⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣿⣿⣿⣿⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⣾⣿⣿⣿⣿⣄⡀⠀⣀⣤⣤⣿⣿⣿⡖⠒⠒⢒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⣒⣒⣒⡒⠒⠒⠒⠒⠒⠒⠒⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⢿⢸⠟⠛⠋⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⣿⣿⣿⣿⠀⢀⡼⣼⠇⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣷⡙⢲⣿⠞⢁⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡦⠬⠴⠛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡒⢒⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣉⣙⣻⠿⠒⠒⠒⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠤⠄⠀⠀⠀⢀⣀⣀⡞⠀⢁⣾⣿⣿⣿⣿⣿⠉⠙⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠒⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢠⣸⣿⣿⣿⣿⣿⣿⣶⣶⠶⠒⠦⠤⣄⣀⠀⠀⠀⢀⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⠟⠁⣀⠀⣀⠀⠀⠀⠉⠙⠶⣤⡀⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⣿⣿⡿⠟⠽⠊⠀⠀⠀⡽⡎⡸⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠉⠀⠀⠀⠀⠀⠀⢰⠇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⠀⡐⠒⡀⠀⠀⠀⣠⠏⢠⣿⡇⠘⠀⠀⠀⠀⠀⢠⣿⠀⠰⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡙⡆⠀⣻⣥⠃⠀⢀⡴⠋⠀⣸⡏⣿⡀⠀⠀⠀⠀⡀⠘⠫⠁⠀⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣀⡞⠉⠀⠀⠀⠀⢀⣴⠟⠀⠁⠳⣄⠀⠀⠀⠀⠀⠀⠀⣴⠃⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣿⠳⢤⢤⣤⠠⠴⠛⠁⠀⠀⠀⠀⠈⠓⠦⣤⣀⡤⠖⢿⠁⠀⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣰⠃⠀⡞⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠸⣆⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⡏⠀⣸⠃⡰⠃⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣦⡹⣆⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠃⢠⠇⢸⠁⠀⠈⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⢿⣧⠀⠀⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠤⢀⠀⠀⠀⠀⠀⢀⡎⡎⢠⢏⡴⢿⡀⠀⠀⠀⠈⠉⠑⢲⣾⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡻⣧⡀⢹⡄⠀⠉⠉⠓⡒⠒⠒⠒⠒⠚⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⠫⠄⠀⢀⡠⠆⠀⣴⣿⢰⢇⣿⠞⠛⠛⠳⢦⡀⠀⠀⠀⢀⡼⠻⠾⠃⠀⠀⠀⠀⣀⣤⣾⣿⡿⠀⠹⣷⡀⢷⣤⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠖⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⢜⡏⡿⣾⠃⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣛⣛⣁⠀⠀⠀⢹⣷⡘⣏⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀ ⠀⡰⠟⠁⠀⠀⠀⠀⠀⠀⡠⠀⣡⣄⡄⣉⣼⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⢀⣴⡿⠟⠉⠁⠀⠀⠉⠉⢲⣄⠈⢿⣷⣽⡟⠓⣓⠠⢄⡀⠀⠀⠀⠘⢦⣄⠀⠀ ⣸⠃⠀⠀⠀⠀⠀⠀⠴⣶⣿⣫⢵⣾⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⢸⣿⣿⣤⣛⣶⣤⣭⣷⣦⠄⠀⠀⠀⠈⢳⠀ ⠘⢦⡀⠀⠀⠀⠀⠀⠀⡀⢈⣯⣭⡿⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠿⣟⣋⠛⠯⠉⡅⠀⠀⠀⠀⣀⠘⠀ ⠀⠀⠉⠑⠒⠒⠀⠰⣤⣿⣿⡟⠉⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠊⠁⠁⠀⣿⠛⠛⠉⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡽⠿⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠈⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⡛⠈⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠡⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡀⡀⡀⢀⢀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣿⣾⣧⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⣧⣾⣿⣷⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⢀⢀⡀⡀⡀⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠡⠀⠀⠀⠀⠇⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠈⡛⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠈⠀⠀⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠿⡽⣿⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠉⠉⠉⠛⠛⣿⠀⠁⠁⠊⠀⡿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉⡟⣿⣿⣤⠰⠀⠒⠒⠑⠉⠀⠀ ⠀⠘⣀⠀⠀⠀⠀⡅⠉⠯⠛⣋⣟⠿⣟⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢻⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡿⣭⣯⢈⡀⠀⠀⠀⠀⠀⠀⡀⢦⠘ ⠀⢳⠈⠀⠀⠀⠄⣦⣷⣭⣤⣶⣛⣤⣿⣿⢸⠀⠟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⠻⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠿⣿⣿⣾⢵⣫⣿⣶⠴⠀⠀⠀⠀⠀⠀⠃⣸ ⠀⠀⣄⢦⠘⠀⠀⠀⡀⢄⠠⣓⠓⡟⣽⣷⢿⠈⣄⢲⠉⠉⠀⠀⠁⠉⠟⡿⣴⢀⠀⠀⡀⣤⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⣽⣼⣉⡄⣄⣡⠀⡠⠀⠀⠀⠀⠀⠀⠁⠟⡰⠀ ⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠄⣏⡘⣷⢹⠀⠀⠀⣁⣛⣛⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠉⠀⠀⠀⠀⠀⠃⣾⡿⡏⢜⠀⠀⠀⠀⠀⠀⠀⠉⠁⠋⠖⣠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣬⣤⢷⡀⣷⠹⠀⡿⣿⣾⣤⣀⠀⠀⠀⠀⠃⠾⠻⡼⢀⠀⠀⠀⡀⢦⠳⠛⠛⠞⣿⢇⢰⣿⣴⠀⠆⡠⢀⠀⠄⠫⣴⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠉⠚⠒⠒⠒⠒⡒⠓⠉⠉⠀⡄⢹⡀⣧⡻⢰⠀⠀⠀⠀⠀⠀⠀⠀⡄⠦⣾⢲⠑⠉⠈⠀⠀⠀⡀⢿⡴⢏⢠⡎⡎⢀⠀⠀⠀⠀⠀⢀⠤⣴⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣧⠀⠀⣧⢿⢟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢧⠈⠀⠁⢸⠇⢠⠃⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⠀⠀⣆⡹⣦⢿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠃⡰⠃⣸⠀⡏⢃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⣆⠸⡀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢘⠀⡞⠀⠃⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠁⢿⠖⡤⣀⣤⠦⠓⠈⠀⠀⠀⠀⠁⠛⠴⠠⣤⢤⢤⠳⣿⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠃⣴⠀⠀⠀⠀⠀⠀⠀⣄⠳⠁⠀⠟⣴⢀⠀⠀⠀⠀⠉⡞⣀⣷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠁⠫⠘⡀⠀⠀⠀⠀⡀⣿⡏⣸⠀⠋⡴⢀⠀⠃⣥⣻⠀⡆⡙⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠰⠀⣿⢠⠀⠀⠀⠀⠀⠘⡇⣿⢠⠏⣠⠀⠀⠀⡀⠒⡐⠀⡏⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠇⢰⠀⠀⠀⠀⠀⠀⠉⡿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⢿⠙⠀⠀⠀⠀⠀⠀⠀⡸⡎⡽⠀⠀⠀⠊⠽⠟⡿⣿⣿⣼⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣧⡀⣤⠶⠙⠉⠀⠀⠀⣀⠀⣀⠁⠟⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⡀⢀⠀⠀⠀⣀⣄⠤⠦⠒⠶⣶⣶⣿⣿⣿⣿⣿⣿⣸⢠⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⠒⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠒⠙⠉⣿⣿⣿⣿⣿⣾⢁⠀⡞⣀⣀⢀⠀⠀⠀⠄⠤⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠶⠒⠒⠒⠿⣻⣙⣉⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⢒⡒⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⠛⠴⠬⡦⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣼⢁⠞⣿⢲⡙⣷⣿⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢀⠀⠇⣼⡼⢀⠀⣿⣿⣿⣿⠤⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣸⠋⠛⠟⢸⢿⠿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠒⠒⠒⠒⠒⠒⠒⡒⣒⣒⣒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⢒⠒⠒⡖⣿⣿⣿⣤⣤⣀⠀⡀⣄⣿⣿⣿⣿⣾⠒⠒⠒⠒⠒⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⠈⠀⠀⠀⠀⠀⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⢿⣿⣿⣿⣿⣿⣷⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀