Penguin Dot 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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⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⣠⡖⢳⡏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⣠⠆⠀⠀⠀⣰⣿⠁⠀⠀⠀⣠⠞⠃⣰⠋⡇⠀⠀⠀⠀⢀⡇⠸⣆⠀⠀⠀⠀⠙⣧⡀⠀⠈⠒⢦⡀⠀⢳⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⣴⡟⠀⠀⢀⡴⢋⡇⠀⠀⣠⠞⠁⢀⡾⠁⠀⢡⠀⠀⠀⠀⡾⣏⠀⣿⡙⠲⢤⡀⠀⢸⣿⢦⡀⠀⠘⣿⢦⣀⠱⢄⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀⣾⣿⠃⠀⢠⠞⠁⢸⠁⣠⠞⠁⠀⣠⢿⠀⢀⠀⠘⣆⠀⠀⢰⠃⣿⡄⠁⠛⢦⡀⠙⠳⣄⠻⡆⠙⢦⡀⠘⣖⣯⠓⢦⣁⠂⠘⢷⡒⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢇⠀⢠⡞⣽⢹⠀⣰⠋⠀⠀⣧⠞⠁⣀⣤⣶⡿⢿⡷⢾⣧⡀⠹⡀⠀⣾⠀⣿⢧⡄⠐⢦⡿⣶⣶⣪⣤⣹⡄⠀⠙⢦⡘⠯⠳⣖⠚⠛⠋⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⢸⢡⠏⠀⡇⠇⡼⠃⠀⠀⢀⣇⡴⠚⢉⣿⡟⠀⠀⣧⠈⣇⠀⠀⠻⡄⢻⠀⢿⠘⣧⠀⠀⠑⢌⠳⣄⠈⠙⢿⣤⠀⠀⠙⠒⠀⠈⠳⣄⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⡾⠈⠀⢸⠁⠈⠀⠀⠀⠀⣸⠁⠀⢀⣾⣿⡇⠀⢀⣸⣆⣸⡄⠀⠀⠙⠎⠀⠸⣧⢹⠀⠀⣀⣀⣀⡈⢷⡀⠘⡏⠻⡆⠀⠀⠀⠀⠀⠈⠓⠶⠦⣤⡤⠤⢀⠄⠀ ⠀⠀⠀⠀⠄⢀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⢀⣟⠀⣿⣷⣭⣭⣭⣿⡿⣿⣆⠀⠀⠀⠀⠀⡟⣯⣿⣿⣭⣶⣶⣿⣯⣿⣖⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀ ⠀⠀⠀⢸⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡟⢀⡾⢈⣿⠿⣿⣿⣏⢹⡿⡟⣿⡝⣦⡀⠀⠀⠀⢻⡘⣿⣿⢿⣿⣽⡇⢹⣿⣿⣾⣧⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⣄⣿⣿⣿⣼⡇⠀⠘⢧⡈⣷⣤⡀⠀⠘⡇⠘⠃⣴⣾⣿⣿⣼⡇⠹⣿⣯⡻⣗⠒⠲⣶⠖⠛⠉⠁⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⣿⠿⢿⠀⠀⣿⠛⢿⡿⢛⡇⠀⠀⣰⣇⣈⣙⣛⣶⣾⣹⡄⠀⣿⠛⢿⡟⢻⡇⠀⡿⢿⣿⣮⣷⣦⣸⡆⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⠀⠀⠀⢉⡁⠀⠀⣿⡿⠛⠛⠛⠻⣿⡉⠁⠀⣿⠀⠀⠀⣉⠁⠀⠀⣸⣿⠏⠈⡏⢹⡟⠲⡶⢶⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡄⠀⠀⠀⠀⢀⣿⣇⡀⠀⠀⠚⠓⠒⠒⠛⠁⣀⣼⡿⠀⠀⠀⠀⠀⢻⣧⣀⠀⠘⠓⠒⠶⠿⠂⢀⣼⡿⡟⠀⢠⣇⡿⠇⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠀⠀⢠⠁⠀⠀⠀⠀⠀⢻⡟⠿⠷⠶⠤⠤⠶⠶⠿⠿⠛⠋⠀⠀⢠⡆⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⢰⠀⣠⢟⡾⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡄⠀⠘⡆⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠚⣡⡾⠁⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⢤⡀⢳⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⡾⡟⠀⢀⡟⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⠀⠙⣾⡇⠀⠀⠀⠀⠀⢹⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠷⠶⠶⢶⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣇⡇⠀⡾⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡇⠀⢸⣿⠀⠀⢸⣿⡀⠀⠀⠀⠀⠻⡇⠙⣿⣦⡀⠀⠀⠀⠀⠀⣿⣥⠶⠶⠒⠶⠶⢴⣿⡏⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⣿⡇⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠄⠀⠸⣿⠀⢸⣿⡀⠀⠸⣿⣧⠀⠀⠀⠀⠀⢳⠀⢸⠙⠻⣦⣄⠀⠀⠀⠘⢧⡀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⣠⣴⠛⢹⠀⠀⠀⣿⡇⠀⣧⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢂⠀⢻⡆⢸⠀⡇⠀⠀⡇⣿⣇⠀⠀⠀⠀⠸⣆⡜⠀⠀⢨⡟⢷⣦⡀⠀⠀⠉⠙⠒⠛⠉⠁⠀⢀⣤⣶⡚⢿⠸⡇⠸⡇⠀⠀⢿⣇⠀⢸⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢄⠀⢻⡇⠀⡇⠀⠰⣇⠸⡞⣦⠀⠀⠀⠀⢿⡇⠀⠀⣼⠑⣦⡏⠻⣷⣄⡀⠀⠀⠀⢤⣶⣿⡿⢻⣿⠁⠈⡇⢻⡄⢷⠀⠀⢸⣸⠀⢸⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢆⢠⠻⣦⣇⠀⠀⣿⣄⢻⡾⣧⠀⠀⠀⠘⡷⠤⣴⡇⠀⠘⢧⡀⠈⠻⣿⣿⣶⣿⣿⡿⠋⢀⡼⠁⠀⠀⣧⣀⣳⣼⣆⣀⣼⠿⠞⠛⣧⣱⠀⡟⠲⢦⡀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠘⣧⡼⠋⣹⡇⠀⣿⠹⣎⡿⠋⢳⡄⠀⠈⢹⡀⠀⣧⠀⠀⠈⠙⢦⡀⠈⢻⣿⡿⠋⢀⡤⠟⢀⣶⠀⢀⡇⠀⠀⠉⣯⠁⠀⠀⠀⡼⢻⢸⡆⢱⡀⠀⢸⠆⠀⠀⠀⠀ ⠀⠀⠠⠀⠀⠈⢧⣠⠇⠇⠀⢸⣠⠞⠁⠀⣴⠟⣦⠀⠀⢻⡀⠸⠀⠀⠀⠀⠀⢉⣷⡄⠀⢀⡶⠋⠁⣴⣿⣿⡆⡾⠀⠀⠀⠀⠘⣧⠀⠀⢠⠇⠘⡄⢧⠈⠧⠤⠼⠀⠀⣇⡀⠀ ⠀⠀⢀⡤⠶⠦⠤⣄⢀⣠⠖⠋⠉⠳⢶⡚⠁⢠⠞⢳⣄⠀⢳⡀⡇⠀⠀⠀⠀⣸⠀⢧⠀⢸⠁⢸⡀⣿⣿⠟⣱⠃⠀⠀⠀⠀⠀⠘⣦⢀⡴⠒⠒⠣⢬⣵⣂⣀⡤⠖⡋⠉⠙⢦ ⠀⢸⠃⠀⡄⢀⡠⠞⠉⢀⣠⢶⣄⠀⠀⠹⣶⠋⣴⡿⢻⠷⣌⢷⣸⡀⠀⠀⢀⡇⠀⠘⣆⡼⠀⢨⡇⠻⠋⣰⢷⡀⠀⠀⠀⠀⠀⠀⣨⢏⡴⠉⠳⢤⣀⣀⣈⣉⣻⠀⠀⡀⠀⠀ ⠀⡴⠒⠺⡷⣼⣶⣶⣚⣯⠶⢯⣈⡳⣄⠀⢹⠟⠉⠀⣸⠀⠈⠻⣷⣷⡀⠀⣼⠻⣆⣀⣻⣇⣠⠟⣧⠀⣰⠋⠀⢷⡀⠀⠀⠀⠀⢀⡏⣸⠀⠀⠴⠶⠶⢶⡶⠾⣋⡴⠛⠉⠀⠀ ⠀⣇⠀⠀⠀⠀⠈⢻⣴⣏⡴⢫⡇⠀⣻⠀⠈⡇⠀⢰⠇⠀⠀⠀⠈⠛⢧⣴⢻⡶⠋⠀⠀⠈⠃⢤⡾⠶⠃⢀⡠⠄⠳⡀⠀⠀⠀⢸⠁⡇⠀⠀⠀⢸⡆⠸⣦⡞⠁⠀⠀⠀⠀⠀ ⠀⠿⣶⣤⣤⣤⡤⠞⠛⠉⠀⣼⠀⠀⣿⠀⠀⡇⢠⠏⠀⠀⠀⠀⠀⣄⠀⠀⠸⣇⠀⠀⠀⠀⠀⢸⡇⠀⣰⠋⠀⠀⠀⠙⢆⠀⠀⢸⡀⡇⠀⠀⠀⠘⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠏⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠸⡄⠀⢠⡀⠀⡞⠀⡴⠃⠀⠀⠀⠀⠀⠈⢳⡀⠈⢳⡁⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⡿⠀⠀⠀⠘⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢹⡄⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡃⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠻⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠂⠀⠄⠄⢀⠀⠀⡀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠒⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⣋⣉⠅⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠄⠀⣰⠓⠠⣮⢿⠋⡆⠀⢱⡔⠉⠙⢢⠀⠀⠤⢄⠘⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⢠⣞⣮⣮⣤⡁⠀⢞⣇⣠⣀⡈⠀⢠⠀⠀⢣⠀⠈⢢⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⢺⣞⣧⣼⣿⣾⣦⢾⣿⣿⣯⣿⣒⢤⠁⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠸⣷⠏⠀⠈⡹⠋⢿⡋⠁⠩⢙⡷⠋⠀⠀⠀⠀⠀⠀⠀⢇ ⠀⠀⠀⠀⣀⡇⠀⠀⠀⢹⠓⠒⡚⠄⠀⢀⠹⢂⠒⢻⠁⠀⠀⡀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠎⠀⣈⡳⣶⡍⣋⢆⠀⠙⢏⠹⠀⡈⠊⠀⢈⡆⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⢀⢴⣹⠀⣜⠑⠢⢜⡏⠁⠀⠑⠢⣀⠀⠀⠀⣀⡴⠋⢣⠀⠀⠀⢱⠀⠀⠀⠀⣄ ⣸⠱⣀⠄⢎⡱⠆⠈⣿⠄⠒⠠⠤⢄⣉⡖⢿⠯⠐⢂⠹⡄⠀⠀⢸⠒⠚⠒⠢⡏ ⠘⢫⡾⠓⠡⡁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠱⣈⡄⢀⡀⢶⠇⠀⢀⡜⠀⠀⢀⡀⠌ ⠀⠀⠑⢤⠀⠀⠀⢠⣌⠢⣤⠄⠀⠀⠀⠀⠀⠉⣀⣠⣞⣀⠴⠊⠀⢠⠞⠁⠀⠀ ⠀⠀⡎⡯⠤⢤⠒⠈⣾⠉⠀⠀⠀⢠⣶⣦⠀⣠⣤⡄⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀ ⠀⢀⢇⣇⠀⠀⣆⠠⠚⡧⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀ ⠀⠎⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡠⢺⢀⠞⠁⠀⠀⣿⠀⠀⠙⡌⡏⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠁⢸⡎⠀⠀⠀⠀⢸⠀⠀⠀⢱⣣⠀⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠽⡀⠀⠀⠀⠀ ⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠇⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⢀⠀⠀⢀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀ ⠀⢀⡠⠤⠒⠊⠉⠑⠲⢭⢯⡒⠨⠷⠦⠭⢶⡶⠶⠖⠒⠶⠾⣄⡀⠀⢀ ⢠⡏⣀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢀⡄⠙⣆⡞ ⠸⣧⡀⣠⠤⠄⠤⡀⠀⣠⠏⠀⠀⠀⠀⠈⢇⠀⠀⢀⡠⠤⣀⠀⠀⣸⣁ ⠀⡏⡎⠀⠀⠀⠀⣹⡞⠥⡤⠒⢒⣒⣒⣂⡠⠽⣶⠃⠀⠀⠀⠙⡶⡏⠁ ⠀⡇⠣⣀⡀⠀⠐⠁⠑⢤⣇⠀⠀⠁⠀⢸⢀⡤⠯⠣⠀⠀⠀⢀⠇⡇⠀ ⠀⢣⡀⠀⢳⠀⠀⠀⠀⠀⠐⠓⠒⢤⡐⠚⠋⠉⠀⠀⠀⢉⢻⡥⢠⠇⠀ ⢀⡠⠕⠂⣺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⢤⣤⠋⠀⠀ ⠉⠉⢉⡝⣁⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠲⢬⠽⠆⠀ ⠀⠀⢛⠞⠉⣈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⡆⠽⠆⠀ ⠀⢀⠯⢄⣼⢡⡷⠤⠤⠤⠀⠠⠤⠤⠤⠤⠤⡤⠤⠤⣠⡇⠀⣿⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠶⡶⢾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠿⠋⠁⠉⢀⠀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠃⠀⠀⢠⣴⠟⣿⣿⣿⡃⠀⠀⠀⢠⣄⠀⠀⣠⣴⠶⣦⣤⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠌⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⣀⠀⠀⠀⢀⣾⡿⠋⠁⠀⣾⡿⢡⡞⣽⠏⠈⣿⠀⠀⠀⠀⠙⣀⣼⠟⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢤⣤⣀⠀⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣾⡿⠁⠀⠀⢀⣿⢳⡟⢰⡟⠀⠀⣿⠀⠀⠀⠀⢀⣿⣃⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠸⠁⠀⠀⠙⢿⣆⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠂⠀⠀⣠⡿⠃⣾⠀⣸⣄⣀⡀⠉⠀⠀⠀⢠⡾⢻⣿⠀⠀⠀⠀⠀⠀⠠⠛⠀⠀⣷⡀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⢰⣿⣦⣴⣿⠟⠻⣷⡭⣟⢷⣄⠀⠈⠁⢀⣿⣿⣞⣛⣛⣛⡶⢦⣄⡀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠰⣿⡵⢨⢿⣿⡀⢀⣽⣷⣬⣷⡝⣧⣠⣀⣼⣯⢾⣿⣿⣯⣍⣙⠷⣽⡻⣦⣤⣀⠈⠓⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢹⡿⣿⣌⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣍⢻⣿⣾⣿⣿⣿⣿⣿⣷⣾⣿⡁⣦⣹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠯⠀⠀⠀⠀⢸⣧⢿⠙⢻⠟⠉⠀⠈⠉⠻⢿⣽⡿⠿⣿⣿⠿⠿⠍⠉⠻⠿⠿⣿⣿⣇⣶⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣿⡾⣷⠟⣠⢠⠆⠀⠀⣠⠞⠋⠀⠀⢿⡿⡀⠀⠀⠀⢲⡘⢦⢠⣿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠂⠀⠀⠀⠀⠀⠸⣿⡾⣦⣄⣈⣀⣀⣸⡅⠀⠀⠀⠀⠀⠑⢿⣲⠤⢄⣠⣥⣖⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠈⠉⠒⠛⠓⠉⠻⡄⠀⠀⠀⠀⢀⣠⠞⠉⢳⠏⠉⠁⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⢠⠾⠋⠙⠓⢦⣄⠀⠀⢀⣤⣴⣶⡸⣿⠀⠀⠀⠀⢸⣷⡶⠦⠤⣤⠖⠚⠉⠘⢇⠀⡼⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢠⠀⣀⢙⣷⣾⢿⣇⠀⠈⢿⠘⢷⡀⠀⠀⠈⠻⣷⡄⠀⠸⡄⠀⠀⠀⣸⠞⠁⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡤⡾⠁⠀⠀⣸⡿⠟⠋⠀⠘⣯⣾⣇⣠⡿⠀⠈⠻⣄⠀⠀⠀⠈⠛⠶⠤⠷⠤⠴⠛⠁⠀⠀⠀⠀⢀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣾⠋⢀⠇⠀⠀⣸⠋⠙⠓⠦⣄⣠⠾⢿⡏⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠏⠈⣧⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀ ⠀⣼⠋⣸⡴⠾⣄⣀⡴⠿⣄⠀⠀⠀⠀⠙⢦⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⠀⠀⠀⠀⠀⣀⣤⣾⡿⠋⠀⠀⠀⣻⡆⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⢸⡟⣶ ⠀⣿⠞⢧⠀⠀⠀⠀⣠⡴⠛⠳⢦⡤⠄⠀⠀⣿⣿⣇⣀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠉⠙⢿⡶⠾⣿⣿⣿⡉⣀⣤⢴⡖⠋⢹⣷⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⠶⠿⠿⠶⢶⣖⡀⡇⠘ ⣼⣏⣀⣈⣧⣤⠞⠉⠀⢻⡀⣰⠋⠙⠀⠀⠀⣿⣿⠋⠉⠀⠀⠀⠈⠉⠙⠛⠳⠶⠶⠶⢿⡆⠀⠹⡏⠉⠉⠀⠀⠀⢷⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠈⠹⢧⠀ ⠁⢿⣝⠳⠤⣍⣛⣒⡴⠞⢰⠃⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢻⡀⠀⠀⠀⠀⠈⢷⣀⣼⡇⠀⠀⠀⠀⡀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣ ⠀⠀⠉⠹⣟⠓⠋⠁⠀⠀⢾⡀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⢷⡀⠀⣀⣠⡤⠞⠋⣿⠁⠀⠀⠀⠀⢁⣾⠃⠀⠀⠀⠀⠀⢀⣠⡤⠤⠶⠄ ⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡇⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠁⠀⠀⣼⡏⠀⠀⠀⢀⣠⡟⠁⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⢦⡄⠀⠀⠀⠀⠀⠀⠀⢠⣷⣔⠈⠽⠶⣶⣶⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⡾⠛⠁⣀⣀⡴⠟⠉⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠶⣾⠇⠀⠀⠀⠀⠀⠀⣀⣸⣏⢹⣷⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠁⢸⣿⣀⣠⡤⠤⣴⠚⠋⠁⠀⢸⡎⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦⡀⠀⠀⢀⣠⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⡜⡇⠀⠀⠀⠘⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣄⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣄⠸⡇⠀⠀⠀⠀⠀⣇⠀⠀⣀⣴⠿⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠏⠙⠷⠿⣤⣀⣀⣀⣠⠼⠶⠚⠉⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⣀⣤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⠶⡏⣶⢎⡿⢻⡏⠶⢞⡇⠀⠀⠀⠀ ⠀⠀⣠⡾⠋⠁⠀⠀⠙⠐⠚⠁⠀⠛⠲⠛⠙⢷⡄⠀⠀ ⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⢠⢆⠀⠀⠀⠀⢠⢲⠀⠀⠀⢿⠀ ⢸⡀⠀⠀⠀⠀⠀⠀⠈⠢⡑⠤⢀⡠⢃⠎⠀⠀⠀⣬⠀ ⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠁⠀⠀⠀⣰⠏⠀ ⠀⠘⠵⣴⣆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡤⡾⠋⠀⠀ ⠀⣀⣠⡿⠉⠛⣳⣶⠶⠶⠾⣿⠶⠛⠋⠉⣹⣧⡀⠀⠀ ⠈⠫⣎⣷⠀⠋⡜⢳⠀⠀⠞⢫⣑⠂⠀⠐⠁⢃⣉⢠⠄ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠐⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⢤⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⠿⠛⠁⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣤⡴⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀ ⠀⠀⠀⠀⢀⣾⣿⣿⢿⣯⣭⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄ ⠀⠀⢀⣼⣿⣿⣷⠿⢿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣿⣿⠏⠀⠀⠉⠉⠉⠉⠉⠉ ⠀⠀⣼⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⢁⣿⣿⣿⣿⣯⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠿⣿⣿⠿⠿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⢏⡤⠶⢦⡀⠀⠀⣀⠤⣄⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠈⢉⡿⣿⣿⡿⢸⠁⠰⠀⢹⠀⢰⠃⣤⠀⢳⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡼⢠⠆⠙⠃⠈⠳⠤⠴⠋⠀⠸⣄⢀⣠⠞⢸⣿⡟⢰⠈⢻⣿⣿⣿ ⠀⠀⠀⠀⠀⡇⢿⡀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠈⠛⠃⠀⡗⠚⣿⣿⣿ ⠀⠀⠀⠀⠀⢳⡀⠳⣄⠀⠀⠀⠻⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡇⠀⠀ ⠀⠀⠀⣀⣀⠀⠣⡀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⡸⠁⠀⠀ ⠒⠒⠒⣣⢤⠇⠀⠙⢦⣄⠀⠈⠉⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⢀⣠⡞⠁⣏⠣⠤ ⠀⠀⣰⠋⣸⣦⣀⣀⣀⣈⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣷⣮⡳⣄ ⠀⢰⠓⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀ ⠀⢰⠟⠉⠛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠉⠀⠀⠈⣧⠀⠀⠀ ⠀⡿⠀⠀⠀⠀⠀⠈⠙⠶⠶⠖⠒⠒⠚⠒⠲⠛⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀ ⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀ ⢸⠇⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇ ⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀ ⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠞⠋⠀⠀ ⠀⠀⠀⠀⠈⠉⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀