⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠳⢤⣈⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡇⡸⠤⠤⠤⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠉⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢒⡶⣤⠞⠋⠁⠑⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⢀⡶⠦⢤⡀⠸⠷⢦⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣼⣾⠅⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠉⢻⠁⣸⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢼⡴⠋⠀⡀⠀⡼⡀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠙⡄⢠⠀⡎⢀⡟⠛⠓⠾⡄⢠⣤⡴⡄⠀⠀⠀⢤⢤⣶⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⣠⠞⠀⠀⢰⢀⣸⠃⢇⠀⠀⠀⠀⡏⢻⡉⠲⠄⠀⢹⡈⣦⠇⢸⠀⠀⠀⠀⠘⣾⣀⢈⡷⠀⠀⠀⠺⢦⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⢰⠏⠀⠀⠀⢸⠁⡏⠀⠘⢄⠀⠀⣊⣧⣤⣵⡄⠀⠀⠀⠃⢸⠤⣏⣇⠀⠀⠀⠀⠉⢻⡛⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⡟⣸⠀⡆⠀⠸⣤⡷⠟⠀⠈⠳⣄⠉⢹⠝⠋⢝⢦⡀⠀⣸⣸⡇⠀⣼⡄⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢀⡇⣿⡀⢣⠀⠀⡟⢰⠁⢰⠀⠀⠈⠑⢺⠀⠀⠈⡇⡸⢦⣿⣷⣹⣰⣻⣇⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⢯⢧⣸⣷⣀⣇⠘⡀⢸⠀⠀⠀⠀⠈⠦⠤⠜⢱⠃⣴⠗⢻⡏⠑⠄⢭⠽⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⡀⠀⠀⣰⠋⠀⠀⠀⠀⠈⠛⢻⡎⢉⡆⠭⠁⢀⣤⠤⠤⢄⠀⠁⠁⣸⠞⠁⠀⢸⡟⠳⢿⢾⡆⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⡰⠁⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢸⣰⠻⣄⡀⠀⠘⠄⠀⠀⠸⣀⣤⡞⠁⠀⠀⠀⠸⣇⠀⣸⠘⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⡸⠁⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠉⡽⣙⢿⡋⣵⠹⣧⠀⣀⣀⣀⣠⡽⠦⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀
⠀⠀⣼⠁⠀⠀⠀⠀⠀⢰⠃⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢾⣼⠟⡏⠉⠈⣆⣼⠉⠁⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀
⠀⢰⡇⠀⠀⠀⠀⠀⠀⡎⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⢋⡔⠁⣸⠃⠀⠀⠀⠹⡄⢀⣠⢴⣶⣒⣦⡄⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀
⠀⢸⡇⠀⠀⠀⠀⠀⢰⢁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⢀⢎⡀⢠⠻⢄⠀⠀⠀⠀⠉⢉⡏⠉⣁⣤⢟⡗⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠘⣇⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣲⣿⡀⣞⡏⠀⡇⠈⢝⠀⠀⠀⠀⠀⣞⣾⣿⠽⢾⢏⠀⠀⣿⡸⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀
⠀⠀⢻⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢳⠏⠙⠻⡄⠀⣰⠁⠀⣘⣀⠀⠀⢠⠞⡀⠀⠀⢠⢾⠟⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠹⣄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡟⠀⠀⣠⢿⡋⠁⠉⠚⡁⠈⡍⠑⢡⠀⠈⠑⡶⣫⠋⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠛⢦⣀⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠘⣇⠀⠀⠙⠦⣍⣾⡭⢭⣇⣀⣗⣒⣒⣣⣒⣯⠒⠉⠀⠀⠀⣼⠃⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⡼⢣⡞⢳⣘⡇⠀⠀⠀⠈⠁⡟⠾⢿⠗⠚⢹⣧⣤⣴⠃⠀⠀⠀⢀⡼⠃⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠥⠞⠀⠀⠁⠀⠀⠀⠀⠀⡜⠀⢠⠏⠀⠀⣾⠀⢠⡏⠀⠀⢀⣠⣞⣀⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⠏⠀⠀⢠⡇⠀⡾⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡏⠀⠀⠀⣸⠁⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢰⡲⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀