⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠆⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣃⣥⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⡆⠀⠀⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢡⣶⡿⠟⠋⠉⠉⠁⠀⠀⠀⠀⠩⡉⠉⠻⠒⠓⢤⣠⠔⠂⠌⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⡺⠁⣴⠟⢁⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠰⠀⠆⠀⠀⠀⠀⠀⠀⢈⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠤⢄⢒⡀⠁⠀⡀⠀⡆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢹⢄⠀⠀⠀⢡⠐⣄⠀⠀⠀⠀⢀⡞⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⢠⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠈⡈⠢⡀⢀⢸⡂⠘⠲⠄⣀⠴⠚⡝⣄⠀⠘⣶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⢰⡎⡀⠘⠁⢧⡠⠀⠀⠀⠀⠀⠈⠃⠀⠩⡀⢸⠘⣧⠀⠀⠀⠀⠀⢛⣿⣳⡄⢻⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠈⠁⠀⠰⠐⠉⢁⠘⠦⡀⠀⠀⢐⣠⣤⣤⣶⢸⣤⡏⠀⠀⠀⠀⠀⠘⡟⢷⡝⣿⡟⠫⣦⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢰⡇⠀⢰⡆⠘⡀⣀⣀⣭⠵⠥⠙⠠⢄⠈⠹⣿⣿⡇⠁⠀⠇⠀⠀⣀⠀⠀⠀⡇⠘⣿⣝⡇⠀⠀⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠌⢣⠀⠈⠁⠀⠹⠹⣿⣿⠀⠀⠁⠀⠀⠀⠈⢻⣿⠇⠀⡘⠀⢀⡔⠁⠀⠀⠀⡇⡄⠸⡹⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢂⠀⣷⣦⡈⢄⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣖⠶⡏⠀⠀⠀⡰⠀⡇⠰⠁⢁⠿⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⠃⣙⣸⣿⣇⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠚⠀⠀⠠⢺⣿⡄⣧⡈⠅⠘⠀⢻⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠈⠀⣿⣧⣄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⠁⢠⣴⡡⢻⡿⣥⠁⠀⠊⠀⠀⠀⢷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠘⠀⠀⠇⠙⢿⣿⡆⠂⠤⢀⡀⠀⣀⠠⡶⠋⠀⡆⠾⣿⠻⠂⡾⠁⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠀⠀⠀⠀⢀⢀⢠⠀⠀⠀⠀⣀⠙⠀⠀⠀⣀⣠⣤⣤⣀⡀⠀⠀⠈⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠣⠒⠆⠠⠒⠒⠒⠓⠓⢀⡐⠁⣹⣿⣿⣿⣿⣿⣦⠀⠀⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠔⠀⢀⠂⠐⠋⠀⠀⠀⠀⠀⠀⣸⣷⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠀⢰⡦⠆⡀⠀⠀⡀⠀⠀⠀⣀⢿⣿⣿⣧⣾⣿⡟⠀⠀⣸⡇⠀⣸⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣬⣩⣴⣶⣶⣤⣶⣶⣿⣿⣮⡛⠛⠉⢀⣠⣼⡿⠁⠀⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⢠⡀⢀⣤⠟⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⠿⠛⠁⠀⢸⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣼⣿⢸⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣿⣿⣾⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⡾⠃⠀