⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣿⣿⣿⡿⠿⠟⢿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣿⣿⡿⡿⠅⠀⠀⠀⠀⠈⠀⠉⠹⠉⠛⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣽⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣽⣿⢟⡁⣻⣶⣽⣿⣶⣿⣿⣷⣷⣶⣦⣯⣟⢂⢦⣆⣛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣦⣈⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣟⣿⣿⣿⣿⣿⣿⡿⠉⢝⡉⢀⣝⢿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣾⣿⣿⣿⡿⢫⡿⡁⢠⣿⠀⠈⣸⡍⢠⡶⠆⠀⠉⣿⣿⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣽⣿⡇⣾⣾⣷⣿⣷⣷⣣⣿⣷⣾⡇⠀⠄⡴⢫⠈⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⢻⣿⣏⣿⣿⣿⢰⣿⣟⣽⡟⣽⡿⢻⣿⣏⣿⣄⢰⣾⡏⣸⢷⡟⣻⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⣿⣯⣿⣿⡿⣸⣻⣿⣿⣿⣷⣦⡾⠋⣽⣷⣯⣿⣿⣾⣟⣼⣇⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⢿⣾⡅⣿⠱⣿⣟⡿⠿⠟⠁⣼⣿⣿⢿⣿⢿⣿⣟⣿⣿⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡴⢦⣀⡀⠀⠀⠀⢀⣀⣀⣸⣿⣿⣿⣇⣟⣾⣷⣌⣡⠀⠀⠘⠿⡻⢡⣿⣷⣿⣅⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡤⠖⠋⠀⠀⠈⠙⠿⣿⣟⠉⢉⢽⡿⣰⣿⢿⢿⡇⠈⠙⠛⠋⠀⠀⠀⢰⡇⢸⣿⡿⣻⣿⣿⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢀⡟⠀⣿⣹⣸⢸⣇⠀⠀⠀⠀⠀⠀⢀⡼⠻⢶⣾⣣⣼⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢹⣟⡏⢸⣿⣦⠀⠐⢦⣤⣄⠀⠀⠀⢀⣼⣿⣽⡿⠃⠉⠙⠒⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⡇⣹⣄⠀⠀⠀⠀⣀⠀⠀⣸⠃⠀⠀⣸⣿⡂⢸⣟⣿⣷⣄⠀⢀⣠⣤⣶⣞⣻⣿⠷⣿⠁⠀⠀⠀⢀⣠⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢻⢿⣮⣳⣄⠀⠀⣿⣿⣦⢇⣠⣶⣺⣿⣿⣌⣼⠈⢿⣿⣿⣿⡿⠛⢿⡿⢟⣿⣿⣾⠇⠀⣀⡴⠾⠋⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢈⣿⣿⣿⣿⣧⣐⠸⣥⣿⣿⣷⠋⢸⣿⣯⣿⡇⠀⠀⣿⣿⣿⣱⣶⣦⡙⢎⣾⡟⡞⢀⡾⠁⠀⣠⣾⡆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⣇⠻⣟⣟⣿⣿⣦⡹⣿⣿⡵⠀⣾⣿⠹⣿⣿⠀⢀⣼⣟⣿⣿⠉⠉⠙⢓⣿⣿⣡⡟⠁⠀⣼⢿⡿⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣦⠀⠉⠛⠻⣿⣷⣿⣍⢀⣼⣿⣿⣾⣿⡟⠀⠘⠘⠋⢻⣟⠀⠀⠀⣸⣿⣿⡟⠁⠀⣼⣯⡞⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡍⢧⠀⠀⠀⠈⢻⣿⣿⡿⢟⣽⣿⡿⣿⣇⠀⠀⠀⠀⢸⣟⠀⠀⠈⢻⣿⣿⡄⠀⠼⠋⣁⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡷⠘⣆⢤⢀⡤⠿⠛⠉⠀⣾⣿⡿⠁⢨⣿⠀⠀⠀⠀⣼⠇⠀⠀⠠⢶⣿⡭⢁⣤⢶⡿⠁⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣞⠁⠉⠻⣮⡿⠂⠀⠀⠀⢈⡿⠯⠇⢀⡼⠃⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢹⣿⠋⣡⠟⢁⡼⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣧⡀⣠⡟⠀⠀⠀⠀⣰⠏⠀⠀⣠⠟⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠋⣷⡴⠃⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⣰⡟⠀⠀⣰⠋⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⣹⠁⠀⢰⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠠⡄⠀⠀⢸⡏⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠁⠀⠀⠀⢀⡟⠀⠀⣾⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⡄⠀⣸⠇⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢹⡀⢀⠀⠀⣼⡇⠀⠀⣿⣷⡀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠹⣶⠇⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢷⣾⣦⠀⣿⡇⠀⠀⣿⣿⣳⣄⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣠⣴⠞⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣿⣿⡍⣿⣳⠀⣀⣿⣿⣿⣿⣿⣦⣿⣿⠀⠀⠐⣦⣴⣿⣿⡇⠀⠀⠀⡸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣟⣻⠿⠏⣛⣩⢼⣿⣮⣛⠿⣿⣠⣤⣾⣿⣿⡿⣹⠃⠀⠀⢠⣿⣻⣿⣿⣶⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠻⣿⣿⣿⡻⢉⣉⠀⠉⠻⣿⡹⣛⣿⣿⣿⣿⣿⡟⣴⠏⠀⠀⠀⣼⠃⣿⣿⣟⣻⣿⡇⠉⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⠄⠿⣿⣿⣷⣿⠁⠀⠀⠀⠈⠻⣄⠘⣿⡁⣿⣿⣽⠋⠀⠀⠀⠘⠁⣼⣿⣿⠻⢿⢸⡇⠀⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡟⠀⡀⢹⣞⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠘⣧⢸⣿⠁⠀⠀⠀⠀⠀⢰⡏⢿⣿⠀⠀⠘⠃⢰⡟⠀⠀⠉⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⡇⣸⣷⠀⢿⡽⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣶⠚⠃⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⢣⣿⣿⠀⠘⣷⣿⠀⠉⠓⠀⠙⢶⣦⣤⣴⣾⣟⠍⣀⣤⣤⡾⠓⠧⣄⣀⣈⣿⣧⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⢸⣻⣿⠠⠀⢻⣿⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣶⣿⠿⠛⠁⠀⠀⠀⠀⠉⢻⣿⡏⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣧⣼⣿⣿⡇⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⣲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⠍⣿⣿⣿⡇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣰⣾⡶⠖⠒⠳⢦⣄⡀⢠⣿⡷⣷⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⢰⣿⣯⢿⣿⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣻⣟⠁⠀⠀⠀⠀⠀⠙⣿⣾⣿⣿⣿⣟⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢼⡃⠘⣿⣼⣾⣿⠀⠀⠀⣇⠀⠀⠀⠀⣤⣄⣤⣾⡿⣏⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣿⣿⣿⣿⣷⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⢦⣻⣥⡿⣿⠀⠀⠀⣿⠀⠀⠀⠀⠛⠉⠉⠀⠀⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠈⡻⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿⣄⡐⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢦⠀⠀⠈⣷⠠⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⣿⠇⠀⠙⢻⣧⢸⠀⠈⠉⠉⠑⠛⠿⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡙⣶⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣌⠦⠀⠀⢿⣆⠀⠀⠂⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠻⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣾⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⢿⣦⡀⠘⢿⣧⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠖⠶⠴⢾⣿⠀⠀⠙⢿⣷⣮⣿⣷⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣻⣿⠗⠋⠀⠿⠀⢀⣤⣾⣿⠏⠻⢿⣿⣷⣄⠀⠀⡏⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣯⣧⡀⠀⠀⠀⠀
⠀⠀⢠⡤⢞⣡⣼⠷⣤⣀⣶⣿⠿⠿⠋⠀⠀⠀⠈⠛⠿⣿⣶⡇⠀⢀⣄⣀⢼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠄⠙⠋⠉⠻⣿⣷⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡽⠿⣷⣦⣤⣤⣶⡾⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠘⢯⡉⠛⠛⠛⠛⠿⠿⠯⣭⣽⣂⣀⣄⣀⣤⡠⠤⠀⠀⡀⠀⠀⠀⠀⡰⣯⣟⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀