⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⢿⠀⠀⠀⢀⣠⣤⣤⡤⣤⣤⣤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣄⣠⣾⡿⠗⠋⠉⠉⠉⠉⡛⠣⠈⣟⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢺⣿⠟⠛⠉⠀⠀⠀⢰⣤⣄⣠⣤⢻⡄⠀⠘⡇⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣸⣷⣀⠀⢰⣷⣤⣸⣿⣿⣿⣿⣾⠃⠀⢸⠃⠀⢻⢦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡠⠖⣹⣶⣿⠿⣷⡄⠙⢿⣿⣿⣯⣿⣿⣾⣤⡄⢸⢲⠀⠸⣦⣹⣦⡀⠀⠀⠀⠀⠀
⠀⣠⣮⠕⡺⠙⠿⠿⢚⣟⣇⡠⣦⣙⢿⠛⣿⣿⣿⠀⠀⠈⠉⢇⢀⣿⠈⢉⡗⠀⠀⠀⠀⠀
⠘⠛⠁⡰⠁⡴⡄⠀⠘⣿⢿⣿⣮⣿⣿⣇⠹⠟⣿⡀⠀⡆⣀⣼⣾⢿⡾⠛⠁⠀⠀⠀⠀⠀
⠀⠀⢠⣇⡜⠀⣷⡀⠀⢿⡜⠿⠃⠀⠈⠉⠀⢠⣏⡇⠀⣏⣁⣽⣓⣯⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡟⠀⠸⣧⣟⣿⣼⡾⣄⣀⠀⠀⠀⢀⣸⣷⣻⠀⣇⠀⠿⢽⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠁⠀⠀⠀⠹⣿⣿⠃⣡⡞⠋⢉⣻⢩⣿⢃⣯⣟⢏⠀⢀⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⢿⣄⠇⠀⠈⠉⡀⠿⣇⡼⢩⡋⠉⠉⠚⠿⠧⣱⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠞⢡⣿⣿⡏⢀⠤⢒⡉⢱⠀⠘⡴⢁⣙⠢⢄⣀⡀⠀⢼⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⢹⠼⠋⠁⡀⢻⣜⢄⢧⢎⡠⣮⡿⢲⠀⡆⠉⠑⣦⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡜⠙⠛⢤⡈⣇⠸⣄⠹⡄⠉⢀⡰⠋⡠⣇⣰⠁⢰⣾⣿⣿⣧⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⡀⠈⠛⣖⠋⠣⢬⣶⣪⠔⢊⠀⠘⡉⠓⠋⠙⢿⣿⠃⠙⢆⠀⠀⠀
⠀⠀⠀⠀⣼⠁⠀⠀⠀⡇⠀⠀⠈⣳⠠⡀⠀⠀⠔⠡⢄⡀⠱⠀⠀⠀⣰⡇⠀⠀⠈⢢⠀⠀
⠀⠀⠀⣼⡎⠀⠀⠀⠀⡇⢀⣤⠎⢸⡀⠈⠦⠔⠋⠀⠀⠉⠲⡀⣠⠞⠋⠀⠀⢰⠀⣰⢳⡀
⠀⠀⣰⡏⠀⠀⡇⠀⢀⣥⡾⠉⢀⡼⠃⠀⠀⠀⠀⡄⠀⠀⢠⠛⡗⣶⠦⣄⣐⠲⠚⠁⣸⠇
⠀⠀⢻⡈⠢⢄⡐⣀⣼⡇⡇⡠⠋⠀⠀⠸⠀⠀⠀⠘⢆⢀⡏⠀⡇⣿⠀⢰⠈⠓⠂⠚⠋⠀
⠀⠀⠈⠻⠦⠤⠞⢹⣿⢿⠟⠁⠀⠀⠀⠀⢣⠀⠀⠀⣌⢻⡀⠀⡇⣯⡇⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⢿⡿⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⠏⠀⢠⡇⡜⢻⣼⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡸⢻⣼⡧⣔⡀⠀⠀⠀⠄⠀⠀⠗⢄⠀⠀⠀⠼⠙⡿⣼⣧⠀⠀⠀⠀