⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣤⣤⡀⠀⠀⠀⠀⣀⠧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣤⡀⠀⠉⠙⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⡔⠋⢁⣠⣴⣾⣿⣿⣿⣿⣿⡟⠹⣿⣿⣿⣿⣿⣷⣄⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣶⣿⣿⣿⣿⣿⣿⣿⢿⣿⢷⡀⠘⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠰⢾⡷⠒⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠀⠀⠀⠠⣧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠘⠃⣰⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⣛⠋⠉⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠉⣿⣿⡆⠀⠀⢰⣿⠟⢿⡇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⠉⢿⣄⠀⡿⠁⣀⠘⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⡎⢠⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢇⠀⠀⣴⣿⣿⣿⠿⣻⣿⣿⣿⣿⣿⣿⣷⠋⠀⡌⢻⣴⣦⢠⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⢀⡰⠁⠘⢒⡺⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠚⠛⢉⡁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣷⡘⠿⠋⣼⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠴⠟⠒⢤⠀⡏⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠃⠀⠒⣺⠽⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢹⣷⡀⣼⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⡖⠈⣷⠀⠀⠀
⠀⠀⠀⠀⠘⠛⠉⠑⢦⠀⡴⠁⠀⢀⣼⣿⣿⡿⠟⠁⣰⣿⣿⡿⠿⣿⣿⡿⡎⢿⣿⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⡘⢿⣿⣿⡿⠀⢀⣠⣿⠀⠀⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⠃⠀⠀⠾⠿⠛⠁⠀⠀⢰⡿⠟⠉⠀⠀⣿⡿⠁⠸⡘⠿⠟⡼⣿⣿⣿⣿⠉⠻⣿⣿⣿⣧⠀⠙⠻⠃⣴⣿⣿⡿⠀⢸⠑⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢀⠴⠢⠤⠔⠉⠳⣀⢸⣏⠀⠀⠀⢣⠀⣰⠁⠈⠿⣿⣿⠃⠀⠹⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠁⠀⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⠎⢀⡤⠔⠒⠒⠤⢄⡀⠀⣹⠀⠀⠘⣦⠇⠀⠀⠀⠈⠁⠀⠀⠀⠈⠛⠃⢠⣄⣴⠟⣻⣿⣷⠀⠀⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠃⠀⠰⠋⠀⠀⠀⠀⠀⠀⠈⢆⠈⠑⠆⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡟⠵⠆⣲⢛⣞⡇⠀⠀⢸⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⠋⠓⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣹⣿⠟⢡⣄⣼⣵⣟⠞⠀⠀⠀⢸⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣾⠁⠀⣤⠾⢋⣽⢏⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡀⣼⢷⣇⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠴⠃⢛⠟⠀⢀⠋⢍⣼⣃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⢺⡧⢸⣿⣾⠀⠀⠀⠀⠀⡌⢀⠏⠁⠀⣠⣄⠀⠀⠀⠁⣰⣿⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠠⠀⠆⣾⡞⢷⣾⢧⣿⣷⡀⠀⢠⠴⠃⡜⠀⠀⣾⣿⣿⣷⣿⡇⢀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣱⣤⣤⣶⡃⢹⣿⣾⠀⠙⠻⢷⣄⣎⠀⠀⡇⠀⠀⣿⣿⣿⠟⠉⣰⡿⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣟⡇⣾⣓⡇⢼⣿⣿⡀⠀⠀⠀⠈⠀⢙⠆⠹⡀⠀⣿⠟⠁⠀⠀⠉⣠⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡜⣟⣷⡜⢿⣿⣷⡄⠀⠀⠀⠀⣼⠀⠀⠈⠲⢅⣀⣀⣠⠴⠚⡡⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡇⢸⣿⡇⠀⢹⣿⠇⠀⠀⠀⠀⠈⠁⠐⢆⠀⠀⢀⡤⣀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡌⠻⣿⡄⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠘⠤⠄⠊⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇⠀⠈⠃⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀