⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⣀⣀⣀⡀⠀⠀⣠⡀⣄⣀⡀⢀⣀⢀⣀⠀⣀⡀⠀⠀⢀⣄⡀⢀⢀⡀⠀⣀⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠛⠙⠋⠙⠛⠛⠛⠙⠿⠛⠛⠛⠟⠛⠏⠙⠛⠛⠂⠛⠛⠛⠛⠛⠛⠛⠿⠻⠞⠛⡿⠿⠟⠛⠉⠛⠛⠿⠏⠛⠛⠋⠿⠛⠛⠛⠋⠓⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠖⠛⠛⠉⠉⠉⠉⠉⢙⣿⣿⡿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⡀⠀⠀⠀⢳⣌⣿⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡉⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⠗⠰⡏⠙⠛⠉⢙⣛⠳⠤⢤⣿⣤⡀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠒⠒⠒⠢⠤⠤⢤⣤⣤⡀⠀⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡷⣏⠀⠚⢾⣷⣄⠀⠈⣙⢶⣄⠈⠻⣆⠀⠀⠉⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠀⠘⠀⣿⠁⣤⡀⠉⠛⢧⡄⠉⠳⣿⡄⠀⠙⣧⠀⠀⣧⠀⠈⠋⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠈⢷⣀⣠⡴⠛⠃⢈⡿⠓⠺⣧⠀⠀⠈⢷⠀⠀⢸⣇⠀⠸⣧⠀⠘⣄⠈⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⣦⣀⣤⠶⢻⡏⠀⡄⠀⣼⠁⠀⢀⣼⠀⠀⠀⢸⡆⠀⠈⣿⠀⠀⠸⣧⠀⢹⣦⣻⡍⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢳⡞⠛⣻⠃⢀⡟⠀⡴⠀⣼⠃⠀⠀⣸⡿⠀⠀⠀⣼⡇⠀⠐⣿⣆⣄⢠⣿⠤⣤⣿⣿⣧⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡏⢀⡞⠀⣼⠃⠀⣼⠃⢰⠃⢠⡇⠀⠀⣼⡏⠁⠀⠀⣼⣿⡀⣠⣶⣿⣿⠿⠿⠿⠿⠿⡅⠻⣿⣶⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⢰⠃⡜⢀⣾⠇⠀⣼⠁⢰⡏⠀⣿⠀⢀⡾⣿⣧⣤⣤⣾⠿⠿⠻⠟⠋⠈⠉⠀⠀⠀⠀⠀⠛⠀⢻⣿⡇⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠸⢁⡾⣏⠀⣈⣿⣤⣘⣇⣴⣿⣿⠿⠿⠟⠿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣏⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣇⡀⣠⠶⢺⣧⣼⣷⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⣿⣧⣤⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣍⣿⣿⣄⣾⡷⣿⠿⠿⠿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢸⣿⣅⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⢨⣿⢻⡏⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠚⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⢟⡿⣿⣿⡇⠀⠀⠀⢈⣤⣀⣀⣀⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣾⣿⣷⣦⣀⠙⢷⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣷⡇⠀⠀⣴⣾⣿⣿⣿⣿⣿⠿⠛⢷⣤⡀⠀⣠⣄⠀⠀⣧⣀⣰⣿⣿⣿⡿⠛⣽⣟⡟⠽⣿⣿⡀⠘⣿⣿⣿⠟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠈⣷⣾⣿⣿⠀⠀⢧⣻⣿⣿⣿⣿⣷⣾⣾⣿⣿⣿⣾⣿⠘⠛⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣤⣷⣄⣀⢼⣿⡿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢸⣹⣿⣿⠀⠀⣃⣹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡟⡄⠈⠑⣿⡻⣿⢿⣿⣿⣿⣿⣿⢺⡟⠛⠿⣿⣿⣄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⡾⠿⢻⣿⠀⢺⢿⡿⠛⠉⠻⢿⣿⣿⣾⣿⣿⣿⣿⡟⠀⡄⠀⠀⢨⠙⠻⣿⣿⡻⠿⣷⣴⣶⣴⣿⡅⡬⢿⣇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢿⡀⣠⠾⠻⣦⣀⣬⣿⣛⣩⣵⣾⣿⣿⠋⠀⠀⣀⢰⠀⠘⠃⠀⠀⠉⠙⠛⠓⠉⠁⠀⠀⠀⠛⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠁⠀⠐⠛⠙⠛⠛⢛⣯⣽⣿⠟⠡⠀⠀⢀⡿⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⠀⠚⠛⠋⢠⣤⣶⠟⠀⢠⠟⠇⠀⠀⠀⠀⣿⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⣶⣖⠀⠠⠤⣀⢠⣀⣠⡄⠀⠀⠐⠁⢀⣠⣤⣾⣿⣿⠏⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡟⣿⠻⣶⣄⡙⠛⠿⠙⣧⠀⠀⣄⣾⣿⣿⣿⣿⢿⣿⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣤⣿⠛⠈⠻⣿⣿⣷⣜⣤⣤⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⠀⣿⣿⠛⢠⣾⣿⣿⣷⣤⡀⣻⡄⠀⣿⣿⣿⣿⣿⣟⡟⠋⠙⠻⢿⣦⣼⣿⣿⣿⣿⣿⣇⣁⣠⣶⣷⣤⣾⣿⣿⣿⣿⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠺⣇⢀⣿⣿⠀⣤⣾⣿⣿⣿⣿⣿⣿⣷⡀⠸⣿⡟⢻⣿⣿⣿⣧⣤⣀⣰⣈⣉⣩⣍⣉⣉⣭⣭⣿⣿⣿⠟⠉⣿⣿⡙⠙⣿⣿⠿⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣻⣿⣿⣀⣶⣿⣿⣿⣿⣿⣿⠿⢛⣿⠀⠉⣿⣀⢿⣿⣿⡚⠫⠿⠿⠿⢿⡿⢿⣿⣿⠿⠛⠉⠉⠁⠀⢀⣿⠈⠁⣴⣿⣿⣆⠀⠈⠙⣿⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠿⣿⣿⣿⣿⣿⡿⠟⠋⠁⢀⣾⡿⠃⢰⣴⣿⡿⣾⣿⣿⡿⢤⠀⠀⠀⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⢀⣟⠁⢠⣴⡿⠋⢰⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀ ⢙⢿⣦⣿⡿⠟⣩⡅⢠⣾⡷⢰⣿⣿⢣⡇⠀⣿⠈⠻⣾⣿⣯⠉⠂⠀⠀⠰⣾⠿⠿⠿⠛⠛⠛⠋⠀⠀⠈⡈⣠⣿⠟⠁⠀⢸⡟⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣶⣄⡀ ⠿⠛⠉⢠⣴⡿⠁⣰⣿⡿⢠⣿⣿⡿⢸⣧⠀⣿⢠⠀⠀⠉⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣴⣿⠟⠃⠀⠀⠀⣼⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣹⣿⣿⣿⣿⣿⠃⣼⣿⣿⡇⣸⣿⠀⢿⡼⡇⠀⠀⠀⠻⣄⠀⢀⠀⠄⠀⠀⣠⣄⣀⣀⣀⣴⣿⡿⠋⠀⠀⠀⠀⣰⠏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣾⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⡇⣿⣿⣧⣾⣧⡹⣄⡀⠀⠀⠟⣷⠈⠱⣦⣿⣿⣿⣿⣿⣿⣿⠟⠋⠠⠀⠀⠀⠀⣼⠟⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⠙⣷⣦⣀⠀⢉⡀⠤⢙⡻⠿⠿⠛⠋⠉⠁⠀⠀⢀⠀⠂⣴⡿⠋⠀⠀⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿