⣿⠋⣛ ⣩⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭ ⡿⠀⣿ ⣶⣿⣿⣿⣿⢿⣿⣿⣿⢿⡛⠛⠛⠛⣿⣿⣿⣿⣿⣷⣖ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠛⠋⣹⣷⣾⣿⣵⣶⣿⣿⣷⣶⣌⣉⣙⣻⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣴⣶⣿⡿⠟⠉⠉⠉⠉⠉⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⣀⣀⣀⠀⠀⠀⢠⣤⡶⠶⠤⠀⠀⠀⠀⠀⠀⣹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠈⢉⣉⣉⣀⠀⠀⣀⣤⣤⣶⣦⣤⣤⠤⠀⠀⣴⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢁⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠞⣻⣯⡽⠟⠀⢰⣦⠉⠚⠛⠁⠀⠀⢘⣰⣺⣿⣯⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⣠⣼⣿⣽⣿⠟⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣀⡀⠀⢸⡿⢦⣄⠀⠀⠀⠀⠸⡿⢻⣯⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⣠⣿⣿⢫⣿⣿⣦⣄⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣼⠟⠦⢤⣶⡶⠟⠉⢷⡀⠀⠠⠆⠀⡎⢟⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⣰⡟⣋⡀⠈⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢿⣤⣤⡶⠶⠶⣶⣶⡿⠃⠀⠀⠀⢠⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⣠⣾⣿⡷⠞⡟⠁⣹⣿⣿⠀⠀⠀⠀⠸⣿⣿⣷⡀⠀⠀⠉⢻⡟⠒⠛⢉⠉⠀⠀⢀⡀⢀⣼⠃⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡏⠀⠈⣽⣿⠁⠀⠀⠁⣰⣿⡿⠃⠀⠀⠀⠀⠀⢹⣿⣿⣷⣄⠀⠀⠨⠿⠶⠿⠿⠟⠀⠀⡾⠀⠿⠋⢠⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⢻⣿⠀⠀⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⣀⣤⡾⠁⠀⢠⣶⣿⠿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠉⠀⢠⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣛⠻⠿⠛⠋⠁⢀⣠⣾⡿⠋⠁⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠇⠀⠓⠶⠶⣿⣾⣿⡿⠛⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣾⣿⡿⠿⣿⣿⠿⠿⣿⣾⠿⠛⠉⠀⠀⠀⣠⣾⠏⠉⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡀⠀⠀⢀⣾⣿⣿⠋⠁⠀⣠⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠈⠛⢳⣦⣠⣿⣿⣿⡿⠀⢙⣾⣿⠛⠛⠛⠛⠉⠉⠁⠀⠀⢀⣼⠟⠋⠀⠀⢠⣿⣿⣿⣿⣷⡀⠀⠀⢀⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⡠⣀⣼⣿⠿⠛⣻⣿⣇⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣤⣀⣠⣿⠟⠙⠿⣿⣿⣿⣶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⢠⢡⣧⣿⡁⠀⠐⣿⣿⣿⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⠟⠋⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣁⣠⣼⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠴⣾⣸⡏⡀⠂⠈⠻⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⠉⢀⡤⢹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⢁⣿⣤⣤⠞⠋⣀⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠧⡀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠉⢛⠛⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢉⣠⣶⠖⠋⠀⠈⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣠⣾⣿⠛⠁⠀⠀⣿⠀⠀⠀⠀⠀⣠⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣴⠿⠉⠀⠀⠀⠀⠀⠸⣿⣇⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⣿⣿⡇⠀⢠⣾⠿⠋⠀⠀⠀⡠⠀⢹⡇⠀⠀⢰⣾⡿⠿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⣿⣿⠁⠀⣉⣁⣤⣴⠆⣠⡾⠁⠀⢸⡇⠀⢀⣾⣿⣄⠀⠀⠀⠉⠉⠉⠙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⣿⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡄⠀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⢰⣿⣿⣆⣾⠏⠙⠋⣠⣾⣿⢀⠆⢀⢸⡇⠀⠸⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⠋⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀ ⡇⠀⣿⠀⠀⠀⠀⣿⣿⣿⣷⣄⣴⣾⣿⠋⣱⣿⠟⡎⣸⣧⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠀⠀⠀⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡀⠀⠀⠀ ⡇⢀⡿⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠛⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠂⠘⣿⣿⣷⡀⠀⠀