⣤⣀⣤⠤⢴⠚⠉⠀⠀⢠⣴⠋⠀⢸⠀⡜⠀⡇⠀⢀⣿⡇⠀⠀⠀⠀⠀⣸⡹⢠⡞⡷⠞⠋⠁⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀
⠴⠋⠀⢠⡏⠀⠀⠀⢠⣿⠇⠀⠀⠀⢿⠁⠀⢳⠀⢸⣿⡃⠀⠀⠻⣓⢦⡿⣷⡟⣽⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢦⣤⠀⠀⠀⠀⠀⠀
⢀⡄⠀⣾⠀⠀⠄⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠘⣆⡞⢻⡇⠀⠀⠀⣾⣀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣀⢔⣿⠟⠁⠀⠙⠲⠤⣀⠀⠀⢠
⠏⠀⣸⡏⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⡇⠀⠀⠀⢼⣿⣱⡿⠃⠀⠀⠀⠀⢀⡠⠞⣡⡾⠁⠀⠀⠀⠀⠀⠀⠀⣠⡠⠞
⠀⢀⡟⡇⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢳⠀⠀⠀⣸⡟⡱⠁⠀⠀⢀⡠⠖⠉⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⢐
⠀⢸⠇⣷⠀⣀⣏⣀⣀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢣⠀⣰⠋⡰⢁⡠⠔⠊⠁⢀⣠⠞⠋⠀⠀⠀⠀⢀⣀⠴⠒⠉⠀⠀⠀⠀⢸
⠀⢸⠉⢹⡆⠙⡏⠉⠁⠀⠀⠀⠀⠉⠙⢿⡿⠻⠷⠂⠀⠀⠀⠳⢃⠼⠋⠁⠀⢀⣠⣶⣏⣀⠤⠤⠤⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⣸⡀⢸⣧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⡆⠙⢿⣿⣬⣿⣧⣤⣶⣤⣒⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⢶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠱⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠋⠙⠛⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸
⣧⠀⠀⡇⢈⣿⠀⠘⣿⣿⣿⡟⢻⣿⣷⡙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⠀⠀⠀⠀⠀⢸
⣿⣆⠀⢹⡇⠘⣆⠀⠻⣯⡿⢿⣾⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀
⣿⣿⣧⣜⡏⠀⠈⠳⣄⣙⠛⠚⠷⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠛⣉⣓⣲⣒⣦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⣰
⣿⣿⣿⠙⣻⣶⣶⡶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⢀⡴⠟
⠙⢿⡇⠀⠀⠉⠀⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⣿⣿⣿⣯⣙⣿⠿⣿⣿⣿⣿⣯⣍⡓⠐⠋⠀⢀
⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣯⡷⠠⣼⡟⠉⠙⢻⣿⡿⠶⠒⢢⠏
⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠞⠛⠉⢀⣠⡴⠋⠁⠀⢀⡴⠋⠠
⠀⣼⣷⠴⠒⠋⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢙⡶⠾⠍⠀⠈⠀⠀⠀⢠⠞⠁⢀⣹
⡴⠋⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣠⣶⣿⣿
⠀⣀⣧⠇⠀⠀⡴⠓⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⣿⣿⣿⣿
⠀⠀⡇⠀⠀⡜⢀⡠⠄⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡴⠀⣼⣿⣿⡿⢋
⠀⠀⢳⣀⣼⠟⠁⠀⠀⠘⡟⠓⠢⡀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⣴⣿⣿⣿⣷⣿
⠀⠀⢀⡽⠃⠀⠀⠀⠀⡸⠁⠀⢀⣿⣿⣿⣿⠿⠛⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢋⡴⠛⠉⠁⠀⠀⠈⠙
⠀⣰⠃⠀⠀⠀⣠⠴⠊⠁⠀⢀⡾⠼⠿⣿⡏⠀⠀⠀⡘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢇⠀⠀⡰⠋⠀⠀⠀⠀⡰⢋⠔⠀⠀⢨⡗⢦⡀⢸⣷⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢤⣤⡾⠛⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⢘⡶⠋⠀⠀⢀⡠⠖⠛⢷⡇⠀⠀⠀⡼⠦⠤⠾⢟⠻⡏⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⣁⣤⠄⠉⠀⠁⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡜⠀⠀⠀⡷⠊⠀⠀⠀⣸⡇⠀⠘⢷⣿⡄⠀⠀⠈⠦⠙⡆⠀⠀⢀⣀⣤⣶⠏⠐⣿⠟⠁⠀⠀⣀⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠱⡀⢀⠞⠠⢄⣠⠴⢺⠁⠻⣄⠀⠈⢷⠘⣶⣤⠴⣯⡴⢿⣿⣿⣿⣿⣿⡟⠀⢘⣡⣤⣶⣾⣿⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠈⢁⣀⣴⣋⡤⠖⡟⠀⠀⢈⠟⠒⠋⠀⠘⢶⠶⡏⠿⠸⠹⢯⠛⢿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⠟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀