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⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⢈⡁⠅⠈⠉⠐⠒⠤⣈⢳⣄⠆⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡠⢎⠵⠊⠁⠀⢀⣠⡤⡶⣶⣶⣦⡷⢿⣦⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣺⠜⠁⠀⣀⣤⣾⣿⣿⣿⣿⣷⣭⣻⢵⣀⢿⡼⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡜⡋⢐⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡹⡉⢃⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣥⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣧⠈⠚⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⠟⠃⣸⠃⠠⢽⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣿⣿⣿⡯⣿⣶⢄⡰⠋⠠⣶⣾⢼⣿⣿⡏⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠊⠉⡿⣿⣇⠈⠉⠀⠀⠀⠀⠉⠁⢠⣿⡿⠓⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢦⡀⠀⠀⠀⠀⢀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣼⠋⡷⣦⣴⠾⡏⠣⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣹⡟⡅⠟⠻⣝⣁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠤⠊⢡⢃⡿⢿⣿⣤⣤⣿⣿⠿⡞⢇⠑⠢⢀⠀⠀⠀⠀⠀
⠀⠀⠀⡤⣾⠁⠀⠀⣇⣞⡻⡿⣿⣿⢻⣿⣿⣿⣳⣸⠀⠀⠀⣷⠤⡀⠀⠀
⢆⠈⠁⡜⠁⢑⣒⡆⠋⠉⡼⣾⢷⣏⣘⣷⢷⡷⡈⠙⢰⢒⡒⠁⠙⡀⠉⣀
⠀⠉⢰⠓⠉⠪⣛⠣⢄⠜⣼⣏⣿⠇⠀⣿⡞⣷⠑⡀⠜⢘⠣⠊⠐⢇⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⢈⡁⠅⠈⠉⠐⠒⠤⣈⢳⣄⠆⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡠⢎⠵⠊⠁⠀⢀⣠⡤⡶⣶⣶⣦⡷⢿⣦⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣺⠜⠁⠀⣀⣤⣾⣿⣿⣿⣿⣷⣭⣻⢵⣀⢿⡼⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡜⡋⢐⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡹⡉⢃⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣥⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣧⠈⠚⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⠟⠃⣸⠃⠠⢽⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣿⣿⣿⡯⣿⣶⢄⡰⠋⠠⣶⣾⢼⣿⣿⡏⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠊⠉⡿⣿⣇⠈⠉⠀⠀⠀⠀⠉⠁⢠⣿⡿⠓⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢦⡀⠀⠀⠀⠀⢀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣼⠋⡷⣦⣴⠾⡏⠣⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣹⡟⡅⠟⠻⣝⣁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠤⠊⢡⢃⡿⢿⣿⣤⣤⣿⣿⠿⡞⢇⠑⠢⢀⠀⠀⠀⠀⠀
⠀⠀⠀⡤⣾⠁⠀⠀⣇⣞⡻⡿⣿⣿⢻⣿⣿⣿⣳⣸⠀⠀⠀⣷⠤⡀⠀⠀
⢆⠈⠁⡜⠁⢑⣒⡆⠋⠉⡼⣾⢷⣏⣘⣷⢷⡷⡈⠙⢰⢒⡒⠁⠙⡀⠉⣀
⠀⠉⢰⠓⠉⠪⣛⠣⢄⠜⣼⣏⣿⠇⠀⣿⡞⣷⠑⡀⠜⢘⠣⠊⠐⢇⠈⠀