⠀⠀⢀⣀⠤⠿⢤⢖⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡔⢩⠂⠀⠒⠗⠈⠀⠉⠢⠄⣀⠠⠤⠄⠒⢖⡒⢒⠂⠤⢄⠀⠀⠀⠀
⠇⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠈⠈⡨⢀⠡⡪⠢⡀⠀
⠈⠒⠀⠤⠤⣄⡆⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢕⠱⠀
⠀⠀⠀⠀⠀⠈⢳⣐⡐⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠇
⠀⠀⠀⠀⠀⠀⠀⠑⢤⢁⠀⠆⠀⠀⠀⠀⠀⢀⢰⠀⠀⠀⡀⢄⡜⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠄⡷⠢⠤⠤⠤⠤⢬⢈⡇⢠⣈⣰⠎⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢸⡇⠀⠀⠀⠀⠀⠈⢪⢀⣺⡅⢈⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠶⡿⠤⠚⠁⠀⠀⠀⢀⣠⡤⢺⣥⠟⢡⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣀⠤⠿⢤⢖⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡔⢩⠂⠀⠒⠗⠈⠀⠉⠢⠄⣀⠠⠤⠄⠒⢖⡒⢒⠂⠤⢄⠀⠀⠀⠀
⠇⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠈⠈⡨⢀⠡⡪⠢⡀⠀
⠈⠒⠀⠤⠤⣄⡆⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢕⠱⠀
⠀⠀⠀⠀⠀⠈⢳⣐⡐⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠇
⠀⠀⠀⠀⠀⠀⠀⠑⢤⢁⠀⠆⠀⠀⠀⠀⠀⢀⢰⠀⠀⠀⡀⢄⡜⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠄⡷⠢⠤⠤⠤⠤⢬⢈⡇⢠⣈⣰⠎⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢸⡇⠀⠀⠀⠀⠀⠈⢪⢀⣺⡅⢈⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠶⡿⠤⠚⠁⠀⠀⠀⢀⣠⡤⢺⣥⠟⢡⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

///////⣸⣿⣿⡶⢦⣤⡀⠀⠀⠀⠀⠀⠀⣇⠀⣾⠛⢁⣠⣴⠴⢾⣧⠀⠀⠀
⠀⠀⠀⠀⣿⣿⡎⣿⣿⣾⣻⣾⣿⣿⣿⣯⣷⢚⣞⣛⣙⣛⠿⣿⣬⣹⠀⠀⠀
⠀⠀⠀⠀⣿⣿⢮⣿⣿⣿⡿⣵⣿⣿⣿⣿⣿⣿⣿⣭⣝⢿⣿⣷⣘⣿⡀⠀⠀
⠀⠀⠀⠀⢻⣿⣶⣿⢿⣵⣿⣿⣿⣿⡟⣿⣿⣿⣿⡜⣿⣿⣤⠛⢿⣮⠀⠀⠀
⠀⠀⠀⠀⣿⣭⣶⢣⣿⡿⣿⣿⣿⡿⡄⣿⣿⣿⣿⣿⢹⣿⣿⣿⡜⣿⡀⠀⠀
⠀⠀⠀⣿⣿⣿⢡⣿⢛⡆⣿⣿⢟⣼⢤⣿⣿⡿⢻⣿⣷⢻⣿⣶⣥⣿⣿⠀⠀
⠀⠀⣾⣿⣿⡏⣿⣿⣿⣫⣶⡊⠀⣿⣶⣮⣙⣾⢛⠁⠀⣾⣶⣤⢻⣿⡸⣧⠀
⠀⣸⣿⣿⣿⡘⣿⣿⡅⣿⣿⠀⠀⣿⣿⣿⣿⡀⣯⠀⠀⣿⣿⣿⣸⣿⡇⣿⡄
⠀⠀⠀⣿⣿⣧⢿⣿⣿⣰⣭⣛⣰⢟⢛⣭⣾⣿⣶⢤⣛⣭⣭⢢⣿⣿⣿⠀⠙
⠀⠀⠀⠹⠋⢻⣦⢻⢣⣶⣙⢿⣿⣿⣬⣭⣵⣷⣭⣼⡿⢛⣴⡿⠙⣿⡇

///////⣸⣿⣿⡶⢦⣤⡀⠀⠀⠀⠀⠀⠀⣇⠀⣾⠛⢁⣠⣴⠴⢾⣧⠀⠀⠀
⠀⠀⠀⠀⣿⣿⡎⣿⣿⣾⣻⣾⣿⣿⣿⣯⣷⢚⣞⣛⣙⣛⠿⣿⣬⣹⠀⠀⠀
⠀⠀⠀⠀⣿⣿⢮⣿⣿⣿⡿⣵⣿⣿⣿⣿⣿⣿⣿⣭⣝⢿⣿⣷⣘⣿⡀⠀⠀
⠀⠀⠀⠀⢻⣿⣶⣿⢿⣵⣿⣿⣿⣿⡟⣿⣿⣿⣿⡜⣿⣿⣤⠛⢿⣮⠀⠀⠀
⠀⠀⠀⠀⣿⣭⣶⢣⣿⡿⣿⣿⣿⡿⡄⣿⣿⣿⣿⣿⢹⣿⣿⣿⡜⣿⡀⠀⠀
⠀⠀⠀⣿⣿⣿⢡⣿⢛⡆⣿⣿⢟⣼⢤⣿⣿⡿⢻⣿⣷⢻⣿⣶⣥⣿⣿⠀⠀
⠀⠀⣾⣿⣿⡏⣿⣿⣿⣫⣶⡊⠀⣿⣶⣮⣙⣾⢛⠁⠀⣾⣶⣤⢻⣿⡸⣧⠀
⠀⣸⣿⣿⣿⡘⣿⣿⡅⣿⣿⠀⠀⣿⣿⣿⣿⡀⣯⠀⠀⣿⣿⣿⣸⣿⡇⣿⡄
⠀⠀⠀⣿⣿⣧⢿⣿⣿⣰⣭⣛⣰⢟⢛⣭⣾⣿⣶⢤⣛⣭⣭⢢⣿⣿⣿⠀⠙
⠀⠀⠀⠹⠋⢻⣦⢻⢣⣶⣙⢿⣿⣿⣬⣭⣵⣷⣭⣼⡿⢛⣴⡿⠙⣿⡇

///////⣸⣿⣿⡶⢦⣤⡀⠀⠀⠀⠀⠀⠀⣇⠀⣾⠛⢁⣠⣴⠴⢾⣧⠀⠀⠀
⠀⠀⠀⠀⣿⣿⡎⣿⣿⣾⣻⣾⣿⣿⣿⣯⣷⢚⣞⣛⣙⣛⠿⣿⣬⣹⠀⠀⠀
⠀⠀⠀⠀⣿⣿⢮⣿⣿⣿⡿⣵⣿⣿⣿⣿⣿⣿⣿⣭⣝⢿⣿⣷⣘⣿⡀⠀⠀
⠀⠀⠀⠀⢻⣿⣶⣿⢿⣵⣿⣿⣿⣿⡟⣿⣿⣿⣿⡜⣿⣿⣤⠛⢿⣮⠀⠀⠀
⠀⠀⠀⠀⣿⣭⣶⢣⣿⡿⣿⣿⣿⡿⡄⣿⣿⣿⣿⣿⢹⣿⣿⣿⡜⣿⡀⠀⠀
⠀⠀⠀⣿⣿⣿⢡⣿⢛⡆⣿⣿⢟⣼⢤⣿⣿⡿⢻⣿⣷⢻⣿⣶⣥⣿⣿⠀⠀
⠀⠀⣾⣿⣿⡏⣿⣿⣿⣫⣶⡊⠀⣿⣶⣮⣙⣾⢛⠁⠀⣾⣶⣤⢻⣿⡸⣧⠀
⠀⣸⣿⣿⣿⡘⣿⣿⡅⣿⣿⠀⠀⣿⣿⣿⣿⡀⣯⠀⠀⣿⣿⣿⣸⣿⡇⣿⡄
⠀⠀⠀⣿⣿⣧⢿⣿⣿⣰⣭⣛⣰⢟⢛⣭⣾⣿⣶⢤⣛⣭⣭⢢⣿⣿⣿⠀⠙
⠀⠀⠀⠹⠋⢻⣦⢻⢣⣶⣙⢿⣿⣿⣬⣭⣵⣷⣭⣼⡿⢛⣴⡿⠙⣿⡇

///////⣸⣿⣿⡶⢦⣤⡀⠀⠀⠀⠀⠀⠀⣇⠀⣾⠛⢁⣠⣴⠴⢾⣧⠀⠀⠀
⠀⠀⠀⠀⣿⣿⡎⣿⣿⣾⣻⣾⣿⣿⣿⣯⣷⢚⣞⣛⣙⣛⠿⣿⣬⣹⠀⠀⠀
⠀⠀⠀⠀⣿⣿⢮⣿⣿⣿⡿⣵⣿⣿⣿⣿⣿⣿⣿⣭⣝⢿⣿⣷⣘⣿⡀⠀⠀
⠀⠀⠀⠀⢻⣿⣶⣿⢿⣵⣿⣿⣿⣿⡟⣿⣿⣿⣿⡜⣿⣿⣤⠛⢿⣮⠀⠀⠀
⠀⠀⠀⠀⣿⣭⣶⢣⣿⡿⣿⣿⣿⡿⡄⣿⣿⣿⣿⣿⢹⣿⣿⣿⡜⣿⡀⠀⠀
⠀⠀⠀⣿⣿⣿⢡⣿⢛⡆⣿⣿⢟⣼⢤⣿⣿⡿⢻⣿⣷⢻⣿⣶⣥⣿⣿⠀⠀
⠀⠀⣾⣿⣿⡏⣿⣿⣿⣫⣶⡊⠀⣿⣶⣮⣙⣾⢛⠁⠀⣾⣶⣤⢻⣿⡸⣧⠀
⠀⣸⣿⣿⣿⡘⣿⣿⡅⣿⣿⠀⠀⣿⣿⣿⣿⡀⣯⠀⠀⣿⣿⣿⣸⣿⡇⣿⡄
⠀⠀⠀⣿⣿⣧⢿⣿⣿⣰⣭⣛⣰⢟⢛⣭⣾⣿⣶⢤⣛⣭⣭⢢⣿⣿⣿⠀⠙
⠀⠀⠀⠹⠋⢻⣦⢻⢣⣶⣙⢿⣿⣿⣬⣭⣵⣷⣭⣼⡿⢛⣴⡿⠙⣿⡇