⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⣄⣀⣀⣤⣤⣤⣠⡤⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠤⣤⣤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡿⠛⠉⠀⠀⠀⠀⠈⣱⡿⠛⠉⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠠⠈⠈⠀⠉⠉⠉⠉⠙⠛⠛⢛⣿⣿⠶⠒⣲⣿⡏⣿⣿⣄⠀⠀⠀⠀⢀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠸⣳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣄⠀⠀⠀⠀⠀⠀⢀⠀⣠⣴⠞⠋⠁⠐⠲⡶⠿⣫⠀⣿⣿⣿⣿⣤⠀⣰⡾⣠⣿⣿⣇⢀⠀⠀⠀⠀⠀⢨⣷⢹⠛⢦⣀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢯⡀⢿⣷⣀⠀⠀⠀⠀⢉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣄⡀⣰⣿⠃⠀⠀⢈⣟⢦⢻⡍⠉⠉⠛⠓⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢐⣿⡏⠘⢧⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣾⡏⣮⠈⣿⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣄⠀⠀⠀⠀⠀⣿⠟⢤⡄⠀⠙⠂⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠠⣾⠟⠁⠸⡇⢸⣄⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⢶⣌⡉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢺⣿⢾⣿⣿⣟⣿⡿⢹⣿⣿⣿⣿⣿⡄⡀⢠⣶⢀⠀⢰⡀⣿⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢻⣆⠀⢸⣿⣿⣿⣿⣿⣿⢿⡏⠙⢻⠆⠀⣿⠇⣾⣿⡿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣷⣾⠃⠈⣷⡄⠁⠘⣧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡇⢠⠀⠀⢻⣷⣿⣿⣿⣿⣿⣯⠍⠋⠀⠀⢼⠀⠀⣿⣤⣿⣟⣱⣿⠁⢰⣿⠛⠛⣟⣿⣿⣿⣿⡇⠀⠀⢸⡇⢀⠀⢹⡄⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⢀⣴⣿⣿⣿⣿⢿⣿⣷⣶⣿⣿⣶⣦⣆⠈⡋⣿⡿⢿⣿⣏⣀⢸⣿⠀⢐⠟⢹⣿⣿⣿⠀⠀⠀⠸⡇⠈⠀⢸⣇⣠⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠈⣿⠀⢠⣾⣿⠁⣿⣿⣿⠃⠀⠈⢻⣿⣿⣿⣿⣿⣿⠀⡇⢹⡇⣰⣿⡿⢘⣿⣿⣿⣿⣷⣦⣾⣿⡿⠀⡀⠀⡎⣧⠀⠀⠈⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣶⠒⢀⣀⣸⣿⠆⠀⠈⣿⣶⣿⣿⣯⣄⠀⠀⠀⠙⠛⢻⣿⡿⠛⠀⠀⠘⢛⣿⡟⣠⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣠⡏⠀⢻⣟⠀⠀⠀⢹⣆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠖⠠⣭⡭⣽⡿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣾⣧⣤⣤⠀⠀⠀⠉⣠⣤⣤⣤⣾⣿⣿⣭⣿⠿⠿⠿⠿⠟⠉⠀⣠⣿⡟⢠⣿⣾⣿⠁⠈⠀⠈⣷⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⣤⠠⢴⡆⢸⣇⠀⣄⠀⢻⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠲⣶⠶⣦⣤⣿⣿⣷⡿⠟⣱⡏⠀⠀⠀⠀⠸⣧⠴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠒⠂⠀⡃⠸⣿⡀⠘⡃⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠠⠀⠀⠀⠀⣹⣿⠛⠋⠁⠀⣀⣤⣴⣶⣤⣾⣻⣿⡿⠟⠋⠁⣠⣼⠛⠀⠀⠀⠀⡇⠀⢻⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⠀⠀⠀⠀⠛⠹⣧⠀⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣤⣠⣀⢈⣭⣿⣿⣷⡿⠛⠋⠁⠀⠀⠀⠠⠋⢩⡄⠀⠀⠀⣼⠁⢰⡈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣿⡷⠶⠶⠶⠶⣿⣯⡄⠈⠙⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⢀⣽⣿⣿⣶⣿⠿⠛⠉⠀⠀⠀⠀⣰⢠⡞⠀⠀⠀⢸⢀⡀⢀⢠⠇⢰⣼⡇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠾⣷⣤⣧⣤⣴⡿⠉⢳⡀⠀⠀⠨⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣠⣰⠏⠀⠀⠀⠀⢠⡾⠛⠃⠈⣴⢂⣾⢹⢻⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢷⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠐⠋⠀⣀⣤⡾⢣⣿⠏⠀⠀⠀⣦⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠉⠙⠻⣧⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⢀⣀⣤⣴⠶⠛⠉⢁⣴⣿⡟⠀⠀⠀⠀⡏⠀⠀⠈⠛⢶⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⣀⣀⠀⣀⣀⣀⣀⣤⣤⣶⣶⠶⠾⠛⠛⠉⠁⠀⠀⢀⣴⠟⣽⣿⠁⠀⠀⢠⠀⡇⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣝⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠁⠀⠀⢙⣀⣤⣤⣼⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣦⣤⣴⣶⣦⣤⣤⣤⢶⣿⣟⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢛⣹⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀⠀⠀⠰⢿⣿⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢉⣿⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠈⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⠀⠈⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⢹⣠⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⣈⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⡛⠶⢤⣙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠈⠻⢦⣈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠄⠀⠀⠀⠙⢶⣄⡀⠙⠳⣄⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠄⡈⢻⣦⠀⠘⢷⡀⠀⠉⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⣿⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠀⠀⠛⠓⠂⠙⠓⠿⣿⣦⡀⢹⣂⡀⠄⠀⠉⠛⠀⠀⠀⠀⠀⠀