢰⡦⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠰⠿⣷⣤⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠐⠀⠄⠆⠐⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠓⠶⢬⣧⡀⠀⠀⠀⠀⠀⣨⠟⠀⠀⠀⠀⠀⠀⠺⣅⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣤⠴⠆
⠀⠀⠀⠀⢀⣤⠴⠖⠛⠉⠉⠛⠶⢤⣄⣾⠁⠀⠀⠀⠀⢀⠀⠀⠀⠈⢳⣀⣠⡤⠴⠖⠛⠋⠉⠛⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠛⠲⠆⠀⢾⣿⣿⠀⠀⠘⠉⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠾⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠸⡇⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠻⡄⠀⠀⠀⠀⠘⢿⡿⠇⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠙⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⢀⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⢖⡶⠟⢋⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⡠⣶⡿⠞⢋⡩⠝⠋⠉⠁⠀⠀⠉⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡿⠋⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⣤⡄⠉⠳⣄
⠀⠀⠀⠀⠀⠀⢠⣦⠞⢡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠛⠉⠉⠙⠛⠓⠙⢷⣄
⠀⠀⠀⠀⠀⣰⠿⠃⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⣠⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡄
⠀⠀⠀⠀⠀⢿⠀⠀⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠐⢐⣀⣀⣀⣀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠘⢧⡀⠃⠘⣇⢰⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠾⠶⠯⣅⡀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⢀⡞⣠
⠀⠀⠀⠀⠀⠀⠈⢳⡄⠂⠘⢦⣆⠀⠀⠀⠀⠀⣞⠀⢀⡠⠤⢄⡀⠈⢿⠓⢤⡀⠀⠀⠀⠀⠙⠳⢦⣤⣤⣴⡿⠞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⡿⢧⡀⠀⠀⠈⠃⠀⠈⠀⠀⠀⠉⣆⢸⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡜⣻⠇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣏⠀⠀⠀⠀⢛⠦⣀⠀⠀⠉⠀⠀⠉⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣧⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠉⠀⠀⠀⠀⠀⠈⡆⢠⠞⢉⠙⢦⣀⣴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡷⠒⠒⠶⣤⡄⠀⠀⠞⠋⠀⢀⣴⣾⣟⠻⣻⡏⠀⠀⠁⠈⢠⠋⠀⢸⡝⢆⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⣶⣶⣶⣄⠀⠀⠀⠀⠀⣸⣏⠻⣿⡿⣰⠏⠀⠀⠀⠀⢰⠀⠀⢠⡟⢷⡈⢃⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠘⣿⣧⡀⠀⠀⠀⠙⠨⣵⠶⠞⠁⠀⠀⠀⠀⠀⠻⠀⣠⡞⠀⠀⠳⡄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⠷⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢣⡘⠀⠀⠀⠙⢆⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠳⡀⠀⠀⠀⠈⢂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠸⠀⠀⠀⠀⠀⣀⡐⠂⠀⠀⠀⠀⣠⠞⣹⣿⡿⢦⡘⠢⠀⠀⠀⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠠⢄⡀⠀⠈⠋⠀⠀⠀⠀⣠⠞⠁⠀⠁⠸⡇⠀⠙⠿⡶⣦⣄⡀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠆⢣⡙⢳⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠶⠶⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⣽⡄⠀⠀⠀⠀⠀⢳⠀⣧⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⠀⠀⠀⠀⢰⡏⠻⣄⠀⠀⠀⠀⠈⡄⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠛⠉⠁⠀⠀⠀⠀⠀⣼⠁⡤⣽⠳⣄⠀⠀⠀⡇⢸⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⡇⠁⠀⠈⢳⡀⠀⠁⢸⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⣧⠁⠀⠀⠀⠀⣇⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⣟⢀⡀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠠⣪⠿⣷⡀⠀⠀⠀⣿⡴⢋⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠏⢀⣾⠩⠤⠇⣝⢡⣄⣢⣤⢴⡟⠀⠀⠔⠁⠀⠈⣧⠀⠀⣰⠋⢡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⣼⠃⠤⠀⢀⣠⠾⠋⢉⠀⣼⠁⠀⠀⠀⠀⠀⠀⢸⡆⡴⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠁⠁⢉⡏⢀⣛⣴⠟⠁⠀⠐⠈⢠⡏⠀⠀⠀⠀⠀⠀⢀⣼⡿⢾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⢀⣠⡼⠛⠋⢩⠏⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢀⣠⡴⣻⡟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠆⠀⣄⡴⠛⠁⠀⠀⢀⡟⠀⠀⠀⠀⣠⠟⢁⣠⡤⠶⢚⣋⣥⡶⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡼⠋⠀⠀⠀⠀⣠⠞⠁⢀⣠⣴⠯⠵⣶⠿⠓⠚⠛⠉⣩⠟⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠒⠒⠚⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠋⠁⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠓

⠛⠉⠉⠛⠉⠉⠀⠀⠀⣠⢀⡄⠀⠀⠀⠀⣀⣀⣀⣀
⠀⢀⣤⡴⠷⢛⣶⠞⣰⣶⠏⠀⠀⠀⢰⣬⣭⣁⣽⣧
⠀⠿⢧⣄⢰⣿⣷⡇⠊⠉⠛⡯⣿⠦⢸⣿⣷⡿⣯⣻⡇⠀⢀⠀⢀⣀
⠀⠀⠀⢹⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠈⢿⣿⠿⠟⠟⢀⣶⢈⣨⣼⣹⣾⣆⡤⢠⢄
⠀⢀⣄⣠⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠈⣟⡙⢤⣬⣿⣻⣭⣿⣼⣿⣽⢳⣿⣾⣥⠤
⢰⣾⡟⢿⡯⡀⢈⡭⠋⢹⠀⠀⠀⢀⣀⢶⢷⠻⠟⢿⣿⡟⠃⣿⠈⡝⢸⠺⣯⢷⣿⣽⣾⣝⡀
⠙⣿⣤⡈⠈⣷⣿⢷⣵⠆⠀⣀⠨⡹⣉⢁⡺⠷⣀⠄⠀⠨⠉⠋⠀⠀⠈⠀⠋⠁⠫⢸⣿⠿⠟⠀⠦
⡄⠀⠈⠛⢻⣿⣿⣾⣛⣦⣼⢹⢿⣷⣦⡄⢂⣅⣾⠑⠖⠶⠿⡿⢿⠛⢓⣦⣤⠤⠴⠚⠁⡀⢀⣘⢡⣜⢦⡀
⡇⠀⠀⢠⠈⣿⣿⡿⣿⡏⠀⠘⠞⠇⠁⠀⠈⠛⠃⢤⡄⣶⣄⣽⣿⡾⡭⢏⣻⠢⠀⠈⣿⣿⡿⢻⠯⡏⢻⣾⣤
⣧⣶⣆⣼⣿⣿⠹⡿⡟⢅⣷⣽⣅⠀⣀⣴⣾⣿⠷⣿⢃⣝⣻⠏⠉⠁⠀⠀⠀⠀⠂⠰⣏⣥⠃⠀⠀⠀⠀⢹⠏
⡟⣿⣿⣭⣛⣿⣤⣾⣿⡺⣿⣽⣟⡆⠿⠫⡅⠁⢊⠈⢦⡈⠁⠀⢠⣄⠰⠆⣀⣄⢀⠀⠘⣋⣇⣀⡈⠀⢠⣀⣉
⡷⠶⠟⡿⠟⠛⠛⠋⠛⠓⠚⠛⠛⠛⠒⠚⠛⣓⠚⠉⠁⠉⠉⠉⢉⡉⠉⠀⠀⢈⠉⠀⡄⠀⣦⠀⠀⠀⠉⠉⠁
⡇⢀⢰⡠⠦⣰⠄⠀⠀⠀⠀⠀⠀⠀⢀⠖⠙⠀⠛⠿⠂⠀⡤⠄⢨⢻⣗⠀⢻⣼⣿⣿⣷⣾⣧⣄
⡇⣷⡾⡅⠞⠁⠀⠀⠀⣰⠶⣄⣀⠀⢸⢷⠀⠀⢀⡆⠄⠀⠑⠀⠄⠄⠃⠀⢐⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀
⠀⠙⢒⠃⠀⠀⣤⣰⣾⣷⢢⠡⡟⢤⠸⢯⣌⣧⣶⠾⠁⠀⠀⠀⠀⠒⡀⢀⠸⣿⡟⢿⣿⣿⣿⡇⠈⢡⣼
⠀⣾⣿⡿⢦⠀⣿⣿⡿⠋⠙⠅⡂⠀⠀⠀⣠⣥⣶⣶⠄⠠⠀⠉⠀⠀⠘⠙⠀⠹⠃⣾⣿⣿⣿⣿⣶⣿⠷⠚⠙
⠀⢶⣿⣿⠋⠀⠈⢉⢊⠟⠁⢐⣐⠀⠃⠀⢃⡤⢂⡀⠀⠀⠀⠀⣤⠘⠤⢀⠀⠀⠈⠉⠉⠉⠋⠉
⠀⠀⠁⠀⠀⠀⠀⠿⠳⠖⠀⠉⠙⠋⠀⠀⠀⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣼⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣶⣤⣠⠿⠿⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠉⠙⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠗⣦⡄⠀⠸⢷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢠⡀⠀⠀⣦⡄⠀⠸⢷⡆
⠀⠀⠀⠀⢀⡀⠀⠀⢤⣄⡀⠀⣶⣤⣀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⢸⡿⠀⠀⠻⠇
⠀⣀⠀⠀⠀⣿⣷⣶⣾⠛⠿⢷⡟⠙⠻⣿⡅⠀⠀⠀⠀⠀⠘⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⣴
⠀⠈⠙⠒⢤⡀⠈⠙⠻⠇⠀⢸⣿⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠿⠿⢛⡇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠈⠙⠀⠀⢸⣷⠀⠀⠀⣤⣀⠀⣻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢻⣿⣿⣿⡏⠙⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⡧



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣧⠀⠀⣠⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣾⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⣱⡄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠿⡿⠟⢩⠀⠀⢻⡇⠀⠀⢿⡄⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⣰⣤⢄⡀⠀⠀⠀⠀⠀⡀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠉
⠀⠀⠀⢠⣦⣄⣀⠉⠉⠻⠆⠀⠀⠀⢸⡧⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠉⠛⠿⠃⠀⠰⢿⡇⠀⠘⠿⠀⠀⠙⠃⠤⣶⣶⣤⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⡇⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠅
⣿⣿⣿⢿⣿⠿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣶⣾⣷⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣅⢻⠀⣠⠞⢳⣄⢰⣇⣹⣇
⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣷⢾⡿⢽⡇⠀⠀⣹⡿⣻⢷⣟⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⢤⣀⠀⠈⢹⡶⣏⠻⣟⡲⢞⣿⢋⣿⢾⠋⠀⢀⣠⡤⣄⣀⣀
⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠾⢷⣾⣿⣻⣿⣟⠿⢿⣥⠿⠙⣷⣍⡡⣿⠹⠧⣽⡿⢟⣻⣿⣻⣿⣶⠾⠶⠶⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡿⢍⣻⠏⣙⣿⡉⠀⠀⣩⣿⣋⠽⣟⡽⣟⡉⠁
⠀⠀⠀⠀⢤⠤⠤⠤⠤⠤⢤⣴⣯⣿⡯⠿⣯⣭⣿⡏⣿⣈⡿⢚⡳⣿⣨⡮⢻⣯⣭⣿⠯⣽⣯⣿⣦⡤⠤⠤⠤⠤⢤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠻⠟⠋⠉⠀⣸⡷⣟⣹⣟⡵⢝⣿⣍⣷⢿⡅⠀⠉⠛⠿⠛⠑⠋
⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣮⣿⢾⣯⣾⡇⠀⠀⢹⣶⣽⡾⣯⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠉⠉⠹⣆⡴⠋⠉⠉⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠒⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣠⣿⣦⠄⠀⠀⠀⠀⠀⢀⡈⠓⠶⢄⣀⣀⣀⡀⣀⣀⡤⠴⠊⠀⠀⠀⠐⠙⢧⣄⠀⢀⡀⠀⠀⠀⠀⣀⣀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠉⠒⠀⠂⠀⣠⠼⠿⠷⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠉⠛⢿⡓⠀⠀⡀⢀⣀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡟⠉⠠⠀⠀⠂⠀⢰⣶⣒⣒⣒⣻⣶⣶⣤⣤⣦⣤⣤⠋⣿⠀⠀⠀⠀⣀⣀⣴⣿⣿⣥⣷⣶⣬⣥⣼⣦⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠈⠀⠀⢦⠙⣒⣛⠓⠒⢒⣉⠭⠤⠜⠋⠁⠈⠀⠀⠀⠀⠀⠀⠈⠛⣺⠿⣿⣿⣿⣿⣿⣿⣹⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⣿⣿⣿⣿⣿⡿⠀⠃⠀⠀⠆⠀⠰⡇⠹⣿⣿⡟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠐⠚⡿⢿⣛⣛⣻⣷⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⠙⠺⣿⠿⠿⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡇⡁⠀⠀⠀⠀⠀⠀⠀⠀⣶⠊⣩⣴⠆⠻⠇⠀⠀⠀⠀⠇⠀⠀⠀⠁⠈⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⡈⢶⣀⡠⣮⡷⣦⣤⣤⣤⠤⢤⣀⣴⣿⡿⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠉⠁⣰⡀⢾⣷⣄⡀
⠀⠀⣠⣤⣤⢤⣤⢴⣤⣴⣤⣤⣦⡭⣿⣦⡹⣷⠿⣧⡤⣤⣶⡆⢐⣻⠧⣬⡉⠓⠿⡀⠀⠀⠀⠀⢀⣀⠖⡞⣿⠀⣰⣋⠁⣁⡌⠐⠉⠭⡑
⠉⠉⠉⠉⣉⣿⣿⣬⣭⣭⣽⣷⣭⣭⣍⠉⢹⣬⣶⣿⣷⣌⣿⡿⢭⣤⣴⣉⣷⣤⣴⡁⠀⠀⠀⠀⣯⡈⢇⠱⡙⠲⣇⢰⢉⣉⣠⡷⢦⣴⡤⠀⣦⡀
⠀⢀⣴⣮⣿⠉⠉⠻⠭⡭⠭⠽⠏⠉⠲⣽⣾⣅⢠⣤⣉⡋⣿⣿⣇⠀⠉⠸⣿⣏⠀⠹⣆⠀⠀⠀⢧⡑⢌⠢⡁⠈⢮⢾⡏⠀⠀⠀⠰⣾⡇⠀⠘⠇⠀⠀⠀⠠
⢲⣿⢿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⣿⣷⣽⢯⣿⣹⣻⣿⣛⣿⣶⣿⣿⠀⠀⢹⡆⠀⠀⢸⡙⢾⣦⡈⢢⡐⣾⡇⠀⠀⠀⢠⠛⣆⠀⡆⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⢻⣿⣿⣿⣿⣿⣿⡻⣷⣄⣰⠃⠀⠀⠀⢧⣼⡛⠿⣦⡈⠻⢧⣤⣀⠠⢾⠀⠙⣄⣇⠇
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⣿⣿⣿⣿⣿⣿⣿⣮⣿⣷⣄⠀⠀⠀⠈⣧⣸⢤⡤⠉⠳⣾⢿⣿⣧⡎⡤⣺⠿⡟
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⡄⠀⠀⡽⠒⢾⡇⠀⠀⠀⠙⠟⠁⡄⡼⣄⡳⣝
⣶⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⠛⠒⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣟⣦⣀⠃⠀⠘⣶⣒⡛⢲⢄⡀⠘⠖⢠⢮⠉⠛⠂
⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢸⣿⣷⣿⠀⠀⢠⡿⢿⣝⣎⠀⠀⠀⢀⡿⠀⣧⡿
⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢿⠙⣿⣿⣻⣾⣶⣿⣿⣿⣿⣾⣿⣿⣼⣿⣿⡿⠀⢀⡼⢗⠏⢽⠏⠀⠀⠀⡸⠀⠀⠈⠇⢣
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠘⣆⠿⠴⠶⠶⠶⠦⠤⠤⠤⠤⢴⡿⠟⠋⠁⠀⠛⣾⣄⣡⠤⡞⠀⠀⠀⣶⠃⠀⢀⡼⡁⠀⢱
⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡽⢿⠿⣿⣷⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠎⠀⠀⢀⡾⠁⠀⠀⠈⡇⢹⠀⠀⡇
⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣖⣰⡷⡷⠿⠾⠭⠤⠤⠤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠏⠀⠀⢀⠞⠁⠀⠀⠀⢰⡇⠠⡀⢰⠁
⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢠⣤⠟⠀⠀⢀⠎⠀⠀⠀⠀⠀⡌⠁⠀⢡⡜
⠘⣦⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡆⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⢸⡀⠀⠀⠀⢠⣾⠁⢀⠀⡸⠣⣀
⠀⢸⡿⣏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⠀⠀⠀⢰⠡⣤⠖⠶⠤⣼⠀⠀⠀⢠⠟⠛⠒⠲⡿⢄⡀⠈⠓⢤
⠀⠀⣷⠨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⢠⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠀⠀⠀⠀⠀⠀⢰⠏⠁⠀⢠⡇⠀⢀⣰⠎⠀⠀⠀⡤⠇⠀⠉⠑⠒⠋
⠀⠀⢻⠀⢿⣿⣏⡿⣿⣿⣿⣿⣿⣩⣿⣿⣿⠉⡇⠈⣇⠸⡄⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⣗⠀⠀⢸⠀⠀⡏⠁⠀⠈⣦⡤⣽⣀
⠀⢀⡤⣧⡦⡭⠷⠶⢿⣼⠿⢿⠿⠿⢿⠋⡇⢰⡇⠀⢸⢐⡇⣀⣀⣀⣀⣀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢠⣈⠃⠀⢸⠀⡸⠀⠀⠀⠈⠉⢵⣒⣈⣳⡀
⢀⣼⠁⢻⡿⠗⠂⢰⡘⣀⣀⣘⣆⠀⢸⠀⣧⡞⠹⣶⡀⣿⢏⣉⣉⠉⠉⠉⢻⡅⠀⠀⠀⠀⠀⠀⠀⢠⡾⢤⡉⢀⡘⠊⠀⠀⠀⠀⠀⠀⢆⠀⠈⠙⠿⠂⣀⣀
⣾⡏⠳⣿⠛⠛⠻⠿⠽⠿⠿⠿⠿⠿⠿⠷⣾⡟⠀⠹⣷⣿⣾⣿⣿⣿⣶⠀⢨⡗⠀⠀⠀⠀⠀⠀⠐⠋⠀⠗⠼⠛⠽⠖⠀⠀⠀⠀⠀⠀⡜⠢⣄⣴⣶⣾⣿⣏⡧
⣿⡇⢰⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣿⠗⠀⠀⠆⠀⠄⠀⠠⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠠⠀⠨⠀⠀⠀⠀⠈⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⢀⠄⠀⠴⡮⢀⡀⠀⠀⠀⠀⠈⠁
⠠⢴⣆⠀⠀⠀⠐⠀⠀⠀⠀⢰⡄⠉⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⠂⢀⡀⠀⠀⠀⡄⠀⠀⠀⠀⢀
⠀⠀⠈⠀⠀⠀⣸⠀⠀⠀⠀⠸⠁⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⡎
⠀⠀⠠⠀⠁⠀⠉⠋⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠐⠀⠁
⠀⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠀⠀⠀⢀⠠⡀⠀⠀⠐⠀⠂
⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣤⣥⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢩⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠔⢳⣦⡀⠀⠀⢀⣀⣴⠞⠃⠀⡾⣿⣿⣿⣦⣀⣀⡀⠀⣠⠶⠶⢛⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⣡⠴⣻⣿⡛⣳⣖⡭⠋⠉⠀⣀⠀⠙⠿⣿⡇⠘⠉⣩⣿⣾⢧⡄⠀⢾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠺⢽⠿⠛⠉⠀⡠⠶⠖⠋⣽⣷⡦⠀⠉⠁⠠⣾⣿⣿⢿⣷⡦⠀⠈⠋⠀⢹⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠘⠛⠷⠍⠀⠀⠀⠀⠀⠈⠉⠑⣿⣀⢤⡐⠄⠀⢺⣿⣿⣿⣿⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⡄⠀⠀⠉⠛⠻⢿⡪⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣴⣶⡶⠶⠶⠶⠿⣿⣤⣴⣧⣧⣧⣶⣶⣿⣀⣠⣴⣾⠶⠷⠤⣴⣿⣷⣤⣤⠤⠤⠤⠴⣾⣿⣶⣀⣠⣤⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠒⡒⠒⠾⠭⠽⣛⣷⣤⣀⠀⠀⠀⠀⠀⠤⠤⠤⠬⣉⣉⣉⣉⠐⠒⠒⠢⠭⠍⢙⠒⠲⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠭⠍⠉⣙⣒⡲⠭⢍⣓⠂⠤⠀⠀⠠⣤⣤⣄⣀⣶⣦⣬⣭⣭⠓⠒⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠠⠤

⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⣼⣿⣧⡀⠀⢀⠀⠀⠀⠀⢀⣼⡏⢻⡗⢄⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢠⣿⣿⣿⣄⢀⣿⣧⠀⠀⣰⠿⠉⢆⠀⢻⡀⠈⠢⢄⣤⣶⣿⡏⢢⡀⠀⠀⢀⣤⣀⣠⡾⠃⠑⣤⣆⢰⣿⡀
⠀⣿⣿⣿⣿⣷⣼⣿⣿⣄⣼⣿⣦⣄⠀⠑⠈⢧⡀⠀⢘⣿⡿⠋⡇⠀⠉⢶⠲⢅⠘⣿⢝⠁⠀⠀⣼⣿⣿⣿⣇
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠉⠓⠀⠀⠀⢁⣴⠿⠋⠀⠀⢻⠀⠀⠀⠑⠀⠑⠘⠀⠀⠀⢀⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠸⠿⣟⣿⣿⣿⣿⢿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⣀⡀⠀⠀⢠⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣟⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢦⡞⣏⠰⣶⣶⣮⣴⢞⣤⣤⠰⣦⣀⠐⠯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣿⣾⣿⠖⢤⢀⣀⡨⣀⣀⣦⣗⢰
⢐⡻⡄⠋⢙⠿⣟⣡⠈⢨⢸⡗⣫⠩⡟⠊⡩⡼⢀⣀⣀⢀⣄⠀⣀⣠⣠⠟⣤⢝⡎⢼⠨⣏⣮⠹⣿⠫⡐⢓⢻⠤⢳⠾⣇
⠈⠇⢑⠦⡋⠏⢹⡼⢎⣽⢨⠶⣨⡷⠚⣶⢑⣯⣘⣿⠹⣏⠋⣿⣿⢿⣟⣿⢍⣜⣄⡼⡔⠿⢆⠓⢿⡧⠙⢠⠙⡏⣸⢳⡟
⠐⠀⠾⡖⣩⠓⢞⠋⠂⠶⢊⢌⡽⠋⢔⣠⠋⡐⣬⡱⢏⢀⣀⠈⠗⠞⠣⠊⢄⣿⡸⢆⡲⢌⣆⠛⠶⢦⢘⠀⢅⠱⢗⠊⢍
⠀⠀⣰⠀⡌⡙⠂⣀⠀⠀⠀⠀⠀⠋⠀⠓⠀⠙⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠀⣆⠁⢲⠌⢺⡷⠄⠈⠀⠁⠙⠁⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⠁⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠖⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⡇⠀⢸⣿⠃⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⡘⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠋⠀⢠⠃⠀⣾⣿⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢀⠇⠀⠀⢀⣴⣿⡿⠛⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⠀⡠⠃⠀⠀⣿⣿⠀⠀⠀⢀⠞⠀⠀⢠⣶⣦⠀⠀⠀⣿⣿⠀⠀⠀⡜⠀⠀⢠⣾⣿⠋⠀⢀⠆
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢰⣿⣿⠁⢀⠞⠀⠀⠀⠀⣿⣿⡄⠀⡠⠊⠀⠀⠀⠈⠛⠋⠀⠀⠀⣿⣿⠀⠀⡘⠀⠀⢀⣾⣿⠇⠀⡠⠊
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣼⣿⡧⠔⠁⠀⠀⠀⠀⠀⢹⣿⣧⠜⢀⡠⠤⡄⠀⢀⣤⣤⠀⠀⠀⣿⣿⠀⡜⠀⠀⠀⣼⣿⡏⣠⠞⠁
⠀⠀⠀⠀⠀⠘⢄⣀⡀⠤⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣠⠊⠀⣰⣿⠀⠸⣿⣿⠀⠀⠀⣿⣿⠜⠀⠀⠀⢠⣿⣿⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⢀⠜⢻⣿⣏⠀⣰⣿⡇⠀⠀⢻⣿⡀⠀⠀⣸⣿⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⢀⡌⠀⠀⠻⠛⢰⣿⡿⠀⠀⠀⠀⠙⠷⠤⠊⠈⣿⡄⠀⡠⠊⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠞⠁⠀⣿⡇⠀⠀⠀⠀⠐⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠤⠔⠁⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⣴⠿⠛⠓⡀⠀⠀⠀⠀⢀⣤⣾⣷⣶⣶⣶⣶⣶⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⣤⡄⠘⣿⡀⠀⢠⣿⡏⠀⠀⠀⠇⠀⠀⠀⠜⠉⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠆⠀⠀⢇⠀⠘⡄⠀⠀⢀⣤⣉⠁⠀⠈⠙⠂⣾⣿⠀⠀⠀⡘⠀⠀⠀⣀⣀⡀⠀⠀⢠⣏⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣣⠇⠀⠀⠈⠢⠤⡧⠤⠔⣾⣿⡟⠀⠀⠀⠀⢀⣿⣿⠀⠀⢠⠁⠀⢠⣾⡿⠉⡁⠀⠀⠸⣿⣆⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⡇⠀⢠⣿⣿⠁⠀⠀⠀⠀⢸⣿⣧⠀⡰⠁⠀⠀⣾⣿⢁⡔⠁⠀⠀⠀⠹⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢀⡔⣿⣿⡀⠀⠀⠀⠀⠀⠀⠇⠀⠸⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⠜⢁⣀⠀⣀⢽⣿⡏⠀⠀⠀⠀⢀⠔⠋⢻⣿⣦
⠀⠀⠀⠀⠀⠀⡎⠀⢹⣿⣇⠀⠀⠀⠀⠀⠸⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⢀⣿⣿⠀⠈⠉⠇⠀⠀⠙⠳⠤⠠⠔⠊⠁⣀⠄⠀⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠃⠀⠀⢻⣿⣆⠀⠀⠀⠀⠇⠀⠀⠀⠘⢿⡄⠀⠀⡠⠔⠁⢻⣿⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⢀⠜⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠻⣿⣄⡠⠃⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠁⠀⢒⣴⣾⠿⠛⠋⠛⠄⠀⠀⣠⠄⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠲⡀⠀⢀⣴⣿⡿⠋⠙⡆
⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⣠⣿⡟⠃⠀⠀⠀⣠⠂⢀⡾⠁⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠆⢠⣾⣿⠋⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢲⣿⡿⠤⠤⠤⠄⠊⠁⠀⣾⠇⠀⠀⠀⠠⠁⠀⠀⠰⠆⠀⠀⢸⣿⠀⢀⠌⠀⣾⣿⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⡠⠁⠀⠀⠀⣀⡀⠀⠀⢸⡏⢠⠊⠀⢸⣿⠇⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⢀⠔⠁⠀⠀⠀⢠⣿⡇⠀⠀⢸⡟⠁⠀⠀⣸⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠂⢀⣀⠀⠀⠀⠆⢹⡇⠀⡠⠺⣿⠀⠀⡠⢿⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠜⢰⡏⠀⠀⡜⠀⠀⠙⠊⠀⠀⠻⡤⠎⠀⢸⣇⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⢀⠔⠁⠻⠟⠀⣿⠁⠀⡰⠀⢀⠀⠀⢀⡀⢀⠀⠀⣀⠀⠘⣿⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠠⠔⠁⠀⠀⠀⠀⠀⣿⣧⠖⠀⠀⠘⣷⠁⣿⡠⢹⡤⠀⣿⠇⠀⠘⢷⣄⡠⠃⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⡀⠀⠀⠀⢀⡀⠀⠀⠉⣀⠀⠤⠤⠄⠀⣀⡀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠀⠀⠀⣿⡆⠀⠀⠈⠁⢠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠂⢤⣾⡟⠁⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠲⣶⡄⠀⠀⡌⠀⠀⠀⠀⣸⣿⠃⠀⣼⣿⠀⠈⠐⠀⡠⠂⠉⢑⡄⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠈⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⣿⡄⠸⠀⠀⠀⠀⢰⣿⠏⠀⠀⣿⡇⠀⠀⠀⡜⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢹⣿⡆⠀⠀⠀⢀⣿⡏⠀⠀⠀⢿⡇⢀⠜⣷⡅⠀⣰⡿⠁⠀⠀⢀⣴⠟⠛⢳⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢿⣷⠀⠀⠀⣼⡿⠀⠀⠀⠸⠀⠉⠁⠀⠘⠃⢰⡿⠁⠀⠀⠀⣿⠃⠀⢀⢾⡿
⠀⠀⠀⠀⠀⠀⢀⣤⡀⠡⡀⠀⠀⠈⠉⠀⠀⠀⣿⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⡔⠙⠂⠊⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣵⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⡠⠊⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠣⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠣⠀⠀⠀⢀⠀⢐⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠐⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣮⣝⡀⠀⢀⠁⡊⠀⠀⠈⢻⢦⠀⠴⢂⡿⡄⠀⠀⠹⡦⡐⠐
⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠈⠓⢍⠓⢤⣁⠀⠀⠀⠀⡟⢀⠀⢀⠞⠀⡟⠀⠀⢠⠀⠹⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠈⢧⠀⠈⠳⡀⠐⣦⡙⢮⠢⢸⠁⢠⠃⠀⡠⠋⠀⠈⡇⠀⢀
⠀⠀⠀⠀⠀⠀⢖⠈⣀⣀⡀⠀⠀⢸⡤⠀⠀⢧⢠⣇⠹⡌⢳⠘⣆⡿⢀⡞⠁⠀⠀⢀⠆⢀⠎⢣⠀⡀
⠀⠀⠀⠀⠀⠈⠀⣈⠉⢳⡎⢢⡀⢸⠀⠶⡀⠈⠻⠂⠀⢱⠀⠀⡿⢽⣼⠀⢠⠀⢀⡌⢀⠠⡀⡏⠐⠁
⠀⠀⠀⠀⠀⠀⠈⢹⠙⠸⡇⢀⠱⣾⡄⢁⠈⠢⡀⢠⡄⡞⠀⢀⠇⡄⠋⡠⢁⢣⠏⠀⢸⢣⢰⠇⢀⢦
⠀⠀⠀⠀⠀⢀⣆⢺⡊⠀⠹⣇⠰⠠⢄⠀⠂⠀⠰⠂⢠⠃⢀⡞⡐⢸⠐⠀⢠⠃⠀⡰⠃⣸⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠘⡏⢦⣀⠀⠀⠈⠳⣝⢤⡈⠲⠀⠀⡄⢸⢠⠟⠐⠀⢾⠀⠂⡇⣠⠏⠀⣀⡎⠀⣠⢀⡸
⠀⠀⠀⠀⠀⠀⠱⣄⠈⠑⠢⢤⡀⠘⡄⠱⠀⠀⠀⠆⠈⠿⠀⠀⠀⠀⠀⡆⢹⠇⡄⢠⠎⢀⡰⣻
⠀⠀⠀⠀⠈⢻⠆⠈⠲⢄⠀⣄⡙⠶⣗⠀⠁⠀⠀⠘⢄⠈⠂⠰⠀⠀⠀⠐⡤⠊⢄⣮⠖⢋⡜⠁⣦⡀
⠀⠀⠀⠀⠀⠘⠒⠠⠱⠀⠱⡀⠂⠑⠄⠀⡄⠀⠀⠀⠀⠉⠂⣤⠀⠀⠀⠀⠄⠐⠎⠥⢈⠏⡀⠀⠁⡗
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠢⡀⡇⠀⠀⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⢐⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠙⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠈⠨⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠓⢤⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⠀⣀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠉
⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠂⢀⠁⠀⠀⡀⠁⠀⠔⠀⡀⠀⡀⠀⠀⢐⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠈⠐⠀⠀⠈⠈⠀⠀⠁⠀⠈⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠄⠀⠀⠀⢀⣤⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡀⠀⣻⣤⡲⢀⣤⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⠄⠂⠀⠀⠠⡼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣿⡀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣌⡆⠀⠀⢠⠟⠞⢃⡾⣹⢧⡹⡏⡜⠛⠁⠀⠀⠀⠀⣀⡤⠒⠋⠘⠁⠠⣶⡀⠀⢸⡞⢻⣀⡀⠀⠀⢠⣷⡄⠀⠀⠀⡩⡀⣥⣾⡀⣠⣿⣄⣾
⢀⣄⢠⣿⠀⣰⡰⡚⠛⣸⣦⣴⣃⣶⣤⣴⣏⠀⠙⠿⠀⠘⠁⢀⡠⢔⣾⡏⠀⠀⠀⠀⠀⢴⣿⣆⠀⠼⣇⣾⡍⠁⠀⠀⣦⢷⣰⢀⠀⢰⡟⢻⣠⡏⢳⣿⣸⣇⢿
⢸⣿⣫⣭⣷⣿⢉⣿⢉⣻⡿⢩⠇⢸⣧⠁⣾⡆⣸⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⣎⣻⢸⡤⣀⣽⣏⠹⠶⠀⣠⣤⣿⡉⢼⠁⠼⣷⣚⣡⣇⣸⣧⣹⠙⡛
⢸⣿⣽⡉⣿⠟⠁⣈⢈⡉⢹⣿⣠⣾⣧⡖⢁⣿⣏⠈⡝⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣷⢿⣌⣥⠈⠾⡟⠳⠇⠀⢈⣡⣯⡛⠆⣉⠰⣾⡿⢋⣍⠁⢹⡻⡦⣿
⢸⣯⣴⣿⡝⠛⠋⠈⣿⡛⠛⣿⣿⣿⡿⣥⣿⢿⣿⣆⣻⣿⣾⣧⣦⣷⣶⣴⣄⣤⣄⡤⠚⣇⣼⣮⣙⣥⡀⡇⠀⣀⣴⡌⢀⣧⢥⠔⢣⡴⢤⣿⣯⣿⣷⣼⣿⣁⣿
⢸⣿⣿⣿⠧⠾⣀⣼⠞⢷⣶⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⣯⣛⣧⣿⣿⠖⣉⣿⠈⣧⡙⢯⢻⣿⣟⡣⠾⣙⣿⠅⠞⡔⠢⠗⢤⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⡄⣠⠏⠈⣄⠀⢳⣀⣻⡇⠿⠛⢿⠈⠟⠻⡿⣿⠟⠙⠛⠙⠿⠿⣿⣿⡿⢛⣡⣻⠆⠁⣹⡚⠻⡿⢓⠦⠓⠆⣹⢇⡠⠃⡤⠧⡘⠾⢿⡿⡿⡻⠻⠻⣿
⠈⠋⠻⢯⣀⡴⠦⠤⠊⠓⠛⢿⣄⣀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⣡⠀⣥⠀⢈⣍⠠⡬⠃⠈⠋⠸⡀⠤⣹⠇⡴⢳⠀⡉⠙⡈⢃⠁⠀⠀⠀⠁
⠀⠀⠦⠴⠁⠀⠦⠀⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠐⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⢸⣿⡄⣸⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠃⠞⠁⠟⠹⡆⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠞⠀⠀⠂⠀⠀⠀⠀⠃⠉⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣶⢦⢀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⠶⡡⢿⡞⡏⠀⠀⠀⠀⢰⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡂⢀⠟⡉⠀⠁⣘⢳⢿⡄⢸⠀⠀⢨⠻⠻⣤⣇⢀⣖⠦
⠀⠀⠀⠀⠀⠀⣴⣥⠄⡀⠀⣹⡗⣡⣾⣿⠃⣰⡇⡸⠀⣿⠿⣄⣠⣿⢣⡀⠈⠹⣾⠁⠀⠈
⠀⠀⠀⠀⠀⠠⠋⠉⠛⠳⢾⣯⣾⣻⢳⠃⢠⣿⠇⡇⠀⢿⣾⡘⡈⢻⣇⢻⣤⠬⢶⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⠉⠭⠙⠒⠋⠛⢻⣿⡄⠚⠛⠓⠓⠘⠻⡏⢁⡤⠔⠈⣷⣀⠄
⠀⠀⠀⠀⠀⠢⡀⠀⠀⡀⠘⠇⠀⠀⠀⠀⠀⠀⢸⢸⡇⠖⠂⠀⠀⠀⠀⣹⣀⠀⠀⠀⡸⠋
⠀⠀⠀⠀⠀⠀⠈⠑⠤⠷⠞⢀⣀⠀⠀⠀⠀⠀⡄⢸⠃⠀⠀⠀⠀⢀⠌⠀⢠⠋⠱⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠈⠉⠀⠉⠉⢉⡉⠉⢩⡀⠴⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣦⠀⠀⠀⠀⢀⣴⣿⢦⠀⢀⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⣠⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣴⠟⣷⣿⣿⣿⣿⣿⣿⣦⠂⣴⣿⣿⣿⣯⣴⣿⣿⣀⢀⠠⡀
⠀⠀⠀⠀⠀⢀⣶⠿⠮⣿⣿⡘⣿⣿⡄⣌⠀⣠⣦⣦⢀⠸⠃⠀⠀⠁⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⢢⣍⠛⠘⠻⢾⣿⣿⡏⣌⣧⣥⢤⠄
⠀⠀⠀⠀⢀⣾⡜⢂⣀⣽⣿⣿⣽⣿⡑⣿⣿⣆⡻⣿⣥⣤⡚⢿⣎⡀⠐⢳⢯⡿⢿⣋⣙⣛⣬⡉⢿⣿⡏⢰⣷⡞⢴⣾⢏⡙⢿⣿⣿⣿⣌⣃
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣄⡻⣿⣿⣿⣏⣀⠀⣝⠳⡀⣽⡀⢀⣿⠿⢻⣿⡆⢵⣾⣿⣧⠐⢿⠠⣤⡙⠈⠁⣈⠿⣿⠛⣻⣿⣇
⠀⠀⠀⡼⡿⣿⡿⠛⡩⢚⣿⡏⢹⣧⣾⣯⡿⢿⣾⣿⣿⣿⣧⣼⣮⣿⣿⣌⣓⣨⡿⠘⢿⣿⣿⣦⢿⣿⣿⣿⣿⣧⣹⡿⠇⣀⢼⣦⣡⡚⢻⣿⣿⡄
⠀⠀⢠⣇⠀⠃⣀⣸⣿⣿⣿⣶⣿⣿⣿⣷⣦⣦⣼⣿⣿⣿⣿⣿⣿⣿⡿⢛⣽⣿⣿⣶⣦⣬⣟⣻⣷⣿⢿⣿⣿⣿⣿⣷⣄⣼⣎⣿⣿⣿⣼⣷⣆⣄⡀
⠀⠀⠀⠉⠉⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠯⠭⠍⠉⠉⠉⠹⠟⠉⠉⠈⠛⠛⠟⠿⠿⠉⠉⠛⠛⠿⠿⠛⠛⠛⠛⠛⠛⠛⠻⠿⠟⠛⠛⠛⠛⠙⠛⠛





⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣙⡛⣉⣙⣛⡟⣫⣿⣻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⡸⠓⣧⣎⠀⡀⢀⠁⡠⠈⠀⣨⠻⢈⣠⣀⡐⠫⠓⡦⢲⡖⣔⡀⠀⠀⡧⡤⢀⠪⢇⡠⠽⣿⢸⡸⠈
⠀⠀⢣⠠⢀⡇⠛⠠⢯⣧⣟⣉⣶⣴⡐⠚⡩⢤⠈⣙⡏⠙⢏⠁⠠⣬⠛⣫⢬⠅⠆⢹⣡⠀⢠⢂⡈⠧⢀⠉
⠀⠀⠠⠂⢸⠓⣌⠘⠳⡞⣽⡟⢒⠯⡇⠀⢠⡀⠈⠋⢹⠼⠘⡠⠔⠃⠀⠘⠰⣎⠀⠘⠂⠂⢉⣁⣀⡠⠴⠦⢴
⠀⠀⣠⡀⠆⠈⢀⠄⠀⠁⠉⠙⠚⠦⡼⠀⠲⡷⡤⢤⠬⢶⠛⠀⠀⠀⠀⠀⠀⠈⠡⣿⣿⡿⣿⡛⣥⣀⡂⠐⠨
⠀⡆⢩⠘⢠⢚⠀⢂⣐⡂⣐⠤⣄⠀⡘⡄⣟⣍⢍⣿⣿⡏⠀⡀⠴⠀⠁⠈⠀⠐⠀⢻⣈⣹⡇⣷⢏⠁⠸⡈
⠀⠓⠐⠋⣶⠀⣤⣭⣶⠀⠀⠀⣤⡑⡆⢹⢤⣿⠀⣿⣿⠱⠀⠿⠿⠇⠀⠀⠿⠉⠆⢸⡿⡿⣿⣝⠀⡁⠈⠀⠢
⠀⠀⠰⣦⢸⠟⠙⠘⠋⠃⠀⠺⠯⠿⠇⢫⠒⠛⠃⡿⠿⠀⣇⠠⠄⠀⠀⠀⠀⠠⢀⣬⣼⣥⣬⣧⣼⠁⢸⢅
⠀⢐⢾⣷⠀⠀⠓⢄⠀⠀⠀⠀⡠⠒⠀⠀⢀⠐⠀⢠⠄⠉⢘⠀⠀⠐⠀⠀⡞⠀⢽⢯⣤⣤⣀⡀⢉⣠⣨⡀
⠀⠘⢰⢸⡉⠀⠀⢀⠍⣲⢦⡀⠀⠀⠀⢸⠊⢀⣂⡉⢸⠀⣇⠤⢀⣠⣀⡀⠘⠄⡍⠐⠈⡗⠮⢤⢠⠀⢠⠀⢀
⠀⠀⠰⢸⠀⢠⡪⠑⠦⣤⣜⠟⠳⠀⢠⠆⢰⠀⢽⠏⢠⠊⠁⣦⠉⠀⠈⣰⠆⠀⠘⡆⣇⣁⣿⠀⢸⠀⠰⠤⠉
⠀⠀⢥⠿⡄⢠⠀⠸⡶⢣⢝⣲⢾⢰⡇⠘⠘⠂⠙⠀⢨⢠⠀⠁⠀⡀⠀⠘⠀⢠⠄⢿⡍⣉⣉⣉⣙⡂⡤
⢀⡀⢠⡄⠀⢺⠀⠱⢨⢋⠦⢱⡾⡟⠀⡀⠀⠀⠀⠀⠙⢿⢘⠀⠀⠀⠀⢀⠀⠈⠄⠗⠒⢰⣐⠀⠈⠃⠰
⠙⠋⠶⡄⢻⠸⠀⡖⠢⠍⠖⠸⠀⠓⡄⢠⢀⠰⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠀⠀⢀⠀⣀⣀⣈⣂⠂
⠀⠀⢬⣀⡌⠁⡰⠀⠀⠈⡁⠀⠉⣁⢱⢸⡂⠀⠀⠀⠀⡸⠀⣀⠀⠀⠀⠈⠀⠀⠀⢀⠁⠲⠤⠽⣽⠀⠈
⠀⠀⠛⢉⡖⠐⠀⠀⠠⠀⠀⠸⠀⠘⡂⠃⠃⠀⠀⢀⣖⡃⠐⠁⠁⢀⡀⡀⠀⠤⠄⠈⣉⠛⢛⢛⢃⠀⠈⠉
⠀⠆⠽⢸⠀⡤⠀⠀⠀⠂⠀⠀⠀⠀⠇⠸⠷⠶⠦⠉⢯⡄⢀⠒⠄⠉⠀⠓⠀⢀⡄⠀⠂⠀⠀⠻⠾⠓⢾⢾⡀
⠀⠆⡽⢸⢧⡀⠀⠀⠀⠀⠀⣄⠀⠢⠄⢖⡁⠀⠀⠀⠀⡃⠉⠀⠀⠃⠀⠰⠠⡄⠀⣴⠠⠀⡀⠀⠘⠂⢨⠀⠈
⠀⡄⢠⡼⡾⠡⠄⣀⠀⠀⡔⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⡀⠀⠀⠘⠀⠈⡀⠙⠙⠁⠀⠆⠀⠀⢀
⠀⠉⢠⣐⠢⠲⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠿⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠄⠒⠀⠃⢀
⠀⠀⠘⢉⠈⠐⠲⣦⠀⠀⣠⠐⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠾⠀⢐⠀⢸
⠀⠀⠀⠈⠀⠀⠀⠉⡀⠈⢹⠘⡆⠀⠀⠀⠀⠘⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠉⢆⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⢧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠋⡰⢃⣞⠣⣀⠀⠁⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠠⠔⣿⡿⠃⠀⢠⣾⡿⠀⠈⠀⠀⠀⠙⢳⣦⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⡇⠀⠀⢀⡀⢀⡤⢞⣉⣤⡖⠘⢟⡉⠀⠀⠀⢦⡀⠀⠀⠀⠻⢦⠀⠐⡶⣶⣿⣿⠉⣆⠀⠀⠢⣄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢐⣲⣾⡿⠿⠿⠛⠉⠁⠝⠒⢂⣠⣴⣶⣶⣿⣿⣿⣤⡀⠀⠙⠃⠀⠀⠈⠻⣄⡀⠀⠀⠈⠓⠠⠀⠈⠛⠁⠀⠛⠓⠦⢄⡈⠑⠤⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠾⠿⠿⣿⣿⣿⡿⠟⠋⠁⠈⠻⢶⡆⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⠄⠀⠀⠀⣤⣤⣤⣼⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣀⡀⢠⠄⠀⡀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠈⡀⠀⠀⢀⡀⢹⢦⣘⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⠄⠄⠀⠀⡁⠤⠘⣁⠠⠐⠂⢢⣁⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⠀⠰⠤⠐⠞⢀⣀⡀⠀⠀⠠⠉⠱⠒
⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠶⠵⢆⡠⠀⠠⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠃⡠⠐⠀⠀⠀⠀⠒⢄⠀⠀⠀⠐⡀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠠⠴⠀⠔⢄⡀⠀⡠⢁⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⡀⠘⠀⢰⡆⠀⠰⡦⢠⠁⢘⠅⠕⣨⣀⠀⢀⡄⠀⡇
⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⡀⠀⢨⠀⠂⠀⣤⠀⠀⣀⠁⠁⠀⢀⡔⠁⠈⠑⢀
⠀⠀⠀⣠⠀⠀⠪⡜⠒⠒⡄⠀⠀⠀⠀⠈⠆⠀⠀⠀⠤⠈⠃⠀⡄⡠⢚⠀⠀⠀⡀⣶⢓
⠀⠀⠀⠁⠀⠀⠁⠉⣉⣩⢇⡀⠀⠀⠀⠀⠀⡀⠆⠤⠌⢠⠄⠊⢰⠀⢐⠦⢈⠀⠈⠃
⠀⠀⠀⠀⠀⠄⡀⠤⢤⣤⠺⠂⠀⠀⠀⠀⡀⡘⠉⠁⠐⠉⢄⣧⢀⠓⠂⠉⠁⠒⢘⠀⠀⡄⡀⡌
⠀⠀⠠⡏⠈⠁⢀⠀⠮⠘⠈⢀⠀⠀⠀⠀⠳⡃⠠⠬⠉⠐⠀⢙⠃⠀⠨⠀⣍⡍⢩⠑⠉⠉⠁
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⣴⠊⠁⠀⠀⠀⠀⠑⡒⢒⠒⠊⠀⢠⠀⠀⠀⠐⠈⣣⣼
⠀⠀⠀⠀⠀⠀⠐⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⠃⢸⣃⢇⠀⠀⠢⢀⠀⠀⠀⠉⡩⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢰⣿⣿⣾⠟⠉⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠃⢿⡿⠛⠁⢠⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⠡⠙⠿⣦⣶⣤⡀⣠⡀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣤⠀⠀⢀⣹⣿⣿⣿⡿⣿⡿⠆⠀⠤⣄⠀⠤⡀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠼⠟⠋⠉⠉⠉⠀⠀⠀⠀⠈⠁⠀⢤⣀⣤⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣿⡃⢠⣤⣤⣤⡄⠀⠀⠶⣲⣷⠒⠒⠾⣿⡏⠀⢠⣿⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡀⢿⣿⡿⠑⡄⠀⠀⠀⠿⠿⠀⠀⠀⠉⠃⢠⣿⡟⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠋⠏⠀⠀⡴⠁
⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠾⣷⣦⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣴⣮⡄⠈⠁⠀⡸⠁
⠉⠁⠀⣀⠿⡇⠀⠐⣧⡀⠀⠀⠀⠀⠙⠿⠧⢀⠸⣿⣿⣦⣀⠀⠀⠶⠖⠀⠀⡠⣺⣿⣿⡇
⠀⠀⠀⠡⠤⠀⠀⠀⢈⣽⡗⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡆⠙⣶⠦⠄⠀⠀⢰⡈⠳⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠘⠋⠀⠀⣰⣆⣀⠀⠈⡡⠊⠉⠉⠉⠛⠛⠅⠀⠀⠀⠈⣿⡀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠊
⠀⠀⠀⠀⠀⢤⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣠⣶⣤⣄⡄⠀⢀⡀⣤⣴⣶⣤⣶⣄⣐⣥⡘⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠷⢶⡶⠾⠿⠿⠛⠋⠻⢿⣿⣿⣿⣷⣾⣿⣶⣿⣿⣸⣿⣿⣿⣿⣿⣿⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣶⣤⣀
⠀⠀⣿⣶⣤⣤⡀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣷⣤⣄⣀⣀⣀
⠀⠀⠛⠛⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣆⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣈⣙⣛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠦⠤⠤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣶⣶⣴⣤⡌⠉⢉⢉⠓⠒⠒⠶⠤⠤⢤⣀⣀⣀⣠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⡇⠀⢸⡄⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⠙⡿
⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣄⠰⡁⠀⠀⠀⠀⠀⢸⣿⣿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠛⠛⠛⠛⠃⠀⠸⠿⠿⠷⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠉⠉⠙⡿⠋⠁⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⡏⠁⠁
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣴⣾⣶⣦⣤⣦⣤⡀
⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠤⠤⠄⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠁⠀⠀⠀⠀⠀⢰⣶⣶⣶⡇⠀⢰⣿⣾⡇⢸⣿⣿⣦⣴⣷⣤⡀⠀⠀⠀⢀⣤⣤⣤⣤⣶⣦⣤⣴⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠉⠈⠉⠛⠶⣄⠀⠀⢀⣤⠶⠛⠋⠉⠉⠉⠉⠉⠙⠛⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠉⠉⠉⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⣀⣠⣄⣀⣀
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠉⠀⠀⠈⠉⠛⣦
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠈⠙⢶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⡁
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣛⣲⠖⣶⠶⢶⢿⣏⢩⣽⠇
⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⣇⠀⠀⠀⠀⠀⠀⣀⡼⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣯⠉⠺⣧⠀⠀⠀⢹⡿⠷⣦
⠀⠀⠈⠳⢦⣤⣄⣀⣠⣤⣤⠴⠶⠛⠉⠀⠈⠛⠓⠲⠶⠒⣿⢿⡀⠀⠛⠻⣿⢶⡶⢤⣤⣤⡶⣾⠻⣾⢣⡞⠛⣻⡀⠀⠀⣴⢃⣤⡿⠁⣰⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠻⠂⠙⠶⠶⠶⠿⠂⠻⠶⠿⠈⠳⠾⠇⠀⠟⠒⠚⠉⢛⣓⡚⠁⣛⣛⣛⣛⡃⢘⣛⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣃⡾⠋⣭⣽⢏⡴⠛⠙⠻⣴⢋⣿⢃⣦⡹⣏⣙⣦⡿⠉⠻⣎⢻⡉⠉⠉⠻⣮⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⣷⣀⣸⡅⠀⠀⠐⣿⡉⠁⣿⢨⡷⠈⣹⡏⠀⠀⠀⢹⡆⠙⣿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⠟⢷⣤⣤⣤⡾⣡⠷⠛⠙⠻⢿⡜⢧⣤⣄⣠⢿⣷⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⡴⠶⢶⡶⡀⢿⡀⠀⠀⠀⣴⢋⣄⢶⡶⣤⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⡟⣴⢻⡌⠷⣶⡶⠾⢣⡞⠹⣎⢳⣌⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⣛⠋⢸⡇⠻⢶⡴⠟⢿⣠⣶⠟⠀⢙⡇⠉⣭⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣏⡼⣦⡿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠾⣵⣦⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⠄⠈⠀⢀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⡀⠀⠀⠐⡀⢀⣠⠀⠀⠀⠰⡷⡄⠀⡀⢦⡀⠆⠠⠆⢈⣧⢸⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣷⡄⣠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⠘⠃⢤⠍⢧⣿⣧⠉⢻⡄⠀⠶⣿⡿⠈⢣⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠒⠲⢛⡃⠒⠠⣄⠀⣺⡿⠂⠘⢧⣼⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠘⢯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣳⣄⠈⠙⣿⣧⠱⣄⠈⣿⣀⠀⢠
⠀⠀⠀⠀⢀⣤⣾⡄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⢈⠁⠀⣀⡀⠈⠂⠂⠖⠈⠉⠑⢻⣿⣄⣿⡀⢹⡶⢠⡯
⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⣌⣑⣈⣃⡀⠀⠀⠀⠀⢀⣀⣴⣿⣿⡙⢷⣈⣿⣼⣧⠖
⠀⠀⠀⢹⣿⡿⠟⠁⠐⠿⢷⣮⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⢀⡽⠛⣶⡶⠾⣿⣿⣄⣿⣿⠁⢀⣿⣿⣿⠗⠂
⠀⠀⠀⢸⡟⠀⢀⠀⠀⠀⢠⣿⣷⡀⢸⣽⡿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡟⡄⡩⠴⡞⠋⡀⠀⡀⠀⠈⢹⣿⣧⠈⣿⣿⡟
⠀⠀⠀⠿⠶⠒⣿⣧⣾⣿⣿⣿⠿⠇⠜⠻⡄⠀⠿⣿⠟⢿⡿⠿⣿⠿⢛⠛⠻⠋⠊⠟⠀⠂⠒⢿⡐⠛⣺⡟⢿⢀⡏⠑
⠀⠀⠀⠀⠀⠀⢀⣿⣶⣦⣬⢀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠛⠛⠚⠛⠛⠛⠉⠋⠉⠁⠀⠀⠀⢀⣸⣿⣿⣿⡧⠀⢻⠶
⠀⠀⠀⠀⠀⣀⣄⣤⠛⢉⣈⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣠⣄⣀⣶⣿⣿⣿⠿⠟⣿⠋
⠀⠀⠀⠀⠀⠈⠉⠛⠛⣛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠈⠉⣉⢉⢛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⢄⠀⠀⠀⠀⠀⠀⠀⡌⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢱⠄⠀⠀⠀⠀⠈⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⡀⠀⢁⠆⠀⠀⠁⠆⠀⠀⠀⠁⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠇⠤⠀⠀⠀⠀⠀⠀⠀⠀⢑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠑⡠
⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⠀⠀⠀⡆⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠌⠢⡀⠀⠈⠃⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇⡏⠀⠀⡠⠂⠀⠀⠀⠈⢆⠀⢀⡀⡨⠓⠀⠀⢀⣀⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡆⠀⡀⠀⠀⢠⣮⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⣰⠀⠀⠀⠀⠈⠸⡁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠈⠉⠀⠸⠀⠠⠀⠀⡀⠀⠀⢀⠀⠀⠀⢰⠀⠀⠀⠀⢀⡀⠀⠍⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠀⠀⠠⠀⣀⠀⠀⠰⠀⡠⠀⣀⡠⠜⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠑⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠑⢄⠀⢱⡁⠉⠀⢀⣀⡀⠄⠁⠀⣠⠂⠀⠀⡀⢠⠀⠀⡈⢁⡀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠠⠆⠀⠀⠀⡀⠀⢀⠀⢅⠊⠓⠤⣄⣀⣀⡠⠤⢚⠀⠠⠒⠉⠁⣈⢀⠀⠘⢇
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠁⠈⠐⠐⠀⠉⢄⡰⠁⠀⠀⠑⠂⠤⠀⠤⠤⠵⠒⣉⠒⠤⠤⠤⠚⢉⠀⠄⠀⠀⠉⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢁⠠⠄⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡣⣀⠐⠁⠎⠐⢀⠂⠈⠀⠀⢠⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠊⡑⠒⠒⠒⠚⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠎⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⠧⢄⡠⠤⠤⢀⣰⡦⢄⣰⡖⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠔⠁⠀⠀⠠⠤⠤⠀⠢⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢸⡆⠀⣧⠀⠀⡖⠀⠀⠀⡆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠈⠃⢀⣁⠀⠈⠀⠀⠇⠠⠇⢸⠃⢰⠃⣰⠃⠀⢠⠆⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠙⣰⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⡀⠀⠁⠸⡱⠃⣰⢋⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠉⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣈⠁⠋⠀⣀⡤⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣾⣭⣭⣟⣛⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢸⠏⠀⢀⡟⠉⠈⢿⠛⠶⠿⣭⣿⣛⡿⢿⣿⣿⣿⣿⣿⣇⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠏⠀⢀⡘⠀⡀⠀⡘⠀⠀⡐⠀⠀⢉⠛⠛⠶⣮⣭⣛⡻⠟⠀⠤⣌⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠂⠀⢠⠀⢠⣿⡇⢰⡏⢀⠃⠀⣶⠇⠀⣤⠇⠀⠀⡜⠀⠀⢩⠃⠀⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠆⠀⠀⣼⠀⠘⢻⡆⠈⢀⡞⠀⣤⡞⠀⠈⡟⠀⠰⣶⠁⠀⢀⡇⠀⠀⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠤⠤⠤⠤⠄⠀⢀⣿⣷⠆⠉⢹⣶⣿⠃⠐⣿⡧⢴⣿⠃⠠⣶⠇⠀⠘⡟⠀⠀⠲⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⠄⠀⠀⢸⡿⠋⢰⡆⢸⣿⡏⢀⠀⢿⠃⣸⡟⠀⠠⡞⠀⠰⡾⠁⠀⠒⠦⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⠦⢴⣦⡄⠘⣿⠁⣾⠀⠘⢀⣿⠁⢰⣶⡈⢢⣴⠃⠀⠐⠦⣄⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢸⠃⢀⠀⢹⠇⢸⣏⣰⣿⡇⠀⣼⡏⠀⣿⠿⠁⣸⠇⠀⠠⠤⣄⡀⠉⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠒⠒⠛⠀⠀⡟⢀⣿⠀⡾⠀⣼⠃⢸⡟⢑⡶⠛⣦⣤⠄⢲⣿⡏⠀⠀⠲⠤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⢀⠃⣸⣯⣴⠃⢰⡏⠀⡾⠀⣼⠁⣸⣿⡟⢀⣿⡟⡀⠀⠐⠒⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀⣿⣿⡟⠀⠀⠀⣸⠃⢰⠇⢠⣿⡿⠁⣼⡿⠁⠁⠀⠓⠒⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠠⠶⠒⠛⢉⡁⠀⠀⡏⢸⡟⢻⠃⢀⠀⢀⡟⠀⡿⠀⣾⣿⠇⣸⣿⠃⠀⠀⠙⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡤⠄⠀⣷⠀⠀⡞⢀⣿⠀⣼⠁⣸⠃⢰⣿⡟⢠⣿⠇⠀⣌⣉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡠⠆⠙⢦⣼⣇⢸⡇⢰⡏⢠⡟⠀⠻⣿⠁⠾⠏⢀⡀⠀⠉⠙⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⡠⠆⢀⠄⡉⢙⠓⠾⠧⣼⣅⣀⣠⣃⣠⠎⠀⢤⣉⡉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⠞⠀⠃⢸⠀⢰⠀⢠⠀⣉⢉⠉⠀⡀⠐⠦⡄⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠘⠀⢸⠀⠸⠸⡆⠀⠹⡄
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⠹⠄

⠀⠀⠀⠀⠀⠀⠀⠐⠂⠙⠂
⠀⠀⠀⠀⠀⠀⠒⠒⠻⠼⡁
⠀⠀⠀⠀⠀⠘⡂⢀⡄⠈⠉⠁
⠀⠀⠀⠀⠀⠘⠛⠻⠤⠄⢶⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠠⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⡨⠆
⠀⠀⠀⡀⠀⣠⠂⠀⠶⢷⡝⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢀⣀⠴⠶⢤
⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣵⣄⣤⣶
⠀⠀⠀⠶⠠⣰⠆⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡁⠀⢄
⠀⠀⠀⠀⠔⠁⠀⠒⣀⠀⠶⣀⡀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠛⠁⢀
⠀⠐⠧⠄⡤⠀⠀⢀⠙⣀⡀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣘⢀⠤⠚⠐⠾
⠀⠀⠀⠀⠸⠇⠂⠉⡀⢀⡉⠹⠄⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠐⠪⣭⣋⠠⣤⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣤⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣶⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⢀
⠀⠀⠀⠀⠀⢀⡄⢦⣄⠀⠃⠎⠙⠂⠀⢶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⠀⣤⢀⠀⠀⠈⡏⠀⢻⡦⠀⢦⡀
⠀⠀⠀⠀⠀⠀⣁⠀⢉⠰⣄⠀⠀⠀⠐⠦⢙⡀⣜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠸⠃⠀⠁⠈⠃⠀⠀⠁⠀⠈⠀⠀⠈⠃⠀⣀
⠀⠀⣠⠀⠃⠀⠏⠀⠈⠀⠙⢶⡇⠘⠀⠤⣀⠑⠈⡀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⣤⠔⠀⠀⠀⠀⠀⠐⠀⠇⠀⠆⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠆⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⢸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠸⢻⠷⣤⠀⢀⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠟⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠙⠏⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢢⡀⢠



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠈⠆⠈⢡⡙⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢫⠀⢀⡁⠀⠐⣤⣄
⠀⠀⠀⠀⣠⠂⢠⠀⡜⠑⣀⠀⢀⠀⠀⠀⠙⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⣶⣧⡈⠀⠀⠀⠈⠁⠠⣄⠀⠹⢦⡀
⠀⠀⠀⠀⠁⠂⢘⠀⠀⢀⠉⠀⠜⠀⠀⠀⢼⠁⠘⢿⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠛⢿⣿⣦⡀⠐⠁⠀⠀⠀⠑⣄⣀⠉⢲⣤
⠀⠀⡀⠓⢠⠀⠸⣆⠀⠀⡠⠀⠀⠀⠘⢦⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠛⠻⣿⣷⣄⠀⠀⠀⠀⠈⢿⣷⣜⠻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡤⠦⠀⡆⠀⠀⠀⠀⠳⣼⠄⠀⠀⢀⠀⠀⡄⠀⠏⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠢⣤⡀⠀⠀⣨⠀⠀⠀⣸⡤⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠉⢲⠉⠀⠈⠲⠈⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣀⠀⢀⡸⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠤⢻⠃⠀⠈⢑⠉⠀⠀⠹⠓⢤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡒⠀⠏⠀⠈⠀⠀⠀⢾⠦⡀⠀⠀⠀⠈⠇⠀⠖⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢀
⠠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⡞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤
⠀⠈⠂⠱⣄⣱⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⣐⣠⠴⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠼⠀⠀⡀⠀⡀⠀⠈⠢⣧⠞⠁⠀⠀⠀⢰⠀⠸⠥⠞⠁
⠀⠀⠀⠀⠐⠛⠃⢠⣄⠀⠀⠀⠇⠀⠀⢠⣄⠐⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠓⠄⣀⠀⠀⠀⣄⠀⠀⢀⣧⠴⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠉⠈⢑⠊⠁⠀⠁⡖⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠉⣶⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⡀⢀⡨⣄⡀⠀⣀⢧⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢄⡀⠀⣀⡿⠀⢀⣀
⠀⠀⠀⠀⠤⣤⡄⠘⠋⠀⠀⠙⡏⠀⠀⠘⠋⠠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠞⠿⠀⠀⠈⠋⠁⠀⠈⡟⠦⣤⠄
⠀⢀⠐⠰⠋⡙⠀⠀⠀⠀⠀⠔⠓⠀⠀⠀⠀⠀⠹⠙⠲⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢲⠀⠐⠁⠀⠁⠀⢀⠔⡟⢦⡀⠀⠀⠀⠸⠀⢠⡒⢦⡀
⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠉⠀⠀⠀⠀⠀⠀⠁⢀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣍⢺⣷⣶⣖⢲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⣼⠆⢼⡃⠀⠇⢙⣷⠈⢱⣤⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⣿⠻⣾⣷⣆⣷⠟⠈⠓⢶⡒⢧⠀⠀⠀⠀⠐⣦⡜⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢿⡶⢻⣻⠉⠉⠀⠰⢣⣾⢏⡏⢡⠀⠀⠀⠀⢾⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠺⡿⣶⣯⠓⣒⣄⠀⠉⠁⢸⡏⡈⠀⠀⠀⠀⢀⣹⣿⣷⣜⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠛⠻⢮⢿⣿⣟⠁⠁⢀⣠⠀⣧⠏⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣝⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠻⣿⢿⠷⢦⣬⣤⠂⠈⠄⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣝⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢰⡆⢚⣏⠐⣾⣟⠛⣷⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡝
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢻⣿⣷⠀⣿⡧⠤⠿⢧⣌⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⠯⣀⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈⢷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠘⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⢺⣿⡆
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⣿⣿⣿⣿⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠻⣿⡄⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣄⡀⣰⣿⡿⠃⠀⢠⡇⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡼⣿⠁⠀⠀⠸⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⢀⣴⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠘⣿⣿⣷⠈⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣦⠀⢻⣿⣿⣿⣿⣆⠀⠀⠀⢤⡀⠀⢀⣿⣷⡀⠀⠀⣸⣿⣿⡟⠀⢤⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⢋⣼⣿⣿⣿⣿⡇⠀⠀⠀⢱
⠀⠀⠀⢤⡀⠀⣴⡿⠀⡀⠙⣿⣿⣿⣿⡆⠀⠀⢸⣷⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⠁⠀⠈⣿⣷⡄⠀⠀⠙⠻⣿⣿⡿⠁⢸⣿⣿⣿⣿⣿⣷⣤⣀⣤⣿
⠀⠀⠀⠈⣿⣶⠟⠀⠀⣿⣦⣾⣿⣿⣿⠇⢀⣴⣿⠟⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣿⣿⣿⡀⠀⠀⠀⠀⠉⣰⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣇⠀⢀⣿⣿⠀⡀⠀⠘⢿⣿⣿⣿⢟⣴⣿⣿⠋⠀⢠⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣀⠀⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟
⢿⣿⣿⣿⣿⣇⣀⣽⣷⡀⠈⠙⠿⢋⢸⣿⣿⣿⣷⣤⣾⡇⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠘⣷⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠘⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⣿⣌⣿⣿⣿⣿⣿⡿⢡⣾⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣠⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⢠⠀⠙⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⡟⠀⣿⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣷⣶⣿⣿⣿⣿⡟⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣘⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⡟⠛⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⢾⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⠉⣰⣎⡴⢃⣰⠃⠀⠈⠢⡀⣠⢴⣏⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡒⠁⠁⠁⠊⠈⠀⣠⠏⡸⠀⠀⠀⠀⠘⢏⠋⢸⡆⠈⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣄⢰⡇⠀⠀⠀⠀⠀⠊⠁⠂⠁⠀⠀⠑⠄⠀⠀⠁⠀⠀⠀⢠⠀⣸⡆⢠
⠀⠀⠀⠀⠀⣸⣄⣾⣷⣿⣸⣇⣧⠀⢰⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢰⡄⠀⣰⠀⣼⣇⣿⠧⠟⠂
⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⣿⣿⣿⡀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⣧⣠⡿⠖⠋⠁
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⡲⢤⠄⠠⠷⠘⠛⠒⠛⠉⠁
⠀⠀⠀⠀⣰⣿⡆⠀⢰⡀⠀⠀⠀⢀⡀⢄⡴⠏⠚⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠺⠇⠰⢉⣰⣡⡊⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣷⠀⠀⡀⠀⠀⣺⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠏⠙⢄⠢⢄⠀⠄⠰⣿⡇⠀⢸⣿⡄⢠⡇⠀⣠⠿⠿⠆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠀⠀⢀⡜⠀⠀⢣⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⡘

⠀⠀⠀⠀⠀⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠘⣇⠈⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣸⠀⠀⠀⠀⠀⠀⠀⠰⠋⡇⣦⠀⠀⠀⠀⠀⠀⣠⣤⡄
⠀⠀⠀⠰⡆⣨⢛⢥⡶⠀⠀⠀⠀⠀⠀⢸⢸⣄⣧⣠⠀⠀⠀⠀⠀⢀⠀⣲⠛⡏⠀⠀⠀⠀⠀⠀⡾⡿⠜⡄
⠀⠀⠀⣷⣼⢀⡾⣤⠦⡼⠀⠀⠀⠀⢸⣾⠈⡟⠙⢻⠀⠀⠀⠀⠀⠘⢟⢫⣿⣀⡀⠀⠀⠀⢀⠠⢇⠠⣤⢷⡄
⠀⠀⠀⠘⠦⠾⠇⠘⠃⠁⠀⠀⠀⠀⠀⠁⠰⠛⠖⠁⠀⠀⠀⠀⠀⠀⠀⠱⠐⢯⠃⠀⠀⠀⠘⣷⠛⠘⢆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠜⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⡀
⠀⠀⠀⠀⠘⡿⡏⡅⠀⠀⠀⠀⠀⢀⢀⠀⣿⢣⣀⡀⠀⠀⠀⠀⠀⠀⠎⣼⣿⢰⡀⠀⠀⠀⠀⠀⡄⣾⡼⣃⡋
⠀⠀⠀⠀⠸⣧⠛⣇⠀⠀⠀⠀⠀⠈⠉⢷⠾⡌⠛⢛⡁⠀⠀⠀⠀⢰⣜⣇⢹⡾⣧⡀⠀⠀⠀⠀⡁⢏⢁⢹⠠⠇
⠀⠀⠀⠸⣆⣿⢶⣼⠀⠀⠀⠀⠀⠀⣻⡛⠀⡿⣆⠛⠇⠀⠀⠀⠀⠸⣿⠹⢰⡀⠻⠀⠀⠀⠀⠠⣼⡾⢿⡘⢾
⠀⠀⠀⠀⠀⠰⠏⠋⠀⠀⠀⠀⠀⠀⠈⠃⠻⠅⠙⠋⠀⠀⠀⠀⠀⠀⠙⠘⠋⠃⠀⠀⠀⠀⠀⠀⠈⠃⡎⠻⠞

⣷⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠶⠦⠤⠄
⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿
⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣶⣶⣶⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⠋⠉⣻⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠛⠃⠀⠀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⡿⠿⠛⣿⡇⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠀⠘⠿⠿⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡎⢇⠀⠀⢒⠄
⠀⠀⠀⡠⠔⠒⠒⢢⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠡⡀⠀⠀⢀⠜⠀⠈⢆⠀⠀⠀⣀⠤⣀
⠀⠀⠀⡱⠀⠀⠀⠘⢲⠶⡏⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠂⠀⠀⢊⠀⠐⢳⠂⠁⠐⠲⡛⠀⠰⠁⠀⠈
⠀⠀⠈⢳⠀⠀⠀⠀⠀⡆⢣⣴⠃⠀⡄⠀⡠⠀⠀⠀⠀⠀⠀⠀⢐⠇⠀⠀⠀⠐⣷⣖⡁⠀⠀⠀⠀⣑⣤⠀⠁⠒⠈
⠀⢠⠤⠶⠀⠈⠁⠈⠄⠉⠁⠈⡆⠰⠀⠀⠀⠂⠀⠀⠀⠀⠀⠒⡡⠤⠀⠄⣀⣀⡤⠋⠀⠀⠀⠀⠀⠈⠢⢄⡀
⠀⢇⠀⢀⡁⠀⠀⠀⠐⠀⠀⢐⡍⡂⠀⠐⠀⣊⠀⠀⠀⠀⠀⢊⠤⠀⠀⠀⠀⢈⠽⠋⠙⠀⠂⠠⠐⠀⠛⢍
⠀⢰⠁⠀⠀⠐⠀⠁⠀⠀⠀⠀⡇⠀⠀⠠⠀⠀⠒⠀⠀⠀⠒⠁⠀⠀⠠⠀⢌⢑⡶⠀⠀⠀⠀⠀⠀⠀⠴⣖⠉
⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠥⠄⠀⠠⠤⠤⢤⠤⠀⠀⠤⠵⠂
⢹⠀⠀⠒⠒⠒⠁⠀⠈⠉⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠤⠀⢀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠚⠀⠀⠀⡇⠀⡀⢀
⠀⠀⠀⠄⠀⠀⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠃⠀⠀⠀⢀⠀⠀⣀⣀⠤⠀⢀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⢸⠀⠀⠁
⠀⢧⣀⠄⠀⠀⢣⣀⠄⠀⠀⠀⠳⠤⠂⠘⠦⠄⠀⠘⠦⠔⠀⠈⠳⠤⠤⠂⠈⠳⠤⠤⠔⠊⠀⠳⠤

⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⡄⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡠⠂⠀⠀⠣⠖⠚⠋⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡰⠀⠘⣄⠀⠀⡀⢊⢻⡅⣀⣠⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄⠀⠀⠀⠆⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⢀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠐⡄⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⢀⡐⠖⠒⠀⠀⠈⠀⠀⠀⠀⠈⠙⢧⠀⡄⠀⡠⠐⠉⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠉⠑⠖⠒⠆⠙⠁⠀⠀⠐⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠲⠂⠁⠀⠀⠀⠀⠀⠒⠐⠒⠒⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣀⡀⠀⠀⠀⣅⠀⠈⠀⠀⠀⠠⣶⡀⠀⠀⠀⠉⠡⠘⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⡘⠂⠀⢀⡀⠀⠀⠙⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⣌⣻⣶⣶⡄⠀⠀⠀⠀⣀⠚⠤⣀⠇⠀⠀⠈⠀⣀⣀⠀⠁⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣔⣋⣀⣀⡄⠋⡀⢲⡶⠛⠈⠉⠉⠀⢂⠄⡠⠞⠀⠀⠀⢈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠐⠠⠒⠀⠤⠐⠂⠀⠀⠀⡀⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣛⠛⠉⠀⠀⠀⢀⡀⠀⢠⡄⠀⠀⠐⢆⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⢀⠀⠀⠀⠀⠀⡠⠄⠂⠠⠀⢲⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠁⠀⠀⠈⠂⠉⠁⠀⠀⣴⠀⠀⠀⠈⡄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄⠀⠀⠀⠀⡾⠀⠀⢀⠂⠀⠀⠳⡀⠀⠀⠘⠷⠄⣀⡐⠠⠀⠀⠴⠀⠇⠀⠀⠀⠀⠀⠈⠲⡀⣼⠇⠀⠀⠀⠀⡇⠀⠀⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠐⠄⠤⢶⠀⠀⠠⡏⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢉⡅⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⣀⠠⠀⠀⢰⡇⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⣄⠀⠀⠈⡄⠀⠓⠀⠐⠀⠀⢀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⡠⠂⣽⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠄⠒⠀⢧⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠦⠀⠀⢁⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠉⡔⠀⠀⡠⠊⠐⢀⡆⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠤⠶⠤⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠶⠄⢀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠘⠆⢸⡅⠀⠄⣸⠃⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠀⠀⠀⢀⡠⠉⠀⠓
⠀⠀⠀⠀⠀⠀⠀⡆⠀⣼⠁⠀⡶⢋⠀⠀⠀⠀⠀⠀⠒⠀⠀⠤⣦⠤⣤⢤⣤⣤⣤⠀⠐⠛⠒⠈⠉⠉⠉⠉⠉⠉⠳⢾⡃⡟⠀⠉⠁⠀⠀⠀⢀⠦⠠
⠀⠀⠀⠀⠀⠀⠀⠐⡀⢈⣠⠀⡃⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⡀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣙⠷⣏⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠸⠄⠈⠂⠈⠠⣤⢵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⡀⠈⠂⠤⠀⠀⠀⡄⠀⠈⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠹⣦⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣦⠀⠑⠄⠀⢰⡃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠀⠀⢀⠀⠀⠀⣄⡀⠠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠒⠀⠘⢦⡀⢀⠞⠉⠉⢰⠶⠆⠠⣤⢄⣰⡒⠀⢹⣄⠈⢢⠈⠓⠤⠤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡕⢤⡀⠀⠆⠀⠀⠉⠐⢄
⠀⠀⠀⠀⠀⠀⢀⡆⢄⠁⣀⠴⠀⠄⠀⠹⡄⢀⡀⢀⡀⠛⠀⠀⠀⢦⠁⠁⠤⠉⠙⣦⠀⠱⠄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠬⢒⠠⠦⠄⠀⠀⠀⢠
⠀⠀⠀⠀⡐⠒⠣⠠⠔⠂⠀⠀⠀⠀⠀⠀⠈⠲⡙⠂⠑⠂⠀⢀⢀⠀⠱⣄⠀⠤⠀⠀⢳⣄⠀⠢⡀⠙⠦⠠⠐⣄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡄⠐⠆⠤⠀⢀⡼
⠀⡀⠀⠀⠁⠉⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢢⡀⠀⣀⠺⠄⠀⠀⠈⢢⡀⠀⣀⣸⡜⢣⡀⠀⠄⡀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢰⠀⠀⠀⢀⠈⠙
⢈⡁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠙⢶⡁⠀⠀⠁⠔⠒⠀⠙⠦⠀⠬⠥⠽⠽⠶⠠⠘⠖⠐⠚⠓⠒⠋⠉⠁⠀⠀⠀⠀⠀⠸⠀⠐⠀⠀⠙⢤
⢸⠇⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡁⠂⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠄⠀⠀⡀⠀⠀⢀⡀⠀⠀⠃⢠⡀⠀⠀⠀⢰
⠰⠃⠶⡤⠀⠀⠈⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⡕⢶⡀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠒⠀⠁⠐⠁⠀⢀⣂⡈⠓⠺⠛⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣳⠄⠁⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⣆⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣴⠶⠚⠛⠉⡉⢹⡇⡀⠀⢐⢀⡴⢀⠴⠛⢆⠀⠀⠀⠘
⠠⠀⠀⠀⢂⡑⣾⠃⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡃⠀⠀⢘⣆⢠⡙⣢⣤⣴⣴⠖⠒⠉⢉⢛⣄⡀⢠⣀⡈⠀⢰⡂⣈⠙⣻⣰⡀⠁⠀⠀⠀⠈⢂⡀
⠀⠈⠀⠁⠈⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⣸
⡇⣠⠿⠀⡀⣤⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢹⣿⡉⠀⠺⣳⠀⢸⡟⠀⡄⣸⠀⠀⠀⢸⡄⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐
⣾⣥⣌⠉⣠⡼⠂⠸⢁⣘⢻⣯⢀⣼⣴⡯⠤⣾⣠⠀⠀⡀⠁⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡿⢿⡶⠂⠠⠤⠀⢀⣬⡍⠼⣥⠀⣿⣿⠛⠂⢹⣿⣄⣼⢁⡀⢀⠁⡀⠀⣰⠀⡀⠀⢠⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⢀⡀⣀⠀⢠
⡷⠨⣙⣟⡳⠒⠀⢸⡟⣀⣘⠟⡯⣿⠛⡘⣋⡀⣽⣿⠟⣛⣦⣿⣼⡇⢰⡿⢻⣧⣶⡾⠇⣴⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣠⣶⣿⣡⡏⣾⣿⣵
⠀⠀⠀⠀⠈⠈⠀⠘⠛⣷⠍⠂⣼⡻⠂⠠⠤⠀⢐⣿⣧⠆⠰⣿⡗⠭⢿⡥⠄⢿⣿⡷⠼⣿⡿⢲⣾⣆⡀⢀⣄⣤⣿⣿⣿⣿⣿⣿⡿⠥⠽⠿⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⢯⡃⢦⣤⠄⠀⠉⢻⣇⠐⠈⢻⡿⢠⢽⣏⣀⣋⣿⡥⠀⢹⣇⣈⣿⡿⣿⣿⠿⠟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠶⠾⠿⣯⣘⡛⣷⣀⠊⢿⡧⢴⢺⣄⣐⠈⣷⡆⢸⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⠚⠛⠶⠿⠿⠿⠒⠛⠉⠉⠁





⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣵⣶⣤⣿⣵⣿⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⢀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢠⣾⣥⠜⠀⠁⠀⣀
⠀⢀⣀⣴⣄⠀⠰⣦⠔⠃⣀⠀⢴⣄⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢠⣿⣷⡶⡈⠀⠀⠘⢿⡀
⠀⠉⠉⣥⠴⣾⠧⠾⠦⠀⠉⠙⠳⠨⠓⠀⠀⠀⠀⠀⡀⢠⡴⣰⠾⢃⣶⣿⣿⡿⠈⡥⠐⠀⠀⠀⠐⠀⣀⣴⡞
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⢁⡼⡿⠋⠉⠈⠐⠺⠃⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣞⢀⣾⣧⠆⠈⠁⠀⣀⡤
⠀⠀⠀⠀⠀⠀⣰⠻⢏⣾⣿⡶⢦⠀⠀⠀⠙⢧⠀⠐⡆⠀⢸⣆⣠⣄
⠀⣠⠄⣴⠂⠞⣻⣶⣿⣿⡿⠂⡀⠀⠀⢠⡄⠀⠲⢤⣀⣆⣾⠿⣋⣁⠀⠀⠀⠀⠀⢀⠠⢆
⠀⣀⠀⡄⠀⢸⡿⠋⠀⠚⠀⢀⣿⡀⣶⣼⣧⣾⣾⣤⡾⠿⠷⣶⡿⠋⠀⠀⠀⠀⠠⠁⠀⠀⡀
⢀⣿⣼⣷⡀⢠⣤⣾⣶⣴⣿⣾⡿⠟⠻⠿⠛⠉⠁⠀⠴⠟⠛⠉⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠈⡆
⠈⠉⠉⠙⠓⠫⢤⣀⣀⠂⣨⠉⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠀⠉⢄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠛⠒⠼⠿⠶⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠡⠖⠁⠀⠀⠀⠀⠀⠀⠀⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣆⡀⠀⠀⠀⠐⠟⠁⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠸⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠠⣾⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠋
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠁⠀⠀⠀⠀⣤⣴⡄⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⠛⠀⠀⠀⠾⠋
⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠂⠀⠀⢠⣶⠿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶
⠀⠀⠀⢠⣶⣿⠋⠉⣿⣇⣤⣶⠿⠿⣷⡄⠀⠀⠿⢷⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠘⠋
⠀⠀⠀⠀⢸⣿⣤⡶⠟⠋⠉⠀⣀⣀⣸⡇⠀⣴⢶⣦⣄⡀⠀⢹⣧⠀⠀⠀⠀⢠⣿⠃⠹⣧⡀
⢀⣠⣴⡾⠟⠋⠁⢀⣀⠀⠲⠟⠋⠙⢻⡇⠀⣿⡀⠈⠙⠻⠷⣾⣏⡀⠀⠀⢠⡿⠃⣀⣀⠹⣷⡀
⢻⣯⠀⢀⣠⣴⠾⠟⠋⠀⠀⠀⠀⠀⢸⣇⣠⣿⠛⠷⣦⣄⣀⠀⣹⡟⠀⢠⣿⣷⡾⠟⠙⠻⠿⣷⡀
⠀⠻⠿⢻⣿⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠙⠛⠁⠀⠀⠀⢹⡟⠿⠟⠀⠀⠘⢻⡷⠀⠀⠀⠠⣾⡟⠁
⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⣾⠏⠁⠈⠙⣷⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⢙⣷⣄
⣶⠿⠛⠛⠛⠛⠻⢷⣦⣴⠿⠿⠿⠿⠿⢿⣧⣄⠀⠀⢀⣸⣷⣶⠶⠿⠿⠿⠷⣶⣤⣤⡶⠿⠛⠛⠛⠛⢷
⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿
⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣠
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⢷⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⣟⣘⡾⠾⣼⣼⣰⢢⢄⠀⠀⠀⠀⠀⠈⡈⠁⠀⠄⠀⠠⠀⠁⠀⠐⢀
⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⢀⠈⠻⡇⢠⣴⠀⠈⠉⠛⠺⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠶⠷⠶⢤⣄⣑⡆⠙⠂⠕⠚⣣⡰⠟⣠⠋⠀⠀⠀⠀⠰⠁⠀⠄⠀⠀⡀⡐⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠉⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠀⠐⢠⡄⠀⠀⡁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠐⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⢸⠃⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠜⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡇⠀⠘⠆
⠀⠀⠀⠀⠀⢈⠀⠀⠀⡄⠓⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡈
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠈⡐⠒⠅⠀⠀⡒⠲⡁⠈⠀⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠴⠦⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜⠒⠶⠶⠶⢤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠶⢤⡀

⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠢⣄⠘⠃⣠⠴⠀⠀⠀⠢⢀⢠⠀⠀⠀⠀⠀⠀⢴⣷⣙⣋⣾⡦⠀⠀⠀⠸⣿⣿⣷⣾⠇
⠀⠀⠀⠀⢠⡄⢹⠇⣄⠀⠀⠀⠈⢀⠀⠙⠃⠀⠀⠀⠀⠀⢴⣶⢛⡛⣶⣦⠀⠀⠀⠺⡿⣿⡿⢿⡆
⠀⠀⠀⠈⠁⠀⢸⡆⠀⠉⠀⠀⠀⠀⠂⠐⠀⠄⠀⠀⠀⠀⠀⠁⠻⠟⠈⠁⠀⠀⠀⠀⠀⠙⠃


⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠂⢠⣴⣦⡄⠒⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠙⠃⢠⡀⠸⠃⠀⠀⠀⠘⠃⢀⡆⠀⠛
⠀⠀⠀⠀⡀⠸⢿⡿⠂⣀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠴⠆⢈⡁⠰⠆⠀⠀⠀⠰⠆⠀⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠃


⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡀⠲⡆⢠⡀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⢀⣀⠸⡷⣤⣤
⠀⠀⠀⠀⠀⠀⢶⡖⠀⠀⠀⠀⠀⡚⠁⡰⠧⣈⣣⠀⠀⠀⠀⣹⣿⣿⣯⠀⠀⠀⠀⠀⣿⠸⡷⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⣀⣄⠘⠃⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⠉⢱⡷⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠉
⠀⠀⠀⠳⢤⡄⣚⢠⡴⠛⠀⠀⠀⠀⠀⣀⢄⠀⠀⠀⠀⠈⠁⠀⢀⡀⠠⠀⠀⠀⠈⠁⠀⠀⢀⠀⠀⠈⠁
⠀⠀⠀⢀⣠⠌⠧⠡⣄⣀⠀⠀⠀⠀⠀⠳⠼⠀⠀⠀⠀⠀⠀⠀⠘⡛⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠋⠁⠀⣹⠀⠀⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢀⡀⠀⢿⡏⠀⣠⡀⠀⠀⠀⠱⡀⠀⡜⠀⠀⠀⢀⣤⠀⢈⣿⠀⢀⣄⠀⠀⣀⠀⠀⠇
⠀⠀⠀⠘⠐⡖⢩⡉⣿⠁⠁⠀⣀⣀⡀⣼⢲⡄⠀⡀⠀⠀⠉⠛⡂⠋⠞⠋⠉⠀⠀⠈⠁⣶⣷⡄⠈
⠀⠀⠀⢠⣤⠓⢬⡥⠛⢔⡆⠀⠀⠀⢀⠌⠙⢄⠀⠀⠀⠀⣶⠟⠡⡦⠙⠳⡖⠀⠀⠔⠈⠉⠋⠁⠢⠄
⠀⠀⠀⠀⠉⠀⠶⡷⠀⠀⠀⠀⠀⠀⠊⠀⠀⠈⠆⠀⠀⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⣴⣤⠂⠀⠀⢀⣿⣿⣷⣄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢟⠀⠊⠁⠀⠀⠀⠚⠁⣿⣿⣿⣿⣆⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣦⡀⠙⠳⠌⠺⢦⣄
⠀⠀⠀⡀⣀⣀⣀⣄⣀⣀⢀⣀⣀⠀⣀⢀⡀⢀⣀⡀⠀⡀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠉⠁
⠀⠀⣩⣍⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠰⠿⠿⠿⣦⣤⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⠿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⣀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⠿⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⢻⣿⣿⠟⠋⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠛⠀⠀⠀⠀⠋⠙⢿⣿⣿⡿⠏⠉⢻⣿⣿⣿⣿⡟⠛⠁⠀⠛⠋⠀⠀⠀⠀⣀⣀⣀⣀⡀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠄⠙⠋⠛⠛⢻⠁⠀⠀⣤⠙⠉⢀⣿⣿⣿⠿⣿⣭⡄
⢟⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⣀⣀⡀⣠⣤⣤⣄⣘⠀⠀⠀⠀⠀⣀⣚⠋⣡⡉⠀⠺⠛
⣿⣿⡿⣦⣤⣾⣿⣿⣿⣷⣴⣿⣿⣿⣷⣶⣾⣽⣿⣿⣿⣶⣾⣿⣿⣿⣷⣿⢿⣿⣿⣿⣻⣿⣿⡋⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣠⣾⣿⣷
⣿⠿⣿⣿⣽⣿⠿⣿⣿⣯⣝⣻⣿⣿⣿⣽⣿⣿⣿⣵⣿⡻⠿⣿⣿⣿⣻⣿⣿⣿⠏⠀⣿⣿⠓⠂⠀⠁⠀⠀⢸⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢠⡞⠃⢀⣄⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠂⠀⢰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⢸⡛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⡾⡿⠟⠁⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⡾⣿⣧⡀⢀⣼⣿⣷⣿⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣼⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢇⣤⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢡⠀⢠⠟⠙⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠧⡀⢠⡆⠀⠀⠀⠈⣧⠄⠐⠸⠀⡤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠉⠀⡰⠉⠷⠀⠐⠑⠀⠃⠀⣤⡠⠞⡷⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⠸⢤⡇⠀⠄⠀⠀⠀⠀⠀⠀⠉⠀⠐⡁⠘⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠈⠁⡐⠂⡰⠁⠀⠀⠀⠤⠂⡳⠀⠇⠆⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣦⡱⡄⠲⠇⠘⠀⠀⠀⠀⠀⠀⢀⠀⠞⠀⠔⢁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠌⠁⢐⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠊⠐⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠈⡤⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢥⡀⠀⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠮⠴⠖⠖⢤⣼⢶⡿⣷⣾⣷⠋⢻⣿⣷⡖⠦⢤⡄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⣤⣤⣴⠞⠋⠀⣸⠁⢀⣿⢻⣆⠀⠙⢯⣟⠉⣷⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢹⣁⣀⣠⣶⡇⠀⠸⣿⠄⣻⡆⠀⠈⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠈⣿⠷⠏⠛⠉⠘⠶⠶⠞

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠠⣰⠏⠀⠀⠀⠀⠀⠀⠀⢶⣄⡠⠀⣄⡑⢾⠂⣁⢀⡀⢠⡄⠀⠀⠀⢠⡀⠀⠀⠀⢸⣟⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣤⠒⢤⢍⠀⡀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠂⣼⣈⣿⣊⣹⠼⠿⠉⠁⠀⠀⠀⠀⠉⠿⣶⣐⠶⠧⢶⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠰⠦⠶⡦⢶⠰⣿⡧⢺⠰⡗⠗⠗⠒⠀⠀⠀⠀⠀⠶⣍⢸⡏⢾⢘⡋⢑⠶⠀⠀⠀⠀⠀⠀⠀⠈⣤⣓⢽⣾⣝⣣⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠖⢤⠜⣏⡁⠈⠀⠀⠀⠀⠀⠀⠀⢒⣦⠜⢋⢉⣾⡉⠙⢣⣄⡂⠀⠀⠀⠀⠀⠀⣬⣾⢵⣩⢩⣻⢷⣮⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠂⠀⠀⠎⢷⡀⠀⠀⠀⠀⠀⠀⠺⠋⠁⠀⠉⡡⣶⢌⠁⠈⠈⠙⠃⠀⠀⠀⠰⠋⠈⠈⠀⢔⣴⠂⠀⠈⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⢀⠀⢀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠑⠶⠔⠁⠀⡀⢀⢠⠀⠀⠀⠀⠀⠀⠀⢆⠈⡆⣿⢰⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣆⠆⠀⡐⡼
⠀⠀⠀⠀⠀⠀⠀⠘⡣⠧⢀⡀⢲⠂⢀⡄⠷⡙⠀⠀⠀⠀⠀⠀⠘⠳⢦⣕⡶⠼⢴⡊⠴⠞⣠⡀⣀⠀⠀⠀⠀⡐⠂⠙⠀⠄⠝⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢘⠀⢈⡁⢀⠀⠀⠀⠀⠀⠀⣤⠒⠉⠉⡁⢾⠀⠀⠀⣽⡣⠤⠤⠖⠋⠀⠀⢠⣴⠵⡦⠈⢰⣿⢈⠀⢦⠶⠶
⠀⠀⠀⠀⠀⠀⠀⣠⠑⡆⠈⠀⢙⡁⠈⠃⡶⣊⠀⠀⠀⠀⠀⠈⠉⣥⡖⣪⢷⠲⠺⠓⠝⡓⠂⠀⠀⠀⠀⠀⠀⠈⡀⢨⡄⠆⢠⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡰⠄⡀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⡐⠁⡘⢸⡇⠡⣄⠱⡀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠐⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠚⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡥⠒⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⡄⠐⠢⣿⠔⠂⣤⠀⣠⡄⠀⠀⠀⠀⠀⠠⠽⣎⠀⣤⠀⣱⠟
⠀⠀⠀⠀⠀⠀⠀⠘⢁⠦⣀⠀⢘⡃⢀⣂⣥⠧⠀⠀⠀⠀⠀⠈⠙⣷⣷⣀⠀⢿⠀⣀⣿⡞⠉⠀⠀⠀⠀⠀⠀⢠⣄⠙⣀⠍⣠⠋⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢱⣿⣿⡎⠓⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⢉⣃⣾⣞⡋⠀⠀⠁⠀⠀⠀⠀⠤⣦⢤⠤⢥⣽⣿⣯⡍⢡⣄⣆⡀
⠀⠀⠀⠀⠀⠀⠀⢑⡲⡦⠙⠃⣹⡉⠈⠋⡶⣉⡁⠀⠀⠀⠀⠀⣁⣶⡖⠛⠁⣾⠈⠙⣶⣖⡀⠀⠀⠀⠀⠀⠀⣤⠖⠃⡼⡛⢅⠒⣤⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠃⢀⡠⢴⣌⠀⠀⠁⠈⠈⠀⠀⠀⠀⠘⠉⠀⠇⠀⡠⣽⣄⠀⠛⠈⠙⠂⠀⠀⠀⠀⠀⠀⢀⠾⠀⡇⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠉⠀⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⠛⠛⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⢰⡏⠀⠀⢀⣴⠟⠋⠉⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢀⣤⡾⠷⠶⢶⡿⠁⠀⠀⠀⠀⠀⠀⢹⣶⠶⠶⠶⣤⣀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢿⣄
⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⠟⠉⠉⠉⠙⠻⣦⠀⠀⠀⠀⠹⣧
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠹⡷⠾⠿⠷⢶⣽⡇
⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀
⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀
⠹⣧⡀⠀⠠⣄⢰⣆⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⢿
⠀⠈⠛⠶⠶⣾⠿⠿⡷⠶⠶⠶⠶⠶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠠⠚⢳⠚⢦⠀⠀⠀⢦⡀⣸⣷⣀⠔⠀⠀⠀⠀⢦⣀⣸⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡝⠁⠈⣿⠿⠶⠶⠶⠶⠶⡿⠿⠿⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠠⡀⠀⡆⠀⣠⢀⠜⢦⠔⠳⡀⠀⠀⠀⠀⠰⠛⢲⠚⠣⡀
⠀⠀⠀⠀⠀⠀⣀⣈⡖⠙⢺⣁⣀⠀⠘⠀⠀⢀⠀⢠⠀⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢈⠷⡤⠾⣄⠀⠀⠀⠀⠀⠈⣳⠚⠓⣎⣀
⠀⢤⡀⢰⠀⠀⡀⠁⠀⠃⠀⠈⠀⠀⠀⠀⠉⠉⣹⢤⡤⢏⠉
⣀⣀⣹⠊⠙⣎⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠃⠀⠑
⠀⠀⡽⢦⡤⢯⡀

⠀⠀⠀⠀⡅⠢⠄⠀⠔⠁⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⠂⠀⠀⠀⡀⢤⡝⣦⠉⠁⠀⠀⢀⡘⢧⡛⠂⠀⠀⠀⠀⠀⠈⠑⠒⠂
⠀⠀⠀⣸⡱⡀⣀⠎⠀⠀⠀⠀⠀⠀⠢⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠃⠃⠺⣂⢠⡄⢨⣥⠤
⠀⠀⡀⠹⣱⠡⠃⠀⠀⠀⠀⢀⠀⠀⠀⠨⣄⣷⠄⠒⠀⢲⢏⣄⠀⠀⠀⠀⠀⠀⣽⣍⠦⠀⠮⣶⠻⠀⠀⠀⣀⠀⣄⠀⠀⠀⠠
⠀⠀⡇⠀⠉⠀⠀⠀⠀⢀⠔⠁⠀⢀⠔⠉⠁⠀⠀⠀⢠⠊⢃⠿⠀⠀⠀⠀⠀⠀⠆⠉⠀⠀⠀⠀⠈⠀⠀⢀⡻⠋⢛⡶⠂⠀⡆⠀⢈
⠀⠀⠁⡀⠀⠀⠠⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢀⣾⠛⡆⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣶⠺⠧⠀⡘⠀⠀⣈
⠀⠀⠀⠩⡀⠀⠀⠠⠂⠀⠀⢠⢃⠤⠔⠒⠒⠁⠀⠀⠘⠿⠞⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣼
⠀⠀⠀⡇⠉⠁⠀⠀⠀⠀⣠⠋⣁⣴⣾⡟⠋⠲⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠠⠛
⠀⠀⠀⠙⣄⠀⠀⣀⣠⠞⠉⢀⠉⠁⠚⠒⠊⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠈⠑⠺⠇⠀⠠⢀⡈⣁⠀⠀⠀⠀⠀⠀⠀⠤⠔⠪⠁⠓⣒⠒⠢⡄⠀⠤⡀⠀⠀⠀⠀⢀⣀⠤⠐⠊⢁⣀⠀⣠⠀⡴⢩⠁⠀⢀⠀⢤
⠀⠀⠀⠀⠀⠀⠈⢄⡀⠆⠀⠀⠀⠉⠲⣤⣀⣀⡀⠀⣀⣀⡤⠂⠀⠀⠀⠀⠘⠀⠀⠘⢄⠔⠒⠽⠷⠃⠀⠀⠀⢠⠎⢂⣁⠴⠛⠁⠀⠀⡴⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠑⠤⣀⣀⠠⢤⠀⠐⠀⠀⠸⡛⢻⡋⠀⠐⠒⢊⣠⠅⠓⠘⠤⠤⠀⠀⠊⠴⢔⢋⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⡀⠀⠀⡀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠦⢤⠤⠘⠀⠀⢃⣈⠭⠛⠁⠀⠀⠀⠄⠀⠀⠀⢀⢀⡀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣄⣀⣘⠦⠄⠀⡇⠀⠀⠀⢀⠄⠂⠀⠀⠠⠀⠀⢸⠀⢧⠤⠤⡬⡥⠢⡀⠀⠀⠀⠀⡄⠀⠀⡨⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠀⠀⠱⡄⢲⡆⠀⢸⠀⠀⠀⡰⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣁⡴⠊⠉⠀⠀⠀⠀⠀⠹⣻⣇⠀⡜⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣠⣔⠰⢠⠏⠀⠀⠀⠙⡄⠀⠀⠀⠀⢻⠈⢦⢀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠪⡄⠉⣰⡟⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⡹⠁⠀⢠⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡚⠂⠀⡰⢡⣅⠀⠀⠑⠲⠤⣀⠀⠀⠀⠀⢸⣧⠎⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠢⣀⠁⡠⣉⠀⢢⠀⢄⠀⠀⠉⠒⠠⠀⡸⠁⠀⠀⠐⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠙⠲⡥⣀⠀⠑⠀⠑⠀⡁⠤⠄⠀⢁⡀⠀⠠⢚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⣠⡇⠀⢠⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠋⠀⢀⣾⠟⠁⠀⠀⢀⠄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⢀⣴⣿⡏⠀⠀⣠⣴⡏⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⢳⣿⢀⠠⠾⢻⣿⠀⠀⢠⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⣿⡿⣱⣿⡿⠃⠀⠀⣼⣿⣼⠠⠄⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣽⣿⣿⣿⣿⣆⣠⣾⣿⢿⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢟⣿⡿⣿⣿⣿⣿⣿⢣⣼⣿⡎⢷⣇⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⢏⣾⡟⣸⣿⣿⣿⣿⡇⡾⣿⣿⢻⡌⠻⣆⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⢀⢠⠁⣿⠟⣿⡿⣰⣿⣿⣿⣿⣿⡘⣇⢸⣿⣿⣿⠀⠙⣷⣄⠠⡱⣄
⠀⠀⠀⠀⠀⠀⢸⠀⢀⣿⣾⣿⡇⣿⢸⣿⣿⣿⡿⠧⠀⣼⡈⣿⣿⡇⢢⠘⣿⣧⠙⣿⣦
⠀⠀⠀⠀⠀⠀⢸⡀⣼⢿⣿⣿⠀⣿⣼⠳⠏⢠⣷⢀⣼⣿⠃⣸⢹⡇⣸⡄⠸⣿⡇⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠘⣧⢹⡜⣿⣿⡄⢹⣿⠀⠀⢸⣾⡈⠻⣿⢀⡟⣹⠇⣿⣥⠀⣿⣷⠀⢻⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠹⣿⣿⣿⣦⡿⣷⣄⡈⠻⠏⠀⡹⣾⣱⠏⣼⣿⣧⠀⣿⣿⠀⢸⠇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⣻⣯⣛⣿⣿⡝⢷⣂⠠⣼⣷⣿⢏⠼⠁⢸⡇⢰⣿⡟⠀⣸⢄
⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠀⠈⠋⣉⣿⣿⣿⣷⡙⠿⠿⠯⠁⠀⢀⠴⠋⣴⣿⠟⠁⣰⢃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⣿⣿⣿⣿⣷⣦⣤⣤⣤⣷⣼⣿⣿⠗⢀⡴⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣹⣿⣿⣿⣿⣿⣿⣿⠿⢛⣡⠴⢋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣧⣴⣿⡭⠤⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠿⠟⢻⠟⢿⠿⢻⡿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣰⡆⠀⠀⣰⣿⣿⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⣤⣿⣿⣤⣶⣶⣶⣯⣴⣷⣭⣿⡆⠀⠛⢲⡀⢛⣒⣶
⠀⠀⢀⢸⣇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⡏⢿⣿⣿⠀⢀⢀⡐⢾⢈⣦⣠⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⣰⣶⠟⣤⢿⡏⢈⡷
⠀⢀⣾⣿⣿⣧⣷⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡀⠀⠀⠋⠀⢀⡌⣦⣠⢷⣏⣿⣯⣯⣧⡐⠀⠀⠉⢈⣍⣉⣩⣍⣭⣥⣤⡄⠀⣜⣿⣶⣼⠟⢹⣏⣸⡅
⠀⣼⣿⠏⠀⢿⣿⣇⠀⠀⠸⣿⣿⢿⢿⣿⣿⠃⠀⠀⢀⣜⣾⣷⣿⣿⣿⣛⣿⣿⣼⣿⣿⣷⣦⡰⣼⣿⣍⠓⢺⣟⡋⠉⠉⠀⠘⠿⠞⢿⣶⣿⠿⠛⠁
⠀⠻⢧⠀⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⣁⣸⣿⣿⡟⠛⠈⠑⠀⠀⠀⠀⡀⠀⠘⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⡀⣴⢠⡀⠀⠀⠀⠀⠀⠀⠆⡐⠂⡆⠐⠀⠀⠀⠀⢰⠀⠀⠀⣿⣿⣿⣿⠇⢀⠀⠀⠀⠀⣠⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⣸⢼⣠⢧⣟⣳⢼⡰⣅⣷⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠉⠁⡄⣑⣘⣄⠀⣀⣙⣦⡴⣃⠀⠀⠀⢠⡀
⠀⠀⠀⢸⡆⠀⠀⣯⣻⣾⣾⣿⣿⣿⣾⣷⣿⣷⣿⡄⠀⠀⠀⠀⠀⢀⣼⣧⣶⡤⣄⠀⠀⠀⠀⢀⠙⠐⠀⠑⠿⠟⠀⢠⣞⣿⡻⣞⡽⠁⠀⢠⣤⣽⠆
⠀⣰⢠⡿⢁⡀⠀⠈⠛⠛⢉⠉⠉⠉⠙⠛⠛⠛⠋⠀⠀⠀⠀⢠⣼⣽⣿⣿⣿⣿⣿⣤⠀⠀⣀⡴⠛⢦⡞⠀⠀⠀⠀⠀⣹⣟⣿⣏⠀⠀⢰⣛⣦⣹⣦
⠀⢿⡈⢷⣼⣄⠀⠀⠀⣠⢿⣆⣤⠀⠀⠀⠀⣦⣷⡄⢣⣀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣞⠀⡄⡟⢷⡜⣮⣷⣴⠁⠀⠘⠛⠛⠛⠛⠛⠛⠛⠀⢈⣽⣿⠁
⠀⢸⡿⢸⣿⣿⠇⠀⣰⣯⢾⣿⣏⣦⠀⠀⠲⣬⡟⣷⣦⡙⣷⠀⠁⢸⣿⣿⣿⣿⡟⠃⠸⣧⣿⣿⣵⣿⣟⣿⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢰⣿⡟⠋
⠀⣾⣷⣾⣿⣿⠀⠀⣿⡇⠀⠋⢹⡿⠀⠈⣧⣿⣷⣿⣼⣷⣡⣧⠀⠻⣿⡟⢽⣿⡅⠀⠀⣽⣯⣿⣿⣿⣿⣻⡇⠀⠀⣀⣤⣴⣆⡀⠀⠀⠀⠉⢻⣿⣦
⠀⠈⠛⠛⠛⠋⠀⠀⠈⠛⠀⠐⠋⠁⠀⠀⠙⠛⠉⠋⠋⠙⠛⠋⠀⠀⠘⠀⠘⠋⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠃⠀⠾⠿⠿⠿⠿⠟⠛⠗⠀⠚⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⡤⠀⣀⣀⠀⡀⣤⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⢻⡀⣀⠄⢻⡟⡼⠀⠀⢠⢸⠁⠘⠁⢀⠀⠀⠐⠌⠀⣷⠀⡏⢆⠰⡅⣿⠘⠇⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢣⢈⡎⣧⠇⠀⢸⣧⠀⡐⠋⠀⡘⠀⠀⢠⠎⠀⠀⠀⠘⣀⣷⡟⡁⠁⠀⢠⣿⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠀⢹⠀⠀⢸⣿⠀⠁⠀⠀⣧⡤⠰⠋⠀⠀⠀⠀⠀⠀⣷⠰⠀⠀⠀⠀⢹⠆⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣆⠀⢸⣿⠠⠈⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣿⠻⠀⠀⠀⠀⠘⣋⣠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢽⠀⠀⡀⠀⠀⠀⢸⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣿⡷⣴⠒⠛⠁⠀⠀⠀⠀⢀⣠⣶⣶⣄⣸⣠⡾⣶⣦⡀⢰⠨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⠇⠀⠀⠀⠀⢀⣠⡶⢿⣿⣿⣿⣿⣿⡛⣅⠉⠙⠃⢸⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⡇⠀⠂⢀⣠⡶⠟⠉⠀⠀⠙⠻⣿⣿⣿⡇⢸⣿⣦⡀⠘⡇⢏⣀⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⠉⠷⣿⣿⣇⣤⠞⠋⠅⠈⠀⢀⠀⠀⢠⠠⡄⡙⢿⡟⢸⣿⣿⣿⣷⣧⡇⠸⡿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠌⢀⣠⢼⣿⠛⡇⠀⢀⡶⠒⠲⠓⠐⠁⠀⠀⡗⣱⢾⣏⡼⣿⣿⣿⣿⣿⣿⠦⣀⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢉⣠⠖⠋⠡⢼⡿⠀⢃⡴⠻⣤⠀⠀⢠⠀⠀⠀⠀⠀⢹⣾⡇⠃⠀⢙⣿⡟⣿⢶⣟⣿⡄⠆
⠀⠀⠀⠀⠀⠀⣤⡴⢞⠋⠀⠠⡄⡀⢸⣷⠓⡟⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⣿⡿⢀⣴⣿⣿⣿⡟⢸⣿⡟⡃⡄
⠀⠀⠀⠀⠀⠀⠈⠀⢻⠀⠂⠐⠛⠙⢾⣿⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡇⢾⣿⣿⣿⡏⡧⢸⡽⡆⢳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⢸⣿⠇⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⡟⢹⣿⣿⣿⡇⣷⢸⠇⣣⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠆⠀⠀⠀⠀⢠⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⣠⣾⣿⣷⡺⢿⣿⣿⣧⡏⠘⡇⣏⢸
⠀⠀⣤⣄⠴⣶⣼⣿⣾⠀⠀⠀⠂⡀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠐⢀⣾⣿⣿⣿⡟⡁⣾⣿⣿⢿⡇⣠⠃⣿⢸⣦
⠀⢸⣿⣿⡿⣿⣟⣿⣿⠀⠀⠀⠀⠁⢸⣿⣿⣅⠀⠀⠀⠀⠀⡄⠀⣰⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⢸⡗⣿⠀⡏⢸⡷
⠀⢸⣿⠿⠷⡯⠿⡿⠿⠀⠀⠀⠀⠀⢸⣿⣇⠋⠀⠀⠀⠀⠀⠁⠚⠻⡿⡻⠛⠟⢿⣧⠊⠟⠿⠿⢸⣷⡿⠟⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⡅⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠀⠀⠘⠛⠁⠀⠀⠀⢸⠋⠁⠀⠀⢰⡇
⠀⢀⠀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣄⡤⠼⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠚⡇
⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠛⠛⠛⢿⣷⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠉⠀⠀⠀⠈⠙⢿⣷⣄⣀⡀
⠀⠀⠀⠀⢀⣤⣾⣿⡏⠀⠀⠀⠀⠈⠛⠋⠙⢻⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠿⣿⣷⡀
⠀⠀⠀⣰⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣄
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⡟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣧
⠀⠀⠀⢻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠋⠀⠀⠀⠀⣀⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⢠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⠀⣠⣾⣿⠇⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠰⣿⣷⣶⣾⣿⣿⣶⣶⣿⡇⠀⠀⠉⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⢠⣤⣄⣀⣼⣿⣧⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠈⣿⣿⠁⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⣠⣾⣷⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⠟⠋⠻⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣦⣾⣿⣿⣷⡄⠀⠀⠀⠘⠛⠋
⠀⠀⣴⣿⡿⠃⠀⠀⠀⠀⠀⢼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣦⣀⣤⣿⣿⣄⡀⠀⠀⠀⢀⣴⣿⠆⠀⠉⠁⠀⢹⣿⡏⠀⠀⠉⠁
⠀⠀⠛⠋⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠙⢻⣿⡟⠋⠛⠿⠃⠀⠀⠰⣿⠟⠁⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⣀⣀⠀⣀⣿⣿⡀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠛⠻⣿⣷⣄
⠀⠀⠀⠻⢿⣿⡿⠟⠿⣿⣿⠿⠋⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⣠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠘⠻⣿⣧
⠀⠀⠀⠀⣸⣿⣇⠀⢀⣿⣿⣀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠸⠿⠋⠀⠀⠀⠀⢀⡀⠀⠀⠀⠸⣿⣧⠀⠀⢀⣿⣿
⠀⠀⠀⢿⠿⠛⢿⣿⣿⠟⠻⢿⡷⠀⠀⣀⣤⣶⣶⣦⣄⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⠀⠀⢰⣿⣿⣿⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⣰⣿⡿⠿⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠟⠉⠙⢿⣿⣶⣦⡀⠀⠀⠀⠀⣼⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢿⣿⣄⠀⠀⠀⠉⠙⢿⣿⡄⠀⠀⢰⣿⣿⣿⣿⡀⣸⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠻⢿⣿⣷⣄⡀⣀⣾⣿⠃⠀⠀⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣠⣤⣴⣿⣿⣤⡀⠀⠀⢸⣿⡇⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⢸⣿⣇⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣴⣿⡿⠛⠙⠛⢿⡿⠛⠛⠙⠛⢿⣿⣧⡀⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⠟⠛⠙⠻⢿⠿⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⣴⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣴⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠛⣿⣿⡿⠟
⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋

⠀⢘⣛⡛⠯⣪⢿⣿⣿⡿⡦⠹⠇⠺⣿⣐⣦⣼⡊⠞⡉⠊⡠⠐⠈⠈⡸⠃⠀⣶⠋⠀⠂⠀⠀⢈⠀⠲⠌⢀⢭⣴⣂⣿⠂⠻⢏⡼⣿⢿⣯⡯⣴⠟⣛⣛⡛
⠀⢸⡏⢩⡆⠰⣿⠿⠛⢻⡽⠎⠲⠶⣰⠈⡻⠒⡀⠁⠄⣠⠤⠴⠀⣊⣤⠴⡾⢬⣙⣒⣒⠀⠔⠤⣍⣑⠒⠶⣈⠓⠂⡒⢂⣒⣽⢿⡟⠛⠿⣿⢁⢮⣌⠈⡟
⠀⠘⠣⢙⠑⣡⡇⣬⡿⠋⢐⡿⡙⡢⢃⠔⠠⠂⣠⠖⢋⡤⣶⠛⣿⡩⡓⣏⠘⡾⡅⠿⣹⠏⣻⡶⢦⣬⣙⠲⣄⠑⢄⠑⠴⣥⡲⢦⢱⡿⣗⡨⣄⠀⠙⠐⠷
⠀⢸⠏⢸⣿⡿⠷⠭⣍⡛⡮⠍⠊⠔⣁⡴⢞⣷⢋⡾⠋⠻⣠⠂⣸⠆⡇⣘⣼⠶⠛⠲⠿⢾⣭⣧⡸⠰⠛⣳⣌⠁⠀⠀⠤⣤⣭⣭⢩⢉⠭⠶⠯⣽⣧⠙⡿
⠀⢸⢇⢘⠏⡶⣿⠗⠈⠃⡥⢋⠔⡁⢊⡴⢻⢛⡼⡈⡆⢆⢹⠰⡄⣱⠞⢋⠠⣤⠊⠉⡀⠀⣠⠌⠹⣼⢶⠋⡈⡷⣄⠀⠀⠈⠻⣿⣇⠘⠼⣛⠷⡌⡏⣰⣧
⠀⢸⡟⣽⠄⣒⠒⣪⢂⠞⠁⠀⠔⣠⣿⡘⣸⢻⡳⢁⠋⠜⠄⢎⣾⣇⠴⠃⣰⠃⡠⠊⡠⠃⠑⣔⢀⡟⡌⡎⣱⢁⠽⣶⡄⠀⠀⠈⢿⡌⢦⢛⢛⣀⣏⣿⣟
⠀⢸⣭⡟⠀⢤⠒⡴⠏⠠⠀⠌⣰⣿⣰⢶⣛⣿⣖⠵⠓⠋⣿⣛⣉⣁⣀⣠⡇⣊⣥⡬⠀⠰⠆⣌⣾⣃⡹⡸⠁⣁⣂⣯⡼⣄⠠⠀⠄⢻⡄⠲⡚⠉⠛⣽⡿
⠀⢸⢋⢔⣦⠆⠟⡐⠀⠁⢀⣴⡇⡿⣅⢀⣨⢣⣿⠀⢀⣔⡘⣋⣿⡍⠡⠈⢼⣿⠇⠀⠀⡐⣾⣹⣗⣿⡃⣷⣉⠀⣩⡎⣵⠜⣦⠀⡈⠀⢻⡄⠡⢷⢢⡜⢿
⠀⢠⠱⣷⣖⡡⠀⠀⠀⢀⣿⠃⡇⣹⡟⢫⣉⡎⢹⡀⢪⠳⠉⡜⢻⡘⠢⣄⠀⠉⠈⠀⠀⠁⠀⣰⢧⢡⢋⣩⠿⡜⢋⡜⣛⠁⠻⣧⠀⠀⠀⠛⢌⢲⡧⡸⣦
⠀⢐⠒⠆⡊⠀⠀⠐⠀⣎⠌⢢⡜⡇⣇⣼⠙⢘⣆⡌⡆⣆⡇⢳⠌⣷⣼⡈⠳⣤⢀⠐⢒⡠⣔⢧⣸⢞⡈⢋⢀⣿⠎⢞⢩⡄⢢⣽⢆⠀⠀⠀⠈⠔⢷⢬⡟
⠀⢸⣟⡄⠃⠀⢀⠁⣸⣯⠂⠈⣁⣿⢻⣇⣨⣣⣏⢌⣴⣭⣹⡌⢾⠟⢼⣛⣦⡈⢢⡼⠘⣧⡙⠘⠇⢜⣹⠀⢟⢀⣡⣽⡿⡠⠟⠍⣻⡄⠂⠀⠐⠘⣿⢸⣿
⠀⢰⠍⡔⣠⠁⠀⠀⡸⢻⣶⡷⠿⠿⠈⠻⣇⠝⢹⠯⠀⠀⣰⡿⢸⡞⢓⡏⠡⠀⣾⠇⠂⢀⠙⠲⣄⠠⢩⡼⠣⣡⣿⢿⡷⠿⣷⣻⠋⡇⠀⠀⠀⠃⢸⡷⣿
⠀⢸⠧⡔⠹⠀⠀⠀⠀⡾⣬⣝⣃⠀⠀⠀⢯⡞⠟⠛⣁⠛⢟⣀⣿⠁⣟⠀⠂⢸⡏⠀⢊⠁⡠⠂⠈⢷⣾⢂⢖⣿⠀⠀⠀⢛⣫⣥⣧⠀⠀⠄⠀⠀⠈⢣⠙
⠀⠀⠉⠁⠀⠄⠀⢀⢰⠟⡯⠥⢧⢤⡤⣤⣌⠳⣇⠨⠧⢊⠆⣿⠇⢸⠁⠈⢀⣿⡍⠀⠀⠀⢳⡄⠀⠀⠻⣆⣾⣁⣀⣠⣤⠬⠥⢊⢺⡄⣄⠂⡀⠀⠀⡈
⠀⢐⠒⠒⠒⠒⠒⠚⢸⡇⠉⠒⣸⢉⡅⠂⠙⢷⡌⠙⠲⢦⣔⡾⠀⠘⣇⠀⠈⣿⠇⠀⠀⠀⣼⢛⢦⡀⠀⠈⠻⡟⠉⣿⣫⠐⢧⣛⣿⡇⢙⢀⠈⠁⠉⠄⠤
⠀⢘⡀⢀⣀⣀⡀⢸⢸⣏⡁⢠⡟⢸⢾⠶⠲⠋⡽⢦⡀⠀⠈⠳⠀⠀⡼⣇⠀⢸⠀⠀⠀⢰⣏⡟⣸⠝⣦⡀⢸⠀⠀⣸⢟⠂⠀⡺⢏⡄⠀⢰⠀⠀⠀⠀⠥
⠀⢨⢶⠂⢕⡄⣩⢀⢸⡟⣡⠟⡘⡃⣎⠐⣡⠈⡷⣻⣼⠗⣦⣄⣡⡾⣡⢿⡄⠀⠀⠀⠀⣾⡟⣴⡅⣾⢹⣷⣬⣀⣴⢫⣎⢣⠱⠘⡈⡇⠀⢈⢩⡝⠉⣌⠛
⠀⢰⠂⢠⣸⢁⠛⢸⢸⡦⠳⠀⢇⠜⢈⡞⡠⡏⠁⡇⡝⠠⠷⣀⣭⢺⣼⠾⡇⢀⠀⠀⡀⢿⣇⢡⠋⡌⣧⣸⣮⢋⡸⢫⠟⡘⢸⢇⢣⡇⢠⢸⣆⢳⢀⠊⣶
⠀⠈⠀⣸⢃⠆⠀⢸⢸⡶⠖⠛⣌⣋⠒⠤⠤⣵⡳⠊⢲⠤⢲⣹⠾⣻⡇⢨⠀⠄⡠⠊⡠⠚⢿⠻⣤⡠⢷⡷⡥⠬⢴⡧⠾⠶⠓⠚⢢⡇⢰⢸⠈⠄⢿⠀⢹
⠀⢠⠀⣽⠘⡀⠀⠘⢸⡧⢀⣴⠏⣼⣅⡀⣀⣾⢡⢞⣦⣠⠞⠁⢰⠃⢡⢠⠰⢊⠔⠃⠀⠀⠘⡆⠈⠳⣼⢏⡀⢈⣍⣴⣯⡂⢀⠐⢋⡅⢸⠈⠀⡘⣸⠀⣨
⠀⠀⢠⠁⠱⠈⠳⠀⢸⢡⠡⢡⠶⠌⣸⢇⠹⣠⢏⣦⡾⠋⠀⢠⠏⠀⠈⡤⠞⠁⠀⠀⠀⠀⠀⢹⠀⠀⠈⢳⡟⡙⢇⡾⢫⠅⡰⠃⢣⡆⢸⠸⠃⠐⠁⢁⠈
⠀⠀⠃⡀⡱⡡⠀⢠⢸⡄⠇⠎⡤⣄⡣⢸⠗⣵⣿⠋⠀⠀⠀⠞⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠙⣷⡎⣷⣿⠀⡇⢃⠈⡃⢸⠀⠸⡕⠁⢈⠿
⠀⠀⠠⠋⠈⠁⠀⠈⠀⡵⢈⠂⠑⡄⠠⡟⣴⡟⠁⠀⠀⠀⠌⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢷⣷⠱⢠⢃⠼⡄⡆⠰⠀⠀⠁⠈⢣
⠀⠀⡆⢀⢂⠅⡆⠀⠀⣷⠘⢪⠖⢫⢋⣴⠏⠀⠀⠀⠀⠈⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⢻⡄⠱⡄⠒⣼⡆⢸⠀⡀⠀⣆⠀⡄
⠀⢰⢇⠸⣤⠀⠀⠀⠀⣿⡯⠴⢲⣿⡾⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⢻⣇⠈⢩⡽⡇⢸⠀⠀⢀⡿⠰⢰
⠀⢠⡸⢆⠹⣆⡶⠀⠀⣿⢀⣎⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠈⡰⡇⢸⢠⡄⡾⢠⢧⠈
⠀⢠⡁⠘⣇⠹⣀⠀⠀⣿⣷⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⠌⢷⣱⡇⢸⢈⡿⠰⠇⠀⡆
⠀⢨⠱⠾⠄⠲⢻⠀⢨⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢸⢸⡥⠁⠀⠎⣠
⠀⣠⣀⣀⣀⣀⡘⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡞⢀⡀⣀⣀⣁⣈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣦⢠⣶⠀⢠⡄⢠⣶⢀⣾⠀⣰⡆⣠⣄⣾⡏⣠⡶⠄⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⣸⡇⢸⡿⠀⣼⡇⢸⣿⢸⣿⠀⣿⠃⣿⢏⣿⢃⣿⠇⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠸⣇⢿⡇⠀⢹⡇⢸⡿⢸⡇⠸⣿⠐⡿⢸⡿⠸⣿⣤⢣⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⢸⣇⠀⠈⠃⠀⠀⢸⡇⠀⠉⠀⠀⢸⡇⠀⠀⠀⢸⡏⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⢠⣿⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⣿⡇⣀⠀⢀⣛⠀⣾⡏⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⢸⣿⢡⣿⠀⣾⡟⢸⣿⡇⣨⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⢀⠸⣿⢸⣿⢀⣿⣇⢸⣿⡟⣽⡇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠊⠀⠋⢸⣏⠈⠛⠋⠀⠉⠀⠘⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠶⠶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠞⠛⠛⠛⠛⠶⣦⣤⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣤⣤⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡶⠶⠶⠶⢶⣤⡀
⠀⠀⠀⢀⣀⣴⠟⠋⠉⠻⠋⠀⠀⠈⢻⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⣴⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⡀
⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⡀
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠙⠛⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⠟⠉⠉⠉⠉⠻⡶⠛⠛⠛⠷⣦⣰⡟
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠛⠷⣦⡀
⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠙⠷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣽⣽⣿⢭⡇⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢤⡆⠀⠀⠀⠀⠀⠀⠀⠈⠾⠽⠶⠁⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡗⣺⣗⢺⠂⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣻⣿⣻⡟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠃⠀⠀⠀⠀⠀⢾⡷⣽⠆⠀⠀⠀⠀⣴⡖⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠹⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠸⣗⡿⣗⡟⠀⠀⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⢲⢆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠙⠀⠀⠀⠈⠩⠣⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢟⣺⢿⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⣾⣆⣿⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣁
⠿⠿⠿⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠆
⠀⠀⠀⠀⢹⣿⡀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠋⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢂
⡄⠀⢠⠄⠈⠁⢠⠀⠙⠧⠀⢀⡀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠽⠞⠂⠀⠀⠀⠀⠀⢀⠀⠘⠓⢆⠀⠀⠀⠀⠀⢀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣼⣄⣦
⣷⡀⠈⣰⠂⣠⣾⠇⠀⠀⠀⣾⡇⢠⡧⠀⣠⣠⠀⢠⡄⣀⠀⠀⠀⠀⢀⡄⠀⠐⠛⠓⠆⠀⡀⠀⠀⢀⠀⠴⠋⠀⠀⠀⠈⠷⠀⣄⠀⠀⠿⣿⣿
⠿⠧⠀⠃⢠⣿⡿⠯⠀⠠⠀⠛⠙⣿⣷⠀⢻⡆⢰⣏⠁⠉⠀⠠⡆⠀⠈⠁⠃⠀⠀⢀⣀⠀⠱⠦⠠⡞⠒⠼⢁⠑⡈⠀⣦⢠⠀⠁⠀⠀⠀⠉⠋
⠀⠠⠂⠀⣼⣿⡧⠀⠀⠀⠀⠈⠀⠉⢉⡁⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠃⠐⠶⠿⠇⠶⠾⠀⠁⣸⣿⠀⠈⢰⣇⢠⡀⢰⡄
⡸⠃⢠⡆⠛⠛⠓⠀⢤⣄⣀⡀⠙⠂⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⣧⠈⢗
⠁⢀⣿⣓⠀⠻⡄⠀⠀⠉⠁⢀⠁⠀⠀⠀⠀⡀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣄⡀⠀⠀⢀⡀⠀⠀⠀⠥⠀⠀⠈⠉⠉
⠀⣰⣧⡈⠁⠀⠀⠀⠈⠀⠀⠈⢿⡀⠀⠀⠀⣈⠁⠀⢰⣆⡀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠈⠛⠑⠖⠀⢒⣢⡀⡙⣠⣤⣤⣼⠇⠀⠀⣀⣀
⠀⠽⠻⠋⠁⠀⠀⢀⣀⣄⢀⣀⣬⣿⡤⠥⠤⠾⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠼⠷⢦⣄⣀⡙⠃⠤
⠀⠀⡀⠀⠀⠈⢀⣀⣤⡾⡛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠶
⣀⣠⣤⡴⠶⠾⠛⠛⠛⠋
⠉
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⢁⠟⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⢠⣪⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠻⣿⠙⠛⢿⠿⢿⣿⣿⣿⡿⢿⣟⠛⡇⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣸⡇⡅⠈⡟⠋⠁⠀⠠⠗⠀⠈⠛⣿⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⡇⠀⡛⠆⠀⠀⠀⠀⠀⢀⣰⣿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣼⣀⣷⣦⣀⠀⠀⠀⠐⣷⡟⠿⠀⠀⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⣠⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⡭⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠞⢃⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣔⡀
⠀⠀⠀⢀⠀⠉⠀⣄⢱⣶⠀⢀⣴⠿⠠⣤⣄⣀⣴⣾⣿⣿⠀⣀⣀⣀⡀⠀⠀⠀⠘⠻⣿⢿⣿⣿⣿⣿⣿⣅
⠀⠀⣶⣼⡇⣷⣤⣿⠶⠃⣠⡾⠁⠀⠀⠀⠈⠉⠛⠛⠛⠙⠛⠉⢩⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⢿⣷⣶⣤⣀⡀
⠀⠀⢿⠻⠙⠾⢉⣥⡾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣶⣤⡀
⠀⠀⠺⢀⣠⠞⠋⠉⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣀
⠀⣠⡴⠛⠁⠀⠀⠀⣸⡇⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿⣿⡿⢿
⣾⠋⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠈⠛⢶⣤⣀⡀⠀⠀⠐⢶⠲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⠃
⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⢉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠗⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣦⣀⡀⣀⠀⠀⠀⠀⠀⠀⣈⣀⣠⣤⠶⠞⠛⠉⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠟⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣿
⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⠿⠛⠋⠉⣿⣿⣿⣶⠶⠶⠯⠋⠉⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠀⢀⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⣷⣤⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠉⠀⠙⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠞⣶⡞⠛⠛⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠠⣄⣀⣉⠒⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⠀⠀⠀⠈⠓⠉⣙⣍⡉⠧⠄
⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⣠⠇⠀⠀⠈⠑⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣁⣶⢠⡄⢰⡌⠳⢟⡀⠀⠀⠀⠐⠒⠙⠀⠐⠖⠀⠈⠲⢄⡀
⠀⠀⢠⠀⠀⠀⢘⣁⡤⢄⡐⠚⢁⠀⠀⠠⠀⠀⠀⠘⠉⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠩⡥⠾⠳⣦⠙⢛⡋⢁⣠⣀⠀⠀⣠⡤⠤⠤⠄⠀⠡⣀⠀⠙⣦
⠀⠀⠿⠀⠀⣀⠀⡡⠐⠀⠀⠀⠀⠈⠢⡀⠀⢆⠀⠀⡇⠀⠘⡀⠀⠀⠀⠀⠀⣀⠴⣤⠶⠶⠀⠀⠀⠙⠃⣼⡙⣯⡁⠂⠀⠀⠀⠀⠀⠰⠄⣀⣀⠀⠋
⠀⣤⡆⠈⠁⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢰⠀⡠⠁⠀⠰⠃⠀⠀⠀⠀⠄⣹⡿⣹⢇⣠⠀⠀⠀⠰⠿⠈⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘
⢠⣿⡒⣤⣤⠂⠀⠀⠂⠈⠉⠀⠀⠈⠐⠄⠀⣼⡂⠁⠀⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⣨⣯⣤⠰⠷⣰⠶⣟⠂
⠃⢻⣝⠄⠀⠀⠁⠀⢀⠄⣀⠤⠀⠀⠉⢺⣦⣿⠗⠂⠀⠘⢻⢧⡴⠀⠀⠀⠀⠀⠀⠀⢴⢶⣼⠇⠀⠹⠿⡏⢋⠀⠀⠀⣄⡀⣠⡆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⣠⠊⢃⣹⠀⠀⠀⠀⠀⠀⠀⠰⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠟⠙⢷⣶⠄⠀⡀⠀⠀⣙
⡄⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠠⡞⠁⠀⠀⠀⠀⠀⠀⠠⢀⣴⠿⡇⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣧⡤⢾⡆⠀⢠⠁⠀⠀⠙
⠘⣶⠒⠈⠁⠀⣠⠖⠀⠀⠀⠀⠀⢀⣀⣠⠴⠎⠀⠀⠀⡾⣿⡶⠋⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⡌⠀⠀⠀⣿
⠀⠉⠤⠠⠄⠂⠁⠀⠀⠀⣼⠶⠋⢉⣠⣦⡤⣄⠀⠀⠈⡁⠋⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⡟
⢸⡆⠀⠀⠀⠀⠀⡐⢀⡾⠁⢤⣾⠟⣿⣟⣀⠈⠃⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠹⣦⣀⣀⣠⣈⡴⠛⡠⢣⠀⠀⠘⠉⠋⠀⠀⠀⠀⠀⠠⠀⢈⡁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠘⠀⠀⠀⢀⣰⠄
⠀⠀⠀⠉⠺⠷⠀⠀⢀⣀⠀⢉⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢦⡻⠀⡰⢦⣌⠑⠶⣄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠉⠁⢀⣀⠀⣠⠆⢠⠋⡉⠀⠀⢀
⠀⠀⠀⠀⠀⣄⠐⢠⠄⠀⠋⠁⠘⠂⢤⡀⠀⠀⠀⠀⠀⠀⣀⢀⠔⠁⠀⠀⠀⠀⠈⡀⠀⠀⠳⣄⡤⠲⠲⣿⠷⠁⠀⠀⠀⠄⣨⡍⣶⠋⣠⠿⠊⠁⠀⠐⣼
⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⡄⠀⠀⡀⠀⠉⣈⠉⠁⠀⠀⠉⠉⠣⣄⠀⠀⠀⠀⣀⡀⠠⢄⠀⠀⢹⡦⣶⡷⠂⠀⠤⠤⠴⠄⠚⠩⡆⠻⡉⢀⣀⠀⠠⠄⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⣧⠀⠀⠀⠇⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠒⠉⠀⠉⢄⡀⠀⠀⠀⣸⠇⠈⢧⠀⠤⢤⣴⠶⠛⠁⠀⢸⠀⠀⠁⠀⠀⠀⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⡆⠀⠀⠠⡄⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠘⣟⠙⡀⠀⠀⠈⣶⢖⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣐⣦⠴⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⣤⡘⠒⠒⠂⠳⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⡟⠐⢷⡒⠟⠶⠾⡌⠐⢄⠀⠀⠀⠀⢀⠖⠀⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⡠⠤⠃⠀⠀⠙⣧⢸⣷⠁⠀⢸⡀⠀⠀⠀⠌⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡠⠊⣀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠹⣿⣿⡀⠀⡜⠀⠀⢀⠊⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣰⡔⣺⠋⠀⠃⢠⡘⠇⠀⠀⠀⠀⠀⢹⡇⠻⡄⠁⠀⠠⠃⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣴⠛⠿⠉⣴⡇⠀⠀⠀⠁⠀⠻⠀⠀⠀⠀⠀⠈⣷⠀⠻⢞⠄⠁⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⢊⡄⠙⢃⠀⡐⢻⠍⠑⠢⣄⡀⠀⠀⠂⠀⠀⠀⠀⠀⣿⠀⡠⠊⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡉⠀⠀⡔⠀⢷⡀⢀⠀⠀⠉⠐⠢⠆⣀⠀⠀⠀⠀⣿⠞⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠢⢼⠀⠰⣾⠀⠈⢢⡀⢤⡀⠀⠀⠈⠑⠂⠤⢰⠏⠀⠀⠀⠈⣁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠘⠳⣼⣄⠀⠀⠱⠀⠘⠂⠀⣁⡠⠤⠀⠃⠀⡀⠀⠠⢲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠈⠳⡉⠑⠲⠦⣠⣄⣁⡀⠠⠴⠖⠛⠁⠀⣀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⣼⠉⠁⠒⠒⠠⠤⣤⣥⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠲⣿⠀⠀⠀⠀⠀⠀⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⡌⠀⢰⡇⠀⢀⠀⠀⢸⠀⢸⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠙⠿⣀⣠⣿⡇⠀⣸⠀⠀⣻⠀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⢈⠉⠉⠉⠉⠈⠓⠂⢿⣇⡀
⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠇⡇
⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣧

⠀⠀⠀⠀⠀⣸⣿⣦⠀⠀⠀⠀⠀⠀⣠⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⢀⣼⣇
⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣤⣸⣿⣿⡀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣄
⠀⠀⢰⣷⣿⠇⠀⢻⣷⡆⠀⠀⢰⣷⣿⠿⣿⣿⣆⡄⠀⠀⠀⠀⢻⣿⣿⣿⣶⣇⠀⠀⠀⠀⢸⣿⣿⠻⣿⣶⠀⠀⠀⠀⡄⣿⣿⠏⢿⣿⡆
⠀⠀⠸⣿⠁⣰⣦⠈⣿⡇⠀⠀⢸⣿⠿⠀⠘⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠐⣶⡿⠁⡀⠛⣿⠀⠀⠀⠀⣿⡿⠁⠀⢸⢿⡿
⠀⠀⠀⠙⠦⡙⢛⠴⠋⠀⠀⠀⠀⠻⠄⠀⠀⠠⠟⠀⠀⠀⠀⠈⠻⢿⣿⡿⠟⠁⠀⠀⠀⠀⠹⠄⢾⡿⠀⠋⠀⠀⠀⠀⠙⠧⠀⠀⠀⠜⠁

⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣠⣿⣷⠀⠀⠀⠀⠀⠀⣆⢸⣿⡄⡄⠀⠀⠀⠀⠀⠀⣸⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⣾⣷⡀
⠀⠀⠀⠀⣼⣿⣿⡿⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡀⠀⠀⠀⢠⡄⣾⣿⢿⣿⣀⡄⠀⠀⠀⠀⣶⣻⣿⣷⢀⡄
⠀⠀⠀⢸⣿⣿⣿⣇⣷⠀⠀⠀⢈⣿⣿⠏⠻⣿⣿⣶⠀⠀⠀⣼⣿⣿⠋⢻⣿⣧⠀⠀⠀⣿⣿⣿⠟⠈⣿⣿⣿⠀⠀⢰⣦⣿⣿⣿⣿⣿⣇
⠀⠀⠀⣷⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⡇⢀⣦⠀⣿⠇⠀⠀⠀⢻⣿⠁⠀⣼⢿⡟⠀⠀⠀⠸⣿⠉⢀⣆⠉⣿⠏⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠈⠛⠻⠟⠛⠁⠀⠀⠀⠀⠈⠁⠘⠟⠁⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠛⠟⠀⠉⠀⠀⠀⠀⠈⠙⠚⠛⠛⠋

⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⢀⣴⣆
⠀⠀⠀⢀⢀⣼⣿⣷⡄⠀⠀⠀⠀⡀⠈⣿⣧⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⠀⡀
⠀⠀⢀⣿⣿⣿⢿⣿⣿⡄⠀⠀⢀⣿⣄⣽⣿⡟⢀⡀⠀⠀⠀⡀⢻⣿⠛⢿⣿⣆⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⡀⣿⣿⣿⣾⣿
⠀⠀⠸⣿⡟⠉⠀⠹⣿⡇⠀⠀⢸⣿⣿⣿⣿⣶⣿⡇⠀⠀⠀⣿⣾⠋⢠⡀⢻⣿⠀⠀⠀⢠⣸⣿⡏⠿⣷⣾⡆⠀⠀⢸⣿⣿⣿⠛⢿⣿⣿
⠀⠀⠀⠻⣧⡀⠀⣰⠟⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠘⢿⣄⣿⣧⡼⠃⠀⠀⠀⠀⠻⡏⠁⠐⢻⡟⠀⠀⠀⠈⢿⡿⠷⠀⠈⣿⠏
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠶⠲⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇⠴⠤⠴⠴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡅⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⣀⣀⣀⣀⣀⠀⣿⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⠀⣿⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⠀⣿⠐⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢋⣠⣾⣿⣿⡿⣿⣿⣿⣦⣌⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣡⣴⣿⣿⣿⢿⣿⣿⣷⣤⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣴⣿⣿⣿⣿⣍⡁⢉⣽⣿⡿⣿⣷⡌⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢡⣾⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣦⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢸⠇⣼⣿⣏⠃⠸⣿⣿⡇⣿⣿⣿⠆⢋⣽⣿⡄⢻⡄⠀⠀⠀⠀⠀⠀⢀⡟⢠⣿⣯⡙⠻⣿⠟⠛⠛⠻⢿⡿⢛⣹⣿⣧⠸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣧⣶⣶⣬⡙⠃⠛⣉⣴⣶⣦⣽⣿⣷⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⣾⣿⣿⣿⣷⠃⠀⠀⠀⠀⠈⣷⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⡛⠻⠟⢋⣡⡄⣤⣍⠛⠿⠟⣻⣿⡿⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⢿⣿⣿⣿⡿⣆⠀⠀⠀⠀⢀⡿⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠹⣿⣏⡄⢸⣿⣿⡇⣿⣿⣿⡆⣬⣽⣿⠃⣾⠁⠀⠀⠀⠀⠀⠀⠈⣷⠘⣿⣯⣥⣶⣿⣶⣤⢤⣴⣿⣷⣦⣹⣿⠏⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠙⢿⣿⣿⣿⣋⡄⣈⣹⣿⣿⣿⡿⢁⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡈⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡙⠻⠿⣿⣷⣿⡿⠿⠛⣁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣈⠛⠿⢿⣿⣾⡿⠿⠟⣋⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠶⠶⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠶⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣀⣀⠘⠢⡀
⠀⠀⠀⠀⠀⠤⢤⣀⣑⣄⡀⠘⠂⠀⠀⣀⠀⠀⠀⠀⠉⠉⠙⠓⠬⠦⣀⠴⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⣲⣖⠦⠤⠈⠀⠀⡠⢂⣐⣂⣤⢄⡀⠀⠈⣳⠤⣀⣈⠠⢤⡀
⠐⢤⣀⡀⠐⠢⢄⡀⠀⠀⠈⠉⠫⠓⠦⡀⠀⢰⣿⢀⣄⣠⣦⠑⣌⡆⠀⢀⡀⠀⠀⠛⠷⣟⠲⠤⣄⣀
⠀⠀⠈⠛⢷⡦⢄⠀⠀⠀⠲⠤⣤⣀⠀⠚⠃⠸⡘⢌⠙⠃⠤⠄⣿⣧⡀⠀⠈⠉⠲⠦⢬⣉⣉⠓⠶⢶⡉
⠀⠀⠀⠀⠀⠈⠓⠦⣀⠐⠢⢄⡀⠉⢿⠷⡖⠀⡈⠢⢥⣤⣴⣿⣅⣔⣙⣄⠀⠀⠩⢶⣦⣤⣌⣉⣁⣂⣀⣈⣤⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⠢⢄⠀⡁⠒⠤⣄⡈⠋⠀⠈⢿⣽⣿⣷⣋⣻⣾⣗⢄⡀⠀⠀⠉⠛⠿⣓⠲⢤⣀
⠀⠀⠀⠀⠀⠈⠉⠒⠲⠤⠀⠀⠀⠈⠁⢢⣄⣀⠀⠀⠀⠈⠛⠋⠉⠹⣿⣿⣿⣶⣵⡀⠀⠈⠉⠉⠙⣛⣳⣶⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠶⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⣿⡏⢹⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣧⠀⢙⣿⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⠀⠀⠈⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⢀⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀⡑⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠰⠳⣄⡎⠀⠀⠁⠠⠀⡜⢆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠈⠆⠀⠀⢀⠀⠰⠁⢸⠈⠰⠃⢰⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⡏⠲⢦⠀⠀⠀⠀⠀⠈⢄⠁⠀⢸⠀⠀⠀⡌⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠈⠂⠀⡘⠘⡐⢚⡇⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⡀⠀⠳⠉⠀⠌⡰⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢤⣄⡀⠀⠀⠀⠀⠂⠄⠐⠂⠀⠀⠁⠄⠂⠀⠀⠤⠊⠉⠈
⠀⠀⠀⠀⠀⣼⠹⣭⢍⣠⢴⠚⢠⣀⣤⡤⡖⠢⣤⢼⣐⠒⣦⠀⢲⢢⡀⠘⠛⣻⣻⡄⢠
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠻⠼⠛⠛⠊⠳⣾⡴⠃⠰⣌⣠⡼⠷⣤⣸⡖⠲⠮⠯⠟⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡲⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢰⠏⠂
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠂⠀⠀⠠⠒⠀⠚⠀⠀⢀⡠⠀⠂⠃⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⢸⡆⣰⣧⣆⠒
⣴⣧⣿⣇⡆⠀⠀⠘⣯⠐⠂⠀⠀⢲⡄⠀⠀⠂⠻⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢰⢷⠀⢠⣾⢷⣭⠌⠛⢶⠒⢠⡆
⣻⡟⢫⣿⣧⣷⣏⡠⠀⠔⠐⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⡔⢯⡀⢘⡁⢂⠪⡦⠴⡘⢦⣝⢳
⠚⣯⡶⢹⣿⣿⠋⠂⠀⠂⠐⡈⢺⣶⣆⣤⣀⣤⢀⠀⠀⠀⢀⡀⣤⢀⣠⡊⠃⣴⠞⠃⢜⡺⠤⠉⠱⣿⠀⠈⠀⠙⢿
⢈⠁⠖⢸⣉⡤⠎⣠⠆⠀⠀⠐⠲⣿⣿⡿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡿⠈⠈⠺⣂⠘⣯⡤⠒⣀⡠⣜⡀⠀⠈⠶⢾
⠸⠄⢠⣟⡉⠠⠠⠶⢀⣰⢿⠑⢠⣙⣯⢓⣹⣭⠟⣋⡁⠀⠀⠀⠙⢿⠀⠈⠙⠳⣎⢢⡟⠒⠉⠈⠣⠌⡂⠀⠠⡀
⠀⠀⢠⡏⠠⢰⠂⢠⠊⠙⢄⣯⡀⠀⠉⠁⠀⢄⣪⣷⣻⣓⣦⣴⡶⠂⠀⡀⠁⣌⠚⢿⣗⠄⣇⠀⢰⡆⠈⠲⡀⡀⠑
⠀⡰⠋⠀⢀⡬⣟⠀⠀⠀⢣⣀⠧⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠉⡋⠀⠀⠉⠐⠉⠄⠀⠁⢿⡁⣀
⠀⠀⠀⠈⠀⠀⠀⠙⠊⠀⠊⠁⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠄⠘⠉⠀⠄⠐⠤⠦⠀⠽⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⢦⣠⠀⢤⠀⢸⠆⡘⢀⡴⡇⠀⣤⠀⣀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣵⡀⣀⣤⠀⠐⢷⡀⢁⡿⠂⠀⣄⡀⢀⣎⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡒⢤⡑⡀⣄⠓⠞⢠⢀⠊⡥⠐⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⢻⠀⢽⡀⢤⠈⢇⡸⢀⡄⢀⡯⠀⠏⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⡛⠞⢌⡒⠿⢠⡇⠿⠗⡩⢳⢚⡰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠳⡄⣝⠺⢟⢸⡕⡿⢗⡯⣠⠞⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠲⢖⠀⠬⣿⡆⢻⣳⠿⡶⣦⡛⢰⣷⠥⠀⣒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⣄⡀⠒⣾⣆⣛⣤⠺⠖⣤⢛⣰⣳⠂⢀⣠⣦⠂
⠀⠀⠀⠀⠲⠖⡿⠤⢈⣹⠇⠐⠶⢞⡗⣻⡷⠸⣋⠶⠂⠐⣏⣁⠤⢾⠲⠖⠀⠀⠀⠰⣉⠶⠶⠄⢈⣉⡡⢚⠶⢸⠂⣾⣟⠰⡇⠶⡰⣍⣉⡁⠤⠶⠶⡹
⠀⠀⠀⠀⠀⠀⠀⠴⠎⠀⢀⢿⠇⣼⠿⢖⡷⠿⣧⡘⡟⢁⠀⠨⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠻⠋⠀⠤⠿⢎⣤⢻⢼⠦⡛⣬⠹⡿⠤⠀⠙⠏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠊⡥⢦⣊⠴⣶⠘⡇⣶⣦⢑⡬⢦⠑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠔⠋⣯⢶⣾⢸⡣⣷⡦⣏⠙⢦⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⠄⠚⡱⠀⠂⡶⢧⠈⠈⠂⡑⠀⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⣤⠄⣺⠀⠙⢀⡏⢹⠀⠃⠈⣗⠢⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠎⠙⠀⠚⠀⢸⠆⠡⠈⠱⡇⠀⠙⠀⠈⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠹⠀⠉⠙⠀⠠⣾⠅⡌⡷⠄⠀⠋⠁⠈⢏⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢄⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢘⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣠⠀⠘⢼⡗⠁⠠⣀⠛
⠀⠀⠀⠀⠀⠀⠀⠰⣢⠀⠀⠀⠻⡀⠀⢜⣇⠀⢀⡟⠀⠀⠀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣆⡆⠀⢍⣫⡜⢠⢺⡑⡀⢧⣟⡡⠀⣀⡸⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢆⡄⢈⣻⡀⢸⡇⢀⡸⡁⢠⡠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡿⢗⡢⠌⣧⠎⣼⣧⢱⣬⠡⢔⡺⡟⠓⠂
⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀⢉⠹⣦⢨⠷⢮⡷⠾⡏⣴⠞⡉⢀⡀⣤⠄⠀⠀⠀⠀⠀⠀⠸⠓⢸⣄⣣⠘⡈⣳⣶⢌⣦⢋⡱⣼⡡⣖⡏⢱⢁⣎⣴⡄⠛
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠺⢦⡟⠻⡦⢽⢣⢷⢟⠳⡴⠧⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠒⣉⠱⠟⠤⣧⣰⣺⠮⠷⣷⣆⣮⠔⠿⢌⡙⠒⠈⣀
⠀⠀⠀⠀⢶⠦⠰⠶⠱⠶⠶⢎⡷⠿⣓⣎⣹⣎⠾⢾⡱⠶⠶⢮⠴⠆⠴⡶⠄⠀⠀⠀⡶⢾⡶⣏⠰⠶⣿⣎⠱⣿⡇⣏⡱⢸⡳⢌⣱⣷⠶⠆⣽⢾⠷⢖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠾⡧⣽⢗⣪⡝⡺⣮⢴⠳⡶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠤⣉⣐⣦⠐⡟⠹⢽⣖⡶⡯⠏⢟⠢⣴⣊⣉⠤⠀⠉
⠀⠀⠀⠀⠀⠀⠐⠟⠉⠁⣈⣰⠟⢚⡦⢞⡷⢶⡇⠻⢆⣁⠈⠁⠻⠂⠀⠀⠀⠀⠀⠀⢠⣤⢹⠟⡹⢡⢃⡸⠷⠂⠟⣌⡱⢻⠐⡿⣇⡰⡈⢏⠺⠯⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠎⠃⢈⣽⠁⢸⡇⠘⢫⡁⠘⠱⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣠⣶⡎⠥⢒⡟⠆⢻⡟⡸⢓⠒⠬⡱⣧⣀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢰⠝⠀⠀⢀⣬⠋⠀⢪⡗⠀⠘⣧⡀⠀⠀⠻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠎⠏⠀⢊⣝⢣⠘⣸⣡⠁⡜⣏⡒⠀⠉⠳⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢈⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⠙⠀⢠⢾⡷⡀⠐⢙⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠊⠃⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⡜⡰⠃⡠⠊⠁⠀⠀⠀⣈⠩⠝⠉⢆⠀⠙⢎⠳⣥⠀⠀⢀⣠⢏⢦⠀⢠⡔⣞⣠⡤⡄⡠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡜⡰⢁⡜⣠⠔⠊⠉⠉⠁⠀⠀⠀⠀⠈⢆⠀⠀⢣⠸⡆⠀⠀⠀⠈⠈⠀⠀⠀⠉⠈⠀⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⢠⠃⠎⡴⠷⠦⣤⡀⠀⠀⠀⠀⣠⠤⠶⠬⣄⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠇⡇⣰⢮⣴⣶⣶⣤⡉⠀⠀⠀⠀⣡⣴⢶⣦⣬⢆⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⢸⢠⡑⡄⠈⣄⣻⣿⠛⠀⠀⠀⢀⠻⣿⢂⡽⠁⠠⢣⡀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡌⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡆⡸⠹⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢸⠈⢧⠀⠀⠠⣄⡀⠑⠀⠘⠀⣠⠄⠀⠀⡸⢠⠃⢸⠃
⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠘⡂⠀⡗⢄⠀⠈⠣⣁⠀⢂⠜⠁⠀⢀⠜⠗⠁⢀⠎
⠶⠈⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢣⠀⠇⠀⣑⢤⡀⠀⠉⠀⢀⡠⢺⠁⠀⢀⠴⠃
⣲⠒⠃⠀⠸⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠚⠣⣴⠊⠀⣰⠊⠉⠀⠈⠉⡅⠸⠒⠂⠁
⠹⠞⢲⠊⠁⠀⠈⠷⢄⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⣇⠀⠀⡥⠔⣯⣃⠀⠀⠀⠀⠀⠈⡧⠤⠄⣀⣀
⠀⠀⠀⡇⠀⠀⠀⠈⡄⢑⡤⠔⠖⠈⠉⠀⠀⠀⡰⠉⢦⠎⠀⢀⠎⠀⠑⠂⠤⠄⠒⠉⠀⠀⠀⠀⠀⠈⠉⠒⠠⣀
⠀⠀⠀⡇⠀⠀⠀⠀⠸⡀⠀⠀⢸⡀⠀⠀⠀⠀⡇⠀⠀⡧⠔⠋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⢆⠂⠂⢧⡀⠀⠀⠠⠛⠢⡘⠀⢀⠔⠁⡀⠀⠠⠜⣡⠆⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⢶⡹
⠀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⡟⠢⣀⠃⠀⠀⠙⣴⠃⠀⠠⠙⣦⠀⠘⡏⠀⠠⠍⠄⠀⠀⠀⠀⠀⢀⠞⠁⠀⠙⢦⡀
⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠣⠤⠌⣹⠦⠀⢰⢃⠀⣀⡢⣄⠀⠓⡤⠦⡞⠀⢀⣀⡄⠀⠀⠀⢀⠏⠳⡄⠀⠀⠀⠙⢦⡀
⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢃⢨⠀⠈⠝⠋⠉⠩⠇⠐⢟⠉⠉⠂⠉⠉⠉⠁⡟⠀⠀⠈⢦⡀⠀⠀⠀⠙⢄
⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢦⡀⠈⠾⡀⠀⠠⠶⠾⠁⢀⣅⠀⢻⡶⡆⠀⠀⠀⢰⠁⠀⠀⠀⠀⠈⠢⣀⢀⣀⠀⢧
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢈⠚⠀⡱⠀⠀⠀⠀⠀⠇⡹⠄⠀⠉⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⡸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠠⣀⡔⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠔⠁
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣻⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠀⠀⠀⣀⣴⠃⠀⠀⢀⡠⠒⠁
⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺⠁⣤⠏⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠩⡁⣀⠞⠁⢀⡱⠔⠊⠁
⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⡄⠘⡏⠹⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⡔⠃⠀⢀⠂
⠀⠀⠀⠀⠈⠑⠒⠂⠀⠐⠒⠉⠁⠀⠀⠀⠙⠶⠓⠁⠀⣠⠮⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠫⢄⣂⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠀⠀⠈⠑⠦⡀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠈⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⠀⠀⢿⡙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⠙⢦⣌⢷⣄⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠙⣆⠙⠷⣤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢛⡓⠦⡀⠈⢷⡀⠀⠀⠀⣿⠀⠀⠘⠁⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⡄⠀⠻⡄⠀⢰⡇⠀⠀⠀⠀⠀⠀⣰⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡆⠀⣠⠟⠀⠀⠀⠹⣄⡀⢻⠀⠸⣇⠀⠀⠀⠀⠀⢰⡇⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣠⠟⢰⡏⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠘⢷⣄⠀⠀⠀⠀⠻⣄⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⡉⠀⠀⠻⢦⣄⣀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠉⠳⢦⣄⠀⠀⠈⠳⡄⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢳⡀⠀⠀⠀⠈⠉⢻⠓⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⠃⠀⠀⠀⠀⢠⣸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢠⡞⠀⠀⠀⢀⣤⠟⣿⠃⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⠀⠀⢹⡆⢀⡤⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⢁⡖⠉⠀⣀⡴⠞⠋⠀⣰⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠅⠀⠘⡇⢸⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠘⢧⣠⠞⠁⠀⠀⠀⠘⠁⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢰⠇⢸⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠁⠀⠀⠀⠀⠀⢠⢀⠞⠁⠀⣰⠋⣠⡾⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠃⢀⣠⠄⣀⣴⠆⢀⠀⠀⠀⠞⠀⠀⠀⠀⠟⠉⠁⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠰⣶⣤⣛⠀⠈⢁⣾⣿⣷⣿⣿⠃⠀⠀⣀⠀⠖⢀⣀⡀⠀⠀⠀⠀⠀⣰⣯⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣭⣍⣻⣦⣄⡀⠀⣀⠐⣀⣈⠛⠻⣟⣻⣿⣿⡿⠟⣋⠀⠀⣠⣤⣤⣤⡶⠿⠛⠁⠀⠀⠀⣀⡼⠯⠤⠤⠾
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠴⠶⠛⠻⢶⣤⣄⣈⣁⣰⣿⡿⣯⣥⣤⣀⡛⣿⣿⣶⣬⣍⠀⠻⠷⠶⢶⣆⣤⣴⣾⣿⣶⣶⣶⠤⠴⠶⠖⣶
⠀⠀⠀⠀⠀⠀⢸⣁⣀⣀⣤⡤⠤⠶⠶⠚⠋⠉⠉⠉⠉⠁⣀⡤⣿⣿⣿⣿⣿⣿⣿⡿⠿⢶⠲⠶⣿⣿⣭⢤⣭⣍⣛⡛⠛⠶⠦⢤⣤⡤⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠋⢑⣻⡿⠟⠋⢁⣀⡈⠉⠉⠉⠋⠉⠛⠒⠾⠭⣅⣀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⣯⣉⣀⠤⠖⠚⠉⠉⠀⠠⠖⠛⢉⣀⡙⠚⠙⠛⠶⠶⢦⣄⣠⣤⡴⠶⠯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⠀⣠⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠉⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠘⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⠄⣶⡿⠂⠀⠀⠀⠀⢀⢿⣿⣿⣷⣄⠀⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠘⠁⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣷⣄⢻⣷⣄⠀⠀⣀
⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⢰⠇⠀⡆⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣿⣿⣿⣿⣿⣦⡀⠉⠿⣦⣈⢳⣤⡀
⠀⠀⠀⠀⢸⣗⠀⠀⡄⠀⠁⠀⢸⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⠻⢧⡙⣿⣶⣄⡀⠀⢀⣀⣤⣤⣄
⠀⠀⡄⠀⣹⣿⡀⢠⣷⠀⠀⠀⢾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⢻⣿⡿⠿⠿⠟⠛⠛⠛⠛⠻⠶⠀⠉⠀⠿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠀⣸⣷⠀⣿⣿⠅⢾⣿⡆⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠿⠿⢿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⡖⣿⣿⢖⣿⣿⣗⠀⢠⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣶⣦⣤⡀⠀⢀⣤⣴⡿⠂⠉⢻
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣤⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠛⣿⣿⡟⢊⠥⠤⠎⢘⣿⣇
⣿⣿⣯⣝⣻⡿⢻⣿⣿⣿⣶⣾⣿⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠁⠀⣀⣤⣤⣿⣿⣶⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠲⢦⣄⠀⠀⠀⢀⣠⡤⠶⠶⠒⠒⠲⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⠻⣆⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⢀⡴⠖⠛⠉⠉⠛⠛⠧⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⢀⣀⣀⣀
⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠉⠉⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠈⣻⡶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣀⣀⣀⡴⢾⡀
⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠿⢫⡟⠛⠛⠻⣤⣞⡃
⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠙⢦⣤⣀⣀⣠⣤⡞⠉⢳⣦⣤⣀⣀⡀⠀⢀⣀⣤⣏⡿⣠⣭⡗⠀⠀⠀⣿⠉⢿⠄⢀⣄
⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⣯⠹⣤⣤⣤⣽⡜⢯⣩⣟⢻⣍⣧⠙⣴⣧⣴⠟⣦⣤⡾⠡⣿⡭⠤⠟⠼⠧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣶⢂⡶⢶⣲⡶⣠⠶⠶⣦⡴⢶⡶⣀⠰⡖⢶⣔⡶⠒⣆⢲⡒⠒⠓⢶⣘⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⢾⡉⢰⡇⠀⠀⢸⣗⠛⢰⠋⣷⠙⣻⡏⠀⠀⠘⣧⠛⢶⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⢧⣤⣤⣤⠟⡴⠞⠛⠳⢷⡙⣦⣀⣀⡴⣷⣦⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡴⠒⢲⢆⡘⣇⠀⠀⠀⣰⢃⡄⢶⠶⣄⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡞⣷⠙⢲⣶⠚⢡⡏⠹⣎⢧⣍⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣭⢁⢺⡄⠙⠶⠛⠹⠷⠖⠋⠀⣸⠂⢰⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠟⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠷⠋

⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⢀⣨⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⣫⠄
⠀⠀⠀⠀⢠⣄⢀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⣩⢧⠶⠂
⠀⠀⠀⠀⣄⣈⣱⣆⣠⠤⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣤⣩⣿⣦⣶⠛
⠀⠀⠀⢠⡌⠉⢡⣎⣁⣀⡄⠀⣠⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣉⣤⣾⣥⡼⠳⠶⠾⠃⢀⠀⣠⠄
⠀⠀⠀⠀⠓⠚⣯⠉⢉⢁⣠⠀⠋⡀⠀⠀⠀⠀⠐⢁⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⠀⡞⠀⠀⠀⢰⠃⠁⢺⣤⠿⢶⣧⡾⢿⣶⠶⠾⠋⠊⠀⠟
⠀⠦⠐⠶⡴⠾⢛⡓⠟⠉⠁⠀⠀⣧⠀⡀⢀⡀⠀⠈⢧⡄⠠⢠⠆⠀⠐⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⣟⣫⡿⠶⢟⡿⠶⠶⠂
⠀⠀⠶⣦⣀⣴⠞⠛⣶⣄⣼⠻⠇⠘⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣳⣫⣿⣭⣿⣟⣻⡷⢶⡾⠇
⠀⢀⣤⣬⣡⣂⣴⣾⣇⠈⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣋⣽⠶⠖⠺⢛⣿⣷⣤⣤⣶⠄
⠀⠉⠉⠉⠙⡉⠉⣹⡋⠛⠋⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠶⠼⠿⠿⣿⣧⣤⣤⡤⠆
⢀⡝⠛⢿⣍⣠⠾⠻⡿⢷⠆⣦⠆
⠈⣿⠏⣉⣈⠈⣀⢾⣧⣀⠀⡾⠟
⠀⠀⠀⠀⠿⠋⠏⠈⠙⠛⠋⠁
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⢀⣴⣷⠈⢻⡏⢀⣾⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣤⣉⣙⣷⣾⣷⣿⣋⣉⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠿⠛⢛⣿⣿⣿⣟⡛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⣀⣀⡈⠻⣿⣿⣿⣿⡿⠋⣠⣄⣀⠀⠠⢶⣿⠋⢸⡇⠙⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢀⣾⣿⣿⣿⣦⣄⣉⣉⣡⣤⣾⣿⣿⣿⣧⠀⠀⠉⠐⠟⠻⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡋⠀⢸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡟⠙⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣇⠀⢸⣿⣿⣿⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡋⠀⢸⣿⣿⣿⣄⣿⣿⡇⠈⠙⠻⢿⣿⣿⣿⣿⠃⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣶⣤⡈⠉⠉⠁⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠃⢸⣿⣿⣿⣿⡇⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠺⣷⠗⢠⣄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢺⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢷⣄⣿⣠⣾⠟⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⢿⣏
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⢶⣿⣿⣿⣷⡶⣾⡇⠀⠀⢸⣿⣿⣿⣿⡏⣿⣿⣿⣿⡀⠀⠠⣾⣏
⠀⠀⠀⠀⠀⠀⠀⠈⢡⣤⣾⠟⣿⠛⢷⣤⣌⠁⠀⠀⣼⣿⣿⣿⣿⠃⢻⣿⣿⣿⣇⠀⠀⢼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠃⢠⣿⣦⠘⠟⠁⠀⠀⢀⣿⣿⣿⣿⡟⠀⠘⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⢹⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠈⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠓⢓⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠈⠀⠠⠀⣶⡶⠀⠀⠀⠠⠀⠀⠀⠀⠐⠖⠓⠶⠀⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣭⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠚⠓⠆⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢀⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠑⠛⠙⠚⠓⠓⡁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠀⢠⠖⠀⠉⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠚⠐⠳⠖⠤⠂
⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠌⣠⠖⠈⠈⣧⣽⠋⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡐⠧⠢⠔⠦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡯⠀⠈⠐⠉⠈⠒⠚⠀⠙⢆⢀⡠⢀⢀⠀⢠⡄⠤⠒⢲⣴⣧⣶⡜⢚⣒⠘⢀⠀⡀
⠀⠀⠀⠀⠀⡠⠐⡐⠒⠊⠉⠁⢡⣹⣷⢰⠀⣰⣶⡆⠀⡄⣯⡴⣄⢅⠠⡌⡛⣿⣏⣴⠀⠌⠁⢉⡁⡀⣀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⣌⠄⠈⠉⢅⣐⣋⠏⡁⢹⠀⢀⡇⠀⣠⠤⠼⠂⠂⡁⠀⠈⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⢀⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠋⠉⠁⠉⠐⠄⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⡀⠄⠀⠀⠀⠐⠂⠀⠀⠒⠀⠀⠐⣦⠚⠹⡀⠀⠀⢈⡔⠙⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡮⠶⢽⡄⠀⠂⠀⠀⢠⣔⣳⡀⠐⠀⢴⣁⡈⢙⡁⠀⢁⡞⣉⠉⢿
⠀⠀⠀⠀⠀⠠⠀⡻⠒⠀⢤⠇⠀⠀⠠⠀⣾⠤⢬⣧⠀⢴⣇⣀⣩⢹⠁⠀⣠⣋⠈⢩⢫⡁⠀⠂
⠀⠀⠀⠀⠐⠀⢘⠗⠒⠠⢤⠷⠀⠀⠀⢐⠗⠒⠢⡷⠴⠧⣀⣀⠈⢫⢁⢀⣞⣁⠀⠉⠻⡁⠀⠐
⠀⠀⠀⠀⠀⠀⠓⠒⡖⡤⠠⠧⠀⠁⠆⠉⠉⣛⠒⣚⣀⣀⣆⣌⣉⡉⠀⠀⠀⢸⢩⢉⣉⣁
⠀⠀⠀⢰⡗⠒⠒⠒⠓⠓⠛⠛⠛⠛⠓⠒⠚⠉⠉⠉⢉⣉⠀⢀⡉⠉⠉⠉⠛⠛⠉⠉⣁⣈⠙⢲⡄
⠀⠀⠀⢸⡇⠀⠑⠒⠀⠐⠂⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠀⠀⠀⠀⠀⠀⠈⢸⡇
⠀⠀⠀⢸⡇⠀⠐⠤⣀⠠⠤⠄⠒⠂⠀⠀⠈⠉⠉⠒⠒⠒⠁⠀⠀⣀⠀⠈⠒⠒⠊⠉⠉⠁⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠤⠔⠒⠒⠀⠒⠒⠒⠢⠤⠀⠀⠀⠀⠉⠀⠉⠒⠤⠤⠤⠒⠀⠀⠀⢸⡇
⠀⠀⠀⠸⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠇

⠀⠀⠀⣠⠞⣉⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣉⡙⢦⡀
⠀⠀⠀⣿⢸⠁⢹⠀⡇⡒⠒⠀⠀⠀⠀⠀⢸⠁⡏⠈⡇⢹⠠⠤⠄⠀⠀⠀⠀⠀⡇⢸⠁⣿⢸⡇⡒⠒
⠀⠀⠀⣿⢸⠀⢸⠀⡇⠂⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⡇⢸⢨⠀⠀⠀⠀⠀⠀⠀⡇⢸⣄⣿⢸⡇⠂
⠀⠀⠀⣿⢸⠀⢸⠀⡇⠥⠤⠀⠀⠀⠀⠀⢸⠀⡇⠀⡇⢸⢐⣀⡀⠀⠀⠀⠀⠀⡇⢸⣿⣿⢨⡇⠥⠤
⠀⠀⠀⡟⢸⠀⢸⠀⡇⡁⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⡇⢸⠐⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⢰⡇⡁
⠀⠀⠀⣷⢸⠀⢸⠀⡇⣂⣀⠀⠀⠀⠀⠀⢸⠀⡇⠀⡇⢸⠨⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⢰⡇⣂⣀
⠀⠀⠀⣿⢸⠀⢸⠀⡇⠆⠀⠀⠀⠀⠀⠀⢸⠀⣷⣾⡇⢸⢈⠉⠁⠀⠀⠀⠀⠀⡇⢸⣿⣿⢸⡇⠆
⠀⠀⠀⣿⢸⠀⢸⠀⡇⠅⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⡇⢸⢐⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⢨⡇⠅
⠀⠀⠀⣿⢸⠀⢸⠀⡇⡋⠉⠀⠀⠀⠀⠀⢸⠀⣿⣿⡇⢸⠰⠒⠂⠀⠀⠀⠀⠀⡇⢸⣿⣿⢸⡇⡋⠉
⠀⠀⠀⣿⢸⠀⢸⠀⡇⡂⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⡇⢸⠨⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⢸⡇⡂
⠀⠀⠀⣿⢸⣷⣿⠀⡇⠍⠉⠀⠀⠀⠀⠀⢸⠀⣿⣿⡇⢸⢘⠒⠂⠀⠀⠀⠀⠀⡇⢸⣿⣿⢸⡇⠍⠉
⠀⠀⠀⣿⢸⣿⣿⠀⡇⠅⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⡇⢸⢐⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⢸⡇⠅
⠀⠀⠀⡏⢸⣿⣿⠀⡇⠒⠒⠀⠀⠀⠀⠀⢸⠀⣿⣿⡇⢸⠨⠤⠄⠀⠀⠀⠀⠀⡇⢸⣿⣿⠐⡇⠒⠒
⠀⠀⡴⢃⣼⣿⣿⣄⠳⡄⠀⠀⠀⠀⠀⢠⠞⣠⣿⣿⣧⡘⢦⠀⠀⠀⠀⠀⠀⡴⢃⣼⣿⣿⣄⠳⡄
⠀⢸⡇⣾⣿⣿⣿⣿⡆⢻⠀⠀⠀⠀⠀⡟⢰⣿⣿⣿⣿⣷⢘⡇⠀⠀⠀⠀⢸⠃⣿⣿⣿⣿⣿⡆⣿
⠀⠈⢧⠙⢿⣿⣿⠟⢡⠟⠀⠀⠀⠀⠀⠹⡌⠻⣿⣿⡿⠋⡼⠁⠀⠀⠀⠀⠈⢧⠙⢿⣿⣿⠟⢡⠏
⠀⠀⠀⠙⠶⠤⠴⠖⠉⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⠤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠈⠑⠶⠤⠴⠚⠉