Surprised Pikachu Emojis & Text

⠐⣶⣾⣭⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠄⠀⠀⠀⠀⠀ ⠀⠹⣿⣿⣧⠈⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⢻⣿⣿⣿⢇⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣿⡄⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⢰⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢷⣀⠀⠀⠀⠀⠀⠹⣦⡀⠀⢀⣀⣀⣀⣰⣶⣦⣀⣀⡀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⢀⣾⡻⠋⠀⠀⡀⣀⣄⣤⡤⣦ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠈⣷⠶⠛⠉⠉⠁⠀⠀⠈⠉⠉⠛⠿⡿⠟⠁⠀⠀⠀⠀⢀⣠⣶⡿⠋⣀⣤⠼⠗⠛⠉⠁⠀⠀⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⢦⣀⣰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⣶⣟⣣⡽⡿⠟⠋⠀⠀⠀⠀⠀⠀⢀⣾⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⡷⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣯⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣴⣿⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡻⣿⣷⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⣿⡿⢿⣿⠃⠀⠀⠀⣀⣀⠀⠀⠀⣿⣿⣿⣿⠇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡤⣤⡈⠉⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠛⠃⢀⣠⣈⣧⠀⠀⣤⣴⡶⠿⠿⠛⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⣦⠀⠀⠀⠳⠤⠴⠞⠛⠦⣤⠾⠃⠀⠀⣼⠋⠀⠈⣿⠀⠀⠈⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠄⠀⣰⡟⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢒⣶⣿⢻⣷⣤⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠙⠳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠋⢸⡷⠞⠋⠀⣀⣠⣶⠞⠿⠙⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠉⠓⠭⣷⣦⣤⣤⡴⠦⣺⠛⠉⠀⠀⠀⠈⣷⠀⢶⣿⣟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠘⣷⣀⣨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣄⣀⣠⡟⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢀⡇⠀⠘⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣛⣿⣁⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢸⣱⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⠻⣤⣉⠷⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣿⠰⠠⡏⠀⠀⠀⠀⠀⠀⣰⠇⠀⢀⡴⢛⣱⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⢷⡀⠈⠳⣄⠀⠹⣦⠀⠀⠀⠀⠀⠀⡟⠀⠀⣷⠀⠀⠀⠀⠀⣰⠏⠀⢀⣴⠚⠉⣸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡀⠈⠃⣦⠘⢷⡀⠀⠀⠀⢀⣧⣤⣤⣿⠀⠀⠀⢀⣼⠃⣀⠒⠛⢀⣤⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣛⣦⠴⢿⢶⣿⣿⡤⢴⣶⢿⡛⠁⠙⣿⣶⣤⣤⣾⣗⢶⣯⣤⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠊⠉⠉⠀⠀⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡠⠼⠴⠒⠒⠒⠒⠦⠤⠤⣄⣀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠔⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡤⠤⢴ ⠀⠀⠀⠀⠀⠀⣸⠁⣾⣿⣀⣽⡆⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⢿⣦⠀⠀⠀⢸⡀⠀⠀⢀⣠⠤⠔⠒⠋⠉⠉⠀⠀⠀⠀⢀⡞ ⠀⠀⠀⠀⠀⢀⡏⠀⠹⠿⠿⠟⠁⠀⠰⠦⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⢘⡧⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀ ⠀⠀⠀⠀⠀⣼⠦⣄⠀⠀⢠⣀⣀⣴⠟⠶⣄⡀⠀⠀⡀⠀⠉⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀ ⠀⠀⠀⠀⢰⡇⠀⠈⡇⠀⠀⠸⡾⠁⠀⠀⠀⠉⠉⡏⠀⠀⠀⣠⠖⠉⠓⢤⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⢧⣀⡼⠃⠀⠀⠀⢧⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣧⠀⠀⠀⣸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢠⠏⠀⠀⠀⠀⠈⠳⠤⠖⠃⡟⠀⠀⠀⢾⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠈⠦⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠙⢦⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡇⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠸⡇⠈⢳⡀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⣀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣷⠴⠚⠁⠀⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⢷⡆⠀⣠⡴⠧⣄⣇⠀⠀⠀⠀⠀⠀⠀⢲⠀⡟⠀⠀⠀⠀⠀⠀⠀⢀⡇⣠⣽⢦⣄⢀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣼⣽⡞⠁⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠈⣷⠃⠀⠀⠀⠀⠀⠀⠀⣼⠉⠁⠀⠀⢠⢟⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠉⠁⢳⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠏⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⡆⠀⠈⡇⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⡀⠀⠙⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢀⡄⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⡀⣰⣀⣀⣀⠀⠀⠀⠘⣦⣀⠀⠀⠀⡇⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⢸⡇⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠀⠀⠈⠉⠉⠉⠙⠻⠿⠾⠾⠻⠓⢦⠦⡶⡶⠿⠛⠛⠓⠒⠒⠚⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡀⠈⠀⠀⠀⡀⠀⠀⠀⠈⠙⠿⣶⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀ ⡀⠐⠀⠁⠂⠈⠄⠐⠈⠈⠐⠀⠀⠀⠈⠛⣿⣯⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⡜⢤⠐⠈⠀⠁⠈⢀⠐⢀⠁⠂⠐⠀⠛⠛⠛⠛⠛⠛⠛⠿⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠻⣷⣮⣱⡄⣌⡤⠒⠈⠀⠠⠐⢀⠂⠄⠀⠠⠀⡀⠀⠄⡀⢀⡀⠉⠙⠿⣷⣤⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⣠⣔⣿⠿⠛⠁⠀⠀⢀⠂⠡⢀⠀⠄⠠⠈⠄⠠⠀⡐⠀⢀⠀⠈⠁⠒⣆⠀⠙⠿⣮⣻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⣿⠟⠁⠀⡀⠄⠡⠈⡀⠐⠀⢂⠐⠈⢀⠂⠌⠀⢁⠠⠈⡀⠐⠠⢐⣿⣿⣿⣶⣄⠈⠙⠿⣯⣟⣳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠄⠂⢀⠐⠀⡁⠀⠠⠈⡀⠄⠐⠀⠀⠂⠈⠄⠀⠂⢀⠂⠁⠀⣿⣿⣿⣿⣿⣦⠀⣀⣀⣉⡛⢷⣯⣻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠂⢈⠀⠠⠁⡀⢀⠁⠐⠀⠐⠀⡈⠐⠠⠁⠂⢈⠐⠀⡀⠂⠀⢻⣿⣿⣿⣿⣿⣧⡯⡜⣭⢛⣦⡘⢿⣞⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠐⠠⠀⠁⠄⠐⡀⠠⢈⠐⠈⢀⠀⠈⠄⠂⠐⠀⠀⠒⠀⢂⠀⡀⣌⠛⠿⠿⠛⠸⣷⡙⢦⣋⡖⣿⣬⣿⣾⣧⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠌⣀⢠⣀⣆⡀⢀⠂⡀⢂⠈⢀⠠⠁⠀⣐⣬⣶⣷⠀⠀⢂⠀⠀⢻⣷⠂⢀⠠⠀⠹⣿⣲⣝⣾⣿⠿⣛⢛⡛⣛⠻⣷⣤⣤⣀⠀⠀ ⠀⠀⢾⣽⣿⣿⣿⣿⣦⡐⠀⠄⢈⠀⡀⠀⠐⠛⠿⢿⠇⠀⢀⠀⢀⣤⡿⠏⠀⠀⠐⣀⣢⣽⣷⣿⣿⢇⣳⣼⡶⣷⣮⣵⣉⠏⣿⣯⠀⠀ ⠀⢨⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠀⠀⠄⡁⢂⠀⠀⣠⣴⡶⡶⠾⠟⠋⠁⠀⢀⣤⣷⣿⠿⢛⣿⣿⣟⣾⣻⢾⣽⣷⣯⣿⡽⣿⡸⣿⡆⠀ ⠀⠒⣿⣿⣿⣿⣿⣿⣿⡿⠀⢻⣧⣄⠀⢀⢀⣠⣾⠛⠀⠀⡀⠀⢀⢠⣠⣾⡿⢛⠍⣰⣬⣶⢻⣿⣞⣷⣻⣿⣿⣿⣿⣿⣿⣟⡗⣿⣇⠀ ⠀⠈⠻⢿⣿⣿⣿⣿⠟⠁⢀⠀⠘⠻⠿⡿⠛⠋⠀⠀⠀⠁⣠⣴⣾⠿⣛⣵⣬⣷⣿⡿⣯⢿⡘⣿⣟⡾⣿⣿⣿⣿⣿⣿⣿⣿⣯⢽⣿⡀ ⢀⣠⣤⣤⣬⣉⡍⠀⠀⠂⠜⢀⣾⣾⣄⠀⠀⠠⠐⣈⣴⣿⢿⣯⣷⣿⣿⡿⣟⣯⣷⣟⣯⣿⣵⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣟⢾⣿⡇ ⣎⡓⠀⠈⢩⡛⠿⣷⣄⠀⠈⢰⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⢿⣿⢻⣟⡟⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣻⣞⣿⠃ ⣜⡹⣒⢖⡫⣜⡳⣜⢻⣆⡈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣟⣿⡿⣽⣾⢿⣞⣿⣾⡇⣿⣯⣟⡿⣿⣿⣿⣿⣿⢯⣷⢯⣿⣷ ⣮⠱⡭⣎⠵⣪⠕⣮⡙⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣿⣯⣿⢿⣽⣯⢿⣞⣿⣣⣿⣿⢾⣽⢯⡿⣽⣻⣞⡿⣽⢯⣿⡿ ⣷⢋⢶⡩⢞⡥⣛⠴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⣾⡿⣷⣿⣯⣿⣷⣿⣿⣿⡿⣿⢿⣿⣻⢾⣻⣽⣿⣿⣿⡽⣯⣿⣿⠀ ⣟⢯⣶⣙⣎⠶⣩⣞⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣽⣳⣯⢿⣽⣯⣿⣿⣯⣷⣻⣿⣿⣾⣟⣿⡇⠀⠀ ⣿⢞⡶⣏⠾⡿⢟⠫⡔⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣯⣿⣿⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣻⢾⣽⣻⣞⣿⠂⠀⠀ ⣿⣿⣶⣮⣷⣼⠾⡱⢌⠳⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣯⣉⠉⢻⣯⣿⣿⣿⣿⣿⣿⣿⣯⣿⣾⣷⣿⠏⠀⠀⠀ ⠉⠙⣿⣿⡿⢃⢎⡱⢊⡕⢢⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢙⣿⣿⣿⣿⣧⢃⡄⠘⣿⣽⡄⠀⠉⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀ ⢠⣾⣿⡟⠁⣘⢎⡱⠣⡜⣡⠚⣼⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠠⠀⣿⣿⣿⢾⣿⠰⡘⡄⠘⢷⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⣿⠏⠀⣌⢣⠒⣌⠳⡘⢤⠓⣬⣿⣿⣿⣿⡿⠁⠀⡀⠀⠐⠈⠀⠠⢽⣿⣿⡿⢣⠱⡱⣘⢃⠈⣿⣏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠸⣷⣦⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠀⠀⠀ ⠀⠙⣿⡄⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⣿⡿⠁⠀⠀⠀ ⠀⠀⠈⠣⡀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⣰⠟⠀⠀⠀⣀⣀ ⠀⠀⠀⠀⠈⠢⣄⠀⡈⠒⠊⠉⠁⠀⠈⠉⠑⠚⠀⠀⣀⠔⢊⣠⠤⠒⠊⠉⠀⡜ ⠀⠀⠀⠀⠀⠀⠀⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡔⠊⠁⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⡇⢠⡤⢄⠀⠀⠀⠀⠀⡠⢤⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⢀⠇⠹⠿⠟⠀⠀⠤⠀⠀⠻⠿⠟⠀⣇⠀⠀⡀⠠⠄⠒⠊⠁⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠰⠤⠖⠦⠴⠀⢀⣶⣿⣿⠀⠙⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠛⢄⠀⠀⠱⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠈⠓⠦⠀⣀⣀⣀⠀⡠⠴⠊⠹⡞⣁⠤⠒⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⡌⠉⠉⡤⠀⠀⠀⠀⢻⠿⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⠁⡀⠀⠀⠀⠀⢸⠀⢰⠃⠀⠀⠀⢠⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢶⣗⠧⡀⢳⠀⠀⠀⠀⢸⣀⣸⠀⠀⠀⢀⡜⠀⣸⢤⣶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣦⣈⣧⡀⠀⠀⢸⣿⣿⠀⠀⢀⣼⡀⣨⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⠿⠿⠓⠄⠤⠘⠉⠙⠤⢀⠾⠿⣿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣤⡤⠤⠤⠤⢀⣀⡤⠒⠂⠈⠉⠁⠒⢡⡀⡔⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠛⠿⢦⡀⠀⠀⠀⢀⢄⡀⠀⠀⠀⢠⣲⡙⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠖⠀⠸⠾⠃⠀⠠⠄⠈⠋⠁⡵⣠⠤⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⣐⡀⠔⠉⢢⠀⠢⠔⠳⡆⠁⠀⢄⠇⢀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⡀⠈⠑⢌⠒⠊⠀⠀⠁⠈⠀⠀⡠⠊⠀⡘⠀⠀⠀⠀⠀ ⡖⠒⠢⠤⠤⠤⠤⢵⡀⠀⠀⠑⠀⠀⠀⠂⠒⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠠⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⣀⡀⠀⣠⡣⡆⡘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠉⠉⠁⠀⡆⠀⣩⠠⡗⡇⣸⠟⢣⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠓⠉⢸⡰⣧⠽⡈⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⠴⢜⣀⠀⠤⢄⣀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠆⠀⠠⡤⠄⠤⣦⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠛⠻⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠈⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠘⡇⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⢤⡿⠉⠙⣦⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⢻⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠁⠀⠁⠀⠀⢸⠀⠀⢰⣿⡿⢟⡿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣆⠀⠀⠀⠀⣿⠀⠀⡟⠋⠀⢸⠃⢀⣠⠴⢺⡇⢀⠔⠋⢹⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠶⣄⡘⣿⠀⢸⡇⠀⢀⡿⠚⠉⠀⠀⣼⡷⠁⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⣸⡇⠀⣼⠗⣺⡉⠉⠙⠻⢤⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣇⣄⠀⠘⠉⠙⠂⢀⡂⠉⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠈⣻⣄⡀⠀ ⠀⠀⡀⠀⠀⠀⢀⡜⠁⠀⣴⠋⠘⣿⣿⡆⢸⣿⣿⣿⡆⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⢹⡆ ⠀⠘⠿⢭⣽⣶⠘⠢⡀⠀⣿⠀⠀⠘⡿⠃⠈⣿⣿⣿⠇⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣀⡼⠃ ⠀⠀⣤⣖⣻⡿⠀⠀⠈⠢⣿⠀⠀⠀⣷⠀⠀⢻⣿⡟⠀⠀⣰⠷⠶⠒⢶⡄⠀⠀⠀⠀⠛⠛⠛⠋⠉⠀⠀ ⠀⠀⠉⠉⠁⠀⠀⠀⠀⢀⠿⡄⠀⠀⣹⠀⠀⠀⠉⠀⣠⠔⠁⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣄⣠⠖⠒⣦⠀⢴⣃⠀⢷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⠀⠋⠀⠀⢸⡇⠀⠈⠙⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣀⣀⠤⣶⠀⠀⢰⣿⣽⠭⠿⠀⠀⠀⠀ ⢿⡀⠀⠀⠀⢀⡾⠃⠀⢠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡿⠀⠀⠈⠻⣭⣲⡄⠀⠀⠀⠀ ⠈⠳⣄⡀⠀⡾⠁⠀⠀⠈⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⡼⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⣀⣀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠘⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠁⠀⠀⠀⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⡀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂⠀⠀⠉⠉⠉⠉⡠⠊⠀⠀⠀⠀⠀⢰⣿⡟⠁⠀ ⠠⢄⣀⠀⠐⠒⠚⠉⠉⠉⠀⠉⠀⠀⠱⡄⠀⠀⠀⠀⠀⠣⠔⠒⠊⠉⠉⠉⠉⠉⠁⠒⠠⢄⡀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀ ⠀⠀⠈⠑⠲⢤⡀⠀⠀⠀⢀⣀⣀⣀⣀⣈⣢⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠓⠢ ⠀⠀⠀⠀⠀⠀⠈⠙⠯⣉⠉⠁⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⢀⡇⠀⢀⣀⣴⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠈⣿⣿⣄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠚⢻⣶⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠛⢦⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣾⣿⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⣠⠖⠓⢦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠴⢶⣶⣦⡤⣀⡀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣿⠀⠀⠀⠀⠑⠀⠒⠀⠉⠑⠤⠤⠄⠀⠀⠀⢠⠃⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠑⠲⣏⠉⠒⣤⠀⢀⡜⠈⣧⣄⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⠃⢀⠞⠀⠀⡼⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⠀⢀⠏⢀⠎⠀⠀⡜⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⠀⠀⣾⡀⠙⢄⣀⡜⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠓⠦⢤⣀⠈⠁⠲⡾⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡇⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠉⢸⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠚⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣶⣶⠿⠛⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⠛⠿⡒⢒⣶⠶⠶⢛⠉⠉⣉⣉⣉⣉⣉⣻⣟⣦⣄⣀⠐⠌⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⡳⠂⠀⠀⣠⣾⡷⠶⠒⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⠀⠀⢀⣀⣀⣠⣤⡴⠶⠛⠉⠉⠁⠀⠀⠉⠉⠉⠙⠛⠲⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣧⠀⠀⠀⠀⠀⣿⠀⠀⢀⣾⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣆⠀⠀⢀⡾⠋⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⣦⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣷⣦⣾⠡⠤⣀⠀⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣾⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀ ⢸⣿⣿⣿⣿⣿⠿⠟⠉⣿⠀⠀⠈⢣⠀⠈⠁⠀⠀⠀⠀⠀⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇ ⠈⠋⠉⠉⠁⠀⠀⠀⠀⠈⢷⡀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡞⠀⠀⠀⣠⣀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⣠⠤⠒⠒⠢⢄⠀⠀⠀⠀⣼⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣴⠋⠀⠉⠣⣄⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⢣⠀⣠⡾⠁⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢀⣼⠾⣯⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠤⠔⠚⠉⠀⠀⠙⣧⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠘⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠒⠚⣻⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠒⠒⠒⠒⢤⣤⠴⠚⠉⠀⡸⠁⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⣠⠖⠋⠀⠀⠀⠀⢀⡧⠞⠣⠤⣀⡀⠀⠀⠀⠀ ⢀⣤⠔⠒⠚⣏⠉⠉⠉⠉⠉⠉⠉⠒⠒⠲⠤⠒⠋⠉⠉⠉⠉⠉⠒⠒⠻⢴⠋⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠉⠑⠲⢤⡀ ⠈⠙⠒⠤⢄⣘⣦⡀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼ ⠀⠀⠀⠀⠀⠀⠈⢉⣿⣗⡒⠒⠒⡾⠁⣠⣶⠒⡆⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀ ⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠙⢦⣀⠇⠀⠻⣼⡿⠁⠀⠀⢠⡄⠀⠀⠸⣷⣼⣷⠀⢸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣏⠀⠀⠀⠀⡿⠖⠲⣄⠀⠀⣤⡀⢀⣤⣀⠀⠀⢀⠈⠋⠁⠀⢸⣿⡉⠓⠦⣀⡀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡇⠀⠀⣸⠀⠀⢸⣯⠟⠛⠛⢿⣿⠋⠀⢰⠟⠉⠹⡇⢷⠀⠀⠀⠉⠓⠦⣄⣠⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠹⡦⠴⠋⠀⠀⠀⢹⡄⠀⢀⡼⠁⠀⠀⣇⠀⠀⢠⡇⣀⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠹⠤⠋⠀⠀⠀⠀⠈⠓⡶⠋⠙⠳⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠑⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⣤⠤⠴⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡆⢀⣠⠤⠒⠒⠒⠂⠀⠀⠐⠒⠒⠒⠒⠲⢦⡀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣷⣮⣿⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠈⠁⠲⢖⡖⡀⠀⠀merry Christmas:3 ⠀⠀⠀⡠⠴⣏⠀⢀⣠⣤⢤⡄⠀⠀⠀⡀⠀⠀⡀⢷⡈⢄⠀ ⠀⠀⢠⣽⠋⢸⢰⠋⠀⡆⠑⢻⠀⠀⢎⠀⠦⡀⠈⡄⢩⠳⣧ ⠀⢀⣺⠁⠀⢸⠘⠲⠤⠤⠐⠁⠄⠒⠢⢁⣂⡐⠊⠀⡄⠀⢸ ⠀⣸⠇⠀⠀⢸⠀⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠜⠀⠀⢸ ⠀⣿⠀⠀⠀⠀⡗⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢀⣼ ⠀⢻⡀⠀⠀⢀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⢃⡃ ⠀⠈⠳⣦⠀⠈⠀⠉⠓⠦⠤⣄⣀⣀⣀⣀⣀⡶⠛⠉⠀⠩⡇ ⡀⣀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢘⡇ ⠑⢄⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⠀⠀⠑⠢⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀ ⠀⠀⠀⢀⢖⠩⠓⢦⣤⣀⣀⡤⣀⣀⣀⣀⡠⠤⠖⠛⢦⡀⠀ ⠀⠀⠀⠸⢥⣤⣄⣀⣠⡄⡼⡆⠀⠀⣷⣀⡰⣆⠀⡗⠶⠳⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠀⠀⠀

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿ ⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠙⠿⠿⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿

⡏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿ ⣿⣧⡀⠀⠀⠀⠀⠙⠿⠿⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⣷⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿ ⣿⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿⣿⣿ ⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣿⣿⣿ ⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠛⠛⠉⠉⠛⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠃⠀⠀⣠⡖⢠⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⣷⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡟⠀⠀⢠⢿⣷⣶⡇⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠀⠀⢸⠸⠻⡿⠇⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⢀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣄⡀⣿⠀⠀⠀⠁⠀⠉⠁⢀⣀⣀⣀⣄⣤⠴⢶⣶⣿⡏⠀⣸⣃⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⠉⠛⠛⠦⠤⣄⡀⢿⡋⠉⠉⠁⠀⠀⠉⠁⠀⠀⢈⡟⢀⡼⠛⠉⠉⠉⠉⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣀⠀⣀⣠⠤⠖⠒⠒⢛⣛⣻⣷⡖⣀⡀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡋⢉⣠⠴⠖⠚⠉⠉⠁⠉⠻⣍⣹⣶⣦⣀⡀⠀⠀⣸⣷⠶⠶⠶⠶⢦⣤⣴⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣀⠀⠀⠀⠀⣀⣠⠤⠖⠛⠙⢿⣄⠈⠉⠙⠻⢿⣇⠀⠀⠀⠀⢠⠟⠀⠘⠛⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⣠⣏⡉⠉⠉⠉⢉⡿⠟⠒⠒⠤⣄⡀⠀⠉⢦⡀⠀⠀⠀⠉⢧⠀⠀⠀⠋⠀⠀⠀⠀⠀⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢷⣶⣿⣿⣭⣭⡉⠑⢦⣴⠃⠀⠀⠀⠀⠀⠀⣙⣦⣠⣄⡹⢦⣀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣆⠘⡇⠀⠀⠀⠀⣶⠶⠞⠉⠛⠋⠘⣇⠀⠈⠳⢦⡀⠘⡆⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠁⠀⠀⠀⠉⠙⠳⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⣧⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠙⠳⡿⣶⣶⣤⣀⣀⣠⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⡘⢧⡀⠀⠀⢿⠀⠀⠀⠀⠀⠀⣼⠀⢀⣠⣤⣄⡼⠁⣼⠀⠀⠉⠉⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣤⡉⠓⠦⠼⣧⡀⠀⠀⠀⣰⡇⢠⠋⠀⠀⠀⠙⠶⣯⣀⠀⠀⠀⣿⠀⠀⠀⠀⡴⠚⠛⠳⣆⠀⠀⠀⠀⠸⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣽⣶⣶⣾⣉⣉⠙⣄⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⡆⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⢰⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠶⢤⡤⠴⠛⠁⠀⠀⠀⢠⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣤⣤⣀⣀⣀⣀⣠⣤⡴⠾⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡵⣇⣠⡴⣞⢯⡻⣜⢧⡻⣜⣧⣻⣼⣧⢿⡾⢷⡿⣾⢷⡿⢮⡷⣮⣗⣯⣞⣵⣺⡽⣷⣿⣵⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣯⡿⢾⣧⢿⡼⣷⣟⣯⠷⠟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠗⠻⠾⠵⠛⠛⢿⣿⣿⣷⣮⣖⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣾⣿⣿⣿⣿⣧⠙⠳⠾⠓⢻⠟⠛⢻⣷⢾⣿⣟⣹⣿⣿⣿⣿⡿⠟⠛⣽⣯⡉⠙⢢⠀⠀⠀⠀⣿⣿⣿⣿⣿⣮⣗⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⠇⠀⢀⡎⢻⣏⠀⢀⣿⣿⣿⡿⠋⠀⠀⣼⣸⢹⡇⠀⠀⣇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣾⣔⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠻⣷⠀⠀⢸⠀⠀⢸⡇⣸⢸⠀⢸⣿⡿⠋⠀⠀⠀⠀⢾⣽⣸⡇⠀⠀⢾⠀⠀⣾⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⠀⠀⢸⠀⠀⠸⣿⡿⢸⠀⠾⠋⠀⡀⠀⠀⠀⠀⢯⢻⣿⠇⠀⠀⣏⠀⠀⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠿⠿⠿⠟⡿⣻⣿⣿⣿⣇⢸⡄⠀⠸⣄⣀⣀⣻⣇⣸⠀⠀⠀⢸⠇⠀⠀⠀⠀⠹⠬⠯⠤⠤⣴⠃⠀⢸⠁⢀⣿⣿⣿⡿⣿⣿⡓⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣻⡿⣿⣿⣿⣿⣶⡇⠀⠀⠰⢿⡷⠆⠀⠀⠀⠀⠀⣯⠄⠀⠀⠀⠀⠀⠰⣺⠗⠋⠁⠀⠀⢸⣠⣾⣿⣿⡿⣟⡋⠉⠁⢷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⣾⣿⠿⠋⠁⠀⠀⠀⠉⠐⠢⠭⣳⢴⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⣛⣼⠀⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠖⠒⠚⠉⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⢀⣠⡤⠤⠤⠤⠤⠒⠒⠒⠛⠂⠉⠒⠔⣦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠐⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⢉⣿⣿⣿⠟⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡼⠀⠀⠈⢆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⠀⠀⢸⣿⡿⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⣾⠟⠡⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠄⢼⠀⠀⢀⣀⣤⠤⠤⠤⣤⣀⣀⡤⠋⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⠚⠉⠁⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡠⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⢷⡀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⣸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡹⣦⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠚⠀⠀⠀⠀⠀⠀⠀⠈⠁⠞⡹⢾⣧⣠⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠮⡍⡏⠀⣿⣽⡄⠀⠀⠀⠀⢀⠀⣠⢶⣿⣿⣧⠀⠀⢠⠞⠀⠀⢠⡏⣳⣯⠚⠉⠯⢽⣷⢤⡀⠀⠀⠀⠀⠀⢠⠴⠚⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀ ⢸⡉⢆⣀⡏⡰⣦⣇⡟⣦⠹⠿⠿⠀⠀⠀⠀⠘⠞⠹⢾⣿⣿⢟⣠⣒⣿⠿⣭⣲⣼⡿⠘⠞⠠⠀⠁⠀⢳⡄⠉⠳⢦⡀⠀⠀⠈⠳⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠢⠇⣴⣆⣺⡵⢹⣿⣉⢿⣇⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⢇⠀⣇⠈⠿⠒⢯⠀⠻⣃⠇⠀⠀⠀⠀⠀⣜⣿⡄⠀⠀⠈⠓⢦⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣑⢫⡵⠀⠈⠈⠳⣟⠀⠀⠙⠒⠒⠢⠤⠞⠁⠀⠀⠈⠀⠙⠣⠽⠶⠋⠀⠀⠚⠋⠀⠀⠀⠀⣼⣿⣿⣷⡀⠀⠀⢀⠜⠁⠀⠀⠀⠀⣹⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢪⠳⠀⠀⠀⠀⢈⠟⠂⣢⣄⡀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⢣⢠⡴⠋⠀⠀⠀⣠⠔⠋⡄⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⡴⠋⠁⠹⠷⣆⠀⠀⠀⢰⠏⠇⠈⠙⠲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⣠⠖⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠁⢀⠀⡹⠄⠀⠀⢸⡄⠈⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣀⠀⠈⠷⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⠀⣨⡷⢻⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣉⣾⣳⣬⣺⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⠟⣇⠀⠁⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠔⢊⠵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠋⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣗⡢⠤⠄⣈⣙⣲⣤⣀⡀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠏⣨⠎⣳⠤⠚⠉⠀⠀⠀⠉⠙⠓⠒⠒⠒⡒⠛⠲⢤⣀⣀⣀⣀⠤⠤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠉⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣓⡍⠉⡒⡾⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠑⠋⠙⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠏⠁⢀⣀⣘⡛⠛⠛⠛⠛⡛⠛⠛⠛⣛⣛⣛⠛⠛⠛⣋⣛⣿⣿⠟⠻⠛⠋⠛⠛⢉⣉⣉⣉⣉⡁⠀⠀⡉⠛⣛⣛⡛⠛⠛⠛⠛⠛⢛⠛⠛⣛⠛⠟⠛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠛⠛⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⠛⠋⠉⣉⣛⣛⠛⠿⣿⣿⣿⣿ ⣿⠟⢁⣐⣛⣛⣋⣀⣐⣛⣛⣋⣀⣀⣐⡛⠛⠋⢁⡀⠲⠟⠛⠻⠟⠁⠀⠀⠉⠀⣤⣾⣿⣿⣿⡿⠛⠀⠀⠀⠈⠙⠟⠉⠀⡀⠐⣀⣴⡿⠿⠛⡉⠡⠴⠾⠿⠿⠿⠿⠿⠿⠿⠛⠉⢁⣀⡀⠠⠀⠀⠖⠒⢂⣀⣉⣩⣭⣭⣤⣤⣤⣴⣶⣤⣤⣤⣤⣤⣤⡄⠠⠌⣍⡁⠀⠀⠂⠄⠀⠈⠉⠛⠻⠟⠁⠀⣥⠄⢨⡉⠻⣿⡄⢹⣿⣿⣿ ⡇⢰⣿⣿⠇⠀⠈⠻⠋⠻⠛⠛⠉⠃⠀⢰⣶⣤⠘⡇⠀⠀⡄⠀⠈⠀⢰⠀⢰⡆⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠃⠈⠁⠁⣴⠂⠈⣠⡴⠒⣢⠀⢲⡀⠀⣴⠖⠀⠀⠂⣉⣩⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⠀⢀⡀⠀⠆⠀⣀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠉⣆⢹⡇⢸⣿⣿⣿ ⡇⢸⣿⣿⣧⣀⣀⣀⣤⣀⣀⠀⠀⠀⠀⣼⣿⣿⠀⡇⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠠⡦⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⠀⠀⡇⠀⢜⡉⠀⠐⠛⠃⠈⠁⠀⠀⣤⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠁⠀⠁⠀⢹⠀⠀⢈⠟⠁⠀⢠⡀⠀⣿⠀⢸⣇⠀⡄⠁⢠⠀⠀⢀⡿⢀⡇⢸⣿⣿⣿ ⣷⣄⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⠋⣹⡟⠛⠛⠁⠈⠀⠀⠀⠁⣠⡆⠀⣨⡀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⠤⠄⠚⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠄⠀⣀⣉⠀⠀⠈⠀⠀⠀⠉⠧⠀⠀⢀⣼⣿⣧⡈⠳⡀⢠⣶⠟⢁⠀⠀⢸⣿⣿⣿ ⣿⣿⠀⠀⢀⣴⣿⣿⠟⠁⣀⣴⡏⠉⢻⣿⠀⠀⠀⠀⠀⣠⣾⣿⣿⠆⠈⠀⣡⣴⣶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⢊⣠⣤⣤⣤⣤⣤⣤⣤⠦⠀⠀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣶⣿⣿⣶⣤⣿⣿⣿⣶⣤⣤⣀⣀⠈⠉⠛⠛⠿⢶⣤⣤⣤⣶⣿⣷⡆⢸⣿⣿⣿ ⣿⣿⡄⢰⣿⣿⠟⠁⢀⣾⣿⣿⣷⣶⡞⠁⠀⠀⠀⢠⣾⣿⡿⠛⠁⠀⣠⣾⣿⠿⠋⠀⠀⠈⢀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠟⠋⣁⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣠⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣆⡀⠀⢈⠉⠻⢿⣿⣿⡇⢸⣿⣿⣿ ⣿⣿⣧⣾⡿⠋⢀⣴⣿⣿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣯⠀⠉⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⣠⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣨⣅⡀⠀⠸⡿⠟⠋⢁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠻⣿⣿⣿⠛⠛⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⠲⢤⡈⠙⢧⣼⣿⣿⣿ ⣿⣿⡿⠏⢀⣰⣿⣿⠛⠻⣿⠟⠀⠀⠀⢀⣾⡏⠉⠁⠀⣀⣴⣿⣿⠟⠁⠀⠀⠈⠐⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡆⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠁⣀⣀⣀⣠⡤⢠⣤⣤⣤⣴⣷⣤⣤⣄⣀⣀⡀⠀⠀⠀⠉⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢶⡄⢻⣿⣿⣿ ⣿⣿⠇⢠⣾⣿⣿⣧⡘⠀⠁⠀⠀⠀⣴⣿⠟⠁⠀⣠⣾⣿⣿⡿⠁⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠄⢀⣬⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣤⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⢁⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠒⠤⣈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠁⢸⣿⣿⣿ ⣿⣿⡆⣿⣿⣿⣿⣿⠏⠀⠀⠀⣠⣂⠘⠁⠀⣠⣾⣿⣿⡿⠋⠀⠀⠠⢀⣴⣿⠟⠉⠀⠐⠀⣠⣾⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⡿⠟⠋⠁⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣉⠒⢤⡈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣾⠟⠁⠀⣠⣾⣿⣿⣿⠋⠀⠀⠀⣠⠀⠸⠟⠁⠀⠀⢀⣴⣿⣿⣿⡿⠏⢀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⠿⠋⢁⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠉⠉⢁⣀⣀⣀⣀⣀⣀⣉⡉⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⠓⢄⡈⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿ ⣿⣿⣿⣿⣿⠟⡀⠀⠀⣰⡿⠃⠀⢠⣾⣿⣿⣿⠟⠁⠀⠀⣠⣾⣿⠤⢀⡀⠀⣠⣶⣿⣿⣿⠟⠁⢀⡀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠀⠀⣤⡦⠂⡈⢻⣶⡄⢠⠽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡙⢦⣀⠙⢿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿ ⣿⣿⡏⣿⠋⠀⠀⢀⣼⠟⠀⢀⣴⣿⣿⣿⡿⠃⠀⠀⡠⢀⡿⢏⠀⢀⡀⢰⣾⣿⣿⡿⠋⠀⣠⠞⢁⣴⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⣀⠠⠶⠀⠘⠷⡈⠃⠀⠀⠘⠛⠓⣀⣐⣛⣿⣿⣿⣿⡟⠻⠿⠿⣿⡟⠻⣿⣿⣿⣶⣤⡀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣦⠙⢷⡄⠙⣿⣿⣿⣿⡇⣿⣿⣿⣿ ⣿⣿⡇⠁⠀⠀⢀⡾⠁⠀⣠⣾⣿⣿⣿⠟⠀⠀⣠⡞⢁⡞⠀⣀⣴⣿⣷⣆⡙⠻⡏⢀⡀⠒⢁⣴⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢻⡿⠟⠋⠁⠠⢴⠘⢀⠀⣯⠤⠄⠉⢁⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦⣉⡋⠠⢿⣿⣿⣷⣤⡈⠙⢿⣿⣿⣿⣿⣿⣷⣄⠹⡆⠈⢿⣿⣿⡇⢸⣿⣿⣿ ⣿⣿⡇⠀⠀⣠⡟⠁⠀⣴⣿⣿⣿⡿⠋⠀⢠⣾⣿⠋⠀⠤⠀⡈⠻⣿⣿⠟⠁⠀⣤⡌⢃⣴⣿⣿⣿⣿⣿⣿⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⢀⠀⣄⠈⡀⠈⠀⠀⣀⣤⣴⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⡙⠻⣿⣿⣷⡄⠙⢿⣿⣿⣿⣿⣿⣦⡈⢷⡀⠻⣿⡇⢸⣿⣿⣿ ⣿⣿⡇⠀⣰⠋⠀⢠⣾⣿⣿⣿⠟⠁⢀⣴⣿⠟⠁⠀⠀⣠⣾⣿⣦⠘⠁⣤⡑⠂⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠁⠄⠸⠀⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⠿⠧⠒⠀⠙⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⣿⣿⡇⢰⠃⠀⣠⣿⣿⣿⣿⣏⣀⣰⣿⡿⠃⠀⠀⢠⣾⣿⣿⡿⠋⠀⢸⣿⠟⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣠⣴⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⣀⣀⠀⠐⠒⠿⠿⣿⣿⣿⣶⣶⣶⡖⠂⠤⠄⠈⠉⠙⠻⠿⠿⠛⠋⠉⣁⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⢀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣴⣿⣿⡿⠋⢀⡀⠘⠘⢃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⣿⣿⣿⣿⣿⣿⣿⣇⣀⣉⣥⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣀⠉⠛⠻⣿⣿⣿⣿⡿⠶⠒⠈⢁⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾ ⣿⣿⡁⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣠⣾⣿⣿⠟⠀⢠⣬⣤⠄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠙⠋⣁⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿ ⣿⣿⠁⠘⠿⠿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣴⣿⣿⡿⠁⢀⠀⠀⠄⠃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⡀⠻⡿⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢀⠀⠐⣿⣿⣿⣿ ⣿⣿⠀⣅⣁⡒⠒⠀⠨⠉⢉⠀⠀⠠⠾⣿⣿⠏⠀⣠⡄⢀⠓⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣴⡉⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢀⣠⣴⣾⣿⡇⢀⣿⣿⣿⣿ ⣿⣿⢀⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣀⣀⣀⠀⠉⠀⠋⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⡀⣀⠙⠡⣾⡗⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠉⠁⣀⣠⣤⡄⠀⢸⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿ 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⣿⣿⡇⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣉⠳⠄⡀⢀⣀⠉⠙⠻⠿⣿⣿⡿⠁⢀⣴⣿⣿⣿⣿⣷⡶⠀⢰⣾⣿⣭⣭⣭⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠁⠀⠀⠀⣀⣠⣶⣶⣴⣶⣤⣤⠤⠀⠈⠉⠉⢀⡰⠀⠀⣠⠴⠟⠀⣀⣤⡶⠀⣾⣿⣿⣿⡿⠛⠉⢀⠀⢀⣠⣾⣿⡇⢸⣿⣿⣿ ⣿⣿⡇⣿⡄⢀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣈⡛⠛⠶⢤⣤⠀⠈⠀⡴⠋⡿⢛⣿⡿⠟⠉⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⣻⠛⠛⠉⠁⠀⠤⠀⢂⣀⣤⣴⣾⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⢀⠙⢧⢤⠀⠀⠀⠐⠋⣠⣴⣾⣿⣿⠇⠀⣿⡿⠛⠁⢀⠤⠂⣠⣴⣿⣿⡿⠛⠀⢸⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⣷⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⣀⠀⠈⠁⠘⠉⢀⠤⢠⣤⠀⢤⣤⡤⣤⣶⣶⣶⣶⣶⣶⣶⣶⠖⠛⠛⠛⢋⣉⣉⣤⣤⣶⣾⣿⣿⣿⣿⣿⠿⠟⠛⠉⡀⠠⢠⣞⠀⢀⣀⠀⠀⠠⠜⢃⣀⣴⣾⣿⣿⣿⠛⠿⠟⣰⣆⠀⠀⠠⠂⣀⣴⣿⣿⣿⠟⠉⠀⣠⡆⢸⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⣿⣿⣷⣦⡈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⡐⠀⠀⠀⠐⠀⠉⠡⣭⣭⣭⣿⣿⣿⣿⠟⡛⠲⣾⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⢉⣀⣠⣄⠐⠀⠱⠀⠚⠋⠀⠘⠋⡀⠔⢀⣺⣿⣿⣿⣿⣿⣿⡿⠗⢀⣾⣿⣿⣷⣦⠐⢿⣿⣿⡿⠋⠀⣀⣴⣎⠀⠄⣿⣿⣿⣿ ⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡗⢠⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⡿⠿⠟⠛⠋⢉⠀⣠⣤⣤⣶⣿⣿⣿⠟⠻⠇⠠⠀⢊⣀⣤⣴⣾⣿⣷⣿⣿⣿⣿⣿⠿⠛⠉⢉⣄⡘⢿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⣰⠎⡉⠀⠙⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡗⠀⢘⠀⢀⡀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦⠄⠀⠐⠂⠠⠤⣤⣤⣌⣩⣍⣉⣉⣉⣭⣭⣭⣭⣭⣀⣤⣤⣤⣴⣦⣤⣴⣶⣿⣿⣿⣿⣿⣿⡿⠻⠟⢻⢀⣉⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⢁⣀⣤⣶⠶⢛⣿⣿⣄⡙⢿⣿⡿⠟⢉⡤⣾⡶⢧⠙⠄⠁⣸⠉⡈⠀⢺⣿⣿⣿ ⣿⣿⠀⢿⣿⣿⣿⣿⣿⣤⡇⠀⢠⡞⢀⠀⢠⡀⠀⢀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⡐⠀⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⠿⠿⠷⠈⠛⠛⠛⢻⣿⣿⣿⣿⣿⣍⣽⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⢀⣠⣴⡾⠟⢋⣩⣴⣾⣋⣽⣿⣿⣷⠈⠋⣠⡴⠘⠃⠘⠇⠘⢁⡄⠀⠀⣀⣤⡆⢸⣿⣿⣿ ⣿⣿⠀⣄⡙⠻⢿⠿⠛⠟⠻⠄⠙⠃⠈⠀⠄⠁⠘⠤⠂⠀⠤⠀⠈⠉⠛⠻⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⠷⠲⠷⠶⠿⠿⠿⠿⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⢀⣀⣠⡄⠐⡟⠉⠋⠡⢴⠾⠿⠿⢿⡿⠿⠿⠟⠉⠠⠀⠀⠿⠏⠀⠀⠀⣀⠀⠀⠠⢴⣿⣿⣿⡇⢸⣿⣿⣿ ⣿⣿⠀⣿⣿⣷⠀⣴⣾⣷⣿⣷⣿⣿⣶⣶⠿⢶⡷⠶⡖⢶⣶⣶⣶⣶⣿⣶⣾⣿⣿⣿⡞⠉⠀⠉⠻⣿⡟⢿⡟⠁⠈⠹⠁⠀⠰⣶⣶⣶⣶⣿⣷⣶⣶⣦⠙⣿⣿⣿⠁⣴⣾⣶⣶⣶⡶⠶⠖⢀⣴⣶⣶⡖⣶⣾⣿⣿⣿⣿⣿⠗⢀⠀⡀⠲⣶⣿⣶⣶⣿⣿⣿⣿⣷⣶⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⡄⢹⣿⣿⡇⢸⣿⣿⣿ ⣿⣿⠀⠙⠻⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣏⠀⢀⣹⠎⠀⠄⠀⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠉⠉⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠰⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⢸⣿⣿⣿ ⣿⣿⠀⣶⣤⣀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠓⠛⠛⠛⠛⠛⠛⠷⠄⠀⠠⠼⠿⠶⠾⠧⠤⠤⠴⠤⠠⠾⠿⠿⠿⠿⠿⠿⠿⠿⠋⢀⣆⠠⠀⡀⠈⠛⠻⠿⠿⠿⠿⠾⠿⠿⠾⠿⠿⠷⢷⣾⠿⢿⣿⣿⣦⡌⠀⠡⠼⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠋⠀⣸⡿⠟⠁⣸⣿⣿⣿ ⣿⣿⠀⣿⣿⡿⠀⠀⠀⠀⠀⠒⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣦⠄⠲⢶⡶⢶⣶⣶⣦⣶⣶⣦⡄⠂⠰⠦⠀⠈⢻⡇⢈⣉⣤⣤⡴⢲⠶⠿⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠟⠋⢁⣠⡴⠶⠶⠖⢂⣀⣤⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡶⠞⠉⠀⠀⠀⠿⠿⠿⣿ ⣿⣿⠀⠙⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣠⣦⣄⡀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⣭⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣯⣤⣤⡤⠠⣴⣶⣶⡶⢀⣤⣤⣾⠿⠟⣩⠅⢤⠄⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣤⣤⣤⣧⣤⣤⣤⣤⣤⣴⣶⣶⡿⠁⠀⣿ ⣿⣿⡀⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠸⠧⡀⠀⠀⠀⠀⠀⠀⠉⠉⣠⠘⠄⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠄⠀⠉⠁⠈⠀⠀⠀⡇⠀⠁⠁⠈⠉⠁⠙⠀⠀⠈⠀⠈⠀⠈⠈⠉⠉⠉⠈⠛⠁⠀⠀⠀⢠⠋⠈⠀⠁⢹⠉⠉⠁⠀⢹⣿⣿⣿⣿⠏⠀⢀⣾⣿ ⣿⣿⡇⣿⣿⣿⣇⣀⣀⣀⣀⣿⣷⣶⣶⣤⣤⣄⠀⠀⠀⠁⠀⠂⠀⠰⠶⠶⠦⡄⢀⣄⣉⡉⢉⠉⠙⠛⠛⠀⢠⠖⠀⢰⡶⠂⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠲⣶⣤⣼⣿⣷⣦⠰⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⠒⠀⣶⣶⣷⡶⠲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢂⣶⣾⣷⣶⣶⣶⣾⣶⣶⣶⣶⣾⣿⣿⡟⠁⠀⣴⣿⣿⣿ ⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣌⣁⣈⣱⣿⣿⣿⣿⣿⡖⠀⢠⣿⠀⠀⠘⠀⠀⠀⠙⢻⡄⠀⠀⠀⠀⡀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⡟⠋⣠⣾⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⠋⠀⢀⡀⣿⣿⣿⣿ ⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠛⠛⠛⣛⣛⣛⣛⣛⣃⣘⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⠛⠻⠟⣻⡦⠴⠷⠆⠈⣁⣘⣛⣛⣛⣃⣘⡛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠓⠚⠻⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⢀⣴⣿⠇⣿⣿⣿⣿ ⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣿⣿⣿⣿⠓⠒⠛⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠛⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠛⠛⢋⣠⣿⣿⣿⣿

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⠈⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠀⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣿⡧⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⠀⠀⠀⢠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⡖⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠉⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢢⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢀⣠⠤⠴⠒⠒⠒⠒⠒⠒⠒⠲⠤⢤⣀⡀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⣀⣠⠤⠔⠒⠉⠉⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠈⠳⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠀⠀⣀⡤⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⣀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣠⠴⠚⠁⢀⣠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣾⣿⢉⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⢹⣿⣦⡀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠸⣿⣿⣷⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣶⣿⣿⡿⠀⠀⠐⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⢻⡀⠀⠀⠀⣀⣀⣀⡤⠤⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⣿⢶⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣴⣶⣶⣾⡇⠀⠀⠘⢫⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⢿⣝⣯⢿⣆⠀⠀⠀⠀⠙⠒⠒⠋⠉⠈⠙⠒⠒⠋⠀⠀⠀⠀⣰⣿⣻⢮⡷⢯⡗⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢮⣻⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⢷⣯⣟⣿⠃⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⢷⢾⡿⠉⠓⠦⣄⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠻⡁⠀⣀⠴⠋⠁⠀⠀⠀⢀⣀⡤⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⣷⠋⠁⠀⠀⣀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠁⠈⠲⠶⣦⡄⣀⠤⠤⠀⢐⠛⠁⠀⠀⠀⠀⠀⠀⠹⡄⢀⢦⣻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣮⣟⣽⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⢺⠛⠢⣼⠁⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠃⠀⠀⠀⠀⡇⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⢯⡳⡀⠈⠑⢆⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⣀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⡴⠛⢉⣼⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⡽⠘⠓⢦⣀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⠂⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠴⣋⡠⠔⣺⣻⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠈⠳⣄⠀⢀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⢠⡞⠄⠀⠀⣠⠞⠁⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢖⡂⡀⠈⠁⢿⠀⠙⢦⡀⠀⠀⠀⠀⠀⣼⣄⣦⣴⣥⡷⠀⠀⠀⠀⠀⣠⠋⠀⣄⠑⠘⠁⢀⣠⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣖⣢⡾⠾⠴⠚⢳⣦⣠⣤⡶⠶⠛⠀⠀⠀⠘⠲⡤⣄⣀⣀⡞⠳⢤⣶⡏⣀⣠⡷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿ ⣿⣧⡀⠀⠀⠀⠀⠙⠿⠿⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⣷⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿ ⣿⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿⣿⣿ ⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣿⣿⣿ ⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔

⡏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿ ⣿⣧⡀⠀⠀⠀⠀⠙⠿⠿⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⣷⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿ ⣿⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿⣿⣿ ⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣿⣿⣿ ⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠀⠀⠀⠀⠀⠀⣠⢾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢻⣿⣿⠏⠀⠀⠀⠀⣠⠞⠁⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢸⣿⡟⠀⠀⠀⢀⡾⠁⠀⠀⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⣸⠟⠀⠀⠀⣠⠟⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣁⣠⠤⠶⠒⠛⠶⠦⢤⣴⠃⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⠀⠀⠀⠀⠀⣀⡴⠚⢻⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢰⡖⣆⠀⠀⠀⠀⠀⡖⠺⣷⡀⠀⠀⠀⢸⡆⠀⣀⡴⠚⠁⠀⠈⠢⡊⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠸⣿⠇⢀⠀⠀⠀⠀⠻⢿⣿⠇⠀⠀⠀⠀⡷⠞⠁⠀⠀⠀⠀⠀⠀⠈⠀⠙⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⢆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡴⠉⠉⢢⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢷⡼⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠱⢤⡠⠎⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣤⡀⠀⢀⠀⠀⢠⡴⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⢤⡴⢚⡉⠉⠉⠙⠳⣄⠀⣀⡚⠁⠙⣦⠉⠳⢤⡁⠢⠀⢙⡦⢤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡧⡀⢠⢾⡁⠀⠀⠀⡀⣽⣠⠟⠛⠂⠀⣾⢀⡤⢞⡧⠀⠀⠈⠉⠙⢦⣠⢴⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠧⣼⢿⡷⢿⣾⣿⣿⣿⣿⣿⡆⣠⡶⣷⡋⠙⠁⠀⢀⣀⡤⠶⠚⠋⠉⠿⠗⢀⢤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣠⣾⣶⠶⢿⣿⣿⣿⣿⣿⣿⢯⡇⠈⠙⢦⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠸⠜ ⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣾⣻⣿⡛⠭⠝⣿⣕⠼⢿⣿⣿⣿⡟⣴⣿⠀⣠⡴⠋⠀⠀⠀⣹⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠶⠞⠛⢚⠳⠮⣄⡚⢿⣦⣤⣴⠟⢻⡆⢸⣿⣿⣿⣟⡎⢹⠛⠉⣻⣦⠴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⢞⣅⡀⠀⣾⣿⣷⠀⠀⠙⣦⠈⢿⠃⣉⣽⣗⡾⠿⠛⢻⣿⣷⡿⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⠳⣿⣿⣯⠀⠙⠛⠋⣠⣶⡄⠈⣧⠘⡗⣯⣽⣟⠁⠀⠂⠀⠹⣿⣷⣦⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⣉⣍⠉⠀⠀⠀⠘⣿⣿⡿⠀⢸⡗⣿⠏⠀⠉⠉⠛⠒⢶⠺⣯⣿⠛⠿⠿⠿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣼⣿⣿⡃⠀⠀⠀⠀⣠⣤⣄⠀⢸⣷⠃⠀⠀⠀⠀⠀⠀⠈⠙⠓⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣜⠛⠛⢃⣴⣶⣆⢸⣿⣿⣿⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢦⡀⠘⢿⣿⠿⠀⠈⠉⣠⠞⠃⠀ ⠀⠀⠀⠉⠓⠦⠤⠤⠤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⣺⡶⢤⠄⠀⠀ ⠀⠀⠀⠀⣾⣿⠙⠓⡄⠀⠀⠀⢠⠏⠉⢀⣞⠓⣿⠀⠀⠀⠀ ⠀⠀⠀⢸⣽⣽⡤⠞⠁⠀⠀⠠⣮⢤⣶⣋⢿⠫⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠑⠶⠭⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠻⡀⠀⠀⠀⠀⡀⠜⠁⠀⠀⣀⢀ ⣴⢦⠀⠒⠠⠤⠒⠏⠁⠀⠈⠉⡏⠈⠈⠀⠀⢀⠞⠁⠀⠀⠉ ⠀⠀⠱⠀⠀⠀⠀⠀⠩⣔⠢⠤⡜⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⢠⠅⠀⠀⠀⠀⠀⠀⠈⠑⠋⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠛⠉⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠸⡆⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠃⠀⠀⠐⠚⠻⢷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢁⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⣼⠏⣼⣧⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⣤⡾⢿⠐⣿⡿⠃⠀⠀⠀⢀⡖⠒⣦⡀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠁⢸⠀⠀⣤⡄⠀⠀⠀⢸⣧⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄⠀⠀⠀ ⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡠⠃⠀⣀⡈⠀⠀⠀⠀⠘⢿⣿⣿⠟⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀ ⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢹⡟⠓⣶⠀⠀⠀⠀⣨⣤⣤⡀⠀⠀⠀⠀⢸⣿⣶⣦⣤⣶⣾⣿⣿⣿⣆ ⢠⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠘⣧⠀⠀⠈⣄⠀⡏⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣸⡟⠀⠉⠙⠛⠛⠿⠿⠿⠛ ⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⣿⠟⠋⠀⠀⣠⣴⡿⠿⣷⣄⠀⠈⠓⠁⠀⠀⠀⠈⠿⣿⡿⠏⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⢾⣿⣯⡀⠀⢸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠛⠛⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣶⣦⣤⣀⠈⠙⢿⣶⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⠃⣠⣿⢋⣽⣷⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣶⣿⣧⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠈⠻⢦⣤⣤⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⠋⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣧⡀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⠙⠓⠶⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠋⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⠁⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣉⣀⣀⣀⣤⣾⣿⣷⣶⣶⣶⣿⡿⠿⠿⠛⠛⠿⣷⣤⣄⡈⠀⠉⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠂⠀⡤⠔⠊⢩⢁⠔⠁⠀⠀⠀ ⢀⡀⠤⡤⠤⠤⠤⠤⠤⠀⠠⠄⠀⠠⠤⠬⣄⠔⠁⠀⠀⡠⠊⠉⠁⠂⠤⣀⠀ ⠈⠑⠂⠼⠤⣀⣀⣀⡰⠀⣀⡀⠀⠀⠀⠀⠀⠀⢆⠂⠁⠀⠀⠀⠀⠀⠀⣠⠃ ⠀⠀⠀⠀⡔⠉⠑⢄⠇⠨⠷⠁⠀⡄⠀⠰⣽⡆⢸⣀⠀⠀⠀⠀⠀⠀⡔⠁⠀ ⠀⠀⠀⠀⢸⠀⠀⠘⠉⢢⠀⢢⡴⠶⣤⠄⢀⠤⢼⢣⠉⠒⠤⣀⢀⠌⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⠀⠘⡖⠋⠀⠈⢆⢀⠎⠀⠸⡀⡰⣠⠆⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡄⠀⠈⠢⠄⠀⠈⠁⠀⢀⠤⠊⠀⠀⠉⠒⠄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣀⣀⡀⠠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢾⠗⠒⠉⠁⠀⠀⠀⠀⠀⠉⠑⠢⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡄ ⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⣶⣶⣶⠖⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢀⠎⠀⠀⠀⠈⠙⡀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠈⣿⠟⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇ ⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠈⠀⠠⡄⠊⠁⠀⠀⠀⢀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠋⠉⠀⠀⠀⠀ ⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⢰⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣧⠀⠀⠀⠀⠀ ⢀⡎⠘⠋⠀⡄⠀⠀⠀⢠⣈⣵⠀⢠⣆⢠⣶⡕⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀ ⠸⡀⠀⠀⠀⢤⣀⢀⣾⡿⠿⠇⣾⠀⣿⡄⡏⢀⣿⢣⡷⠂⢳⣦⣀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⢄⠀⠀⠸⣄⣀⣀⣥⣤⣷⣿⠀⢹⡷⠀⠘⠁⣿⠇⠀⢸⣿⠈⣷⣦⣄⠈⢿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⢢⢄⡘⠉⠉⠙⠻⣿⡿⠄⠀⠀⠀⠀⠰⠋⠀⠀⢸⠇⠀⣿⣿⠉⢦⣼⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡏⠀⠈⠉⠁⠀⠀⠀⠁⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⢸⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣀⠀⣰⣷⢳⣤⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⡠⠊⠀⢻⡥⢻⣾⢿⠅⢀⠎⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠀⠉⠀⠀⡔⠋⠀⠀⡀⠏⠁⠈⠁⠀⡠⠊⠀⠨⡀⠀⠀⠀⠚⠛⠉⠉⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⢡⣤⡞⡼⠀⠀⠀⠰⣀⢰⠀⡀⡀⠞⢉⡡⠔⣋⠩⠭⠽⢷⡾⠇⠀⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠗⠣⠎⠁⠠⣊⣠⣐⣀⣠⣀⡤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⠀⠀⠀⠀⠀⢹⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿ ⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠙⠿⠷⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⣸⣿ ⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿ ⠀⠀⠀⠀⠀⢾⣿⣿⣿⠏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⢹⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿⣿⣿ ⠀⠀⠀⠀⠀⣸⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿

⢿⣷⣶⣤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠈⢿⣿⣿⡇⠈⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢶⣿⣿⣿⡿⠁⠀⠀⠀⠀ ⠀⠈⢻⣿⣇⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⣸⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⢀⣀⠤⢤ ⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠘⠦⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠊⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⢀⣀⠤⠔⠚⠉⠁⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠊⢁⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣶⡿⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⢻⣶⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⣿⣿⣶⡿⠀⠀⠀⠀⢀⠀⠀⠀⠀⢿⣶⣿⣿⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠚⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠤⢄⡈⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠉⠁⠀⣀⣀⡇⠀⠀⢠⠤⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠙⡄⠀⠀⠀⠢⠤⠴⠊⠒⠤⠠⠖⠀⠀⠀⡴⠋⠀⠀⢹⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢠⡎⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢖⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⣲⠋⠈⢒⡤⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠈⡤⠒⠉⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠀⠀⠀⠀⢣⢀⡦⣶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⢏⢀⣀⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡖⣏⠒⢼⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢸⢀⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣮⠢⠀⠑⠂⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⡤⠊⢡⣮⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⡠⠃⠀⠀⠈⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⠀⡄⠙⢄⠀⠀⠀⠀⠀⡃⠤⠄⡰⠀⠀⠀⠀⡰⠁⢀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠴⠓⠒⠂⠧⢤⡴⡖⠊⠀⠀⠀⠙⠀⣤⣤⡎⠒⠀⢇⣀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀