Năm Thường Bắt Đầu Vào Thứ Bảy Emojis & Text

⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣤⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿ ⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠙⠿⠿⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿

⠸⣷⣦⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠀⠀⠀ ⠀⠙⣿⡄⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⣿⡿⠁⠀⠀⠀ ⠀⠀⠈⠣⡀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⣰⠟⠀⠀⠀⣀⣀ ⠀⠀⠀⠀⠈⠢⣄⠀⡈⠒⠊⠉⠁⠀⠈⠉⠑⠚⠀⠀⣀⠔⢊⣠⠤⠒⠊⠉⠀⡜ ⠀⠀⠀⠀⠀⠀⠀⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡔⠊⠁⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⡇⢠⡤⢄⠀⠀⠀⠀⠀⡠⢤⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⠀⠀⠀⠀⠀⢀⠇⠹⠿⠟⠀⠀⠤⠀⠀⠻⠿⠟⠀⣇⠀⠀⡀⠠⠄⠒⠊⠁⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠰⠤⠖⠦⠴⠀⢀⣶⣿⣿⠀⠙⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠛⢄⠀⠀⠱⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠈⠓⠦⠀⣀⣀⣀⠀⡠⠴⠊⠹⡞⣁⠤⠒⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⡌⠉⠉⡤⠀⠀⠀⠀⢻⠿⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⠁⡀⠀⠀⠀⠀⢸⠀⢰⠃⠀⠀⠀⢠⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢶⣗⠧⡀⢳⠀⠀⠀⠀⢸⣀⣸⠀⠀⠀⢀⡜⠀⣸⢤⣶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣦⣈⣧⡀⠀⠀⢸⣿⣿⠀⠀⢀⣼⡀⣨⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⠿⠿⠓⠄⠤⠘⠉⠙⠤⢀⠾⠿⣿⠟⠋

⢰⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⡏⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀ ⠀⠀⢹⣿⡇⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⢾⣿⣿⣿⡟ ⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠋⠁⠀⠀⣸⣿⣿⡟⠀ ⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣠⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣶⣦⡀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⣯⣀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣬⣿⡇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠻⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⡾⠋⠉⠉⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠉⠛⢶⡄⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣇⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢀⣠⠤⠴⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⡇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠉⠳⠶⠶⠞⠁⠀⠀⠀⠀⠀⠀⢾⡅⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠙⠷⢦⡤⠴⠛⠁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣠⣠⣠⣠⣠⣀⣀⣀⣀⣀⣀⣄⣄⣄⣄⣄⣠⣀⣀⣀⣀⣠⣠⣠⣠⣠⣠⣀⣀⣀⣀⣀⣼⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀

⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⠀⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⠀⠀⠀⠈⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀ ⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⣶⣿⣿⣿⠃ ⠀⠀⠀⠹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠞⠛⠉⠁⠀⠀⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠤⢤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣴⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⣼⡏⣹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢶⣶⡄⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⢠⣴⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⡀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠈⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⠉⠙⠻⣦⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠛⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⡟⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⡇⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢲⣾⣿⣿⠃ ⠀⠀⠈⢿⡀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠀⠀⢸⣿⡿⠃⠀ ⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠛⠉⠉⠉⠉⠉⠉⠉⠑⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢸⣀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣨⣿⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠘⠿⠛⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⢃⡤⠖⠒⢦⡀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⡀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢸⡀⠀⠀⢀⡗⠀⠀⠀⠀⢀⣠⠤⠤⢤⡀⠀⠀⠀⠀⢸⡁⠀⠀⠀⣹⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡀⠙⠒⠒⠋⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠙⠲⠴⠚⠁⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠾⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠦⠤⠤⠤⠤⠤⠤⠤⠼⠇⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣤⡤⠤⠤⠤⢀⣀⡤⠒⠂⠈⠉⠁⠒⢡⡀⡔⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠛⠿⢦⡀⠀⠀⠀⢀⢄⡀⠀⠀⠀⢠⣲⡙⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠖⠀⠸⠾⠃⠀⠠⠄⠈⠋⠁⡵⣠⠤⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⣐⡀⠔⠉⢢⠀⠢⠔⠳⡆⠁⠀⢄⠇⢀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⡀⠈⠑⢌⠒⠊⠀⠀⠁⠈⠀⠀⡠⠊⠀⡘⠀⠀⠀⠀⠀ ⡖⠒⠢⠤⠤⠤⠤⢵⡀⠀⠀⠑⠀⠀⠀⠂⠒⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠠⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⣀⡀⠀⣠⡣⡆⡘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠉⠉⠁⠀⡆⠀⣩⠠⡗⡇⣸⠟⢣⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠓⠉⢸⡰⣧⠽⡈⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⠴⢜⣀⠀⠤⢄⣀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠆⠀⠠⡤⠄⠤⣦⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠊⠉⠉⠀⠀⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡠⠼⠴⠒⠒⠒⠒⠦⠤⠤⣄⣀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠔⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡤⠤⢴ ⠀⠀⠀⠀⠀⠀⣸⠁⣾⣿⣀⣽⡆⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⢿⣦⠀⠀⠀⢸⡀⠀⠀⢀⣠⠤⠔⠒⠋⠉⠉⠀⠀⠀⠀⢀⡞ ⠀⠀⠀⠀⠀⢀⡏⠀⠹⠿⠿⠟⠁⠀⠰⠦⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⢘⡧⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀ ⠀⠀⠀⠀⠀⣼⠦⣄⠀⠀⢠⣀⣀⣴⠟⠶⣄⡀⠀⠀⡀⠀⠉⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀ ⠀⠀⠀⠀⢰⡇⠀⠈⡇⠀⠀⠸⡾⠁⠀⠀⠀⠉⠉⡏⠀⠀⠀⣠⠖⠉⠓⢤⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⢧⣀⡼⠃⠀⠀⠀⢧⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣧⠀⠀⠀⣸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢠⠏⠀⠀⠀⠀⠈⠳⠤⠖⠃⡟⠀⠀⠀⢾⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠈⠦⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠙⢦⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡇⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠸⡇⠈⢳⡀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⣀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣷⠴⠚⠁⠀⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⢷⡆⠀⣠⡴⠧⣄⣇⠀⠀⠀⠀⠀⠀⠀⢲⠀⡟⠀⠀⠀⠀⠀⠀⠀⢀⡇⣠⣽⢦⣄⢀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣼⣽⡞⠁⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠈⣷⠃⠀⠀⠀⠀⠀⠀⠀⣼⠉⠁⠀⠀⢠⢟⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠉⠁⢳⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠏⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⡆⠀⠈⡇⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⡀⠀⠙⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢀⡄⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⡀⣰⣀⣀⣀⠀⠀⠀⠘⣦⣀⠀⠀⠀⡇⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⢸⡇⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠀⠀⠈⠉⠉⠉⠙⠻⠿⠾⠾⠻⠓⢦⠦⡶⡶⠿⠛⠛⠓⠒⠒⠚⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢰⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿ ⠀⠘⢿⣿⣿⣿⣿⣦⣀⣀⣀⣄⣀⣀⣠⣀⣤⣶⣿⣿⣿⣿⣿⠇ ⠀⠀⠈⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⡏⠆⢹⣿⣿⣿⣿⣿⣿⠒⠈⣿⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣷⣶⣿⣿⣛⣻⣿⣿⣿⣶⣾⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⡁⠀⠈⣿⣿⣿⣿⢟⣛⡻⣿⣿⣿⣟⠀⠀⠈⣿⡇⠀⠀ ⠀⠀⠀⢿⣶⣿⣿⣿⣿⣿⡻⣿⡿⣿⣿⣿⣿⣶⣶⣾⣿⣿⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀

⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠒⣶⣶⡶⠂⠀ ⠀⠀⠀⠀⢸⢀⠠⠔⠒⠒⠒⠒⠂⠤⣀⠤⠒⠉⠀⠀⠀⢀⡠⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⠠⠐⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢃⣖⢢⠀⠀⠀⠀⠀⣠⢤⣄⠀⠈⡄⠀⠀⣀⠠⠄⠀⠒⠒⠀⠇ ⠀⠀⠀⡜⠈⠛⠛⠀⣐⠂⠀⠀⠻⠿⠏⠀⠀⡗⠊⠁⠀⠀⠀⠀⠀⠀⡜⠀ ⠀⠀⢰⠉⢱⠀⠱⠞⠁⠉⠒⡖⠀⢀⠔⠢⡄⡇⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀ ⠀⠀⠀⢶⠊⠀⠀⢣⠀⠀⢠⠃⠀⠘⢄⣀⢾⠃⠀⡤⠤⠤⠤⠤⠔⠀⠀⠀ ⠀⠀⠀⠀⢱⢄⠀⠀⠢⠔⠃⠀⠀⠀⠀⢀⢎⢢⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣌⠀⠁⠂⠀⠀⠀⠀⠀⠐⠈⠁⢸⡤⠓⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⣄⡀⠀⣰⢸⠀⠀⠀⠀⢀⢀⠂⠀⠀⠀⠀⠄⢳⡈⢁⡀⠀⠀⠀⠀⠀⠀⠀ ⢿⣷⠁⠀⠈⡄⠀⠀⠀⠈⡞⠀⠀⠀⠀⡰⠉⠀⢈⠻⠿⠀⠀⠀⠀⠀⠀⠀ ⡇⠈⡆⠀⠀⠱⡀⠀⠀⠀⡇⠀⠀⠀⢠⠁⠀⠀⠈⢀⠇⠀⠀⠀⠀⠀⠀⠀ ⠘⡄⢀⠀⠀⠀⠱⡀⠀⠀⠁⠀⠀⡠⠁⠀⠀⢰⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠉⠀⠐⠛⠶⠒⠣⠦⠤⠗⠒⠒⠒⠚⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⡴⠑⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡇⠀⠿⡀⠀⠀⠀⣀⡴⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⢄⣠⠾⠁⣀⣄⡈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠁⠀⠀⠈⠙⠛⠂⠈⣿⣿⣿⣿⣿⠿⡿⢿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⣁⣀⠀⠴⠂⠙⣗⡀⠀⢻⣿⣿⠭⢤⣴⣦⣤⣹⠀⠀⠀⢀⢴⣶⣆ ⠀⠀⢀⣾⣿⣿⣿⣷⣮⣽⣾⣿⣥⣴⣿⣿⡿⢂⠔⢚⡿⢿⣿⣦⣴⣾⠁⠸⣼⡿ ⠀⢀⡞⠁⠙⠻⠿⠟⠉⠀⠛⢹⣿⣿⣿⣿⣿⣌⢤⣼⣿⣾⣿⡟⠉⠀⠀⠀⠀⠀ ⠀⣾⣷⣶⠇⠀⠀⣤⣄⣀⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠉⠈⠉⠀⠀⢦⡈⢻⣿⣿⣿⣶⣶⣶⣶⣤⣽⡹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠲⣽⡻⢿⣿⣿⣿⣿⣿⣿⣷⣜⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣮⣭⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠛⠻⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠈⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠘⡇⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⢤⡿⠉⠙⣦⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⢻⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠁⠀⠁⠀⠀⢸⠀⠀⢰⣿⡿⢟⡿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣆⠀⠀⠀⠀⣿⠀⠀⡟⠋⠀⢸⠃⢀⣠⠴⢺⡇⢀⠔⠋⢹⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠶⣄⡘⣿⠀⢸⡇⠀⢀⡿⠚⠉⠀⠀⣼⡷⠁⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⣸⡇⠀⣼⠗⣺⡉⠉⠙⠻⢤⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣇⣄⠀⠘⠉⠙⠂⢀⡂⠉⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠈⣻⣄⡀⠀ ⠀⠀⡀⠀⠀⠀⢀⡜⠁⠀⣴⠋⠘⣿⣿⡆⢸⣿⣿⣿⡆⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⢹⡆ ⠀⠘⠿⢭⣽⣶⠘⠢⡀⠀⣿⠀⠀⠘⡿⠃⠈⣿⣿⣿⠇⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣀⡼⠃ ⠀⠀⣤⣖⣻⡿⠀⠀⠈⠢⣿⠀⠀⠀⣷⠀⠀⢻⣿⡟⠀⠀⣰⠷⠶⠒⢶⡄⠀⠀⠀⠀⠛⠛⠛⠋⠉⠀⠀ ⠀⠀⠉⠉⠁⠀⠀⠀⠀⢀⠿⡄⠀⠀⣹⠀⠀⠀⠉⠀⣠⠔⠁⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣄⣠⠖⠒⣦⠀⢴⣃⠀⢷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⠀⠋⠀⠀⢸⡇⠀⠈⠙⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣀⣀⠤⣶⠀⠀⢰⣿⣽⠭⠿⠀⠀⠀⠀ ⢿⡀⠀⠀⠀⢀⡾⠃⠀⢠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡿⠀⠀⠈⠻⣭⣲⡄⠀⠀⠀⠀ ⠈⠳⣄⡀⠀⡾⠁⠀⠀⠈⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⡼⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⣀⣀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠊⠉⠀⢀⠴⠊⠉⠋⠙⢿⡖⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⣾⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⢀⣴⢿⠁⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢸⣿⠀⢀⡴⠋⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢾⣧⣘⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⣿⠖⠁⠀⠀⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀ ⠀⠀⠀⣀⣤⣶⠟⠋⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣶⣿⠤⠖⠚⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀ ⠀⢠⣾⣟⠁⠃⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⣶⡶⢿⠉⠉⠀⠈⢆⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⠙⣿⢿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡖⣻⡟⠀⢸⠀⠀⠀⠀⠈⡆⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣨⠇ ⠀⠀⠀⢹⡀⠀⠉⠉⡿⠲⣶⠒⠒⠒⣿⡏⠉⠁⠀⠀⠉⢉⡴⠒⢺⠀⠀⠀⠀⠀⢹⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⣬⠃⠀ ⠀⠀⠀⠀⠳⡀⠀⠀⢧⠀⡾⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠸⣦⣀⣸⡇⠀⠀⠀⠀⠈⡆⠀⣰⣿⡇⠀⠀⠀⠀⢀⡴⠁⠀⠀ ⠀⠀⠀⠀⠀⠱⡀⠀⠈⢯⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠛⠛⢳⠀⠀⠀⠀⠀⣷⣴⣿⣿⡇⠀⠀⠀⢀⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣱⡀⠀⠀⠑⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣿⠛⠿⣿⡇⠀⠀⢠⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⢦⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣹⠀⠀⠈⠁⠀⢠⠎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠁⠀⢙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢦⡀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⡀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣴⣿⣷⠾⠃⠀⠀⠀⠀⠀⠀⠀ ⡼⠟⠳⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⢁⣀⡀⢀⣀⡀⠀⠀⠀⠀ ⡇⠀⡀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠟⠳⡀⠀⠀⠀⠀⠀⠀⢸⣤⡞⠉⠀⠀⠰⡟⠙⠳⣄⠀⠀ ⢹⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢳⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⠀⠹⣄⠀⢹⣇⠀ ⠘⡆⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⣠⣾⣿⣿⠇⠀⠀⠀⠀⢀⠈⠙⣿⣿⠀ ⠀⠸⡄⢹⠆⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠤⠊⢁⠟⣿⢿⣦⣀⣀⣾⣿⠟⣧⣴⠿⡯⠀ ⠀⠀⠉⠉⠳⢄⡙⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢸⠀⢀⡠⠊⠀⠘⢦⣢⡈⠉⠻⢿⠿⠋⢀⠔⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠶⠒⠒⠒⠈⠉⠉⠉⠉⠉⠉⠒⠒⠪⠷⠒⠛⠊⠉⠀⠠⠄⠀⠤⣌⠛⠳⠦⠤⠴⠒⠁⠀⠀⠀

⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⡗⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄ ⠀⢻⣇⠀⠈⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⣹⣿⡿ ⠀⠀⠹⣆⠀⠀⠀⠀⠙⢷⣄⣀⣀⣀⣤⣤⣤⣄⣀⣴⠞⠋⠉⠀⠀⠀⢀⣿⡟⠁ ⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀ ⠀⠀⠀⠀⠈⠻⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠃⠀⢠⠒⣆⠀⠀⠀⠀⠀⠀⢠⢲⣄⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡏⠀⠀⠈⠛⠋⠀⢀⣀⡀⠀⠀⠘⠛⠃⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡟⠛⢳⠀⠀⠀⠀⠀⣉⣀⠀⠀⠀⠀⣰⢛⠙⣶⠀⢹⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡗⠛⠋⠀⠀⠀⠀⣾⠋⠀⢱⠀⠀⠀⠘⠲⠗⠋⠀⠈⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠿⠋⢀⣀⣀⣀⣀⣤⣤⣶⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⢋⣉⣁⣉⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⠉⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⣽⣿⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣤⠈⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⣀⠙⣿⣿⣿⣿⣿⣿⠀⠸⣿⣷⣿⣿⠟⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀ ⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⢸⣿⣧⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⠟⠉⣀⣤⣤⣶⠶⠿⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠛⠿⣷⡄ ⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣶⣤⣭⣭⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠙⠿⣿⣿⣿⣿⡿⠟⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀ ⠘⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⠟⠋⠁⣀⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣷⣦⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀ ⠀⠀⠉⠛⠿⠷⣶⣶⣶⣶⡶⠿⠟⠛⠉⠁⠀⠀⢠⣾⣿⡿⠟⠛⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⣤⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣷⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⢿⣿⣿⣿⣿⣿⣷⡄⠹⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠿⣦⡙⢿⣿⣿⣿⣿⣿⣦⡄⠙⠛⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣤⣄⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠈⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⣿⣿⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠻⠿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀

⢻⣶⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀ ⠀⢻⡀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⣿⡟ ⠀⠀⠣⡀⠀⠀⠀⠑⢄⢀⣀⣀⣀⣀⣀⣀⠤⠒⠉⠀⠀⠀⢠⠟⠀ ⠀⠀⠀⠑⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀ ⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢤⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⡘⠀⠀⢮⣽⠀⠀⠀⠀⠀⠰⣭⡇⠀⠀⠈⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⢃⠠⢄⠈⠁⠀⠰⠶⠀⠀⠀⠈⠀⡀⣀⠀⠸⡀⠀⠀⠀ ⠀⠀⠀⢸⠠⣀⣠⠇⠀⠀⡠⠐⠒⡄⠀⠀⠨⡀⢀⠅⠀⡇⠀⠀⠀ ⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠘⠤⠠⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀ ⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠰⠀⠀⠀

⢸⣿⠀⢸⣦⠀⠀⠀⠀⠀⣀⡧⠄⠒⠒⠒⠉⠉⠉⠑⠒⠂⠤⢄⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⡆ ⢸⣿⣇⣸⣿⣧⡒⣤⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⠗⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙ ⢸⣿⠉⠉⠉⠉⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴ ⠘⢿⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣝⣷⠒⠒⠒⠒⠒⠒⠒⠒⠋⠉ ⠀⠈⠀⠀⠀⡇⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠀⠀⣤⣿⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢶⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠀⠀⡼⠀⠀⠀⠻⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣾⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⢸⠀⢰⠗⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠸⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠸⡆⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀⡧⣀⠀⠉⠓⠢⢤⣀⠀⠀⢰ ⢸⣿⠀⠀⠹⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢠⡟⠀⠀⠈⠑⠒⠤⣀⠀⠉⠓⠲ ⢸⣿⠀⠀⠀⠙⣾⡁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄ ⢸⣿⠀⠀⠀⡰⠁⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠔⠁⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⢀⠇⠀⠀⠀⠀⠈⠓⠢⢤⣀⣀⣀⣀⣀⣀⣀⣠⡤⠖⠋⠀⠀⠀⢸⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢣⠉⠓⠤⢄⡠⠔⢊⠕⠀⠀⠀⠀⠀⠀⠘⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⢸⣦⢄⡀⠀⠀⠀ ⢸⡟⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⡀⠀⠀⢸⠹⡆⠈⠓⢤⡀ ⢸⡇⠀⠀⡜⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣇⣇⠀⠀⢸⠀⠀⠀⠀⠀⠉ ⣸⡇⠀⢠⡇⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡇⠀⢹⡛⠀⠀⢸⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠘⣿⣶⡖⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⣶⣿⠟ ⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⠀⠈⠳⠤⠔⠒⠉⠉⠉⠑⠒⠤⠔⠉⠀⠀⢀⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠁⠀⠀⠀ ⢋⠒⠒⠤⠤⣀⣀⠀⠀⠀⠀⡘⢀⣤⢀⠀⠀⠀⠀⠀⢀⣤⣀⠈⡄⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠉⠉⠒⢲⠇⠈⠛⠛⠀⠀⢀⠀⠀⠈⠛⠋⠀⢃⠀⠀⠀⠀⠀ ⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡇⠀⠠⢠⠤⡄⠀⠀⢠⣾⣷⢸⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⠉⢹⠂⠀⢀⠎⢆⠉⠀⠀⠀⠈⠂⠁⠀⠀⠀⠉⢉⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⢠⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠃⠀⠀⠣⢄⡸⢠⠀⠀⠀⢣⠀⠀⠀⢀⠄⠀⠀⢠⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠒⠢⠤⣀⠀⠇⠀⠣⡀⠀⠀⢆⠀⠀⢸⠀⠀⢀⠞⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⢅⣸⠀⠀⠀⠙⢤⠴⠚⠂⠀⢮⣤⣤⠎⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⠂⢤⠤⠤⠤⠤⢤⡤⠤⢤⡊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠒⠁⠀⠀⠀⠀⠀⠈⠒⢤⣷⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡿⠟⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶ ⡍⢳⣤⣀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡏ ⠙⠻⢦⣈⡛⡦⣄⡀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠙⠻⣿⡟⠀ ⣄⠀⠀⠈⠙⠲⢬⣛⠲⣤⣀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣷⠤⠤⠤⠤⢤⣀⣀⠀⣠⠞⠁⢀⠄⠀⠀⡜⠁⠀ ⠈⠙⠦⣄⡀⠀⠀⠉⠓⠶⣍⡓⢦⣄⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠸⣵⠄⠀⢀⡰⠄⠀⠀⠀⠀⠀⠀⠉⠛⢣⣤⠔⠉⠀⠀⡾⠁⠀⠀ ⣦⣀⠀⠀⠉⠒⢦⣀⠀⠀⠈⠉⠳⢮⣛⡶⣄⡈⠓⢦⣀⠀⠀⠀⢀⡾⠁⠀⣰⣿⣿⠆⠀⠀⠀⠀⠀⣴⣶⣤⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀ ⢷⣽⡛⠶⣄⣀⠀⠀⠙⠲⢤⣀⠀⠀⠈⠛⠲⢿⣳⢦⣈⠙⢦⣴⠋⠀⠀⣀⠘⠋⠁⠰⠖⢧⡄⠀⠀⠻⣿⠿⠃⠀⠀⠀⠿⣄⠀⠀⠀⠀ ⠀⠈⠙⠳⠦⣍⡛⠦⣄⣀⠀⠈⠓⠦⣄⡀⠀⠀⠉⠛⠯⣿⣾⠃⠀⢰⠋⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠘⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠒⢤⣍⡛⠦⣤⣀⣴⠟⠲⢤⣀⠀⠀⠈⢹⠀⠀⠘⠷⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣞⣉⣈⣷⠀⠀⠀⠀⠀⢹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣍⡛⠶⣤⣄⠈⢹⣦⣄⡘⣆⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠙⠳⠟⠋⠀⠀⠀⠀⠀⠀⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠶⣍⡻⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠯⣿⣿⣷⣿⣟⡿⠶⢤⣀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠯⣍⡛⠲⢤⣍⠛⠦⣄⡀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠉⠓⠦⣍⡛⠶⣭⣉⠓⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠓⠦⣍⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⢄⣀⡀⠉⠀⢀⣀⣤⡤⢶⡒⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⢱⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠠⣏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠈⠂⠄⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢈⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠖⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀

⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡣⣀⣀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣜⣀⠈⠁⠈⠇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢹⠉⠓⠠⠤ ⠀⠀⠀⠀⡀⠀⠀⢰⠁⠈⡆⠀⠀⠀⠀⡙⠀⠀⠀⠛⠉⠳⠄⠀⠀⠸⠀⠀⠀⠀ ⠀⠀⠀⡰⢛⠒⠤⡸⡄⣠⠃⠀⠀⢹⠟⠳⢤⡠⠂⠀⢀⠤⠤⣄⠀⡄⠀⠀⢰⠂ ⠀⠀⠀⠷⠉⠁⠀⠈⢫⠁⠀⠀⠀⠘⠀⠀⡜⠀⠀⢠⡇⠀⠀⢸⢠⠁⠀⠀⠀⠀ ⠀⠀⠀⠸⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠧⠜⠀⠀⠀⠀⠳⣈⡠⢞⠂⠀⠀⠀⠀⡄ ⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠈⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⢄⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠈⢆⠀⠀⢠⠀⠀⠀⠈⠪⠭⠕⠂⠀⠀⠀⠀⢀⡀⠤⠄⠈⠲⡒⠒⠃ ⠀⠀⠀⠀⠀⠈⢷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠈⢆⢀ ⠀⠀⠀⠀⠀⠉⠈⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡦⡀⠀⠀⠀⠀⢸⠀ ⡇⢀⣔⣀⣀⠀⠀⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡮⣑⡢⢤⣴⢾⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠛⠛⠛⠛⠛⠛⠓⠶⠶⢶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣶⣶⣦⣤⣤⣤⣤⣶⣶⣶⠶⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⣷⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣾⣿⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣷⡀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⢰⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣷⡀⠀⠀⠀⣴⠟⠁⠀⠀⢠⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⣀⣼⠏⣀⣀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠉⠳⣄⠀⠙⠿⠟⠋⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀ ⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⢻⣆⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡇ ⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⣰⠇⠀⠀⠀⠀⡀⡀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠷⠶⠟⠁⣀⣀⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣄⡀⠀⣠⠞⢻⠾⣆⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⣰⡿⠁⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡾⠁⠀⠀⠀⠙⠳⣆⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⡾⠋⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠾⢿⣦⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣀⣠⠶⠞⠋⠁⠀⠈⢿⣆⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡏⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⢀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢀⠀⠀⠀⢸⡿⠛⠛⠛⠛⠛⠉⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⣿⣿⣿⣄⠀⣼⠀⠀⠀⢂⣀⣀⡀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⡷⠋⠈⠀⠀⠀⠀⠀⠀⠀⠈⠘⠣⡀⠀⠀⠀⠀⠀ ⠀⠈⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⡀⠀⠀ ⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣦⠀ ⠀⠀⣸⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⠀⣤⡟⠛⠋⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠈⠋⠈⢿⣿⡿ ⢀⡉⠀⠀⣀⣤⣄⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣤⣤⣄⠀⠀⣴⡄ ⠘⢇⠀⠰⣿⣿⢟⢼⣿⣿⣿⣿⣿⣿⣿⣿⡿⢜⠿⠿⠿⠀⡀⠀⠀ ⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠴⢴⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⢛⡏⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠉⠉⠙⠛⢓⣶⠴⠛⠁⠀⠀⠀⡼⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⣸⣧⠾⠷⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⡤⠤⣤⠶⠶⠶⠶⠶⠶⠦⠤⠤⠤⠤⣤⣀⣀⣀⡤⠴⠚⠛⠓⠒⠶⠤⠤⠤⠤⣼⣆⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⣠⡼⠛⠁⠀⠀⠀⠀⠈⠙⠲⠤⣄⡀⠀⠀ ⠺⣿⣇⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦ ⠀⠀⠈⠙⠳⠶⣤⣙⣦⣄⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣟⣛⠛⠒⠓⢺⡏⠀⢀⣴⡗⠓⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠈⠉⠳⡄⠀⢸⠁⠀⢾⡁⢗⣾⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣅⣽⢿⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠿⡦⠀⠀⠀⠀⠈⢳⣯⣀⣀⠈⠉⠉⠁⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠙⢿⣶⠿⠁⠀⣿⣿⠲⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣿⠋⠉⠙⢷⡀⠀⠀⢶⣤⣤⣴⠷⢶⣄⡀⠀⢰⡄⠈⠀⢀⣀⣀⣸⡘⣇⠀⠈⠙⠲⣤⣀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣷⡶⠛⠛⠛⠻⣿⡿⠛⠀⠀⣴⠟⠁⠈⠹⡇⠻⡆⠀⠀⠀⠀⠈⠙⠲⢤⣀⣰⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠹⣧⣄⣤⠟⠁⠀⠀⠀⠸⣧⠀⠀⠀⢀⡾⠁⠀⠀⠀⡇⠀⠀⠀⢠⡇⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⣠⠟⠁⠀⠀⠀⠀⠳⣄⣀⣰⠿⠷⣶⣊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⠽⠋⠀⠀⠀⠉⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣀⣀⣀⣀⣀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⣹⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⠀⡀⠀⠀⠐⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣡⢿⣠⡤⠖⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠦⣄⣀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡿⣛⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢉⡙⢒⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠄⣀⡀⡀⠤⠐⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⢤⠔⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠏⠀⣀⣀⡀⠀⠀⠀⠀⢀⠀⡔⢻⣦⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠸⠀⠰⠛⣇⣹⡜⡄⠀⠀⠸⢠⣿⣿⣀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠔⡉⠤⠐⠒⠒⠒⠂⠠⠬⣁⠒⠠⢄⡀⠀⢠⠀⠐⠠⠿⢿⡇⠀⠀⠀⠀⠈⠛⠉⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡐⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠄⡁⠒⠱⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⣒⣀⣴ ⠰⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠌⣉⣶⣶⣦⣄⣀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⢁⣠⣴⣾⣿⣿⡟⠁ ⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠉⠛⠿⠿⠛⠆⠤⠄⠀⣀⣀⣀⣀⣀⡀⠔⢁⣤⣾⣿⣿⣿⡿⠟⠁⠀⠀ ⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠀⠀⠄⠀⡀⠀⠁⠐⠒⠂⠠⠤⢤⣤⣤⣶⣾⣿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀ ⢇⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠉⢂⠀⢱⡀⡰⢠⡃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⢄⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⢄⡁⠂⠤⢀⣀⠀⠀⠀⠀⣀⣀⣼⣿⠀⠀⠀⠀⣮⣤⣶⣶⣦⠋⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⠂⠤⠄⠀⠀⠠⠾⠿⠿⢻⣿⠀⠀⢀⣴⣿⣿⣿⡿⠁⡀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⢃⠤⠐⠁⠀⢰⣾⠟⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠆⠀⠀⠀⠀⢸⡟⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢰⠀⠀⠀⠀⠀⠀⣇⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠸⠀⠀⠀⠀⠀⠀⢹⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⡀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⣆⠁⠀⠀⠀⠀⠀⠀⠀⣿⣷⢠⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠁⡀⠔⠉⠁⠙⡗⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠁⠀⠀⡠⠊⠀⠀⠀⠀⠀⠘⡄⠀⠑⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⢀⣼⠋⠳⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡆⢀⠔⡀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠻⠬⠤⠤⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠇⠀⠀⠐⡀⠀ ⠀⠀⣠⠴⠞⠒⠤⢀⣀⠀⠀⠀⠀⠀⠀⣤⡤⢮⠔⠒⠙⠀⠀⠀⠀⠐⡀ ⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀⠈⣉⡭⣽⠋⡇⠀⠀⠂⠀⠀⡇⠀⠀⠀⠀⣰ ⠀⠀⠐⡀⠉⡟⢻⠉⠉⠛⠉⠀⠈⢱⠈⡇⠀⠀⠘⠀⢀⣇⠀⠀⠀⠰⠃ ⠀⠀⠀⠐⡀⠘⢎⠀⠈⠁⠀⠀⠀⠈⠛⢳⠀⠀⠀⣧⣿⣿⠀⠀⡴⠁⠀ ⠀⠀⠀⠀⣷⣄⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡃⠉⠋⠀⡜⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⡎⠀⠀⠀⠀ ⠀⣀⠀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⡶⠖⠀⠀⠀⠀ ⢸⢁⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠄⠀⠀⠀⠀⣡⠔⠂⢰⠶⢄⠀ ⠸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⡀⠀⠀⣴⣿⠃⠀⠀⠣⢤⣇ ⠀⢣⣱⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠃⠄⢊⠻⡿⢤⣠⣶⣣⠼⡋ ⠀⠀⠀⠁⠂⠥⠤⠤⠤⠀⠀⠀⠀⠤⠵⠤⠦⠐⢁⠀⢑⠳⠤⠉⠥⠊⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⢻⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⣿⣿⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡆⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠀⣠⠟⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠒⠂⠒⠛⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠠⣼⣿⡿⠁⠀⠀ ⠠⣀⡀⠀⠀⠐⠖⠒⠒⠛⠛⠛⠋⠉⠉⠉⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⢸⣄⠤⠔⠒⠛⠛⠉⠉⠉⠉⠛⠓⠒⠤⢄⣀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀ ⠀⠈⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠐⠦⣄⣀ ⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⣠⣤⣤⠤⠤⠤⠒⠒⠒⠒⠒⠻⢦⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⠄⢀⡟⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣸⠁⠀⠀⢦⣾⣿⠋⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⣿⣿⣦⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⠉⠙⣿⣿⡇⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⢧⡀⠀⠙⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣾⣿⣿⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⣠⠶⢦⣄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣺⡆⠀⠀⠀⠀⠠⣄⡀⣀⣀⠤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠲⠾⢭⣛⣳⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠑⠲⢬⠉⠙⠲⣤⡄⠀⠀⡼⢁⣸⣤⡀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢀⡟⠀⢀⡾⠀⠀⠀⣿⡉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢀⡾⠀⢠⠞⠀⠀⢀⡼⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⣼⠃⣠⠋⠀⠐⠀⡞⠁⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣴⣇⠀⠙⠦⣄⠀⡼⠁⠀⠀⠀⠀⠈⠙⠧⣄⠀⠀⠀⠈⠻⢧⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⢦⣀⡀⠀⠈⠉⠒⠦⣈⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣤⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠷⣄⠀⠀⠀⠀⠀⠀⣠⡶⠢⠤⠐⠒⠃⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣇⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⢿⡇⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⢦⣄⣀⠀⠀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⢀⡴⢿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⢸⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣄⠀⠷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣹⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣤⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣴⣾⡿⠛⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣿⠥⣍⣁⣀⣀⣀⣀⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⣾⣝⡋⠝⠉⠰⣄⡙⢮⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢃⠀⠈⠙⠦⠀⣰⣿⠛⠉⠉⣠⣄⣤⣤⣤⣤⣤⣤⣴⣦⣬⣽⣬⣿⣷⣦⣤⣄⣙⣦⡷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢃⠞⠀⠀⠀⢀⣼⣿⡿⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣠⣤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣧ ⠀⠀⣀⣤⣶⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⣼ ⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢷⣆⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣿ ⣾⣿⣿⣟⢛⣛⣛⣛⣋⠭⠥⠿⣿⣿⣷⣤⠀⠀⠀⢀⣀⣀⣠⣀⡀⢿⡇⠀⣸⡇ ⣿⣿⣿⠻⢧⠙⢯⡀⠈⠉⠙⠛⠳⢦⣝⢿⣷⢠⣾⣿⣿⣿⣿⣿⣯⣬⡥⢰⡟⠀ ⢹⣯⣛⠯⢿⣾⣷⣍⡳⣤⣀⠀⠀⠀⠉⠳⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀ ⠈⠹⣿⣿⣾⣿⣿⣿⣿⣷⣭⣛⠷⢦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⢋⣵⡾⣣⣤⣦⢻⣿⣿⣿⣻⠻⣿⣿⣿⡏⠖⢻⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⣱⣿⡟⠼⣻⣿⣿⢸⣿⣿⡇⡛⠀⣿⣿⣿⣧⡠⣸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⢹⣿⣿⣿⣏⢿⣿⣷⣕⣧⣿⣿⣿⢿⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣠⢿⣿⡟⣿⣷⣭⣻⠿⢿⠿⠷⢞⣫⣵⠿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⣎⢿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠁⠻⣷⡝⣩⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⣿⣿⣿⠉⠙⢻⢟⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⡧⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠒⠚⣻⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠒⠒⠒⠒⢤⣤⠴⠚⠉⠀⡸⠁⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⣠⠖⠋⠀⠀⠀⠀⢀⡧⠞⠣⠤⣀⡀⠀⠀⠀⠀ ⢀⣤⠔⠒⠚⣏⠉⠉⠉⠉⠉⠉⠉⠒⠒⠲⠤⠒⠋⠉⠉⠉⠉⠉⠒⠒⠻⢴⠋⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠉⠑⠲⢤⡀ ⠈⠙⠒⠤⢄⣘⣦⡀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼ ⠀⠀⠀⠀⠀⠀⠈⢉⣿⣗⡒⠒⠒⡾⠁⣠⣶⠒⡆⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀ ⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠙⢦⣀⠇⠀⠻⣼⡿⠁⠀⠀⢠⡄⠀⠀⠸⣷⣼⣷⠀⢸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣏⠀⠀⠀⠀⡿⠖⠲⣄⠀⠀⣤⡀⢀⣤⣀⠀⠀⢀⠈⠋⠁⠀⢸⣿⡉⠓⠦⣀⡀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡇⠀⠀⣸⠀⠀⢸⣯⠟⠛⠛⢿⣿⠋⠀⢰⠟⠉⠹⡇⢷⠀⠀⠀⠉⠓⠦⣄⣠⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠹⡦⠴⠋⠀⠀⠀⢹⡄⠀⢀⡼⠁⠀⠀⣇⠀⠀⢠⡇⣀⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠹⠤⠋⠀⠀⠀⠀⠈⠓⡶⠋⠙⠳⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠑⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⣤⠤⠴⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡆⢀⣠⠤⠒⠒⠒⠂⠀⠀⠐⠒⠒⠒⠒⠲⢦⡀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣿⣧⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⢸⣿⣿ ⣿⣿⡄⠘⣷⣤⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣥⣶⠇⢠⣿⣿⣿ ⣿⣿⣿⣦⠈⠻⣿⣷⣄⠻⡿⠋⠙⠉⠋⠛⢿⡟⢡⣶⣿⡿⠃⣰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣦⣈⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠐⢿⠿⢋⣤⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⡤⠄⠀⠀⠀⢀⠤⡀⢰⣿⡿⠛⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷⡾⠀⠀⠀⢸⣶⡇⢸⠟⠁⠀⠈⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠁⠤⠬⠤⠄⠉⠀⢀⠀⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⢟⣵⢄⣀⡀⠀⠀⣀⣠⣰⣿⡶⣆⡄⣀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣟⣾⡏⣿⣿⣿⣿⣿⣿⣿⡷⣿⣯⣿⣿⣿⣇⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣤⡈⢷⢹⣿⣿⣿⣿⣿⣿⠁⡿⢟⣿⣿⣿⣹⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠉⠻⣿⣿⠟⠀⠘⢸⣿⣿⡿⣡⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⠀⠀⠀⢠⣭⣭⣵⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠼⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠋⠳⣄⠀⠀⢀⢎⣔⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀ ⠀⢠⠞⠁⠀⠀⠀⠹⣶⢛⠘⡋⠀⢠⣎⣦⠀⠀⠈⠙⠲⢤⡀⠀ ⣰⠏⠀⠀⠀⠀⠀⠀⢰⠀⠰⡤⡀⠀⢛⣋⠀⠀⠰⣄⣀⣠⣿⣆ ⠛⠒⠶⠶⢶⡶⠄⢀⣨⢦⡀⠢⠃⠀⠸⣿⠇⠀⢰⠃⠉⠉⠉⠉ ⠀⠀⠀⠰⠿⣤⣀⠛⢧⣌⡇⠀⠀⠀⠀⠀⠰⠉⠙⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣣⣞⣽⣇⠀⠈⠑⢄⠀⠐⢄⣀⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⣿⣿⠁⠉⠠⡀⠀⠀⡆⠀⠀⠀⢹⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡿⠇⠀⠀⢈⠁⠊⠀⠀⠀⠀⠈⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠀⣀⣦⣀⣤⣤⠴⠾⣄⡀⠺⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀ ⠀⠀⠀⠀⢀⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠒⣶⣶⠆⠀⠀⢀⠔⠁⢠⠀ ⠀⠀⠀⠀⠘⢀⠼⠤⠀⠀⠀⠄⡠⠐⠈⠀⠀⠀⠀⡰⠟⠁⠀⢀⠔⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢜⡁⠀⠀⠀⣖⣦⠀⠀⠤⣤⠄⠐⠂⠁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⡸⠷⢁⡀⢀⡀⠈⢉⠤⢄⠀⠈⡀⠀⠀⠀⠀⣔⡁⠄⠄⠀⠀⢀⠠⠂⠁ ⠀⠀⢠⢻⠀⠹⣿⠿⡇⠀⠡⠔⠜⠀⠀⢁⠀⠀⠀⠀⢡⠀⠀⢀⠄⠊⠁⠀⠀⠀ ⠀⠀⠀⠫⡀⠀⠐⠤⠃⠀⠀⠀⠀⢀⠀⠀⢂⠀⠀⠀⠀⢃⠀⠸⠀⠀⠀⠀⠀⠀ ⢀⠠⠐⠂⠉⠢⠀⡀⠀⠀⠀⠀⠖⠉⠉⠀⠀⢧⡀⠀⡠⠒⠀⡠⠀⠀⠀⠀⠀⠀ ⢸⡘⠀⠀⠀⠀⢢⠈⠂⠀⠀⠀⠘⢤⣄⣤⠄⠀⠈⢊⠢⣠⣎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠒⠒⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⣾⠿⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⣀⣀⠀⠀⢀⣀⡀⠤⢊⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⣥⠒⠉⠉⠑⠂⠠⠤⡤⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⠀⠀⠀⠀⠀⠀⠀⠐⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⡿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣝⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢌⢷⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠙⠓⠒⠒⠶⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣼⣶⠟⠲⣦⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣽⣶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠉⠀⠀⢠⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠀⠉⠉⠛⠲⠶⢤⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣶⣯⣧⣤⣄⡐⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠇⠀⠀⠀⠀⠀⠀⠙⠓⠂⠀⢉⡻⣶⡀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠰⣦⡀⠀⢀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡿⠇⢟⠦⢤⣀⠀⠀⢻⡇⠀⠀⢀⣼⠇⡀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣦⡀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡤⠔⠒ ⠀⠀⠀⠀⠀⠀⠀⡿⢃⣀⡶⠀⠀⠈⠓⢦⡀⢿⡀⣄⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠉⠛⣷⠖⠋⠁⠀⠀⠀⢀⣴⠾⠋⠉⠉⠙⢷⣄⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⣴⠟⠗⠂⠀⠀⠀⠁⠙⠺⣟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢱⡟⠀⠀⠀⠀⠀⠀⣼⣯⠀⠀⠀⠀⠀⠀⢻⡀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢰⡿⠓⠀⠀⠀⠀⠀⠀⣸⠇⣸⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠰⠆⠀⠀⣰⡿⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⢧⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣤⣤⠶⠛⣱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡛⠲⠶⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢮⣉⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠉⠳⣶⠒⠚⠛⠋⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡖⠛⠉⠉⠁⠀⠀⠈⠉⠁⠀⠀⠈⢳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣳⣄⡀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣷⡍⠳⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡦⠤⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁⠀⠀⢿⣦⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⡙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⣏⡀⠀⠀⣀⣤⡄⢀⡀⠀⠀⠀⠐⠒⠀⠘⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠈⠛⠶⣄⡀⠀⠀⠀⢀⣤⣾⣷⣰⣶ ⣯⠀⠀⢤⣭⣬⣤⣠⣤⣀⣠⠀⡀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡛⢦⣤⣀⣉⡉⣛⣛⣽⠿⠣⣿⡟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠒⠂⠠⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⡠⢠⠂⠀⠀⠀⠡⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢰⣷⣾⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⢨⠢⠔⡀⠀⠠⠘⠛⠛⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⢀⣀⣀⠀⠀⠀⠰⠀⠀⠀⠀⠡⡀⠀⠈⠀⠒⠂⠄⡀⢀⠀⡀⠀ ⠀⡴⠊⠀⠀⠀⠉⢆⠀⡔⢣⠀⠀⠀⠀⠐⡤⣀⠀⠀⠀⠀⠀⣀⠄⠀⠀ ⢸⠀⠀⠀⢠⠀⠀⠈⣼⠀⠀⠣⠀⠀⠀⡰⡀⠀⠉⠀⠀⠰⠉⠀⠁⠠⢄ ⢰⠀⠀⠀⠀⠇⠀⢀⢿⠀⢀⠇⡐⠀⠈⠀⠈⠐⠠⠤⠤⠤⠀⠀⠀⠀⢨ ⠀⢓⠤⠤⠊⠀⠀⢸⠀⠣⠀⡰⠁⠀⠀⡀⠀⠀⠀⠸⠀⢰⠁⠐⠂⠈⠁ ⠀⠀⠑⢀⠀⠀⠀⠈⣄⠖⠉⠑⢄⠠⠊⠀⠢⢄⣠⣃⣀⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⠠⢀⣀⠎⠀⠀⠀⠈⡄⠀⠀⠀⢠⢃⠠⠃⠐⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠯⠉⠤⢴⡃⠁⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⡁⠀⠀⠀⠠⠂⠀⠀⠀⠀⠑⢄⠀⠀⢀⠲⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠒⠑⠔⠁⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠙⢤⡷⣤⣦⣀⠤⠖⠚⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⡿⠢⢄⡀⠀⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⠷⣶⠂⠀⠀⠀⣀⣀⠀⠀⠀ ⢸⣃⠀⠀⠉⠳⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢉⡭⠋ ⠀⠘⣆⠀⠀⠀⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀ ⠀⠀⠘⣦⠆⠀⠀⢀⡎⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⣠⠔⠋⠀⠀⠀⠀ ⠀⠀⠀⡏⠀⠀⣆⠘⣄⠸⢧⠀⠀⠀⠀⢀⣠⠖⢻⠀⠀⠀⣿⢥⣄⣀⣀⣀⠀⠀ ⠀⠀⢸⠁⠀⠀⡏⢣⣌⠙⠚⠀⠀⠠⣖⡛⠀⣠⠏⠀⠀⠀⠇⠀⠀⠀⠀⢙⣣⠄ ⠀⠀⢸⡀⠀⠀⠳⡞⠈⢻⠶⠤⣄⣀⣈⣉⣉⣡⡔⠀⠀⢀⠀⠀⣀⡤⠖⠚⠀⠀ ⠀⠀⡼⣇⠀⠀⠀⠙⠦⣞⡀⠀⢀⡏⠀⢸⣣⠞⠀⠀⠀⡼⠚⠋⠁⠀⠀⠀⠀⠀ ⠀⢰⡇⠙⠀⠀⠀⠀⠀⠀⠉⠙⠚⠒⠚⠉⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢧⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣶⣶⣿⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠀⠀⠀⠙⢿⣳⠞⠳⡄⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠹⣄⣀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠞⠉⠀⠀⠀⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣦⠀⣠⣤⣄⣀⣠⠤⠞⠋⠛⠛⠛⠉⠙⠛⢶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢀⣤⣄⡀⢀⣶⢤⣀⣉⣯⣍⡁⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢿⡀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠋⠉⠉⠛⣾⣇⡀⠙⠋⠁⠀⠈⠁⠀⠈⠙⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀ ⠀⠀⠀⢰⠏⠀⠀⠀⠀⢀⣾⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠚⠛⠛⠛⠛⠛⠓⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀ ⠀⠀⠀⢸⣄⠀⢠⡴⠶⣫⡷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀ ⠀⠀⠀⠀⠻⠷⠋⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⡟⣧⠀⠀⠀⠀⢾⡗⠛⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⣀⣀⡀⠀⠀⠀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠙⣆⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠈⣿⠀⠀⢰⡏⠈⠙⠶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢹⡄⠀⠀⠀⠀⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠙⠓⠒⠋⠀⢠⣿⡇⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠸⣇⠀⠀⢀⡼⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⣾⢸⡇⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⡀⠀⠀⠀⠀⢹⠀⠀⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⣰⠏⢸⡇⠀⠀⠀⠀⢸⡇⠀⠈⠻⣇⠀⠀⠀⠀ ⣠⡶⠶⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠙⢶⣄⠀⠀⠀⢼⣟⠀⠈⠉⠀⠀⠀⢀⣾⠀⠀⠀⠀⠙⠳⢶⣄⠀ ⢿⡇⠀⠀⠀⣠⠞⠛⠻⣦⠀⠀⠀⠀⠘⣷⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⠏⠁⠀⠀⠀⢻⣄⠀⠀⠀⠀⣤⣾⡇⠀⠀⠀⠀⠀⠀⣠⡿⠀ ⠈⠛⠒⠶⢿⣥⣄⣀⡀⣿⠀⠀⠀⠀⠀⢹⡄⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠙⠳⠶⢾⣟⡇⣸⠃⢠⡾⣆⠀⠀⢀⣿⠁⠀ ⠀⠀⠀⣼⠉⠀⠀⠉⣧⠙⣦⡀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠈⠉⠓⠲⠶⠶⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣾⣟⡇⣰⠏⠀⣼⣀⠿⣄⠀⣰⡟⠀⠀ ⠀⠀⠀⢻⣄⠀⢀⣼⠃⠀⢸⠇⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⢾⣄⡀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠶⠚⠋⠁⣤⠴⠋⢹⣿⠟⠀⠀⠈⠙⣻⡎⠙⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⢛⣉⡀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠛⢿⡉⣿⣋⡉⠉⠁⣀⣀⣀⡤⠶⠚⠋⠀⠀⢀⡾⠋⠀⠀⢠⣶⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠉⠙⠓⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠈⠿⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣠⡴⠋⠀⣴⣦⣀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠛⠁⠀⠀⠀⠻⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⣀⡤⠴⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠻⣆⣀⣠⡴⠶⠦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢶⣦⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣵⠛⠛⠳⡆⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡾⠁⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡟⡴⠛⠋⠀⠀⠀⢀⣤⠞⠛⠛⠛⠛⠦⣤⡀⢠⡟⣧⠀⢀⣤⠼⠞⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⣠⠾⠀⣧⣀⡤⠖⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⢲⣶⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⢰⡶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⠀⠀⢸⢻⠞⠀⠀⡀⢘⠀⠲⠀⠀⠀⣰⣧⣷⡄⠘⡶⠉⠁⠐⡆⠻⠋⡖⠒⠀⠎⣳⠀⡄⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀ ⠀⠀⡄⠀⠀⡀⠀⠀⣹⣿⠤⠔⢁⠼⠀⠀⠡⠥⠠⠤⣯⡄⢀⡴⣃⠀⠀⠸⠖⠃⢰⡇⠠⠇⠐⠀⡇⠠⠖⠫⠿⠄⢿⡗⡦⠚⠀⢾⠟⠉⣷⡴⠄⠀⠦⣤

⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⢻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠃⢰⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢠⡀⠐⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣷⡄⠀⠣⣄⡀⠀⠉⠛⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣦⠀⠹⣿⣷⣶⣦⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣷⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⢛⡙⢻⠛⣉⢻⣉⢈⣹⣿⣿⠟⣉⢻⡏⢛⠙⣉⢻⣿⣿⣿ ⣿⣿⣇⠻⠃⣾⠸⠟⣸⣿⠈⣿⣿⣿⡀⠴⠞⡇⣾⡄⣿⠘⣿⣿⣿ ⣿⣿⣟⠛⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣠⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣯⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀ ⢼⣿⣿⣆⠀⢀⣀⣀⣴⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⠋⠙⢿⣿⣿⡀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠿⢆⣀⣼⣿⣿⣿⣿⡏⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣨⡙⠟⣩⣙⣡⣬⣴⣤⠏⠀⠀⠀⠀⠀⠀⣀⡀ ⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣀⣤⣾⣿⣿⡇ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣇⠀⢸⣿⣿⠿⠿⠛⠃ ⠀⠀⠀⠀⢠⣿⣿⢹⣿⢹⣿⣿⣿⢰⣿⠿⠃⠀⠀⠀⠀ ⠀⢀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⠀⠀⠀⠀⠀⠀ ⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠓⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠄⠄⠄⢰⣧⣼⣯⠄⣸⣠⣶⣶⣦⣾⠄⠄⠄⠄⡀⠄⢀⣿⣿⠄⠄⠄⢸⡇⠄⠄ ⠄⠄⠄⣾⣿⠿⠿⠶⠿⢿⣿⣿⣿⣿⣦⣤⣄⢀⡅⢠⣾⣛⡉⠄⠄⠄⠸⢀⣿⠄ ⠄⠄⢀⡋⣡⣴⣶⣶⡀⠄⠄⠙⢿⣿⣿⣿⣿⣿⣴⣿⣿⣿⢃⣤⣄⣀⣥⣿⣿⠄ ⠄⠄⢸⣇⠻⣿⣿⣿⣧⣀⢀⣠⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⠄ ⠄⢀⢸⣿⣷⣤⣤⣤⣬⣙⣛⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡍⠄⠄⢀⣤⣄⠉⠋⣰ ⠄⣼⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢇⣿⣿⡷⠶⠶⢿⣿⣿⠇⢀⣤ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣶⣥⣴⣿⡗ ⢀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄ ⢸⣿⣦⣌⣛⣻⣿⣿⣧⠙⠛⠛⡭⠅⠒⠦⠭⣭⡻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠄ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⡆⠄⠄⠄⠄⠄⠄⠄⠄⠹⠈⢋⣽⣿⣿⣿⣿⣵⣾⠃⠄ ⠄⠘⣿⣿⣿⣿⣿⣿⣿⣿⠄⣴⣿⣶⣄⠄⣴⣶⠄⢀⣾⣿⣿⣿⣿⣿⣿⠃⠄⠄ ⠄⠄⠈⠻⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⠄⣿⣿⡀⣾⣿⣿⣿⣿⣛⠛⠁⠄⠄⠄ ⠄⠄⠄⠄⠈⠛⢿⣿⣿⣿⠁⠞⢿⣿⣿⡄⢿⣿⡇⣸⣿⣿⠿⠛⠁⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠉⠻⣿⣿⣾⣦⡙⠻⣷⣾⣿⠃⠿⠋⠁⠄⠄⠄⠄⠄⢀⣠⣴ ⣿⣿⣿⣶⣶⣮⣥⣒⠲⢮⣝⡿⣿⣿⡆⣿⡿⠃⠄⠄⠄⠄⠄⠄⠄⣠⣴⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣴⢶⣾⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡀⠀⠀⣀⠀⢉⡶⠠⣤⣀⡀⠀⠉⠉⠛⠙⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡇⠀⠘⢁⣴⣿⠀⠀⣠⣿⣿⣽⣦⣤⡀⠀⠀⠀⠀⠘⢦⣄⠀⠀⠀ ⠀⠀⢀⠞⠉⠙⢀⣤⣾⣿⣿⠀⣼⣿⡿⠛⠛⠿⠋⠁⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀ ⠀⣠⠃⠀⠀⠀⠙⢟⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢳⡀ ⠀⠇⠀⠀⠀⠀⠀⠀⠈⠺⣷⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⣧ ⣸⠀⠀⡠⠀⠀⣰⢟⡛⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿ ⡇⠀⠊⠀⠸⢿⠿⠆⠀⠌⣿⣿⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣿ ⣧⠁⠀⠀⠀⠀⢰⠀⠀⠀⣿⣿⣿⣷⣄⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⢀⠔⠀⣼⠇ ⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣧⣀⠚⠿⢯⣀⣀⠀⠤⠔⠉⢀⣾⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣯⣿⢿⣿⣿⢄⠀⠀⠀⠀⢀⣠⣴⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠿⣷⣶⣶⣶⣶⠾⠟⠋⠁⠀⠀⠀⠀

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⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀ ⠀⢸⣿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⣿⡇⠀ ⠀⠈⣿⡀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⢀⣿⠃⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⡀⠀⠀⣀⣀⣀⣀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠋⣿⣿⣿⣿⣿⣿⣿⣿⠙⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠛⠛⣻⣿⣿⣟⠛⠛⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣷⣄⣀⣀⣴⣿⣿⣿⣿⣦⣀⣀⣠⣾⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠛⢿⠟⠻⡿⠛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣅⠀⠉⢻⣿⣿⣧⣤⣤⣤⣤⣼⣿⣿⡟⠉⠀⣨⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣷⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣾⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⣀⣤⣴⣶⣾⣆⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠠⣤⣤⣤⠄⢤⣴⣶⣿⣿⣿⢟⣿⣿⣿⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⣀⣠⣤⡾⢏⢠⣶⣶⣾⡑⡀⢸⠋⠁⠄⢠⣾⣿⣿⣿⠄⠄⠄⠄⠄ ⠄⢀⣠⣶⣿⣿⣿⠟⠁⠁⠰⣋⢫⢲⡇⠛⠄⠄⢀⣠⣤⣉⠻⠿⠿⠄⠄⠄⠄⠄ ⢰⣿⣿⣟⣋⣉⣁⠄⠄⠄⠄⠻⣆⣂⡕⠼⠂⠉⣿⣿⡇⢏⠉⠉⠁⠄⠄⠄⠄⠄ ⠄⠙⢿⣿⣿⣿⣿⠃⢸⢋⡁⢊⠒⣲⡶⠊⢁⣴⣿⣿⣿⣦⣦⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠙⠻⣿⡟⠄⡆⢸⣧⣾⣶⣤⣤⣾⡿⣿⣿⠿⡻⣻⣿⠁⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠘⠠⣾⣿⣿⡿⠿⠿⣥⣾⣿⠿⣛⠅⢰⣗⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠸⣶⣶⣿⣟⣛⣛⣛⠲⠿⣵⣿⣟⢅⠂⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢹⡟⠋⣠⣤⣤⣤⣍⡑⠂⠬⢉⣾⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢠⠁⣿⣿⣿⣿⠿⠿⠿⠿⠷⢶⡄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠘⠄⢉⣁⣀⣤⣤⣤⣤⣤⣤⣤⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⣀⠈⠙⠿⣿⣿⣿⣿⡍⠟⢁⣠⣤⣶⣶⣤⣄⡀⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⢀⣾⣿⣿⣷⣦⣀⠉⠿⣿⡇⠄⣾⣿⣿⣿⣿⣿⣿⣿⣶⡀⠄ ⠄⠄⠄⠄⠄⠄⢠⣾⣿⣿⣿⣿⣿⣿⣷⡄⠹⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄ ⠄⠄⠄⠄⠄⠄⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠄⠄⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠊⠉⠉⠁⣽⣿⣿⡿⠋⠀⠀⠀⠀⣠⠖⠁⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠇⢀⣀⣀⣀⣀⣀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣀⠴⠋⠉⠁⠀⠀⠀⠀⠀⠉⠙⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀ ⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⣾⢙⣶⡄⠀⠀⠰⢤⣠⡤⠤⠔⠒⠂⠉⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀ ⠀⠀⠀⠀⠀⠀⣮⣞⣹⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠃ ⠀⠀⠀⠀⠀⢰⠛⠿⠁⣈⣀⣀⣀⣤⠀⠀⠀⢠⠖⠒⠲⡄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢰⠧⠤⠔⠂⠐⠈⠈⠀⠀⠀⣠⠔⠊⠁⠀⠀ ⠀⠀⠀⠀⢠⡟⣇⠀⠉⢿⣿⣿⣿⣿⠀⠀⠀⢯⡐⠲⣠⡇⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣦⡟⠀⠀⠈⢿⠟⠛⢻⠀⠀⠀⠀⠙⠚⠋⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠳⣄⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⠬⠷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠃⠢⢄⠀⠈⢣⡀⠀⠀⠀⠀⠀⢀⡽⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⠔⠊⠁⠀⠀⠀⠈⠳⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠈⠀⠀⠘⡿⢆⠀⠀⣠⠔⠉⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⡏⠸⠀⠀⠀⠀⠀⠀⠀⢢⠀⠈⠳⢄⣀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⣀⡀⠀⠀⠀⠱⡈⠣⡀⠀⢠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⠦⢤⣀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠤⠼⠛⠁⠀⠀⠀⠀⠘⣆⠙⢶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠒⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠳⣾⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⣀⡤⠔⠲⣶⣆⣀⡀⠀⠐⠤⠤⠔⠒⠉⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣥⠤⢴⠚⠉⠀⠀⠀⠈⠉⠒⠂⠤⠤⢤⡤⠞⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢺⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣷⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢹⣿⣿⣿⣿⣿⡿⠛⠙⢿⣿⣿⣿⣿⣿⣿⡿⠋⠛⢿⣿⣿⣿⣿⣿⡏⠀⠀ ⠀⢀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⢿⣿⣿⣿⣿⡀⠀ ⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀ ⠀⢸⣿⣿⡿⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢿⣿⣿⡿⠀ ⠀⢸⣿⣿⡇⠀⠉⠉⠉⠛⠛⠿⣶⠄⠀⠀⠠⣴⠾⠟⠛⠛⠛⠛⠀⢸⣿⣿⡇⠀ ⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀ ⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⣠⣶⡀⠀⠀⠀⠀⢀⣶⣄⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀ ⠀⠀⠀⠈⠻⣦⡀⠀⠘⠻⠿⣿⣧⣤⣤⣤⣤⣼⣿⠿⠟⠃⠀⢀⣴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⣶⣶⣶⣶⣶⣶⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⠀⠀⠀⡼⠀⠀⠀⡰⠋⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⡼⠁⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢸⠀⠀⡸⠀⠀⡰⠁⠀⠀⠀⢠⠏⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠘⡆⢀⠇⠀⢠⠃⠀⠀⠀⢀⠏⠀⠀⢀⡔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡄⠀⠀⠹⠞⠀⠀⡜⠀⠀⠀⠀⡎⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡔⢦⡀⡴⠁⠀⠀⢀⡤⠖⢦⠀⠀⣠⠖⠒⠀⠀⠐⠒⠒⠢⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⡝⠀⠀⠀⢀⣿⣧⣤⣿⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡆⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⡏⠉⠉⠒⠠⠇⡸⠀⠀⠀⠀⢸⣟⡋⣿⡏⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⣠⡟⠁⠉⣦⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀ ⢣⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠿⠿⠋⠀⠀⠧⠤⢀⣀⢤⣀⡀⠀⠀⠀⠀⠀⣰⠁⠀⢠⣿⣷⣶⣶⣿⠀⠀⠀⠀⠀⠀⣸⠤⠐⠀⠀⣠ ⠀⢣⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⡷⠚⠉⠉⠉⠑⠒⠒⠃⠀⠀⠸⣇⣀⡀⢹⡿⠀⠀⠀⠀⠰⠚⠁⠀⠀⠀⡰⠃ ⠀⠀⠱⡀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀ ⠀⠀⠀⠘⢦⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠒ ⠀⠀⠀⠀⠀⠈⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⣿⣿⣷⣶⠄⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠈⠻⣿⣿⣦⠀⢀⣩⣿⣶⣶⣶⣶⣶⣶⣶⡶⢶⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⡤⠀⠀⠈⠥⢀⠘⠛⠛⠛⠿⠟⠛⠛⠉⠁⠄⠁⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⢍⠁⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡗⠯⢓⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀ ⠀⠈⡟⠀⢀⣮⣹⣆⠀⠀⠀⠀⢠⠿⡬⣆⠀⠀ ⠀⠀⣇⠔⣾⠀⠀⠈⢦⠤⠤⠤⠼⠀⠀⢹⠀⠀ ⠀⢠⠷⢪⠏⣀⠴⠒⠶⣄⣀⣠⠖⠲⢤⡀⠹⡄ ⠀⡞⠀⡏⢰⠇⠀⠀⠀⠀⠉⠀⠀⠀⠀⢹⠀⢷ ⢸⡥⢚⡧⠚⢷⣤⠈⠉⢀⣄⡀⠉⠁⣤⣿⠦⡞ ⢸⡴⠋⠹⠄⠾⠟⠀⠀⠁⠀⠈⠀⠀⠿⠟⢰⠁ ⠘⡆⠀⢠⣂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣆ ⠀⠹⡄⢸⠿⡟⠦⣍⣑⡒⠒⠒⣊⣉⡩⠛⣿⡃ ⠀⠀⠙⢾⣀⠘⢦⣀⠀⠉⠉⠉⠀⣀⡤⣎⠞⠀ ⠀⠀⠀⠀⠈⠙⠲⣾⠭⠽⠭⠭⠭⢖⡺⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠉⠉⠉⠉⠉⠙⠻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⣠⣴⢶⣦⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⢀⣼⣟⣁⣀⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠙⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣶⣶⣾⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⣰⣾⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡷⠆⠀⠀⠀⠀ ⠀⠈⠉⣩⣿⣿⡄⠀⠀⠀⢸⡿⠟⠋⠉⠉⠉⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⡇⣾⠟⣷⡄⠀⠀⠀⣾⠛⣷⡀⠀⠛⠋⣿⣿⣿⣿⣿⣦⡀⠀⠀ ⠀⢀⣴⣿⣿⣿⡇⣿⣦⣿⡇⠀⠀⠀⣿⣆⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠗⠀ ⠀⠙⠻⢿⣿⣿⠁⠛⠛⠛⠁⠀⠀⠀⠛⠛⠛⠀⠀⣤⣾⣿⣿⣿⣯⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⡀⠀⠀⢾⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⠿⠿⠛⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣦⣄⡈⠛⠿⠿⠟⢁⣀⣤⣴⡶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⠠⠤⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡎⠀⠀⠀⠀⠀⢀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡜⡔⠉⠉⠉⠉⠁⠀⠀⠀⣀⠀⠀⢀⠠⠤⠠⠤⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀ ⠱⡱⡀⠀⠀⠀⠀⠀⠀⠑⠄⢀⣤⣀⡀⠀⠀⠀⢀⣄⡀⠻⠁⠀⠀⠀⠀⠀ ⠀⠀⠪⣒⠄⣀⠀⠀⠀⠜⠀⠌⠘⢿⡇⠀⠀⠰⡿⢽⠘⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠒⠈⠤⢐⣚⣄⠈⠈⠀⠁⠀⠀⠀⠁⠈⢉⡰⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠦⣀⠀⠀⢀⡴⣖⠃⠄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠘⠀⠀⠉⠁⠀⠣⡀⠈⠐⠌⡂⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⣦⢊⣀⢠⡄⠀⠀⠀⠀⠀⣆⡈⠲⣤⠀⠈⢢⢣⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠠⠊⠀⠀⠀⠀⠀⠀⠱⡀⠡⠟⠃⠀⠀⠇⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡀⠀⠀⠀⠀⠀⡀⢰⠀⠀⠀⠀⠀⡄⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠄⠀⠀⠀⠀⠸⢈⠀⠀⠀⠀⢠⢁⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢸⠀⠀⠀⡠⠃⣘⢀⣀⠠⠔⡡⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⢠⠓⠒⠒⡎⠀⡴⠀⠀⠤⠔⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠠⠔⠂⠈⠁⠀⣀⠤⠀⠀⠀⠣⢀⠈⠐⠠⢀⡀⠀⠀⠀⠀⠀ ⠀⣠⠴⠍⠀⠀⠀⡠⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⡀⠀⠁⠂⠄⡀⠀ ⠀⡡⠊⠁⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⢌⠚⢣ ⠀⠉⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡐⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠑⢄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠑⢄⣰⠉⠢⣀⠐⡀⢀⣀⠤⠐⠂⠉⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⣼⠁⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢴⣶⣾⣿⡟⠲⢤⣀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀ ⠀⣨⣿⣿⣷⣄⠀⠈⠑⠢⠄⠛⠛⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠞⠁ ⠈⠉⠻⣿⣿⣿⣷⣄⠀⣤⣤⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡷⠂⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠟⠁⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⣧⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠞⠁⣀⣤⣴⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠆⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢆⠀⠀⢀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢈⣶⣶⣾⣿⣦⣤⠄⠀⠀⢠⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⣿⣿⣷⣄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣁⣴⣿⡿⠟⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠒⠒⠒⠤⠤⠤⠀⢀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠈⢻⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⡿⠛⠙⠃⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⡸⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣥⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡌⠁⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⡇⠀⠀⠀⡸⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠁⠀⣀⣠⡤⠖⠚⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⠃⠀⠀⠀⠀⠀⢩⠉⠉⠉⠉⢻⠉⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⡷⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣜⡀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⣼⣠⣾⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣇⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠏⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⠿⠛⠿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠄⣀⡤⢤⣤⣈⠁⣠⡔⠶⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠄⠄⠄⣼⣿⠁⡀⢹⣿⣷⢹⡇⠄⠎⣿⣿⣿ ⣿⣿⣿⠿⠛⠉⠁⠄⠄⠄⠄⠄⠄⠄⠹⣇⣀⣡⣾⣿⡿⠉⠛⠒⠒⠋⠉⢸ ⡿⠋⠁⠄⠄⢀⣤⣤⡀⠄⠄⠄⠄⠄⠄⠈⠙⠛⠛⠉⠄⠄⠄⠄⠄⠄⠄⠈ ⠄⠄⠄⠄⠄⢹⣧⡈⠿⣷⣄⣀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⣠⢄⣾ ⠄⠄⠄⠄⠄⠈⠻⢿⣶⣌⣙⡛⠛⠿⠶⠶⠶⠶⠶⠖⣒⣒⣚⣋⡩⢱⣾⣿ ⠄⠄⠄⠄⠄⠄⠄⠄⠈⠉⠛⠛⠛⠻⠿⠿⠟⠛⠛⠛⠉⢉⣥⣶⣾⣿⣿⣿ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠒⠶⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠈⠻⣿⣿⣿⣿⣿⣿ ⣿⡿⠛⠛⠛⢻⣿⠿⠛⠛⠛⢿⣿⣿⡿⠛⠛⠛⢻⡟⠛⣿⡿⠛⣻⣿⣿⣿ ⡟⠄⣼⣿⣿⣿⡇⠄⣾⣿⣧⠄⢻⡏⠄⣼⣿⣿⣿⡇⠄⡟⢀⣴⣿⣿⣿⣿ ⡇⠄⣿⣿⣿⣿⡄⠄⣿⣿⣿⠄⢸⡇⠄⣿⣿⣿⣿⡇⠄⣀⠈⢻⣿⣿⣿⣿ ⣿⣄⠈⠙⠛⢻⣧⡄⠙⠛⠉⣠⣿⣷⣄⠈⠙⠛⢹⡇⠄⣿⣧⠄⠻⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠃⠀⠀⠐⠚⠻⢷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢁⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⣼⠏⣼⣧⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⣤⡾⢿⠐⣿⡿⠃⠀⠀⠀⢀⡖⠒⣦⡀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠁⢸⠀⠀⣤⡄⠀⠀⠀⢸⣧⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄⠀⠀⠀ ⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡠⠃⠀⣀⡈⠀⠀⠀⠀⠘⢿⣿⣿⠟⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀ ⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢹⡟⠓⣶⠀⠀⠀⠀⣨⣤⣤⡀⠀⠀⠀⠀⢸⣿⣶⣦⣤⣶⣾⣿⣿⣿⣆ ⢠⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠘⣧⠀⠀⠈⣄⠀⡏⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣸⡟⠀⠉⠙⠛⠛⠿⠿⠿⠛ ⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⣿⠟⠋⠀⠀⣠⣴⡿⠿⣷⣄⠀⠈⠓⠁⠀⠀⠀⠈⠿⣿⡿⠏⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⢾⣿⣯⡀⠀⢸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠛⠛⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣶⣦⣤⣀⠈⠙⢿⣶⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⠃⣠⣿⢋⣽⣷⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣶⣿⣧⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠈⠻⢦⣤⣤⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⠋⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣧⡀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⠙⠓⠶⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠋⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⠁⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣉⣀⣀⣀⣤⣾⣿⣷⣶⣶⣶⣿⡿⠿⠿⠛⠛⠿⣷⣤⣄⡈⠀⠉⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀

⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣾⣿ ⣿⣿⣿⡿⠉⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠙⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⠀⠀⠀⠀⠈⠙⢦⡄⠀⠀⠀⠀⠀⢀⣠⡴⣞⣿⠟⢻⡟⠻⣿⣳⢶⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⠀⠀⢸⣿⣿⡿⠋ ⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢲⡄⠀⢀⣴⠟⢁⡼⠛⠉⠀⠀⡇⠀⠀⠙⠷⣌⡙⠳⣦⡀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀ ⠀⠀⠈⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⠁⢠⡞⠁⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⣹⣦⣬⣿⣶⠏⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣤⣶⣾⣶⣦⣿⣤⣶⣶⣶⣾⣿⣿⣿⡿⢹⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣤⠤⠐⠺⣿⣿⠿⠿⠛⠉⣁⣀⣀⣀⣈⣉⡙⠻⠿⠿⠿⣿⣁⠈⣄⠀⢀⡠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣟⣿⣵⣦⣤⠶⠾⠛⠛⠛⠛⠛⠛⠛⠛⠻⠶⠤⠤⠤⠽⠗⢻⡏⠉⠀⠀⠀⠀⠀⢀⡴⠊⠉⠣⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠉⠁⠀⠀⠀⠀⠈⠉⠑⠒⠤⢄⣀⡀⠀⠀⠀⠀⢀⡠⠖⠦⠖⠻⡀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⣤⣄⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠉⠁⠀⠀⠀⠀⠀⢇⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠊⣿⠀⢠⣟⡿⠂⠀⣼⠀⢀⣤⣶⣿⡿⣯⣛⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢶⠋⠁⠀⠀⠀⣏⢠⣿⠟⠉⣠⡶⠒⢄⠙⢯⢳⡀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢶⣦⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠓⠒⡦⠀⠀⡟⣿⡟⠀⣾⣿⣧⣀⣼⡆⠈⣿⣇⠀⠀⠀⠀⠀⠀⢸⣧⣠⣼⣿⣧⠄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡅⠀⣼⠷⡏⢧⠀⠹⣄⢈⣿⡞⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⠏⠀⢀⡴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⠀⠹⣎⠳⣀⠀⠉⠁⢀⣠⣾⡿⠁⠐⠆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣰⠋⠀⢸⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⢹⠓⠾⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⢀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⠼⠒⠂⠙⠛⢧⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⢀⡼⠁⠀⣹⡶⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠰⠾⠿⠦⠤⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⢀⣾⠃⠠⣆⠠⠤⠤⠤⠤⠤⠄⠀⢤⡴⠀⠀⠀⠀⠁⠀⢳⣀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢀⣠⣾⣿⡆⠀⠈⠙⠲⠤⣄⣀⣠⠤⠖⠉⢀⡠⠀⠀⠀⠀⠀⠈⣏⡽⠃⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡖⠶⠒⠚⠉⠙⠟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⢸⠁⣠⣞⣁⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠉⢩⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠙⠦⠤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⡆⠀⠀⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⣀⣠⡴⠋⠁⢀⡇⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠈⠉⠐⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡏⠙⡇⠀⣉⣉⠀⢸⠋⢹⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿ ⣿⠀⠀⠀⠀⠀⠉⠉⠛⢿⠇⠀⠀⠀⠉⠉⠀⠀⠀⢸⡿⠛⠉⠉⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⢸⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣇⠀⠀⠀⢀⣴⣾⣿⣿⣶⣄⠀⠀⠀⠀⣠⣶⣿⣿⣷⣦⡀⠀⠀⠀⣸⣿⣿ ⣿⣿⣿⡆⠀⠀⢿⣿⣿⠁⢹⣿⣿⠗⠀⠀⠺⣿⣿⡏⠈⣿⣿⡿⠀⠀⢰⣿⣿⣿ ⣿⣿⣿⠇⠀⠀⠀⠉⠻⠀⠸⠛⠁⠀⠀⠀⠀⠈⠛⠇⠀⠟⠉⠀⠀⠀⠸⣿⣿⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⣠⡀⠀⠀⣀⣀⣤⣤⣀⣀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠈⠻⣿ ⣿⣿⣿⣿⣷⠀⠀⠀⠘⠿⠻⣿⣿⡏⠉⠉⢹⣿⣿⠟⠿⠃⠀⠀⠀⣾⣿⣿⣿⣿ ⣿⣿⣿⡿⠃⠀⠀⣀⠀⠀⠀⠹⠟⠀⠀⠀⠀⠻⠏⠀⠀⠀⣀⠀⠀⠘⢿⣿⣿⣿ ⣿⣿⣿⣷⣶⣾⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣷⣶⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⣶⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⢁⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⠋⠀⠀⠀⣰⡟⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠡⠀⠀⠀⠀⣴⡏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⣤⠤⠤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠉⠙⠛⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠚⢻⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡿⠛⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡟⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠋⠉⠉⠛⠲⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣇⣠⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡏⠀⣿⡆⠀⠀⠀⠹⣤⣀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣷⠀⠀⠀⠀⣠⠤⠤⣄⠀⠀⠀⠈⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣧⡀⢠⣞⠁⠀⠀⠈⠳⣄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢷⣞⠈⠳⠦⠤⠤⠶⠋⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⢷⣄⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⢤⣀⣀⣀⡤⠴⠛⠁⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠿⠲⢦⣤⣄⠀⠀⠀⠀⠀⠀⢦⣦⣤⠶⠞⢿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⢰⠀⢀⣤⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⢀⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⡀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠾⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠶⠶⠶⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⢀⣀⢀⠠⡀⡀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⡼⠅⠠⢼⡁⣸⢤⡧⠠⣠⣜⣃

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⣶⠖⠛⠓⠶⣦⣤⠶⢛⣹⣋⣉⠉⠛⠳⣦⣄⣤⣤⠶⠶⠶⠶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⣏⣧⠀⠀⣀⡼⠓⠋⠉⠉⠉⠉⠉⠓⡢⢤⡉⠉⠀⢀⡠⠖⢲⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⢿⣻⣳⠞⡇⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠙⢢⡐⢯⡀⢀⠇⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⠈⣳⠃⢸⠁⠀⠀⢀⣀⡀⠀⢠⠏⠀⠀⠀⠀⠀⠙⡄⠙⣏⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⢰⡏⢀⡼⠔⠚⢹⠉⠉⠉⠉⠙⠲⢤⣀⠀⠀⠀⠀⠘⡆⠹⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⢸⠻⡋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡸⠋⢻⣷⡀⠀⠀⠀⢻⡙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⢸⡀⣇⠀⣀⠤⠚⠒⠒⠢⠤⣀⠀⣰⣇⣠⣾⣿⡇⠀⡜⠀⢸⡇⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⠸⣿⣿⡚⠁⠀⠀⠀⠀⠀⠀⠈⡽⢿⣿⣿⣿⢿⠀⣼⠇⠀⣾⠉⠢⡀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⢀⣼⣿⠙⢦⡀⠀⠀⠀⢀⡴⠋⠀⠘⠶⠚⠁⣸⡾⠋⢀⣼⠏⠀⠀⠘⡄⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⣴⠟⠁⠘⣷⡄⠈⠙⠒⠋⠁⠀⠀⠀⢀⣠⡴⠞⢋⠟⠀⠚⠱⢄⡀⠀⠀⢸⡏⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⣼⡯⢶⠚⠙⠚⠻⣦⡀⠀⠀⠀⠀⣠⡶⠋⠉⠀⣠⠋⠀⠀⠀⠀⠀⢙⣆⢀⠞⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⣿⠀⣇⠀⢀⣀⡀⢸⡟⠶⣄⣠⡼⠋⠀⢀⡴⠚⠉⠉⠁⢀⣄⠀⠀⡜⠹⣉⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⣷⠀⡇ ⡇⠀⣿⣄⡹⠋⠁⠀⠈⠻⣇⠀⠀⠀⠀⠀⢰⡛⠉⠉⠑⢤⠔⠁⠀⢳⡊⠀⢠⡟⢱⠀⣠⣿⡇⠀⠀⠀⠀⠀⣀⣤⣾⣋⠀⠀⣿⠀⡇ ⡇⠀⢹⣿⡀⠀⠀⠀⣰⡒⣿⠀⠀⠀⣠⣞⢩⡇⠀⠀⠀⠈⢆⠀⠀⢘⡇⣰⠟⠀⣼⠔⠁⣿⣁⣀⣀⣤⣴⣾⠋⠉⠉⠉⠑⢦⡟⠀⡇ ⡇⠀⠀⠹⣷⡀⠀⣾⠉⢻⡟⠁⠀⠀⢀⣽⠓⠚⣷⠀⠀⠀⡼⠀⣀⣼⠟⠋⠉⠉⠙⠻⢾⣿⠉⠻⣍⠀⠀⠈⢙⣦⡀⠀⡰⣿⠃⠀⡇ ⡇⠀⠀⠀⣸⡟⠛⢺⡏⠉⠀⠀⠀⠀⠀⠙⠛⠯⠽⠢⠶⠾⠛⢛⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠈⢳⠒⠊⠉⠀⢳⠞⣹⡟⠀⠀⡇ ⡇⠀⠀⢸⡟⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣷⠀⠀⡇⠀⠀⠀⢸⣴⠏⠀⠀⠀⡇ ⡇⠀⠀⣾⡷⡤⠴⠶⠞⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠲⠤⣀⣀⣀⣀⣀⡤⠖⠛⢇⠀⢹⣧⠀⡇⠀⠀⣤⡿⠁⠀⠀⠀⠀⡇ ⡇⠀⠀⢸⣧⢣⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⢫⣇⣴⠿⠋⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⢻⣮⡧⠤⠤⠤⠤⠚⠛⠳⣦⣀⣀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠸⡀⠀⠀⠀⠀⠀⢸⡴⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⣀⣴⡿⠻⠷⠤⠀⠀⠀⣀⣠⢾⡟⠛⠻⠿⠶⠶⠿⠿⢿⣯⡉⠲⠷⠶⠶⠶⠒⠋⠁⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⡼⢋⡵⠋⠉⠙⡆⢀⣀⣨⡴⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⡀⠀⠀⠀⠴⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠸⣽⣏⣀⣤⡤⠶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⣉⣁⣀⣀⠤⣈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡁⠀⠸⡄⠀⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⣧⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠿⠶⠶⠶⠆⠶⠡⠲⠾⠖⡆⠏⠶⠤⠦⡄⠄⠄⠠⠀⠀⠤⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⡀⡀⡀⠀⢀⢀⢀⢀⢀⢀⠀⠀⠀⡀⡀⡀⡀⣀⡀⠀

⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀ ⠀⠸⣿⣿⣶⣄⡀⠀⠀⣶⣦⡀⢀⣾⣿⣠⣾⣿⡇⠀⡀⠀⠀⢀⣠⣴⣿⣿⠇⠀ ⠀⠀⢿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣴⣾⣿⣿⣿⣿⡿⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⡏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⣿⣿⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠈⢻⣿⣿⣿⣿⣿⣿⡟⠁⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⣿⣇⠀⠀⠈⠉⠻⣿⣿⠟⠉⠁⠀⠀⣸⣿⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⡿⢿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⣠⣼⣿⣿⣿⣇⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⣸⣿⣿⣿⣧⣄⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀ ⠀⢼⣿⣿⣿⢿⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⣀⣤⣴⣿⣿⣿⣿⣿⡿⣿⣿⣿⡧⠀ ⠀⠀⠙⠉⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠉⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠉⠉⠙⠋⠉⠉⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⣿⣿⣿⣿⣿⣆⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣧⡀⠀⢠⣿⠟⠛⠛⠿⣿⡆⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠙⠿⠿⠟⠋⠀⠀⠀⣠⣿⠇⠀ ⠀⢸⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠋⠀⠀ ⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀ ⠀⠈⢿⣷⣤⣤⣄⣠⣤⣤⣤⣤⣶⣶⣾⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀ ⠀⢸⣿⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀ ⠀⠀⢻⣧⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠟⠀⣠⣾⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⣤⣾⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣶⣦⣤⣤⣤⣤⣤⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠳⡄⠀⠘⢌⢂⠹⡄⠀⠘⡆⠀⠀⠀⡮⡒⡇⣰⡿⢀⡇⣦⡎⡱⠂⢀⢠⣹⡶ ⣄⠀⠈⢢⡀⠈⢊⢆⠹⡄⠀⢡⠀⠀⠀⡇⡇⡜⢹⠃⣸⠀⣿⣿⡽⢀⣰⣯⡏⣩ ⣕⢷⣄⠀⠑⢄⠀⠙⣆⢳⡀⢰⣸⣧⢠⠇⡿⢠⡏⠀⣿⠀⠸⣿⣿⣛⣵⠾⡛⠁ ⠈⠓⢬⡳⣄⠀⠠⡀⠈⢂⣷⠿⢋⠈⢻⠻⠃⠈⠀⠐⢼⡀⢠⠜⠩⠛⡝⠀⠀⠀ ⣶⣖⣶⣾⡶⣷⡦⣤⠤⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⣤⡤⠤⢀⣀⠀⠀⠀ ⠙⢿⣷⠦⣀⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⢣⠀⣀⠿⠀⠀⠀ ⠀⠀⠙⢄⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠘⣿⠁⠒⠀⠀⠀ ⠀⠀⠀⠀⢑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠇⢰⠋⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣨⣇⠀⠀⠀⠀⢸⠒⠤⣀⠀⠀⠀⠀⠀⠀⠓⠈⡠⢹⢨⡇⠀⠀⠀⠀ ⠀⢀⣤⣶⣟⡉⠇⠀⡐⠀⠈⢦⡀⠁⠈⡩⠇⠀⠀⠀⡠⠞⢄⣾⣽⠃⠀⠀⠀⠀ ⣴⣿⣿⣿⣠⠎⠽⠀⠠⠡⡀⠸⣌⣙⣉⣀⡠⠤⠐⠈⠄⣠⣾⣾⣯⠐⠂⠄⡀⠀ ⠿⠻⠷⠷⠟⠛⢿⢿⣦⣤⣀⣄⣈⣑⣲⣵⣤⣬⣦⣶⣺⣽⣿⣿⣿⣧⠄⠀⠀⠀ ⠀⠠⣤⡊⠀⣜⡿⢏⡟⠿⣟⣿⣟⣿⣿⡟⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣄ ⠀⠀⠠⣞⡭⢿⣴⣏⣵⣿⣽⣿⣓⣟⣫⣍⣁⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠠⠚⢉⡶⠛⠛⠛⢛⠛⠛⢟⡟⠹⡟⢹⡭⠍⠙⡍⢫⡉⢉⡫⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡄ ⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⣶⣶⣶⠖⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⢀⠎⠀⠀⠀⠈⠙⡀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠈⣿⠟⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇ ⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠈⠀⠠⡄⠊⠁⠀⠀⠀⢀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠋⠉⠀⠀⠀⠀ ⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⢰⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣧⠀⠀⠀⠀⠀ ⢀⡎⠘⠋⠀⡄⠀⠀⠀⢠⣈⣵⠀⢠⣆⢠⣶⡕⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀ ⠸⡀⠀⠀⠀⢤⣀⢀⣾⡿⠿⠇⣾⠀⣿⡄⡏⢀⣿⢣⡷⠂⢳⣦⣀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⢄⠀⠀⠸⣄⣀⣀⣥⣤⣷⣿⠀⢹⡷⠀⠘⠁⣿⠇⠀⢸⣿⠈⣷⣦⣄⠈⢿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠑⢢⢄⡘⠉⠉⠙⠻⣿⡿⠄⠀⠀⠀⠀⠰⠋⠀⠀⢸⠇⠀⣿⣿⠉⢦⣼⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡏⠀⠈⠉⠁⠀⠀⠀⠁⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⢸⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣀⠀⣰⣷⢳⣤⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⡠⠊⠀⢻⡥⢻⣾⢿⠅⢀⠎⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠀⠉⠀⠀⡔⠋⠀⠀⡀⠏⠁⠈⠁⠀⡠⠊⠀⠨⡀⠀⠀⠀⠚⠛⠉⠉⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠖⢡⣤⡞⡼⠀⠀⠀⠰⣀⢰⠀⡀⡀⠞⢉⡡⠔⣋⠩⠭⠽⢷⡾⠇⠀⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠗⠣⠎⠁⠠⣊⣠⣐⣀⣠⣀⡤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⠤⠄⠒⠒⠈⠉⠉⠉⠉⠐⠒⠒⠒⠂⠤⣤⡄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢻⠒⠤⢀⣀⣀⡀⠄⠄⠠⠠⠤⠤⠤⠒⠊⡸⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠸⡀⠄⠄⢀⠄⠂⠄⠄⠄⠄⠄⠄⠄⠄⡰⠁⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠱⡀⠈⠄⠄⢀⣀⣤⣊⣀⣀⣀⠄⡰⠁⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠻⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠃⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢹⣫⣙⣛⣛⣛⣿⣟⣻⡻⠃⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣿⡟⣯⣽⣾⣿⣟⣻⠁⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣨⣿⣿⣿⣿⣗⣹⡇⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣀⡼⠋⠈⠉⠉⠉⠉⠉⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⡠⠞⠉⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⣠⠶⠋⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⢀⣠⠴⠛⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⢀⣀⣀⡤⠤⠖⠛⠉⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠉⠉⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⡀⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄oil floats on water⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠄⠄⠄⠄⠄ ⣿⣿⣿⣿⣿⢟⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣟⣽⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠄⠄⠄⠄⠄ ⣿⣿⣿⣫⣶⣿⣿⣿⣿⠿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣯⣾⣿⣿⣿⡿⣋⣷⣿⣿⣿⣿⣿⣿⠄⠄⠄⠄⠄ ⣿⣿⣿⣿⣿⣿⣿⠿⣫⣾⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⡿⢫⣾⣿⣿⣿⣿⡿⣻⣿⣿⠄⠄⠄⠄⠄ ⣿⣿⣿⣿⡿⢟⣵⣿⣿⣿⣿⡿⠿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⣛⣫⣽⣾⣿⣿⣿⡿⢟⣭⣾⣿⣿⣿⠄⠄⠄⠄⠄ ⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣭⣴⣾⣿⣿⣿⣿⣿⣿⠄⠄⠄⠄⠄ ⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠄⠄⠄⠄ ⣿⣿⣿⣿⣟⣯⣾⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡿⣫⣿⣿⣿⣿⢫⣾⣿⣛⣿⣿⣿⢻⣿⣿⣿⠄⠄⠄⠄⠄ ⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣵⣾⣷⣿⣟⣿⣞⣽⣿⣟⣾⡿⣫⣞⣿⣿⣿⣿⠄⠄⠄⠄⠄ ⣿⣿⣿⠟⠉⡉⡉⣶⠤⠄⠤⠹⠯⠭⠝⠛⠻⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢷⣭⣾⣿⣶⣿⣿⣿⣿⠄⠄⠄⠄⠄ ⣿⣿⠏⠄⠄⢘⣥⣤⡤⢄⡀⠄⠄⢂⣀⣈⠄⠄⢿⣿⣿⣿⣷⣾⣿⡿⣿⣿⢟⡿⣷⣿⣿⢿⣿⣿⢿⣽⣿⣿⠄⠄⠄⠄⠄ ⡿⢋⡤⣲⠬⣘⣫⠽⠛⠺⠓⠄⢲⠟⠛⡋⣉⣁⡄⢽⣿⣿⣿⣿⣿⣿⣿⣽⣿⣵⣿⣿⣿⣾⣿⢍⣾⣿⣿⣿⠄⠄⠄⠄⠄ ⡤⠻⠐⢯⡓⢦⣄⣀⡀⣖⠦⠄⡈⣹⠦⠍⣡⣧⠈⡾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠄⠄⠄⠄⠄ ⠘⢶⠄⠈⢿⣹⢷⣤⣼⡉⠓⠒⠛⡗⠒⣎⣯⣿⢸⠁⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠣⡀⠄⠙⠦⣀⡏⠙⠛⡟⢻⡿⢿⢿⣿⡿⢸⡀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠈⣒⣷⣣⠔⢭⠙⡒⠳⠾⠶⠟⢛⠩⠄⠘⡁⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⣠⠟⠁⣿⠈⠿⡷⢦⣈⣁⠄⠄⠄⠄⠄⠁⣰⠃⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⡴⠛⠁⠄⠄⣷⠄⠄⠙⢦⠄⠄⠉⠉⠓⠒⠊⠉⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⣿⠄⠄⠄⠈⢷⡀⠄⣀⠄⡄⠄⠄⠄⠄⠄⠄⠄⡀⠄⡤⠄⠄⠄⠄⠄⢀⠄⢀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⡿⠄⠄⠄⠄⠄⢧⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄wait for it to rain ⠄⠄⠄⠄⢸⡇⠄⠄⠄⠄⠄⠄⠄⠄⠄⠁⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠸⠇⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ cover yourself in oil ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⣤⠖⠒⠒⣒⠶⠒⠒⠲⠶⠒⣶⣶⣤⠤⣤⣀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⡰⠟⠄⠠⣐⠹⠦⠉⠒⠒⢀⠁⠐⠒⠂⠤⠄⠍⡀⠓⢦⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣠⡞⠄⠄⠄⣀⢨⣾⣿⣿⣛⡳⣦⠄⢀⣘⣤⣴⣦⣦⡄⠄⢘⢧⣀⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⡜⠋⣴⠞⢻⡛⠶⠦⠴⠞⠄⠈⠙⠋⠄⠈⢹⡉⠉⢀⣀⣴⠶⠕⡁⣿⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢇⠄⢧⠒⢻⡉⠓⢶⣄⣀⡀⠐⣟⣫⣤⠄⠈⣹⠷⠄⡈⢁⣧⢐⡣⡿⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣴⠻⣆⠄⠄⠙⣯⢻⠷⣦⣤⣿⡉⠛⢛⠒⠻⣶⠒⢺⣏⣿⣿⠄⣿⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠘⢧⡈⠄⠈⠛⣄⡀⣹⠟⠛⠛⢿⠿⢿⣿⢿⣿⣿⣿⣿⠄⣿⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣴⠄⠄⠹⢶⣗⣴⡢⠉⡛⠶⢤⠤⣿⣀⣼⣡⡼⣥⠿⠾⠃⠄⢈⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠚⠄⠄⠄⠈⠉⠘⠚⠮⣍⡐⠄⠂⠤⠉⠙⠓⢒⢀⡨⢒⡴⣼⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⡴⢛⠟⠛⢿⠶⠤⣤⣀⣄⣀⣠⣷⠞⠁⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠚⠄⠄⠄⠄⠄⠄⡴⠋⢀⡞⠄⠄⠄⢷⣄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣹⠄⠄⠄⢀⣤⠚⠄⠄⡼⠃⠄⠄⠄⠄⠙⠳⣤⡀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⡾⠃⠄⠄⢰⡇⠄⠄⠄⠄⠄⠄⠄⠈⣧⠄⠄⠄⠚⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠈⠁⠄⠄⠄⢸⠁⠄⣴⠄⠄⠄⠄⠄⠄⠈⠄⠄⠄⠄⠚⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢼⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣏⠚⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠘⡆⠄⠄⠄⠄⠄⣏⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣴⠄⠄⠄⡇⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣴⠄⠄⣠⣿⣀⠄⠄⠄⣹⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢠⠋⠄⠄⠄⠙⢶⡄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢰⠟⠄⠄⠄⠄⠄⠄⠹⣄⠄⠄⠄⠄⣧⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣠⠏⠄⠄⠄⠄⠄⠄⠄⠄⠙⢷⡀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣰⠏⠄⠠⠄⠠⢤⣤⡴⠄⣀⣄⠈⣷⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⢀⠄⠏⠄⠄⠐⠃⠄⠙⠛⠛⠛⠛⠛⠄⠈⠐⠛⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⣀⣀⠄⠄⠄⠄⠄⠄⠄⠘⠶⠤⠤⠄⠄⠄⠄⢀⠄⢀⠄⢀⣀⣀⡀⠄⠄⠄⠄⠄⠄⣀⢀⣀⣀⣠⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠉⠉⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢴⣴⠶⠚⠉⠁⠘⠓⠋⠉⠉⠄⠄⠄⠄⠄⠄⠄⠉⠉⠉⠉⠉⠄⠄⠄⠄⢶⣤⣠⡖⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠐⠂⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⣠⠗⠄⠄⠄⠖⡭⠭⠿⢅⡠⡀⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⡀⠄⠄⠄⣄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠰⠾⢿⠄⣄⣀⣸⢸⣸⠄⠄⢂⠱⢆⡄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⡈⠉⠄⠄⠄⠁⣲⠆⣀⣀⣀⠄⠄⠄⠄⠄⠄⠄⠄⢈⣱⣟⢥⣿⡸⠤⢆⡀⠄⡰⠌⡁⠠⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠈⠄⠄⠠⠄⠄⠙⠃⠉⠓⠂⢓⠦⣤⣆⡤⠴⡒⠒⠚⠉⢀⣰⠈⢶⣧⠄⢳⣄⣠⡖⠃⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠉⠄⠄⠄⠄⠛⠻⠶⠤⠤⠛⠙⠂⠉⠁⠄⠄⠄⠄⠄⠃⣿⣄⠄⠢⠓⠈⢛⠕⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠗⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⠄⠄⠄⠠⢀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄fly⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣠⡄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⣤⣤⣤⣤⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣿⡇⠄⠄⠄⠄⣿⣿⡿⣷ ⠄⣿⣾⡤⣿⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣶⣾⣿⣿⣷⣶⠄⠄⣿⣿⡗⣿ ⠄⣿⣾⣶⣟⣀⣤⣤⣤⣾⢿⡿⣿⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣠⣶⣦⣶⣶⣤⣿⣿⣏⣹⣏⣿⠄⠄⣿⣿⡗⣿ ⣠⣿⣿⣦⣿⢿⣹⣏⣿⣿⢾⡷⣿⠄⠄⠄⠄⠄⠄⠄⣶⢶⡷⣷⡆⠄⠄⢹⣧⣿⣿⣤⣿⣿⣿⣯⣹⣏⣿⠄⠄⣿⣿⣿⣿ ⣹⣿⣿⣿⣿⢿⣉⣯⣹⣿⢾⡷⣿⠄⠄⣤⣶⡦⠄⠄⣿⢻⡗⣿⠄⠄⠄⢺⣍⣿⣿⣉⣿⣿⣿⣏⣹⣏⣿⣆⣰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣾⣷⣿⣄⢀⣿⣿⣤⠂⠄⣿⢻⡟⣿⡆⠄⠄⣼⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡿⠷⣶⣤⣄⡀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⢀⣠⣤⣶⠾⢿⣿ ⣿⡇⠀⠀⣨⣿⣿⣷⠀⢠⣿⣿⠿⠋⢉⡉⠙⠿⣿⣿⣄⣤⣾⣿⣿⣅⠀⠀⢸⣿ ⢸⣧⠀⣰⣿⣿⣿⡏⢀⣿⣿⡏⢠⣾⣿⣿⣷⡄⢹⣿⣿⣿⣿⣿⣿⣿⣆⠀⣼⡇ ⠈⣿⣴⣿⣿⣿⣿⡇⠈⣿⣿⣧⣾⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⠁ ⠀⢹⣿⣿⣿⣿⣿⣿⣄⠙⢿⣿⣿⣿⣿⣿⠏⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣶⣄⣈⠉⠉⣉⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀ ⣴⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡉⠛⠛⢉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁ ⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀

⡆⣐⢕⢕⢕⢕⢕⢕⢕⢕⠅⢗⢕⢕⢕⢕⢕⢕⢕⠕⠕⢕⢕⢕⢕⢕⢕⢕⢕⢕ ⢐⢕⢕⢕⢕⢕⣕⢕⢕⠕⠁⢕⢕⢕⢕⢕⢕⢕⢕⠅⡄⢕⢕⢕⢕⢕⢕⢕⢕⢕ ⢕⢕⢕⢕⢕⠅⢗⢕⠕⣠⠄⣗⢕⢕⠕⢕⢕⢕⠕⢠⣿⠐⢕⢕⢕⠑⢕⢕⠵⢕ ⢕⢕⢕⢕⠁⢜⠕⢁⣴⣿⡇⢓⢕⢵⢐⢕⢕⠕⢁⣾⢿⣧⠑⢕⢕⠄⢑⢕⠅⢕ ⢕⢕⠵⢁⠔⢁⣤⣤⣶⣶⣶⡐⣕⢽⠐⢕⠕⣡⣾⣶⣶⣶⣤⡁⢓⢕⠄⢑⢅⢑ ⠍⣧⠄⣶⣾⣿⣿⣿⣿⣿⣿⣷⣔⢕⢄⢡⣾⣿⣿⣿⣿⣿⣿⣿⣦⡑⢕⢤⠱⢐ ⢠⢕⠅⣾⣿⠋⢿⣿⣿⣿⠉⣿⣿⣷⣦⣶⣽⣿⣿⠈⣿⣿⣿⣿⠏⢹⣷⣷⡅⢐ ⣔⢕⢥⢻⣿⡀⠈⠛⠛⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠛⠛⠁⠄⣼⣿⣿⡇⢔ ⢕⢕⢽⢸⢟⢟⢖⢖⢤⣶⡟⢻⣿⡿⠻⣿⣿⡟⢀⣿⣦⢤⢤⢔⢞⢿⢿⣿⠁⢕ ⢕⢕⠅⣐⢕⢕⢕⢕⢕⣿⣿⡄⠛⢀⣦⠈⠛⢁⣼⣿⢗⢕⢕⢕⢕⢕⢕⡏⣘⢕ ⢕⢕⠅⢓⣕⣕⣕⣕⣵⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣕⢕⢕⢕⢕⡵⢀⢕⢕ ⢑⢕⠃⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⢕⢕⢕ ⣆⢕⠄⢱⣄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢁⢕⢕⠕⢁ ⣿⣦⡀⣿⣿⣷⣶⣬⣍⣛⣛⣛⡛⠿⠿⠿⠛⠛⢛⣛⣉⣭⣤⣂⢜⠕⢑⣡⣴⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢰⣦⢸⣿⠶⠶⣿⡇⣴⡆⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀ ⠀⣿⣿⣿⣿⣿⣶⣶⣤⡀⣸⣿⣿⣿⣶⣶⣿⣿⣿⡇⢀⣤⣶⣶⣿⣿⣿⣿⣿⠀ ⠀⢸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡇⠀ ⠀⢸⣿⣿⣿⠀⣠⣿⣿⣿⣿⣿⣿⣿⣉⣉⣿⣿⣿⣿⣿⣿⣿⣄⠀⣿⣿⣿⡇⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠸⣿⣿⣿⡿⠋⠁⠀⠀⠉⠻⣿⣿⣿⣿⠟⠉⠀⠀⠈⠙⢿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⢹⣿⣿⡀⠀⠀⣾⡆⠀⠀⣨⣿⣿⣅⠀⠀⢰⣷⠀⠀⢀⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⣿⣶⣄⣿⣇⣤⣾⣿⣿⣿⣿⣷⣤⣸⣿⣠⣶⣿⣿⣿⣇⠀⠀⠀ ⠀⢠⣾⣿⣿⣿⣿⣿⠟⢿⣿⣿⠿⠿⠛⠛⠿⠿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣷⣄⠀ ⠀⠀⠀⠀⠈⣿⣿⣿⣧⣀⣄⠀⠀⢰⣶⣶⡆⠀⠀⣠⣀⣼⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⠿⣿⣿⣿⣆⣠⣿⣿⣿⣿⣄⣰⣿⣿⣿⠿⣿⣿⣧⡀⠀⠀⠀ ⠀⠀⠀⠈⠉⠁⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠈⠉⠁⠀⠀⠀

⠄⠄⠄⠄⠄⠄⠄⣠⣴⣶⣿⣿⡿⠶⠄⠄⠄⠄⠐⠒⠒⠲⠶⢄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⣠⣾⡿⠟⠋⠁⠄⢀⣀⡀⠤⣦⢰⣤⣶⢶⣤⣤⣈⣆⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⢰⠟⠁⠄⢀⣤⣶⣿⡿⠿⣿⣿⣊⡘⠲⣶⣷⣶⠶⠶⠶⠦⠤⡀⠄⠄ ⠄⠔⠊⠁⠁⠄⠄⢾⡿⣟⡯⣖⠯⠽⠿⠛⠛⠭⠽⠊⣲⣬⠽⠟⠛⠛⠭⢵⣂⠄ ⡎⠄⠄⠄⠄⠄⠄⠄⢙⡷⠋⣴⡆⠄⠐⠂⢸⣿⣿⡶⢱⣶⡇⠄⠐⠂⢹⣷⣶⠆ ⡇⠄⠄⠄⠄⣀⣀⡀⠄⣿⡓⠮⣅⣀⣀⣐⣈⣭⠤⢖⣮⣭⣥⣀⣤⣤⣭⡵⠂⠄ ⣤⡀⢠⣾⣿⣿⣿⣿⣷⢻⣿⣿⣶⣶⡶⢖⣢⣴⣿⣿⣟⣛⠿⠿⠟⣛⠉⠄⠄⠄ ⣿⡗⣼⣿⣿⣿⣿⡿⢋⡘⠿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠄⠄ ⣿⠱⢿⣿⣿⠿⢛⠰⣞⡛⠷⣬⣙⡛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣓⡀⠄ ⢡⣾⣷⢠⣶⣿⣿⣷⣌⡛⠷⣦⣍⣛⠻⠿⢿⣶⣶⣶⣦⣤⣴⣶⡶⠾⠿⠟⠁⠄ ⣿⡟⣡⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣙⡛⠓⠒⠶⠶⠶⠶⠶⠶⠶⠶⠿⠟⠄⠄⠄ ⠿⡐⢬⣛⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠟⠃⠄⠄⠄⠄⠄⠄ ⣾⣿⣷⣶⣭⣝⣒⣒⠶⠬⠭⠭⠭⠭⠭⠭⠭⣐⣒⣤⣄⡀⠄⠄⠄⠄⠄⠄⠄⠄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠄⠄⠄⠄⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠋⠁⠀⠀⠀⠀⠉⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⠂⠀⠀⠀⠀⠀⠀⠀⢀⡴⣆⡀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⣿⣆⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣼⣿⣿⡆⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡛⠋⣉⣼⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣧⡀⠀⠐⡦⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⢽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⡀⠀⠘⢿⣶⣄⣀⣀⠈⠁⠀⢀⣀⣀⣀⣀⣀⡤⠴⣾⠋⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢿⣷⠀⠀⠀⠀ ⠀⣠⣿⡉⠓⢦⣈⢯⡻⣷⠈⠉⠉⠉⠉⠀⠀⠀⣼⣇⡤⠊⣁⠼⠀⠀⠘⡇⠀⠀⢀⣀⡠⠴⠚⠋⣹⠟⠀⠀⠀⠀⠀⠀⢀⢸⠁⠀⠀⠈⢇⣤⠀⠀ ⠸⣿⠋⢏⠉⠀⠈⠉⠛⢯⡳⠦⢤⣤⣤⡤⠴⢒⣋⣭⣖⠊⠁⠀⠀⠘⠒⠛⠒⠋⠉⠉⠀⠀⠒⣾⠻⣶⡆⠀⠀⠀⠀⠀⠀⢺⣧⡀⣤⠀⠸⣿⠀⠀ ⠀⠈⠻⣎⠀⠀⠀⠀⠀⠀⠉⢹⡶⠒⠛⠉⠉⠉⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡴⠟⠀⠀⠀⠀⠀⠀⠀⢘⡇⣿⢿⠀⢀⠈⣧⠀ ⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠈⣧⡏⠀⣻⡆ ⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⣀⣀⣀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠿⢷⡀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠉⠉⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢴⠖⡶⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣼⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣈⣤⡤⢤⣀⢸⠓⠶⢤⣀⣀⣀⣀⡤⠶⠚⠉⠀⠀⠀⢠⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠙⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⣤⣀⣀⣀⣀⣠⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡴⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣁⠀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⢿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠀⠀⠀⠀⢀⡏⠁⠀⠀⠀⠀⢘⡉⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⠿⠿⠟⠷⠶⠶⠶⠶⠶⠒⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⢿⡟⠙⣶⠏⢳⣞⢙⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣟⡷⠟⣻⠛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣄⠀⢤⡀⣀⢄⣼⣇⢀⢀⣄⣤⠎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠘⣷⣿⡻⣿⣿⣿⠇⢂⣴⠏⣀⣤⠔⠀ ⠠⣄⣀⠐⣬⣿⢹⣿⣿⠀⠀⠈⢻⡹⠞⠋⠉⢠⣿⡿⠟⠟⠁⠀⣀ ⠀⠈⢿⣿⣾⣯⡸⡟⠃⠀⠀⠀⠀⠱⡀⠀⠀⠈⠉⣠⣦⣶⡾⠛⠁ ⠀⠀⠐⠻⣿⣯⡀⢀⠀⠀⠀⠀⠀⠀⢡⢀⣀⣬⣽⡿⠟⠛⠉⠁⠀ ⠀⠀⠀⠀⠀⠙⠻⣿⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠶⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⡀⠀⠀⠀⠀ ⢠⡞⠁⣀⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣸⣿⣦⠀⠀⠀ ⠘⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠛⠟⠀⠀⠀ ⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⠀⠀⠀⠀⠀ ⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀⠀⠀ ⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀ ⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡽⣦⣤⣀ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⣷⢛⠛⠀ ⢀⣤⣽⣿⠿⠟⠛⠋⠉⠉⠉⠉⠛⠛⠻⠿⣷⣤⣀⣀⣼⡟⠀⠀⠀ ⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠗⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿ ⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⠀⠀⠀⠀⠀⠹⣿⣿ ⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠘⢿⣿⡟⠀⣠⣤⣤⣀⠀⢹⣿ ⣿⡏⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣦⣀⣀⣠⣴⣿⣿⣿⠟⠀⣸⣿ ⣿⡇⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⣠⣴⣿⣿ ⣿⡇⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁⣀⣤⣶⣿⣿⣿⣿⣿ ⣿⣷⡀⠈⠛⠛⠻⠟⠛⠛⠛⠛⠉⠉⠁⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿ ⣿⡇⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿ ⣿⣿⡄⠘⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣷⡀⠘⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿ ⣿⣿⣿⣿⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣠⣿⠟⠁⣠⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣄⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡿⠛⠁⣠⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⠉⠙⠛⠛⠛⠛⠛⠛⠉⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⠛⠋⠉⠉⠉⠙⠛⠻⣿⣶⣦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⡄ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⣴⠶⣶⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣠⣾⠟⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠾⢿⣷⣶⣶⣦⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁ ⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠻⠿⠿⠿⠛⠛⠉⠉⠁⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠉⠳⣤⠀⠀⠀⠀⠀⠙⢦⠡⠹⣆⠀⠘⣿⣆⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠃⣤⡞⢻⣾⣰⢻⠀⠀⢠⣾⣿⠏⠀⣾⡇⠀⣦⢶⠈⠞⠙⢣⠤⠄⠀⠀⠀⠁⠈⠻⣶⣇⣤ ⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠈⢷⡀⢘⣆⠀⠘⣿⡆⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢺⣷⠋⡼⠹⡇⠀⣠⡟⣿⡟⠀⠀⣿⠀⠀⣿⣾⣿⡀⣀⡘⠂⠀⠀⣠⠀⠀⣧⣴⣿⣿⠋ ⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠻⡆⠸⣆⠀⠹⣿⡄⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢾⡇⠀⡇⠀⠇⣴⠯⢿⣿⠁⠀⣼⣿⠀⣶⣿⣿⣿⣧⠻⣷⠀⠀⠀⢬⢠⡦⢿⣿⢿⡿⠋ ⣧⡀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠹⣆⠹⣆⠀⠹⣷⡀⠀⠀⠀⠸⡇⠀⠀⡀⠀⠀⠀⣿⡇⢀⠇⢀⡾⠉⢀⣿⠃⠘⠀⣿⣿⠀⠸⣿⣏⣻⣿⣿⡽⠃⢠⡆⣱⣿⣾⣾⣷⠂⢐⣤ ⠻⣙⢷⣄⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠘⢷⡘⣆⠀⢹⣷⠀⠀⠀⠀⡁⠀⢸⣷⡀⠀⠀⣿⠀⢸⢢⣾⡃⠈⣸⡟⠀⠀⢠⣿⡇⠀⠀⠹⣿⠿⣿⣿⣷⣦⣾⣿⠛⣁⣠⣦⣴⠞⠻⠃ ⣤⡈⠻⣿⡷⣄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠙⢞⣦⠀⠹⣧⠀⠀⠀⣿⡀⣾⣿⣧⠀⢠⢸⠀⢈⣿⠇⠀⢰⣿⠁⠀⠀⣾⣿⡇⠀⠀⠠⢿⣷⢮⣭⣛⣛⠻⢥⣿⣿⣿⣿⣛⣁⡀⠀ ⠛⢿⣦⣈⠙⠯⣷⣤⡀⠀⠀⠀⠳⣄⠀⠀⠀⠈⠻⣇⠀⠹⡇⢤⣸⣿⣿⣿⠈⠹⣧⣾⣿⣄⣾⣟⠁⠀⣾⠏⠘⠀⢀⡈⣿⡇⠀⠀⠀⠈⠻⣿⣯⣭⡿⣿⡿⣿⡇⠀⠀⠉⠀⠀⠀ ⠀⠀⠉⠛⢷⣦⡉⠻⣿⣦⡀⠀⠀⠈⢳⡀⠀⠀⠀⠘⢆⠀⣿⣿⣿⣿⠋⠠⠀⠀⠘⠗⣿⠛⣿⠁⠀⠢⠁⠄⠈⠁⠈⠶⢹⣇⠀⠀⠀⣠⡾⠋⣀⣴⠾⠋⢀⡿⠃⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⡉⠛⢦⣄⠙⠿⣦⡀⠀⠀⠙⠦⠀⠀⢀⣈⣣⣿⠏⠋⠐⠀⠸⠁⠔⠂⠠⠃⡀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠴⠋⠀⠈⠉⠀⠀⠠⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣻⠩⢽⣿⣿⣿⡿⠷⣶⣾⣿⣶⣤⣤⣤⣤⣀⣸⣿⢛⠁⠀⠠⢀⠇⠀⠀⠐⠀⠀⠴⠡⠀⠀⠀⠀⠀⠚⠈⠀⠀⠀⠊⠐⠙⢷⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣶⣶⡖⢋⠿⠉⠳⠚⢉⣛⠿⣜⠋⠛⠐⠐⠉⡭⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⡈⠀⠀⠀⣴⠀⠈⠹⣿⣿⠀⠈⠉⠋⠛⢻⣷⣶⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⣿⣿⣷⣮⣂⣠⢀⠀⡁⠘⡀⠱⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⣾⢷⡀⠀⠘⣿⣄⠀⠀⠀⠀⢺⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣯⡯⠞⠩⠑⢦⢄⣀⡁⡉⠁⠀⣀⠀⡀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⠈⢷⠀⠀⠈⢿⣤⣠⣴⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⠀⠱⠄⠄⠀⠘⠐⠀⠄⠀⠠⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠸⣦⠀⠀⢘⣿⣯⣟⣁⠤⠶⠒⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠸⣟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⣿⠄⠀⣰⡟⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⣷⡄⠈⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠁⠀⣰⠇⠀⢠⣿⠓⢈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠂⠀⠀⠄⠀⠀⠂⠀⠀⠀⢰⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣿⣀⣤⠞⠉⠀⢠⡟⣿⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡀⡂⠀⠐⠀⠀⠀⠠⠀⠀⢸⡇⠀⠉⠛⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁⠀⣰⠟⢢⡿⠇⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣭⣿⠿⠋⡭⣆⡰⠀⠀⠀⢉⢐⠀⠀⠈⢿⡀⠀⠀⠀⠻⡏⠉⠛⠳⠶⢶⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠁⠀⣼⡇⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣶⣿⣿⢰⠆⣃⣠⡀⢴⢀⠠⢉⠈⢀⡨⠀⢀⠀⡈⣿⣤⡀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠁⠀⠀⣠⡾⠋⠈⢦⢰⣿⢏⢾⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣶⣿⣿⣿⣿⣿⡟⡛⣛⣃⢾⡤⢈⡖⠈⠘⡡⠀⢄⠀⠀⠀⠠⣮⠟⢳⠶⣤⢴⡶⠛⠁⠀⠀⠀⠀⠀⠀⠁⣀⣴⠞⠁⠀⠀⠀⣸⣿⡛⢿⣿⡿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⢿⣙⣿⣿⣿⣾⠠⡼⢾⣄⣦⢾⠖⢂⣠⠿⠆⠀⡶⠀⠀⢹⣿⣴⣎⣀⠻⠠⠤⠀⣄⢐⣀⣀⣤⡴⠞⠛⠁⠀⢳⡀⠀⣠⣾⣿⢹⣙⣿⣿⣧⠀⠈⠙⠓⠦⢄⣀⠀⠀⠀⠀ ⣿⢿⣽⣿⣿⡿⢻⠏⠻⠮⣵⣒⣬⣥⣶⣷⣘⡌⡐⢂⡀⠐⢶⡐⠀⠈⢙⠿⣭⣛⠛⠛⠛⡟⠉⠉⠉⠀⢣⡀⠀⠀⠀⣀⣧⣾⣿⣟⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠉⠉⠂⠀⠀ ⢿⡿⠿⠿⠿⠷⠿⠶⠼⠿⠿⠿⠛⢻⣿⣿⣿⣿⣦⢄⣀⣀⠆⡍⡄⠀⠤⠀⠩⢙⠻⣶⣦⣽⣤⣀⣀⣀⣤⣷⣤⣶⡿⠿⢛⣿⣹⠻⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠃⠀⢀⣴⡿⢋⣹⣿⣿⣿⣿⣿⣿⣶⣷⣿⣶⣽⡷⣾⣶⣿⣿⣿⣿⡽⣿⠿⣿⣿⣿⣿⣫⢹⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⠐⠠⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⡶⠯⡥⠖⠦⣼⠿⡟⣶⡿⠫⣰⣿⠿⣿⣿⣿⢿⣿⣯⣿⢿⣽⣿⣾⣿⣿⡿⢻⣮⣿⣿⣿⣿⢻⣻⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣄⠀ ⠀⠀⠀⠀⠿⢿⣿⣄⣀⣀⣠⣿⣷⡿⠋⠉⣨⣿⡅⢀⡟⣹⣿⣾⣿⣿⣿⡇⣿⣿⢰⢿⣿⣅⣹⣿⣦⡿⠷⠟⠋⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶ ⠒⠓⠉⠀⠀⠀⣠⣬⣤⠄⣙⣿⣯⠅⣰⣾⠟⠘⣨⣾⣿⣗⣿⣿⣯⣿⠿⠷⢿⡟⡋⢍⣉⠉⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⠀⠀⠀⠅⠀⠛⠦⣸⣿⠛⠛⠻⣿⣿⣿⣿⢷⡿⣿⣴⣿⣯⣽⣶⣿⣤⣤⣾⣧⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠑⠃⠀⡀⣾⠏⠈⠻⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢻⣿⣿⡟⢿⣿⡉⠉⠉⠉⠉⢻⣟⠛⠻⡟⢛⠛⠛⠛⠻⣟⠛⠛⠛⠛⠛⠻⠛⠋⠉⠉⠉⠁ ⠀⠀⠀⠀⡀⠊⠋⠀⠀⢀⣰⢿⠏⠉⠉⠉⠉⠉⠉⠉⠭⠭⠍⠉⠩⠭⠿⣯⣏⠀⠀⠈⢻⠇⠀⠸⣿⡇⠐⠓⠒⠤⠤⢺⡆⠄⠹⣮⣶⠤⠤⢤⡴⢗⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠐⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠂ ⠄⠄⣰⣾⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠄⠄ ⠄⠄⣿⣿⣿⡿⠋⠄⡀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⣉⣉⣉⡉⠙⠻⣿⣿⠄⠄ ⠄⠄⣿⣿⣿⣇⠔⠈⣿⣿⣿⣿⣿⡿⠛⢉⣤⣶⣾⣿⣿⣿⣿⣿⣿⣦⡀⠹⠄⠄ ⠄⠄⣿⣿⠃⠄⢠⣾⣿⣿⣿⠟⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠄⠄ ⠄⠄⣿⣿⣿⣿⣿⣿⣿⠟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠄ ⠄⠄⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠄ ⠄⠄⣿⣿⣿⣿⠋⢠⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠄ ⠄⠄⣿⣿⡿⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⠗⠄⠄⠄⠄⣿⣿⣿⣿⣿⣿⣿⡟⠄⠄ ⠄⠄⣿⡿⠁⣼⣿⣿⣿⣿⣿⣿⡿⠋⠄⠄⠄⣠⣄⢰⣿⣿⣿⣿⣿⣿⣿⠃⠄⠄ ⠄⠄⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⡇⠄⢀⡴⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⠄⠄ ⠄⠄⠃⢰⣿⣿⣿⣿⣿⣿⡿⣿⣿⠴⠋⠄⠄⢸⣿⣿⣿⣿⣿⣿⣿⡟⢀⣾⠄⠄ ⠄⠄⢀⣿⣿⣿⣿⣿⣿⣿⠃⠈⠁⠄⠄⢀⣴⣿⣿⣿⣿⣿⣿⣿⡟⢀⣾⣿⠄⠄ ⠄⠄⢸⣿⣿⣿⣿⣿⣿⣿⠄⠄⠄⠄⢶⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣾⣿⣿⠄⠄ ⠄⠄⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠋⣠⣿⣿⣿⣿⠄⠄ ⠄⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣼⣿⣿⣿⣿⣿⠄⠄ ⠄⠄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣴⣿⣿⣿⣿⣿⣿⣿⠄⠄ ⠄⠄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⣴⣿⣿⣿⣿⠗⠄⠄⣿⣿⠄⠄ ⠄⠄⣆⠈⠻⢿⣿⣿⣿⣿⣿⣿⠿⠛⣉⣤⣾⣿⣿⣿⣿⣿⣇⠠⠺⣷⣿⣿⠄⠄ ⠄⠄⣿⣿⣦⣄⣈⣉⣉⣉⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠉⠁⣀⣼⣿⣿⣿⠄⠄ ⠄⠄⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⡿⠟⠄⠄ ⠠⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⡀⠀⣴⣿⣿⣦⠀⢀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⡈⠻⠟⢁⣴⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣷⡀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⠋⢠⣤⣤⣀⡉⠛⠉⢉⣉⣉⡉⠉⠛⢉⣀⣤⣤⡄⠙⣿⣦⡀⠀⠀ ⠀⢠⣾⣿⡿⠀⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⠀⢿⣿⣷⡄⠀ ⢠⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡄ ⣾⣿⣿⣿⣧⠀⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⡿⠟⠻⣿⣿⣿⣿⠀⣼⣿⣿⣿⣷ ⣿⣿⣿⣿⡏⠀⣿⣿⡿⠁⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠈⢿⣿⣿⠀⢹⣿⣿⣿⣿ ⣿⣿⣿⣿⠁⢸⣿⣿⡇⠀⣶⣶⡄⢸⣿⣿⡇⢠⣶⣶⠀⢸⣿⣿⡇⠈⣿⣿⣿⣿ ⢸⣿⣿⣿⠀⣿⣿⣿⣧⠀⠛⠛⠁⣸⣿⣿⣇⠈⠛⠛⠀⣼⣿⣿⣿⠀⣿⣿⣿⡇ ⠀⢿⣿⣿⠀⢹⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⡏⠀⣿⣿⡿⠀ ⠀⠈⢻⣿⣇⠈⢿⣿⣿⣧⣀⠉⠉⠉⠛⠛⠉⠉⠉⣀⣼⣿⣿⡿⠁⣸⣿⡟⠁⠀ ⠀⠀⠀⠙⠿⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠖⢉⣌⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠀⠈⠉⠲⣿⣿⡜⡀⠀⠀⠀⠀ ⡔⢉⣙⣓⣒⡲⠮⡇⠀⠀⠀⠀⠀⠀⠘⡿⡇⡇⠀⠀⠀⠀ ⡇⠘⣿⣿⣿⠏⠀⠀⠠⣀⡀⠀⠀⠀⠀⡇⠈⠳⡄⠀⠀⠀ ⢹⠀⢻⣿⠇⠀⠀⣀⣀⠀⡍⠃⠀⠀⣠⣷⡟⢳⡜⡄⠀⠀ ⠈⣆⠀⠋⢀⢔⣵⣿⠋⠹⣿⠒⠒⠚⠁⣿⣿⣾⣷⢸⠤⡄ ⠀⡇⠀⠀⢸⢸⣿⣿⣶⣾⡏⡇⠀⠀⢀⡘⣝⠿⡻⢸⡰⠁ ⠀⢳⠀⠀⠈⢆⠻⢿⡿⠟⡱⠁⠰⠛⢿⡇⠀⠉⠀⡸⠁⠀ ⠀⠈⢆⠀⠀⠀⠉⠒⠒⣉⡀⠀⠀⢇⠀⡇⠀⠀⢠⠃⠀⠀ ⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⢉⡱⠀⠀⠉⠀⢀⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⠦⣀⣉⡉⠁⢀⣀⣠⠤⠒⠥⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⣉⣀⣀⡠⠭⠛⠀⠀⠑⠒⠤⠤⠷⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣇⡴⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣩⠏⠀⠀⣧⣄⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡽⠁⡰⢤⡀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠖⣺⠟⢀⠜⠀⠀⠙⢦⡀⠀⠀⠛⠛⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⠯⠓⠚⠉⡉⠉⠁⠯⣄⠀⠀⠀⠀⠑⣄⠀⠀⠠⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠜⠉⣠⠤⠒⠋⡹⢉⠷⠒⠒⢌⠳⡄⠀⠀⠀⠘⣆⠀⠀⠁⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⠞⢡⡖⠋⠀⠀⠀⢰⢁⠏⠀⠀⢀⡈⢣⠹⡄⠀⠀⠀⢸⠀⠀⠰⠥⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣲⢌⡓⢤⡀⠀⠀⡏⢸⠀⠀⠀⣿⢿⢻⠀⡇⠀⠀⠀⢘⡇⠀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⡳⢭⡲⢝⡢⡀⢹⠘⣆⠀⠀⠿⠟⡸⢀⡇⠀⠀⠀⢸⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢦⡉⠳⣝⡮⡳⡳⣈⠲⠤⠴⣞⣡⠞⠀⠀⠀⢠⣯⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠢⣄⠙⢮⣚⡎⠉⠒⠚⠉⠁⠀⠀⢀⣴⣷⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣁⣰⠄⢀⣼⣧⠤⣶⣯⠟⣿⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠐⠋⣰⠿⠚⡿⠁⠈⠉⠉⡼⠓⠢⠤⠤⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢠⠀⠀⠀⠀⢰⠁⠀⠀⠀⢙⣲⠄⠀⢀⣀⢼⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⣴⠋⠀⣠⣀⠀⣉⣓⣦⠀⣾⣿⡖⠋⠉⠁⢀⣠⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⣠⢾⠈⢷⡾⠃⠙⢯⡞⠉⠳⣾⢡⣌⢹⡄⢠⠞⠉⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀ ⠀⣀⢴⡞⠁⠀⢀⣀⠴⠊⠁⢸⠳⣤⡰⠛⢦⣀⣱⠛⠲⢅⡼⠈⠛⣻⠃⠀⢀⠴⠒⠒⠒⠢⣄⠀⠀⠈⢆⠀ ⠈⢿⣭⣷⠶⠊⠉⠀⠀⠀⠀⠀⣇⣸⠇⠀⠀⠙⠁⠀⠀⠀⠁⠀⢠⡇⠀⢠⠇⠠⠤⢤⠀⠀⠈⣇⠀⠀⠘⡆ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢧⡀⠀⣸⠄⠀⠀⡼⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠈⢣⡀⠀⠈⠉⠀⠀⢀⡴⠁⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⣰⠖⠚⢧⡀⠀⠀⠀⠀⠀⠉⠓⠢⠤⠴⠒⠉⠀⠀⠀⠀⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢷⡀⠀⠀⢀⡇⠀⠀⠀⣽⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠽⠦⠤⠥⠤⠀⠼⠃⠀⠀⠀⠻⠤⠌⣙⠶⠤⠤⠤⠤⠤⠤⠤⠔⠚⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⡏⢹⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀ ⣾⡟⠻⠷⣶⣤⣀⣀⣠⣶⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⣶⣄⣀⣀⣤⣶⠾⠟⢻⣷ ⠙⠿⣶⣄⡀⠉⠛⠻⢿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡿⠟⠛⠉⢀⣠⣶⠿⠋ ⠀⠀⠈⠙⢻⣷⣦⣀⠀⠀⠉⠛⠻⠟⠀⠀⠻⠟⠛⠉⠀⠀⣀⣴⣾⡟⠋⠁⠀⠀ ⠀⢀⣀⣤⣿⣿⡏⠛⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⢹⣿⣿⣤⣀⡀⠀ ⣾⣿⣿⣿⣿⣿⡇⠀⠐⠟⠙⢻⣷⣦⣤⣤⣴⣾⡟⠋⠻⠀⠀⢸⣿⣿⣿⣿⣿⣷ ⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⡿ ⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⡟⢿⣿⠿⠿⣿⡿⢻⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠸⡟⠀⠀⢻⠇⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡷⢶⣶⣦⣴⣶⠶⢾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣧⠀⠀⣼⡆⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣾⣿⣶⣶⣿⣷⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⠱⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⠒⠧⣤⡤⠤⢼⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⠀⠀⠀⠈⠓⠺⢿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠿⠿⢿⣿⣿⣿⡿⠿⠟⠋⠉⠀⠀ ⢻⣀⠀⠀⠀⠀⠀⣀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⢸⠓⣄⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟ ⠀⢸⠀⣻⢓⡞⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⢠⣴⣾⠿⠋⠀ ⠀⢸⠀⡇⡼⠀⠠⢸⣷⣾⡷⠀⠀⠀⠀⠀⠀⢰⣧⣤⣿⡆⡀⠀⠀⢹⣅⠀⠀⠀ ⠀⢸⢠⡷⠗⠒⠀⠀⠉⠋⠀⠀⣀⣀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠈⠒⢦⣿⣷⣄⠀ ⠀⢰⠋⣀⣀⠀⠀⠀⠀⢀⠀⠀⠉⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠙⣿⣿⣷ ⠀⡇⡞⠅⠀⢹⡀⢀⣠⡞⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢰⠋⠁⠈⢳⡀⣿⣿⣿ ⠀⣇⢷⣀⣀⠼⠀⢀⡠⠟⠒⠉⢹⠉⠙⠲⢴⣋⠙⠀⠀⠸⣄⠀⢀⡼⢡⢻⡿⠙ ⠀⠘⢆⠀⠀⣤⠞⠁⠀⠀⠀⠀⡼⢇⠀⠀⠀⠈⠙⠲⣄⠀⠈⠙⢋⡵⠋⢸⣄⠀ ⠀⠀⢸⡕⠆⠂⠀⠀⠀⠀⣠⠞⠁⠘⡄⠀⠀⠀⠀⠀⠘⠆⠀⠒⠋⠀⠀⢸⠪⠄ ⠀⠀⠸⠁⠀⠀⠀⠀⣀⠴⠃⠀⠀⠀⠙⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢸⡇⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⢸⡿⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠜⡾⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠞⠁⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠈⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠘⡏⢻⣆⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⠉⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⣧⠀⡇⠀⢻⡄⠀⠀⣀⡴⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⣸⠀⢀⣴⠀⠀⠀⠀⠀⢀⡼⠃⠀⠸⣾⠃⠀⠸⡷⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡇⠀⠀⠸⣷⢤⣄⡀⠀⠀⠀⠀⣽⣿⣴⢯⡟⠀⠀⠀⣀⡴⠋⠀⠀⠀⢨⡿⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⡤⠴⠒⣿⠉⠁⠀⣾⠁⠀⠀⠀⠀⣼⢻⠀ ⠀⠀⠀⢹⡀⠀⠀⢸⡄⣈⠙⠲⣄⡀⠀⡇⠘⡿⢸⡇⠀⠀⡶⠋⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⡏⠀⠀⣠⠔⠋⠉⠀⣀⣸⠇⠀⠀⢰⠃⠀⠀⠀⣠⣸⠃⠈⡇ ⠀⠀⠀⠀⢧⠀⠀⠀⢻⡈⠑⢦⡀⠙⢶⣧⠀⠀⠈⣷⣀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⢃⠴⠋⢁⡠⠖⠋⠉⢡⡟⠀⠀⢠⠏⠀⣠⡶⠋⢹⠃⠀⠀⡇ ⠀⠀⠀⠀⠘⢧⠀⠀⠀⢳⡀⠀⠉⢷⣠⡟⢧⡀⠀⠘⢷⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢫⠏⠈⢳⡞⠋⠀⠀⠀⢠⠟⠀⠀⢀⡟⢀⠼⠁⠀⢰⡟⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠱⣄⠀⣰⠏⠀⠀⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣋⣠⠞⠀⠀⠀⠹⡄⠀⠀⣴⠋⠀⠀⢠⣞⡙⠻⠀⠀⢠⠏⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠘⢷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⢿⣠⠞⠁⠀⠀⣠⠏⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠉⠀⣀⣄⡀⠀⡶⠲⣆⠀⠀⠀⠀⠀⣠⠖⢲⡆⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡴⠟⠒⠶⣾⣛⠃⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⣼⠉⠈⢳⡀⢱⡀⣸⠀⠀⠀⠀⢠⣿⠀⣰⠃⡴⠋⠉⢳⡄⠀⠀⠀⠀⢀⡰⠋⠀⠀⠀⠀⠀⠈⠛⠲⠶⠶⠶⣶⠖⣼⠇ ⠸⣿⡟⠋⠉⠉⠙⠛⠛⠳⠾⡄⠀⡟⢦⣀⠀⢳⠀⠓⠞⠀⠀⠀⠀⠀⠻⡾⠋⣸⠁⣠⡴⡟⢻⠀⠀⠀⡤⠿⠤⠶⠒⠚⠛⠛⠛⠛⢛⡷⠂⠀⣰⠏⢠⡿⠀ ⠀⠉⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⢠⡇⢸⢙⡷⣌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡾⢻⠀⡇⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⣴⠏⢀⡾⠁⠀ ⠀⠀⠀⠀⠈⠉⠓⠲⢤⣄⣀⠀⠈⣧⢸⡀⠳⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠻⠞⢠⡇⠀⡇⠀⠀⠀⠀⠀⠀⣠⡤⠚⠋⠀⠀⠀⢀⡼⠃⣠⡾⠁⠀⠀ ⠀⠀⠀⠀⣴⣶⠶⠒⠋⠉⠁⠀⠀⢸⡎⢧⡀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⡞⠀⢰⠇⠀⠀⠰⠶⠾⣭⣥⣀⡀⠀⠀⠀⣴⣿⣤⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⠲⠦⣤⣤⣤⡀⠀⠹⢮⣉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⣠⠎⠀⠀⠀⠀⠀⢀⣀⣠⠴⠟⢋⣤⠞⠁⠸⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠙⣄⠀⠀⠀⢤⣀⡀⠀⠀⠛⠟⠀⠀⠀⠀⠀⢀⣠⠖⠀⠀⠀⠀⣰⠶⠚⠋⠉⣀⣀⣠⣴⣻⡅⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡞⠃⠈⠳⣄⠀⠀⠈⠙⢿⡗⠒⠒⠒⠒⠒⢺⣿⠏⠁⠀⠀⣠⡴⠚⠁⢀⡤⠖⠛⢉⣥⠞⠋⠉⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠙⠶⣤⣀⠀⠙⠦⣄⠀⢀⣠⠞⠁⣀⣤⠶⠛⠉⠀⠀⠀⠋⠀⢀⡴⠟⠳⣄⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢰⡀⠀⠀⠀⠀⠉⠉⠓⠒⠶⠿⠗⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡅⠀⠀⠙⠶⣄⣀⣀⡀⢀⣴⠟⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣸⣷⡄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⢷⡀⠀⠀⠀⠈⣿⠙⠋⠉⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠷⠝⢧⣄⡀⠀⠀⠀⠙⠻⠦⣤⣀⣀⠀⠀⠀⠀⠀⣀⡴⠞⠃⠀⠀⠀⠘⣇⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠻⣤⡀⠀⠀⠈⠙⠲⣶⣤⣤⣤⣤⣤⣬⠟⠛⠒⠒⠒⠻⣍⠀⠀⠀⠀⠀⣀⣴⢿⠀⠀⠀⠀⠀⠹⣄⠀⠀⣼⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠈⠙⠓⠒⠲⢶⡾⠃⡟⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠹⣟⠒⠒⠒⠋⠉⠀⢸⠀⠀⠀⠀⠀⠀⠹⣦⣴⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠀⠳⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣤⣠⡤⠤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠤⠴⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⣤⣶⣿⣿⣷⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣴⡿⢿⣿⣿⠿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⣴⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠛⢿⡟⠛⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⣠⡖⠀⠀⢀⣸⡿⠁⠀⠘⠿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢔⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⢸⡇⠀⢀⣴⣿⣿⠃⠀⠀⠀⠀⢀⣼⣿⣿⣿⣉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⣛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠊⠀⣶⣿⣿⣿⣿⠀⠀⠀⠀⣴⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡝⢷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⠉⢿⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠙⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠈⣧⢀⣾⣿⣿⣿⣿⣿⣿⣿⡀⢀⣾⣿⣿⣿⣿⠖⠀⠀⠉⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⢿⣦⠀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⢿⣧⠀⠀ ⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⣿⣇⠀ ⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢯⣛⣛⣥⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢹⣿⡄ ⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣿⣿⣿⣿⣿⡟⠁⠀⠀⠉⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⣿⡇ ⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⠿⠿⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿ ⢸⡇⠀⠀⠀⢠⠞⠓⢄⠀⠀⢀⣴⣿⡟⢱⢆⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣿⣿ ⣸⡇⠀⢀⡴⠁⠀⠀⢀⣷⣿⣿⣿⣿⡀⠃⠈⠀⢀⢚⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿ ⣿⡇⢠⠎⠀⠀⠀⠀⠸⠏⠘⡿⠋⠟⠃⠀⠀⠐⠃⢸⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢸⣿⡏ ⣿⡇⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠁⠀⠀⠀⠀⠈⡿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⣿⣿⠃ ⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⢇⢻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⢀⣾⣿⠏⠀ ⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠘⡌⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⣠⣿⣿⡟⠀⠀ ⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡙⢿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠉⠙⠻⠿⣷⣤⣀⣀⣀⣤⣤⠶⠞⠋⠁⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣍⡛⠿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣮⣝⠻⢿⣿⣿⡿⢿⡿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣦⣽⣿⣷⣤⣤⣦⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⡅⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢨⣿ ⣿⣿⡄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢠⣿⣿ ⣿⣿⣿⡄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢠⣿⣿⣿ ⣿⣿⣿⣿⡄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢠⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣶⣄⡀⢀⣴⡿⢻⡏⠉⠀⠀⠉⢹⡟⢿⣦⡀⢀⣠⣶⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠸⣷⠀⠀⠀⠀⣾⠇⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠙⠷⣦⣴⠾⠋⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⢠⣿⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠟⠻⣧⠀⠀⢰⣿⣿⡄⠀⠀⢠⣿⣿⡇⠀⠀⣼⠟⠻⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⠁⠀⠀⣿⡄⠀⠀⠙⠛⠛⠀⠀⠛⠛⠋⠀⠀⢠⣿⠀⠀⠈⢿⣿⣿⣿ ⣿⣿⠏⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⠀⠀⠀⠀⠹⣿⣿ ⣿⠃⠀⠀⢀⣤⣾⣿⣿⣿⡄⠸⣷⣦⣀⣀⣴⣾⠇⢠⣿⣿⣿⣷⣦⡀⠀⠀⠘⣿ ⣿⡀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣄⠙⠛⠛⠛⠛⠋⣠⣾⣿⣿⣿⣿⣿⣿⣦⡀⢀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠂⠀⡤⠔⠊⢩⢁⠔⠁⠀⠀⠀ ⢀⡀⠤⡤⠤⠤⠤⠤⠤⠀⠠⠄⠀⠠⠤⠬⣄⠔⠁⠀⠀⡠⠊⠉⠁⠂⠤⣀⠀ ⠈⠑⠂⠼⠤⣀⣀⣀⡰⠀⣀⡀⠀⠀⠀⠀⠀⠀⢆⠂⠁⠀⠀⠀⠀⠀⠀⣠⠃ ⠀⠀⠀⠀⡔⠉⠑⢄⠇⠨⠷⠁⠀⡄⠀⠰⣽⡆⢸⣀⠀⠀⠀⠀⠀⠀⡔⠁⠀ ⠀⠀⠀⠀⢸⠀⠀⠘⠉⢢⠀⢢⡴⠶⣤⠄⢀⠤⢼⢣⠉⠒⠤⣀⢀⠌⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⠀⠘⡖⠋⠀⠈⢆⢀⠎⠀⠸⡀⡰⣠⠆⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡄⠀⠈⠢⠄⠀⠈⠁⠀⢀⠤⠊⠀⠀⠉⠒⠄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣀⣀⡀⠠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢾⠗⠒⠉⠁⠀⠀⠀⠀⠀⠉⠑⠢⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣟⠓⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡤⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡀ ⠀⠀⠀⠀⠀⠀⠚⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃ ⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠁⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠋⠀⠀⣇⠀⢀⣴⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣇⠀⣠⠋⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣄⠀⠀⠀⠈⢆⠀⠀ ⣿⣿⣿⡿⠟⡏⠁⢢⠙⠛⠀⠀⠀⡄⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠈⠳⡀ ⠉⠁⠀⠀⠀⠘⢆⣠⠀⠀⠀⠀⣞⠁⠀⠀⠀⠀⠈⢿⣿⠏⢀⣀⠀⠀⠀⢠⠃ ⠀⠀⠀⠀⠀⠀⠀⠙⢢⠊⠉⠢⡳⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠈⣄⡴⠃⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠠⠒⠉⢣⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠈⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃⠀⠀⠀⠀⠀⠀⠄⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠻⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣧⣄⣀⠀⢻⡇⠀⠀⠀⠀⠀⢀⡀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠿⠻⢿⣷⣤⣤⣤⣤⣭⣭⣥⣼⣿⣡⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠀⠀⠀⠉⠛⠻⢿⣭⣉⠉⠉⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛ ⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣿⣷⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠙⠻⣿⣿⣿⣿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⢿⣿⣿⣽⣿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠴⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠ ⠀⠻⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⠀⠀⠈⢻⣷⣤⡀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣽⡿ ⠀⠀⠀⢸⡏⠈⣹⣦⡀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡷⠀ ⠀⠀⠀⢸⡇⠀⠈⣿⠹⣶⣄⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⣼⡇⠀⠀⣹⠀⠈⢻⡿⠁⠀⠀⠀⢀⣤⣴⡶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⣿⠇⠀⢀⣿⠀⢀⣿⠇⠀⠀⠀⠀⣿⣿⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠉⠉⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠹⢹⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⢸⣿⠀⣼⡟⠀⠀⠀⢠⡀⣿⣿⣷⣿⣿⣿⣿⡿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣴⣿⣿⣿⡇⢲⠀⠀⠀⠀⠀⠀⠀⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⢸⡏⢰⡿⠀⠀⠀⠀⠀⠣⠙⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠁⠀⠧⡀⠀⣄⡀⠀⠀⠘⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⣸⣧⣾⡷⠶⠿⠗⠀⠀⠀⠀⠄⠈⠻⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠉⠛⠿⣶⣄⢸⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⡿⢀⣾⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣦⡀⠀ ⠀⠀⠀⢡⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡛⢋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⢀⣿⠏⠀⣀⣤⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿ ⡆⠀⣼⠏⢠⣾⡿⠃⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠇⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠙⠻⣷⡀⠀⠘⣿⣿⣿⣿⣿⣿ ⠀⠀⣿⠀⣼⡟⠀⡆⠀⠀⠀⠀⣿⡇⠀⠀⢀⣠⣶⣿⡏⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣌⠀⠀⠀⠀⠀⠠⠄⣴⡿⠁⠀⠀⠀⠀⠀⠀⢿⣷⠀⢀⣿⣿⣿⣿⣿⣟ ⠀⠐⣿⠀⣿⣇⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠈⠉⠁⠉⣷⣧⣤⣤⣶⠾⠿⢶⡶⢶⣶⣦⣤⡀⠀⠀⣀⣼⣿⣷⣶⣄⠀⠀⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⡄⢸⣿⠀⣸⣿⣿⣿⣿⠿⡇ ⠀⠀⢹⣆⠘⣿⣧⣀⠀⠀⣠⣾⠟⠀⠀⠀⢀⣀⣴⣶⠿⠋⠁⠀⠀⠀⠀⢸⡇⠀⠀⠈⠙⠛⠿⣾⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⣠⣿⠇⢰⡟⢿⣿⡟⠁⠚⠃ ⠀⠀⠘⣿⡄⠀⠉⠉⢛⠛⠋⠀⠀⢀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠄⠉⠻⢿⣶⣄⣀⠀⠀⠀⠀⠀⠈⢿⣷⣦⣤⣥⣾⠿⠃⢠⣿⠁⣸⡟⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⣦⠀⠀⠀⢠⠀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠿⣷⣦⡀⠀⠀⠀⠀⠀⠈⠉⠉⠀⣠⣴⡿⠁⠀⢸⣷⣀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⡳⣄⠀⠀⠉⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠈⣿⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠛⣿⣆⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⢈⣯⠿⣆⠀⠀ ⠀⠀⠀⠀⠀⢿⡋⣽⣷⡇⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡓⠀⠀⠠⢶⡿⠛⠃⠀⠀⠀⠀⠀⠘⡿⠒⣨⣤⠀ ⠀⠀⠀⠀⠀⢸⣷⡏⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣇⡀⠙⠋⠀ ⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⡛⠃⡀⠒⠀⠀⠀⠀⠀⠀⠤⠀⢻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠀⠀⠘

⠀⢀⣴⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⡀⠀⠀⠀⣀⣤⣤⣤⡤⠤⠶⠶⠦⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡟⠛⠛⠛⠛⠛⠉⠁⠀⠀⣈⣷⠴⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢦⣄⢠⡟⠈⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡟⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⣠⣶⣶⣄⣤⣶⣦⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠃⠾⠋⠉⠳⣄⠙⠿⠋⠀⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⠀⠙⠿⠋⢀⡴⠞⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⣀⣀⣠⣤⣤⣄⣀⡀ ⣼⠀⢠⠀⠀⠀⠈⡇⠀⠀⠀⠈⠛⠿⠿⠿⠿⠟⠻⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠉⠉⠀⠀⠀⠀⠀⠀⠘⣷ ⡟⢳⣄⠀⠁⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⡇⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠶⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⣶⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠀⠀⠀⠀⠀⠀⠉⠛⣿⢶⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⢠⠖⠒⠛⠛⠛⠛⠉ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣿⣄⠀⠀⠀⠀⠀⠀⢠⣾⠟⣻⡟⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⡄⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀ ⢸⣦⡀⠀⠀⠀⠀⠀⢠⣀⡀⣠⡏⠁⠘⠷⠤⠤⣤⣤⡴⠏⠉⢛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⢻⡷⠟⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀ ⠈⢿⡄⠀⠀⠀⠀⠀⠀⠉⠉⠙⠷⢦⣤⣤⣀⣀⣀⣀⣤⣴⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀ ⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠸⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣶⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⠶⠚⠓⠒⠶⠦⠤⠤⠤⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⠀⠀⢀⣤⠤⠴⠖⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢰⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⡆ ⢸⣿⣿⡆⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⣿⣿⣿⣿⡇ ⢸⣿⣿⣇⠀⠀⢀⡀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⢠⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⡄⠀⠘⣿⣶⣤⣀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⢀⣠⣴⣾⠃⠀⢀⣾⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⡄⠀⠘⢿⣿⣿⣷⣦⣀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢀⣤⣾⣿⣿⣿⠃⠀⢀⣾⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣄⠀⠈⠻⣿⣿⣿⣿⣷⣤⡀⠈⢿⣿⣿⣿⡿⠟⠛⣿⠿⠛⡿⠿⣿⣿⣿⣿⣿⣿⠟⠀⣀⣴⣿⣿⣿⣿⡿⠃⠀⢠⣾⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣿⣦⡀⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⢻⡿⠁⢀⣾⣿⣿⣿⣿⣿⠟⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠈⠛⢿⣿⣿⣿⡿⠆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠴⣿⣿⣿⣿⣿⠟⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠉⠻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⠟⠋⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣴⣶⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣼⠋⠙⡆⠀⠀⠀⠀⠀⠀⠀⣰⠋⠙⣆⠀⠀⣿⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣦⣴⡧⠀⠀⠀⠀⠀⠀⠀⣿⣦⣴⣿⠀⢰⣿⣿⣿⠏⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⠇⠀⠀⠀⣀⠀⠀⠀⢹⣿⣿⡟⠀⠸⠿⠛⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠛⠋⠀⠀⠀⠈⠛⠁⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠑⠒⠋⠉⠑⠒⠋⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡻⢿⣧⣴⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢉⣴⣿⣿⢋⣶⣤⣄⣀⣀⣀⠀⢀⣀⣀⣤⣶⣷⣌⢿⣿⣷⠭⠛⣿⣴⣧⠀⣠⣆⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⣠⣾⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡀⠸⠻⣿⡇⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⣿⣿⣿⢿⢸⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡀⠻⣿⡀⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠀⢠⣿⠛⠇⣶⣾⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠙⠂⠸⠋⢿⣿⣿⣿⣿⣿⣿⡿⠁⠁⢀⡾⠁⣾⣾⣿⣿⣿⣿⣿⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⢻⡿⠁⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠛⢋⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠤⠤⠾⠿⠷⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤ ⣿⡿⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠿⣿ ⠋⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠈ ⣇⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢠⣾⠏⠁⠀⠀⠀⠀⣠ ⠻⣷⡀⠀⠀⠀⠀⠀⢹⣶⠿⠋⠉⠉⠁⠈⠉⠉⠙⠻⢶⣟⠁⠀⠀⠀⠀⢀⣴⣟ ⠀⠈⠻⢷⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⣶⠿⠛⠉ ⠀⠀⠀⠀⠙⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⢻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡟⠀⣾⣧⣼⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣷⣼⣷⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠻⠿⠿⠟⠀⠀⠀⢻⢿⠀⠀⠀⠙⠿⠿⠟⠀⠸⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠟⠛⠲⡄⠀⠀⠀⠀⢀⡼⢮⡀⠀⠀⠀⠀⢀⡴⠛⠻⣿⠀⠀⠀⣀ ⠀⠀⠀⠀⢹⣇⠀⠀⣹⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⢸⠀⠀⢰⣿⠶⠞⠛⠉ ⠀⠀⠀⠀⠈⢿⣶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠋⠙⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠉⢷⡈⢻⣆⠀⠀

⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀ ⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿ ⢹⣿⣿⣿⣿⣿⣶⣤⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣤⣶⣿⣿⣿⣿⣿⡏ ⢸⣿⣿⡁⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢈⣿⣿⡇ ⠘⣿⣿⡇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢸⣿⣿⠃ ⠀⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⢀⣿⣿⣿⣿⣅⣈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣁⣨⣿⣿⣿⣿⡀ ⣼⣿⣿⣿⣿⣿⣿⣷⣄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣠⣾⣿⣿⣿⣿⣿⣿⣧ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⠀⠀⢀⣀⣀⣠⣤⡴⠶⠛⠉⠉⠁⠀⠀⠉⠉⠉⠙⠛⠲⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣧⠀⠀⠀⠀⠀⣿⠀⠀⢀⣾⣿⣷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣆⠀⠀⢀⡾⠋⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⣦⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀ ⢀⣾⣿⣿⣿⣿⣿⣷⣦⣾⠡⠤⣀⠀⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣾⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀ ⢸⣿⣿⣿⣿⣿⠿⠟⠉⣿⠀⠀⠈⢣⠀⠈⠁⠀⠀⠀⠀⠀⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇ ⠈⠋⠉⠉⠁⠀⠀⠀⠀⠈⢷⡀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡞⠀⠀⠀⣠⣀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⣠⠤⠒⠒⠢⢄⠀⠀⠀⠀⣼⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣴⠋⠀⠉⠣⣄⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⢣⠀⣠⡾⠁⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢀⣼⠾⣯⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠤⠔⠚⠉⠀⠀⠙⣧⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠘⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢊⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠔⠊⠁⢾⠂⠀⣀⣠⣤⡤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣔⡤⠊⠁⠀⣐⣲⠾⠛⢫⣦⣉⢁⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡸⢟⣀⣤⠖⠋⠁⠀⠀⣰⣿⣿⣿⣯⠠⢤⣤⣤⣀⣀⣀⠀⠀⠀⠀ ⢸⠖⠉⠈⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⢳⡄⠀⣀⣀⣬⣭⠟⠛⠀⠀ ⠁⠀⠀⣾⣿⣿⣶⡄⠀⠀⠀⠹⣿⡿⠀⠈⣿⡜⣟⣉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⡿⠋⣠⠀⠀⠀⠀⠈⠇⠀⠀⣸⢡⡈⣭⣿⣿⣷⣶⣦⡤ ⠀⠀⠀⠉⠀⣠⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠇⣏⣿⠻⠛⠋⠉⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢺⣟⠀⢀⡀⠀⠀⠀⠀⠀⣰⣶⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣶⡾⠁⠀⠀⠀⢠⣞⡋⠩⠕⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣡⣿⣟⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣯⡟⣁⣨⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠛⠛⠀⠀⣠⠟⠛⠛⠿⠿⠶⠶⠶⣤⡍⠙⠋⠹⠿⠛⢫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣴⣤⣴⣾⠃⠀⣴⣧⣤⣄⡤⠖⠋⠉⠉⠉⠛⠛⠀⠀⠀⠀⢀⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⠎⠉⠋⠁⢾⣷⣀⣀⣈⣡⠟⣻⠟⠻⣦⣴⣶⣶⣶⡄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢿⣿⠀⠀⣿⡦⠀⣠⣶⣿⡿⠟⢻⣏⣀⣼⣥⣶⢠⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣷⣾⣧⡞⠉⠟⠉⠀⠀⠘⢛⣿⡿⢁⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣆⠃⠹⡟⠀⣠⠴⠚⠛⠳⣔⢿⣿⢁⡼⣵⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⢀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠳⣄⢀⡼⠁⠀⣀⣀⠀⡿⠘⣿⣿⣾⠁⢀⡴⠶⢦⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⡈⠛⢀⣴⣿⣿⣿⢾⣧⠀⣸⠁⢿⠀⠀⢳⣀⠀⠉⠀⣸⡟⢿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣻⠿⠷⠎⠀⠉⠁⢠⣿⡿⠞⠁⢀⣈⣷⣄⡀⠈⠛⠓⣚⡿⠃⠀⠉⠻⢿⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠹⣆⣀⣠⡀⣀⣴⣿⢿⡀⠀⠀⣿⢉⠉⢻⡙⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠉⠛⠞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠁⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣽⡄⠀⢻⡼⣇⣈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠙⠶⠿⠶⠋⠛⠋⠉⣉⣿⣿⣿⣿⡿⢉⣷⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⢋⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣋⣠⣾⣿⣿⣆⠈⣧⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠟⠀⢸⠃⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠐⠛⢿⣆⡴⣄⠀⣤⣄⣾⠋⣻⠋⠀⠀⠉⠻⣿⣿⣿⣿⣿⣷⣸⡇⠀⣠⣄⡉⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⡵⡄⠀⣿⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⡅⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆⠈⠻⡃⠀⠉⠀⢻⡀⢠⡞⠛⢦⡘⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠙⣆⣿⣿⣿⣿⣿⣿ ⣿⡿⠀⡿⠀⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣡⣀⠀⢹⡄⠀⠀⣀⣤⣴⣶⣶⣾⣿⣿⣶⣾⣦⣄⡀⠈⣷⣸⣧⠀⢈⣿⡿⣿⣿⣿⣿⣿⣦⡈⠳⣄⣀⣹⡿⣝⠻⣿⣿⣿ ⣿⣧⣼⣣⣼⡥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣳⣼⠗⠛⠋⠉⠈⠛⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠛⠛⠛⠋⠰⡜⣿⣿⣿⣿⡿⢿⣿⡟⢻⡍⠳⣌⠙⢾⣿⣿ ⣿⣿⣿⠁⠸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢀⡤⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠳⡀⠀⢳⡘⢿⣿⣯⣤⣾⣿⣿⡄⠹⣦⣈⠳⢄⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠾⣥⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⠆⠀⠁⠈⢻⣿⣿⣿⣿⣿⣿⣆⣹⣿⣷⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣯⣤⣤⣶⣏⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣀⣠⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡏⠁⣾⠁⠀⣭⠀⢘⡏⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⣿⣿⡶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣾⣿⣿ ⣿⣿⠀⠀⠈⠓⢤⡀⠀⠀⢀⡤⣶⠞⠟⠲⣲⢤⣀⠀⠀⠀⢀⠴⠊⠀⠀⢹⣿⠟ ⠈⠻⢄⠀⠀⠀⠀⠙⢤⠖⢁⠞⠁⠀⢸⠀⠈⠑⣮⣑⣄⠔⠁⠀⠀⠀⢀⠜⠁⠀ ⠀⠀⠀⠑⠠⣀⠀⠀⢸⣿⣾⣶⠶⠶⠾⠶⢶⣾⣿⣿⠻⠀⠀⢀⡠⠒⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⡳⣲⠯⠭⢤⠖⠒⠛⠒⠲⠯⠭⠭⠶⢗⠂⠁⠀⠀⡠⠔⠂⠀ ⠀⠀⠀⢀⡀⠀⢰⠋⠀⠀⠀⠀⠈⠁⠒⠠⠤⠀⠤⠒⠀⠉⠆⠀⡴⠊⠀⠀⠀⠀ ⠀⠂⡇⡼⠟⠀⡄⢠⣴⠶⠦⢖⣄⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⠤⡄⠀⣧⡟⢡⣾⣈⡆⢱⡆⠀⠀⠀⢠⣇⣹⣦⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠇⠸⠺⡱⡘⠠⠗⠁⣸⡇⡀⠀⠀⠀⠻⠿⠋⢠⠒⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡀⢱⠹⣶⣶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠇⡀⢀⠤⠂⠀⠀ ⠀⠀⠀⠀⠀⢀⠕⠊⠁⠈⠱⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⡣⠊⠠⢞⣁⡀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⠀⠀⠀⣰⡃⠲⣀⠀⠀⠀⢀⠔⠀⠀⠈⠘⡤⡀⠀⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⠤⠐⠚⠿⡇⠀⠀⠉⠀⠉⢀⠔⠁⠀⠀⠀⢱⢁⣞⣁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢨⠲⡀⣀⠜⠁⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠈⡆⣠⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡴⢷⠀⢸⡷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠂⠛⠠⠊⠀⢸⠇⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿ ⣿⣿⣿⠟⠉⠈⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿ ⣿⡟⠁⠀⠀⠀⠈⣿⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠏⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣿⣿ ⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⠀⠀⠙⢿ ⠀⠀⠀⢀⠴⠁⠀⠀⠀⠀⢀⠎⠀⠀⢀⡤⡀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠘⢆⢀⡜ ⠀⢀⠔⠁⠀⠣⡀⠀⠀⡠⠁⠀⠀⠀⢸⣉⣱⠀⠀⠀⠀⢠⠀⠀⠙⢡⠂⢹⣧⣄ ⣔⠁⠀⠀⠀⢀⡨⠗⠁⠐⡄⠀⡠⠀⠤⡛⠛⠀⠀⠀⠀⠀⡇⣠⡀⢀⣴⣿⣿⣿ ⣿⣍⠉⠉⠉⠀⠀⠀⠀⠀⢈⠦⢄⡀⠀⡸⠀⠀⠀⠀⠀⠀⡎⠀⠈⢿⣿⣿⣿⣿ ⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠆⠀⢠⣾⡏⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣄⣀⢠⣿⡓⠀⠀⠀⡀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣏⠈⠛⠑⠀⠀⠀⠈⠢⢀⣠⠤⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣠⣠⣤⣤⣤⣤⣤⣤⣤⣦⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠊⠉⠉⠀⣠⠶⠋⠉⡏⠉⠻⣷⡶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣼⣧⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⣾⡟⠉⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠨⣿⡇⠀⠀⠀⣠⠚⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣰⡿⠁⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⣿⡇⢀⡴⠊⠁⠀⠈⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⢿⣧⣄⣁⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣿⡗⠋⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⣀⣏⢀⣠⣤⠴⠖⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀ ⠀⠀⠀⣠⣴⡿⢿⠟⠉⠀⠀⠀⠉⠛⠲⠦⢤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⣿⣿⠝⠏⢻⡉⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀ ⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⠿⠋⡇⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄ ⠀⠀⠀⠙⢿⢾⣭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡶⠟⣿⡿⠀⠀⡇⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡿ ⠀⠀⠀⠀⠸⡀⠀⠉⠛⠓⢶⣦⣤⣤⡤⠤⠤⠤⢴⣷⡶⠚⠛⠋⠁⠀⠙⠛⠛⣡⡤⠤⡇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡿⠁ ⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⢸⡇⠀⢹⡇⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠘⢷⣀⣼⠃⠀⠀⣠⡤⢦⣀⠀⠀⠀⠀⠀⠀⠀⢹⣖⣦⣤⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠠⣰⣿⣿⡇⠀⠀⠀⠀⠀⢀⣤⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠈⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⣧⠀⠀⠀⠀⠀⠀⢸⣷⣴⣿⣿⣿⡇⠀⠀⠀⠀⢠⣻⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢸⢸⠿⣿⣿⣿⡇⠀⠀⠀⠰⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣄⠀⠀⠀⡾⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢸⢸⠀⠀⠙⠿⠇⠀⠀⢀⡟⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠳⡄⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢡⣿⠀⠀⠀⠀⠀⠀⣄⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢉⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣄⠀⠀⠸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⣳⣤⣄⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⡄⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠿⠛⠹⡆⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠋⠁⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀ ⢸⠀⠀⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡟⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡴⠟⠉⠁⠀⠀⢰⡾⠛⠷⣦⡀⠀⠀ ⢸⡄⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠘⢷⡀⠀⠈⢿⣄⠀ ⠀⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠳⢤⣀⣸⣿⡀ ⠀⢳⡀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣧⠀⠀⠀⠀⢠⣴⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⡀⠈⠛⣚⣿⡇ ⠀⠈⢷⠀⠙⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠸⡄⢀⣠⠞⠉⣰⠛⣿⣿⣧⡀⠀⠀⣠⣾⣟⠿⣧⣀⣤⣿⢿⠁ ⠀⠀⠈⠳⠴⢷⣄⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⡇⠁⠀⠀⣰⠏⠀⠹⡌⢩⠛⠻⠿⢿⣿⣿⣶⣽⠛⠉⢠⠟⠀ ⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⡉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠹⣄⡀⠀⣸⠁⣀⡤⠞⠁⠀⠀⠀⠙⠦⣳⣄⡀⠀⠙⠛⠛⠁⣀⡼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡉⠙⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠚⠛⠛⠛⠉⠁⠀⠀⠠⠤⠀⠐⠲⢤⡈⣙⡛⠛⠒⠒⠒⠛⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠈⣿⣿⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣷⣶⣿⣿⣿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣶⣤⡈⠙⢿⣿⠉⠀⠀⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢿⣷⣶⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⡇⠈⣿⣿⣿⡏⠀⣿⣿⡆⠈⠋⢉⣀⣀⣀⣈⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣷⣶⣿⣿⣿⣿⣶⣿⡟⠁⣠⣾⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⢹⣿⡟⢀⣾⣿⣿⡿⢿⣿⣿⣿⡿⢿⣿⣧⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⠁⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⢀⣿⣿⡆⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣧⡀⠀⢀⣼⣿⣿⣿⡇⠀⠀ ⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠲⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠊⠉⠀⠀⢀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠉⠓⠶⠶⠶⠖⠒⠒⠒⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠒⠲⠖⠋⠁⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣤⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢀⣤⢤⡀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⣾⣅⠀⢻⡄⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⢀⡤⠴⠲⢤⣄⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢰⣿⣿⣦⠀⢳⡀⠈⣷⣤⣤⣤⣤⣤⣤⣤⡾⠃⠀ ⠀⣰⠋⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣯⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣼⣿⣿⣿⣤⠾⠃⢀⡏⠀⠀⠀⠀⠀⢀⡿⠂⠀⠀ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣺⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠙⠛⠉⠁⢀⣀⡴⠟⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣤⣤⠔⠛⠉⢠⡄⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠓⠒⠤⠴⠛⠀⠀⠀⠀⠀ ⠘⠷⣄⣀⡀⠀⢀⣠⣿⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⢿⠉⠁⢹⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⡶⠶⠚⠉⠰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠈⣧⠀⠀⠀⠀⢨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢦⣀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡀⠀⢻⠀⢀⣠⠞⠁⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⢀⠉⣻⠦⣤⣀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⣷⠛⠁⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⣼⠿⣇⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⢳⡄⠀⠀⢀⣤⡟⠙⢷⡄⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢀⣠⡴⠛⢁⣤⠞⢻⡏⠀⠀⠀⠉⠓⠤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⢹⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡶⠚⢻⡇⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢸⣌⢳⠤⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢳⡾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⣠⠴⠖⠛⠛⣿⣶⠶⣶⠂⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⡾⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣠⡞⠁⠀⠀⠀⠀⠀⠹⡄⠙⠶⠞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⡀⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⠾⠿⠦⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠥⠶⠬⠷⠤⠤⠤⠤⠽⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓⢶⣤⣴⣖⣒⠒⠒⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠓⢦⣽⡷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⠀⠀⣶⣶⣦⣄⡀⠀⠀⠀⠀⢀⣠⣴⣶⣦⠀⠀⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⡆⠀⢹⣿⣿⣿⣿⣦⣤⣤⣴⣿⣿⣿⣿⡇⠀⢰⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⡏⢠⡄⠀⢻⣿⣿⢙⣿⣿⡋⣿⣿⡏⠀⢠⡄⢹⣿⣿⣿⡇⠀⠀ ⠀⠀⣿⣿⣿⣿⠀⣼⣿⡄⢸⣿⣿⠿⠛⠛⠿⣿⣿⡇⢠⣿⣧⠀⣿⣿⣿⣿⠀⠀ ⠀⢰⣿⣿⣿⡏⠀⣿⣿⡇⢸⣿⣿⣀⣀⣀⣀⣿⣿⡅⢸⣿⣿⠀⢻⣿⣿⣿⡆⠀ ⠀⢸⣿⣿⣿⣇⢀⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⡀⣸⣿⣿⣿⡇⠀ ⠀⣾⣿⣿⠿⣿⣿⠿⠛⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠿⣿⣿⠿⣿⣿⣧⠀ ⠀⠻⠏⠀⠀⠀⠁⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠀⠀⠀⠹⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠁⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⣰⣧⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⠀⠀⠀⠀⠹⣿⠁⠀⠀⠤⢤⣶⣶⣶⣶⣶⣿⠿⠛⢻⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡄⢀⣴⠟⠋⠀⠀⠀⣀⣠⣤⣤⣴⢿⣶⣶⠶⠖⣂⡀⠉⠛⠛⠉⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⣡⣶⠟⠁⠀⠀⠀⠀⢀⣀⣤⣤⠶⠞⠛⠉⠀⢀⣾⣿⣿⣦⣄⢀⣤⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣶⡿⠁⠀⠀⣀⣤⣴⠿⠟⠋⠉⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⠿⠋⣀⣤⣶⣿⣿⠟⢀⠄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠛⠿⢿⣿⣶⣶⣶⣶⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⣡⣴⠿⠛⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢛⢻⣿⣿⠷⠖⠂⠀⠀ ⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠃⠘⣿⣷⡀⠀⢀⣀⣤⣴⣶⣶⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀ ⡾⠁⠠⠀⠀⢠⣶⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠃⠀⠀⠹⣿⣷⡀⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠃⠀⠀⠀⠀⢻⣿⡧⠀⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⢸⣿⡇⢀⠀⠉⠙⠛⠛⠻⠿⢿⣶⣶⣤⣤⣄⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⣿⠟⠁⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⣸⡟⢠⣾⣆⠀⣾⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⡿⠿⠟ ⠀⠀⠀⠀⠀⠐⠿⠿⠃⠈⠁⢀⣠⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢸⡇⢿⡇⢿⣿⣿⣿⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⡇⢸⡇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⡐⢄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⣤⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠟⠛⠛⠛⣁⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣫⣤⡤⠴⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀