⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠋⠉⠀⠒⠲⢭⡒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢎⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⠤⠖⣂⠋⠭⡉⢍⠩⢍⡑⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⠃⡴⢨⠑⣬⠓⢌⡙⢢⡙⡌⢃⠦⣈⠻⢄⠌⡳⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⠔⡒⠩⣉⠔⣂⠦⣹⠀⢬⠱⡌⣿⣎⠦⡈⣇⠴⢉⡎⠔⠊⠀⠀⠣⡅⢢⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡴⠛⠒⠈⢉⡿⢉⠜⣠⢓⢸⡀⢎⡱⢸⡷⣾⢖⢠⣙⣦⠠⠴⡀⣀⢤⠀⢀⣈⣟⡎⢌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠘⠣⠌⢆⣚⣐⠬⡖⡟⠣⡜⠡⣿⣹⠈⢦⢡⢹⠻⡑⢆⠱⣊⠜⣂⠖⡈⢷⡈⠆⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⣁⣀⠤⢆⡰⢂⡽⠑⣤⣿⡳⢌⡁⢿⡼⡄⠈⢣⠂⣇⠈⢮⡑⠤⡙⡔⣊⢳⡈⢷⡈⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡼⢃⣆⡟⣈⠦⣑⢃⡿⣰⢡⠏⢻⡰⢡⠸⣟⠆⠀⠀⠻⡘⡄⠀⠙⢇⠱⡘⠤⢂⢷⠈⣧⠡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⡡⠋⣿⠡⢎⡔⢣⠎⣿⠃⣼⠀⠈⢣⡑⢆⢻⠀⠀⠀⡀⢭⣿⣄⣴⣬⠳⣌⠱⡈⠼⣇⢸⡃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡿⠁⠀⡏⡸⢆⠸⣁⠾⣷⠈⡇⠀⠀⠀⢹⡀⠎⡀⠀⠀⢹⣿⣿⣿⠿⠿⠁⢸⣆⢱⠸⡏⣆⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡼⠁⠀⠀⡧⡑⣬⠲⢡⢺⣿⠂⡇⠀⠀⣀⣀⠙⢦⣇⠀⠀⠀⠉⠀⠀⠀⠀⠐⢻⠈⣧⡂⡍⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡇⢅⣾⡃⢇⣚⣿⣇⣧⡀⣷⣿⡿⠧⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⠿⣽⣷⣞⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡇⡾⠀⢧⢒⠸⣿⣚⣯⢟⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⢟⣶⢿⣏⢧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢣⡗⠀⠘⣆⢣⡿⣝⡮⣏⢷⠀⠀⠀⠀⠀⠀⠀⣞⡩⠜⠋⠀⠀⣠⣴⣹⣏⢎⣿⣯⣖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⠇⠀⠀⠘⢿⡷⢹⡞⣽⢺⡧⣤⣠⣀⣀⠀⣀⣠⣠⣤⣴⠆⠁⠘⢻⣿⢋⠆⣷⣳⣯⢗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡉⣿⡜⣧⣿⡱⣏⣿⣟⡽⣫⠿⣟⣿⠜⠁⠈⠑⢾⣷⢨⢸⣿⡿⡥⣾⠋⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣷⢻⣖⣯⡳⣽⣿⣜⣾⡱⣏⣟⣻⡄⠀⠐⠀⣾⡟⠄⣾⡿⣱⡟⠁⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⣇⠻⣼⣏⡿⢻⣿⣿⣷⡭⢶⡹⠆⠀⠀⢰⢯⡇⣸⡟⣶⡏⠀⢀⠀⠀⠀⢣⠄⣠⢤⣶⣦⠤⠤
⠀⠀⠀⠀⠀⠀⢀⠀⣴⣶⢤⣄⣿⣿⢦⠉⢿⠂⠀⠻⣮⣿⣿⣧⣛⡏⠀⠀⣮⣿⣼⢏⣾⠏⡀⠀⢸⠀⠀⡠⢀⣾⣯⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⣿⡼⢿⣿⡜⢇⠼⠀⠀⠀⠻⣿⡿⣿⡣⣿⠀⠀⣧⣿⢛⣿⠃⢄⠃⠀⣸⢀⢀⠃⢸⣿⣇⣧⠀⠀⠀⠀
⠀⠀⠀⢠⡎⣠⠁⠀⠀⠀⢰⡇⣻⢸⣵⠈⠻⡇⠀⠀⠀⠘⢿⣾⣻⣯⣇⢸⣿⣯⡿⡁⠎⢰⠀⠀⣇⠀⠀⠀⠘⣿⣿⡿⣧⠀⡀⠀
⠀⠀⠀⠀⢀⠃⡀⠂⣀⣤⣾⢻⣼⡸⢾⠀⠀⠈⠀⢹⠠⠀⣇⡈⠻⣵⢼⣜⣷⠟⠡⠘⣀⡏⠀⠐⠃⠀⠀⠀⠀⠻⣿⣿⡽⣣⡄⠠
⠀⠀⠀⠠⡦⠩⠄⢺⣟⡿⣏⣟⣮⣟⠇⠀⠀⠀⠀⠀⡇⠀⠀⠁⠓⠠⢟⠟⡃⢬⡵⠒⠊⠀⠀⠀⠀⡤⠀⠀⠀⠀⠈⠙⠻⠟⡗⠀
⠀⠀⠀⠀⢳⡂⠀⠀⠻⠼⢿⣫⡮⠋⠀⠀⠀⠀⠀⢰⠀⠀⠀⣠⡒⢼⣾⣶⠆⢂⠘⢢⠀⠀⠀⠀⠀⠠⠀⠢⣀⠀⢀⡠⠂⠈⠀⠀