⠀⠀⠀⠀⠀⠀⠠⢠⠀⢠⠰⡄⠀⣴⣴⠀⣠⡆⢀⣶⠀⢀⣦⣶⣶⣶⠀⣶⣴⣶⡠⢰⣶⣆⠀⡔⡄⠀⣀⠀⠰⡐⢠⠄⣂⠄⢰⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠐⠤⢠⠏⡰⢁⣾⣿⣯⣀⠹⣣⣿⣿⡄⡞⣿⣿⣿⣿⢾⣿⣿⣿⣿⣾⣷⣧⣲⣿⣷⣠⡏⡆⠈⡃⠈⡄⠠⡘⠢⠉⠁⠀
⠀⠀⠀⠀⠀⠒⠲⠠⠃⠠⡴⢾⣿⣿⣿⣿⡷⢻⣿⣿⣿⣿⣿⣿⢟⢅⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢰⡀⠀⠐⠀⠁⠐⠀⠄⠀
⠀⠀⠀⠀⡀⢐⠀⡀⡀⠀⠀⠈⠉⠙⠛⠻⢿⣽⣿⣿⣿⣿⣿⡏⣰⣿⡿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣾⣷⠀⠀⢀⡤⠀⠀⠈⠀
⠀⠀⠀⠀⠑⠴⡨⠂⠐⠀⠀⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⣙⠫⢑⡀⣀⠤⠠⣒⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠜⡇⠀⠀⠀⠀
⠀⠀⠀⠀⣉⢁⡀⠀⠂⠂⠶⠂⢄⢀⠀⠀⠀⠣⢿⣿⣿⣿⣧⡽⡁⠃⠀⠀⡚⣺⣯⣤⣤⣴⣾⣭⣭⣿⣿⣿⣿⣿⠃⠎⡜⡇⠀⠀⠀⠀
⠀⠀⢀⡔⢑⣾⡇⠀⠀⠀⡐⢀⡀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⡷⡣⠀⠀⠀⢉⡁⠀⠀⠀⢠⣤⣤⣬⣭⣭⣿⣿⣿⠘⡀⢀⠛⠀⠀⠀⠀
⠀⠀⠈⢊⠜⢻⣿⣦⣤⣴⣿⣧⣱⡀⠕⢀⠀⠀⠀⢹⣿⣿⣿⣿⡷⣧⢂⣼⣿⣧⡀⠀⢀⣼⣿⣿⣿⡏⡑⡿⣻⠃⢨⣇⡽⠃⠀⠀⠀⠀
⠀⠀⠠⡂⡙⠆⢿⣿⣿⠿⠿⠿⠛⠀⠆⠈⠃⠀⠀⢼⣿⡟⠄⣽⣾⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⢞⡾⢡⣟⢰⠐⠜⠐⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠳⢂⣬⣉⣭⣤⣴⡦⡀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠐⠹⢙⡿⣗⠍⠛⡻⠿⠿⠿⠿⢛⣭⡮⠼⠃⣾⠏⠎⡀⡔⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠛⢖⣶⣭⣿⣿⡿⣋⣘⠄⠀⠄⠀⠂⠀⠀⢸⢿⣿⣿⣿⣦⣝⣶⣭⣊⡵⢶⣾⣿⡿⠟⣋⣤⣾⣿⢯⠰⠔⠾⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣢⣿⣿⣿⣿⣿⣿⣿⣷⠸⠀⠀⡄⠀⠀⠀⢸⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠠⣻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠄⠀⠀⠀⠀⢘⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢨⣸⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠽⣻⢿⡿⢋⡂⠀⠨⠀⠄⠀⠀⡀⠄⡴⣷⣆⣽⡼⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⢰⠟⠤⠑⢐⠉⠁⠉⠀⠀⠠⠑⠀⢡⠁⠘⣿⡇⡏⣿⣿⣿⣿⣿⣿⣿⣿⡿⡫⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢈⠖⡄⠈⠀⡀⠐⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠞⡗⢹⣿⣿⣿⣿⣿⣿⢟⡩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⣄⡀⣠⡭⡢⢛⡛⣻⣿⡿⣋⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠖⠊⢷⢹⡗⣇⡞⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡉⢴⢻⠐⣿⡸⢩⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢣⣿⠠⣟⠟⡏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⢡⢹⠃⠀⠁⢠⣿⡸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠬⠖⠀⠀⠀⠀⢀⣝⣇⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡄⢘⣀⠀⠀⠀⡀⡀⠈⠚⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠏⠀⠀⠌⠑⠅⠸⡇⡜⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢨⡇⠠⣳⢃⠨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠉⢈⡄⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⡟⠁⠀⠀⢈⢪⣿⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠖⠀⠀⠀⠀⠀⠀⠀⡀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠙⠟⣵⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠧⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡆⣉⡚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀