Squid Game Dot Art

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠞⠛⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠒⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⣠⡴⣾⣿⣿⣭⣭⣭⣽⣿⣳⢦⣤⡀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⣠⣾⡿⠟⠋⠉⣉⣥⣾⣶⣶⣎⣉⠉⠛⠿⣿⣶⣄⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⣾⡿⠋⠀⢀⣴⠟⢋⣤⣿⣤⣤⣬⡙⠻⣤⠀⠀⠙⢿⣷⡀⠀⠀⠀⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠀⠀⠀⣰⡿⠋⠀⠀⣠⡿⢑⣴⠟⠉⠀⠀⠀⠉⠻⣷⡈⣿⡄⠀⠀⠙⣷⡄⠀⠀⠸⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⢰⣿⠃⠀⠀⠀⣿⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⣷⠀⠀⠀⠙⣿⡄⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠀⣿⡏⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢻⣷⡀⠀⢸⡄⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⣼⣿⠀⠀⠀⠀⠀⢿⡆⢸⣧⡀⠀⠀⠀⠀⠀⢀⣴⠏⣸⡟⠀⠀⠀⠀⠘⣿⡇⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⢠⡿⣿⠀⠀⠀⠀⠀⠀⠻⣦⡙⠿⢦⣄⣀⣠⡴⠟⢁⣴⠟⠀⠀⠀⠀⠀⠀⣷⢧⠀⠰⡇⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⢸⡇⣿⣤⣄⡀⠀⠀⠀⠀⠈⠻⢶⣦⣬⣭⣴⣶⡾⠛⠁⠀⠀⠀⠀⢀⣀⣤⡿⢸⡀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⢸⠇⢻⠶⣬⣭⣙⣛⡛⠒⢲⣾⣷⣿⠿⠿⠿⣷⣷⣶⠖⠒⢛⣻⣿⣭⣥⢴⡇⢸⡇⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⢸⡇⠘⣇⠀⠀⠉⠉⠉⠉⠛⠛⠻⠿⣿⣿⡿⠟⠛⠛⠛⠉⠉⠉⠉⠁⠀⣼⡇⢸⡇⠀⣷⠀⠀⠀ ⠀⠀⠀⢠⣿⠀⠘⣷⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣼⠁⠀⣿⠀⠀⠀ ⠀⠀⠀⠸⣿⡀⠀⠹⡆⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢰⡇⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⢻⡇⠀⠀⢻⡄⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣠⡏⠀⠀⢸⡏⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⡀⠀⠀⠻⣆⠈⠻⣦⡀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⢀⣴⠟⠀⣰⠏⠀⠀⢠⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠈⢳⣄⡈⠻⣦⡀⠀⠀⠀⣽⡄⡇⠀⠀⠀⣀⣴⠟⢁⣤⠾⠁⠀⠀⢠⡾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠈⠙⠻⠶⠿⢿⣷⣦⣿⣿⣷⣤⣶⣿⠽⠶⠟⠋⠁⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠿⠷⠶⠶⣦⣤⣤⣤⣴⣦⣿⣿⣿⣶⣦⣤⣤⣤⣤⠶⠶⠶⠿⢿⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⣷⠀⠀⠀ ⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⢸⠃⡾⠓⠒⠺⠓⠚⡷⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠘⣧⠀⠀ ⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⣿⢀⣿⠶⠶⠶⠶⠶⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⡇⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⡟⢸⡇⠀⠀⠀⠀⠀⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⢿⡀ ⠀⢸⠇⠀⠀⠀⠀⠀⢰⡏⣷⢸⣷⣀⣀⣤⣤⣴⡷⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡆⠀⠀⠀⠀⠀⢸⡇ ⠀⣾⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⢷⠀⠀⠀⠀⠀⠈⣇ ⢰⣿⠀⠀⠀⠀⠀⠀⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⡇⠀⠀⠀⠀⠀⣿ ⢸⣿⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⡇⠀⠀⠀⠀⠀⢻ ⢸⣷⠀⠀⠀⠀⠀⠀⡇⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⢸⡇⠀⠀⠀⠀⠀⣿ ⠘⢿⣄⣀⣀⣀⣀⣾⡇⠀⠈⢻⡗⠾⢶⡶⣶⠶⠶⣾⠿⠟⢷⣶⠶⠶⣶⢶⡶⠶⢺⡏⠁⠀⢸⣧⣤⣄⣀⣀⣠⡿ ⠀⣠⣿⠉⠉⠉⠉⠈⢻⡄⠀⣼⠷⠦⠾⠿⠿⠷⠴⠿⣷⣶⠼⠿⠷⠴⠿⠾⠷⠶⢿⣿⠀⢨⡟⠁⠀⠀⠈⠉⢻⡄ ⢠⣿⠃⠀⠀⣶⠷⣆⠈⢷⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣴⣿⠁⣰⠾⣶⠀⠀⠈⣷ ⢸⣿⢰⡄⠀⢿⡄⠘⠿⠿⢯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⡸⠿⠞⠃⢠⡿⠀⣰⡇⣿ ⠀⠙⣷⡻⣄⠘⢿⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡾⠁⣠⢟⣼⠏ ⠀⠀⠈⠛⢿⣷⣬⡿⠀⠀⣸⡷⢤⣤⠀⠀⠀⠈⠙⠛⢳⣿⡿⠛⠛⠁⠀⠀⠀⣶⠶⠼⡇⠀⠀⢾⣡⣴⡷⠟⠁⠀ ⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣹⣅⣸⣿⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣄⣠⣷⠀⠀⠀⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢸⡟⠀⠀⠀⠀⠀⠀⣿⠈⡇⠀⠀⠀⠀⠀⠀⢸⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⣇⠀⠀⠀⠀⠀⠀⢸⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣀⣼⡧⠀⠀⠀⠀⠀⠀⡏⠀⢻⠀⠀⠀⠀⠀⠀⢸⣇⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡧⠤⢤⣤⣄⣀⣀⡀⠀⠀⣇⠀⢸⠃⠀⣀⣀⣀⣀⣤⡤⠤⠿⣤⣄⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⢶⡿⠀⣸⡶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀ ⠀⠀⠀⢸⡷⢤⣤⣄⣀⣀⣀⣀⣀⣤⣤⡤⠴⣒⣺⡿⠇⠀⠸⣿⣟⣒⠦⠤⣤⣤⣄⣀⣀⣀⣀⣠⣤⡴⣿⡆⠀⠀ ⠀⠀⠀⠀⠙⠿⠶⠦⠤⠤⠤⠴⠶⠶⠾⠛⢋⠉⠀⠀⠀⠀⠀⠀⠀⣉⠙⠻⠷⠶⠶⠤⠤⢤⠤⠴⠶⠟⠋⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠖⠒⠒⠒⠒⠒⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⣀⠤⠶⠒⠒⠶⠤⣀⡀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀ ⠀⠀⣠⠏⠀⠀⠀⣀⠔⢋⣀⣀⣤⡤⢤⣤⣀⣀⡉⠲⣄⠀⠀⠈⢧⡀⠀⠀⠀ ⠀⡼⠁⠀⠀⠀⡴⢁⡞⢉⣠⠤⠤⠴⠶⠤⠤⣌⡉⠑⡎⢣⠀⠀⠀⢳⡀⠀⠀ ⣾⠁⠀⠀⠀⡾⠁⢸⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢷⠀⢳⠀⠀⠀⠱⡄⠀ ⡟⠀⠀⠀⢸⠁⠀⡟⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠈⡇⠀⠀⠀⠹⡄ ⡇⠀⠀⠀⡏⠀⠀⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡆⠀⢹⠀⠀⠀⠀⡇ ⡇⠀⠀⢸⡇⠀⢀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡇⠀⢸⡇⠀⠀⠀⡇ ⡇⠀⠀⡏⡇⠀⢸⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⡇⠀⢸⢹⠀⠀⠀⡇ ⡇⠀⢠⠇⠳⡤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠏⠸⡆⠀⠀⡇ ⡇⠀⢸⠀⠀⢳⡀⠀⠀⠉⠉⠉⠉⢻⠉⠉⠉⠉⠉⠁⠀⢠⠏⠀⠀⡇⠀⢸⠃ ⣧⠀⢾⡀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⣀⠗⠀⣼⠀ ⢹⡀⠀⠈⠲⣄⠈⢧⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠞⠀⣠⠞⠁⠀⢀⡇⠀ ⠀⠙⢦⡀⠀⠈⠳⣄⣳⡀⠀⠀⠀⢸⠀⠀⠀⠀⣰⣋⣠⠞⠁⠀⣀⡴⠚⠀⠀ ⠀⠀⠀⠉⠳⢄⡀⠘⢦⡙⢦⣀⠀⢸⠀⢀⡤⠊⢁⡴⠃⣠⠴⠚⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠲⢬⣳⡀⠈⠙⠛⡞⠉⢀⣠⠾⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣰⣶⠒⣿⡇⠰⠶⣿⣟⣿⣿⣿⣿⣾⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣹⣿⠿⠟⢈⣁⣠⣤⣬⣭⣬⣿⣥⣄⣉⠉⠛⢿⣽⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⠻⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⢿⣟⠀⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⣽⣿⣿⣿⣿⣯⢼⣿⣤⣿⢿⡟⢹⣿⣷⢿⡷⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⣤⣼⡛⠋⠛⠁⠀⢠⣿⣦⣿⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣉⣻⣿⣿⠂⠀⠀⠀⠛⣻⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣆⠀⠀ ⠀⣠⣾⣿⣿⣿⣿⣿⣿⡉⠛⠋⠁⠀⠀⠀⠀⠉⠉⠛⠋⠀⣿⣷⣾⣿⣿⣿⣿⣿⠿⠂ ⠙⠛⣻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⣉⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⠿⠷⠀ ⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠈⠛⠋⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠈⠹⠟⢿⣿⣿⣿⣿⡟⡟⠒⠒⠋⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡁⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⠤⢲⣿⠋⠈⠻⠟⣳⣿⠀⠀⠀⠘⢿⣿⠿⠟⠋⠉⢈⣳⣬⢻⣦⠀⠀⠀ ⠀⠀⣾⣫⠤⢶⡟⠡⠤⢤⣀⠀⠘⢿⣷⠶⣤⡶⣿⡟⠀⠀⢀⣔⣿⢿⣋⡉⠛⢤⣀⠀ ⠀⠀⠈⠛⢶⣬⣉⠉⠙⠓⠾⣷⡄⠈⣿⡷⠤⠴⣿⡇⠀⣠⣿⠟⠁⠀⠀⠉⢑⣦⠿⠃ ⠀⠀⠀⠀⠀⠈⠉⠙⢲⣤⣀⣈⢿⣆⢿⡇⠀⠀⡟⠁⣴⡿⢃⣀⣠⠤⠶⠚⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠓⠤⠤⠟⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢄⡠⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡇⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⡠⠊⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠈⠑⠠⣄⠀⠀ ⠀⠀⡙⠁⠀⠀⠀⣠⣾⣏⣿⠛⣿⣳⢄⠀⠀⠀⠀⠈⢣⠀⠀ ⠀⡘⠀⠀⠀⠀⣘⣹⣇⡿⠘⢇⢻⠹⣦⣱⣄⠀⠀⠀⠘⡆⠀ ⠠⡇⠀⠀⣠⣾⣽⣿⣭⠁⠀⠀⠈⢡⡾⣷⣾⣷⣦⠀⠀⡇⠀ ⠀⠇⠀⡸⠇⣿⣶⣿⣿⠇⠀⠀⠀⢿⣷⣿⣽⣿⡇⠣⢀⣨⠇ ⠀⣸⡀⠁⠸⡈⠙⠛⠁⠀⠀⠀⠀⠀⠉⠛⠉⡘⠀⠀⢈⡿⠆ ⠀⠀⠑⢄⠀⠑⠠⡀⠀⠀⠐⠀⠀⠀⠀⣀⠔⠁⡀⣰⡟⠀⠀ ⠀⠀⠀⠀⢱⣀⣀⠀⠈⢐⣶⠒⢶⣆⣉⣀⠤⠚⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢩⡷⠟⡏⡷⠤⢶⠇⢻⠛⢖⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⣀⠔⠓⠚⢦⠞⠂⠙⣄⡌⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠇⡇⠀⠀⠀⢸⢸⣍⣉⡿⡇⢨⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢀⢃⡤⠀⠀⢸⠀⠀⠀⣤⢰⠀⠀⡄⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⢸⡿⠃⠀⠀⢸⠀⠀⠀⠹⢾⠀⠀⢣⠀⠀⠀ ⠀⠀⠀⠀⢧⣀⣀⢷⡶⠶⠒⢺⠒⠒⠲⢶⡿⣄⣀⡼⠀⠀⠀ ⠀⠀⠀⠀⠀⣟⣿⢾⡇⠀⠀⢈⡃⠀⠀⢸⡇⢸⣏⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⢸⡇⠀⠀⢠⡆⠀⠀⢸⡇⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⡇⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢸⡇⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢲⢶⢶⠊⠘⠢⠶⡶⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢹⠀⠀⢰⠉⠉⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠉⢉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣬⣿⣿⣷⣦⣤⣄⣻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⠻⣿⡉⠳⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠿⠿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠃⢠⠇⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣘⡄⠀⠀⢪⣍⠳⡄⠀⠀⠀⢀⣼⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣦⣴⣿⠿⡆⢹⡄⠀⣠⣼⣿⣿⣿⣿⣿⢿⡏⣿⣻⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⡠⢤⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⢻⣠⠟⠋⣤⣽⣴⡇⢸⣹⡿⢻⣿⣿⣿⡇⡌⣧⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠁⢠⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠟⠛⠉⠑⢸⡇⢸⣿⣤⣼⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⢧⡘⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⠛⠉⢹⣤⣶⡆⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣧⠀⠉⠉⣿⣿⡿⡿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣿⣿⡿⠀⠀⣸⢻⣿⣿⣿⣿⣿⣿⡀⠀⠈⢫⠀⠀⡀⠉⠁⠈⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⡾⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀ ⠾⣿⣿⣿⣧⣀⠀⣿⠀⢈⣙⣿⣿⠿⣿⣧⠀⠀⢯⣤⣤⣹⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓⠒⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠻⣷⠈⣿⡟⢋⡼⠁⠀⢸⣿⡄⠀⢀⣹⣽⣉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⠋⣠⠎⠀⠀⠀⢾⣿⣿⣄⠛⢉⣟⠻⠛⠃⠀⠀⠀⡰⣿⣿⣿⣿⣿⣿⣿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠈⠉⠁⠀⢀⡠⠾⢿⣿⡿⢿⣧⣀⠀⠀⣀⡤⠶⠂⠀⠀⠻⣿⣿⣿⣿⣿⠿⣭⣉⣓⣢⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢳⡆⣀⣈⢉⣉⡴⠖⠛⠛⠚⠋⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠁⠉⠙⠦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⣿⣁⠔⠋⠀⠀⠀⠀⣠⠂⢀⣾⣿⣿⣷⣄⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣯⣀⡀⣠⡄⠀⠀⠀⢀⣤⣤⢳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠿⠉⢀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⡿⠋⠀⠀⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣖⣿⢻⣿⣏⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣸⣿⡇⠀⠀⠀⢻⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⢿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⠀⠀⠀⠘⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡄⠀⠀⠀⢿⢣⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠈⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠉⠉⠉⠹⣿⠉⠉⠉⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢓⡦⣤⠀⠀⠀ ⠀⠀⠉⣹⠏⠁⠀⠀⠀⠀⠀⢀⣤⢻⣾⢹⢿⡟⢫⣷⣝⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀ ⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣠⢞⣿⠇⡏⡏⢸⣧⠈⣏⡟⡼⡆⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠏⢨⣿⢠⣇⡇⠈⢿⡄⢸⣷⠹⡷⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⢀⡴⠿⣛⣟⠿⠲⠿⠀⠀⠀⠙⠺⠿⠖⢊⣿⣿⣉⢙⣶⣄⡀⠀⠀⠀⠀⣿⠀⠀ ⢾⡇⠀⠀⠀⢠⣶⣿⣿⡿⢿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⣰⣿⠿⢿⣿⣿⣷⡟⡟⣆⠀⠀⠀⣿⡀⡀ ⠈⡇⠀⠀⢠⡎⡇⢸⣿⣦⣾⣿⣹⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⣶⣾⣟⣹⣿⡿⡇⠘⣦⠀⠀⠈⡹⣿ ⠀⣇⠀⠀⡾⠁⣿⠘⢿⣿⢿⡿⣿⡻⠁⠀⠀⠀⠀⠀⠀⠹⣟⡟⢻⣟⣿⠝⢱⠇⠀⠈⠀⣶⣶⠟⠁ ⠀⣿⣧⠀⠁⠀⠸⡄⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⡾⠀⠀⠀⠀⡈⣿⣿⠃ ⠀⠋⠻⣀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢀⣬⣿⠋⠀⠀ ⠀⠀⠀⠈⠢⡀⠀⠀⠈⠑⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠀⠀⣤⢀⣾⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠉⠑⠲⠶⣤⡤⣤⣤⣤⡶⠒⠉⠁⠀⣀⡠⣾⠷⠋⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠼⠧⠶⣦⢦⡀⢀⣀⣤⢞⡝⠁⠀⠈⢳⡝⣶⣤⣖⣛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⣟⡽⠷⡿⠸⣷⣲⣶⡶⢿⠇⠘⣏⠑⠺⣝⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡟⠁⠀⢸⣇⣀⡹⣄⠀⣠⢋⣠⠤⣿⠀⠀⠘⢏⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣼⢁⣖⡴⠃⠀⠈⠉⠛⣿⠗⠉⠀⠀⠀⢳⣽⡤⢸⡸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⡏⠈⡏⠀⠀⠀⠀⠀⠀⢸⠀⣯⠉⠉⠉⣿⣿⠀⠀⣇⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠛⠒⠒⠚⠛⢹⡀⠀⠛⣽⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠚⠀⢰⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣸⠀⣶⡆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡟⡆⢸⡀⠀⠀⢸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣿⣿⣽⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢱⣿⣼⡇⠀⠀⠀⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⢿⡍⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⢹⡇⠀⠀⠀⢸⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣧⣀⠀⠀⢀⣿⣵⢶⠾⠿⠿⠿⢿⠿⠿⠿⠿⡿⢿⡿⣿⣄⠀⠀⢀⣼⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣯⠭⣽⣏⣺⢸⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠈⣷⡇⠘⣿⠽⠿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡝⠿⡟⢻⢸⠀⠀⠀⠀⠀⣠⡴⠆⠀⠀⠀⠀⡏⡇⠀⣷⠿⣠⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⢸⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣷⡇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⠀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⠀⢸⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣴⣦⣤⣶⡤⠋⠉⠷⣄⣠⣤⣴⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣩⠭⣹⠃⠀⠀⠀⠘⣏⣩⢭⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢸⡄⠀⠀⠀⢰⡏⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⣠⠼⠃⠀⠀⠀⠈⠳⠤⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠖⠒⠒⠒⠒⠒⠒⠦⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠹⡄⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢀⣿⣤⣶⣾⣿⣿⡿⡿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡏⠀⠀⠀⣀⣴⣾⣿⠿⠿⠿⠿⢟⠉⠀⡇⠈⢻⠟⠛⠛⠛⠛⠻⡿⣷⣦⣄⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠏⠀⠀⣠⣾⡿⠛⣷⠁⠀⠀⠀⠀⠘⢧⠀⣿⢠⠏⠀⠀⠀⠀⠀⠀⣧⠈⠙⠿⣷⣤⠀⠀⢻⡀⠀⠀⠀⠀ ⠀⠀⠀⡟⠀⠀⣼⡿⠏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢳⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣷⡄⠈⣷⠀⠀⠀⠀ ⠀⠀⣼⠁⠀⣼⣿⡇⠀⠀⢀⣿⣦⡶⠶⠶⠶⠒⠚⠛⠛⠛⠛⠛⠛⠉⠉⢉⡿⠛⠦⣄⠀⢸⣿⣿⣧⠀⠸⡆⠀⠀⠀ ⠀⠐⡿⠀⢀⣿⣿⡇⢀⡴⠊⠁⠈⠉⠳⠦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣴⣞⣉⣀⣀⣀⣈⣑⣾⣿⣿⣿⣧⠀⢿⠀⠀⠀ ⠀⣾⠃⠀⣼⣿⣿⣷⠿⠶⠒⠒⠒⠊⠉⠉⠉⢻⡉⠉⠉⠉⠉⣽⠏⠉⠁⠀⠀⠀⠀⠀⢀⡞⢻⣿⣿⣿⠀⠘⡆⠀⠀ ⠀⣿⠀⠀⣿⣿⣿⡏⢳⣤⣀⣀⣤⣤⣤⣤⡀⠈⢳⠀⠀⠀⣰⠃⠀⣤⣶⣶⣶⣶⣿⣿⠏⠀⠘⣿⣿⣿⡆⠀⣷⠀⠀ ⠀⣿⠀⢰⣿⣿⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣦⣼⣷⣀⣠⣿⣠⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣹⣿⣿⣷⠀⣿⠀⠀ ⢸⡿⠀⣼⣿⣿⣿⠤⠤⠤⠼⠿⠿⣿⣿⣿⣿⠛⡽⠸⠀⠈⣇⢹⡏⢻⡿⢿⣛⣉⡉⠉⠉⠉⠉⢹⣿⣿⣿⠀⢹⠀⠀ ⠸⡇⠀⣿⣿⣿⣿⡆⠀⠀⣀⡤⠴⠛⠉⠀⢸⣴⡇⢸⠀⠀⣿⠀⢧⣸⠁⠀⠀⠉⠙⠓⠦⣤⣠⣿⣿⣿⣿⠀⢸⠀⠀ ⠀⡇⠀⣿⣿⣿⣿⣷⣶⣯⣥⣀⣀⣀⣀⠀⠈⣿⠀⢸⡀⠀⣸⣀⣸⣏⣀⣠⡤⠤⠒⠛⢻⡿⢻⣿⣿⣿⣿⠀⢸⠀⠀ ⠀⡇⠀⣿⣿⣿⣿⣿⡎⠓⢤⡀⠀⠀⠀⠉⢹⡿⢯⣉⣉⣉⣉⣉⡟⠻⡄⠀⠀⠀⣠⠶⠁⢀⣿⣿⣿⣿⣿⠀⢸⠀⠀ ⠀⣇⠀⢿⣿⣿⣿⣿⣿⡀⠀⠙⠲⢄⡀⢠⣎⣴⣾⡿⠭⣉⡽⣷⣶⣶⣽⣆⣠⠞⠉⠀⠀⣸⣿⣿⣿⣿⡿⠀⢸⠀⠀ ⠀⠛⣦⡀⠙⠻⢿⣿⣿⣇⠀⠀⠀⠀⠙⢻⡟⠻⢭⣝⣓⠶⢛⣡⡴⠚⢻⡟⠁⠀⠀⢀⣴⣿⣿⡿⠟⠋⢀⡴⠛⠀⠀ ⠀⠀⠀⠉⠓⢦⣀⠈⠙⠻⢿⣷⣦⣤⣀⠈⢳⡀⣰⠋⠉⠉⠉⠘⢧⣀⡞⢀⣤⣴⣿⡿⠟⠛⠁⣀⡴⠚⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣀⣈⠉⠛⠿⠿⣾⣿⣧⣤⣶⣶⣶⣶⣾⣿⠿⠿⠛⠉⣁⣠⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠗⠲⠶⠤⡄⠉⢻⣿⣿⣿⣿⣿⣿⠁⠀⠀⠚⠉⠉⠉⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠉⠉⠉⠁⠀⠀⢠⡀⠀⠀⠀⠀⠀⠙⢲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠘⢳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀⠀⠀ ⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⢠⣿⣀⣀⠀⠀⠀⠀⠀⣠⠞⣿⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⢦⡀⠀⠀⠀⣠⡤⠒⠛⢿⡀ ⠀⢀⡟⠀⠀⠈⠙⠲⢤⣀⡼⠃⢀⡏⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢳⣤⠖⠋⠀⠀⠀⠀⠀⣧ ⠀⢸⣇⡾⠀⡀⠀⠀⠀⠙⣷⠀⣼⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣿⠁⢀⡀⠀⢠⠀⠘⣶⠏ ⠀⠀⠻⡇⢰⡏⠠⠶⣤⣴⠏⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠻⣏⠙⠀⣨⣿⠾⠃⠀ ⠀⠀⠀⠉⠛⢧⣤⣤⡼⠃⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠈⠛⠚⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡶⢦⣤⣀⣀⠀⠀⠀⣴⣯⣼⣇⠀⣀⣀⣤⡴⠖⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠈⠉⠉⡿⠁⠀⠀⢹⡉⠁⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣄⣀⡀⠀⠀⠀⢠⠇⠀⠀⠀⠸⡇⠀⠀⠀⢀⣀⡤⠼⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠀⠉⠙⠶⣄⣀⣼⠀⠀⠀⠀⠀⢷⢄⣠⠞⠉⠀⠀⠀⠀⠉⠹⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡆⠀⠀⠀⠀⢸⣤⣀⡀⠀⠀⠀⢀⣀⣤⡴⣾⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠭⣿⣿⣿⣿⣿⡯⠽⠞⠋⠀⠀⠀⠀⠀⠈⠛⠲⠬⠭⠭⠭⠵⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⢤⣤⣀⣀⣀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⡿⢿⢻⣿⣟⣿⣟⣿⣿⣿⣿⣟⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠻⠟⠙⠚⠻⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⠀⣀⣀⡀⢀⣀⣀⣀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⣿⡿⠿⠛⠛⠛⠿⢿⣿⣷⣄⠀⠀⠀⠀⠀⢸⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⢿⣿⡄⠀⠀⠀⠀⠀⠀ ⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀ ⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀ ⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀ ⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀ ⠀⠈⢿⣿⣶⣄⡀⠀⠀⠀⢀⣀⣴⣿⡿⠋⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀ ⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀ ⠀⣴⠟⠛⠛⠛⢷⣄⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⣸⢿⡄⠀⠀⠀ ⣼⠃⠀⠀⠀⠀⠀⢻⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣰⡟⠈⢿⡄⠀⠀ ⢿⡀⠀⠀⠀⠀⠀⣸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⡟⠀⠀⠈⢿⡀⠀ ⠘⢷⣄⣀⣀⣀⣴⠟⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣿⠀⠀⢰⡟⠀⠀⠀⠀⠈⣷⡀ ⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡤⠴⠶⠶⠶⠶⠶⠶⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⠛⠋⠉⠉⠉⠛⠛⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⣠⡾⢋⣠⣤⡴⠶⠶⠛⠛⠛⠛⠛⠛⠛⠳⠶⠶⣦⣤⣀⡈⠻⣦⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀ ⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⢀⣼⠋⢰⡟⠉⠀⣀⣠⣤⡤⠤⠴⠶⠶⠶⠦⢤⣤⣀⣀⠀⠉⠻⣇⠙⢷⡀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀ ⠀⣠⡟⠁⠀⠀⠀⠀⠀⢀⣾⠁⠀⣼⠃⠀⣼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⡄⠀⢿⡀⠈⢷⡄⠀⠀⠀⠀⠈⢷⡄⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⡿⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⡇⠀⠈⣷⡀⠀⠀⠀⠀⠈⢿⡄⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣷⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⢻⣆ ⢠⡇⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢸⠇⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣿⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢻ ⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⡆⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢸ ⢸⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⢸ ⢸⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⢀⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⢸⡇⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⢸ ⢸⠅⠀⠀⠀⠀⣿⢻⡇⠀⠀⢸⡇⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠈⡇⠀⠀⢸⡟⣿⠀⠀⠀⠀⠀⢸ ⢸⠀⠀⠀⠀⢰⡏⢸⡇⠀⠀⠸⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠇⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⣾ ⢸⡄⠀⠀⠀⣼⠃⠘⢷⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡿⠀⠈⣷⠀⠀⠀⠀⣿ ⢸⡇⠀⠀⠀⣿⠀⠀⠀⢿⡄⠈⠉⠙⠛⠛⠛⠶⠶⠶⠶⠶⢶⣶⠶⠶⠶⠶⠶⠶⠶⠖⠚⠛⠛⠋⠉⢹⡏⠀⠀⠀⣿⡀⠀⠀⠀⣿ ⢸⡇⠀⠀⢰⡏⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇ ⠸⣧⠀⠀⢸⡇⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢸⡇⠀⠀⣸⠇ ⠀⣿⠀⠀⠈⠻⣦⡀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣠⡴⠟⠁⠀⠀⣿⠀ ⠀⢻⡇⠀⠀⠀⠈⠻⢷⣄⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⣠⡾⠋⠀⠀⠀⠀⢸⡏⠀ ⠀⠈⠿⣦⡀⠀⠀⠀⠀⠙⢷⣄⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀⣠⡿⠁⠀ ⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠻⣷⣤⣼⣷⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⣾⣏⣤⣤⡾⠋⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠀⠈⠻⣆⠀⠙⢷⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⡾⠋⠉⠉⣼⠟⠁⠀⢀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⠙⣷⡀⠀⠙⠷⣦⣀⣀⣿⢀⣠⣴⠞⠋⠀⠀⢠⡾⢃⣠⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣌⣿⣄⠀⠀⠀⠉⡟⠛⡟⠉⠀⠀⠀⣀⣤⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⣄⣀⡇⠀⣧⣠⣤⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡠⢴⣴⣾⣿⡿⠓⡠⠀⠀⠀⠀⠠⢄⠁⢀⠀⠀ ⠀⠀⠀⠀⠀⠳⣽⡽⠀⠀⡠⢊⣴⣿⣿⣿⣡⠖⠁⣀⡤⢖⠟⠁⡠⠀⡙⢿⣷⣄ ⠀⠀⠐⡀⠀⠀⠀⠀⢠⣾⣿⣿⢽⣿⣿⣿⣥⠖⣻⣯⡾⠃⠀⡔⡀⠀⣷⢸⢿⣿ ⠀⠀⠀⢰⠀⠀⠀⢠⢟⣿⠃⢀⣾⣿⠟⠋⢀⡾⢋⣾⠃⣠⡾⢰⡇⡇⣿⣿⡞⣿ ⠀⠀⡤⣈⡀⠀⢀⠏⣼⣧⡴⣼⠟⠁⠀⠀⡾⠁⣾⡇⣰⢿⠃⢾⣿⣷⣿⣿⣇⢿ ⠀⠀⠱⠼⠊⠀⠄⡜⣿⣿⡿⠃⠈⠁⠀⢸⠁⢠⡿⣰⢯⠃⠀⠘⣿⣿⣿⣿⣿⠸ ⠀⠀⠀⠀⠀⠀⡘⡀⣸⣿⣱⡤⢴⣄⠀⠈⠀⠘⣷⠏⠌⠢⡀⠀⢿⣿⣿⣿⡟⡄ ⠀⠀⠀⠀⢀⣌⠌⣴⣿⣿⠃⣴⣿⣟⡇⠀⠀⠀⠟⠀⠀⠀⠈⠢⢈⣿⡟⣿⡗⡇ ⠀⠀⢀⡴⡻⣡⣾⠟⢹⡇⠀⡇⢄⢿⠇⠀⠀⠀⠀⠀⠀⣽⣶⣄⡀⠘⢷⡹⣿⣿ ⠀⠀⣧⣾⡿⠋⠁⢀⡜⠙⡄⠓⠐⠁⠀⠀⠀⠀⠀⠀⡼⠛⠻⣟⠛⣆⠈⢷⣿⣿ ⣴⣾⣟⣵⣿⣿⣿⣁⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠠⠔⡹⠀⢸⠀⣼⣿⣿ ⠿⡽⢫⡉⠀⣠⠔⠁⡀⠕⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠊⠀⠀⢊⣾⢿⡿⠉ ⠀⠁⠀⡹⢨⠁⠐⠈⢀⡠⠐⠁⠄⠡⡀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢛⡨⠊⠀⠀ ⠀⠀⡜⠀⠈⣂⠀⠀⠀⠀⡠⠐⠉⡆⠀⣀⢀⣀⣀⣀⡀⠀⠀⣀⠴⣁⡀⠤⠀⠀ ⠀⠈⠀⠀⠀⡇⠑⢄⠀⠀⠀⠀⣲⢥⡎⠀⢰⠀⢸⠀⢀⠉⠙⣿⣧⣀⣀⣂⣤⣼ ⠀⠀⠀⠆⠁⠃⠀⠀⠈⠒⠒⠊⣸⠚⠁⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠈⠚ ⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠋⢆⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⣾⠿⠿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠉⠉⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⢀⡀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⣿⡏⠀⣠⣶⠿⣿⣆⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣶⣶⡶⠶⣾⡿⠀⠀⢿⣧⣔⠛⣿⡄⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠿⢿⣿⠟⠻⢻⣿⡿⠿⠿⠿⠿⣿⣶⠶⣿⣷⣶⣶⣤⣭⣿⣷⣾⣿⣶⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣴⣿⣣⣶⠄⠺⠟⢀⣴⡿⠀⣰⡿⠁⠴⠿⢷⣶⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠟⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠟⠛⠛⠛⠛⠿⠿⣿⡟⢿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡗⢈⣿⣿⠄⠀⠀⠀⠀ ⣠⣤⣤⣾⡇⠀⣾⡿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢿⣦⠀⠀⠀⢀⣀⣀⣀⠹⣿⣿⡏⠁⠀⠀⠀⠀⠀ ⠈⣉⣹⣿⠀⢸⣿⡀⣼⡇⢀⣴⣾⣿⣿⣿⠿⢷⣦⠀⣿⡇⢀⣿⠇⠀⠀⢈⣉⣉⠉⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠙⠛⠋⢿⣆⠀⠻⠿⠟⠁⠸⣿⣿⡟⠁⠀⢀⣼⡿⠀⠙⠿⠾⠟⠀⠀⠀⠈⠙⠛⠛⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⠟⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠇⠈⠙⠛⢿⣶⣄⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠋⠁⠀⠀⢀⣴⣿⠿⢿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⡿⣷⣄⠀⠀⣠⣿⣿⣷⣄⣀⣀⣠⣿⣿⣦⠀⠀⠀⢀⣠⣶⠿⠋⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠏⠀⠈⠻⣷⣴⡿⠁⣿⡏⠉⠉⠉⠉⣿⡏⢻⣷⣠⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀ ⠀⠀⢀⣾⠏⠀⢀⡀⠀⠈⠉⠁⢠⣿⠀⠀⠀⠀⠀⢹⡇⠀⠙⠟⠁⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀ ⠀⠀⣼⡟⠀⠀⢸⡟⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣧⠘⠟⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀ ⠀⣸⣿⠁⠀⠀⣸⡇⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⢸⣿⠀⣀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀ ⢠⣿⠇⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠘⠛⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡄

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

⣿⣀⡞⠀⠀⠀⣠⠞⠈⠀⣴⠋⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⣠⡴⠟⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⣿⡿⠁⠀⠀⡴⠃⠀⠀⣰⠁⠀⠀⠀⠀⢠⡟⢀⣠⠤⠒⠛⠉⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⠃⠀⠀⡾⠁⠀⠀⣸⠃⠀⠀⠀⠀⠀⡾⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠈⠙⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⠀⢀⡾⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠠⠤⠴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⢀⡜⠐⢦⣀⣀⡏⠀⢀⣀⣤⣤⣼⣧⣴⣶⣶⣶⣦⣤⣀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸ ⣿⡟⠁⠀⠀⠈⣽⠻⣿⣿⣿⡿⢱⠟⠛⠛⠛⠛⢛⣿⣷⣯⣗⢦⣀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸ ⣿⠁⠀⠀⠀⢠⠇⠀⢻⣻⣿⢢⠟⠀⠀⠀⢀⡶⠋⠀⠀⣈⡙⠷⣮⡳⣄⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠀⠀⠀⠈⠙⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢸ ⣿⠀⠀⠀⠀⡿⠀⠀⠀⠻⢇⣼⣦⣀⣠⣤⣬⣥⣤⣤⣤⣉⣉⣀⣿⣙⢮⡃⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⣖⣒⣚⣽⣶⣶⣶⣾⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢸ ⣿⠀⠀⠀⢸⠃⠀⠀⠀⢀⣼⠧⢛⣻⡯⠼⠋⣛⠡⠤⣗⣛⠿⠁⠀⠀⠀⠁⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣻⠋⠋⠉⠉⠉⠉⠉⠛⠛⢻⡿⠿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠘⣦⣸ ⣿⠀⠀⠀⡞⠀⠀⠀⠀⣩⡿⠒⠋⠁⢀⣀⡬⠵⣒⡊⠉⠀⠀⠀⠀⠀⠀⠀⢰⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠶⢤⣄⣀⠀⢀⡴⠋⠀⠀⠀⠉⠻⣿⣿⣶⣄⠀⠀⠀⠈⢿ ⣿⠀⠀⢀⡇⠀⠀⠒⠉⣾⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠿⢺⣧⣀⠀⠙⠓⠂⠀⢹⢹⣿⣿⣷⣤⣤⣤⢾ ⣿⠀⠀⢸⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⣙⢩⣗⣶⣤⣤⣾⡿⢟⡿⠏⠁⠀⠀⣸ ⣿⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠈⠓⠊⠓⠉⠀⠀⠀⠀⠀⢠⣿ ⣿⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢸ ⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿ ⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿ ⣿⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⣤⠤⠖⠖⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠯⢿ ⣿⠀⠀⠀⠀⠀⡾⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⢀⣦⠖⠁⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⡇⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠃⠀⢀⣞⣠⡤⠴⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⣿⡄⠘⡿⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣤⣴⣾⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡾⠋⠀⠀⠀⠀⣠⢿ ⣿⠀⠀⠀⠀⠀⣿⣷⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⢀⣴⠟⠁⢸ ⣿⠀⠀⠀⠀⠀⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠏⠁⠀⠀⠀⠀⠉⢛⡿⠛⠛⠛⠛⠻⠻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠧⠴⢶⢛⡽⠁⠀⠀⢸ ⣿⠀⠀⡇⠀⠀⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢀⣴⡷⢻⡀⠀⠀⠀⢸ ⣿⠀⠀⣿⠀⠀⣿⡿⢹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢀⡴⡟⠋⠀⢈⡇⠀⣀⣤⣾ ⣿⠀⠀⢹⡀⠀⣿⠃⠈⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣻⠁⡼⢸⠃⠀⠀⣼⡧⢿⡟⠁⢸ ⣿⠀⠀⠀⡇⠀⣇⠀⠀⢸⣿⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⣰⠟⣧⣀⡇⣀⣤⣶⣿⢃⣿⠁⢀⣾ ⣿⠀⠀⠀⢻⠀⢻⡄⠀⠀⣿⣼⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⢀⣠⠤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⣴⣿⠀⠀⠀⣽⣿⣿⣿⡿⢸⣇⡤⠞⢹ ⣿⠀⠀⠀⠸⡆⠸⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠁⣀⣴⣻⠋⣿⡀⠀⢰⣿⣿⣿⣿⠁⣿⠋⠀⠀⢸ ⣿⠀⠀⠀⠀⢻⡀⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⠴⠚⣩⠞⠁⠀⣼⣿⣶⣿⣿⣿⣿⣿⣻⡟⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⠀⣇⢸⡀⠀⠀⠸⣿⣿⣿⣿⡏⡾⠃⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣟⣛⣩⣽⣿⠏⢀⣴⠞⠁⠀⢀⢾⡵⣿⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸ ⣿⡀⠀⠀⠀⠀⠘⣆⢧⠀⠀⠀⣿⣿⣿⢃⡾⢷⣀⢸⡜⣿⣿⣦⣀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠾⠋⠁⢀⣠⣶⡿⢋⡼⠃⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸ ⣿⣷⣄⠀⠀⠀⠀⠹⡜⣧⠀⠀⢸⣿⠃⡞⠁⠈⠛⢻⡧⠈⢻⣿⣿⣿⣿⣿⣿⣿⣛⣛⡻⠿⠿⡿⢿⢿⢟⣛⠛⠁⢀⣀⡤⢶⡿⠛⣁⣤⣾⠁⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸

⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠄⠀⠢⠤⠤⣄⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣁⡀⠉⢣⠀⡀⠀⠈⣷⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⣶⣦⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣿⣿⣿⠀⠀⡇⡇⠀⠀⢸⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠸⣿⡿⠀⠀⢸⠀⢷⣄⠀⠀⠀⢀⣶⠋⠳⣄⣉⢁⣀⡴⠁⠁⠀⠀⢸⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⣀⣠⠴⠛⠀⠀⠉⠛⠲⠶⠛⠁⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡾⠁⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠞⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⢳⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣴⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⣼⠳⢄⡙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⢋⣠⠾⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⢀⡾⠁⠀⠀⠉⠓⠤⣌⡉⠒⠦⠤⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⡤⠤⠒⢉⣡⠤⠚⠉⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⢀⣀⠤⠔⠚⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠢⠤⠤⢤⣉⣉⣉⣉⡥⠤⠤⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗⠢⢤⣀⠀⠀⢸⣿ ⣿⡇⠠⠀⣠⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠉⠂⢸⣿ ⣿⡇⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢸⣿ ⣿⡇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢸⣿ ⣿⣧⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣧⣤⣤⣼⣿

⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡵⡅⠋⢳⣹⣆⠁⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢶⠖⠂⠀⡤⠀⠀⠀⠀⠀⠀⠀ ⣝⢦⡈⠲⢤⣀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠁⢻⡾⣵⣦⣾⡏⡿⡀⠁⠀⠀⠀⠀⠀⠒⠙⠒⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣴⣵⠷⠊⠉⠀⠀⠀⠀⠡ ⠀⠙⠺⠷⣀⣀⠴⠂⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢠⢾⢿⣿⢶⣶⢆⡈⠻⠿⣧⡻⣆⡠⠀⠀⠀⠀⠀⠀⣨⡵⣾⣱⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡥⡄⠀⣠⢸⠀⠀⠀⠀ ⠄⠀⠀⣀⠜⠉⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠩⣯⢯⣻⡳⡿⠙⠙⢦⡀⠀⠙⠻⢝⠳⡄⠀⠂⡀⠀⢾⣿⣫⣿⠇⠀⠀⢀⣀⣠⡤⠤⠤⢴⣖⣛⣛⣭⡄⡇⠐⢁⠣⠀⠀⠀⠒ ⣠⠴⠚⠁⠀⠀⠀⢀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣿⣻⣂⣀⠀⠀⣻⡄⠀⠀⠀⢻⣷⡀⢸⡧⢠⣿⠟⠃⠁⣠⣴⣾⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠓⠛⠋⠉⠋⠙⠋⠀⠃⠀⠀⠀⠀⡏⢷⢺⡇⠘⡿⠀⢀⡞⢡⣾⣿⡟⠋⠁⣴⣮⣹⣿⣿⣿⣿⡿⢡⡿⣄⡷⠂⠀⠀⠀⠀ ⠠⠀⠀⠀⢀⣾⡕⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⢶⣶⣲⣲⡶⠶⢤⣄⡀⠀⠀⢀⡇⣿⣼⣷⣤⣷⣀⡼⣸⣿⣿⡟⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⢁⡜⠀⢹⠁⡎⡞⠀⠀⣴ ⡁⠀⠀⠀⣵⣯⠴⠶⢿⠀⠀⢀⣀⣤⢴⣖⣋⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣛⢦⣤⣿⣾⠿⡟⣏⠻⣿⣿⣇⣿⠛⠻⠷⠶⠶⠾⣿⢿⢿⡿⠿⣋⣡⠞⠁⠀⢸⣿⢰⠁⣀⡀⠀ ⠈⠁⢂⠶⠃⠀⠀⣤⠾⣛⣛⣡⣴⣾⣿⣿⣿⠟⠋⠀⢸⣿⣙⢿⣿⣿⣿⣿⣿⣿⠿⣝⣿⠷⣄⢿⣾⠰⠿⠟⢿⣛⡿⠛⠙⠛⢿⠟⢟⡿⠛⠛⠛⠋⠀⠀⠀⠀⠈⣇⡋⡸⢀⠹⡄ ⣂⡈⠀⠀⠀⠀⠀⢘⣦⣌⠻⣿⣿⣿⣿⡿⠁⠀⠀⠰⣿⣿⣿⣿⣿⣿⡟⣿⣵⣾⡿⠏⠉⠓⠀⢸⣿⡇⠀⠀⠀⠉⠓⠀⠀⠀⠀⡠⡺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠃⠟⢧⢻ ⣿⣤⣤⣄⠀⠀⢀⡼⠀⡟⢧⣈⠻⣿⡟⠀⠀⠀⠀⢸⣿⣿⡿⢟⣫⣷⡿⣻⣽⣿⠁⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⢰⠀⠘⠸ ⠈⠙⠲⠤⣀⣀⣾⠟⠀⡇⠀⠙⣷⣌⣙⠳⠶⠶⠶⢚⣻⣵⢾⡿⠏⠁⠈⢡⡿⠃⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⠀⠀⠀ ⢦⡀⠀⠀⣤⣿⣁⣀⡀⣧⠀⠀⠈⠻⣿⣿⣟⡻⢋⢙⡫⠚⠁⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡜⢠⠘⢃⠀ ⢀⣹⠦⠾⠯⠤⣴⣖⣂⣿⠀⠀⠀⠀⠀⠀⠙⠓⢷⣫⡄⠀⠀⠀⡠⠒⠅⢻⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⠀⢰ ⣏⣀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣦⡤⠀⡠⢀⠀⠘⡿⣶⣶⣦⣤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠄⠁⠀⡞ ⠉⠻⣽⡶⣤⡿⠉⡷⣦⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠊⢀⢔⡴⠋⠀⣪⣾⠟⠗⠉⠃⢀⣠⣤⣠⣤⣶⠶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠁⣸⢀ ⠻⣦⣀⣉⣷⣷⠈⡟⢦⣹⣮⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢖⠁⠀⠀⢈⢾⡿⠁⠀⢀⣴⣶⣿⡿⠿⠿⠖⠛⠛⠚⠷⠶⣯⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠶⠾⣿⠋ ⠀⠈⠻⢿⡷⣼⡄⢹⡠⣝⢯⡳⣷⡀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣡⡾⢋⣜⡿⠋⠀⣠⣖⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢒⠄⢠⢀ ⠀⠀⠀⠈⠹⣿⣧⡀⠁⢈⣙⣻⡝⢷⡀⠀⢀⠀⠀⠀⢠⣟⣾⠟⠱⠋⠈⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⡀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⢳⣷⣄⣷⣿⣷⡁⠛ ⠀⠀⠀⠀⠀⠈⢯⣷⣄⠘⢧⡉⢿⡌⣷⣤⢿⣆⠀⠐⣾⠿⡵⣠⠃⠀⠀⣠⡿⠋⠀⠀⠀⠀⣠⡴⣶⡿⢫⠟⠻⠛⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⣿⣿⣏⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣝⢷⣄⠙⣦⡉⢩⡏⠀⢹⣆⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⣀⣤⠞⢁⢞⢕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣾⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⢹⣿⣦⣹⡟⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⢐⠕⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⡿⣱⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⢹⣿⡟⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢏⡿⣳⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣿⠃⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣾⣟⣥⣾⡽⡿⠁⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠇⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢀⣀⣤⣤⣶⣾⣽⣿⣿⣿⡿⣻⣟⣾⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡽⣻⣶⣶⣦⣄⣀⠀⠀⠀⠀⢀⣀⣤⣶⣶⢿⣿⣿⣿⣿⣷⣶⢿⣿⣿⣿⣿⣿⣟⣵⣿⢯⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠻⢿⣿⣯⣴⣿⢟⣿⡿⣿⣿⣿⣿⣿⣿⣻⣿⢿⣿⣿⣿⣻⣟⢄⣾⢿⣏⡟⣽⢟⡾⣵⣳⣷⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠙⠛⠻⠿⠿⢿⣯⣟⣟⣿⢿⣋⣽⢋⣿⣿⡿⣱⣿⢏⣾⣯⢯⣾⣿⡽⢛⣿⣿⢏⠘⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣫⣾⡟⠘⣵⣿⣯⣿⣿⣿⣿⣟⣿⣿⣿⢯⢯⢿⣇⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠳⢆⠀⠀⠀⠀⠀⢰⡧⠚⠉⠁⠀⠉⠙⠲⣄⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⢀⣾⡷⣿⣿⣿⣿⣷⣯⢯⣾⠇⣟⠛⠛⠚⠚⠤⣬⣛⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠈⢳⡄⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣞⣟⡿⢽⣷⣻⣿⢡⢯⣿⣦⣻⠀⠀⠀⠀⠀⠀⠈⠉⠛⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠹⡄⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢱⡿⣳⠀⠀⠙⣿⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀⠀⠀⢸⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡟⠛⠛⠋⠟⠀⣀⣀⣩⣿⣿⣿⣶⣶⣤⣀⣁⣴⠋⠁⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠐⠒⣀⡈⠀⠠⠀⠀⠀⠀ ⡗⠀⠀⠀⠀⠀⣿⣿⠻⣿⡻⠿⣭⣽⣛⣻⡟⠁⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣄⠀⠀⠀⠀⠀⠈⢷⣄⣴⣶⣶⣿⣿⣉⠁⡤⠤⠖⠀⠉⠀ ⡟⠀⠐⠐⢾⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⠃⠀⠀⠀⠀⢀⣴⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡿⣷⣄⠀⠀⠀⠀⢈⣿⣿⣿⡿⠿⣷⣿⣇⣥⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣰⡿⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⢹⣿⠟⠃⠀⠀⠈⠋⠡⣤⠀⠀⠀⠀ ⠈⠀⠘⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⢿⣟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠇⠀⠀⠀⢆⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢴⠄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⡿⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⡏⠉⠉⠛⣛⡿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣹⡎⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⡁⠚⠁⠀⠀⠀⠀⠀⠀⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⠀⠈⠁⠀⠀⣤⠸⠿⢿⣿⡄⠀⠀⣀⡀⠀⠈⠻⣿⣿⣷⣮⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⢀⢀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠶⠖⠲⠇⠀⠀⠀ ⣽⣶⡆⠀⠀⠀⡀⡀⢉⣿⣿⣶⣶⣤⣿⡇⠀⠀⠈⠛⣿⣶⣶⣌⡻⢿⣿⣿⣿⣯⣲⣄⡀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠟⢠⣲⣾⣿⣿⠗⠀⠀⣸⣻⣿⣿⣿⣿⣶⡤⠀⠀⣀⣠⣤⣶ ⣿⣿⣿⣾⣶⣿⣿⣿⣿⣿⣿⠟⠉⡀⠉⣿⠀⠀⠀⠀⠘⢿⣿⣿⣿⣶⣍⠻⣿⣿⣿⣿⣿⣴⣶⣿⣿⣿⣿⣿⢋⣠⣾⣿⢟⣿⠋⠀⠀⠀⢠⡿⠛⠋⠛⢿⣿⣷⣶⣿⣿⣿⡿⠟⠋ ⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣾⣿⣄⢸⡀⠀⣾⡟⠉⠀⠈⠬⢍⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠉⠁⠀⢶⣤⠀⣼⠇⢀⣶⡄⠈⣿⠿⠟⠛⠋⠁⠀⠀⠀ ⣤⣬⡹⠟⠉⠛⣿⣿⣿⣿⠀⠸⠿⣿⣿⣿⡇⠠⣿⣹⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⣜⡿⠀⣽⣴⣿⣿⣿⠀⢼⡄⢀⣴⣦⣀⣀⠀⠀ ⣿⣿⣷⣄⠀⢀⣿⠛⠻⣿⣇⠀⢸⣿⣿⠁⣧⠀⠹⣧⡳⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⡼⣿⠁⢀⡏⢸⣿⣿⠁⠀⣸⠷⡿⣿⣿⣿⠂⠄⠀ ⠀⠀⠀⠉⠀⠈⡀⠀⣠⣾⣿⣦⣜⠻⣿⣷⣽⡀⠀⠹⣷⡄⠠⣄⡀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠻⣧⡙⠲⣄⡀⠀⢀⣠⠴⣊⣿⠇⠀⢸⣷⣿⣿⡟⠀⣰⠟⠀⠀⠈⠉⠀⠀⠀⠀ ⣿⣶⣤⣤⣀⣀⣁⣀⣀⣈⣉⣹⣿⣦⡀⠉⠙⡇⠀⠀⢿⢿⣳⣦⣭⣭⣿⣾⣿⣿⣿⡟⢸⣿⣿⠀⢿⣦⡨⢽⣶⣶⣤⣶⣾⡿⠟⠀⠀⡿⢿⠟⢁⣴⣾⣁⣠⡀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣿⠀⠀⠈⠋⠻⣿⣿⣿⣿⣿⣿⣿⡿⠁⢸⣿⣿⠆⠸⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢰⠃⢀⣴⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⡤ ⣄⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠟⠃⠲⠤⠉⢩⠴⠦⠟⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣍⡉⠀⠀ ⣿⣿⣶⣤⣀⠀⠹⢿⠛⠙⢿⣿⣶⣤⣄⣈⡉⠛⢿⠀⠀⠀⠀⠀⠘⢿⡿⠛⠁⠀⠀⣠⣾⣿⣿⣷⠀⠀⠀⠈⠻⣿⡿⠃⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣇⡹⠿⣿⣿⣿⣿⣿⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣟⣻⣿⣿⣟⣿⣶⣄⣀⡤⠉⠀⠀⠀⠀⠄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⣀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣄⣛⠛⠿⠿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠛⠍⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⡤⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠻⠿⠿⠿⣦⡀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣄⣀⣀⣤⡄⠀⠀⠀⠀⠄⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠀⠀⠀ ⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⡟⠳⣄⡀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⣿⣯⣿⠉⡶⠀⠂⠀ ⡷⠶⢭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠒⠈⠉⠩⢽⣿⣿⣻⣿⣇⠀⠈⠙⣦⣄⠀⠻⣿⣿⣿⣿⣿⡿⠃⢀⣤⠞⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⡷⠀⠀⣀⣀⣀⣲ ⠷⠤⠴⠾⠿⠿⠟⠛⠛⠛⠛⠻⠿⢿⣿⣶⠆⠀⠀⠀⠀⢀⣀⣿⠀⠀⠀⢻⡍⠓⢦⣄⣈⠉⢉⣀⣤⠞⢋⡼⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⣥⣤⣿⣿⠛⠛⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠒⠒⠤⣄⠀⣠⠾⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣷⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢰⠃⠀⠀⠀⠀⠀⠀⣠⢾⣯⢞⣅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢠⣯⡙⠯⣿⣟⡅⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡤⠴⠴⠒⠒⠚⢛⣝⠭⢧⠀⣇⠀⠀⠀⠀⠀⣠⠏⠀⠙⠢⡟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⢠⡶⡶⠄⠀⠀⢛⣻⣟⠛⣆⣿⠀⠀⠀⠀⠀⢻⠢⢤⣀⣸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⠉⣿⣟⡆⠀⠀⠘⢿⠿⠛⢻⡿⠀⠀⠀⠀⢀⡇⠀⠀⢨⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠉⠀⣺⢿⣒⣀⠀⠀⡾⠁⠀⠀⣀⡠⠞⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⡀⠸⠯⣿⡿⠋⣠⠞⠉⠳⢎⡉⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠉⣳⣖⠛⠛⡏⠙⣄⠀⢀⠴⠋⠀⠀⠀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⡀⠀⠀⢸⠇⠈⠛⠋⠁⠀⠘⡟⠳⠦⣄⣠⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⢉⡩⠞⠛⢧⠀⠀⠀⠀⠀⢠⠇⠀⢠⠏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠘⠳⣄⠀⠀⠳⡀⠀⠀⠀⡎⠀⠀⡞⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢀⡠⢼⠀⠈⠳⡄⠀⠱⡄⠀⢸⠀⠀⡸⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠁⠀⠀⣠⠖⠉⠀⢸⡇⠀⠀⠘⢦⠀⠹⡄⡎⠀⣰⠃⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣏⠀⠀⣰⠃⠀⠀⠀⢸⠃⠀⠀⠀⠈⢣⡀⢳⡇⢠⠏⠀⠀⠀⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠈⠉⠒⣷⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠱⣜⣧⡏⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⠞⠳⣄⡀⣰⠃⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⢸⣯⡄⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣷⠀⠀⢀⡽⠁⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡞⠀⢧⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠙⠳⡤⠤⠤⢄⣀⣀⣠⠇⠀⠸⣆⣀⠤⠔⠚⠻⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡖⠉⢦⡀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠙⠒⢤⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣂⠤⠤⠞⢇⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠛⠒⠦⣤⣤⡏⠑⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠓⠢⢤⣤⣽⠉⠲⢤⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⢤⣀⡀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡤⣄⣀⠀⠀⠀⠀⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠈⠉⠉⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢳⣿⣨⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡟⣿⣯⠿⠃⠀⢈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠷⣷⣈⡉⢀⣠⡴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⡏⠀⢀⡵⠛⡛⠛⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣹⡷⠾⠏⠀⢾⣯⣶⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠿⠛⠛⠛⠛⠛⠛⠳⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠿⠭⢽⠆⠀⢀⣤⣬⠭⢳⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠏⠀⠀⠸⣏⡀⢀⡞⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀ ⠀⠀⠀⠸⣤⡀⠀⠀⡟⠶⠿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠖⠛⠉⠉⠛⠶⣤⡀⠀⠀⠻⣆⠀⠀ ⠀⠀⠀⢀⡜⠿⣶⠾⠃⠀⠀⠈⠳⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⣛⣡⣤⣄⣀⣀⠀⠀⠀⠀⠹⣷⡄⠀⢹⡄⠀ ⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢀⣾⠿⠛⠉⠉⠀⠀⠈⠉⠙⠶⣄⠀⠀⠈⢿⣆⠀⣷⠀ ⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⣤⣴⠖⠒⠒⠲⣤⣀⠈⠳⣄⠀⠈⢿⡄⢸⡆ ⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠉⠉⠉⠙⠳⢤⡀⠙⢿⣄⠹⣧⠀⠘⣷⢸⡇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠹⣿⣄⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠹⣄⠀⠻⣧⢿⡆⠀⢿⢸⡇ ⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠙⠻⠿⣷⣤⣤⣄⣀⣀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠛⠓⠤⣄⠈⠙⠻⣧⣻⡄⠀⢻⣿⣧⠀⢸⣿⠇ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠲⢤⡀⠀⠀⣀⡀⠘⢷⣦⣤⣄⡈⢳⡄⠀⠈⢿⡇⠀⠀⢻⣿⠀⢠⣿⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠙⣿⣶⣄⠙⣆⠉⠻⣦⣿⠀⠀⠈⡇⠀⠀⠈⡇⠀⣸⠇⠀ ⢻⣇⠀⠀⠀⠀⠀⢠⠏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠹⣶⡙⢷⣸⡄⠀⢻⡾⠀⠀⠀⠃⠀⠀⠀⠁⠀⠉⠀⠀ ⠘⣿⡄⠀⠀⠀⠀⢸⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⠀⠀⠀⠙⡆⢠⢯⣇⠀⢻⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣷⡄⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⣷⡞⢸⡏⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠝⠀⡾⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣷⣄⠀⣄⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⢷⣄⡙⠦⣀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣝⠂⠈⠳⣄⠈⠛⢷⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠹⣷⡀⠀⠈⠉⠉⠛⠉⠙⠓⠒⠒⠒⠒⢛⣛⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠘⣿⡄⠀⠀⠀⢀⣴⡾⠟⠛⠓⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠙⣷⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⣀⣀⣹⣧⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡍⢱⠈⠿⠗⡛⢻⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⡇⢸⣦⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣶⢯⣭⠆⣀⣾⣋⣁⣀⡟⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣴⣿⣽⣿⣿⡿⣭⣀⣼⡏⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⣾⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣖⣊⣉⣁⣀⡀⠀⠀⠀⠀⠉⠉⠒⠦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠤⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢄⡀⠀⠀⠀⠈⠳⡀⠀⠀ ⠀⠀⠀⡰⠁⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠹⡀⠀ ⠀⠀⠀⢱⡒⠂⠒⠒⠒⡾⠁⠀⠀⠀⠀⢀⣀⠤⠖⠒⢤⡀⠀⠀⠑⣄⠀⠀⢣⠀ ⠀⠀⢠⣾⣿⡏⠒⣄⠀⠧⠤⠤⠤⠒⠊⠉⠀⠀⠀⠀⠀⠉⢢⡀⠀⠘⡄⠀⠘⡆ ⡤⠤⢾⣙⠛⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣤⣤⣀⠀⠙⡄⠀⣧⠀⠀⡇ ⠘⢦⡀⣹⠉⠉⠉⠀⢿⠳⡦⣤⣄⣀⡀⠀⠈⢇⠀⠿⣿⠏⢣⣠⠃⢀⣼⣀⣀⡀ ⠀⠀⢹⠃⠀⠀⠀⠀⠘⢦⣁⡏⢠⡏⣹⠄⠀⠈⠑⠒⠒⠒⢻⠏⠀⡸⠀⠀⡰⡇ ⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡷⠒⠊⢀⠇ ⠀⠀⠀⠀⠀⠈⠑⠢⠤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⡤⢴⠏⠀⠀⡰⠹⣄⠀⡜⠀ ⠀⠀⠀⢠⠎⢩⠓⠢⣄⠀⠈⡟⢫⠉⣩⠋⠁⠀⢸⡀⢏⣀⣀⠜⠁⠀⠘⠶⠁⠀ ⠀⠀⠀⢸⠀⠘⠚⢠⠋⠉⠉⡇⠈⡿⠟⠉⢳⣀⣀⠑⡆⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠣⠤⠔⠳⠤⠄⢼⠁⠀⡇⠀⣠⠇⠀⠈⠙⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠈⠉⠉⠙⠦⣀⣀⣀⣀⣀⡼⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⡴⡇⢀⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⢠⠋⠀⠙⢆⠀⠀⣀⣀⣼⠁⠛⠉⣵⣋⡀⠀⠀⣠⠖⠋⠙⡄ ⠀⡞⠀⠀⠀⠈⠓⠋⠁⠀⠃⠀⠤⠴⠚⠃⠉⠙⠚⠁⠀⠀⠀⡇ ⠀⡇⠀⡶⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⢹ ⢰⠁⠀⡇⠀⠀⢸⣵⣿⡇⠀⠀⠀⠀⠀⢰⣹⣿⠀⠀⠀⡇⠀⢸ ⢸⠀⠀⡇⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⡇⠀⢸ ⢸⠀⠀⡇⠀⠀⠀⠻⠟⠃⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⡇⠀⡾ ⠈⠒⠖⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡤⠃ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⢿⣿⠆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⢳⡀⠀⠀⠀⠰⠶⠶⠛⠙⠷⠦⠄⠀⠀⠀⠀⣸⠁⠀⠀ ⠀⠀⠀⠀⠱⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠒⠦⠤⠤⠤⠤⠤⠤⠖⠋⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠏⠀⠀⢣⢩⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠾⠃⠀⡀⠀⠀⠈⣼⡀⢱⡘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣶⡏⠁⠀⠀⢰⠃⢀⣀⠀⢣⣧⣤⣷⣄⣙⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⢿⢸⠁⠀⠀⣀⡤⢶⢻⣿⢶⠆⠷⠘⡜⡀⠀⠀⢬⡙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⠈⣀⣠⠖⠋⠁⠀⠀⣦⠀⠸⣧⠀⠀⢱⢁⠀⠀⠈⡇⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡟⠋⠉⠀⠀⠀⠘⣦⠀⠸⣧⠀⢻⣇⣀⣀⣈⣠⣤⣤⣤⣀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⡆⢀⠀⠀⠘⡄⠀⠹⢀⣠⣴⠶⢻⣿⣿⣽⡿⣽⠟⢿⠛⢯⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⠸⠂⠀⠀⣠⣴⡞⠛⠉⠀⠀⢸⠸⣿⣿⣿⣿⣷⣾⣷⣾⣷⣺⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡏⠀⢀⣴⡿⠛⠛⠋⠉⠁⠀⠀⠀⢣⡹⣏⡙⣿⣿⣿⣿⣿⣿⣿⣿⡶⠆⠀⠀⠀⠀⠀⠀ ⠰⣮⣷⣴⣿⣿⠃⢀⣠⣶⣦⣀⠀⠀⠀⠀⢀⣴⠿⣿⣿⣿⡛⠋⠙⣹⠛⠓⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⣻⢿⡿⣿⠰⠋⣿⣩⣿⣿⠀⠐⠀⠀⠀⣷⣶⣿⣿⠻⣿⡶⠚⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢧⠐⠻⣿⡄⠀⠿⣿⡿⠟⢀⢤⣤⠤⢄⠙⠛⠛⠋⡰⢻⣷⣄⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠓⠤⠤⣿⢻⠳⣄⠀⠀⠘⠦⠭⠤⠚⠀⠀⣠⠔⠃⠌⣸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⡌⠃⠈⠹⣦⣤⡤⠤⠤⠶⣶⣿⡅⠀⣠⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⣀⣤⡄ ⠀⠀⠀⠀⠀⣿⣿⣿⣦⣀⢀⣿⡁⠀⠀⡤⠚⢁⣿⣿⣿⣿⣿⣿⠋⠇⠀⣴⣲⣦⠞⠛⠙⠏⠀ ⠀⠀⠀⠀⢰⣿⣿⣩⡛⣯⣿⣷⣟⠢⠤⠤⠔⣻⣿⢙⠋⠈⢩⢿⡄⢸⡐⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠁⠀⠀⡾⣿⣿⣿⣆⠀⠀⠀⣿⣿⠏⠀⠀⠀⠘⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⡏⠀⠀⠀⢠⣿⢿⣿⣿⠀⠀⠀⣿⣿⣧⡀⠀⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣤⣤⣶⣾⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀ ⠸⣿⣿⡿⠛⠉⠉⠛⠋⠁⠀⠀⠀⠀⠉⠀⠀⠀⠈⠙⢿⣿⣷⡀ ⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇ ⠀⢿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⢸⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣿⣿⡟ ⠀⠈⣿⡇⠀⠀⠀⠀⠐⣷⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⣰⣿⣿⡇ ⠀⠀⢹⣷⣄⡀⠀⠀⣀⣿⣦⣀⣀⣀⣠⣾⣷⣶⣶⣾⣿⣿⡟⠀ ⠀⠀⠘⣿⣿⡿⠛⠋⠉⠀⠀⠈⠉⠈⠛⣿⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⡿⠿⠿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡄⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣧⣤⣼⣿⣿⣿⣿⡿⠿⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠂⠈⠉⠉⠉⠉⠉⠉⠛⠉⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⢀⠀⠀⢀⡔⢀⠈⢡⠆⠀⠀⠀⠀⠀⠁⠢⡀⠀ ⠀⠀⠀⠀⠀⠔⠁⢀⠄⠀⡠⠁⡠⠐⠵⠂⠁⠀⠀⠹⠢⡀⠰⡀⠀⠀⠀⠈⠢ ⠀⠀⠀⢀⢎⠀⢀⣞⢄⠌⠇⠈⠀⠀⠄⡀⠀⠀⡀⠀⢀⠈⠢⢳⡰⡀⠇⠀⠀ ⠀⠀⠀⡌⠂⠀⡼⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠈⢣⢠⠀⢁ ⠀⠀⡐⠀⠀⡘⠁⠳⢶⢶⣤⣤⣴⠿⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⢻⠀⠀ ⠀⢀⠃⠀⢀⠃⠀⠀⠘⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠈⣟⣣⣶⣶⣶⠒⢺⠀⠀ ⠀⠘⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠀⠈⠀⠀ ⠀⡀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠ ⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀ ⢸⠀⢰⡄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀ ⠸⠀⢸⠄⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⣿⣿⣿⡿⠉⠉⠉⠀⠈⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⠀ ⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠤⠒⠤⣸⣿⣿⣿⣿⣿⡇ ⡏⣿⣿⡧⠀⣀⠀⠀⠀⠈⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇ ⣇⣿⣿⡇⢀⡖⢦⠀⠀⠀⢰⢒⡦⠀⢸⣿⣿⣿⣿⣿⡇ ⠉⠻⣿⣿⠈⠛⠋⠀⠀⠀⠈⠋⠁⠀⠸⣿⣿⣿⣿⣿⡇ ⠀⠀⣉⡏⠀⠀⠀⢀⣀⣀⣀⠀⠀⣠⡤⢙⣻⣿⣿⣿⡇ ⠀⠸⣿⣜⢢⣄⡀⠈⠢⠤⠏⠀⣀⣻⣶⣿⢿⣿⣿⣿⡇ ⠀⠀⠀⢸⣺⠇⢹⣿⡿⡛⡛⠉⢸⢋⣏⠿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠉⠀⣼⢁⡷⣍⣧⡖⠚⠈⡜⢻⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⣧⡎⠙⠋⠀⠀⠀⠘⡄⢸⣿⣿⣿⣿⡀

⠀⢷⣿⡿⠟⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠢⢀⡀⠀⠀⠀ ⠀⠀⡤⠒⠟⠻⠛⠛⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀ ⠀⠠⡄⠀⢄⠀⠀⠀⠀⠄⠈⠂⠀⠀⠀⠀⠀⢀⣀⣀⡤⢤⣈⠂⠀⠀ ⠀⠀⣘⣆⠀⢁⡠⠸⢠⠄⠀⠀⠀⠀⠸⣉⠀⠁⠀⢀⡈⠸⣿⢹⣄⠀ ⠒⡎⡸⠠⡦⠞⠀⠀⢯⠀⠘⠋⠀⢀⡰⠿⢦⣀⡀⢈⣡⠔⣿⠀⡛⠃ ⠀⢷⠁⠀⢇⠀⠀⠀⠀⠉⠉⣹⠟⠋⠀⠀⣸⠇⠀⠀⠁⠀⣸⢠⠃⠀ ⠀⠀⣱⡄⠸⡀⠀⠀⠀⠀⡞⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⣾⠊⠀⠀ ⠀⠀⣿⠈⢱⠀⠀⠀⠀⠘⢇⣀⣀⠔⠋⠀⠀⠀⠀⠀⠀⡸⡙⠀⠀⠀ ⠀⠠⡿⠀⠈⡆⠀⠀⠀⠀⠀⠀⢲⡤⠤⢤⠤⠀⠀⠀⣰⠁⡇⠀⠀⠀ ⠀⠀⡇⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢰⢹⠀⠃⠀⠀⠀ ⠀⢸⠇⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⡈⢸⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⡇⢸⠀⠀⠀⠀ ⠀⡬⠀⠀⠀⠀⠀⠀⢀⠗⠢⠤⠀⣄⣠⠊⠁⠀⠀⢰⢰⢸⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⣿⣿⣋⣤⣶⡾⠿⠿⠿⢿⣿⣿⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⢋⣼⠿⠛⠋⢉⣠⣴⠶⠾⠟⠛⠛⠛⠛⠛⠛⠛⠿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠋⠁⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣦⡀⠀⣠⣾⣿⣿⠿⠿⠿⢿⣿⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣾⣿⡿⠉⠀⠀⠀⠀⠀⠈⢻⣿⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⠿⠿⠿⠿⠿⠿⣷⣶⣄⡀⠹⣿⣷⡀⠀⢀⣠⠄⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡘⣿⣷⣴⠋⠀⠀⠀⠀⢰⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⢀⣠⣴⡾⠿⠟⠛⠿⠿⣷⣤⣀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣜⣿⣧⡀⠀⠀⠀⠀⣼⣿⡿ ⠀⠀⠀⢀⣠⣶⣾⣿⣶⣶⣿⣿⠇⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡄⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⣶⣄⡀⠀⠀⠀⠈⣿⣿⣿⣇⠀⠀⠀⣴⣿⣿⠇ ⠀⠀⣴⣿⡿⠋⠉⠉⠙⢿⣿⣿⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡿⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⢈⣿⣷⠀⠀⠀⠀⠈⢿⣿⣿⣤⣤⣾⣿⡿⠃⠀ ⠀⣼⣿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣤⠞⢻⣿⠀⠀⠀⠀⠀⠸⣿⣿⡿⠿⠟⠋⠀⠀⠀ ⣼⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢠⡴⠶⢶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣶⡾⠃⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⢀⡤⠖⢺⣿⣿⡇⠀⠀⠀⣴⡏⠀⠀⠀⣹⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⢠⡏⠀⠀⠀⢿⣿⣇⠀⠀⠀⢿⣷⣤⣤⡾⠛⣿⡏⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠘⠿⣿⣿⣿⡾⠋⠀⠀⠀⠀⠀⢾⡤⠄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⣿⣦⣄⣀⣀⣠⣴⣾⣿⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⡄⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠛⠻⠿⠿⠟⠛⠋⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⣤⠞⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣷⣶⣤⣄⣀⣀⣀⠀⢀⣀⣀⣀⣠⣴⣶⣾⣿⡿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠁⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⣴⣶⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣾⣿⣿⠁⠀⠀⠀⠀⠐⣆⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠉⠁⠀⠀⠈⠙⠻⣿⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠉⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠙⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠙⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢀⣾⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠀⠀⢀⣠⣾⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⣦⣌⣻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣣⣤⣶⣿⣿⣿⣧⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣶⠟⠋⠉⣀⣠⠍⠛⠿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⢀⠀⠉⠛⢿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⠟⢉⣤⡞⠃⣴⣿⠛⣉⣤⣤⡾⠉⠉⣩⡉⠉⣹⣯⣄⣀⣠⣽⣿⠉⢛⣿⡛⠛⢻⠛⠉⢉⣭⣙⠻⣿⣶⡄⠀⢲⣄⡈⠙⠻⣶⡶⠿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡾⣿⡏⣠⣾⠟⠿⠿⣻⡿⠃⢀⣤⣾⡟⠁⣠⣿⠟⠛⠛⠛⠛⠿⠾⠿⠛⢿⣦⣈⠻⣶⣤⣈⠛⢿⣿⠛⠻⣦⣀⣻⡿⠷⣦⣼⡧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠻⡿⠟⠁⠀⠀⠀⠻⣷⣶⠿⠋⢿⣧⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠿⠏⠉⠛⠛⠋⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⢀⠀⠀⠀

⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⡿⡡⠭⣀⡤⠾⠿⠛⠉⠀⠀⢽⣄⣼⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠘⣼⣿⣿⢹⢸⢳⡟⣠⠀⠀⠀⠀⡄⠀⢄⠰⣶⣿⣿⡏⡇⣿⣿⡆⠀ ⠀⠀⠀⠀⠁⡏⣏⣿⣿⡄⢸⢠⡻⢀⣗⢲⢆⢰⡤⢼⣆⢣⢻⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⢸⡇⣿⣿⣿⣧⣮⡎⡇⢸⢸⢸⢸⣸⣷⣾⡟⣿⣿⣿⣿⣿⣿⣿⡷⠀ ⠀⠀⠀⠀⢸⣇⣿⣿⣿⣿⣿⣁⣧⡿⠙⠟⠀⠛⠹⢟⣳⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⢠⠘⣿⠸⡿⢻⣿⡇⠸⠚⠏⠀⠀⠀⠀⠈⢉⣟⣻⣿⣿⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠢⣿⣇⣧⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⢹⣿⣿⣿⠀⠀ ⠀⢠⢢⣀⡔⢁⣘⣿⢿⣿⣇⠑⠄⠀⠀⢀⣀⠀⠀⠀⠀⢰⣿⣳⣿⣿⢧⣿⠀⠀ ⠀⢈⣿⣄⣠⣬⣷⣵⡟⣿⣿⡦⣀⠀⠈⠁⠀⠈⠀⣀⣴⡿⣾⣿⣿⠟⣼⣿⡄⠀ ⠀⢸⣿⣿⣿⣿⣿⡟⣇⣿⣿⣯⢹⡟⣶⡤⠤⠐⣿⢡⣇⣿⣽⣷⡟⢰⣿⣿⡇⠀ ⢠⣾⣿⣿⣿⣿⣿⣧⡿⣥⣿⣿⢸⣇⠋⠀⠀⠀⠸⡼⡿⣿⣿⣿⢁⡿⠟⣿⣧⠀ ⣴⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⡟⣼⣧⣄⣀⣀⣠⣤⡟⣷⣿⣿⠁⣼⢣⢠⣿⣏⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡿⣱⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⠏⢸⣿⣾⣥⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⡕⢳⣽⣿⣿⣿⣿⣿⣿⣿⠃⠈⠚⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⡽⣿⡄⢀⢻⣿⣿⣿⣿⣿⣿⣿⢀⢋⠈⡧⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠋⠛⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠷⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠛⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⣦⣤⣴⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⠀⠀⠀⢠⡌⢷⡀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠉⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢠⡟⠀⠀⠀⠘⣿⡌⣷⠀⢀⣠⣄⣀⣾⢣⣤⣤⣄⣀⣠⣤⣤⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢠⣿⡇⠀⠀⠀⠀⢿⣷⣾⡷⣿⠉⠈⢻⡿⢶⣤⣤⣿⣿⣯⣤⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠟⣿⠀⠀⠀⠀⠀⢸⣿⣟⢿⣽⣷⡶⠟⠀⢸⡇⠀⢸⡇⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣿⠙⢷⣼⠉⠉⣻⣦⣾⠁⠀⢸⡇⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠛⣿⡶⠚⣿⠉⠀⢀⣿⠀⠀⢸⣎⢻⡀⠀⢸⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣿⣿⠀⣿⠀⠀⣼⣇⣀⡀⠘⣿⠾⢿⡶⢾⣿⠶⢾⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⣿⠀⣿⠀⠀⠉⣿⢻⣿⢻⡟⠀⠸⡇⢸⣿⡆⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡿⢻⣶⠏⠀⠀⠀⣿⣸⣿⣤⡇⠀⠀⣷⣼⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⣿⡟⠛⢿⣿⡟⢻⡿⠛⣻⡟⠛⡛⠛⢻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⡟⠀⡧⠈⣿⡇⠈⡀⠸⣿⡇⠀⣉⣉⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⣁⣰⣶⣄⣸⣇⣸⣿⣄⣘⣇⣀⣉⣉⣹⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣧⡄⢠⣼⠀⠿⠇⢹⠀⠤⢼⣿⣿⠿⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⣶⠀⢸⠀⠓⠚⣿⡀⠸⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⠈⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⠿⠟⠛⠋⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡟⠀⢰⣶⣦⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣟⠛⠙⢠⣾⣿⣿⣿⡇⢀⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣷⣾⣿⣿⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣼⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣶⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⡆⠀⠀⠀⠀⢀⠀⣴⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣆⣀⣤⣴⣿⣶⣿⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣯⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⢾⣶⣿⣦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡟⢻⣿⣿⣿⣿⠻⣿⣿⠟⢧⠀⢀⡁⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣧⢠⣿⡇⠛⠿⠢⣿⣍⡤⠜⠛⢩⣷⠀⠀⠈⢿⣿⣿⣿⣿⣿⡟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⣭⡙⠂⢀⡴⠛⠁⠀⠀⠀⣼⠃⠀⠀⠀⢈⣿⣿⣿⡛⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⢀⣤⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣮⠛⠉⠀⠀⠀⠀⠀⣼⣿⣤⣤⣀⣀⡟⠋⢀⣌⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⠟⠛⣉⣩⣤⣤⣭⣙⠛⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠸⣏⠈⢙⣃⣽⡿⠀⠉⠉⠁⠀⠀⠀⢠⣤⣤⣴⣿⣿⣿⣿⣿⣿⡿⠋⣠⠔⠛⣁⣤⣤⣤⣤⣄⠙⠂⣈⠻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣏⠁⢀⣤⣤⣤⣤⣤⣬⣭⣷⣤⣉⠛⠚⣦⢸⠁⠀⠀⢀⣀⣄⣠⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡼⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡈⠂⠘⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠀⠙⠚⠉⣠⣾⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣸⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢇⠸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡀⢀⣴⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⡇⢸⠀⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢣⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡇⡼⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⢇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣹⠃⢰⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⢀⣀⣀⣀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠳⢌⡻⢿⣿⣿⣿⣿⣿⠟⣩⠟⠁⣰⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠁⠀⠀⣠⠖⠉⠉⠉⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⠉⠓⠾⠭⠭⠶⠖⠋⠁⣠⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⠋⠀⠀⢀⡴⠃⣦⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣤⣤⣶⣾⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠏⠀⢀⣠⠶⠋⠀⡀⠘⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⢰⠋⠀⠀⠀⠀⢿⡇⠘⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡏⠳⡄⠀⠀⠀⠈⣷⠀⠀⠀⢀⣀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡴⠋⠁⠀⠻⣄⠀⠀⠀⢸⡄⠠⠚⠉⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣆⠀⠉⠀⠀⠀⠸⡇⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠈⢷⡀⠀⠀⠀⠀⠘⡆⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢣⡀⠀⠀⠛⣄⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⠀⠈⢧⣶⣿⣿⣿⣿⣿⣿⠟⠛⠁⣠⡟⠐⢀⣙⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢣⡀⠀⠀⠀⠀⠈⢳⣻⣿⣿⡟⠋⠙⢦⡀⣠⠟⢀⣴⠟⠁⠙⢻⣿⣼⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠙⢦⡀⠀⠀⠀⠀⢻⣞⠃⠀⠀⢀⣼⠟⠿⣦⣿⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠙⢆⠀⣠⡴⠋⠉⠳⣤⣾⣟⣋⡠⢀⣬⣿⣿⣷⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣄⠀⠀⠀⠈⢻⣯⡀⠀⢠⡴⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣷⣤⡀⡴⠛⠉⣻⣷⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣦⣤⣀⢠⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀ ⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠶⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣋⣀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡏⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢹⠟⢇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣟⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⡾⠀⢸⡀⠀⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠉⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⡼⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣤⠀⠘⠂⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆⠀⠀⠀⠀ ⠀⣠⣄⠀⠀⢹⡷⣦⣄⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⠶⢶⣶⢟⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠶⠟⠁⣧⢀⣦⠀⠀ ⢀⣿⢈⡉⠳⢦⣽⣿⢶⡏⠉⠉⠉⠉⠉⠉⠀⠀⣽⣧⠴⢋⣤⠏⠀⠀⠀⣇⠀⠀⢀⣀⣤⢶⣖⡋⢹⡇⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⢠⣴⠘⠋⢻⠀⠀ ⢿⡛⢿⣄⠀⠀⠀⠉⠳⣝⡲⠤⠤⠤⠤⠤⠶⢻⣯⣤⣾⠋⠁⠀⠀⠀⠘⠛⠛⠋⠉⠀⠀⠀⠀⡿⠛⢦⣤⠀⠀⠀⠀⠀⠀⠘⣿⣧⣾⣿⠀⠀⢸⡇⠀ ⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠉⣿⠒⠒⠒⠛⠛⠉⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⢀⡀⠈⣿⡄ ⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠃⠸⣿⣿⣿⡀⢸⠂ ⠀⠀⠀⠀⠈⠳⣄⡀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢀⣀⣀⣠⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠛⠛⢻⣳⡾⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⢦⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠉⠉⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡆⠀⠀⠀⣸⣾⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢾⠙⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢀⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣀⣀⠀⢈⡷⣤⣀⡀⠀⠀⠀⣀⣀⡤⠖⠋⠀⠀⢀⣼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠈⠋⠉⠉⠓⢾⡃⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⡤⢞⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠛⠓⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠓⠒⠒⠒⠚⠉⢉⣡⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡤⠾⢷⣦⣄⠀⠀⠀⠀⢠⣟⠁⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠴⣾⣯⣁⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠾⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⢿⣥⣴⣛⣳⣄⣀⣀⣀⣀⣀⣤⠤⠤⠞⠋⠀⠀⠀⠀⠸⣇⡤⢤⣠⡤⣄⣰⠶⣦⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⢀⣉⣉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢧⣤⣿⣤⡼⣯⣴⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣄⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣴⣟⣿⡿⠋⢉⣠⣤⠾⢻⡫⣻⣈⡉⡉⠛⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⢋⣽⠟⠛⣻⡶⠿⠿⣤⣐⣞⠙⢛⣸⣏⣺⣶⣲⣄⣀⠉⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠟⣰⠿⠃⣠⡾⠋⠂⠀⠀⠀⠈⣹⡟⠻⢦⣬⡽⠖⠂⠈⠻⠁⣀⡐⠌⢛⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⣴⠏⢀⣼⠋⠀⠀⠀⠀⠀⠀⠈⠃⠀⣠⢾⠉⡙⢲⣦⡶⠒⠃⢸⡷⣖⣴⠛⢙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠃⢠⡾⠁⠀⠀⠀⠀⠀⠈⠀⠀⡀⠸⠇⣄⠀⣴⠿⠏⢙⣷⣶⠚⢛⣿⢿⢶⡞⣳⣽⣦⠀⠀⠀⠀⠀⠀⠀ ⣗⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠂⠟⠁⠅⣰⠟⠀⢈⣻⣶⡛⢿⣽⣟⣿⡻⣻⣷⡀⠀⠀⠀⠀⠀ ⢹⡟⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠈⠃⣤⣠⣿⣍⠈⢻⣦⡿⠿⠭⠉⠈⠺⣷⡀⠀⠀⠀⠀ ⠘⣇⠐⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣈⣽⣽⣟⠉⠳⣄⠀⠀⢦⣢⡈⣿⡀⠀⠀⠀ ⠀⢻⡄⠘⢟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⣀⠀⠉⠂⠈⠈⠑⣄⢘⣶⡄⠙⢟⣦⠈⣷⠀⠀⠀ ⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢀⠁⠀⢻⣥⣤⠴⠖⠻⣇⠀⠀ ⠀⠀⠘⢿⣷⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⡶⠟⠹⣆⠀⠀⠀⢻⡄⠀ ⠀⠀⠀⠈⢿⡝⣷⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⠏⠀⠀⠀⣹⣷⠶⠒⠚⡇⠀ ⠀⠀⠀⠀⠈⠻⣾⣿⣿⣷⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⣰⣾⠻⢹⣦⡐⠄⢿⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⢀⡾⠁⠈⠀⠈⢹⣏⠐⢸⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢮⣺⣿⣻⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⢠⡟⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⢹⣆⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠯⣽⡻⢿⣿⣿⣿⣿⣷⣶⣦⣾⠁⠀⠀⣾⠃⣀⢀⠀⢀⠀⠐⢦⣿⣼⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢯⣽⣽⣟⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣷⡿⡷⢾⣦⡾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠓⠚⠓⠓⠒⠓⠛⠛⠉⠉⠁⠀⠀⠀

⣤⣤⣤⣀⣀⣀⠀⠀⠙⠲⠤⠤⠤⠤⠖⠈⠀⠀⠀⠀⠀⠀⠀⢀⣠⡝⣻⣵⡶⣛⣫⢭⣿⠛⢻⣒⣂⣙⠛⠿⢿⣿⣿⣿⡀⠈⠁⠀⠀⠀⠀⠀⢀⣴⣇⠸⠷⠄⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣀⡀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣾⣿⣿⣿⣛⣓⠻⣿⣛⣿⣿⣿⣿⣿⣷⣶⣾⣽⣿⣟⣷⣦⣄⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⣯⣽⣿⣿⣿⣿⡟⡻⣿⣯⣿⣿⣷⣮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⡷⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⡿⢏⢚⠿⣿⡿⢿⣿⡿⣟⣾⠟⡚⣥⣾⣿⣿⡛⣩⢍⣿⣿⣿⣿⣿⣷⣌⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣻⢿⣿⣿⣿⣶⣶⣤⣀⣀⣀⣀⣀ ⢳⠯⢔⠀⡄⠒⠮⡝⡺⣽⡒⠈⣽⣿⣿⣿⢿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡈⢿⡻⣿⣿⣾⣝⡿⣦⣄⠀⡀⠀⢐⠈⠉ ⡆⠌⠐⡈⠉⡐⠈⢡⣚⠩⢠⡾⣫⣾⣿⣷⣶⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣦⡙⠿⣿⣿⣷⣿⣻⢷⣦⣉⠀⠀ ⡐⠀⠀⠀⠀⠀⠠⠃⠃⣡⡏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣿⣄⠈⠻⢿⣿⣿⣿⣮⣻⡿⠿ ⡀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡹⣿⣧⡀⠀⠉⠛⠛⠛⣻⠃⠀ ⠁⠀⠀⠀⠀⠀⢀⣾⡿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡽⣿⣇⠀⢠⠀⠀⢠⡏⠀⠀ ⠈⠀⠀⠀⠀⢠⣾⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⡄⣰⡿⠀⠀⡀ ⠈⠀⠀⠀⣰⣿⣿⣿⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣤⣤⣤⣤ ⠀⠀⠀⣰⣿⣿⢣⡟⠀⠀⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠋⠉⠉⠉⠉ ⠀⠀⣴⣿⣿⠃⣸⡇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡏⠀⠀⠀⠀⠀ ⢀⣼⣿⣿⠇⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⡇⠘⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣆⠀⠀⠀⠀⠀ ⣼⢻⣿⠋⢀⢰⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⡇⠀⠘⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡄⠀⡀⠀⠀ ⡟⣾⡁⠀⣸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⣿⣷⠀⢣⠀⠀ ⠀⠈⠻⣾⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡴⢿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⢿⣟⣿⠁⠀⣿⣿⣿⣿⣿⡿⢿⣿⣿⣋⣻⣿⣿⣿⣿⣿⠉⢻⣿⣿⣿⣿⣿⣯⣧⠘⡇⡀ ⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣿⡿⣿⣿⡇⢸⣿⣿⣏⡿⠛⠁⠀⠰⡿⠋⠉⣶⠿⠓⠚⠉⠉⠉⢸⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⡼⡄⢸⡁ ⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣿⣿⣿⠿⠳⠆⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⣇ ⠀⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣿⣿⣿⣿⣿⣶⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣼⣻⣿⣿⣿⣿⣿⣿⡇⠀⠸ ⡀⠇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢛⣿⣟⣹⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡄⠀ ⠷⠤⠀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⢀⡤⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⠀ ⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣿⣇⡇⠀ ⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡇⣿⣿⠇⠀ ⠀⠀⠀⢹⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣺⠵⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠈⠉⠹⠟⠛⠒⠲ ⠀⠀⠀⢸⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⢀⡿⠛⠋⠙⠻⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠙⠓⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⣵⠟⠀⢸⣿⣿⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢠⠏⠀⠀⠀⠀⠀⠀⠹⡎⣿⠟⠛⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠶⣶⣶⣶⣶⣶⣿⣿⠏⠈⠀⠀⠀⢸⣿⣿⣿⡇⣿⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠀⠀⠙⣌⢿⣿⣿⢿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠛⠛⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⢡⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡄⠀⠀⠘⠾⢿⣿⣟⣿⣧⠈⠉⠓⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠻⣿⣞⢿⣦⠀⠀⠀⠀⠀⠈⠉⠓⠒⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢞⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⣀⡾⠉⢀⣼⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⣶⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣾⠟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⡾⠿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣾⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠛⠓⠒⠦⠤⠤⠤⢤⡄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢭⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⠶⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⡀⠀⠀⢀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣾⠇⠀⣠⠞⡅⠀⣰⠋⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠁⠀⠀⠀⠀⢰⠏⣠⠞⠁⣰⣇⡜⠁⠀⡏⠀⢠⡇⠀⢠⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⣠⠴⢋⣵⣿⡟⠀⠀⠀⠀⠀⣾⡞⠁⠀⢀⡿⢫⠇⠀⠀⡇⡰⣿⡀⠀⣼⡆⠀⠀⠀⢻⢻⡀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠇⢀⠏⠀⠀⠀⠀⣀⠴⠋⣡⣾⣿⣿⣿⠀⡀⠀⠀⠀⠀⠋⣀⠀⠀⠘⢀⣾⠀⠀⠀⡿⠃⠀⣴⣰⣿⣿⡄⠀⠀⠀⢿⢧⠀⠀⠀⠀⢠⡄⠀⠘⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠃⢠⠎⠀⠀⣀⡤⠚⢁⣴⣿⣿⣿⣿⣿⡿⠀⡇⠀⠀⠀⢀⡼⠁⠀⠀⣠⣿⡟⠀⠀⠀⠁⠀⣠⣷⣿⣿⣿⣷⡀⡇⠀⠘⣿⡆⠀⠀⠀⢰⣷⡄⠀⠀⠳⣿⣄⠀⠀⠀ ⠀⠀⣠⡾⠁⢠⣏⣤⡤⠖⠁⣀⡴⠛⢿⣿⣿⣿⣿⣿⡇⣼⠁⠀⠀⣴⡞⠁⣀⣠⣴⣿⣿⡿⡾⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⣿⣆⠀⠸⣿⠀⠀⠀⢸⡏⢧⠀⠀⠀⠙⢯⣧⡀⠀ ⣠⣾⡿⠀⠰⣿⠟⠋⢀⣠⡞⠃⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠀⠀⣼⣟⠎⣰⣿⣿⣿⣻⣿⣧⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢦⡀⢻⡆⠀⡄⣸⠀⡬⣇⠀⠀⠀⠀⠀⠙⣤ ⢉⡞⠁⣠⠏⠀⢀⣴⣿⣿⣿⠁⠀⠀⠀⠀⠀⢻⢿⣿⣿⠁⠀⣴⢯⢋⣾⣿⣿⣿⣿⣿⣿⡁⠰⡼⣰⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠱⣄⢧⠀⣧⡇⢀⣀⣾⡆⠀⠀⠀⠀⠀⡏ ⡼⣠⡴⠋⣀⡴⣿⣿⣿⣿⣿⣧⠄⠀⠀⠀⠀⠘⢮⣛⡿⠀⣰⣋⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣾⣿⣿⡿⣿⢫⡝⣦⠀⠀⠀⠀⠀⠈⠻⣷⡿⠀⢀⣼⣿⣿⡄⡀⢀⠀⢠⣷ ⢿⡟⣠⡾⠋⣰⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⡄⢠⢏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠻⠤⠤⠟⠀⠀⠀⠀⠀⠀⠀⠘⣛⣶⣿⣿⣿⣿⣿⣵⠘⢆⠈⣿ ⣼⣼⡟⠀⢠⣿⣿⣿⣿⣿⡹⣿⣿⣿⣷⣤⡀⠀⠀⢀⣧⣿⣞⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢀⣀⣶⣾⣿⣿⣿⣿⣿⣿⠋⠈⠓⡌⢷⡉ ⢹⣿⠃⢀⣾⣿⣿⣿⣿⣿⡇⠈⠻⢿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿⠿⣿⡿⣿⣿⣿⣦⣴⡀⢠⣄⣤⣤⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣠⠇⠀⣁ ⢸⠇⠀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠉⠻⢿⣿⣿⣿⣿⣋⠉⠁⠀⠀⣽⡿⠀⠀⠐⠋⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⢻⣿⣿⠿⠿⠛⠉⠉⠀⠀⣠⠄⠀⢠⣿⢖⡞⠉ ⡾⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠰⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⢿⣷⣾⠁⠀ ⠃⠀⢠⣻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⢻⡋⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠖⣶⡶⣶⠲⠀⠀⠀⠀⠀⣴⠋⠀⠀⠈⡇⠀⣴ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⣀⣀⣀⡠⠤⠶⠶⠶⠚⠛⠟⠁⠀⠈⠁⣰⣿⣿⡟⠀⠀⠀⠀⢀⡼⠃⢀⠀⠀⠀⣡⣾⢃ ⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢻⣶⣶⡒⠒⠒⠚⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⠞⣥⣿⡟⠀⠀⠈⠆⣠⣿⣿⣿⣤⣴⣶⣾⣿⠷⠟ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠙⢿⣿⣶⣦⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⡿⠃⣠⣿⡿⠁⠀⠀⣠⣾⣿⣿⣿⣿⠿⠛⠋⣁⣀⣠⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⢿⣯⡍⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠂⢬⠟⠁⠀⣾⣼⣿⠿⠛⢋⣁⣤⣴⣶⣾⣛⠛⠿⢿ ⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠙⣄⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⢀⣴⣧⣴⣶⣿⣭⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢸ ⠀⠀⠉⠉⠑⠲⠦⢄⣀⣀⡀⠸⣦⡙⠻⣿⣿⣿⣿⣿⣿⣿⣎⠲⣄⢈⣳⣄⠀⠉⠛⠿⠿⠿⠿⠟⠛⠉⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿ ⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠉⠓⢿⣦⣁⢌⣻⣿⣿⣿⣿⣿⡿⠿⠚⠋⠈⠙⠳⠶⠚⠉⠓⠒⠒⠒⢶⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣉⣉⠩⢿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉ ⢸⣿⠛⢿⣿⣿⣦⣤⣀⠀⠀⠀⠘⠃⠘⣿⣿⡟⠛⠉⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢁⣀⣬⠶⡿⢓⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⡤⠖⠒⠒⠲⢤⣄⡀⠈⢻⡝⠳⣆⠀⠀⢀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⢀⣠⣴⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠳⠦⣄⠀⠀⠀⠉⠳⣦⣹⠀⠈⣧⣰⠋⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠹⣆⠀⡠⠊⠉⢰⠋⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠙⠃⠀⠸⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡿⠀⠀⢰⣇⣤⠔⠋⠁⠀⠀⠀⢀⣸⡿⠟⠀⠀⠀ ⠀⠀⠀⣦⡄⢀⣠⣶⡛⠛⠛⠓⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠁⠀⠀⠾⠋⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⠙⢯⣍⠉⠙⠶⣄⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠷⠖⠶⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⢿⡀⠀⠈⠙⠒⠶⢾⠿⠶⠀⠀⠀⣀⣠⠤⠤⣤⣀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⡤⠶⠞⠻⠃⠀⣠⣿ ⠀⠀⠀⠈⠻⣆⡀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⣀⣨⣿⣦⡀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⣀⣤⠴⠶⠦⣄⣀⡀⠀⠀⠀⠐⠛⠳⠶⠦⠤⠴⠖⠋⠁⣸ ⠀⠀⠀⠀⠀⠀⣉⣛⡒⠛⠛⠙⢧⡀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠈⢻⢦⣄⠀⠘⣦⡀⠀⠀⠀⢰⠇⠀⢀⣴⡾⠋⠁⠉⠳⡆⠀⠀⠈⠉⠓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋ ⠀⠀⠀⣠⡴⠊⢉⡏⠀⠀⠀⠀⠈⣷⢤⡀⠀⠀⠀⢻⡄⠀⠀⠀⣸⠀⠉⢓⣦⣽⣦⡄⠀⢠⣯⣤⡖⠋⠀⡇⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⣠⡟⠈⠉⠓⣶⣒⡒⠒⠒⠋⠁⠀ ⠀⠀⡾⠋⠀⠀⣼⠀⠀⠀⠀⠀⠀⠙⣆⠉⠒⠦⣤⣀⡙⠒⠒⣛⣡⡤⢖⡿⠟⠉⠁⠀⠀⠀⠈⠉⠻⣷⣤⣝⠦⣤⡤⠞⠁⠀⠀⢀⣠⢞⡿⠀⠀⠀⠀⢳⠈⠙⠲⣤⠀⠀⠀ ⢀⣾⠁⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣀⣀⣉⣉⣩⡧⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⢭⣓⣶⣶⣶⣶⣖⣫⠴⠋⠀⠀⠀⠀⠀⣸⠀⠀⠀⠈⢳⡀⠀ ⢸⡏⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⢷⠀ ⢸⡇⠀⠀⠹⣇⠀⠀⠈⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⣸⠃⠀⠀⢸⠀ ⢘⢿⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠉⠀⠀⢀⣼⡟⠀⠀⠀⡞⠀ ⠛⢾⣷⣖⣉⣉⣉⣷⣄⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⣰⠯⣟⡀⠀⠀⣴⠃⠀ ⠀⠀⠙⢷⣍⠉⠁⠉⠻⣷⢄⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠋⠉⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣤⡾⠧⢤⣀⣉⣙⣾⠷⠀⠀ ⠀⠀⠀⠀⠈⠻⣆⠀⠀⠈⠳⢽⡶⣄⡀⠀⠀⠙⠳⢤⣀⣠⠤⢴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠦⢤⣠⡴⠚⠁⠀⠀⢀⣠⡾⠟⠋⠀⠀⢠⣤⠞⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠙⠛⠿⣷⡤⣄⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⣠⣤⡾⠛⠉⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⠀⠀⠀⠀⠀⠉⢺⠁⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⢻⠋⠁⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣄⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠁⠀⠀⢀⣾⠁⠀⠀⠀⠀⢰⡶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡛⠛⠃⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⢀⣧⣀⡀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢴⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣄⣀⣸⣧⣙⠳⠦⠤⠤⠤⠴⠛⠀⠈⠙⠛⠓⠚⠛⠋⠙⢷⣄⣀⣀⣀⣠⣾⡷⣄⣀⣀⣀⡤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⢻⡉⠓⠢⠤⣤⣄⣀⣠⣠⡤⠤⠤⠦⠤⠤⣤⣀⣀⣉⣉⣋⡭⠟⣹⢣⡟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠳⣄⠀⠀⢸⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⡟⠀⡴⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⢧⠀⠈⠻⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠃⢠⢧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⢸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢃⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠸⡎⢳⡀⢀⡀⠀⠀⠀⠀⢀⣀⠀⡞⢡⠃⣼⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⣷⡀⣧⠈⣷⠋⠹⡄⠀⠀⠐⡟⠉⢹⠁⣸⠼⠃⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⠉⠛⠒⠛⠒⠛⠛⠋⠛⠉⠉⠉⠉⠉⠁⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⣀⣠⡤⠤⣤⣀⣀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠤⠤⠤⠤⠉⠙⡛⢷⣜⠻⠻⣿⣿⣿⣿⣇⢸⣿⣿⡿⢏⣛⣉⢐⣛⠋⠛⠂⡄⠑⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣋⣑⣾⠗⢒⣛⣲⣦⡀⠁⠒⢿⣷⡄⢙⢿⣿⣿⣿⣼⣿⣯⣾⣿⣿⣿⣿⣥⣀⣀⣀⣉⠷⣎⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢫⠿⠋⢁⣴⠚⠋⠛⠻⢿⣿⣦⡀⠀⠉⢷⣌⢿⣻⣿⣿⢏⣿⣿⠟⡛⠶⠒⠲⣿⣯⣭⣉⠙⢦⣌⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣾⣶⠏⣠⡴⢏⡓⠦⠀⢻⢿⣿⣷⠀⠀⠙⢯⢻⡽⣏⣯⡟⢙⣡⡶⠶⢞⣓⣒⣀⣭⣟⣷⡄⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢁⣠⣾⠶⠶⢾⠟⠁⠀⠋⠹⣿⡃⠀⠀⡈⠀⢷⣼⠁⣠⡟⣉⣠⣾⣿⣿⣿⠁⣿⣿⣎⠿⣦⣀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡴⠛⢁⣈⡡⢀⡟⠀⠀⠀⡇⠀⣿⣿⠀⠀⠳⣄⡆⣹⡼⠟⣰⣿⣿⣿⣿⡏⠹⣶⣷⣿⣇⣳⡌⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠏⣠⠴⣫⡵⢚⣽⡷⠤⢤⣴⣧⠀⢹⣿⣇⣀⠀⠈⠛⠿⢷⣿⣿⠙⢿⣿⣿⡇⡌⣿⣿⠈⣿⡹⣿⡈⢷⣌⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡾⣹⢞⡽⠚⣡⣾⡇⠀⠘⢻⠃⠀⠀⢽⣿⣷⠀⠀⠀⠀⢸⡟⠀⠀⠀⠉⣿⣁⣿⣿⡋⠀⢸⣇⠙⢿⣞⣿⣦⠀⢻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡞⠁⢀⢔⣠⣿⣿⠇⠀⠀⡿⠃⠀⠀⣿⠉⠻⡄⠀⠀⣀⡿⠀⠀⠀⠀⠀⢹⣿⣿⡟⠁⠀⠀⣿⠀⢸⣿⣿⣿⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⢁⣤⣶⣿⣿⠗⠉⠂⣿⢲⠃⠀⠀⠀⠁⠀⠀⠁⠀⠠⣾⠇⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠸⣧⣼⣿⣿⣿⡼⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠋⣰⣿⡿⠛⠋⢁⣠⣴⣿⡉⢸⠀⠀⠀⢰⡀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⣿⠟⢻⣿⣶⡝⡆⢧⠀⠀⠀⠀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⣠⠟⢟⡶⠒⢊⣭⠆⠀⠇⣷⠈⣧⠀⣀⡄⢻⡀⠀⠀⣠⡿⡀⠀⠀⠀⠀⠀⣘⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣁⣈⠀⣟⢻⣿⣽⠘⠀⠀⣠⠞⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⢀⣾⣴⣾⡿⣿⡁⢰⡆⠿⢧⣘⣿⣏⡀⠈⡇⠄⢰⣿⠱⠁⠀⠀⠀⠀⣴⣿⡟⠀⠦⠶⠀⠀⠀⠀⢠⢩⣿⣿⠇⣿⠉⠉⠓⠀⢀⡾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠛⡏⢠⡿⣿⣄⠳⠀⠀⢹⣿⣿⣷⣄⢻⣴⡿⠣⠁⠀⠀⠀⠀⠀⣿⣏⣴⣾⡿⣦⡀⠀⠀⠀⠈⢸⣿⠏⢠⣿⡄⠀⠀⢰⡟⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⠇⠃⢿⡄⠀⠀⣾⢿⣿⡇⠀⢸⣿⣆⣀⠀⠀⠀⠀⢀⣴⣿⠛⢿⣿⣻⣿⣿⡇⠀⠀⠀⢸⢇⣠⠟⠀⢣⠀⠀⠀⣻⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⡿⢹⣧⠀⡟⠈⠻⣿⣶⣶⠿⠛⠏⣰⣶⣾⣿⣿⣿⣿⣷⣾⣿⢟⣵⣿⠇⠀⠀⢀⣿⢿⢷⠀⠀⠸⣄⣠⠞⠻⣝⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣼⢃⡏⢹⡄⠃⠀⠀⠙⣿⣇⠀⣠⠀⠉⣿⣯⠿⣷⠉⠛⠿⠯⠀⠉⠀⠀⠀⠀⠀⣼⡿⢸⡾⠀⠀⢠⠏⠀⠀⠀⠙⢯⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠘⠀⠀⢷⡀⠀⠀⠀⠉⢻⣶⣧⠀⢀⡈⢤⢰⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⡇⢸⡇⣰⠀⠀⠀⠀⠀⣀⣴⣿⡟⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣣⡇⢸⡄⠈⠻⣄⠀⠀⠀⠘⣧⣌⣧⡘⠧⠹⠿⣷⣿⠆⠀⠀⠀⠀⠀⠀⣠⣾⡿⣷⠇⢸⣇⠀⠀⠀⠀⣰⣾⡿⠁⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣉⣻⡜⢿⣿⣿⣿⣷⣄⠀⠀⠀⠉⠛⢿⣿⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⢳⢠⡾⠙⣦⡀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⡀⠈⢋⣿⡃⠛⠿⣿⣿⣿⣿⢦⣄⠀⠀⢠⣿⡈⠁⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣯⣀⣰⠏⠀⢀⣨⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠛⠁⠀⣘⣹⣆⠀⠀⠙⢿⣟⣿⢷⣮⣙⣒⠻⠿⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣅⣠⣴⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⢀⣤⣟⢧⣧⠀⠀⠐⢻⣿⣿⣶⡦⢤⣀⡙⢿⣧⣤⣭⣝⣻⣚⠻⣿⣭⣉⣛⣛⣛⣿⣿⣿⣿⡿⣇⠈⠛⢿⣿⣿⣿⣿⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂ ⠀⠀⠀⠀⠀⢰⡟⣽⣿⢿⣿⣜⣿⣆⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣿⡁⠈⠿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣤⣼⣷⣄⡀⠛⢿⣯⡳⠿⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠇⠀⡈⣿⣿⡈⠿⣿⣷⣀⣰⣿⣿⣿⣿⣭⣿⠟⢽⣷⡀⠀⠉⠛⠛⠛⠿⢻⣿⣿⣿⣿⣿⡿⣇⠈⠁⠉⠉⠛⠻⣶⣶⣽⣿⣴⣺⣯⣧⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⢠⡾⠁⠳⡱⣍⡳⣽⣿⡿⣿⣿⣿⡟⠀⠛⠛⠛⠛⠛⠛⠒⠒⠀⠀⠒⠒⠛⣿⣿⣿⣿⠋⢰⠈⠛⠳⣦⣤⣀⠀⠙⢿⡄⠉⠉⠀⣷⡿⣻⢦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣧⠘⠛⣷⣾⣿⡄⠙⢾⣿⣯⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢀⣤⣤⠄⠀⠀⠀⠀⢿⣿⠟⠁⠀⢘⣷⣤⣀⣈⠙⠻⣿⣷⣦⣽⡆⠀⠀⣿⣆⢨⠁⠉⠙⠲⣄⡀⠀ ⠀⠀⠀⠃⣀⡳⣀⠀⣿⠀⢳⣦⡀⠀⣿⣿⣿⣿⣿⠀⠀⣠⣶⡞⢛⡟⢉⣉⣸⡷⣾⠿⣿⣿⠟⠁⠀⣠⣾⣾⣿⣇⠉⠻⣿⣶⣤⣹⣿⡅⠀⠀⠀⣸⠹⣿⢿⡇⠀⣄⡀⠑⠀ ⠀⢀⣴⣿⣿⣿⣿⣷⣿⣶⣾⣿⣿⣆⣿⠙⢻⣿⣿⡀⠰⡇⢀⣵⠾⠷⠿⢿⣇⢀⣿⣿⡿⠃⠀⢠⣾⣿⣿⣿⣿⣿⣷⣄⠀⠙⢿⣝⠛⠿⠇⠀⢠⡏⠀⡘⣯⠁⣷⡀⠙⢦⡀ ⢀⣿⣿⠄⠙⠻⠟⠉⠉⡿⠟⣋⣹⢿⣿⣴⣿⣿⣿⣟⣀⣻⣟⣡⣴⢃⣠⣾⣻⣿⡿⠋⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢿⡶⠄⠀⣰⡿⠁⠀⢁⡏⠀⠋⠁⠀⠀⣠ ⣼⡿⠁⠀⠀⠀⠀⠀⡠⠀⣠⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣥⣴⡿⠟⣡⡀⢀⡿⡁⠶⠀⠀⠀⠀⢿ ⣿⠁⠀⠀⠀⠀⠀⡘⢁⡐⣻⠿⠛⢫⣿⠟⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⡟⠁⢀⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣋⣿⣾⣿⣧⠾⠃⢁⣀⠀⠀⢀⣴⢺

⠀⠀⢀⣴⣿⣿⣿⡿⣯⣷⢞⣿⣷⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⣿⣿⣿⣿⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣰⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡟⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⢿ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⢧⣿⣿⣿⣽⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⡛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⢻⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⠟⢉⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⣿⣿⣿⣷⣿⡿⠁⠙⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⡿⣿⣿⣿⣿⣿ ⠋⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣼⣿⣿⣿⣿⣿⠟⠀⠀⠀⠹⣿⣿⣾⣿⣿⣿⢿⣿⣿⣧⣿⣿⡛⣿⣿⢿⣿⣿⣿ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣫⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢰⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣼⣿⣿⡇⣿⣻⣷⣽⣿⣯⣿⣿⣿ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣧⣿⣿⣿⡿⣿⡟⠁⠀⠀⠀⢰⣿⣿⣿⠟⣱⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⣿⣿⡇⣿⣿⣻⣿⣿⣿⣿⣿⣿ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⢋⡾⠋⠀⠀⠀⠀⣠⣿⣿⠟⠁⠐⠁⠀⠀⠀⠀⢀⣠⣤⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⡻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⠿⣷⣮⣄⡀⠀⠀⠀⣰⠿⠋⠀⠀⠀⣀⣤⣶⡶⠶⠋⠉⠀⠀⠀⢻⠁⢻⣿⣿⣿⣿⣿⣗⢸⣿⣿⣿⣿⣿⡿⠿⣷ ⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣽⠟⠁⠀⠀⠙⠛⠛⠶⠀⠚⠁⠀⠀⠀⠴⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣿⣿⣿⣟⣿⣿⣾⡿⠛⠁⠀⠈⠃⢀⣼ ⣿⣿⣿⣿⠟⢫⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣅⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢿⣿⣿⣿⣿⡿⡟⠀⠀⠀⠀⠀⠀⠀⠻ ⣿⠿⠋⠁⢀⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⡟⠙⠿⣿⣷⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣶⡾⠿⠋⠀⠀⣿⠟⠋⠙⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⢠⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠓⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⢀⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆ ⠀⠉⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤ ⣀⣼⣿⣿⣿⣷⣾⣿⢺⣿⣿⣿⡟⣧⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⣛⣿ ⣿⠿⠽⣾⣟⣿⢿⣿⣾⣟⣿⣿⣷⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠿⠛⠋⠀ ⣷⣿⣿⣿⣟⣽⣿⣿⣿⣿⡿⢫⣿⣿⡎⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣼⣾⣿⣿⣧⡀⠀⠀⠀⠀ ⠉⠉⠉⣹⡿⣿⣿⢿⡏⠉⣷⡟⠁⠘⢿⣿⣿⣧⡀⠀⠀⠀⠀⢀⣤⣖⣾⣏⣛⠁⠀⣀⣈⣤⡈⠛⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⢠⡾⡆⠀⠀⠀⠀⣼⣦⢧⡉⢛⠿⣿⣿⣷⣄⠀⠀ ⠀⢀⣾⡿⠟⠉⢀⡿⠀⢠⡟⠀⠀⠀⢸⣿⣿⣿⣿⣤⡀⢀⣀⣿⠿⠛⠉⠉⠉⠉⠉⠁⠀⣰⠟⣻⡿⢻⣿⣿⣿⡷⠀⠀⢀⣴⡿⠁⣇⠀⠀⠀⢐⡈⢮⢳⡝⣎⢧⡀⠉⠛⠿⣷⣄ ⠀⠛⠈⠀⠀⠀⠉⠀⢠⡟⢳⠀⠀⢀⣾⣿⣿⣿⣿⠾⠛⠉⠀⠀⠀⣀⣀⣀⣤⣤⣤⡴⠾⣥⣀⣈⣀⠈⢿⣿⣿⣇⣠⠔⢋⣿⣷⣾⣿⣆⠀⣠⠋⠀⠈⢆⠀⠈⠉⠻⡄⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠢⠐⣩⣿⠿⠟⠉⠀⠀⣀⡠⠴⠚⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢯⣉⡉⢛⣿⣿⡿⢁⣴⣿⣿⣿⣿⣿⠘⣆⣁⡀⠀⠀⠈⢧⠐⠁⠀⠹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⣱⠋⠀⣀⠴⠋⠉⠉⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠭⣿⡟⢹⣿⣿⣿⣿⢟⣿⣿⣿⡇⠸⡄⠀⠉⠙⠒⢮⣆⠀⠀⠀⠹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣴⠃⠀⠘⠁⠀⠀⢀⣤⠤⠒⠒⠉⠀⠀⠈⠉⠉⠉⠉⠉⠓⠛⠛⠛⠀⠀⢭⡀⠀⢻⣿⣿⣽⣿⣿⣿⣿⣧⠀⠻⡄⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⡤⠆⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣢⠞⠁⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⡳⢄⣀⡀⠀⠹⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣞⡿⠿⠿⠿⠟⢛⠋⠉⣹⠟⠋⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠙⢒⣿⡇⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣒⡿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⡴⠃⢸⣧⢤⣉⠑⠒⡄ ⠀⠀⠀⠰⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠶⠶⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠦⣀⡠⠋⠀⠀⠸⣿⠤⠀⠉⠀⠀ ⠀⠀⠀⠄⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⣇⠀⠀⠀⠀⢷⣧⠀⠀⠀⠀ ⣤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⢀⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢻⠀⠀⢀⡄⠀⣿⠀⠀⠀⠀ ⣿⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣡⣴⣾⣿⣿⣿⣄⣀⡀⠀⠀⠀⠐⠶⠚⠛⠛⠀⠀⠀⢀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠸⣀⡴⠋⠀⠀⢿⡀⠀⠀⠐ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⠒⢶⢤⣤⡴⡶⠶⠶⣒⣺⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠀⠉⠻⡟⠤⣄⣀⠀⠈⡇⠀⠀⠀ ⣿⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⢸⠠⠊⣠⢧⠀⠀⠈⠉⢺⡇⠀⠀⠀ ⣿⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡠⠤⠤⠤⢾⣀⠞⢀⢞⠀⠀⠀⠀⠀⡇⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠒⠛⠚⠉⠉⠙⣻⠏⣻⡶⣲⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠖⠉⣩⠟⠋⠀⠀⠀⠀⣀⠴⠚⠉⠁⠰⣷⡾⣿⣶⠾⣋⡿⠿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡥⢀⡴⠛⠁⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢽⣯⡿⠿⡷⢌⣁⣴⡿⣧⡉⠛⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⣃⠔⠉⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡞⢿⣦⡵⠖⣿⣲⡄⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⢀⡴⠋⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡋⢳⣾⡉⢳⣝⢦⣦⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⢀⡴⠋⣠⢞⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⡿⢫⣡⠾⣟⠻⡄⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⣰⠋⣠⢞⡷⠃⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠜⢿⣦⡈⣦⡹⢶⢄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡇⠀⢠⡞⢁⡜⡡⠋⣠⠞⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢟⣧⠟⢖⠻⣅⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⣠⠏⢠⣿⡞⢁⡞⢁⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠋⣻⣧⣈⣷⠼⠷⣄⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣧⠏⣰⢯⠏⣠⠏⣴⢃⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠂⠴⠊⠀⠛⣁⡀⠒⢏⠻⣄⣀⠀⠀⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⢠⣿⡟⡴⢃⡼⡵⠋⡰⠃⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠔⠛⠂⠙⢿⡶⠞⢫⣿⣬⢷⠉⣀⠹⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡎⡾⣹⢁⣞⡿⠁⡼⢁⠞⢀⡴⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⠈⢠⣶⣯⠟⠳⣦⠀⢀⣀⣹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣱⠇⡾⡼⢁⡾⣰⠃⣴⠋⢠⠞⢁⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠉⠁⠀⠀⠀⢦⠙⣿⠓⠂⠉⢿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣧⣿⣼⣾⠁⡜⣰⢃⡜⢁⡴⠃⡴⠋⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠑⣡⣄⡤⢄⡀⢲⠈⢧⠙⣦⣀⠀⠚⣻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠿⡌⢻⡉⢸⢁⡟⡞⢁⡞⢠⠎⠀⡰⠋⣠⠆⣠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣏⠕⣪⢕⡦⠖⢷⠘⣆⠘⣿⠉⠿⠿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠙⣌⠸⣼⢡⡞⢠⠋⢀⡞⠀⡼⠁⡴⠃⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⡿⣞⣥⣖⠭⠽⣆⣘⡆⠹⣦⠤⠤⠾⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠘⢳⣀⡞⢠⡏⢀⡎⠀⡾⢁⡜⢀⡜⠁⡴⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠝⢋⣠⠔⠊⠙⣅⠘⠂⢹⡄⠀⠀⢻⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠙⣦⣚⠀⡾⢀⡼⠀⡞⢁⡞⢠⡞⠀⡼⢁⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠹⡆⠀⠀⠳⠀⠀⠘⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⡇⣧⣜⠳⣄⠸⠁⣼⠁⡼⢀⠏⢀⠞⣰⠃⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠘⣆⣀⣀⠤⣼⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣁⠘⢸⣽⢍⠳⣤⡃⣼⠃⡾⢀⠏⡼⠁⡰⠃⣰⢋⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠺⡏⠹⡆⠀⠠⠬⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠿⠸⢠⢀⠙⢷⣄⠁⣎⣸⠁⡼⢁⡼⣱⠏⣠⢇⡀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⠴⣫⢁⠀⣀⠀⠻⡀⢹⡀⠉⠉⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⢸⢸⣾⢠⡙⠳⣬⡃⣼⠁⡼⢰⠃⣰⢣⠞⣰⠀⡀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠁⢰⣿⣺⡭⠄⠃⠀⢷⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠘⡇⢸⢡⠃⡾⡛⢦⣈⠁⠻⢰⣇⠟⡼⢁⡾⡽⢁⠏⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠉⠴⢂⡥⠀⠀⠘⡄⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠁⢸⠀⡆⡇⡇⢰⠈⠻⢦⣄⡈⠙⠳⣾⣾⢡⡎⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢧⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣤⡀⠀⠃⡇⢸⠘⡄⡖⣶⢬⡛⠶⣤⣈⠉⡟⠒⠤⠄⠀⠀⢠⢿⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣶⣖⡲⠽⢿⣓⣯⣭⣷⣿⢿⣶⣄⠀⠈⠇⢧⢱⠸⡾⡷⣆⣀⠉⠙⠲⠶⣤⣀⣈⢹⢗⣾⣸⣁⡞⣴⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢹ ⠀⠀⠀⠀⠀⣀⣤⣴⣖⡻⣭⣴⣾⢿⠿⣟⣿⣽⣷⡻⣿⣷⣿⣿⣷⣼⣧⣼⠯⣇⣳⡽⣻⡘⡆⢷⢶⡦⣤⣀⠉⠙⠓⠦⣬⣉⡓⠓⠿⣼⣧⡀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⡼ ⠀⠀⠀⢀⣶⡾⠭⠛⡓⠭⣉⣠⡬⢿⣻⣿⣿⣽⣿⣿⣿⢿⣿⣿⣿⣿⡿⡟⢿⣿⣾⣷⣿⣝⣮⠈⣆⠹⣜⡏⢳⡼⣦⢤⠀⠉⠙⠒⢦⣤⣈⠉⠛⠹⠤⠃⠔⠀⠀⠀⠀⠀⢸⢀⡇ ⡀⠴⠾⢓⡯⠿⣒⣊⠩⠽⣖⣒⣭⡷⠷⣟⣿⣯⡻⣿⣺⣿⣿⣿⣷⣟⣿⣿⣷⣻⣿⣿⣿⢿⣿⣶⣾⣷⣿⣿⣶⣻⣼⣜⣆⠀⠀⠀⠀⠀⢈⠉⠉⠛⠲⠶⢶⣤⣤⣈⣉⣁⣼⠟⠁ ⣀⡤⠴⣚⣋⣭⡴⠶⠛⣛⣉⠤⠔⠒⢋⣙⠧⠟⣳⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣽⣧⡿⣾⣻⣿⣿⣿⣿⣻⣿⣿⣿⢍⢻⣟⠻⣟⠛⡲⣖⢶⡶⢶⣶⡶⣶⣾⣿⣿⣾⣿⣿⠇⠀⠀ ⠁⠀⠈⠉⠋⠁⠐⠖⢉⣉⡤⠴⢒⣪⡭⣵⣲⢭⣿⡶⠽⠛⢋⣻⡵⠼⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣾⣿⣿⣾⡿⢞⠙⣭⣷⣿⣯⡷⣿⣯⣷⣽⡿⢿⡿⠿⠛⠛⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠖⠛⢉⡰⠿⠿⠒⠛⠉⠐⠋⣁⠤⠴⠚⣋⣡⢤⣖⡿⠿⣛⣻⠬⠿⣿⣿⣿⣾⣿⣿⡿⠿⣿⣿⣬⢷⣿⡿⢿⡾⠿⠝⠛⠿⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⢭⠵⠒⠉⠉⠀⣒⣭⡟⠿⣿⣿⢻⣡⣔⡊⣉⠉⣛⢋⡁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣧⣤⣤⣼⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣾⣶⣷⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠃⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣖⠷⠖⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣮⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡀⢻⣿⣿⠙⣿⣿⣌⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠄⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣷⡘⣿⣿⣷⡜⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠈⡀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠠⠜⠃⢡⠀⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⣿⣿⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⢠⢄⢠⠀⠀⠀⠀ ⡠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣼⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠇⠈⣿⠘⢦⠈⣿⣿⣿⣿⣿⣿⣿⠀⡷⢻⡟⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠄⠄⠉⠀⠀⠀⠀ ⠀⢀⠴⠁⠀⠀⣤⣤⣤⣤⣴⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⡿⠖⠛⠛⠳⢾⣷⣇⣹⡿⠿⠟⠛⢃⣼⠷⠶⢿⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡴⠋⠀⠀⠀⣠⣿⣿⠿⢫⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡏⠀⠀⠀⠀⢀⣄⠹⣿⢷⣦⠀⠀⠀⢻⣏⡄⠀⠀⢸⢿⣿⣿⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢ ⠖⣠⢞⣵⠞⣡⣿⡟⡀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠘⣿⠀⠸⠇⠀⠀⠀⠀⠘⢽⡇⠀⠀⢸⢸⣿⣿⣿⡞⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡷⣋⡴⢟⡵⣿⡧⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⣿⣿⣿⣿⢿⣿⡄⠀⠀⠀⠀⢀⠀⠀⣀⠷ ⣿⢟⣥⠞⠃⠀⣿⣃⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢳⡀⠀⢀⣀⣠⡴⠟⠀⠀⠀⠀⠀⠀⠀⠠⣤⡾⠃⣾⣿⣿⣿⣿⢸⣿⣇⠀⠀⠀⠀⠈⠑⢦⣿⡻ ⢿⣫⠄⣀⠄⠒⣿⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣻⠋⢍⣏⣁⡄⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠰⠘⣿⣿⣿⣿⣿⣸⣿⣿⡄⢀⡀⠀⠀⣀⠀⢫⡿ ⣫⠖⣊⡥⠂⠀⣿⣼⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠀⠈⠊⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⢿⡇⢸⣟⠿⣴⣆⡀⠈⠁ ⢶⣫⠵⢂⣠⠴⣿⡟⣭⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡇⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠸⠃⢸⣯⡻⣿⣬⣿⢷⣦ ⡯⠵⣛⣭⠤⠂⠛⠉⠛⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⠋⠋⠀⠉⠉⠛⠷ ⣚⣯⠅⢀⡀⠀⠀⠀⠀⠀⠸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠷⣒⣋⠉⠀⠀⠀⣀⣤⠀⠀⠘⣷⠹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⢿⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣽⡆⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⡭⠿⣶⣶⣿⣭⠥⠀⠀⠀⠀⠀⠈⠂⠀⢘⣯⠟⠉⠀⠀⠀⠀⠉⠙⠻⠿⠯⣿⠷⠤⢷⣄⡉⠉⠒⠶⣤⣤⣤⣤⣶⣿⣿⢿⡿⣋⣉⠑⠃⠀⠉⠳⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲ ⣉⣭⠽⠿⠷⠖⠂⠀⠀⠀⠀⠀⠀⠀⣴⠏⠁⠑⠲⡀⠀⣠⠞⠙⠒⠦⢄⣀⠈⠙⠦⣄⠀⠈⠉⠑⠲⢬⣛⠮⣽⠛⠿⣾⠿⠭⣁⠈⠙⠳⣄⡀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠂⠤⢠⣉ ⣒⣛⣛⡻⠉⠠⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢹⡈⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢄⡙⢦⣤⠤⠤⠤⠬⣿⣻⠷⠞⢿⣿⢶⣭⡟⢦⣄⠀⠙⢦⠀⠀⢳⡄⠀⣀⣀⠀⠀⠒⠂⠠ ⣒⣒⣒⡒⠂⠒⠂⠂⠒⠒⠒⠀⢠⠇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣸⣿⣿⣿⣶⣭⣓⣦⣼⣿⣿⣿⣷⡄⠈⠓⣦⡈⢳⡀⠀⢳⠰⢽⢬⣥⣦⣤⢀⣀ ⠭⠭⠭⠥⢤⠤⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⡄⠀⠀⠙⢦⣹⣣⠈⣷⢄⠲⣶⡾⠶⠀⠠ ⣽⣍⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣾⣿⡿⠀⠀⠹⡿⠿⣿⣧⠀⠀⠀⠐⠛⠻⣆⢻⣛⣛⣛⣛⣋⣉⣉ ⣿⣓⡒⠢⠄⠀⠉⠉⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠰⡀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠉⠀⠀⠀⠀⠈⠳⣄⡈⠳⡄⠀⠀⠀⠦⡈⠻⣧⣬⣬⡤⠦⠤⠶ ⣿⡶⠬⣭⣀⡀⣀⣀⣀⢀⣀⠀⢻⣤⠀⠀⠀⠀⠀⢳⡀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡈⢦⡀⠀⠀⠘⢄⠈⢳⣶⠖⠒⣚⣉ ⣿⣭⣓⡲⠬⣭⣿⣟⠷⢿⣿⡄⠀⣏⣆⠀⠀⠀⠀⠀⢱⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢳⡀⠀⠀⠀⠳⡀⠙⣦⣬⣽⣽ ⣭⣒⠮⢍⠓⠲⣿⣟⢿⣶⣿⠇⢠⡟⣟⡄⠀⠀⠀⠀⠀⠹⣼⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢳⠀⠀⠀⠀⠹⡄⠈⣿⠻⣻ ⣷⢯⣝⠲⠄⠀⣿⢏⡀⡴⣿⣆⡟⠉⠙⠿⣄⠀⠀⠀⠀⠀⠹⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢺⡇⠈⡆⠀⠀⠀⠀⠀⠀⢈⣉⠽ ⢯⡓⢦⣙⡀⠀⣿⠄⢳⠛⣿⠻⢿⣛⠲⢄⡈⠳⢄⠀⠀⠀⠀⡿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡜⡞⢰⠀⡇⠀⠀⠀⠀⠀⠀⠸⡦⠒ ⠳⣌⠻⢬⡙⠲⣿⣄⠀⠙⣿⠆⠀⠈⠳⣄⣙⡦⣄⠙⠒⠤⣄⣷⣤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡸⢱⠁⠁⢸⠂⡇⠀⠀⠀⠀⠀⠀⠀⣗⣉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⢴⠤⠖⠒⠶⠒⠦⠤⣤⣀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⠲⢄⡀⠀⠀⠀⠀⠈⠉⠲⢤⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠴⠚⠋⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡐⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⢸⣿⣿⣿⣿⣿⣿⠿⠛⠉⣹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⢿⣿⣿⣿⣿⠟⠋⣀⣤⣴⣶⣿⣿⠿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⢿⣿⡀⠀⠀⠀⠀ ⠁⣰⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣵⣶⣄⡜⣿⣿⣿⠟⣡⣶⠿⠿⠛⣻⣿⡟⠛⠂⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠙⢧⠀⠀⠀⠀ ⣰⣿⣻⠋⣩⠥⠹⣿⡄⠀⠀⢀⣤⣾⣿⣿⣿⣿⣭⠃⢩⣿⡇⢻⡿⠁⠚⢻⣿⠀⠀⠔⠋⠀⡟⠀⠀⢀⣼⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠃⠀⠀⠀ ⠉⠉⢡⡾⣅⠀⠀⢷⡇⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⠀⠘⠛⠁⠈⠃⠀⠀⠘⣃⣀⣤⣤⣤⢴⠃⠀⠀⠚⠋⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢧⣄⠀⠀⠀⣷⣰⣿⣿⣿⠿⠟⠛⠛⢷⡷⠖⢶⣞⡉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠆⠀⢀⣿⣿⠟⠋⠀⠀⠀⠀⠀⡟⠁⠀⠸⢿⠟⢀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢠⠞⠉⢳⢻⣿⣿⣿⣿⣿⣷⢻⣿⡈⠻⣿⡇⠀⠀⠀⠀⠀⠀ ⢀⡠⡀⠤⠞⢀⡴⢿⠟⠁⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠈⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡋⢓⡂⠀⢸⣿⣿⣿⣿⣿⣿⣇⠹⣷⣀⠾⠇⠀⠀⠀⠀⠀⠀ ⣏⠀⠀⣠⠔⠋⠀⠟⢤⣠⡤⠤⠒⠒⠚⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡛⠋⡧⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠹⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠙⢷⡀⣀⣀⣀⣀⣠⣉⣭⣶⠦⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⡯⣥⡴⠃⢀⣿⣿⣿⣿⣿⣿⠿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣄⡀⠀⣀⣤⣾⡿⠿⠛⠉⠁⢐⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠓⠦⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠴⠛⠁⠀⠀⠰⣏⣠⢤⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⡤⢾⡏⠙⠦⣄⣀⠀⠀⠀⠈⠙⠒⠒⣶⢖⠾⠛⠛⠋⠁⠀⠀⠀⠀⠀⢀⣠⠷⠂⠈⣶⣶⣶⣶⠤⠔⠋⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠤⠤⠴⠶⠶⠶⣦⠞⠀⡼⠀⠀⢠⣯⠈⠓⠢⠄⠀⠀⠀⢠⠇⠀⠀⠀⢀⣠⣤⠤⠶⠒⠊⠉⠉⠀⠀⠀⠀⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠙⢲⣤⡴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣶⣶⣶⣈⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⣠⠴⠋⠀⢀⡤⢫⠇⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⣠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠲⢭⡁⠀⠀⠔⠋⢠⠏⠀⠀⠀⠀⠀⣀⣴⣿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⠋⢦⠀⠀⠀⠀⠀⠀⠀⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⡄⠀⠀⣠⠏⠀⠀⠀⢀⣴⣾⣿⡟⠝⠀⣠⡞⠁⣿⣿⣿⣿⠟⠁⠀⣨⢧⠀⠀⠀⠀⣠⢚⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡀⠰⢧⣤⣴⣶⣿⣿⣿⣿⣿⠀⠀⡼⠃⢙⣾⣿⣿⣿⠃⠀⢠⣪⠖⠊⣦⠀⣠⠞⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠰⠊⠀⣰⣿⣿⣿⣿⣿⠀⠐⠉⠀⠀⠀⠈⠯⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣸⡁⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣠⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠴⡿⢿⢧⠀⣿⣿⣿⣿⣿⣿⣿⣿⡗⠲⢼⣿⣿⣿⣿⣿⣿⠀⣀⡤⠖⠋⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠰⢡⠈⡸⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠄⠀⡀⠈⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠋⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⣧⠀⠀ ⠀⠸⡗⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣻⣵⡞⣻⣟⣻⣻⣦⡀ ⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣽⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣮

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣤⣄⣀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠟⠁⢠⡍⠉⠉⠉⠉⠉⠉⠛⠛⠛⠻⠿⣿⣿⣿⣿⠿⠛⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣿⣿⡿⠁⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⢳⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣀⠀⠀⠀⠀⢸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⡿⠀⣿⣤⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣀⣤⣴⣿⣿⣿⡿⠃⠀⣿⣿⣤⠄⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⣤⣠⣤⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣸⠃⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠈⣿⣿⣷⣆⢀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠀⠀⠀⠀⠈⠁⠈⠉⠉⠛⠶⠲⠦⣤⣄⣤⢤⣴⣟⡳⢦⣤⡏⠀⠀⢐⢸⣿⠟⠉⠀⠉⠛⠁⠘⡇⠀⠀⠀⣸⠟⢯⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣿⣄⢿⡇⠀⠀⠀⠘⠻⣆⣀⣀⣀⣀⡤⠾⠃⠀⠀⠀⡻⣄⡀⠁⠈⣿⡇⠀⠀ ⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⡿⠏⣿⣿⣿⡾⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠙⠓⠚⠻⡇⠀⠀ ⠀⠀⠀⠀⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⣀⣀⣤⣄⣀⣻⡄⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⠀⠀⠀⠀⢻⣄⠈⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣶⠟⠀⠀⠀⣾⡇⠀⠀ ⠀⠀⠀⠀⠀⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠀⠀⠀⠀⠀⠙⠳⢶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣾⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣝⠷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⢀⣀⡿⠁⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣠⡴⠞⠋⣽⠃⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⣭⣤⣴⣶⣦⣠⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣞⠁⢀⣠⣾⠃⠀⠀⣠⡀⠻⣦⡀⠀⠀⠀⠀⠀⠀⣰⡿⠿⠿⢿⣿⣿⣿⡿⡿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣽⠃⠀⠀⠀⣿⠃⠀⠈⠻⢶⣄⡀⠀⣠⣼⣟⣿⠟⠛⠛⠛⠛⣿⣷⡇⠛⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⡄⠀⣿⠀⠀⠀⠀⠀⠉⠻⣦⣿⠖⠀⠀⠀⠀⢠⣴⣶⠟⠉⠀⠈⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⡀⠀⠈⠳⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⣿⡇⠀⠀⠀⠀⠀⠀⡀⣿⢿⣶⠤⠤⠤⠾⠟⠁⠀⠀⠀⢠⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠀⠀⠀⢀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⡠⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢿⣶⣄⡀⢀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣠⠟⠅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣯⣧⣬⡉⡩⢻⠛⠿⣿⣿⣿⣷⣬⡛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⠈⠀⠀⠀⠀⠀⣠⣴⢾⣽⣕⡀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⣀⡴⠾⢿⣱⡿⣭⢉⡙⢷⡯⣹⣔⢷⢦⣼⡾⣉⠻⡿⣿⣷⡌⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⣴⣾⠿⣿⣯⣻⣿⣿⠿⣦⣅⠀⠀⠀ ⠀⢀⡼⠃⠀⠀⠀⠉⢻⣳⣌⣭⢀⠚⣋⣀⠼⠣⣯⠘⣿⣲⣦⠿⣄⣙⣦⣄⣘⣦⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⢿⣯⣽⣧⢇⡆⢹⡎⠳⣄⠀ ⣠⠏⠀⠀⠀⠀⠀⠀⠀⢻⣟⣛⠋⢹⠯⢿⣛⠔⢛⠩⠀⠸⠓⢶⢻⠆⠀⣿⣟⣙⠷⢦⣌⣻⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠷⠿⡼⡟⢓⠚⠏⠛⢿⣷⠀⠈⠣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠲⠶⣦⣤⣀⣠⡴⡶⠶⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣾⠛⡟⠘⢾⣶⣦⣀⣈⣿⣝⠛⠫⢷⣦⣀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣾⠋⠃⢠⣤⣶⣬⣿⣽⣿⡟⠛⢛⣷⠒⢤⡙⢿⣻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⡟⠀⠀⢸⣿⡴⣦⣬⣿⢯⣍⡻⢶⡄⠻⣦⣉⢷⣽⢷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡿⠋⠀⢀⡀⠈⠉⣿⣧⣿⣶⣤⠘⢣⣴⡞⣶⣇⣸⣧⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡿⠁⠀⠰⠟⣿⣆⠀⠻⣿⣿⣿⣿⣷⣾⣯⣷⣿⣿⣿⣿⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⠁⠀⠀⢀⣴⣿⠈⣷⣄⠁⠀⠿⢿⣿⣧⡙⠦⣝⡷⠿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡀⠀⢠⡿⠿⣿⣧⠈⠻⠿⣦⡀⢸⣿⣿⣿⣷⣾⣷⡾⠿⠛⠋⠛⠳⠦⠤⢤⣄⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾ ⢻⣇⠀⠀⡿⠁⣰⣿⣿⣷⣦⣤⣬⣙⠚⠻⣿⣿⣿⣿⣿⣿⣶⡀⢤⡤⠒⠈⠁⠀⢩⣅⠙⠛⠻⢶⣶⣦⣤⣤⣤⣄⣀⣀⠀⠀⠀⢀⣠⣤⢾⣿⡟ ⠀⣿⠀⠀⡇⢀⠏⢠⡿⠋⠉⣻⢿⣿⣿⡦⠀⢻⣍⣼⣃⣽⣯⠇⣠⢶⡷⢦⡀⠉⠉⠀⠋⠳⠦⠉⠡⠤⣄⠈⣁⢬⡙⠫⠭⠟⠻⠋⣩⣷⣿⠏⠀ ⠀⢻⣶⡀⢧⠈⢸⡾⠀⠰⢫⣶⡿⠻⠻⣷⡀⠀⢩⣬⣏⣩⣯⡞⣡⠛⠀⢨⢷⡀⠘⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⡿⠟⠁⠀⠀ ⠀⠀⠹⣿⣾⡇⠸⡄⠀⠀⣿⣿⠀⠀⠀⠀⠙⢶⣤⣀⡴⠞⡀⠀⠀⠀⠀⠈⣆⢧⡀⠀⠀⠀⠀⣀⣤⣤⣦⣶⣶⡶⠿⣛⣡⡾⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠿⣿⣶⣷⣄⠀⢻⢿⡆⠀⠰⣤⣤⠄⠈⠉⠁⣸⠃⡀⠀⢀⡇⠀⠀⠘⣿⣄⣷⣿⠾⠛⠛⣉⣁⣤⣴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣄⠀⢸⣿⣌⢿⡟⠀⠘⢿⣶⠂⢰⣍⠀⠀⠀⢰⣿⠀⡇⠀⣼⡇⠀⠀⠀⢸⡋⠉⠀⢀⣴⡟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣿⣷⣏⠳⣼⣄⣿⣦⡙⠦⣀⠀⠻⣄⠀⢿⣄⣀⢀⣾⡇⠀⠇⠀⣿⠃⠀⠀⠀⡼⣇⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣿⣾⠟⠻⠦⢿⡟⡿⣦⣈⢳⣤⠟⣷⠛⠛⠋⠛⣻⡇⠀⡄⠀⢿⡆⠀⠀⢰⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⢿⠀⠀⠀⠀⢼⡃⣷⢿⡏⢿⣥⣶⣯⣿⠀⠀⠀⢻⣷⠀⢹⡀⠈⢧⠀⠀⣾⡷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢷⣝⡾⣿⡜⠾⢷⣾⠿⢤⣄⣴⠶⠿⢷⣼⣇⢤⡀⠀⠀⢻⣇⠸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧⡀⠀⠘⢾⣷⣤⡀⠀⠀⠀⠀⠘⢻⣌⠻⣦⡄⠈⠛⠀⠹⣟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠗⢀⡀⠉⣸⡇⠀⠀⠀⠀⠀⠀⠉⠳⢶⣝⢦⡀⠀⠀⢿⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠟⠀⡼⠁⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⢳⡄⣤⡘⠂⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⣠⡴⢟⡫⢦⠞⡴⠃⣰⣷⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣸⡇⢻⢳⣳⡻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣿⣍⠙⠏⢘⣯⡶⣻⠋⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⢿⡇⢸⡀⣧⠳⢎⡻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡟⠿⠁⣸⠀⣠⣿⣿⡿⢦⣠⣰⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⣄⢹⣿⣤⠈⡇⢹⣇⡀⠙⢏⡛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⡧⠴⠶⠿⠴⢿⡏⠏⠀⣸⣇⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⢹⣿⣿⢡⠞⠿⢾⣿⡿⠀⡾⢻⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⠗⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡤⠶⠾⠿⠻⣿⠀⠘⢀⡿⠷⣴⣇⣀⡙⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⠟⠁⠀⠀⠀⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⣀⢀⣀⣀⣀⡀⠀⠀⣀⣀⢀⣀⡀⠀⠀⢠⠠⠄⡀⠠⣤⠤⠠⡄⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠙⠛⠛⢛⠛⠛⠓⠘⠚⠓⠉⠃⠋⠀⠀⠚⠒⠁⠓⠛⠓⠒⠒⠂⠒⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠿⠿⠿⠿⠶⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣙⣻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡾⢟⣟⠹⠉⠭⡛⠻⣷⣤⡀⠀⠀⢀⡀⠀⣼⣟⣽⡟⠉⠉⠉⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⡿⠛⠋⠙⠛⢶⣤⡿⠋⣀⣙⣿⣄⣰⡿⣿⡀⠛⠛⠁⠀⠀⣴⡶⣶⣄⠈⢿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⡟⢀⣾⡻⢛⣷⡄⢻⠀⣾⣯⢉⣻⣿⡟⢠⠘⣷⣄⠀⠀⠀⠀⢈⣿⠶⣿⠷⠶⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣡⣧⣼⣧⣻⢟⣼⢷⡞⣷⢿⣝⣛⣵⣿⢀⡿⣷⡈⠻⣧⡀⠀⠀⠸⠷⠟⠋⠀⠀⠈⢻⣧⡀⠀⠀⠀ ⠀⠀⠀⢸⣿⢟⡉⠌⠙⠻⣿⣇⣸⢿⡿⣄⣈⣉⣁⣿⣼⣧⣼⡇⠀⠙⠿⢶⣦⣄⡀⠀⢀⣀⣀⣠⣴⠿⣿⠀⠀⠀ ⠀⠀⠀⣿⣷⣾⣷⠐⢠⡄⢘⣿⠱⡀⢠⣀⣝⢩⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠛⠉⢉⣉⣀⢀⣿⠀⠀⠀ ⠀⠀⢸⣿⣥⣿⣿⣶⣿⣿⣼⣿⠀⡍⢺⣏⣿⣿⠛⠂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠀⠀⠰⣾⡋⣹⢇⣼⣿⠀⠀⠀ ⠀⠀⠈⣿⣏⣩⣽⣿⣇⣽⣿⣇⣴⡾⢼⣿⣿⠧⠶⠶⣶⣤⣄⣿⢈⣧⡀⠀⣀⣀⠀⠀⠀⠹⣿⣥⠞⢁⣿⠀⠀⠀ ⠀⠀⠀⢿⡟⢛⣡⣾⣿⣿⡏⣿⠉⣿⣾⡏⣿⡄⠀⠀⠀⠉⠙⣿⡍⠁⠀⢸⣅⡽⠀⠀⠀⠀⣿⣇⣀⣸⡏⠀⠀⠀ ⠀⢠⣤⣼⣿⡟⠻⢷⣿⠘⠷⠟⢿⠏⣈⣻⣟⣿⣄⠀⠀⠀⠀⢀⣽⣦⡶⠺⠿⠻⢷⣦⡀⠀⢹⣟⣹⣿⣥⡄⠀⠀ ⠀⠈⠻⢶⣶⠄⢛⡻⣿⡄⠀⠀⠾⠿⠛⠛⠛⠛⠻⠿⢷⣶⣤⣌⠿⠟⠃⠀⠀⠀⠀⠀⠙⢷⣾⣿⣯⠁⣿⣧⡀⠀ ⠀⠀⠀⠘⢿⣾⣿⣡⣾⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣴⠻⠿⠿⣶⣤⡀⠀⠀⠀⣀⣠⣶⡿⣿⣄⢶⣦⣭⣿⠃ ⠀⠀⢼⣟⠛⠛⢋⣩⣽⡇⠀⠀⠀⠀⠀⠀⠂⠈⠙⠦⣌⣹⡄⠀⠀⠈⠙⢿⣿⠛⢻⣿⣿⡉⢻⣿⣿⠛⠁⠀⠀⠀ ⠀⣴⡾⠛⢁⠚⢋⣉⣠⣿⡀⠀⠀⠀⠀⢀⡀⠒⠄⢸⠉⠉⠁⠀⠀⠀⠀⠈⢻⣿⢉⢹⣏⠻⣦⠉⣉⣿⡆⠀⠀⠀ ⠈⠿⠷⠟⣿⣤⡿⣿⣋⡙⣿⣄⠀⠀⠀⠀⠙⢂⣀⣬⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⣿⣿⡇⢨⣄⠙⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⢴⣟⡏⣽⢻⣟⢿⣦⣤⣤⣸⣏⣀⣀⣀⣀⣴⣆⠀⢰⣦⠀⠀⣿⡏⠉⠈⠻⠿⠛⠷⣾⠗⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢨⣿⢡⣾⣼⡟⠛⠃⠈⠉⠉⠉⠉⠉⠉⠉⠉⢻⣦⣾⢻⣧⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠿⠟⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣗⠒⠶⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⡀⣹⠆⠀⠀⠀⠀⣀⠈⢶⢦⡸⣄⠀⠀⠀⢳⡿⣏⠓⢶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠤⢤⣄⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠈⠛⢦⡳⣵⣿⡀⠀⠀⠀⢳⢻⡀⠀⡆⠈⡙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⡿⠛⢑⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⣿⣿⣿⡷⠀⠀⠀⢸⣾⡇⠀⠏⢸⡇⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⢮⣀⣸⠇⠀⠀⠀⠀⠀⢀⡴⠿⠋⠉⠁⠙⢷⣿⣯⣏⣀⣤⣄⣸⣿⣇⡀⠀⣿⡟⠀⠀⢸⠀⢳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣴⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⠙⠛⣦⣄⡀⠋⢀⡼⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⣤⣤⣴⣟⠃⠀⠀⣠⡿⠋⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠆⠘⡎⢹⣶⣯⣤⡾⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⡽ ⠀⠀⠀⠀⠛⠟⠛⠁⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠘⡇⠈⢳⢄⠀⠹⣆⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢹⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⠀⣷⠀⢸⣿⡝⢦⡙⣆⠀⠀⠀⠀⣰⠟⠀⠀⣠⣼⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣹⠟⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢠⠇⠀⠀⡿⢰⣿⠀⢸⠿⡇⠀⢿⣿⣦⣀⣀⣾⡃⢀⣴⣫⣵⡟⠀ ⠀⠀⠀⢀⣀⣀⣀⣀⣼⣿⣷⣀⡇⠀⠀⠀⠀⢀⣀⣤⣤⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⠃⢸⠃⠀⡼⢀⡗⠀⡼⢹⠀⣿⠉⠛⣷⣿⣛⣵⣸⡇⠀ ⠀⢀⡴⠋⠉⠀⣹⣤⣉⡿⣿⡿⠁⠀⠀⠀⣴⠛⠉⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣰⠏⠀⡏⠀⡾⠁⢸⠃⢠⡇⠘⠛⠃⠀⠀⣿⣟⣯⣥⣼⠀⠀ ⢀⣿⠀⠀⣠⠞⠁⠀⠈⠙⠿⠦⡀⠀⢀⡾⡄⠀⠀⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣿⢁⡼⠁⠀⣼⠁⣸⠀⠀⡼⢀⡞⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⣿⠀⠀ ⠀⣿⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠻⢿⣇⣠⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡾⠀⠀⢸⢁⡼⠃⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⢸⣁⣀⣀⠀⡇⠀⠀ ⠀⣿⠀⠘⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠁⠀⠀⡿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠳⣦⡋⠙⣧⠀⠀ ⠀⠉⣇⠀⠈⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠀⠙⢶⣿⠀⠀ ⠀⠀⠸⣧⠀⠀⠙⢦⣀⠀⠀⠀⠀⠑⠤⣄⣀⣀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠚⠺⠯⣄⡀⠀⠀⠀⠀⢿⠀⠀ ⠀⠀⠀⠙⢷⡀⠀⠀⠈⠙⢲⠶⢦⣤⣴⣶⣿⣟⡞⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠊⠉⠀⠀⠀⠀⠀⠀⠙⠲⢄⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⢹⣷⡄⠀⠀⠈⣧⢀⡽⠋⠁⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢠⣦⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠏⠀⠀ ⠀⠀⠀⠀⣤⠊⣼⣿⢲⡤⡄⢹⣞⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣿⣿⣆⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⠋⣠⢞⣻⠏⡼⠀⢷⣌⠉⠛⣉⣠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣯⣿⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣧⠞⣷⡾⢃⡾⠁⠀⠀⠉⠛⠛⠛⠉⠙⠛⠓⠒⠦⠤⠤⠤⠖⠒⠚⠛⠛⠋⠀⢹⠈⣿⡌⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣩⣤⣴⣋⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢿⣷⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⣿⣆⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣿⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⣿⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⡇⠿⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢾⣧⠖⠲⢤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢴⠋⠀⠸⡄⠀⠀⠈⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡴⣾⠀⡀⠀⠱⣄⠀⢀⠀⠀⠀⠺⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⢸⢰⠇⠀⢇⠀⠀⢹⢶⡵⢋⣀⡀⠀⣀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣂⡘⣿⣠⣶⣜⣲⠄⣸⣟⣴⣿⣿⣛⣷⣬⣲⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⠁⠁⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⡄⠀⠀⣼⣿⣿⠻⢯⣽⣿⣿⣿⣿⡌⡟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠉⢧⠀⢀⣿⣿⣿⣷⠾⢿⣿⣿⣿⣿⣧⢹⣎⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⣼⣷⣿⣷⣼⣯⢿⣷⣼⡀⣼⣉⢿⣿⣿⣿⣧⡙⢷⣄⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣜⣻⣿⣿⣿⣷⣄⠙⢷⣄⡀⠈⠳⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⣼⢯⢳⣸⣿⣿⣿⣿⣿⣐⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⠛⠦⡀⠈⠑⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡟⠙⢿⣿⣿⠟⠿⣿⣿⣄⣬⣿⠿⣿⠁⢠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠈⢷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢷⢾⣯⣾⣿⣶⣾⣿⡟⠀⠀⠀⢀⣏⡩⢷⠀⢸⣿⣾⢿⠀⠉⠙⠛⠛⠉⠉⠛⠻⢿⣿⣧⠈⢂⠀⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣫⠥⠚⢋⣠⠴⠛⢿⣟⣹⣧⠀⠀⠀⠘⣿⣿⣿⡷⠀⢹⡇⣾⠀⠀⠀⢀⡔⢚⡿⣷⢤⡈⣿⣿⡆⢸⣤⢸⡄ ⠀⠀⠀⠀⢀⣠⣴⣾⣽⠟⢋⣁⠤⠒⠉⠀⠀⠀⠘⠻⣍⣸⠄⠀⠀⠀⠻⠻⠏⠁⠀⢾⡓⠛⡇⠀⠀⢸⢰⡟⢙⠻⣳⣽⣟⣿⠁⢸⣿⡾⠀ ⠀⣀⡴⣚⣭⣔⣛⢉⡤⠒⠋⠁⠀⠀⠀⠀⠀⢀⣤⣦⢽⣿⣶⣠⣤⣤⣤⣤⣤⣤⣤⣼⣷⣶⣧⣤⣤⣤⣿⣗⣾⣧⣨⣾⣉⣡⣴⡿⠟⠁⠀ ⠿⠷⠿⠟⠛⢓⠛⠿⣿⠷⠶⡶⠶⠶⠶⠿⢳⢿⣿⣿⡿⢿⣿⡿⠿⠿⢿⣿⣿⢿⣿⡿⢿⣿⣁⣨⣿⣿⣿⣿⣿⠛⠚⠓⠈⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠀⠀⠘⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⡀⠀⣀⡀⢀⣀⡀⢀⣀⢀⣀⢀⣀⠀⣀⡀⢀⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣷⣴⣿⣇⢸⣿⡇⢘⣷⢿⣡⣽⣿⣤⣿⣇⣸⣷⣾⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠁⠀⠁⠁⠈⠈⠁⠉⠈⠉⠀⠉⠁⠈⠉⠀⠉⠉⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠉⠉⠉⠀⢀⣴⠾⣫⣭⣿⣶⣾⣾⣶⣯⣭⣙⡻⠶⣦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠿⠟⠉⠁⣀⣀⣤⣴⣶⣶⣿⠟⠁⣼⢏⣷⣿⣿⣿⣿⣿⣿⡏⢠⣌⣿⣿⠟⠁⣀⠉⠻⢶⣤⡀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠋⣁⣠⣴⣾⣿⣿⣿⣿⣿⣿⡿⠁⢀⣾⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⢀⡔⠋⣠⣴⣶⣶⣾⣿⡄ ⠀⠀⠀⢀⣼⣿⣿⣿⡿⠋⣀⣴⣾⣿⡿⠟⠋⠁⠹⣿⣿⣿⣿⠃⠀⣼⠃⣿⣿⡿⠛⠉⠁⠀⠀⠀⠈⠉⠋⣠⠋⢠⣾⣿⣿⣿⣿⣿⡿⠁ ⠀⠀⢀⣾⣿⣿⡿⠋⣠⣾⣿⡿⠟⠉⠀⣀⣠⡤⠄⢹⣿⣿⣿⠀⠀⣿⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢠⣿⣿⣿⣿⣿⣿⡟⠁⠀ ⠀⢀⣾⣿⣿⡟⣠⣾⣿⣿⣯⣴⣾⠟⠋⠁⠀⣠⡶⠟⣿⣿⣿⡀⠀⣿⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠟⠛⠛⠛⠓⠶⣦ ⠀⣼⣿⣿⠏⣸⣿⣿⠏⠸⣿⣿⡇⠀⢀⠴⠚⢁⡴⠋⣡⠾⣿⣧⠀⠸⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣠⣴⠶⠶⠖⠒⠂⢀⣿ ⢸⣿⣿⡟⣰⣿⣿⠃⠀⠀⠙⢿⣿⣦⠀⠠⠞⢁⡴⠚⠀⣼⠃⠈⠳⣄⣽⣧⡀⠀⠀⠀⠀⣄⣀⣀⣠⡤⠤⢞⣻⡵⢃⡠⢖⡠⣞⣴⠟⠁ ⣾⣿⣿⢁⣿⣿⠏⠀⠀⠀⠀⠀⠙⢿⣷⣤⡈⠁⢀⣠⡾⢋⣤⣶⣿⣿⣿⣿⣿⣶⣤⣤⣀⣀⣈⣘⣚⣛⣉⣉⣓⣾⣭⣴⠿⠚⠋⠁⠀⠀ ⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⠟⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⡆⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⡄⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣆⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠈⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠈⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣌⡻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠙⠻⠷⣤⣄⡀⠀⠀⠀⠀⢀⣀⣤⠾⠛⠁⣠⡞⠀⠀⣼⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣽⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢶⣶⣟⣛⣉⣁⣠⣴⡾⠋⢀⡴⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣯⢉⣉⣥⣴⡾⠋⠀⣸⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠎⣽⡻⣿⡿⠶⢶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣭⣉⣉⣁⣠⠴⠚⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣁⠸⣽⡿⣡⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⣏⠉⠉⢻⣟⢷⣦⣉⣉⠉⠁⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠻⣷⣭⡛⠛⠛⠛⠛⠛⠉⢻⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣈⠻⢿⣷⣦⣤⣀⣀⠀⠈⢿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣌⡉⠉⠉⠉⠉⠉⠀⢹⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⠶⠶⠾⠟⠁⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣶⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⠿⠿⣿⣿⣤⣴⡿⠗⣫⠽⣫⢟⡻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠋⠁⠀⠒⠲⠀⠀⢈⠙⠻⢷⣯⣴⠚⠕⠋⠀⣀⡼⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⢠⣄⠀⠰⠦⠀⠾⠄⠀⠀⠙⠻⣷⣤⡴⠚⣁⠴⠋⣈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠛⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⢀⠀⠀⠀⠮⠙⢿⣦⡤⠖⢋⡡⠔⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣠⠀⠀⠓⠀⢠⡤⠴⠄⠀⠀⢠⡀⠀⠈⠁⠀⠀⡀⠀⠀⠙⢿⣯⠁⣀⡴⢚⣻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠁⠀⠀⣀⣀⠀⠀⠀⠀⠠⡄⠈⠀⠀⠐⠂⠀⠀⠙⠀⠀⠂⠈⢻⣧⣀⠔⢋⡀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁⠀⠀⣿⣿⠛⢻⣆⠀⠀⠀⢸⣷⣆⠀⠀⠀⣴⣿⣿⣶⣄⠀⠀⣈⣿⣷⠐⠋⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠀⠀⣿⣿⣤⣿⡟⠸⠿⠂⢸⣿⣿⠀⠀⠀⢹⣇⣀⣼⣿⠰⢦⠁⢸⣿⣧⣴⣷⡯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠠⣄⠀⢹⣿⠛⠿⣷⣄⠀⠀⠘⣿⡿⠀⠶⠄⠸⣿⠛⠛⠁⠀⠀⠷⢸⣿⣿⠟⠉⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⣀⠀⠀⠙⠃⠀⠈⠛⠀⠀⠀⠙⠁⡀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢀⣸⣿⡇⠠⠖⢁⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠉⢹⡛⠒⢶⣒⣀⣶⡛⠋⠁⠀⠀⠛⠃⠀⠀⢀⠀⠀⣠⡤⠶⢿⢹⣿⡇⣠⠔⠋⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠹⢤⣄⡉⣁⣠⡴⠚⠉⠀⠀⠀⠀⠸⣔⢲⣳⣿⠏⠠⠆⠀⣾⣿⠀⠁⠀⢀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣀⠀⠀⠀⠀⠙⣆⠀⠀⢀⣺⠇⠀⠀⠘⠓⠋⠉⢀⡏⠀⠀⠳⣴⣿⡏⠀⠠⣶⡁⣾⣿⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠉⠁⢀⡀⠀⣀⠘⣦⠀⠈⠙⠁⠀⢀⡄⠀⠀⠀⠈⢷⠆⠀⠀⢹⣿⡇⠶⠊⠁⣸⣿⣿⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⢸⣿⡇⣄⠀⢸⣷⡀⠀⠀⠹⡷⣄⡀⠀⢀⣾⣇⠀⠀⠀⢠⣄⠀⠀⠀⣸⠿⣧⣠⢖⣿⣿⠈⠙⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⡀⠸⣿⡿⣿⣠⡟⠻⣷⠀⠀⠀⠹⠄⠙⠲⣾⠘⠋⠀⠀⢀⡾⠹⣧⡀⢰⠇⠀⠘⠿⠘⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠳⣾⠁⠘⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠓⠀⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣿⣿⣿⠛⡟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣶⣾⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠒⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⠀⢄⡀⠀⠀⢀⣀⣀⣤⠴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡇⠀⠀⢀⡏⠉⠉⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⠀⠀⡾⠁⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠈⢧⡀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⢸⠁⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣴⠂⠀⠀⠀⠀⠀⢷⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⢸⣄⣴⠗⠒⠒⠒⠓⠒⠒⠲⢤⣄⡀⠀⣠⡞⠁⣠⠶⠋⣹⠀⠀⠀⠀⠀⠀⠈⡇⠀ ⠀⠀⠀⠀⢸⣆⡀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠿⠻⢯⣠⡞⠑⣿⣾⣿⡄⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⣠⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠀⠀⠀⢙⣿⠟⠋⠀⠀⢳⣄⠀⠀⠀⠀⢀⣇⡄ ⠀⠀⣰⠏⢺⡄⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⢠⡄⠈⢀⣠⣄⡀⢀⡽⡆⠀⠀⠀⠀⠉⠓⠦⠤⠴⠛⠉⠀ ⠀⢀⡏⠀⢿⣷⠞⠁⠘⡏⢷⡄⠀⠀⠀⠀⡶⠀⢠⠟⠀⠘⡟⢯⠤⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⠀⠀⢀⡇⠀⠀⢸⡇⠀⣿⡆⠀⠀⠰⡆⠀⣏⠀⠀⢠⡇⠘⣆⠀⣷⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀ ⢐⣿⠀⠀⢸⡷⢤⣼⣿⣿⠀⣿⢳⠀⠀⢰⠆⢰⣿⣷⣶⡟⠀⢐⣿⠀⢸⠀⠀⠀⢠⣿⣾⣧⠀⠀⠀⠀ ⠀⢿⠀⠀⢸⣧⠀⣠⣿⠟⠻⡟⣸⠆⣠⣤⣤⣸⣯⢹⣿⠟⠻⣾⢸⠀⢸⠀⠀⢠⣟⣽⣿⠛⡆⠀⠀⠀ ⠀⠘⣆⠀⠀⠙⠓⠷⠿⠤⠞⠋⠁⠀⠸⣿⡁⠀⣹⠛⠿⠦⠾⠷⠛⢀⡾⠀⢠⡟⣽⣿⠃⠀⡇⠀⠀⠀ ⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠐⠲⣖⠚⠋⣹⡗⠁⠀⠀⠀⠀⢀⣠⠞⠀⢠⣿⣿⡿⠁⢀⡾⠁⠀⠀⠀ ⠀⠀⠀⠈⠙⠶⢤⣀⠀⠀⠀⠀⠀⠙⢲⣾⡋⠀⠀⠀⣀⣤⣶⣏⠀⠀⣠⣿⣿⡟⠁⣠⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⡤⠴⠞⠛⠉⠳⢆⣠⣴⣾⣿⣷⠶⠿⠿⠗⢺⣿⡿⣷⣴⣿⡏⠙⠦⠼⠁⠀⠀⠀⠀⠀⠀ ⢰⠟⠉⠁⠀⡇⠀⠀⠀⠀⢸⣿⣿⣾⣿⣯⢻⣷⡀⠀⠀⢸⣿⣷⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡆⠀⠀⠀⡇⠀⠀⢀⡞⠀⠻⢿⡿⠃⣿⣛⡿⣧⣀⣀⠘⣿⣷⣿⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⣷⡄⠀⠀⢹⣀⡴⠛⣷⡆⠀⠀⠀⠀⠀⢸⢀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣇⠙⢶⡶⠚⠉⠀⢠⡿⠁⠀⠀⠀⠀⠀⡼⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠷⢾⠻⢦⣀⣠⠾⠁⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠀⠀⠈⠓⠤⢤⠤⠤⠶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⣧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠙⠒⠒⠒⠚⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⡴⠚⠉⠉⢉⣁⣤⣤⣀⣀⡀⠀⠉⠙⠲⣄⠀⢠⡇⠀⢸⡛⠉⠉⠉⠑⠒⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣇⡀⠀⠀⠀⢸⣄⣀⣠⡶⠋⠀⠀⠀⠀⠀⠉⠙⠦⣄⣀⣨⡷⠟⠀⠀⠘⣧⣀⠀⠀⠀⢀⣠⡤⢤⣌⣉⠉⠉⠙⠲⢤⡀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⢸⠀⠉⠉⠛⠓⢾⣿⡛⠋⣠⣤⡶⣶⣿⣿⣿⣗⢦⡀⠙⣆⢳⡀⠀⠀⠀⠀⢠⠟⢉⡽⠛⠉⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠙⣆⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⢆ ⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠛⣯⠈⠻⣿⣄⣼⣿⣿⣷⣌⡷⠽⠓⠸⣦⣧⠀⠀⠀⢀⣿⣴⢋⣀⣠⣴⠿⣽⣿⣦⣄⡀⠀⠙⢧⣄⣀⡏⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠶⠋⡧⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠉⠛⠛⠛⠉⠁⠀⠀⠀⣠⠇⡟⠀⠀⠀⢸⡏⣿⠀⠀⠻⣟⢤⣿⣟⡷⡏⣹⣷⡄⢠⣭⣩⡟⠒⠒⠒⠒⠚⠋⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⣼⠃⠀⠀⠀⠈⣷⢸⡄⠀⠀⠀⠉⠚⠫⠭⠛⠚⠉⠙⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⡿⡀⠀⠀⠀⠀⠀⠀ ⠀⢸⢻⠁⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⢤⣀⣀⣀⡤⠞⠋⢀⡼⠃⠀⠀⠀⠀⠀⢻⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠙⢦⡀⠀⠀⠀⠀ ⠀⠸⣿⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣱⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⠓⠦⢤⣀⣀⣠⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡴⠋⠉⢻⠀⠀⠀⠀ ⣄⠀⢹⣦⡀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⡟⠀⠀⠀⠀⠀⠀⢰⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⢸⠀⠀⠀⠀ ⠐⠀⠀⢷⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇⠀⢰⢳⠀⠀⠀⠀⠀⢀⡞⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡼⠀⠀⠀⠀ ⠀⠀⠀⢸⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠻⣦⣈⣳⣅⠀⠀⠀⢀⣾⠦⠤⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠃⠀⠀⠀⠀ ⠀⠀⠀⠸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠛⠒⠶⠒⠚⠁⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡔⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢉⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣻⠀⠀⠀⠀⣀⣀⣀ ⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠭⠵⠶⠿⠿⠭⠭⣍⣙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠏⠀⠀⠀⠀⠙⠺⢽ ⡄⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠽⣶⣤⡀⠀⢻⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠒⠒⠒⠛⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⠀⠀⠙⠿⣦⣼⡆⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⢰⠇⠀⠀⠀⠀⠀⠀⣴⡵⠉ ⠀⠀⠀⠀⠈⢻⣷⠀⠀⢈⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡸⠉⠀⠀ ⠀⠀⣠⣶⡯⠖⠛⡆⠀⠀⣇⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣸⠃⠀⡼⠀⠀⠀⠀⢀⡼⠧⣄⡀⠀ ⢀⣾⡟⠁⠀⣠⠖⣷⠀⠀⠘⡆⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣰⠃⠀⢠⡿⠤⣄⣤⠖⠋⠀⠀⠀⠙⣆ ⣿⠟⠀⢀⡞⠁⠀⢸⠀⠀⠀⢹⡀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⠀⠀⠀⣰⠃⠀⠀⡾⣴⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘ ⠏⠀⠀⢸⠀⠀⢀⣼⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠁⠀⠀⠀⠀⠀⡴⠃⠀⠀⣸⠁⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡴⠚⠁⢸⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠤⣤⣤⣤⣤⣤⣤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢰⠇⢀⡇⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣟⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⡞⠀⣼⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⣾⠉⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⡖⢚⣛⡉⠙⠓⠲⠤⣄⡀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠉⠉⣵⠏⠉⢹⣄⡴⠲⣦⠈⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⠋⠀⠀⠀⣼⠁⠀⠀⣰⠏⠀⠀⠸⡇⠈⠋⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠃⠀⠀⠀⢰⠇⠀⠀⢠⠏⠀⠀⠀⢀⡇⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡇⠀⠀⠀⠀⣾⠒⠒⠢⣾⣀⣀⣀⠀⢸⠇⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠁⠀⠀⠀⠀⣿⣴⣲⣄⣿⢀⣀⠈⢳⡾⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡆⠀⠀⠀⠀⠘⣿⣿⡿⢿⣿⣿⣷⡾⠁⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢠⣶⣰⣼⣿⣷⣿⠿⠛⠉⠙⠛⢧⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠠⣶⡾⠋⠁⠀⠀⠈⠙⠶⡄⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢧⡀⠀⠀⠶⢤⣤⣀⣀⣰⣤⡤⠖⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢀⣶⠏⠁⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠹⡿⠿⣇⡖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⣄⠀⠀⠈⢧⠀⠀⢀⡟⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⣺⣿⠴⠒⠒⠲⠦⣄⡀⠀⠀⠀⣿⠀⠀⠀⠀⢰⡇⠀⠀⠙⢿⣦⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⡦⣄⣈⢳⣤⠞⠀⠀⣀⣠⠴⠚⢿⣞⡥⠀⠀⠀⠠⣜⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⢠⠏⠀⠀⠀⣰⠟⠀⠀⠀⠀⠈⢿⠉⠙⠻⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⣯⣶⠀⢀⣄⢰⣾⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣿⣤⡤⠴⠚⠁⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠁⢻⣿⣤⡦⣴⣠⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⠿⠛⠉⠀⠀⠉⠙⢦⣄⠀⠀⠀⠀⠀⠀⣿⠈⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠫⣤⠀ ⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⢠⣿⠀⠀⠈⢿⢦⣀⣀⠀⣀⣠⡴⠋⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠘⣏ ⠀⠀⠀⠀⠀⠀⠈⠷⣄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠸⡇⠀⢀⣰⠟⠁⠀⠀⠀⠀⠀⠈⠙⠟⢿⣄⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⢀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⠤⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢠⡷⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠓⠶⣤⡤⠴⠚⣯⡀⠀⠀⠀⠀⠀⠀⣠⠞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠓⠲⡤⠴⠒⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣀⣴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢦⣀⠀⠀⠀⠀⢀⣠⣴⠋⠉⠛⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣛⠟⠛⠋⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣼⠙⠳⣄⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⢸⣿⡉⠛⢯⣍⢹⣶⣦⣤⣀⡀⠀⠀⢀⣤⣾⡿⠿⠃⠀⠀⢸⣷⣿⢛⣿⣆⡀⠀⠈⣽⢉⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⣿⠛⢉⣿⢻⣿⣿⣂⠀⠀⠀⠀⠀⢿⣧⠀⠀⡉⠳⣟⠊⠁⢀⣩⠿⠛⠋⠉⠀⠀⠀⠀⠀⢠⡿⠛⣿⡉⠹⣿⣶⣀⡴⠃⣼⡿⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣾⣿⡟⢰⠟⠀⢸⡇⣾⠿⠟⢛⣆⠀⠀⠀⠀⠈⣿⣇⠨⠇⢸⡿⢧⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠅⠀⣨⣿⣦⡐⣿⡿⢀⣿⣽⠃⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⣦⣩⣴⠏⠀⠀⠈⣻⡶⡶⢾⣿⢿⡿⣆⠀⠀⠀⢸⣿⢧⣀⣼⣟⠉⠀⠀⠀⠀⠀⣰⣖⡶⢦⣄⡀⣾⣥⣴⣿⣿⡩⠝⢷⡿⣵⡿⠟⣿⠀⠀⠀ ⠀⠀⠀⠀⣻⡟⠁⠀⠈⠓⢎⣴⠖⠓⢷⡄⢠⡟⢡⣾⣿⣿⡷⠀⠀⠈⣿⣆⠙⠛⢃⠀⠀⠀⢀⡴⣛⣅⡀⠉⢷⡌⢹⣿⢀⡾⡉⡀⠹⣦⠈⣷⣿⣶⠟⠁⠀⠀⠀ ⠰⣦⣴⣞⣁⣠⣴⠀⠀⣀⡟⠁⠀⠀⢈⡇⠹⣆⠙⠻⢿⡿⠃⠀⠀⠀⠘⢷⣤⣤⠟⠀⠀⠀⡞⠁⠀⡎⣳⠀⠀⢹⣸⣿⣾⠇⢹⠹⠀⢸⡆⣿⣋⣀⡀⠀⠀⠀⠀ ⠀⠈⠻⢿⣿⣿⣿⠿⣯⣿⠇⠀⠀⠀⣼⠃⠀⠈⣻⡶⠋⠀⠀⠀⠀⣿⢿⣿⡋⠁⠀⠀⠀⣸⠁⢀⠰⠃⢻⠀⠀⠀⣿⣿⣿⠀⡀⠀⠀⠈⣷⣿⠉⣹⠇⢀⡀⠀⠀ ⠀⠀⠀⠈⠻⠿⡷⠿⠛⠋⠀⠀⠀⣴⡏⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠘⣇⠈⠁⠀⠀⠀⠐⢿⡀⠙⠂⠀⠀⠀⠀⢀⡟⡟⠹⣆⠀⠀⢀⣰⣟⣛⠚⠛⣭⣽⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣀⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢽⣷⣤⣀⡀⠀⡟⠀⠓⠦⣤⣀⣀⣠⠴⠛⠀⣷⠀⠈⠛⣻⣯⣍⠻⣿⣷⠛⢩⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠋⠉⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⣀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠛⢋⣿⡇⢸⣿⣶⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠇⣀⣤⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢦⣼⣷⣄⠀⠀⠀⠀⠀⣿⡛⠶⢬⣿⣥⡦⠀⠀⣠⣧⠾⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣹⡟⣉⣵⠾⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣙⣞⣿⠲⠦⣤⣀⡈⠉⠉⠉⠉⠛⣶⡶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢿⡿⠋⠁⠀⠀⠻⣦⣀⠀⣀⣀⡤⠤⠶⠶⠤⠤⠤⠤⠖⣻⠿⢿⡁⣂⠀⠀⠀⠀⣁⡤⠖⣛⣹⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⣌⠻⣆⠀⠀⠀⠀⢸⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢹⣿⢷⡀⠀⣰⠋⣠⣾⣿⣿⣾⡗⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⠓⠺⢇⠀⠀⢠⣾⡝⠂⠀⢀⡀⠘⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠉⠾⣿⣷⡇⢠⣿⢇⡛⣹⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢓⣶⣶⠿⣤⢺⡁⠀⠀⠀⣀⠁⠀⠀⡀⠀⢠⠏⢀⡄⢀⡀⠀⠀⠀⠀⢠⡿⠀⣾⣿⣿⡿⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠺⠷⣾⡃⠀⠀⣤⣉⡆⠀⠀⡇⠀⠈⠀⠘⠧⠼⠔⠻⠓⠀⠀⣼⠇⢰⡟⢘⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠋⠰⢮⡀⠼⢤⠀⣰⠧⠶⡶⡶⢴⣆⠀⠀⠀⠉⠀⠀⣿⢠⡿⠁⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠰⣰⣿⣶⢶⣿⣿⣶⣼⡆⠀⠀⠀⠀⠀⣿⣿⣧⣤⣼⣿⠿⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⠀⠀⠀⠀⠀⠀⢀⡴⠋⠛⠷⠾⣿⠿⠿⢿⡇⠀⠀⠀⠀⠀⣿⠾⠛⢉⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢸⡀⠀⠀⠀⣠⡶⠋⢻⡀⠀⠀⢀⡟⠀⠀⠈⢷⡀⠀⠀⠀⠀⣷⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇⠀⣠⠞⠉⠀⠀⣾⣿⣤⡀⢸⡄⠀⠀⠀⠈⢿⡀⠀⠀⠀⢹⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢻⣶⠏⠀⠀⠀⠀⠈⠻⣿⣿⣛⠿⣤⡀⠀⠀⠀⢳⡶⠞⠋⠹⣇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣃⣀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣤⣈⢙⣿⢶⣦⠀⢿⣆⣀⣀⣟⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣻⣧⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠾⠿⠿⠟⠀⠈⠻⣿⣿⣿⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠋⠁⡞⠀⠀⠀⠀⠀⠀⣰⠋⠀⡴⠃⠀⠀⠀⢠⡟⠀⣰⠫⠂⣠⢠⣿⠇⢰⠿⠶⠒⠒⠛⢯⣥⣤⠀⠀⠈⠉⠉⠒⠒⠒⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀ ⠀⠀⠀⠀⠀⠀⢹⡿⠉⠀⠀⠀⠀⠁⠀⠀⠀⠔⠀⡼⠃⢀⡞⠀⣠⠖⡄⠁⡞⠀⡴⠃⢀⣼⠃⣾⡞⢀⡞⠀⠲⠶⣦⣄⡉⠉⠉⠉⠉⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⣠⠎⠀⡼⠁⣠⠏⢀⡾⢁⡼⠁⣼⢁⡼⠁⣠⢞⡟⣼⡝⢀⡞⠁⠀⠀⠀⠀⠀⢙⠿⣷⡶⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⢀⡴⠃⠀⡼⢁⡔⠁⣠⠟⢀⡾⠁⣸⠣⠋⣠⠞⠁⡾⡹⠁⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢝⠦⣄⡠⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⠛⠀⠀⣼⣡⠋⢀⡼⣣⡴⠋⣀⣰⣧⣤⣾⣿⣶⡾⣱⠁⡰⣼⣷⣤⣤⣴⣶⠾⠋⠀⠀⠀⠀⠀⠙⢮⡟⢦⣤⣘⡶⣶⣤⠤⠤⠤⠤⠄⠀⢀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⢰⠏⢀⣴⣫⠟⠉⢠⠾⣻⠟⠛⠿⢿⣿⣿⢃⠃⡰⣱⣿⣿⣿⣿⣿⣿⣿⠖⠀⠀⠀⠀⠀⠀⠀⠙⣮⡙⠮⣍⠛⠛⠶⣤⡀⠐⠉⠒⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠁⠀⠀⣰⣯⠾⣋⡵⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⢈⣿⡎⣰⣵⣿⣿⣿⣿⣿⣿⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡉⠲⠦⣄⡉⠙⣒⣚⡚⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⢀⣠⡾⢟⡥⠞⠁⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⡼⡞⣰⡿⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣶⣄⣉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⡴⠛⠡⠊⣁⣤⣶⣶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⡻⢡⡟⠁⢳⠤⠄⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠙⢿⣒⠦ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣴⡖⡞⢻⢩⣧⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢣⠞⠀⢀⣠⣤⣴⣖⣶⣶⣤⡶⡖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⢦⡉⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢸⢸⠁⣎⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⠗⢡⠟⢀⣶⣿⣿⡟⠙⠟⠉⠉⠀⠈⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⠙⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠏⢠⣿⣺⡿⣿⡟⠀⠀⠀⠀⠀⠀⠀⡴⡗⣰⠏⠀⣸⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠄⠀⠨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣾⢀⣟⡇⣿⠁⠀⠙⠲⢤⡀⠀⡼⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⣿⡾⡿⠀⢹⡆⠀⠀⠀⢀⣙⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠀⠀⠀⠐⠠⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⡈⢠⣿⢿⠁⠀⠘⢹⣶⣶⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⣼⣟⠇⠀⡞⣠⠘⣿⡟⢋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⡼⢹⡞⠀⡼⡹⣣⠀⡙⢹⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠶⠖⢻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡜⣡⡞⢀⣾⡿⣡⡏⡸⠁⡿⣏⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠏⠁⠀⢀⡀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⢻⠉⠉⠁⠠⠀⣸⣿⢋⡴⠋⠀⢺⣯⣴⣿⢠⠃⣸⡇⢹⡀⠀⠀⠙⠀⠀⢀⣠⠔⠋⠁⠀⢀⣀⣤⣴⣾⣿⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘ ⢘⠀⠀⠀⢰⣤⠟⣵⠏⠀⢀⣤⡞⢻⠁⣧⠏⢰⠏⡇⢸⣷⠀⠀⢀⣠⠴⠋⠀⠀⢀⣤⡶⢟⡿⠟⠛⠉⣿⡤⠋⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀ ⠐⠀⠀⠠⡞⣡⣆⣥⣴⡖⠉⢀⡇⣸⣴⣃⡴⠃⠀⡇⣸⠈⣧⡀⠀⠻⢷⣄⠰⠾⣿⡟⢀⡞⠁⠀⢀⣠⣽⡇⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⣠⡼⠀⠀⠀⠀⠀⢀ ⢶⠒⠊⣿⣿⣿⣿⣿⣿⡇⠀⣸⢷⣋⠘⠿⣷⠀⠀⡇⣿⢠⢹⡷⣄⠀⠀⠈⠙⢶⣾⢥⣾⢀⣠⠖⢉⣷⠏⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⡟⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀ ⠸⠀⣼⣿⣿⣿⣿⡿⢸⡇⠀⢸⠈⢿⡀⢠⣿⢧⠀⡇⣿⢀⢸⣿⠈⠳⣄⠀⠀⠀⠙⢦⡘⠓⠛⠛⠉⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⣾⡿⠃⠀⠀⠀⠀⢀⣠⠄⠀ ⢀⣼⣿⣿⣿⣿⡿⠃⢸⣷⠀⢘⣇⢈⣷⡀⣿⢸⣆⡇⣸⠈⢸⣿⣆⠀⡏⠓⣦⣀⠀⠀⠉⠲⠤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣼⣿⣿⠟⠁⠀⠀⠀⢀⣠⣾⡟⠀⠀ ⣼⣿⣿⣿⣿⣿⠃⠀⢸⡏⣇⠀⣿⠀⠈⢷⣿⠃⠙⢿⣿⠀⢸⣿⢹⡀⡇⠀⣷⡉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⢀⣴⣿⣿⠟⠁⠀⠀⣠⣴⣶⣿⣿⡟⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⢀⣷⢸⡇⠸⣇⠟⡆⠀⠈⢿⠀⠀⠈⢻⡄⠸⣿⢀⢿⣧⠀⠙⣿⠀⡌⢻⢦⡀⠀⠀⠀⠀⠀⠀⣠⡴⢟⣁⣤⣴⣾⣿⣿⠟⣁⣠⣴⣶⣿⡿⣻⣿⣿⡏⠀⠀⠀⠀ ⢛⣿⣿⠟⢻⠃⢸⣿⢸⡇⠀⠉⣧⢷⠀⠀⠀⢧⠀⠀⠀⢿⣀⣿⢸⠃⢿⡄⢀⣹⠀⠅⡿⢸⣿⠷⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⣿⣿⠏⠀⠀⠀⠀⣠ ⣦⣿⠁⠀⢸⠀⢸⣿⢸⡇⠀⠀⠘⡿⡄⠀⠀⠈⣇⠀⠀⠈⣯⣿⢸⡅⣸⠇⡸⢸⠀⢰⣷⢠⠿⡄⡏⡇⠀⠃⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣤⣾⡿ ⠉⠙⠒⢺⣾⠧⣼⣿⣠⣿⠀⠀⠀⢹⣷⠀⠀⠀⠸⡄⠀⠀⢸⣿⢸⣧⠏⠀⠃⠸⣠⢯⡏⣸⠀⢳⣱⡇⠀⢸⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣠⣶⣿⣿⣿⣁ ⠀⠀⠀⠀⣯⢷⡀⠀⠉⠙⡆⠀⠀⠀⢻⡀⠀⠀⠀⢳⡀⠀⠀⢻⣼⠃⠀⠀⠀⠀⢁⡟⣠⠃⠀⢸⣿⣷⣶⣾⣿⣏⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⢷⣷⣄⠀⠀⢹⡀⠀⠀⠀⣇⠀⠀⠀⠘⡇⠀⠀⠀⢣⡠⠀⠀⠀⡠⢋⡾⠁⠀⠀⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢻⢧⠀⠈⢧⡀⣿⡇⠀⠀⠀⢸⡄⠀⠀⠀⢸⡀⠀⠀⠀⠻⣿⡶⠒⠦⠯⢄⣀⣀⡤⢞⡹⡛⢻⢯⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠸⡎⢧⡀⠀⠳⣿⣳⠀⠀⠀⠀⢷⡀⠀⠀⠀⠻⡄⠀⠀⠀⢻⣤⠖⠃⠀⠀⠀⠀⠱⣄⣑⠀⠀⣀⢀⠀⠀⠀⠀⠹⠛⠛⠿⣻⡿⣿⡻⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠙⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠙⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⢠⠼⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢤⡟⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⠶⠞⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠶⢦⣤⡸⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠺⢿⠆⠀⠀⠀⠀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⢴⡾⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢺⡀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⣸⠇⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⣰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠃⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⢻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢀⣾⣿⠋⣿⠟⠛⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠛⣿⠛⠛⢿⣦⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⣿⣿⣷⣿⣄⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣶⣿⡀⠀⣸⣿⣧⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⣤⣤⣴⣶⣶⠚⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠙⠛⠶⣶⣤⣤⣤⣤⡄⠀⠀ ⠀⠀⠀⠈⠻⢦⣄⡉⠙⠻⠶⣤⣀⠀⠀⠘⣿⣿⣿⣿⣿⡿⢿⡿⠃⠀⠀⠀⢀⣤⣤⣶⣶⣶⣦⣤⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⣿⡿⠁⠀⢀⣠⡴⠞⠛⠉⢁⣤⠾⠋⠀⠀⠀ ⢤⣤⠴⠶⠶⠖⠛⠉⠀⠀⠀⠈⠙⠻⠶⣤⣄⣙⣛⣿⣿⣛⣋⣀⣠⣤⡴⠶⠿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠶⣤⣤⣀⣈⣛⣿⣿⣿⣟⣫⣤⡶⠞⠋⠁⠀⠀⠀⠈⠛⠓⠶⠶⠤⢤⣤ ⠈⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⡀⠙⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋ ⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⣉⡿⣏⡁⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣀⣤⡶⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣦⣬⣭⡿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⣿⣭⣴⡴⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠞⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⠦⣤⣤⣄⣀⣀⣀⣀⣠⣤⡤⠶⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⣠⡾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣲⣴⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡜⢡⣷⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠟⠀⠸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣤⣶⣾⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠏⠀⠀⠀⠘⣿⣿⠟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⠉⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀ ⠀⣾⠀⡀⢀⡤⠞⠋⠀⠳⠂⢳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠂⠀⢺⣿⣿⣿⣿⡀⠀⠀⠀⣀⣤⡶⠛⠁⠀⠀⠀⠀⠀⠀ ⢠⡇⢀⡷⡏⠀⠀⠀⠀⠀⠀⠈⢁⣙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣦⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣠⠎⠀⠙⠆⠀⢠⡤⢖⠚⠉⣹⡟⠢⣄⣹⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠟⠀⠀⠀⣠⠞⠛⣿⡿⠒⠒⠓⢿⡄⠀⠙⢧⡈⠻⣯⣗⠲⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠖⠻⢿⣍⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠀⠀⣠⣾⡥⡤⠴⣿⡇⠀⠀⠀⠀⢳⡀⠉⠉⠻⣆⠈⠛⢶⣄⠘⠉⡽⠋⠉⠀⠀⢀⣤⣶⣾⣿⣿⣥⠀⠀⠀⠀⠉⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⢰⠏⡟⡴⠛⠉⠉⢇⠸⣄⠀⠀⠀⠹⣔⢦⡀⠈⠳⢦⣀⡈⢉⡟⠀⠀⠀⠀⣴⣾⣿⣿⣿⡟⡟⣿⣷⣤⣤⣤⡾⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣶⣤⡀⠀⠀⠀ ⡇⠀⡏⢀⡇⡇⠀⠀⠀⠘⣆⠹⣶⣄⠀⠀⠈⠷⣝⢦⣀⠀⣰⡟⢸⠀⠀⠀⣠⣿⣿⣿⣿⡿⢻⡿⠀⠘⣆⠱⡄⢸⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣀ ⡇⢸⣿⡿⠷⠇⢿⡄⠀⠐⣜⢆⠹⣯⠻⠶⣤⡀⠘⢽⣺⡿⠃⠀⠀⠀⠀⢸⢻⣿⡿⢿⣧⡴⠊⠀⠀⠀⢻⠀⢹⣼⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢸⢸⠀⢰⡀⠈⢿⣆⠀⢹⣿⣧⡈⢷⣄⡈⠙⢳⡶⠋⠀⠀⠀⠀⠀⠀⠈⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡾⠿⠿⠿⠿⣿⡿⠿⠿⠿⠉ ⢸⢸⠸⡀⢸⣇⠀⠈⢿⣳⣀⢱⡝⢏⠘⠧⢝⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡾⡀⣧⢸⠘⡆⠀⠀⠻⣍⠳⢹⣌⢧⡈⠺⠏⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣷⡇⠘⡼⡄⠘⢦⡀⠀⠈⢷⣄⠻⣄⢽⡆⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣵⠀⠹⣧⠀⠀⠻⣄⠱⡄⠈⠩⣛⠷⣵⠟⠀⠀⠀⢀⡴⣖⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⡛⢹⡄⠀⠀⠀⠀⠀⣸⠀⣿⣿⣿⠁⢰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢯⢷⡀⠹⡞⡄⠀⠘⢦⡹⣦⣀⠈⣿⡁⠀⠀⢀⢀⣴⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠌⠁⢠⡇⠀⠀⠀⠀⠀⡇⠀⢿⣿⣿⣶⡀⠈⠛⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣆⠑⠀⠹⣹⣦⡀⠀⠙⠮⣝⢿⣿⣇⠀⠀⢘⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⡥⠀⠀⣰⠇⠀⠀⠀⠀⣸⣡⠴⣺⡟⠹⣸⡟⢧⡄⠀⠀⠉⠉⠙⠃⢤⣄⠀⠐⠀ ⠀⠀⠀⠹⡄⠀⠀⠹⣿⣳⣆⠀⠀⠈⢧⠻⡿⣷⣄⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⢠⡿⢸⣴⠟⠀⠀⣿⡇⠀⣻⣦⡀⠀⠀⠀⠀⠀⠀⠉⠘⠲ ⠀⠀⠀⠀⢳⡀⠀⠀⠈⢻⣿⣷⣤⡀⠸⢣⡙⢮⢿⡉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⢳⣼⠟⠀⢠⠇⠈⢷⣲⣿⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⡹⢿⣿⡏⠀⠀⢳⡈⠳⠽⣦⡀⠈⢳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⡖⢺⢿⣿⣧⣿⠟⠀⢠⠏⠀⠀⣠⣿⡧⠀⠀⢨⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠈⠋⢻⡇⠐⣦⡈⣿⣄⠀⠘⡌⠉⠙⣇⠈⠓⠢⠤⠤⣤⡴⠒⠛⠉⣿⡷⠤⣧⣎⣠⠼⠛⠓⠋⠛⡿⣄⣀⣼⣿⣿⠀⠀⢀⣿⣿⡿⠛⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⢹⠀⢷⣧⠘⣿⣦⡀⢹⡄⠀⠹⣧⡀⠀⢸⠘⣿⣷⢀⡤⣼⣿⣇⡤⠞⠋⠀⠀⠀⢀⣠⡆⠀⣽⡿⢻⣿⡏⠀⢀⣾⣿⣿⡇⠀⠈⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡿⣄⠀⠀⠀⠈⠀⠈⠻⢷⡹⣮⡝⢾⣿⣄⡀⢣⠳⣄⢸⡷⣿⣿⡜⣀⡬⠟⠉⠀⠀⠀⠀⠀⠀⠈⠁⣀⣼⠏⠀⣼⣇⡇⠀⣼⣿⣿⣿⡇⠀⠀⠈⢆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⢧⡀⠀⠀⠀⢠⠀⠻⣿⣦⡹⣆⠹⣿⡿⠛⠧⠀⡞⣀⣨⠿⢛⠕⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠟⠁⣫⠴⣾⣿⠏⠁⢰⣿⣿⠃⣿⡇⠀⠀⠀⠀⢢⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠙⢤⡀⠀⢕⢣⡀⠹⣿⡷⠌⢻⣿⠒⠒⠚⠛⠋⠁⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⣠⡞⠻⣅⢀⡞⠁⢰⣿⣿⠀⢀⣿⣿⠃⠀⣿⡇⠀⠀⠀⠀⠀⠳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠘⣿⣦⡈⠀⠙⣄⠈⠻⣄⠀⢙⡳⠤⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢈⣿⣒⣰⣿⡿⣿⠀⣸⣿⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⢹⣿⡟⠲⢤⡈⠢⡀⠘⠷⣄⠙⠶⢤⡉⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠤⣀⠀⠀⠈⠁⢀⡿⠧⣄⣸⣴⣿⣯⣿⣾⣿⢿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠀⠀⠀⠉⠓⢦⢤⣀⠈⠳⢤⣀⣉⣓⣂⣀⣀⣤⣴⣾⣿⣿⣁⣀⣀⣈⣉⣑⣦⣤⣬⣤⣤⣌⣻⣿⡏⠀⣿⠿⠿⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠓⠒⢤⡏⣰⢿⠓⠢⣄⣙⠯⣍⣹⣻⣷⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⢹⠛⢙⡇⠀⠀⠀⠉⣻⠃⠀⡟⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣀⣀⣸⡿⠟⠋⢉⣁⣐⠛⠛⠛⠿⠿⣿⣯⣉⣻⣤⣤⠀⠀⠈⠉⢙⣛⣛⣿⣿⣿⣿⣿⠟⠛⠛⢻⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠉⠛⣿⠟⢉⣤⣶⣾⣿⣿⣿⣿⣿⣷⣤⣤⣴⣶⣾⣯⣍⣉⣛⡟⢷⣾⡟⠛⠛⠛⣿⡟⠛⠛⠻⠛⠛⠛⠛⠘⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣴⣶⣾⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣶⣄⡒⣴⠿⣷⣤⣤⣤⣤⣤⣤⣄⠀⣀⣠⣄⣈⣁⣀⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⠻⣿⡿⢿⣿⣿⣿⣿⣿⣷⣤⣌⣙⡛⠿⠿⠿⡿⠀⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣟⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡏⢀⠈⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣀⣉⣈⠉⠉⠉⠉⠉⠉⠉⠽⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣴⡟⣽⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⠻⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣀⣀⣛⣛⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⣿⣿⠃⠀⠀⠀⠀⠈⠉⠉⠉⢛⡿⠿⣿⢿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡁⠁⠉⠉⠏⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣟⣛⡿⠷⠶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠙⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⣘⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣟⣿⢙⣿⠿⢿⣭⢛⡛⢻⠦⢽⣿⣛⣻⣿⠶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⡿⢡⡾⣭⣾⣯⠶⠾⠿⠛⠛⠒⠾⠿⠿⠿⣿⣷⣾⣭⣽⣟⣻⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢛⣵⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣷⣶⣮⣭⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠭ ⠀⠀⠀⠀⠀⢀⣴⠾⢽⣏⣾⠟⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠉⠙⠻⠿⣿⣶⣯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡏⣼⣶⣸⡇⣿⢰⣿⣿⠇⠀⠀⠀⠀⠀⠙⠛⢶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉ ⠀⠀⠀⠀⣸⡇⣿⢿⣽⡇⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣴⡏⢾⡛⣿⣿⡇⠉⠛⠓⠦⠄⠀⠀⢁⣀⣀⣀⣀⣀⠄⠀⠀⣀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣷⠙⢜⣿⡇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠙⠛⢉⡞⠀⠀⠀⠀⢢⡔⠒⠉⠉⠉⣩⣿⣿⣿⣿⡾⢿⣧⡀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡷⠐⠀⠀⠐⠒⠒⠒⠒ ⠀⠀⠀⠀⣿⠈⢧⠀⠙⣷⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⢀⠏⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⢰⡟⢿⣿⣿⠋⡇⠀⠈⠉⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠈⠳⡴⢿⡋⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠋⠁⠈⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⢿⠀⠀⠀⠙⢸⡇⡆⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠀⠀⠀⠘⣷⣄⣠⡴⠋⠀⠀⠀⠀⢀⠶⣺⣿⣿⣿⣿⣿⣿⢻⠏⠀⠈⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⢀⠀⠈⠻⠵⠂⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⠏⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠂⠀⠀⠀⠀⠀⠀⠀⢠⢻⣿⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⣠⢟⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⣤⣶⣶⣶⣤⣤⣶⣶⣴⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢠⣒⣠⣴⡶⠾⣻⣩⣽⣶⣄⠀⠀⠀⠀⠀⠀⠀⢂⣴⣿⣿⣿⣿⣿⣿⠟⠀⢀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⣿⣿⣿⠟⠀⠀⠀⢀⣠⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠉⠛⠛⠋⠉⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠚⣩⣶⡿⠙⢿⣯⠈⠁⠘⣿⣿⡿⣿⣭⢙⣶⡦⣤⣀⣀⣀⣀⣤⣤⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡀⣠⣿⡇⣸⡟⢀⡀⠀⠸⠋⢧⠀⢀⣿⣿⣷⣿⣿⣿⣃⣂⣀⣈⣉⣉⣉⣀⣀⣁⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣀⣀⣤⣄⣉⣭⣁⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⢀⣴⣯⣼⠿⢻⣶⣿⠇⢨⡁⠀⠀⠀⠀⢳⣾⣿⣿⣿⠿⠋⣿⡟⠿⠿⠿⠛⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠻⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⢀⣴⣻⠞⠙⠿⢢⣾⠏⢹⣿⠀⠀⠀⡀⠀⣰⣿⣿⣿⣿⡏⣤⣀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⢿⡟⠁⠀⠀⣰⣿⠃⠀⢺⣧⡀⢀⠀⠀⢠⣯⣿⣿⣿⣿⣽⣿⣿⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⡏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠓⢯⣀⠀⠀⣠⣿⡏⡀⠀⠈⠹⣿⣄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣾⣿⣧⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣶⣶⣶⣶⣶⣶⣶ ⠆⠀⠈⠙⠶⣿⣿⠁⠀⠀⠀⠈⠩⠻⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠛⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⢿⡿⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠹⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⢉⡷⣄⡀⣧⣄⣀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠀⠀⠀⠀⠀⣀⡜⠀⠙⣷⣌⣁⣴⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣦⣀⣤⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠸⠟⠓⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⡛⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣧⠠⠴⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣤⣀⡀⠀⠀⠀ ⡀⠀⢸⡯⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣆ ⠅⠀⢸⡅⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡆⠀⠈⡏⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠛⢻⣿⣿⣿⣿⡿⠛⣻⣿⣿⣿⣿⣿⣦⡀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⠀⠰⠇⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⣣⣾⣿⣿⣿⣿⣿⣿⠿⣿⡀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢽⣄⠀⠀⠈⣿⣿⣿⣿⣿⣿ ⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠁⢿⣄⣶⣶⣶⣶⣶⣆⣹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣦⡌⣷⣄⠙⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⡿⠿⣟⠛⠉⠉⠁⠈⠉⠙⠛⠉⠉⠁⠀⢀⣀⣦⣠⣿⣿⣿⣿⣿⣿⡽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⡇⠈⡿⣷⡄⠻⣿⣿⣿⣿ ⠀⠀⠀⠻⣿⣿⣿⣿⣿⠏⠑⠚⠋⢀⡀⣁⣶⢞⣇⣠⣾⠿⠟⠣⡄⠀⠀⠀⣤⠔⠋⠀⠘⣝⣟⣻⣿⣿⣟⣽⡇⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣾⣿⣿⣿⡇⠀⠀⠟⣿⣆⠈⢿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⡦⢤⡀⠀⣠⣾⣿⣷⣦⣭⣵⣤⣤⣴⠿⠿⣷⣶⡾⠁⠀⠀⠀⣦⣿⠀⠉⠁⠀⠀⢸⣿⣿⣄⣤⠔⠂⠀⠀⠉⠻⣿⣿⣿⣿⣿⣤⠀⠀⢰⢹⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣈⣿⣧⡀⠀⠀⣠⣿⡛⢯⡁⣀⣠⡤⢤⣤⣤⠀⠘⢿⣿⣿⣿⠄⠀⠀⢸⢾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠨⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡑⢦⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠙⠿⠿⠿⠋⠉⠀⠀⠀⠀⠈⠻⣷⠀⡸⣉⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣱⣾⣿⠙⣷⣿⣿⣿⣿⣿⣿⣿⣇⣈⣧⣤⣴⣲⣶⣦⣀⣀⣀⣀⣤⣶⢾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⡐⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠀⢿⣏⡏⢀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣍⢀⣿⣿⣿⣷⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠃⢠⠟⢀⢾⣿⠈⡗⢻⣿⡿⢿⣿⣿⣾⠟⠉⢹⡷⣾⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣼⡿⠁⠀⠋⡤⠛⠉⠡⢀⣯⡵⣿⣿⣤⠀⡼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣿⢣⡄⣿⡯⣿⡷⣾⠿⠿⠿⠿⠿⣯⣿⣿⣿⣿⣿⡇⢀⣤⠤⠘⣿⣖⠡⠄⠁⠀⠀⠀⠀⠠⠶⣠⡼⠃⢀⣼⣿⣿⣿⠟⣋⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡙ ⠀⠀⠀⢸⣿⣾⣷⣿⣿⣿⣿⣥⣤⣤⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⡏⠁⢠⠀⢿⢿⣷⡀⠀⠀⢖⣩⣤⢶⣋⠁⢀⣴⣿⣿⢿⣿⣧⣶⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡏⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡿⢿⣿⢇⠀⠸⣦⠈⢮⣿⣿⣶⣶⣋⡵⠟⠉⠁⣴⣿⣿⣿⣟⣹⣿⣿⢻⠿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀ ⠀⠀⠀⠀⠈⠁⠉⣽⣿⣿⣿⣤⡤⠦⢤⣴⣤⣼⣿⣻⣿⡟⢰⠸⠈⠃⠦⠿⠷⣤⣈⢻⣿⣿⣟⠀⠁⣠⣾⣿⣿⣿⣿⡇⣾⣿⣿⣿⣟⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⡟⠛⠓⠂⠙⠛⠛⢻⣿⣿⣿⠃⢸⡆⠰⡄⠹⣆⠀⠀⠉⠉⠉⠉⠀⠀⢠⣿⣿⣿⣿⣿⢸⣧⣿⣿⣿⢿⠧⡄⠀⣿⣿⣿⣿⣿⣿⡶⣗⣿⣷⣗⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠂⠈⣿⣿⣿⡀⠀⠀⠀⠀⢀⣸⣟⠃⣿⠀⢸⡟⠳⣄⡀⢿⣄⡀⠀⢀⡞⠀⠀⠐⣿⣿⣿⣿⣿⣿⢸⣷⠔⣴⡆⣬⣀⡄⠀⣿⣿⠿⠤⠤⢸⣇⣤⣿⣶⣿⣧⠀⠀ ⠀⠀⠀⡄⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⢹⣿⣵⢿⣰⣸⢿⣦⣄⣉⠉⠉⢻⡟⠻⠴⠚⠀⣀⣿⣿⣿⢹⣿⠻⢸⡿⡆⢺⢷⣾⡆⢀⣀⣿⣿⣿⢿⠶⣾⣴⢿⣿⣷⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣟⠸⣧⡹⣧⡀⠹⣿⣿⣿⣒⣾⣿⣶⣶⣶⣿⣿⣿⠋⢹⣟⠁⠀⢸⠷⣿⣿⠿⠿⠿⠧⠤⣿⣿⣟⣟⠀⣻⣿⣿⣿⢿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⢀⡼⠃⠘⢿⣆⣹⣿⣿⣿⣿⣿⣿⡿⠋⠉⠈⠙⣧⠀⠹⡄⠀⣸⠶⣿⣿⣶⣶⠶⢦⣤⣽⣿⣽⣿⣛⣿⡿⢡⣾⣟⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠞⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠋⠀⣠⠐⠂⢤⡈⢧⠀⢱⡄⢹⠒⣾⣿⣿⣶⣲⡶⠤⣛⣾⣤⣴⠀⣿⠀⠈⣠⡘⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⡿⠃⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡏⣠⠛⠀⠀⠀⠀⠙⢺⣆⣀⡇⢸⠀⣚⠉⠀⢰⠀⠐⠀⠿⣿⣿⢎⣠⣴⠿⣿⣿⣽⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠀⡏⣠⣧⠞⠉⠹⡄⠈⣿⣿⡷⠾⠿⠼⠭⠭⠭⠽⠿⢀⠀⠀⣶⡾⠀⠀⠀⠁⠟⠐⠋⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢠⡆⠀⠀⠀⣰⠏⣿⢿⠀⣧⠈⣧⠀⠀⠀⡇⢀⣿⣿⣷⣆⣆⠒⠀⠀⠖⠰⠆⠘⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣴⠃⠀⣽⠈⠳⣿⠀⢹⣰⣀⠀⣇⠸⣟⡟⢁⠈⠉⠉⠉⠉⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢠⠇⠀⢠⡾⠁⠀⠀⢹⠀⠀⢈⢷⢈⣿⣿⣶⣿⡄⣨⣿⣷⢠⠂⠀⠀⠙⠛⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠀⠀⣀⡀⠸⠀⠀⠈⣿⣠⣿⣿⣿⣿⣿⣿⡿⠘⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢀⣼⡋⠀⠀⢠⡏⠁⠈⣆⠀⠀⠰⠹⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢠⡞⠁⠉⢯⡉⠋⠀⠀⠀⠘⣆⠀⠀⠀⡏⠉⢹⡿⣿⡯⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⣸⠇⣴⣧⡀⠀⠀⠙⢦⠀⠀⡇⠀⠈⣿⠹⣇⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣐⣦⣤⣖⣾⠗⠋⠉⠉⠙⠲⣄⠀⢸⡀⠀⡇⠀⠀⢿⠀⢹⠦⣎⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣾⠗⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⢴⠁⠀⡇⡄⠀⡈⣷⣾⡆⣹⢹⣼⠀⢸⠟⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⡏⠘⠧⠖⠃⢸⣿⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣠⣄⣀⠀⢀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣬⣉⠓⢺⣤⣴⣶⣾⣯⡙⢿⠆⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣟⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢿⣻⢿⠋⠉⢿⣿⠿⠃⢻⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⠳⡀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣀⣤⣽⣿⣤⣤⣾⣷⣄⡀⢺⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢧⠈⢢⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣭⣾⣾⣻⣿⣷⣤⣄⢻⡏⢸⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠱⢄⠉⠲⣄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣿⠃⣧⠙⠚⠉⠛⠛⠋⢸⠘⣷⠚⠉⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣄⠈⠳⣄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⢻⠀⡿⠀⠀⠀⠀⠀⠀⣸⠀⣇⠀⠀⠀⠈⠑⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⠈⠳⣄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢠⠆⠻⠴⠧⣄⣀⣀⣀⣀⣀⡼⠶⠋⠀⠀⠀⠀⠀⠀⠹⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢄⠈⠳⣄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡟⠀⠀⠀⢀⣤⡿⠛⠛⢻⡟⠲⣄⢀⠀⠀⠀⠀⠀⠀⠀⠸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠓⣄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⠃⠀⠀⣴⣏⢸⠁⠀⠰⠾⠃⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠈⠻⢦⡀⣸⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢸⡆⠀⢰⡿⠃⢀⠀⠀⠀⠀⠀⠀⣼⣼⡀⠀⠀⠀⠀⠀⠀⢼⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⡀⠙⢦⡀⠈⠳⣄⠀⣀⣀⠀⢠⣤⣾⡟⡦⣄⠀⣧⠀⢸⡄⢦⠀⢧⠀⠀⠀⠀⢸⣿⣟⣿⣆⠀⠀⠀⠀⠀⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠙⢦⡀⢨⡿⠁⢈⡷⣼⣿⣿⣿⣿⣾⠷⣿⠀⠀⠳⡄⠳⣄⢳⡄⠀⠀⢸⣥⣍⣉⣿⠓⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣦⣤⠿⠋⠀⣰⡿⠛⣿⠛⠻⣽⣟⣅⡤⣽⡆⠀⠀⠈⠳⣌⠳⠙⠀⢀⡿⢿⣿⡏⡿⠀⠀⠀⢀⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣍⣁⣠⣴⣾⢿⡅⠀⢹⡄⠀⠈⠻⣿⢿⣿⣷⣀⠀⠀⠀⠀⢻⣦⣶⣿⣧⣄⠀⡹⠃⠀⠀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠘⣆⣠⠷⠒⢛⡷⣄⠀⠀⣸⡿⠳⠼⢯⠙⠒⠒⢺⣿⡟⠓⠼⣾⣮⠾⠥⠤⣤⡾⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡴⠋⠀⡼⠳⣾⠁⠀⠀⢀⡼⠓⠶⢤⣀⣹⣴⠆⢴⣩⡿⠤⠶⠞⠁⠀⢘⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⣞⣁⡴⢋⡷⢦⣀⢾⣄⣀⠀⠀⠀⠀⣈⣙⡚⠋⠀⢀⣀⡤⠔⠒⡞⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣪⡴⠋⠀⠀⢸⠀⠉⠛⠛⣿⢯⠉⠛⠛⢻⡏⠀⠀⠀⢰⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠧⣄⡀⠀⠀⠘⡆⠀⠀⠘⣇⠀⠀⢀⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣹⠆⠀⠀⢿⠀⠀⠀⣹⠀⢀⣸⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣍⠙⢧⡀⠀⠀⢸⡇⠀⢠⡇⣴⡯⢧⣭⣿⣦⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣭⣞⣓⣒⣓⣲⠶⠾⠿⠀⢸⣻⣿⣷⣾⣷⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⢀⣤⠶⠒⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠉⠉⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠉⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣰⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣤⡀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⢀⣾⣧⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢀⡞⠀⣄⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⢿⣷⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡞⣸⣭⣿⠯⠟⠛⢻⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⠱⢿⢻⡷⡦⠘⡇⠀⠀⠀⢀⣾⣿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⣠⣄⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣾⣾⠞⠁⠀⣇⠀⠀⢠⠞⢡⡏⠀⢀⣤⠾⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣦⠤⠴⠶⠖⠛⢿⠉⠀⠀⣀⣴⣾⣿⡋⣨⠷⣶⣯⣷ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⢸⠋⠁⠀⠀⠀⢹⢀⡴⠉⠀⢸⠶⠚⠉⠀⠀⣄⣿⣿⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⢿⣆⠀⠀⠀⠀⠈⣷⡀⠀⠘⣻⠽⢿⡫⡦⢗⡩⣾⢿ ⣓⣄⠀⠀⠀⠀⠀⠀⢰⡞⠋⠀⠀⠀⠀⠠⠤⠤⣤⣸⡋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣋⡿⣧⣼⡿⠁⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣀⣀⣬⠿⠂⢸⡿⣺⠗⣋⣞⢍⡯⢛⣁ ⡠⢝⣓⠒⠳⣤⣾⣲⣜⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠟⠛⣩⠟⠁⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣠⣤⣤⡞⠁⠂⣼⡻⣅⣥⡺⣛⠅ ⡮⠛⠥⠶⣻⡿⢫⡽⡏⢨⡇⠀⠀⠀⠀⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⣀⣀⡴⢻⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⣿⣷⣷⣿⣽⣿⣿⣿⣿⠟⠉⠀⠀⣐⡿⣻⠝⣫⣺⡵⡮ ⠞⢀⡴⢟⢱⠞⠉⣱⣉⢻⣄⡀⠀⠀⠀⠀⠀⠉⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⣠⢴⡿⢻⠂⣽⣿⣡⣭⠎ ⢀⣉⠸⠲⣤⣢⣷⣿⣀⡸⡅⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣴⣶⣾⣿⣿⣿⣿⣆⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⣟⣿⠃⠈⢉⡈⠁⢀⣴⣅ ⠋⠉⠓⢦⡌⠙⢟⣯⣚⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠙⡲⣖⣠⡤⣖⣭⣗⡀⠘⢫⣝⠉⠁⣀⣰⡿⣽⣿⣉⣀⠙ ⣼⣳⣀⣰⣧⡀⠀⣿⣍⠠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢩⠗⠈⣠⣄⣈⠁⠠⣤⣿⣯⡍⢷⣿⣿⣛⠡⢙⣿⣿⣯ ⣼⣿⡋⠀⠀⠛⡆⠀⠀⠀⠳⣤⡀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢀⣰⣿⡿⡿⣿⣶⣾⡿⣫⣵⣿⣾⣿⣿⣿⡛⢛⡋⢿⠛ ⣶⣿⣪⣠⢶⡀⢙⡳⠛⢇⠀⢰⡉⢉⠉⠉⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣷⠿⣿⣿⣿⣿⢿⣟⡿⡿⢿⣧⣼⣗⣵⢾⣿⣿ ⠁⣿⣿⠞⣵⠆⢔⡟⣁⣸⣀⣈⠛⠛⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣴⡿⣻⣾⣿⠿⣿⣽⣿⣻⣿⡷⠀⢹⣾⡻⣿⣯⣭⣟ ⣏⠀⠊⠈⠀⠘⣿⣛⣭⢄⣤⡎⠁⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣿⣿⣿⡑⠋⢜⡿⣞⣿⢰⣿⣻⡿⣏⣥⠞⡷⠤⢂⡄⠀⣼⣟⢛