⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠖⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠉⢀⣀⡤⣤⣦⢬⣷⡚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⠀⠀⠀⣠⠞⠉⢀⢜⣡⠠⡆⣰⣴⡝⣿⡏⣆⣀⣠⠤⠖⠚⠉⠙⡆⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢠⡴⠊⠁⠀⡴⣵⢻⢸⠀⣇⢹⢿⡇⢷⣇⡏⠁⠀⠀⣀⡀⠀⠀⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠱⡄⢀⡜⡇⡟⠛⣯⠃⠘⠆⠀⣽⣼⣿⣷⠋⠉⠉⠁⡇⠀⠀⡿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠹⣞⢤⢿⣰⢧⣳⣄⢐⣦⣿⣾⣾⣿⣿⠀⠀⠀⢠⡇⠀⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⢹⣮⣗⡛⣟⣽⣟⡛⠛⠿⠿⠋⣿⣹⡀⠀⠀⢸⠁⠀⢰⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡀⢠⠞⠈⠳⣽⢻⣅⠀⠀⠂⠀⠀⢠⣿⣧⣇⠀⢀⣾⡀⠀⢸⡁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣳⠋⠀⠀⠀⠈⠺⠞⠲⣦⣤⣠⠴⣧⡇⣟⣸⣠⣾⠀⢨⠲⣟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⢸⣜⣆⡰⣿⡇⣧⠸⢿⣤⣠⣸⠀⣸⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⡞⢙⣿⣷⣟⣧⣿⣦⡘⠸⣿⠏⡰⢃⡞⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⢳⡸⢿⡿⢷⣿⡏⠳⣿⣦⠀⠸⣡⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈⠳⠿⣿⠏⠀⠀⠈⢿⣼⡾⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠈⢻⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⡼⡏⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⢰⢻⠃⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣾⡞⠀⣠⠀⡴⣰⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡛⢭⣉⣓⠒⠶⠿⠧⢤⣻⣠⠼⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣫⠟⣠⠞⢁⠟⢩⡏⣻⢛⣿⢉⣍⡇⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣚⡵⠋⢡⠞⢁⡴⠋⢠⢟⡴⠋⠉⠉⠳⣼⡇⢻⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠎⠁⣀⡴⠃⢠⠏⢀⡴⠋⣸⠀⠀⠀⠀⠠⡼⡥⡘⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡼⠰⠃⣤⣚⣿⣥⣤⡭⠀⠬⠖⢋⡍⡇⠀⠀⠀⠀⢻⡳⣧⣻⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣠⢞⡣⢶⣋⣩⡖⠋⠹⣍⠀⠀⠀⠀⠸⠇⢻⠀⠀⠀⠀⠀⢧⢹⡙⡽⣄⠀⠀⠀⠀
⠀⠀⠀⡴⠉⢀⡞⣠⠜⠋⠀⠙⢦⣀⣈⣦⠤⠤⠤⣄⣀⣼⡄⠀⠀⠀⠀⢸⠀⢿⠣⣼⠀⠀⠀⠀
⢶⣿⣛⣁⣀⢸⣸⡁⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠙⠢⣇⠀⠀⠀⠀⢸⠀⣸⠀⠹⡄⠀⠀⠀
⠀⠀⠁⠈⠉⠙⠿⡝⢦⡀⣜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⠀⡇⣏⣢⡀⠸⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀⡿⠁⠈⠧⠴⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠦⣄⠀⠀⠀⠀⢠⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⡜⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢰⢿⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡞⠈⡇⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⠃⠀⣷⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⡏⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⡼⠀⠀⢀⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢰⠃⠀⠀⡼⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡼⠀⠀⡴⠁⠀⠀⢸⠁