⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢟⣡⣤⣴⣶⣶⣿⣿⣿⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣰⣿⣿⣿⣿⢿⣻⣯⣿⢯⣿⣟⣿⣿⣿⣿⣿⡶⠤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠋⢛⣿⡿⣿⣻⣷⢿⣯⣿⡿⣽⣿⣻⣿⢾⣟⣷⣿⣻⣿⣟⣶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣠⣿⡿⣟⣿⣯⣿⣟⣯⣷⣿⢿⣳⣿⣯⣿⣟⣿⣾⢿⣽⣯⣿⣿⣄⣀⣀⣀⣠ ⠀⠀⠀⠀⠻⣿⣿⡿⣿⣿⣿⢿⣧⣿⢿⣻⣼⣿⣿⢧⣿⣻⣼⣿⢿⣿⣟⣿⣻⣿⢿⣿⣿⣿⠇ ⠀⠀⠀⠀⢠⣾⣿⣿⣿⣻⣿⣿⡾⣿⣻⣿⢯⣷⡿⣿⣯⣿⢿⣯⣷⡿⣿⣟⣯⣿⢿⣻⡟⠁⠀ ⠀⠀⠀⢠⡿⣿⣿⣿⣻⣽⣷⢿⣻⣟⣯⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⣿⡄⠀ ⠀⠀⠀⠈⠀⣿⣿⣿⣿⢿⣾⡿⣟⣿⣿⣿⡿⣻⡟⣿⣿⣽⣿⣿⣽⣿⡿⠙⣿⣯⣿⣿⣽⣷⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⡿⠋⢀⡿⢄⠘⣿⣿⣿⣿⡿⣿⣇⠄⢸⣿⣯⣿⠙⢿⡇ ⠀⠀⢀⣾⣿⣿⢿⣿⠏⠙⠻⣿⣿⣯⢀⡤⠾⢶⢦⣌⢻⣿⣿⣿⣿⣿⢗⠓⣺⣿⢿⡿⠀⠀⠀ ⠀⠀⣾⣿⣿⣿⡆⢹⡀⠀⢀⠽⣿⠻⡜⠅⣰⣿⣴⢂⣹⣿⡿⡾⢫⣷⣿⠘⠉⢸⠈⠁⠀⠀⠀ ⠀⠀⠁⢻⣿⡏⠛⢀⣷⣤⣈⢂⠃⠀⠀⠀⢿⣛⡟⠀⠈⠀⠘⡀⠸⠯⠇⠀⡰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠈⠉⠹⣟⣿⣽⣶⠄⡀⠃⠀⠀⠀⠠⣶⠆⠀⠈⠀⠀⢈⡵⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢻⡛⠄⠀⠑⠀⠠⠄⣀⡀⠉⣉⠡⠄⠒⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⢒⣖⡒⠒⠒⢄⡀⣀⠔⣱⡟⠓⢄⡉⠉⠉⠀⠀⠀⠀⠀⡠⠄⠊⠻⣿⡦⡄⠀⠀⠀⠀⠀ ⡞⠰⠋⠀⠸⡦⣠⠠⠝⠁⠀⡿⡄⠀⠘⡽⣶⣦⣤⣤⠤⠂⠘⢴⠴⡀⠀⢸⣷⠸⡀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⣃⠈⠒⠒⠒⢺⣯⢳⡀⠀⠙⠲⣻⣿⡝⠀⠀⠀⠀⠑⢥⣤⣾⢿⣳⠇⠀⠀⠀⠀ ⠹⠿⠿⠿⠟⠛⠁⠀⠀⢀⠎⠈⢷⡹⢦⣊⣵⡿⠋⠉⡰⠀⠀⠀⠀⡸⣧⣻⠾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⣹⢧⣯⣟⣷⣄⠀⠬⠔⠲⡶⣿⣗⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣬⣛⢿⣷⣟⣞⣼⣲⣷⣤⣤⣤⣤⣿⣲⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣏⡀⢺⣿⣯⣷⣿⢾⣿⣽⡾⠋⢹⣿⣽⡿⣯⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣧⣀⣱⠟⠻⢷⣿⣿⠟⠋⠀⠀⠈⣿⣯⣿⢿⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣽⠿⠛⠟⣳⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠁⣠⣾⢟⡫⣝⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢼⡻⣽⠧⠗⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀