⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠒⠊⠉⠉⠉⠐⠒⠶⢤⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢠⣦⠀⣄⣴⣴⠀⡆⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠓⠰⠆⠙⠒⠻⠶⠊⠙⠙⢃⣴⣁⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣲⣶⣦⣤⣤⢀⣀⡀⠀⠘⡆⢠⢀⡄⣄⢀⣈⣱⡄⠀⡄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣽⡷⣿⣿⣿⣿⢏⠓⠓⢸⠘⠺⠜⠋⠙⠟⢿⣻⢇⡀⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠛⠟⠛⡋⢉⣥⡀⣀⢀⣾⢰⢀⣈⢀⣄⣤⠄⡀⠀⢜⣗⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠤⢤⣴⠦⢤⡀⠀⠀⠙⠓⢶⠆⠿⠱⢋⣏⡿⡞⢺⡌⢻⡗⡞⠧⢦⡤⠟⠀⠀⡏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠉⠉⠀⠀⠖⠊⣉⢔⣳⡄⣾⠃⠀⠀⠀⢀⡞⢠⡤⣤⣄⣀⣀⣀⣀⣀⣀⣥⣔⣂⣀⣠⣤⠤⠞⠁⠀⠀
⠀⠀⠀⠀⠀⢀⣴⠏⢀⡴⣶⠂⠀⠀⢀⣠⣮⠿⠟⢾⡇⢻⠀⠀⠀⣠⣞⠵⠋⠀⢩⠏⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣰⣫⣶⣾⠟⣏⠃⢀⣠⠖⠉⠀⠀⠀⠀⣾⡷⡆⠀⣠⡾⠋⠁⠀⠀⢠⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠒⠛⠛⣩⡾⢛⠼⣡⠖⠋⢰⡦⠇⣄⠲⠀⢰⣽⣿⠀⠉⠁⠀⠀⠀⠀⠠⣿⢊⣿⡴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠛⠢⣍⠛⢧⣄⠀⠀⠈⠀⠓⠀⣠⣿⣿⡟⠀⠀⠀⠀⠀⠀⣤⡾⡿⢽⢿⣷⡋⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣠⣼⢷⣦⣌⠛⢦⡀⢀⣠⣶⣿⣿⡿⠶⢤⡀⠀⠀⢠⢼⣯⢎⣷⣼⣿⣻⣿⣷⠒⣟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣴⡶⢛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣳⣤⡂⠀⠙⢦⣤⡤⠾⢺⣿⠒⠛⢻⣱⢹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⡿⠋⠘⠛⠛⠋⢉⢽⡟⣹⣿⣿⣿⣿⡿⢿⡟⣫⣿⡌⢀⢤⣾⡿⠀⠀⣼⣿⣋⣽⣯⣇⣾⣵⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠻⣆⠀⠀⠀⠀⢢⡟⣰⣿⣷⣴⣲⢶⣿⣿⣿⣿⣿⣷⡏⠉⠋⠀⠀⣈⣽⣾⡿⠛⠻⣿⠟⠁⠀⠀⠀⢀⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢷⣖⠒⠒⠶⣄⣾⣿⣻⢞⡽⣻⣻⣿⡿⣿⣿⣿⣷⡀⢀⠔⠫⠿⠛⠉⠀⠀⣰⡃⠀⢸⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡹⣦⠀⠀⠀⢝⠻⢿⣿⡾⠿⠿⠛⡶⠟⠛⡏⣩⠝⠁⠀⠀⠀⠀⠀⢀⡾⡋⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⢀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢧⢻⣧⠀⢩⡟⠁⠀⠙⠻⢟⡲⣶⣗⠒⠚⠛⢻⣄⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⣄⢸⣿⣿⡿⢧⣼⡗⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠻⢄⠀⠀⢰⡇⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⢫⡟⡿⣾⣷⠛⠿⣯⣿⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠳⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⣴⡫⢁⣀⡀⠀⠀⠀⠒⣾⣣⣿⡿⣮⣿⣿⣷⣷⠃⣠⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠳⠤⣤⣤⣤⣔⣂⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠑⢶⣄⣨⣼⣿⡿⣭⣛⣿⣿⡏⢸⡁⠛⠛⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠉⣋⣥⣄⣀⣀⣀⣀⣀⣀⣲⡤⣄⡀⠀⠘⣿⣿⣵⣿⣕⣬⡿⢟⡟⣟⣿⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⣀⣤⠶⠋⠉⠀⠀⠈⠀⠉⠉⠁⠉⠉⠙⠓⠛⠓⠒⠛⠃⠉⢻⡷⢟⣴⠟⡇⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠳⠗⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⢯⣴⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠀⠀⢸⣩⡇⠀⠀⠀⠀⠀⠀⠀⠀