⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠏⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠛⠛⠛⢫⣿⣿⣿⢿⣿⣷⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣈⡿⠟⠁⠐⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⢾⣫⣿⠯⣗⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠄⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢛⣼⡿⠟⣴⣿⣿⠟⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⠙⢿⣴⣙⣿⣿⢋⡜⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣓⣤⣤⣄⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣀⡱⡀⠀⣿⣿⣿⠏⡟⢸⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣝⣻⣷⣮⣼⠁⣸⡇⡀⢤⢒⣡⣽⣶⣿⠿⢟⠹⠀⠀⢹⣿⣿⠀⣗⢾⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡾⡝⢿⣿⣯⠽⣿⣿⣿⣿⠿⣯⣭⣄⣛⠖⠃⢀⡴⠋⢩⠝⠀⠛⢺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡿⡿⣬⣭⡝⠋⠛⠟⣋⣠⣰⣀⢉⣀⢌⢁⡴⠋⠀⠀⢨⠀⠀⡠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣇⢳⠸⢻⢸⠁⠀⣸⠁⢊⠙⢾⣁⣂⡼⠋⠀⠀⠀⢀⠎⠀⠀⡇⠌⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⠀⢸⢿⠒⠟⠚⢿⡀⠀⠀⡏⠁⡀⠤⠀⠀⡄⠊⠀⠀⠀⡇⠄⢸⡧⠤⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣸⠀⠀⣀⣰⣭⡷⠒⠁⠀⠈⠫⢽⠅⠀⠀⠀⠀⠀⡇⡅⠀⢻⣵⡩⢆⠽⢖⠮⣍⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣷⢿⣤⡾⢟⣿⠟⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠐⡣⡆⠀⠈⠹⣿⡜⣎⢎⡵⣾⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⣀⠀⠀⢀⡀⠤⠔⠒⠊⠉⠉⠁⠀⠹⣏⣛⣷⡋⠁⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⢀⣴⣟⡧⠀⠀⠀⠈⠻⢾⣬⢾⠏⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡴⠛⠉⠀⠀⠀⠀⠈⢉⡝⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣳⡝⠓⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⡟⣵⠀⠀⠀⠀⠀⠀⡩⡿⠀⠀⡇⢳⡄⠀⠀⠀⠀⠀⠀⠀
⠠⠋⢠⡾⡄⠀⠀⠀⠀⠀⢨⡇⠎⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡞⡽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠀⢸⠀⠀⠀⠀⠀⠠⢳⠇⠀⠰⡧⡁⢻⠉⠳⠤⣤⣀⣀⠀
⠀⠀⢸⣗⡇⠀⠀⠀⠀⠀⠀⣧⠂⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⡀⢼⣿⣽⣱⡁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢿⡟⠀⠀⡘⡇⠀⠀⡀⢀⣜⡟⠀⠀⠁⣇⡇⠈⣷⠀⠀⠀⠀⠈⠙
⠀⠀⢸⡿⣼⠀⠀⠀⠀⠀⠀⢻⠠⠈⡄⠈⠻⣦⠀⠀⠀⠀⢠⣖⣼⣿⣷⢳⠄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢯⡟⠀⠀⠀⡇⡇⠀⠀⡄⡸⣼⠀⠀⢀⢀⣿⠁⠀⠈⣧⠀⠀⠀⠀⠀
⠀⠀⢸⣿⡹⠆⠀⠀⠀⠀⠀⢸⣇⠡⠘⣀⢂⣹⢷⡀⠀⢀⣴⠿⣹⣿⣿⣧⣤⣀⣤⣤⣤⣾⣿⣿⣿⣿⣽⣿⠄⠀⠀⠀⠸⢳⡀⠐⣡⣻⠃⠀⠀⠀⢸⠸⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⢻⣷⠀⣠⣖⣆⠀⠀⢻⢆⣵⠞⠋⠁⠈⣧⡴⠛⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⠁⢀⠁⠀⠀⠀⠙⣷⣎⢰⡿⣄⠀?