⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠿⠿⠿⠿⣷⣦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢹⣿⣿⠃⠀⠀⠀⠀⠀⠉⠛⠿⣦⣤⣾⣿⣶⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠹⠏⠀⠀⢀⣀⠀⠀⠀⣠⣾⣿⣿⣿⠿⣿⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⢿⣿⣿⡏⠻⣧⠈⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⣼⡇⠀⠀⣽⣿⣿⣤⣿⣴⣿⣿⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠿⢿⣦⣴⣿⡿⠿⢿⣶⡀⠀⠙⠻⠿⢿⣶⡾⠿⠋⠀⠀⠀⠹⢿⣿⡿⣿⣿⣿⠿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣤⡤⠀⣻⣿⣿⠀⠀⠀⣹⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢠⣿ ⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣤⣄⣀⣀⣤⣴⠿⠻⣿⣄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣧⠀⣠⡿⠁ ⠀⠀⠀⢠⣾⣿⠟⠉⠁⠈⠉⠙⢿⣏⠁⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠾⠋ ⢠⣤⣤⣾⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣤⣄⣀⡀⢀⣀⣀⡤⠤⠚⠋⠁ ⠀⠙⠛⣿⣿⠀⠀⠀⠀⠀⠒⠒⠛⣡⣄⡀⠀⠀⢀⣠⣴⡿⠟⠛⠛⠛⠛⠛⠛⠿⣷⣤⣄ ⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⣴⣿⣯⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⡀ ⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠈⠛⠛⠓⠀⣠⡴⠖⠒⠒⠀⠀⠀⠈⢻⣷⡄ ⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄ ⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇ ⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⣿⣟⣉⣄⣀⡀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⡀⠀⠀⢀⣀⣴⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⣄⠀⠀⣿⣿⠿⠛⠻⢿⣦⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⡿⠟⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡀⣿⡇⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣟⠻⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣀⣤⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⢿⣿⣟⠛⠿⣾⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠛⠛⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⢠⡿⣁⣀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠻⣶⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣦⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⢀⣿⠿⠿⣿⣿⣆⠀⠈⠉⠀⠈⠉⠀⠀⠈⠻⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠘⣿⡇⢹⣇⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⢸⠇⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠹⣿⣼⡏⠀⠀⠀⠀⠀⡄⠀⠈⢻⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡾⠷⠶⣄⠀⠀⠀⠈⢻⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠶⠛⢿⣦⡀⠀⠀⠀⠀⢸⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠈⠢⠀⠀⠀⠈⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⣀⣠⣿⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⢀⣤⣤⣤⣾⣿⡇ ⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣦⡀⠀⣿⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠙⠿⢿⣿⣿⡇ ⠀⢸⠋⠀⠀⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⢀⣿⡇⠈⢷⡄⠀⠀⢠⡶⢶⣦⡀⠈⠻⣿⣶⣤⣤⣤⣾⣿⡿ ⠀⠸⡄⠀⠀⠀⠀⠀⠉⠷⣦⡀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⡿⠁⠀⠈⠻⣆⡀⠀⠀⠀⠙⣿⡄⠀⠈⠙⠻⠿⠿⠿⠛⠁ ⠀⠀⠙⢦⣀⣠⠀⠀⠀⠀⠉⠿⣷⣄⡀⠀⠀⠀⢸⣿⡇⢀⣤⣄⠀⠀⢀⣤⣿⠏⠀⠀⠀⠀⠀⠉⠿⣦⣄⣀⣠⣿⣿ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠻⣿⡷⣶⣾⣿⣿⣥⣾⣿⣿⣦⡶⠿⠿⢿⣶⣄⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠻⢿⡆⢀⣀⣀⠀⠀⣿⠋⠀⠉⠿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠛⠿⣦⣏⠀⢸⣅⢀⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠙⣿⡄⠀⠛⢿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣤⣤⣤⣤⣾⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⡿⠛⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡧. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠉⠛⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣀⠀⠀⣸⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⣠⣴⣿⠟⠀⢀⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⣾⣿⡇⠀⠀⣠⠿⠋⠀⣀⣤⣶⠶⠾⢿⣷⣶⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⣿⣿⡿⠖⠊⠁⣠⣶⡿⠋⠁⠀⠀⠀⠀⢹⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⢠⣴⣶⣶⡄⠀⢀⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡏⠀⠀⣠⣶⣿⣷⣶⣀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⣸⣿⡿⠁⢀⣾⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠿⣿⣿⣧⣾⣿⠟⠉⠉⠙⢿⣿⣾⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣤⣴⡾⠟⠉⠀⢀⣾⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⢀⣿⣿⣿⡿⠻⣧⠀⢀⡀⠀⠙⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⣴⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⢠⣾⣿⣿⡿⠐⢦⣾⢶⣿⣿⡆⠀⢸⣿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣾⣿⠃⢸⣿⡇⠀⠀⠀⠀⢿⡿⠋⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠟⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⢿⣿⣿⣧⣴⣿⣿⣧⣄⠀⠀⠀⠈⠻⣷⣶⣿⣿⣶⣶⣶⣶⣶⠶⠾⠟⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠟⠛⢻⣿⠿⣿⣷⣄⠀⠀⠀⠀⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⣠⣤⡀⠘⣿⡇⠀⠙⢿⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⣿⣛⢻⡆⠹⣿⡀⠀⠈⢿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⣉⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⢸⣿⠻⣷⣌⢛⣸⡇⠀⠹⣷⡄⠀⢘⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠸⣏⠁⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⡇⢸⣿⠀⠈⠻⠿⠿⠃⠀⠀⢹⣿⣶⣾⣿⣷⡀ ⢀⡤⠖⠒⠚⠛⠛⠒⠒⠲⠤⢤⣄⣘⢷⣍⠓⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠘⣷⣬⣤⣾⣿⣦⣤⣀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠇ ⢻⡄⠀⠀⠀⢀⡠⠤⠤⠤⣄⣀⡈⠉⠛⠿⢷⣄⠀⠀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⢸⡟⢷⣤⡄⠀⢀⣼⣿⣿⠿⣿⣿⠿⣿⣷⣤⠀⣾⣿⡿⠟⠛⢻⣿⣯⡀ ⠀⠻⣦⡀⠀⠹⣦⡀⠀⣀⡀⠈⠙⠳⣤⡀⠀⠙⠷⣼⣿⡟⠙⢻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⣾⡟⠛⠛⠿⣶⣄⣁⣼⡿⣧⣠⣾⣿⣿⡇⠀⢹⣇⠀⠈⠻⢿⣷⣿⡟⠀⠀⠀⢸⣿⣿⡇ ⠀⠀⠈⠛⢶⣄⡀⠉⠓⠶⠿⠀⠀⠀⠀⠹⣆⠀⠀⠈⣿⣷⣤⣾⣿⠁⠀⣤⠀⠀⣰⣿⣿⣶⣄⠀⢸⠻⣿⡿⠀⣰⣶⡄⢹⣿⠟⠛⠀⠹⣿⣿⠃⢿⣷⣿⣮⣿⡄⠀⢀⣾⣿⣿⣇⠀⢀⣠⣿⣿⡿⠁ ⠀⠀⠀⠀⠀⠈⠉⠑⠒⠶⠤⣤⣤⣀⣀⣤⡼⢲⡟⣼⠋⠹⠈⢹⡟⣧⠀⣿⡇⢰⡟⠉⠀⣿⣿⣷⣼⡄⢻⡇⠀⣿⠻⡗⠀⣿⠀⠀⠀⢠⣿⡇⠀⠘⣧⣌⣿⢹⣿⡀⠈⠿⢿⣿⣿⣿⣿⡿⠟⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢸⢰⡇⠀⠈⡇⢹⠀⣧⣴⣿⠀⠀⢸⠋⣉⠛⣿⣷⣼⡇⠀⢻⣆⣀⣠⣿⢿⡇⢀⣾⣿⠀⠀⠀⠈⠛⠋⠀⢿⣧⠀⠀⠸⣿⣿⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣸⠀⠷⣸⡇⣧⣼⣀⣼⣿⣿⣦⡄⢸⠀⢿⡄⠈⣿⣿⣧⠀⠀⠻⣿⣿⠃⠸⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠈⢹⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡆⠀⣇⠁⢸⣿⠿⠛⢹⠏⠙⢿⣿⣦⣼⠃⣴⣿⣿⣿⡄⠀⢠⡆⠀⠀⠀⣸⣿⣿⣿⠀⠀⢀⣤⣄⠀⠀⠀⠈⢿⣿⣤⣤⣾⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣧⠀⢿⣶⡟⢀⣀⠀⣾⠀⠀⢨⣿⡿⠃⢰⡟⣀⠈⢻⣿⣦⣸⣧⣀⣀⣴⣿⡟⢹⣿⠀⠀⢸⣿⣿⣧⠀⠀⠀⠈⠻⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣷⡾⠛⠀⡞⢻⢠⡏⠀⢠⣾⣿⣿⡄⢸⡇⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⣿⡆⠀⢸⣿⡏⣿⡀⠀⠀⠀⠀⠀⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢰⣼⠏⣸⡇⠀⡿⢡⡏⢻⡇⠸⣷⡿⢀⣾⠟⠙⠻⠿⣿⣿⣇⠀⠀⠀⢿⣧⠀⠀⠙⠁⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⣰⣿⠁⢰⣷⡿⠁⣸⡇⠀⠀⠀⢸⡟⣠⣦⠀⠀⣿⣿⣿⡆⠀⠀⠘⣿⣧⣀⢀⣰⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⠏⢸⠀⠘⠟⠁⠀⣿⠁⠀⠀⠀⣾⣷⣿⣿⡄⠀⣿⣿⣿⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⣿⡄⠀⠀⢀⣼⠃⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠘⠿⠃⠀⠀⠀⠀⣼⣿⠿⠛⠛⢻⣿⣷⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣴⣿⣧⠀⠀⠀⠀⠀⢹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡀⢀⣠⣼⠿⠿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⣿⡧⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⣿⡿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⢹⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡇⠀⢀⣠⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠁⠈⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⠀⠀⣀⡞⠁⠹⠤⢤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢺⢧⡯⣖⠚⠁⢠⠖⢲⡄⢈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣴⣾⣫⣖⡋⣹⣳⡆⠹⣤⡼⠃⢺ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡖⠛⣺⢽⣿⣯⣾⡿⠟⢁⡧⠀⢠⡦⠤⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣫⣽⠟⡥⠞⠁⢻⣶⠿⣿⣠⣾⠽⣫⢇⡞⢁⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡞⢀⡤⣾⠿⠿⣾⢻⢟⣡⣞⡵⣫⣾⡿⢢⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠘⠷⠋⠀⠓⠶⠞⠀⠈⢩⣚⢁⡞⢵⣙⣚⣡⠤⠖⠒⠒⠦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠶⠶⠒⠒⠒⠛⠦⣄⡀⠈⠉⠀⠀⣀⡤⠶⠒⠒⠲⡄⠀⢹⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣶⣯⢭⢉⡽⠀⢀⡤⢝⣡⣄⠀⠈⡇⠀⢀⡤⠴⠒⠚⠀⢸⠃⠀⢀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⡭⠗⣿⣋⣭⣽⣟⡭⢖⣫⠵⠚⠉⠀⣸⠀⢰⡧⣞⢽⣖⣒⢦⠀⠀⡟⣠⣾⡏⢁⣟⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠘⠒⠒⣒⠚⠋⣁⡴⠚⠉⠀⣀⣀⣀⡴⠃⠀⠁⡞⢱⠋⣠⠏⣸⠀⠀⣻⢟⡽⠁⠋⢉⣀⣀⣀⠈⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠒⠒⠦⣄⣀⣀⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣉⡽⢛⣩⠔⢋⣡⠴⢒⣚⣉⠉⠀⠀⠀⣀⣀⣀⣻⡽⠚⠁⢰⠏⢀⣶⠗⠋⣠⠴⠚⢉⣀⣀⠈⢳⠀⢻⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠛⠚⢁⣠⣤⣤⢤⣤⣄⠀⠉⠀⠀⠀⢀⡽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⢡⠴⠋⢠⠞⠉⠀⠛⠛⣋⡭⣤⠀⢀⡞⠁⣈⡭⠶⠚⠋⠉⠉⠀⠈⣠⠴⠋⢀⡴⢚⡉⠀⢈⡇⡼⠀⢸⢀⡼⢉⣴⢺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⡀⠀⠀⢾⡉⠀⠀⠀⢀⣠⠞⠁⠀⠠⡖⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢰⠋⠀⠀⠈⠓⠒⠚⠋⣉⡥⠞⣁⡴⣋⡴⣋⣥⡾⢭⠙⡆⠀⠀⢠⠞⠁⠀⣰⠋⡴⢹⣁⣠⢞⡴⠃⠀⠸⣏⣓⡿⢫⣞⡀⠀⠀⠀⠀⣠⠖⠋⠙⢳⡀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣸⠁⠀⠀⠀⠀⠉⣉⠉⠉⠉⠀⠀⠀⠀⠴⠧⠤⢤⣄⣀ ⠀⠀⠀⠀⢠⠖⠛⠉⠙⠓⠺⠀⠀⠀⠘⠲⠦⠤⠤⠴⠖⠒⣋⣡⠶⠚⠁⣼⠁⠸⠟⣁⡴⠋⢰⠃⠀⣰⠋⠀⠀⣰⠃⠘⣇⣀⣠⠴⢋⡠⠖⠲⣄⣀⣤⠄⢀⣰⠃⠀⠀⠀⡞⢡⢞⡽⠃⣸⠃⣀⡤⠖⠋⠁⠀⠀⠀⡀⠀⠀⠀⠒⢶⣒⣋⣩⡽⠓⠂⠀⣀⣀⠀⠀⢀⡀⠀⠀⠈⠑⣆ ⢀⡖⠒⠚⠛⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⣶⠒⠒⠚⠉⠁⠀⠀⠀⠀⠙⠒⣒⣋⣥⠤⠖⠋⠀⢠⣏⣠⠔⣲⢿⣀⣀⣀⣀⣤⡴⠛⡆⠀⠀⠀⢀⡏⠐⠯⠤⠤⠤⠤⠞⠁⠸⣼⠤⢞⡵⠚⠁⣀⡀⠀⣠⣶⠾⠯⣉⠙⠲⢤⡀⠀⠈⠉⢀⣠⠴⠒⠋⡽⣯⣱⠆⣸⠉⠙⠲⣄⠀⠘⡆ ⠈⠧⣀⠀⠀⠀⠸⣅⠀⠀⠀⠀⠙⡆⠀⠀⢴⣁⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠉⣁⡤⠤⠤⡀⠀⠀⠈⠋⢰⠋⠁⠀⠈⠉⢁⡴⢉⡤⠞⠁⣀⡤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢠⠴⠋⣹⠃⡼⡏⢠⣤⡀⢸⠀⢀⡴⠃⠀⠀⠀⢸⠀⠀⠀⠐⣇⣉⣁⣞⣁⡀⠀⠀⢸⠀⠈⡇⠀⡤⠖⠲⣄ ⠀⠀⠈⠉⢻⡀⠀⠈⠙⠒⠒⠒⠋⠀⠀⠀⠀⢸⠆⠀⠀⠀⣀⡴⠋⠁⠀⠖⠛⠛⢲⡄⠀⣧⠀⠀⠀⠀⠘⠦⣄⣀⣀⣀⡼⠀⠈⠉⠉⠉⠁⣀⡤⠴⠚⠉⣹⠋⣠⠴⠖⠒⣲⠀⠀⠀⠀⡇⠀⠀⡇⠀⢧⣧⣼⡽⢁⡞⣠⠏⢀⡴⢷⠀⠀⢸⠀⠀⠀⠀⢀⡽⠋⠉⠀⢹⠀⠀⣼⠀⠀⡧⠋⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣀⣠⠖⠒⠒⠒⠒⠋⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⢀⣠⠏⠀⢀⣸⠆⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀⠀⠀⢀⣠⠖⠋⠁⠀⠀⢠⠞⣠⡾⠋⢹⢀⡞⠁⣠⣤⠀⠀⢹⠀⠀⠳⣄⣀⣀⣁⡴⢋⡼⠁⣠⠋⠀⢸⠀⠀⣸⠀⠀⠀⢀⡏⣤⡀⠀⣠⠞⠀⣰⠃⠀⠀⠁⠀⠀⠀⠀⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣀⣀⣀⡤⠖⠋⠀⣠⠖⠋⠀⠀⠴⣖⠒⠒⠒⠒⠛⣩⠟⠁⣠⠖⠋⠀⠀⠀⠀⠀⠀⣾⠀⢧⡇⢀⡿⠃⣠⠞⠁⢸⠀⠀⢸⡇⠀⠀⠀⠉⠉⠀⢀⡞⠀⣰⠃⠀⠀⡏⠀⢠⠇⠀⠀⠀⡟⠀⣇⠉⠋⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⠞⠁⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠬⢶⠟⢀⡴⠁⠀⠀⢸⠀⠀⢸⠁⣀⣠⠤⠤⣤⣀⡞⠀⢰⠃⠀⠀⡞⠁⢀⡞⠀⠀⠀⠀⢷⠀⠘⠓⠚⠋⢁⡤⠖⠲⡄⠀⠀⢀⡴⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠴⠚⠉⠀⠀⠀⢠⠞⠁⣠⠎⠁⢀⡤⠞⠉⠉⠙⡆⠀⠀⠀⠀⠀⡴⠋⢠⠎⠀⣠⠴⠚⠛⠀⠀⠸⠋⠁⠀⠀⠀⠀⠈⠀⠀⢸⣀⡠⠎⠁⢀⡞⠀⠀⠀⠀⠀⠈⠣⢤⣤⠤⠖⠉⠀⠀⠀⠈⠛⠋⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⡴⠁⠀⡴⠋⠀⢀⣠⠀⣰⠃⠀⠀⠀⢀⡞⠀⣰⠋⠀⢸⡇⠀⠀⠀⠀⣀⡤⠴⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣸⠁⠀⢸⠁⠀⠀⠧⢤⣶⠛⢀⡴⠃⠀⠀⠀⢀⡞⠀⢰⠋⠀⢀⡤⠟⠂⠀⠀⢸⠁⠀⠀⠀⠀⠀⢈⠇⠀⠀⠀⠀⠀⣰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⠶⠏⠉⠉⠁⠀⠀⠈⠧⠤⠤⠖⠋⢀⡴⠋⠀⠀⠀⠀⠀⡞⠀⢀⡏⠀⠀⢾⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠴⠞⠉⠀⢀⡤⠤⠶⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⡴⠒⠲⢤⡀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⣸⠁⠀⠘⠧⣤⠤⠞⠃⠀⡤⣤⡤⠤⣄⠀⠀⠀⠀⠀⠀⢀⡸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠳⣄⡀⠀⣹⠆⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠈⠓⠶⠶⠶⠶⠒⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⢉⠉⠉⠀⠀⠲⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⡤⠤⠖⠚⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠦⣤⣤⠴⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⠀⠀⠀⣸⢿⡿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⢀⣿⠻⣿⠀⠀⢀⡿⢸⠁⢻⡄ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⠀⠸⣿⢠⣿⣿⣷⢸⡇⠀⢀⠈⣧ ⠀⠀⢀⣤⣄⢀⣼⣿⡿⠋⠁⠀⠹⣿⣆⣀⣠⣾⡟⠉⣿⠘⣧⠀⢸⠀⢹ ⠀⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣿⠏⠛⠛⣿⠃⢠⠟⠀⠹⢷⠏⠀⢸⡆ ⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢀⠀⢸⠃ ⠀⠀⢨⣿⣿⠏⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢺⣧⡟ ⠀⠀⣼⣿⡏⠀⠀⠀⠀⠿⣶⡿⠋⠀⠀⠀⠀⠀⣻⣦⡀⠀⠀⣀⡿⠋ ⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⣀⣴⣿⠿⠿⢿⣿⣏⠁ ⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⣴⡿⠋⠀⠀⠀⠀⠈⢿⣦ ⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⣿⣿⣧⠀⢀⣀⡀⠈⣿⡆ ⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠈⠿⠟⢠⡿⠉⠁⠀⢸⡇ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⢸⣿ ⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡿ ⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⣸⡇ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⢻⣷⡀⠀⢠⣿⡇ ⢸⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⢿⣿⣶⣿⣿ ⠸⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⠃ ⠀⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⡶⠶⠦⣤⣄⣀ ⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⡟⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀ ⠀⠀⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀ ⠀⠀⠸⣿⣿⡀⠀⠀⠀⣿⣿⣿⡿⠛⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁⣠⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇ ⠀⠀⠀⢻⣿⣧⠀⠀⠀⣿⣿⣿⠁⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⠀⠘⢿⡿⠋⢁⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁ ⠀⠀⠀⠈⢿⣿⣧⠀⠀⢸⣿⣟⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⢠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃ ⠀⠀⠀⠀⠈⢿⣿⣧⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁ ⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⢀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣼⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠙⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣴⣾⣿⡿⠋⠁⠀⠀⠀⠀⣀⣴⣾⣿⠿⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢀⣤⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠋⠁⠀⠀⠀⣀⣤⣶⣿⣿⠿⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣿⡏⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣶⣶⣦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡄⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢻⣿⡈⣿⣿⣤⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡿⠿⠟⠛⠛⠉⠙⠛⢿⣿⣿⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣶⣶⣤⣿⣿⣏⡉⠉⠉⣛⡛⠿⢶⣦⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⣸⣿⡇⠈⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣍⡉⠛⠻⢷⣤⣙⡻⢶⣤⣉⣻⣷⣄⠀⠀⠀⠀⠀⠀⠻⠏⠈⠙⢿⣿⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟⠋⠁⠀⠀⠀⣀⣤⣴⣶⣶⡆⠀⠀⣰⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣮⡙⠲⠦⣴⣦⣭⣛⠶⢮⣭⣛⠛⠋⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠈⣿⣿⣠⣶⠿⠿⠿⣷⡄⠀⢀⣴⣿⣿⠟⠋⠀⠀⠀⢀⣤⣶⡿⢟⣻⣿⣿⠟⢁⣠⡾⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣦⣄⠀⠉⠙⠛⠽⣗⣮⣍⡛⠳⣶⣤⣄⣀⢸⣿⠛⣿⣷⠀⠀⣸⣿⣛⣁⣀⡀⠀⣿⣇⣴⣿⣿⣿⠀⠀⠀⠀⣠⣾⠟⠋⠁⠰⠟⠛⣉⣤⣶⠟⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣄⠀⠀⠀⠀⠀⠉⠉⠓⠊⠙⠦⠉⠛⠿⣜⡿⠿⢶⣿⡿⣿⣿⣿⣿⣗⣼⣿⣿⣯⣵⡿⠋⠀⠀⠀⣾⣿⣷⣶⣴⣶⡶⠾⠟⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠿⠿⠿⠿⠛⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⣸⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣶⣶⣶⣿⡿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⠿⠿⠿⠿⠿⣶⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠁⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⣠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⢸⣿⣿⣿⠟⠉⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⠈⢿⡿⠃⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣶⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣠⣄⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣼⣿⠇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣟⣁⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢀⣿⣿⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠈⣿⣿⡄⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⢿⣿⣷⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠉⢻⣿⣿⣿ ⠀⣀⠀⠀⠀⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⡀⠀⣿⣿⡄⠘⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⢺⣿⣿⣷⣶⣼⣿⣿⡄⠀⠀⠀⢀⡀⠉⠛⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⢿⣿⡇⠀⠘⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇ ⠀⠻⣿⣯⠉⠛⠿⣿⣿⣧⣄⠀⠸⣿⣦⡀⠀⠉⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠙⢿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣸⣿⡟ ⠀⠀⠈⠻⣷⣄⠀⠀⠈⠛⢿⣷⣄⡈⠻⢿⣶⣄⣀⢙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡇⠀⠀⠀⣰⣿⡟ ⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⠀⠉⠛⢿⣦⣄⡙⠻⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⣀⣴⣶⣷⣶⡄⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⠃⠀⠀⣴⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⢿⣶⣤⡈⠛⢿⣶⣄⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠸⣿⣿⢀⣼⣿⡿⠿⠿⣿⣿⡄⠀⠀⢠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣤⣾⣿⡿⠛⢉⣤⣾⣿⠋⠀⢠⣾⣿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢯⣟⣿⣷⣄⡈⠛⠿⣷⣤⣀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠘⣿⡇⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⢀⣾⣿⣿⠟⠁⢀⣴⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢬⡻⢦⡀⠀⠙⠻⣷⣶⣤⡀⠀⢸⣿⠏⢻⣿⣿⠀⠀⠀⣿⣿⠋⠀⣀⡀⠀⠀⢠⣿⣇⣼⣿⣿⣿⣷⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠿⠟⠋⠀⣠⣴⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠿⣷⣄⡀⠻⣯⡙⠻⢷⣮⣿⡀⣾⣿⣿⢀⣠⣾⣿⣿⣾⣿⣿⣿⣆⠀⣸⣿⣿⣿⠿⢛⣿⡿⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠈⠻⠦⠀⠙⢿⣧⠙⠿⢿⠿⢟⣵⣿⣿⣿⣿⣿⣿⡟⣰⣿⣿⢿⣥⢠⣾⡟⠁⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⣶⣿⣿⠿⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣤⣶⠟⠋⠀⣿⣿⡿⢻⣿⣿⣿⠟⠁⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠛⠛⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠿⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣸⡟⣿⠻⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⠀⠀⠀⠀⣿⠀⠿⠀⠈⢳⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣾⡟⠉⢿⣧⣤⣤⠀⢹⡆⠀⠀⢄⠀⠹⡄ ⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣦⡀⠀⠘⠿⠂⢸⣿⡟⠻⣷⠈⢷⡄⠀⠈⡆⠀⠹⡄ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⠛⠛⠻⣿⣷⣄⣀⣀⣤⣿⣿⠀⠀⣹⠇⠈⠛⠷⠾⠃⠀⠀⢹⡄ ⠀⣀⡀⠀⢠⣿⣿⡿⠃⠀⠀⠀⠀⠈⢿⣿⠙⠛⠋⠉⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⠀⢈⡇ ⣾⣿⣿⣦⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣼⠃ ⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⣸⠟⠁ ⠈⠻⣿⣿⣿⠇⠀⠀⠀⠀⠀⡀⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⣀⣽⣿⣶⣦⣤⣖⠋⠁ ⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠛⠛⢁⣀⠀⠀⠀⠀⣠⣾⡿⠛⠋⠉⠉⠙⠻⢷⣦⡀ ⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡄⠀⣴⡿⠋⣀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆ ⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⣾⣿⣿⣿⣿⣷⡄⠀⢀⡴⠶⠀⠀⠀⢻⣧ ⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠁⠀⠈⠛⠛⠃⢀⣿⠁⠀⠀⠀⠀⠀⢿⡆ ⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠇⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠸⣿ ⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⣿⣷ ⠀⠀⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⣀⣰⣿⣿ ⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠏ ⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁ ⠀⠀⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⢀⣠⣀⣀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠘⣿⣿⢀⣾⣿⣿⣿⣷⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠁⠀⠀⠙⢿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⢿⣿⣿⣇⠀⠀⠀⠀⠀⠙⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠀⠈⢻⣿⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀⢻⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣀⠀⠙⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣄⡈⢿⣿⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣽⣿⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣷⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣶⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣶⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣶⣦⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣶⣦⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣶⣤⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣶⣦⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣶⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣦⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⢤⣤⣤⣤⣤⣤⣤⣴⣾⡿⠟⠋