⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣦⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⣀⣠⠤⠄⠒⠒⠒⠒⠒⠒⠒⠂⠀⠤⠬⠩⠉⢉⣉⣉⣉⡙⠛⠿⠿⢿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⣁⣠⠤⠤⠶⠒⠒⠒⠒⠒⠂⠠⠤⠄⠀⢀⣀⣀⣀⣀⣀⣀⠀⠠⠤⠤⠴⠦⢬⡉⠛⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⢀⡠⠖⠋⣀⠤⠒⣋⣡⠤⠴⠒⠒⠒⠒⠒⠲⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠤⢤⣄⡀⠀⠀⠀⠀⠈⠙⠿⣶⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠔⠋⢀⡴⠚⣁⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠈⢉⡞⠁⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠠⠋⢠⠞⠁⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⣾⣿⣿⣿⣿⣿⣿⡟⠉⠛⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣤⣶⣶⣶⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⠀
⠀⠀⠀⣠⣾⣿⣿⣶⠶⠦⠤⠀⠀⠀⢴⣶⠒⠀⣼⣿⣭⣾⣿⣿⣿⣿⣿⣷⣦⣄⡀⠉⢻⣿⣆⠀⠀⠀⠀⢀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡷⠠⠤⠤⠤⣤⢤⣄⠉⠻⣷⣄⠀
⠀⣠⣾⢟⡿⠉⠀⢀⣤⣶⣶⣶⣶⣶⣤⣀⠚⠁⠀⠉⠉⠁⠀⣀⣴⡾⠀⠉⠉⠛⠿⣿⣾⠿⠃⠀⠀⠀⠀⠙⠿⣿⣿⠿⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠲⣌⡙⢦⡈⣿⣇
⣼⡿⠃⡾⠀⢀⣼⡿⠋⠁⠀⢰⡄⠉⠛⠻⠿⣷⣦⣤⣤⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣴⣾⠿⠿⣷⣦⡄⢳⠀⢱⣸⣿
⣿⠃⠀⡇⠀⣼⡿⠁⠀⠀⢠⣿⣿⣦⣄⡀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⡀⠀⠀⠈⠻⠿⠿⠿⠟⠀⣼⠀⠀⠉⠁⢸⡄⢸⢻⣿
⣿⡄⠀⣇⠀⢿⣇⠠⣶⣾⣿⣿⡉⠙⠛⢿⣷⣦⣄⣀⠀⠀⠀⢠⠤⠤⠤⠤⠚⢣⣿⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣦⣄⠀⠀⠀⠀⠀⠀⢰⣿⣆⠀⠀⢠⠞⠀⣼⣼⡿
⢻⣷⡀⢹⡀⠘⣿⡆⠀⠀⠈⣿⣧⡀⠀⠀⠀⠙⢿⣿⣿⣶⣶⣤⣀⡀⠀⠀⠀⠸⣿⣆⠐⣿⠿⠿⠷⠖⠀⠀⠀⠀⠀⣠⣿⠿⠻⠋⠓⠢⣄⡀⠀⢀⣾⣿⣿⡇⠀⣠⠤⠚⣱⣿⠃
⠀⠻⣷⣄⠙⠦⣌⡁⠀⠀⠀⠙⣿⣿⣷⣦⣄⡀⢸⣿⡀⠀⠉⠙⠛⠿⠿⣷⣶⣦⣌⣛⣀⠀⠀⠀⠀⠀⠀⠸⣷⣶⣿⠟⠁⠀⠀⠀⠀⠀⣀⣥⣶⣿⢿⣷⣿⣧⠀⠀⠀⣸⣿⠁⠀
⠀⠀⠙⢿⣷⣦⠄⠀⠀⠀⠀⠀⠈⢿⣿⡉⠛⠿⣿⣿⣿⣦⣀⣀⠀⠀⠀⠀⣿⡟⠛⠛⠻⠿⢿⣷⣶⣶⣤⣤⣴⣤⣤⣤⣤⣤⣴⣶⣾⣿⡿⠛⢹⣿⠈⢿⣿⣿⠀⠀⠀⣿⠇⠀⠀
⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⢸⣿⠛⠿⣿⣿⣿⣶⣦⣼⣿⣁⠀⠀⠀⠀⠀⠀⢹⣿⠉⠉⠉⠉⢻⣿⠉⠉⠁⠀⠘⣿⡆⠀⢸⣿⣤⣾⣿⣿⠀⠀⠀⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣾⡿⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣾⣿⣦⣤⣤⣤⣾⣿⣦⣤⣶⣶⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⡀⠀⠀⠀⠀⢠⣿⠇⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄⡀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠛⠛⢻⣿⡿⠿⠿⢿⣿⡿⠟⢻⣿⠏⣽⡿⣱⣿⠃⠀⠀⠀⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠲⢄⣀⠀⠢⢄⡀⠀⠈⠛⠿⣿⣿⣦⣀⣀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠁⠀⠀⣼⡿⠀⢠⣿⠏⣀⣻⣿⡿⠃⠀⠀⠀⠀⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣤⣀⠘⠧⣄⡀⠛⠣⢄⣀⠀⠀⠘⠛⠿⠿⣿⣿⣤⣤⣼⣿⣇⣀⣀⣀⣀⣿⣿⣀⣀⣼⣿⣧⣤⣿⣿⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣄⡈⠛⠢⢤⣈⠙⠒⠤⣄⣀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⣠⠄⠀⠀⡀⠀⠀⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣄⡈⠉⠒⠢⠤⣍⣙⡒⠦⢤⣄⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁⠀⠀⣸⠃⠀⠀⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣶⣤⣀⠀⠀⠉⠉⠓⠒⠲⠦⠤⣍⣉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⡿⠛⠁⠀⠀⠀⠀⠀