⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡠⢤⡴⠶⠛⣛⢿⢿⣿⣿⠻⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢤⣴⣚⣫⡁⠀⠀⠀⠤⠊⠁⡔⢡⢃⡎⠘⢠⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠻⢭⢛⡷⣤⠲⡄⢊⠄⠋⡠⠁⡼⠀⣧⠘⡄⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠙⠴⣋⠉⢷⡝⢤⣎⡀⢰⠇⠀⡌⠀⠁⠘⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡤⠟⠈⡀⠁⠈⠻⣇⢯⣄⣀⡀⠀⠘⠀⠐⠩⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⡦⠔⠚⢷⡈⠀⠐⠋⠂⠳⠁⢹⣿⣿⣷⣶⣤⣤⣔⣲⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠁⠀⠀⠃⠻⣤⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠞⠛⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣸⡀⠀⠀⠀⠀⣿⣿⠄⠀⠀⠸⣿⣿⡟⠄⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡇⠱⡀⢀⠃⠀⢹⣹⡷⠀⠀⠀⢸⣯⠿⡆⠀⠀⠀⣰⣾⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣷⣒⡛⣻⠇⠂⢸⠐⣿⢉⡶⠄⣻⣿⣦⣼⣆⠀⠴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣧⠥⢼⠿⡄⠀⠤⣆⢻⠀⣘⣋⣱⠞⢿⠿⣿⣣⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⠁⣀⣼⣀⣿⡔⠒⠛⠋⠁⠀⠈⢨⣇⠈⠻⣇⣻⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⡥⢿⠀⢻⣟⣛⡄⣠⢠⡀⡄⠞⣾⠢⢤⣀⠀⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡞⢣⠐⠺⠀⢈⢯⠝⣾⠋⢠⣇⡇⠱⡅⠟⢞⠫⣕⠺⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣸⡇⠈⣤⣴⡆⢸⡿⡞⡃⠀⣼⠃⡇⠀⠱⡘⡆⢿⠻⣥⠶⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡧⢡⠀⠹⣿⣇⠘⣄⡰⢇⣀⡿⢸⣿⠀⠀⢱⡟⣤⣷⣈⢣⣀⡉⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢧⢸⠀⠀⣿⣿⡆⣯⣶⠿⡟⣇⢶⣿⠖⠚⡿⡟⣠⣽⡝⡿⣇⠈⠉⡛⠻⣷⡦⠀⠀⠀⠀⠀⠀
⠀⢸⢸⠀⠀⣹⣿⣿⣿⠏⠀⡟⢀⣸⠟⣴⣞⣵⣏⢹⣏⠀⢃⠉⠳⣷⣶⠿⣿⢤⡀⠀⠀⠀⠀⠀
⠀⢸⢸⠀⠀⢸⣿⣿⣿⣷⠀⣏⣍⡻⠚⠋⣿⡿⢏⡀⢹⣦⢸⠀⠀⣈⣷⠳⣻⣍⠛⢦⡄⠀⠀⠀
⠀⢸⢸⠀⠀⠀⠙⠛⢻⡏⡟⣿⣧⣯⣀⣠⣼⡟⢄⠙⠶⢫⠙⣧⡾⢭⣿⣳⣑⣟⡿⢶⣇⠀⠀⠀
⠀⠘⣾⡄⠀⠀⠀⠀⣰⢱⡗⣿⢸⡝⡷⡇⣿⣧⠈⢳⣄⠈⢿⣦⢻⡀⠈⢣⡟⣻⣿⣆⣅⠀⠀⠀
⠀⠈⡿⡇⠀⠀⠀⢰⡏⢸⡻⢽⢰⣷⣡⢣⡿⡼⣷⣜⣿⣷⣞⣻⣏⣏⠉⠙⣿⣹⡿⣿⣿⡄⠀⠀
⠀⠀⣿⡇⠀⠀⠀⠈⣷⣿⣿⣸⡟⠉⢿⡿⢷⢳⠸⣽⣿⣿⠙⠟⣿⡝⣷⣄⠈⢿⣿⠘⣿⣿⡀⠀
⠀⠀⢷⡇⠀⠀⠀⢰⠃⣿⢻⡗⣧⣀⡈⢡⣋⣎⣧⣹⢛⣿⢦⡀⢘⣿⡟⠛⣷⣿⣌⢆⠹⡉⠁⠀
⠀⠀⢸⣏⠀⠀⠀⠾⣵⣷⣿⠅⡿⣉⣿⡾⡏⢹⣿⣿⡿⠁⠞⣿⣅⢻⣹⣼⣿⡟⣿⣎⠳⣷⡀⠀
⠀⠀⢸⣽⠀⠀⠀⠀⣽⣾⡟⠚⣽⣯⣿⢡⡇⡎⣿⡇⡇⠀⣼⣿⣿⣿⣿⣿⣯⣧⢹⣿⡆⣿⣦⠀
⠀⠀⢸⢾⡀⠀⠀⢀⣿⢰⠇⣜⣹⣷⣾⣿⣧⣦⢿⣯⡹⣝⣻⠛⢮⡙⣹⢸⣾⢿⣿⣿⣿⣿⡄⠀
⠀⠀⠘⡞⡇⠀⢀⣾⣾⣿⣠⢻⣿⡟⣿⡏⣽⡇⠀⣿⡿⣿⣿⠀⡄⣹⡾⣝⣿⡊⢿⣿⢿⣿⡇⠀
⠀⠀⠀⣟⣯⠀⠸⣿⠿⣿⣷⣿⡿⡇⣹⣧⣾⢹⣶⣼⣗⣈⡿⢐⡟⣿⣿⣿⣿⡅⢺⡽⣿⣿⡅⠀
⠀⠀⠀⢻⣾⠄⠀⣯⣣⣿⣯⣿⣿⠁⠹⣿⣿⠘⡟⣿⡭⢹⣿⣎⡇⢘⢿⣿⡟⠠⢁⣻⣷⡟⠁⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⣿⣯⢷⡐⣿⡧⠐⣿⣽⡿⣿⣿⢿⣿⣿⡿⢿⣏⣧⢦⣿⣟⠯⠉⠀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣯⣿⣿⣾⣧⣥⣽⣿⣧⣿⣟⣿⣿⣿⢱⢣⣹⣿⣿⠈⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠳⠞⠶⠻⠏⠁⠀⠀⠀⠀⠀