⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢋⡙⢿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⡐⡐⢂⡙⢿⣿⣶⣶⣶⢿⡿⣿⢿⣿⣷⣶⣶⣤⣄⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢀⡑⠤⢁⠢⢄⠙⢿⠇⢄⠢⡐⠄⡂⢄⢂⠡⡉⡙⠛⠿⢷⣤⣴⣾⠿⠟⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⡠⠘⡄⠣⢌⠢⢘⠠⠌⢂⠥⡈⠔⡡⢌⡀⢃⠔⠡⢊⣴⣿⡿⠋⡅⢊⠔⡸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣾⡟⢛⢃⠡⡑⢠⢃⠢⡑⠌⡒⢌⠂⢆⠱⡈⠔⡂⠜⡠⠊⠥⡈⢛⡉⢄⠣⢈⠔⠢⠐⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⠏⡰⢁⢂⠢⢑⠂⢆⠱⣀⠣⠌⡂⢍⡐⠢⡑⢌⠰⡁⢆⠩⡐⣁⠂⡌⢄⠢⡁⠎⣁⠃⢾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣿⠇⡘⢄⠢⠌⢢⠁⢎⡐⠢⢐⠂⠥⢘⡀⢆⠱⢈⠢⢡⠘⡠⢃⠔⡠⢃⠌⢢⠑⢌⠒⡄⢣⢸⣿⡏⢿⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣸⣿⣦⡁⢆⠡⢊⠤⢉⠄⢢⠑⠌⣌⣴⣦⡘⡀⠣⢌⠢⡁⢎⠰⣈⠢⠡⢌⡘⢄⠊⡔⠢⡘⢄⠸⡿⠃⡌⢿⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡏⠛⠿⢷⣿⣤⣶⣬⣬⣴⣾⡾⠟⠋⢻⣷⣌⠡⢂⡑⠌⡄⢃⠔⡨⠑⡂⢌⠢⡑⢄⠣⡐⠌⡐⠠⡑⢄⢺⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠙⣿⣶⣁⠆⡘⠰⡈⠤⢁⠣⢘⠠⡑⠰⡈⠔⣁⠊⠔⡡⠘⣠⣿⢿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣕⡄⠣⢌⠂⡅⢒⡈⠥⡐⢡⠂⡜⣠⣱⣾⠿⠃⢨⣿⠀⠀⠀⠀⠀
⡀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣶⣾⣴⣧⣼⣶⣼⣶⣿⠿⠟⠋⠁⠀⠀⢰⡿⠀⠀⠀⠀⠀
⠻⢷⣶⣤⣽⣿⣀⡀⣴⡿⠳⣦⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣴⣦⣴⣤⡀
⠀⢠⣾⣟⣉⡙⣿⣷⠿⣿⣷⣿⡷⠀⠀⠻⠺⠀⠀⠒⢂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⡉⠍⣹⣿
⢀⣿⠋⣿⣿⣿⡝⢿⣷⣄⡉⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⡋⠙⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⣿⣧⠘⡐⣼⣿
⠘⣿⠀⠈⢻⣾⣿⠟⠋⠙⠿⣶⡄⠀⣠⡀⠀⠀⠀⠈⠻⢿⣿⣿⡿⢀⢠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⢿⣿⣴⣿⡿⢣
⡀⠙⠷⣶⣾⡿⠟⠀⠀⠀⠀⠹⣷⣴⣿⣇⠀⠀⣀⠀⠀⠀⠀⠠⣴⢻⠟⣴⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⣽⣿⢿⠝⠂⠁
⣧⣴⡿⠋⠀⡧⠊⠀⠀⠀⠀⠀⠀⣠⡤⠿⢿⡟⠛⠻⠷⣶⣶⣤⣤⣶⣼⣷⣿⡶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠀⠀⠀⠀
⣿⣅⠀⠀⠀⠓⠊⠑⢲⢀⡤⠀⢸⡇⣠⠟⡂⢸⠄⠀⢲⠀⠈⠍⢹⣿⣁⠀⠀⠀⢀⣀⣀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⠀⠀⠀
⣿⣿⣻⢶⣦⣄⣀⠀⠈⠉⠀⠀⢨⢷⡄⣈⣧⠞⢠⢊⠘⠀⠐⣀⠤⠉⣻⣿⠟⠟⠛⠛⠿⢿⣦⣄⣀⠀⠀⠀⠀⠀⢠⣿⡟⡴⠀⠀⠀⠀
⣿⣏⠛⠷⣮⣍⡛⠻⠶⣦⣄⡀⠈⠛⠿⠽⠂⠀⠈⠁⣎⡴⠁⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣤⣀⣰⣿⠟⡰⠃⠀⠀⠀⠀
⣿⠛⠻⢶⣤⣍⡛⠷⣦⣄⣉⠙⠳⢶⣤⣀⠀⠀⠀⠀⠈⢀⣴⠿⠋⠀⠀⠀⠀⠀⡀⢤⢠⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣮⣁⠀⠀⠀⠀⠀