⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣾⣿⣷⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠊⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣯⢻⣿⢿⣿⣿⣿⢟⣿⡿⠟⠀⢀⡴⠖⠲⢾⣝⠛⢿⣿⣖⢿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣿⣿⣷⢣⢳⡿⢏⣷⡿⠋⠀⠀⢰⢿⣿⡆⣀⡀⠉⠀⠈⣿⣿⢺⣿⣿⣿⣿⣿⣿⠿⠓⠒⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣿⣿⣇⣠⠿⢶⣽⣁⢀⠀⠀⠀⠈⠘⠚⠁⠀⠀⠀⠀⠀⣿⣿⣢⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⡷⡏⠀⣸⡿⠈⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡸⢿⡿⣧⠀⠛⠁⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣟⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡜⠀⠈⢿⣹⡇⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠒⠒⢒⡲⠀⠀⡸⣽⣿⡏⢿⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⡼⡀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⠀⠀⠀⠀⠻⣿⡀⠀⠀⠀⠀⣎⠁⠀⠀⠀⠒⢈⠞⠁⠀⢠⡟⣿⣿⡇⠈⡞⡿⣿⣗⠻⣧⡀⠀⠀⠀⠀⠀⣏⢣⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⣿⣷⣄⡀⠀⠀⠘⠧⠤⠤⠐⠚⠁⠀⠀⣰⡟⠀⣿⣿⠀⠀⡇⡇⣿⡟⠳⠬⣟⣦⠤⠀⠀⠀⡻⢰⡇⠀⠀⠀⠀⠀⠀⠀
⠘⡄⠀⠀⠀⠀⣿⣿⢻⢿⣶⣤⣄⡀⠀⠀⠀⠀⢀⣠⢞⠏⠀⢸⣿⣷⠀⢠⢱⠀⣿⠇⠀⠀⠀⡸⠀⠀⠀⠀⢃⠏⡹⡄⠀⠀⠀⠀⠀⠀
⠀⢸⡄⠀⠐⣄⣿⣿⡾⣸⣿⣿⣏⡟⠓⠲⠤⣖⣋⠔⠁⠀⢀⢿⣿⣹⢔⢇⠇⢀⡿⠀⠀⢀⣴⢷⡄⠀⠀⠀⢎⡠⢃⠗⢄⠀⠀⠀⠀⠀
⠀⢸⣿⣆⠀⣸⣿⢁⡧⣿⠹⣿⣿⣜⢕⠂⠀⠤⣀⠀⠀⢀⣮⢻⣏⠵⣋⠎⠉⡸⠃⠀⠴⠮⠶⠥⠵⣄⣀⡠⠞⡣⡃⠀⠀⠱⣄⠀⠀⠀
⠀⣾⢿⣿⣧⣿⢛⠞⡰⡝⡠⣿⡏⠉⠓⠭⢖⣂⠬⠥⠤⠞⠓⣹⠷⠊⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡊⠀⠐⡄⠀⠀⠈⢳⡀⠀
⢰⡟⢸⣿⣿⣿⣎⣀⠕⠉⠀⡝⠱⡄⠀⠀⠀⠀⠉⠁⠀⠉⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠘⢆⠀⠀⠀⠳⡀
⠸⠁⣿⡿⡿⡡⠄⠘⡄⢰⣎⣀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡠⠀⠀⠀⣠⣶⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠸⣤⡀⠈⠓⢄⠀⠀⢱
⠀⢠⡸⠛⣷⣣⡀⢀⠃⢸⣿⣿⡀⣀⣶⣶⡄⢠⣀⡀⠀⠠⠀⣁⣑⣥⣤⡀⠈⣿⣿⠙⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⡗⠋⠉⠒⠢⢣⠀⢸
⠀⠀⠁⢀⣷⠁⡇⢐⠀⣸⣿⠹⡿⠟⣿⣿⠁⢠⣿⡿⢿⣦⣥⣽⠟⢻⠟⣛⠀⣿⣿⡿⠟⠟⠉⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⢸⡠⠃
⠀⠀⠀⢸⡟⢦⡓⠋⢀⣿⡏⠀⠀⠀⣿⣿⠀⢸⣿⣷⣤⡌⢻⡇⠀⢶⣿⣿⠀⣹⠿⠋⠀⠀⣠⣾⡏⣠⠶⠓⠒⠡⠀⠀⠀⢀⣠⠊⠀⠀
⠀⠀⠀⠀⣷⡄⠙⠒⠛⠛⢟⡀⠀⠸⠿⢿⠀⣸⣿⣧⣈⣃⣸⣧⣴⡾⢻⠿⠂⠀⠀⢀⡄⠀⣼⣿⠟⠁⠀⠀⠀⠀⡠⠄⠂⢩⢄⣑⡄⠀
⠀⠀⠀⠀⠻⢿⡦⠻⠽⢿⣿⣏⠀⣤⣤⣄⠀⠀⣉⡉⠙⠛⡉⠉⠉⠀⠀⠀⠀⠰⣾⣿⣧⣀⡿⠃⠀⢀⢤⣤⣴⠭⠒⠊⠉⠁⡦⠊⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠒⢖⣢⣼⢿⣶⣿⣿⡇⠀⠀⣼⣿⣏⠴⠛⢷⣶⣆⠀⠀⠀⠀⠈⢿⢋⣁⠤⠒⣉⡵⠛⠉⠀⠀⠀⠀⢀⡔⢣⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠥⠼⢿⠧⠤⠜⠛⠋⠉⠉⠒⠦⣍⡛⠳⡦⠤⣤⣔⣊⣁⣀⢠⠮⠊⠀⠀⠀⠀⠀⠀⢀⠎⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣬⡢⢱⠤⢍⡉⣹⠋⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠘⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡹⠓⠇⠀⠀⠙⠛⡵⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠏⠀⠀⠀⠀⠀⠀⠀⠘⢕⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢔⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀