⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠛⠉⠈⠁⠙⠃⠦⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠼⠋⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢐⡮⠁⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡻⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠘⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠼⠅⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⡟⠀⠀⠀⠀⠀⠀⢀⣤⡌⣿⣶⣿⠟⠁⢀⣀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣶⣶⣤⣄⠀⠀ ⣸⠁⠀⠀⠀⠀⠀⠀⣾⣿⡗⠈⠛⠁⠀⠀⣿⣿⠀⠀⠀⠀⣰⣿⣿⣽⣿⣻⣿⢿⣿⣿⡄ ⡟⠀⠀⠀⠀⠀⠀⠀⠿⡿⠁⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⢯⣿⣿⣟⣾⣿⣻⣿⣯⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⠛⠁⠀⠀⠀⠰⢾⣿⣿⣿⣻⣽⣿⣷⣿⣻⣿ ⡇⠀⠀⠀⠀⠀⢀⣴⣿⠿⡛⡉⢉⢉⣙⡻⣿⣄⡀⠀⠀⢰⣿⣿⣿⣿⣟⣿⣷⣿⣿⣿⣿ ⣷⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⢸⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡸⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀ ⠐⣳⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀ ⠀⠘⣖⡀⠀⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢲⣄⠈⠉⠉⠉⠉⠉⠉⠀⠈⠀⠀⢠⣴⠋⠘⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠳⣠⣀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⢀⣨⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠙⠒⠒⠒⠚⠉⠈⣠⣶⣾⣿⣿⣿⢿⣻⣿⢿⣿⣿⣿⣿⣦⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣻⣽⣿⡿⣿⣻⣿⢿⣾⣟⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⣿⣟⣷⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠀⠁⠀⠈⣿⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣾⡿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡿⣾⣿⣿⣾⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⠃⠿⣿⣿⣿⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⢿⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡁⣿⠈⠀⠁⠀⠈⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣷⣟⣿⡿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣟⣾⢿⣿⣻⣿⡿⣿⣽⣻⢿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⣤⣦⣿⣿⣿⣿⢿⣿⣻⢿⣿⣿⣿⣾⣶⣠⠈⠉⠚⠒⠒⠒⠙⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⣨⢀⠁⠛⠴⣠⢀⠀⠀⠀⠀⠀⣀⣠⠳⠙⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⠘⠋⣴⢠⠀⠀⠈⠀⠉⠉⠉⠉⠉⠉⠈⣄⢲⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣻⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣥⣿⣿⣿⠀⡀⣖⠘⠀ ⠀⠀⠀⠀⠉⠉⡟⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣳⠐ ⠀⠏⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡸⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⡀⢸ ⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢠⠀⠀⠀⠀⣷ ⣿⣿⣿⣿⣷⣿⣟⣿⣿⣿⣿⢰⠀⠀⡀⣄⣿⡻⣙⢉⢉⡉⡛⠿⣿⣴⢀⠀⠀⠀⠀⠀⡇ ⣿⣻⣿⣷⣿⣽⣻⣿⣿⣿⢾⠰⠀⠀⠀⠁⠛⣀⣄⣤⣤⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⣿⣿⣯⣿⣻⣿⣾⣟⣿⣿⢯⠀⠀⠀⠀⡿⣿⢠⠀⠀⠀⠀⠁⡿⠿⠀⠀⠀⠀⠀⠀⠀⡟ ⡄⣿⣿⢿⣿⣻⣿⣽⣿⣿⣰⠀⠀⠀⠀⣿⣿⠀⠀⠁⠛⠈⡗⣿⣾⠀⠀⠀⠀⠀⠀⠁⣸ ⠀⠀⣄⣤⣶⣶⣿⣿⣿⣿⢨⠀⠀⠀⠀⣀⢀⠁⠟⣿⣶⣿⡌⣤⢀⠀⠀⠀⠀⠀⠀⡟⢈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢯⠀⠀⠀⠀⠀⠋⡿⣴⢀⠀⣧⢿⠈⠀⠀⠀⠀⠀⠀⠅⠼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⠀⠀⠀⡟⣿⢠⠀⠀⠀⠀⣧⢿⠀⠀⠀⠀⠀⠀⡻⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠙⠀⠃⡿⣴⢀⠀⠀⠀⠀⠀⡀⣿⠹⠀⠀⠀⠁⡮⢐⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠸⠀⠋⠼⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⠞⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⠦⠃⠙⠁⠈⠉⠛⠔⣤⢀⠀⠀⠀⠀⠀⠀⠀