⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⣶⣄⠀⠀⠀⠀⢀⣴⠟⠋⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠈⠛⠿⣿⣦⣀⡴⠟⢁⣴⣦⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠈⠛⠛⠁⣰⣿⠟⣿⡟⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣄⣼⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡃⠀⣿⣷⣿⡿⠿⢿⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⡘⢿⣧⠛⠛⠋⠀⠀⠿⠁⠀⠀⠀⠸⠿⢦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀⠀⠀⠀⠀⢠⡤⠀⠀⠙⠃⠈⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⣠⣴⡶⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⡆⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀ ⢀⢀⣀⣀⣤⣶⣶⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢶⣦⣄⣀⠐⣶⣄⣈⢻⣷⡀⠀⠀⠀⠀ ⠘⠛⠿⠿⢭⣅⣀⣠⡀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢸⣿⠀⢻⣷⡈⠙⢻⣿⡉⠛⠻⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⡀⠀⢸⣿⠀⠐⢻⣷⡀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢠⡞⢷⣦⡀⣿⣿⣷⠀⣾⡏⠀⠀⠈⢿⣧⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⡿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡴⠋⠀⠀⠙⢿⣿⡟⣿⣧⣿⡇⠀⠀⠀⢘⣿⣇⣼⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡉⠁⠈⠿⠟⠀⠀⠀⢺⣿⣿⣿⡿⣧⣤⣤⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⢸⣿⢠⣴⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠁⠘⣿⣧⠀⠄⠀⠀⣉⣽⣿⠃ ⠀⠀⠀⠀⠀⣰⣿⠃⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⢸⣿⠈⠛⠟⠛⠁⠀⠀⠀⠐⠒⠛⠉⠉⠀⠀⠀⠀⢻⣿⣀⣤⣴⣿⠟⠋⠀⠀ ⠀⠀⠀⠀⢠⣿⡇⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⢀⣿⠟⣿⡆⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⢻⣿⣿⡟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢷⣤⣿⣿⣷⣀⣤⣾⣆⠀⠀⣸⣿⠀⠸⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⠉⠁⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣾⡿⠋⠙⢿⣦⣠⣿⠃⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⢀⣤⣤⠀⠙⢿⠇⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢴⣿⣿⣁⣀⣀⣠⣤⣤⣤⣤⣤⣴⣶⣦⣤⣸⣿⣿⣆⠀⣀⣀⣀⣀⣀⡀⢀⣀⣤⣴⣿⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⣻⣿⡿⠋⠉⠉⠙⠻⢿⣭⣉⡛⠻⢈⣿⣿⣯⣭⣭⣿⣿⣿⣿⠛⣩⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⣀⣴⣾⠟⢹⣿⣿⠋⠉⠀⠀⠀⠀⠀⢹⣿⣾⢿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣠⣴⣿⠟⠉⠀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣴⣾⣿⣿⠿⠻⣧⣀⣴⣿⠿⠋⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣩⣿⡿⠃⢀⣴⣿⡟⠁⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⣤⣶⠀⠀⣠⡄⢹⣿⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠏⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⡄⢰⣿⠃⣤⣿⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡆⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣷⠛⠉⠀⢹⣿⡄⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⡿⢶⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣇⠀⠀⠘⣿⣷⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣴⡿⠋⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⢻⣹⡀⠀⠀⣿⣿⡀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⠷⣄⣠⠴⣆⠀⣀⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠈⡟⠒⠋⢀⣈⣁⣀⣸⣋⠁⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠉⠉⢙⡶⠶⠛⠉⠀⠀⠀⠉⠙⠶⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢳⡇⠀⠀⣦⢀⣤⠤⠦⣝⠃⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⣾⠱⠀⠘⢺⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣧⠀⠀⠀⠘⠒⠒⠒⠋⠀⠀⠀⠀⣰⣧⡀⢐⢧⣶⣦⠖⣴⢳⢰⢲⣠⢲ ⠀⠀⢹⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⣽⠘⠊⠚⠉⠊⠋⠘⠋⠈⠙⠊ ⠀⠀⣸⠀⠉⠛⠳⡖⢲⢺⢻⠋⢹⠀⠀⣠⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⣤⣤⣤⠇⣾⢉⢹⡆⠈⠙⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠇⠀⠀⠀⣿⢀⠈⡇⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠀⠀⠀⠀⡏⢀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡇⠀⠀⠀⣸⠁⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠇⠀⠀⢠⡏⠀⠈⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣶⣄⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠻⣷⣄⢀⣤⣾⠟⠻⣷⡀⠀⢀⣀⣤⣶⠿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣶⣤⣄⣀⣼⡟⠀⠀⠈⠻⠿⠋⠁⠀⠀⠹⣷⣾⡿⠛⠉⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣄⠀⠀⠀⠀⢹⡇⠉⠛⠛⠛⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣰⣿⣃⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⠿⠿⠿⠷⣾⣿⣦⣄⠀⣀⣀⣴⣿⡿⠟⠛⠛⠛⠛⠛⠛⠻⠿⠿⣿⣦⣄⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡆⠀⠀⠀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣦⡀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⢿⣿⡏⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⣀⣤⣤⣴⣶⣤⣌⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⠛⠛⠃⣴⣿⠟⠋⠉⠉⠉⣽⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢡⣴⡄⠀⠀⠰⢿⠂⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠈⠁⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣤⣤⣴⣶⡾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⢠⣾⡇⣀⣤⣤⡀⢀⣤⣤⡀⣼⣧⣤⡀⢠⣤⣤⣄⠀⣠⣤⣄⠀ ⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠿⣶⣤⠀⠀⢨⡏⢹⡿⠿⣽⣧⡿⠉⢙⣻⣿⠉⣹⡇⣾⠋⢨⡏⣾⠏⠉⣿⠇ ⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠀⠀⠈⢿⣧⡀⠿⠷⠹⠷⠴⠟⠙⠷⠴⠟⠿⠇⠀⠿⠽⠟⠀⠼⠃⠿⠦⠾⠛⠀ ⠀⠀⠀⠀⠀⣼⡿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⠟⠋⠀⠀⠀⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣇⠀⠙⠻⠿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⡿⠟⠛⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠹⣿⡍⠉⣿⡏⢹⣿⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⣠⣤⣤⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣧⣄⡀⠀⠀⠀⠀⠀⠀⣿⣇⠀⣿⣿⣾⣿⣶⣿⡇⠀⠀⠻⣿⣦⣤⣶⡿⠟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣤⣤⣤⣤⣴⡿⠃⢰⣿⡇⢀⣀⠀⣿⡇⠀⠀⠀⠀⠈⠁⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠉⠉⠉⠉⠀⠀⢠⣿⡇⠈⠁⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢀⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠘⠋⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠰⠦⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠘⠛⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣄⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣄⡀⠀⢀⣿⠀⠙⢷⣴⡾⠋⠘⣿⣀⣤⡶⠟⠋⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⠀⠀⠘⣿⠛⠛⠚⠃⠀⠀⢀⣁⣀⣀⣀⣸⡟⠁⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠛⠻⠶⠶⢿⣦⣄⣀⣠⣴⡿⠟⠛⠋⠉⠛⠛⠛⠿⢶⣦⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⢀⣼⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣷⣀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣿⠁⠀⠀⠀⢴⣶⠀⢀⣤⣶⠶⠶⢶⣬⠉⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⢰⡿⣉⡀⠀⠀⣾⠹⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⡇⠉⠁⠀⠀⠈⣠⡿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⠻⠶⢤⠶⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⢀⣾⣇⠀⠀⠀⢴⣧⣤⣴⣄⣠⡴⣦⣸⡧⣦⢠⡤⢤⣀⣤⢤⡄ ⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠙⢻⣆⠀⣾⢸⣟⣻⡿⣏⣠⣼⡟⢀⡿⣼⠁⣾⢻⣁⣰⠇ ⠀⠀⠀⠀⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠿⠋⠀⠀⠀⣰⡟⠀⠉⠀⠉⠁⠀⠈⠁⠈⠁⠀⠁⠁⠀⠁⠀⠉⠁⠀ ⠀⠀⠀⠀⣿⠀⠙⠛⠷⢶⣶⣶⣤⣤⣤⣴⣶⢶⡾⠟⢛⣿⠁⠀⠀⠀⠀⠀⣨⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⢹⡇⠀⣿⣄⣿⣨⡇⠀⠸⣿⡀⢀⣠⣶⣾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠻⣦⣄⣀⣀⣀⣼⡗⢰⣿⠉⡉⠙⣿⠀⠀⠉⠛⠛⠋⢡⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡏⠉⠉⠉⠉⠀⢸⣿⠀⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢸⡏⢠⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢀⣿⠁⠠⠆⠀⢿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢠⣿⠀⠀⠠⡄⠀⢸⣇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢰⠶⣄⡀⢀⡠⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⠛⢋⡾⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣍⠉⠉⠁⠐⠆⢦⠛⠁⠋⠁⠘⠣⢤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣦⠖⠛⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠳⣄⠀⠀⠀ ⠰⠶⢖⣋⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣿⢲⡂⢷⡪⠧⠀⠀ ⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⢀⠀⠴⣄⣿⡄⡟⠈⢷⡈⡇⠀⠀⠀ ⠀⠠⠿⣲⠄⠀⠀⠀⠀⡄⢸⡏⠀⠈⠉⠙⠃⠀⠾⣿⠧⠤⢄⡀ ⠀⠀⢠⠏⣤⠀⠀⠀⢸⣷⢸⠌⠛⠁⠀⠐⠀⠀⣀⣻⣤⠖⠋⠀ ⠀⠀⠈⠳⢿⡶⠶⣀⡼⠈⠿⠀⠀⠀⠀⠀⠐⠉⢀⣼⠃⠀⠀⠀ ⠀⠀⢀⣶⣋⣐⣂⣉⣡⣄⣴⣄⣀⣀⣀⣀⣠⣔⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⠁⢀⣩⠷⣮⠟⠋⠉⢹⣷⣿⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠴⣶⠚⣤⡶⠋⢁⡾⠁⠀⢀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠁⣼⠏⠀⠀⢸⠃⠀⠀⠸⡦⠏⣼⢸⡆⠀⠀⠀⠀⠀⠀ ⠀⢀⡼⢳⣿⠀⠀⠀⣼⣀⠀⠀⠀⢷⠀⢹⡆⢷⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣄⡀⠀⠀⠀⣠⡾⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠙⠿⣶⣤⠞⢉⣴⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠁⣴⡿⠋⣿⣻⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⠉⠉⠉⠉⠉⠁⠀⢠⣄⠰⣤⠾⠿⠃⠀⠟⠉⠉⠉⢿⣏⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⣤⠀⠀⠙⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀ ⠀⠀⣀⣠⣤⡶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣀⠀⠠⣤⡈⢿⣄⠀⠀⠀ ⠛⠻⠿⢭⣄⣤⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⣿⠀⢻⣏⠙⢻⣏⠛⠻⠃⠀⠀ ⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⢸⣿⡄⢠⣿⠀⠈⢿⡄⠈⣿⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⡠⠋⠈⢿⣾⣿⣿⣼⡟⠀⠀⠘⣿⡄⣿⠁⠀⠀⠀⠀ ⠀⠀⣿⡿⠿⣷⠄⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣿⠀⠀⠀⠀⠈⠃⠘⠿⠃⠀⠀⣾⣿⣿⠿⢤⣤⣤⣀⡀ ⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢀⡏⢴⣶⣶⠄⠀⠀⢀⣀⠠⠄⠀⠀⠈⣿⡇⠀⢀⣠⡾⠟ ⠀⠀⠀⣼⡇⢀⣷⡀⠀⠀⠀⠀⠀⣼⣿⣧⢸⡷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢿⣿⣿⠟⠉⠀⠀ ⠀⠀⠀⠛⢷⣼⣿⣧⣠⣴⣆⠀⢀⣿⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠁⠀⣸⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⣽⡿⠋⠈⠻⣷⣾⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣶⡟⠋⠀⢘⣛⣁⣈⣁⣀⣀⡀⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠛⠛⣻⣿⠟⠛⠛⠻⠿⣿⣛⠛⢻⣿⡿⠿⠿⠿⣿⡟⢛⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⢀⣠⡶⠟⢋⣿⠟⠉⠀⠀⠀⠀⢸⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣤⣤⣼⡇⠀⣠⣾⠟⠉⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢙⣿⠷⠀⣽⣿⠋⠀⠀⠀⣸⡟⠁⠀⠀⠀⢠⣤⠀⢀⡀⢹⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠃⢀⣾⡿⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⣿⣄⣾⠇⣼⡇⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣧⣼⣿⠃⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⢸⣯⠀⠀⢸⣿⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠟⠁⣿⣿⠀⠀⠀⠀⠀⢸⣿⣀⣀⠀⠀⠀⠀⠀⣿⣆⠀⠘⣿⡄⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀