⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⣤⣄⣀⣀⣀⣀⣠⣤⡀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⢤⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⣪⠃⠀⠀⣠⣶⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣾⡽⠁⠀⠀⣰⣿⠃⠀⠀⠈⠉⠙⠛⠛⠛⠶⠤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⢠⡾⣟⣿⠇⡀⢀⣾⢫⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⣦⣤⣄⣀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠰⣿⣞⡽⣿⣾⢷⡿⣱⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠦⣄⣀⠀⠱⠀⠀⠀⠀⠀ ⠐⣿⣡⣾⡋⠹⡆⠿⣧⡄⣀⣀⣀⡀⠘⢶⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠢⠤⣀⠀⠀⠀ ⠈⠻⡿⠛⢷⣄⠀⠀⠈⠉⠓⠒⠛⠹⠭⠭⠯⠭⢽⣟⡛⠛⠛⠛⠛⠛⠻⠿⢷⣶⣤⣤⡀⠀⠀⠘⠀⠀⠈⢣⡀⠀ ⠀⠀⢱⡀⠀⠉⢳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠀⠀⠀⠀⠙⠒⠦⢄⣉⣓⠿⢕⣦⣀⠀⠀⠰⣾⣿⡦ ⠀⠀⠘⣇⠀⠀⠈⠳⣝⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣌⠻⢦⠀⠀⣹⡙⡟ ⠀⠀⠀⢸⠀⠀⠀⠀⠈⠉⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⣟⣖⣿⡘⠂ ⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⣀⣀⣤⣴⣶⡾⠿⠥⠤⠤⢄⣀⣀⣀⡀⠀⠀⠀⠈⠉⠷⢿⣿⠗⠀ ⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⢀⣀⡼⠏⠀⠀ ⠀⠀⢸⡟⣿⠀⠀⠀⢀⡤⠴⠒⠒⠲⠦⠤⣤⣤⣄⣀⡀⠀⠀⠀⠀⡀⣀⡤⠴⠂⠀⠀⠀⠖⠒⢻⡟⠉⠀⠀⠀⠀ ⠀⠀⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠷⠖⠒⠀⠉⠁⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀ ⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠒⠀⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⢀⣀⡠⠆⠀⠉⡉⠉⠉⠙⠒⠶⠶⠤⠤⠤⠤⠄⠀⠀⠀⠀⢀⡀⠀⠀⢀⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⣾⣫⡥⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⠟⠉⠀⠀⠀⠀⠀⣤⠤⠴⠶⠶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡷⡀⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠯⠉⠀⠀⠀⠀⠈⢻⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⢀⣷⢻⣷⣶⣤⣤⣀⠀⠀⠀⠤⠤⠤⠿⠷⠶⠒⢛⣋⣉⣉⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⡜⡆⠀⠀⠀⠀⠀⠀⠀ ⢸⣇⠀⠘⡻⡟⢿⣿⣿⣶⣤⣤⣤⣤⣴⡶⠖⡿⠛⠛⠛⠿⣿⣿⣶⣶⣄⠀⠀⠀⠀⠈⡧⠃⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⣆⠀⠀⠀⠀⠛⣿⡏⠛⠋⠉⠉⠀⢀⠞⠁⠀⠀⠸⡀⠀⠀⠉⠉⠛⠿⢿⣶⣶⢚⠃⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣿⣿⣿⣿⣦⣄⣀⣀⣀⣀⡤⠞⠋⠀⢀⠀⠀⢀⢻⣦⡀⠀⠀⠀⠀⠀⠉⠁⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⡿⠟⠛⠛⠉⠉⠀⠀⠀⠀⡜⠀⠀⠘⣆⠙⢿⣶⣤⣄⣀⣤⢖⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⢀⡾⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢆⠀⠈⠹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣧⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⡀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢈⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢘⢿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢈⠞⠀⠘⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢰⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠳⢄⡀⠀⠀⠀⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠂⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⠘⢦⠀⠀⣤⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠸⡇⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢈⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠋⣛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⢈⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢻⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⠀⡇⠸⡀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣤⠀⠀⢦⠘⠀⠀⠀⡄⠳⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠁⠞⠀⠀⠀⠀⠂⣶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠳⠙⠀⠀⠀⡀⢄⠳⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢰⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⠘⠀⠀⠀⠀⡀⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠘⠀⠞⢈⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢿⠈⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⢿⢘⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⣿⢈⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⢿⠀⠀⠀⠀⠀⠀⠀⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⢳⠈⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢦⠈⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⡄⣤⢀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠙⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣇⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⠏⢀⠀⠀⡀⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠘⠀⠀⣧⠘⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠁⣼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⠹⠈⠀⢆⠈⠀⠀⠀⡇⢸⠀⠀⠀⠀⡾⢀⠀⠀⠀⠋⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠟⡿⢖⣤⣀⣄⣤⣶⢿⠙⣆⠘⠀⠀⡜⠀⠀⠀⠀⠉⠉⠛⠛⠟⡿⣿⣿⠹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡿⣠⠀⠁⠉⠀⠀⠀⠀⠀⡀⣦⢻⢀⠀⠀⢀⠀⠋⠞⡤⣀⣀⣀⣀⣄⣦⣿⣿⣿⣿⠙⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢠⠃⢚⣶⣶⢿⠿⠛⠉⠉⠀⠀⡀⠸⠀⠀⠁⠞⢀⠀⠉⠉⠋⠛⡏⣿⠛⠀⠀⠀⠀⣆⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠃⡧⠈⠀⠀⠀⠀⣄⣶⣶⣿⣿⠿⠛⠛⠛⡿⠖⡶⣴⣤⣤⣤⣤⣶⣿⣿⢿⡟⡻⠘⠀⣇⢸ ⠀⠀⠀⠀⠀⠀⠀⡆⡜⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣉⣉⣋⢛⠒⠶⠷⠿⠤⠤⠤⠀⠀⠀⣀⣤⣤⣶⣷⢻⣷⢀ ⠀⠀⠀⠀⠀⠀⠀⠁⡾⢻⠈⠀⠀⠀⠀⠉⠯⠛⠙⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣰⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢹⡀⡷⠪⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣤⠶⠶⠴⠤⣤⠀⠀⠀⠀⠀⠉⠟⣾⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⣄⣶⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠚⠴⡥⣫⣾⢳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⣾⣤⢀⠀⠀⡀⢀⠀⠀⠀⠀⠄⠤⠤⠤⠤⠶⠶⠒⠙⠉⠉⡉⠉⠀⠆⡠⣀⢀⠀⡇⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠊⠒⠒⠀⠒⠒⠑⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠀⠀ ⠀⠀⠀⠀⠀⠁⣸⠀⠀⠀⠀⠁⠉⠀⠒⠖⠷⠿⠛⠛⠙⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⠀⠀ ⠀⠀⠀⠀⠉⡟⢻⠒⠖⠀⠀⠀⠂⠴⡤⣀⡀⠀⠀⠀⠀⡀⣀⣄⣤⣤⠤⠦⠲⠒⠒⠴⡤⢀⠀⠀⠀⣿⡟⢸⠀⠀ ⠀⠀⠏⡼⣀⢀⠀⠀⠀⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠀⠀⠀ ⠀⠗⣿⢿⠷⠉⠈⠀⠀⠀⡀⣀⣀⣀⢄⠤⠤⠥⠿⡾⣶⣴⣤⣀⣀⢀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀ ⠂⡘⣿⣖⣟⢬⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠉⠉⠈⠀⠀⠀⠀⢸⠀⠀⠀ ⡟⡙⣹⠀⠀⢦⠻⣌⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣝⠳⠈⠀⠀⣇⠘⠀⠀ ⡦⣿⣾⠰⠀⠀⣀⣦⢕⠿⣓⣉⢄⠦⠒⠙⠀⠀⠀⠀⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⢳⠉⠀⡀⢱⠀⠀ ⠀⡀⢣⠈⠀⠀⠘⠀⠀⡀⣤⣤⣶⢷⠿⠻⠛⠛⠛⠛⠛⡛⣟⢽⠭⠯⠭⠭⠹⠛⠒⠓⠉⠈⠀⠀⣄⢷⠛⡿⠻⠈ ⠀⠀⠀⣀⠤⠢⢿⠙⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣄⣤⣤⣤⣤⣤⢶⠘⡀⣀⣀⣀⡄⣧⠿⡆⠹⡋⣾⣡⣿⠐ ⠀⠀⠀⠀⠀⠱⠀⣀⣄⠦⠻⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣱⡿⢷⣾⣿⡽⣞⣿⠰ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⣀⣄⣤⣦⠶⠓⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢫⣾⢀⡀⠇⣿⣟⡾⢠⠀ ⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⢤⠤⠶⠛⠛⠛⠙⠉⠈⠀⠀⠃⣿⣰⠀⠀⠁⡽⣾⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣤⣦⣶⣶⣠⠀⠀⠃⣪⡴⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⢤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠄⠤⠤⠀⠀⡀⣤⣠⣀⣀⣀⣀⣄⣤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀