December Flash - Lucky Star Pokes <3

⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⣦⡀ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣿⠁⠀⠀⠀⣿ ⠻⢿⣿⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⠀⠀⣠⠏ ⠀⠀⠀⠱⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠋⠁ ⠀⠀⠀⠀⠉⢣⣄⠀⠀⢀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠚⢻⠋⠁ ⠀⠀⠀⠀⠀⠘⠢⢧⣴⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⡎ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⢿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⣤⡀⣀⣿⢿⣿⣿⣿⡿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣏⣴⣿⣿⣿⣿⣿⣿⣿⡄⣠⣴⣶⣶⣶⣄⠀⠀⢀⣴⣾⣿⣿⣷⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⠙⠛⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠘⢿⣿⣿⣿⣿⣿⠟⠀⠈⠿⣿⣿⣿⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋

⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⡰⠒⢆⠀⠹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠃⠀⢸⡀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⢸⡃⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢹⠀⠀⣘⠀⣸⠁ ⠀⠀⠀⠀⣀⣤⠤⠤⠤⠶⠴⠤⢤⣘⣆⠈⡆⢀⠏⢠⢇⣀⠤⠖⠚⠉⠉⡉⠉⠒⠲⡄ ⠀⠀⣠⠊⠁⣠⠔⠒⠒⠒⠀⠤⢄⣀⠉⠀⠘⠃⠀⠙⢋⠤⠒⠋⠉⠉⠉⠁⠉⠉⠂⡄⠱⡄ ⠀⠀⡇⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢰⢢⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠏⢀⡇ ⠀⠀⠹⣄⠘⠒⠢⠤⠔⠒⠲⠒⢊⣠⡄⠀⠀⠁⠀⠀⢀⣈⣉⡙⠒⠒⠒⠒⢛⣉⠥⠖⠉ ⠀⠀⠀⠈⠙⠂⠄⠀⠐⠒⠋⠉⠁⢠⠃⠀⡜⠉⢑⡀⠸⡄⠀⠈⠉⠀⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡼⠀⠀⠀⢣⠀⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢠⠃⠀⠀⠀⠘⠄⠈⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣸⠀⠀⠀⠀⠀⡇⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⡇⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⡇⠀⠀⠀⠀⠀⡇⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢣⠀⠀⠀⠀⢀⠇⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢸⡄⠀⠀⠀⢸⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣇⠀⠀⢀⡇⠀⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢸⡀⠀⡜⠀⣸⠁ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⣆⠀⢧⡰⠀⢰⠇⠀⠀⠀⠀⠀⢀⡠⠴⠖⠒⠒⠲⣤⡀ ⠀⠀⢠⠔⠉⢉⣉⣉⡓⠲⢦⣄⠀⠀⠸⡄⠸⠇⠀⣞⠀⠀⠀⢀⡴⠚⠁⢀⡴⠖⠒⠦⣄⠈⢳⡄ ⠀⡴⠁⣠⠊⠉⠁⠉⠉⠑⠶⣄⠙⢤⣀⡝⠀⠀⠀⠙⣆⢀⠔⠉⢀⡤⠖⠁⠀⠀⠀⠀⠈⢳⠀⢹⡄ ⠰⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⢹⣦⠛⠃⠀⠀⠀⠀⠛⠁⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣧ ⡀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠠⡊⢦⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣹ ⢃⠀⣧⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠀⠀⠀⠙⠁⠀⠀⠀⠧⠤⠤⣄⡀⠀⠀⠀⠀⠀⢀⡼⠃⢀⡟ ⠘⡆⠘⠦⡀⠀⠀⢀⠔⢋⡀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢀⣀⠈⠙⠲⣄⣠⠾⠋⠀⢠⡞ ⠀⠹⣆⠀⠀⠑⠖⠁⣴⣋⣀⣤⠞⠁⢀⣴⡆⠀⡀⠰⣦⣄⡀⠙⠲⠮⢽⡦⠀⠈⠀⠀⠀⣴⠏ ⠀⠀⠈⠓⠶⠤⡄⠀⢀⠀⣀⣠⡤⠒⠉⡼⠀⣰⠱⡄⠘⢆⠉⠑⠦⣤⣄⣀⡀⠀⢤⠖⠛⠁ ⠀⠀⠀⠀⠀⠀⢷⠀⢿⠉⠁⠀⢀⡤⠞⢁⣴⠃⠀⠳⣄⠀⠳⣄⠀⠀⢀⣰⠏⢀⡞ ⠀⠀⠀⠀⠀⠀⠘⣧⡀⠓⠲⠚⠉⠀⣠⠞⠁⠀⠀⠀⠈⠷⣄⣈⠉⠙⢉⣠⠴⠚ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠤⣀⣀ ⠀⢀⡴⠒⠛⠛⠛⠒⠢⢄⡀⠀⠀⠀⠀⢀⠞⠛⠀⠀⠈⠉⢱⡀ ⡰⠁⠀⠀⢀⡠⠤⢤⣀⡀⠘⠲⣄⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠈⠱⣀⡠⠔⠒⠉⠉⠉⠉⠑⠲⢤⡀ ⡇⠀⠀⡞⠁⠀⠀⠀⠈⠙⢦⡀⠈⠳⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠙⢆ ⠰⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⣀⣀⣀⣈⣓⣤⠀⠀⠸⠀⠀⠀⠀⡠⢤⡎⠉⠱⠒⢤ ⠀⠈⠦⡀⠙⠲⠦⣤⣤⣤⢤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢀⡴⠋⠁⠀⠀⠀⠀⠉⠁⠀⢀⠃⠀⠀⢸⡄⠀⠀⠀⠀⠀⠘⠧⣄⠀⠀⣀⣠⣤⠤⠠⣤⣤⣀ ⠀⠀⠀⠈⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠏⠀⠀⣠⣖⣩⠭⠛⠀⠀⠀⠈⠳⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⣠⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡠⠛⢦⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠶⢦⣄⠀⠀⠀⢱ ⠀⠀⠀⠀⠀⢠⠊⠀⣠⠴⠚⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣒⠒⠊⠉⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⠀⠀⠀⠀⠀⠈⠙⡄⠀⢸ ⠀⠀⠀⠀⠀⢈⠀⣼⠁⠀⢀⣠⠜⠁⠀⢀⡶⣄⠀⠀⠀⠀⠀⢶⠋⠉⠒⠲⢤⡀⠀⠈⠉⠙⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⢀⣠⡼⠀⠀⡸ ⠀⠀⠀⠀⠀⠘⣆⠈⠙⠛⠉⠀⠀⠀⠀⢸⡇⠈⠙⠲⡄⠀⠀⠈⢧⡀⠀⠀⠀⣿⠀⡟⠋⠒⣒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠒⠒⠒⠒⠚⠉⠁⠀⠀⣴⠃ ⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⢤⡄⠀⠀⠘⠃⠀⠀⠀⢲⡀⠀⠀⠈⠓⠦⠤⠖⢁⡴⠀⡠⠚⠁⢀⣀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠤⠚⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢠⠀⠀⠀⠀⠈⠧⠀⠀⠀⡶⠂⠀⠖⠋⠀⡜⠀⢠⠞⠉⠀⠀⢸⠆⠀⠀⣄⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣀⠀⠀⠘⡍ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⡄⠀⠘⠇⠀⠀⠀⠀⠀⢇⠀⠸⢄⡠⠤⠒⠉⠀⠀⠀⡇⠳⢄⣀⠀⠀⠀⢻⡀⠀⠀⠀⠉⢦⠀⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡙⠀⠀⠀⠀⠀⠀⢱⠀⠀⠿⠀⠀⠀⠀⠀⠀⠳⢤⣀⣀⠀⣀⠀⠀⠀⢠⠀⠀⠀⠈⢆⠀⠀⠀⠹⣄⡀⢀⣠⠞⢀⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⢸⠀⠀⠀⠀⠘⡄⠀⠀⢀⡀⠈⠉⢀⠤⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡀⠀⠘⡈⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⣥⠀⠀⢃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠆⠀⠸⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠁⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⢨⡆⠀⠈⠓⠒⠤⡀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⢇ ⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⢘⡄ ⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⣧ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠰⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠞⠁⠀⠀⠀⠉⠳⢄⠀⠀⠀⠀⠀⠀⠀⢨⠆⠀⠀⠉⠉⠙⠓⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠴⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢐⡀⠀⠀⠀⠀⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⣀⣤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀

⠀⠀⠀⠀⢀⠠⠖⠚⠉⠉⠉⠉⠉⠉⠙⠒⠒⠤⣀ ⠀⠀⢀⠔⠉⠀⠀⠀⣀⡤⠖⠲⠤⠤⠤⢀⡀⠀⠀⠉⠒⢄⡀ ⠀⢀⠏⠀⢀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⡰⠊⠉⠀⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠉⠉⠉⠉⠉⠑⠒⢤⡀ ⢀⡎⠀⢰⠋⠀⠀⠀⠀⢀⡴⠒⠛⠛⠛⠛⠒⠒⠦⠤⣈⠳⢄⡀⠈⠑⢦⡀⠀⠀⠀⢰⠁⡰⠊⠉⠓⢄⠀⠹⡀⠀⠀⠀⠀⠀⢀⠤⠚⢉⡤⠔⠒⠊⠉⠉⠉⠉⠒⠢⢄⠀⠈⠳⡄ ⢸⠁⠀⢸⠀⠀⠀⠀⡴⠁⠀⢀⣠⠤⠴⠒⠢⠤⢄⣀⠈⠓⢤⡙⠢⡄⠀⠙⣦⠀⠀⢸⢀⠇⠀⠀⠀⠘⡆⠀⡇⠀⠀⢀⡠⠖⣩⠔⠊⣁⠤⠒⠒⠋⠉⠒⠒⠢⡀⠀⠈⠣⡀⠀⠈⢦ ⢸⠀⠀⢸⠀⠀⠀⢠⠇⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⠙⢦⡘⠢⡀⠈⢷⣀⡸⢸⡀⠀⠀⠀⠀⡇⠀⡇⣠⠔⢋⡴⠊⣠⠔⢉⡠⠴⠒⠒⠒⠢⣄⠀⠀⠘⡆⠀⠀⠑⡄⠀⠈⣇ ⠸⡇⠀⢸⡀⠀⠀⠘⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠙⣄⡽⠀⠀⠀⠀⠀⠱⣄⡤⠤⠤⠇⠀⠋⠀⡔⠋⣠⠖⣡⠖⠁⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⢸⠀⠀⠀⠸⡀⠀⢸ ⠀⢱⡀⠀⢣⠀⠀⠀⢧⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢠⡖⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄⠣⠔⢁⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢸⠀⠀⠀⠀⡇⠀⢸ ⠀⠀⠳⡀⠀⠱⣄⠀⠈⢢⡀⠈⠑⠤⣀⣀⣀⣀⣀⣀⣠⠎⠉⠓⠢⢬⣧⠀⠑⢤⠇⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⡼⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡏⠀⠀⠀⢰⠁⢀⠇ ⠀⠀⠀⠈⢦⣀⠈⠙⠦⣄⣙⣄⠀⠀⢈⡤⠒⢢⡀⠀⠀⡞⠉⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⣀⣀⣀⡀⠀⢀⣠⠤⣄⠎⣠⠊⠀⠀⠀⢀⡎⠀⡜ ⠀⠀⠀⠀⠀⠈⠙⢤⣀⠀⠀⠈⠀⠀⢸⠀⠀⠈⡇⠀⠀⡇⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠧⠤⠤⠖⠉⢀⣀⡀⠉⠓⢁⠴⠒⠲⡀⠘⢄⠀⠀⣠⠊⢀⠎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⢢⡀⠘⢄⣀⣀⡇⠀⠀⢧⣄⡠⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠁⠀⠈⠙⡄⠈⢆⠀⠀⠘⡄⠈⠒⠉⢀⡴⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⣀⣀⠴⢤⣀⡠⠤⡲⠋⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠱⡄⠘⡤⠤⠖⣡⠖⠒⠚⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢠⠃⠀⠉⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡀⠀⠀⠀⠸⠤⠤⠤⠤⠔⠛⠀⡰⠒⠚⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠹⡄⠈⡗⠤⢄⣀⠀⠀⣀⠤⠚ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠈⠓⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡻⠀⢸⠀⠀⠈⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⠀⠀⡰⠓⠤⠤⢦⠀⠀⠀⠀⠑⠒⠒⠁⠀⡜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢸⠀⠀⠀⢘⡄⠀⣠⠶⠤⣀⣠⠤⠞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠈⡆⠀⢀⠜⢀⠔⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢒⣉⣉⡒⢦⡀⠀⠸⡀⢱⢠⠎⢠⠎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡰⠋⠀⠀⠈⠱⢌⢦⣀⡇⠈⠃⣠⢋⣀⠤⠤⠤⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⠀⠀⠀⠀⠀⠀⠈⣇⠁⠀⡀⠀⠗⠉⣀⠤⠤⠤⢤⡈⢣⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢄⠀⢀⣀⠤⠤⠴⠇⠀⢸⡹⠀⢀⡋⠀⠀⠀⠀⠀⠸⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣈⠓⠋⣠⠔⢒⣲⠀⠀⠀⠀⠀⣈⠓⢄⡀⠀⠀⠀⢰⠀⡍ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⣉⣉⣉⠤⣲⠀⠀⢰⡄⠯⣉⠲⡙⢆⣀⠔⠁⡜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⠦⡤⡤⠴⠃⡰⢧⠘⡌⠒⠬⣉⠋⢈⣠⠴⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢤⠤⠔⠊⠀⠈⢦⡙⠦⠤⠎⢀⠎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠴⠒⠒⠢⢄ ⠀⠀⠀⠀⢀⠔⠒⠒⠲⢄⡀⠀⠀⡜⠁⢀⠤⠤⢤⡀⠱⡀ ⠀⠀⠀⢰⠁⢠⠚⠑⠒⢄⠉⢆⡘⠀⡘⠁⢀⡠⠔⠃⠀⢡⣀⡀ ⠀⠀⠀⡆⠀⠘⠠⠤⠤⢄⢣⠀⠃⠀⣧⠞⢁⡤⠒⡆⠀⣀⣀⠉⠲⡀ ⠀⡠⠊⢁⠀⢶⡀⠒⠂⢤⠉⠃⠈⠀⠀⢠⡯⠔⠊⢀⡴⠃⠀⠑⢄⠘⡄ ⢰⠁⣠⠊⠙⠢⢌⡉⠐⠊⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠈⡆⢸ ⡇⠀⠇⠀⠀⠀⠀⠀⠉⢰⠀⠀⢊⢱⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸ ⡇⠀⡀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠉⠀⠀⣀⠳⣄⠀⠀⠀⠀⢀⠞⢀⠇ ⢱⠀⠱⣀⠀⠀⠀⡠⠚⠁⢠⢻⠀⠀⠀⢞⠀⠑⠢⢍⡙⠛⠋⢁⡴⠋ ⠀⠑⢄⣀⠉⠉⠉⢀⡠⠚⠁⡜⢀⡞⢢⡀⢣⡀⠀⠀⠈⠉⠉⠁ ⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⡇⢸⠀⠀⠱⡀⠑⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡜⠀⠀⠀⢱⡀⠸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢱⠀⠀⠀⠀⣇⠀⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢸⡀⠀⠀⠀⢸⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢧⠀⠀⠀⢸⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡘⢆⠀⠀⣸⠀⡆⠀⠀⠀⠀⡠⠖⠊⠉⠉⠓⠢⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢦⣀⡇⢠⠇⠀⠀⡠⠋⠀⠀⢀⣤⠖⠒⠤⡀⠑⣄ ⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠂⠤⣀⡈⢢⡀⠀⠸⣄⡠⠞⠀⠀⠀⠀⣀⠠⢍⠳⡀⠹⡀⠘⡄ ⠀⠀⠀⠀⣠⠚⢁⠀⢀⡠⠤⣀⠀⠀⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⣀⠀⢱⢱⢰⠃⠀⢡ ⠀⠀⠀⡜⢁⠖⡡⠋⠈⠢⢄⣀⣉⣢⠀⠀⠀⠠⡋⢆⠀⠀⠀⠀⠀⠀⢠⠬⡑⢼⢸⡎⠀⠀⡘ ⠀⠀⢰⠁⡎⢸⠁⡔⠈⣹⠀⠀⠀⠀⠀⠀⠀⠀⠱⡜⠀⢀⡀⠀⠀⠀⠧⣤⡜⠀⠈⠀⠀⢠⠃ ⠀⠀⠀⢣⢣⣸⡀⢇⠀⡇⡔⠒⠲⡄⠀⠀⢠⠤⢤⡀⠀⢆⠀⢱⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃ ⠀⠀⠀⠀⠣⡙⠷⠄⠑⠃⠙⠒⠉⠀⠀⠀⡎⠀⡼⠀⡠⢄⠉⠙⠀⠀⠀⠀⠀⢀⡀⠈⢆ ⠀⠀⠀⠀⠀⠈⠲⠤⣀⡀⠀⢀⡀⠀⠀⠀⠘⠉⠀⠀⢦⠰⡀⠀⠀⠀⡠⢆⠀⢸⡘⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢱⠁⠀⠀⡠⡄⠀⠀⠀⠉⠉⠁⠀⠀⠈⠓⢁⠤⡆⠀⠀⡸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢜⢱⠀⠣⠜⠀⠀⠀⢀⡀⣀⡼⢄⠀⠀⠈⠒⢁⡀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠉⠁⡤⠔⡆⠀⠀⡎⠉⠁⠀⠀⠉⠑⠒⠒⠉⡇⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠈⠉⢀⣠⠞⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠇⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⢧⡠⠤⠤⠤⢤⡀⡴⠁⠀⣀⡠⡤⠀⠀⠈⢆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⣀⡠⢄⠈⠀⠀⠘⠢⣄⠃⠀⣠⠀⠘⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠳⣄⡎⠀⡜⠑⠦⠀⠈⢀⠜⠁⡇⠀⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡞⠢⣀⠈⠀⠘⠢⢄⡜⠀⢀⠀⢇⢠⠃⢀⡎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠱⡀⢸⠀⢠⠤⣀⠀⠁⠲⠇⠇⠈⠁⡠⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⠉⠀⠈⠒⢁⠔⠛⠒⠤⡄⠀⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠢⡀⠀⠱⢄⣀⣀⡰⠁⢰⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⣀⣀⣀⠴⠃

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢁⠎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⡎⠀⠀⠀⢀⣀⠤⠔⠚⠉⠉⢁⣀⠤⠚⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡇⠀⣠⠖⠉⠀⠀⠀⠀⠀⠰⠭⠤⠤⢤⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠔⠒⠛⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⢣⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡇⠀⠀⢳⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠮⢍⡁⠀⠀⠀⠀⠀⠀⠳⣄⡸⠆⠀⠀⠀⠀⠀⢀⠚⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⡞⢹⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠉⠙⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠱⡈⢆⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢣ ⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⢠⠖⢲⠆⠀⠀⢠⠇⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⡆⠀⠀⠀⠀⠀⠘⠦⡄⠀⠀⠀⠱⠤⠤⡶⠀⠀⢰⡇ ⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡇⠀⠈⠦⠤⠤⠊⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⡰⠹⡀⠀⠀⠀⢸⠀⠘⢆⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⠤⠒⠋⠀⠀⠀⡼ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⢰⠃⠀⢇⠀⠀⠀⠈⡆⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁ ⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠙⠢⠤⠤⠤⠔⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⡏⠀⠀⢸⠀⠀⠀⠰⠧⠤⠤⠤⠾⠷⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣠⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠔⠚⠁ ⠀⠀⠀⠀⣠⠴⠒⠊⠉⠉⠉⠀⠀⠀⠠⢤⡤⠤⠖⠒⡆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣀⠀⠀⠀⠀⠘⣆ ⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⠀⠀⠈⠙⢆⠀⠀⠀⠘⡄ ⠀⣸⠁⠀⠀⠀⢀⣀⣀⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠀⠀⢸⠀⢀⡔⠉⠉⠙⡄⡼⠀⠀⠀⠀⡇ ⢀⡇⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠁⠀⢸⠀⠀⠸⡄⡼⠀⠀⠀⠀⠋⠀⠀⠀⠀⡰⠃ ⠈⡇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢸⠀⠀⠀⣇⢹⡀⠀⠀⠀⠀⠀⠀⢀⠴⠁ ⠀⠹⡀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⡜⠀⠀⢠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢸⠀⠀⠀⢸⡀⠙⠢⣄⣀⣀⣠⡶⠛⠲⠦⣄ ⠀⠀⠉⠑⠒⠚⠉⠀⠀⠀⠀⠀⡼⠁⢀⡴⠁⠀⢧⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠱⡀⠘⡆⠀⠀⠀⢣⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡴⠋⠀⠀⠀⢸⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠈⢦⣹⠀⠀⠀⠀⠱⡄⠀⠀⠘⢦⣀⣠⡄⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠙⣄⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠈⠲⠤⣀⡀⢀⡴⠃⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢸⡇⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣠⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠙⢦⡜⠀⠀⠀⣸⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠈⠁⠀⠀⢠⠏⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⠉⠓⠒⠒⠒⠚⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢸⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠖⠋⠀⠀⠀⠀⠀⣠⠏⠀⣀⣤⠀⠀⠀⠀⠀⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣡⠖⠛⠉⡜⠀⠀⠀⠀⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⡼⠁⠀⠀⣠⠞⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣠⠴⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠗⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡑⠦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⠢⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢠⠃⠀⠀⠀⢀⣀⡠⠄⠶⠶⣶⡤⠀⠀⢤⣤⡠⠤⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠙⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢸⠀⢀⠔⠒⠁⠀⠀⠠⠖⢉⣀⣀⠀⠀⢀⣀⣈⣑⣲⡄⠀⠀⠈⠑⠒⢤⣀⠀⡇⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⡎⠀⠀⠀⠘⠚⠁⠀⠀⠀⠀⠀⢀⣀⠤⠤⠬⠛⠛⠭⠄⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠑⠇⠀⠀⠀⠀⠸⡄⠀⠀⠀⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⡠⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠎⠀⢇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡤⠒⠒⠃⠀⠀⠣⡀⢡⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠀⠀⠀⠀⠀⠀⣴⠁⣰⠋⠀⠀⠈⠒⠒⠢⢄⡤⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣠⠖⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⣠⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢠⡞⠁ ⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠈⠢⡀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠸⡉⡆⠀⠀⠀⠘⣄⠀⠀⠀⠀⡴⠉⠀⠀⠹⡄⢀⠞⠁⠀⠀⠉⢆⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⡸⢀⠇⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⡴⠊⠈⠉⠉⠑⠦⣄ ⠀⠀⠀⠀⠀⢀⠎⠀⣠⠄⡖⠀⠀⡇⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⢸⠘⡄⠀⠀⠀⠈⠢⡀⠀⠀⠣⣄⣤⠆⠀⢱⡏⠀⠀⢦⣄⡠⠞⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⡰⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠸⡀⠀⠀⢲⠢⢄⠀⠈⢢ ⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠳⠤⠞⠁⠀⠀⠀⡞⠀⠀⠀⢀⡞⢇⠀⠀⠀⡇⠙⣄⠀⠀⠀⠀⠈⠙⠒⠤⠒⠉⠀⢀⡏⠹⡄⠀⠀⠉⠓⠒⠒⠋⠉⠀⠀⠀⠀⠀⢀⡜⠁⢸⠀⠀⠀⢠⠏⢧⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠙⠦⠤⠊⠀⠀⡇⠀⠀⡇ ⠀⠀⠀⠀⠀⢨⠀⠀⠓⣄⠀⠀⢀⣀⣀⡤⠴⠁⠀⠀⠀⡸⠀⠘⡄⠀⠀⡀⢀⣈⣲⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠊⠀⠀⠈⠲⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣔⣋⣀⣀⣸⠀⠀⠀⡸⠀⠀⢇⠀⠀⠀⠀⠘⠲⠤⢤⣀⣀⣀⣀⣀⡠⠞⠀⠀⢰⠁ ⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡠⠇⠀⠀⠉⠉⠀⠀⠀⠁⠀⢀⣀⣠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⣀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁ ⠀⠀⠀⣀⠴⠒⠚⠉⠁⠀⠀⠠⣤⡄⠰⢶⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⣠⠤⠤⣀⡀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢀⡠⠔⠶⠦⢄⣀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢰⠒⠒⢲⣶⠶⠀⠀⠀⠈⠉⠉⠉⠓⠲⢄⡀ ⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡇⠀⢀⡤⣄⠑⡆⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠁⡠⠤⢤⡀⠀⢸⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦ ⠀⡎⠀⠀⠠⣔⠂⠉⠉⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⢹⠀⠀⡇⡰⠁⠀⠈⠗⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠺⠀⠀⠀⠘⡄⢸⠀⠀⢸⠈⠑⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⠉⠉⠉⢉⠶⠄⠀⠀⠀⡇ ⠘⡄⠀⠀⠀⠈⢳⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢸⠀⠀⢇⢣⡀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣰⢃⡎⠀⠀⢸⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⡇ ⠀⠳⣄⠀⢀⡠⠋⠀⠀⠀⡼⠀⢀⠶⡄⠀⠀⠀⠀⠀⠀⠀⢧⠀⢸⠀⠀⠘⡄⠙⠦⠤⢤⠴⠛⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠙⠳⡢⠤⠒⠋⠁⡸⠀⠀⠀⡞⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠦⡀⠈⢣⠀⠀⠀⠀⠑⠤⣄⣀⡠⠜⠁ ⠀⠀⠈⠉⠉⠀⠀⠀⠀⢸⢀⡴⠃⠀⢱⠀⠀⢰⡄⠀⠀⠀⠀⠳⡌⡆⠀⠀⠱⡄⠀⠀⢏⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣀⣀⣀⡜⠀⠀⢀⡜⠁⠀⠀⢠⣣⠜⠁⠀⠀⠀⠀⢀⣾⠀⠀⠀⡞⠀⠀⠙⢢⡀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠸⡀⠀⢸⡟⢦⠀⠀⠀⠀⠈⠺⠄⠀⠀⠘⠢⢀⠀⠁⣨⠃⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠣⢄⣀⡠⠤⠖⠃⠀⠀⠀⠠⠛⠁⠀⠀⠀⠀⢀⡴⠋⣿⠀⠀⢰⠁⠀⠀⠀⠀⠈⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢰⠁⠀⢸⠇⠈⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢿⠀⠀⠘⣆⢀⣀⢀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠑⠞⠀⠀⡼⠀⠀⠀⢃⠀⠀⠀⠀⠀⢰⠢⢤⣀⣀⢀⣀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⣤⣤⣤⠤⠔⠒⢺⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠘⣆⠀⠀⠘⠏⠀⠀⠈⠳⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⡞⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⢦⣀⠀⠀⠀⠀⠀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠤⠔⠊⠀⠀⠀⢀⠜⠀⣀⡄⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⢶⢤⣀⡙⢆⡀⠀⠀⠀⠈⠑⠒⠒⠒⠊⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠯⠞⠋⡰⠁⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡄⠀⠀⠘⡄⠀⠉⠓⠻⠦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⡘⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⣀ ⠀⠀⠀⢀⡤⣒⣒⣚⣉⣙⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⣀⣠⠤⢤⣀⡀⠀⠉⠲⣄ ⠀⠀⡴⠫⠋⠁⠀⠀⠀⠈⠙⠶⣤⣉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⡠⠖⠉⠁⠀⠀⠀⠀⠉⠓⢤⡀⠀⠳⡄ ⢀⡎⣼⠥⠤⢤⣤⡤⠤⠤⢤⣀⡀⠈⠳⢬⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⢸⡀ ⢸⠐⢁⠔⠋⠁⠀⠈⠉⠙⠓⠦⢍⠳⢦⣄⠙⢦⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⠁ ⢸⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣈⠻⣆⠙⠶⡈⢳⡄⠀⠀⠀⠀⠀⠀⠀⢠⠛⠁⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡾ ⢸⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢬⡳⣄⠉⢲⡙⠢⡀⠀⣀⣀⠀⢠⠃⠀⣤⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡼⠁ ⠀⡆⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⠳⣀⠹⡄⠙⠋⠀⠀⠉⠉⢀⢮⠃⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢡⡾⠁ ⠀⠹⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠒⠲⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⢀⡉⠀⡧⠤⢴⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠎ ⠀⠀⠈⠳⢄⡀⠙⠢⣄⠀⠀⠀⠀⠀⠀⢸⠁⢸⠉⢑⠦⠀⢀⣤⡀⠀⡔⢳⠀⠀⠿⠃⠀⢀⡰⠫⣸⠀⡇⠀⠀⠀⠀⢀⠔⠋⢀⠔⠁ ⠀⠀⠀⠀⠀⠙⠦⡀⠈⠙⠲⣄⡀⠀⠀⠈⢦⡀⠉⠛⠀⠠⠬⠙⠁⠈⠓⠉⠀⣻⠀⠀⡀⠯⠃⠀⠀⠰⢤⣀⡀⡠⠒⠉⢀⡔⠁ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠉⠓⠶⢤⠔⠋⠀⠀⠠⢤⠀⢰⡛⢤⣀⣠⢚⡎⠀⠧⠵⠀⠐⢷⣢⠀⠀⠀⠉⠁⠀⣴⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢤⡀⠀⠀⠀⣀⣀⡀⠈⢠⢋⡃⠀⡀⢡⠞⠀⠀⢠⠤⢀⢸⣻⠎⠀⡔⢳⡀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⡙⠦⡧⠚⢆⠉⠀⠀⠀⠉⢰⡽⢠⡼⡆⢈⣨⠇⠀⠘⠦⠊⠀⢀⡠⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠿⠛⣤⣉⠒⠁⡞⢲⠄⢠⣉⣻⠃⠀⠉⠇⣸⠁⣀⣀⠀⡴⣳⢠⣌⠳⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⢀⠀⠈⠣⢯⠒⢠⠉⠋⢾⣸⠃⣁⡒⠂⡀⢦⠀⠰⠃⠞⠀⠉⠁⠧⣀⠙⠦⡉⠒⢄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣣⠄⣀⡼⠄⠀⠀⠈⠓⠊⢰⠒⡄⠀⢸⣀⠹⠤⢬⠉⣴⢢⡀⠀⢠⢄⠀⢴⠢⠭⣑⡺⠄⠀⠈⠲⢄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⡷⣋⡵⠚⠁⠀⠖⠳⡄⠀⠀⠀⠀⠉⢀⡞⢹⡎⠀⠀⠘⠀⠘⠋⠁⠰⠧⠼⠂⣸⠀⠀⠀⠉⠓⠦⣄⠀⠀⠉⠳⢤⡀ ⠀⠀⠀⠀⠀⢀⡤⠚⡡⠞⣥⠞⠁⣠⠔⠋⠀⠀⠀⠙⠢⠤⡀⠀⠀⠀⠹⠞⠁⠀⠀⢯⠑⠳⡄⢸⠓⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⠀⠀⠈⠓⢤ ⠀⠀⠀⢀⡴⠋⡠⠏⣠⠟⢁⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⢀⠎⣰⠒⠃⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠹⣄ ⠀⠀⡴⠋⢠⠞⣡⠞⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⢈⣉⣁⣠⣄⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⣤⠘⣧ ⠀⡞⠁⠀⠀⡰⠃⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣰⠊⠉⠁⠁⠀⠈⢦⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢱⡇⢸⡆ ⢠⠁⡞⠀⣰⢃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⣠⠀⢰⠇⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⢸⠀⣿ ⢼⢸⡇⢠⡏⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢁⠞⡿⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸⢨⠂⣿ ⢸⠸⡇⢸⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⠎⡰⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣾⠎⢠⡏ ⠈⣆⠙⠾⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠁⣠⣫⠞⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣀⡀⠉⠢⣄⣀⠀⠀⠀⠀⢀⡠⠊⠀⠀⢀⠞ ⠀⠈⠳⠦⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠁⠀⠘⠋⢁⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢬⣉⣛⣒⣊⣉⣀⡤⠶⠞⠉ ⠀⠀⠀⠀⠰⣤⡈⠙⠓⠒⠒⠒⠛⠋⠉⠀⠀⠀⢀⣠⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉ ⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣄⣀⣀⣠⡤⠤⠖⠊⠉

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⠀⠀ ⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⣠⣤⡄⠀⣤⣤⣀⣀⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⣇⣀⣈⡄⠀⠀⣶⣶⣶⣶⣶⣾⣿⣿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⠴⠾⠿⠿⠿⢿⡿⠿⠿⣿⣄⡿⠿⢿⣿⡿⠿⠇ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⣿⡿⠛⠋⢸⣿⠋⢀⣄⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠘⣿⠀⢠⡇ ⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⡇⠀⠀⡇⠀⠐⢾⣿⣿⣿⣿⠁⠀⢾⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⠀⠀⣿⣿⠀⠀⣿⣿⣇⠀⠀⠀⣼⡇ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⣿⣷⣦⣀⢸⣿⠛⠛⡿⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⠀⠀⣿⣿⠀⠀⣿⡿⠿⠂⠀⣰⣿⡇ ⠀⠀⠀⠀⠀⠀⢸⣧⣤⣼⡇⠀⠀⠿⠿⠿⣿⣿⣿⠷⠤⠤⢴⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⣾⣿⣶⣶⣿⣿⣶⣶⣿⢧⣄⣠⣤⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠸⡿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠤⠿⠿⠿⠿⠿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡄⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀ ⣀⣤⣤⣤⣤⣄⡀⠀⠈⢹⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣴⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠛⣿⣿⢹⡟⠻⢝⠋⣿ ⣼⣿⣿⠀⢸⣿⣿⠄⠀⣸⣿⣇⠀⢸⣿⣿⠿⠟⠛⠿⠿⣿⣿⣿⠀⠙⢿⣿⣦⣿⡟⠀⢸⣿⣿⠿⠟⠛⠿⠿⢿⣿⣿⠀⠀⠋⠀⠀⠀⠀⠀⣑⣿⣼⢸⣇⣷⣀⠒⠛⠆ ⢸⣿⣿⠖⢾⣿⣅⡀⠈⠻⣿⡏⠀⣿⡟⢁⣴⣶⣶⣶⡄⣠⣾⣿⠀⠀⠈⣿⣿⣿⠁⠀⢸⠟⠀⣤⣶⣶⣶⣀⢀⣾⣏⠀⠀⣷⣤⠀⠀⣤⠀⠚⣿⠹⣽⣿⣿⡟⠂ ⢸⣿⣿⠀⢸⣿⣿⡇⠀⢀⣿⡇⠀⣿⠀⢸⣿⣿⠉⣋⣴⣿⣿⣿⠀⠀⠀⠸⣿⣿⠀⠀⢸⠀⣾⣿⣿⠉⣋⣵⣿⣿⣿⠀⣤⣿⣿⣤⣾⣿⠁⣡⣿⠃⣿⣎⣉⣨⣿⣷⡀ ⠘⠛⠛⠒⠚⠛⠋⠁⠸⠛⠛⠛⠛⣿⣆⠘⠻⢿⣿⡿⠛⡿⣿⣿⠀⠀⠀⢠⣿⣿⣤⠀⢸⣄⠘⠻⢿⣿⡿⠛⢿⣿⣿⠀⠿⠿⠿⠿⠿⠿⠀⠛⠛⠚⠛⠻⠭⠽⠟⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣢⣤⣤⣤⣔⣾⣾⣿⠀⠀⠀⠈⠉⠉⠉⠀⣸⣿⣷⣢⣤⣤⣤⣴⣮⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡤⠴⠶⣤⣤⣤⣤⣤⠶⠂⠤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢦⣴⣶⣾⣿⣦⠤⠤⠿⠛⠛⠛⠛⠤⠤⢤⣿⣿⣷⣶⣶⠦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⢀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢄⠀⣵⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣷⣦⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡁⠈⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⣀⠀⠑⢴⣿⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣾⠋⠀⠀⣿⣿⠿⠿⣿⡀⠀⢨⣷⣤⣽⣿⣦⣄ ⠀⠀⠀⠀⠀⠀⠀⢠⠋⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠉⢻⠿⠛⠋⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠛⠿⣟⠉⢷⣄ ⠀⠀⠀⠀⠀⠀⠀⣧⣄⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣴⣿⣷⣄⡀ ⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⢀⠔⠻⣿⣛⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡈⢹⡿⠓⠢⡀ ⠀⠀⠀⠀⣰⠾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠹⡏⠓⢦⣀⠀⢀⣎⣀⡴⠛⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢦⠘⢄⣀⣵ ⠀⠀⠀⢠⠃⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣦⣈⢳⣾⡿⣛⣵⠂⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⡆⠈⠙⢿⣧⡀ ⠀⠀⠀⢸⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⢹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣿⠀⠀⠀⢻⡿⠳⡀ ⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣫⣾⣿⣿⣿⣿⣿⣿⣍⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠈⢇⠀⢱⡀ ⠀⡸⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠊⠁⠚⣻⣿⠿⣿⣿⣿⣿⣛⣛⣻⣦⡙⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⢣⠀⠀⠈⠻⣿⣇ ⢰⣇⣀⠎⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣽⣿⠛⣧⣹⣿⡿⣿⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⡦⠀⠀⠀⠙⣿⣦⡀ ⢸⠛⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⠀⢹⣿⡟⣱⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⡧⠀⠀⠀⢀⣿⡿⠋ ⠈⣆⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⡸⠀⠀⠀⣠⣿⡏ ⠀⠈⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡉⠉⣎⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⡜⠉⢹⠃ ⠀⠀⠀⣻⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⣸⣦⣠⠃ ⠀⠀⠀⢻⠁⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⡏⠀⣀⣴⡿⠋⠁ ⠀⠀⠀⠀⢧⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠛⢦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⡜⢀⠞⠛⣿ ⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢴⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⣰⣮⣀⡴⠁ ⠀⠀⠀⠀⠀⠀⢸⠿⠳⣤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣰⣟⣽⣿⣿⣷⣶⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⣷⣾⠟⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⢣⠀⣸⡍⠛⠛⠶⠶⣿⣿⣏⡻⢿⣿⣟⣿⣿⣿⣿⣦⣙⢿⡒⠚⣷⣶⣦⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣤⣏⠀⣼⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣷⡄⠀⠀⠀⠀⠁⠀⠙⢦⣝⣿⣿⣿⣿⣿⣿⣿⠿⣋⣽⠟⠛⠛⠿⣿⠉⠉⠉⣷⣤⣤⣴⣶⠉⠉⢹⡿⠿⢻⣿⡿⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠶⣄⠀⠀⠀⠀⠀⢰⡿⣿⣿⡿⠿⢿⣿⣿⢻⡟⠁⠀⠀⠀⠀⠈⠉⠀⠚⠉⠉⠉⠉⠙⠓⠊⠉⣠⢶⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⣦⠀⠀⠀⢠⡟⠐⣋⡡⠖⠒⠲⢌⡛⠆⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁⢀⠝ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⢿⣷⣤⣀⡿⠓⠋⠁⠀⠀⠀⠀⠀⠉⠒⠬⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⡿⠗⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠾⠿⣷⣶⣴⠖⠤⠤⣤⣀⣀⣀⣠⠤⠤⢲⣦⣶⣾⡿⢷⡤⠒⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⠤⠤⠿⠿⠿⠿⠿⠄⠠⠴⠋⠉

⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠿⠷⠶⠶⢶⣶⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣰⣤⡀⣾⣷⣿⠀⠀⢲⣤⡀⢸⣿⣿⣿⣿⣦⣤⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣿⡷⠿⢿⣷⠶⣿⣿⣿⠟⣿⡷⢦⣸⣿⣷⣿⡏⠉⠉⣹⡿⠛⣃⢶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣽⣿⢾⣿⠁⠀⠀⠉⠛⠛⠛⠁⠀⠈⠛⢶⣝⡛⠛⠋⠀⠀⢸⣟⣤⣤⣽⣿⣍ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢻⡾⠉⠈⠛⠷⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢶⣶⡶⢾⣭⣙⣻⣿⣇⣹⡗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣬⣿⣦⢟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣭⣿⣿⣿⣿⣯⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡠⠞⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣸⣿⣧⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣶⣷⣿⣿⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢻⣿⣟⠷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⠟⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⣤⣬⡉⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⢠⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢀⡀⠀⠀⣾⠋⠀⣀⠘⢷⡄⠀⣠⠆⠀⠀⠛⣦⠀⠀⠀⠀⠀⠉⢩⠿⣦⡸⣿⣶⣿⣿⡦ ⠀⠀⠀⠀⠀⠀⠀⠶⣶⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⢀⡀⠀⢹⣶⣶⣷⣀⣟⣿⣄⣿⣷⣴⣿⠀⢴⣶⡀⣾⣷⣤⣴⣷⢠⣶⣦⡀⠹⡇⠘⠿⠮⠷⠆ ⠀⠀⠀⠀⠀⠀⢀⣠⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣦⣼⣿⣦⣾⡟⠀⠻⣿⣿⣿⣭⠟⠁⠈⢿⣳⠿⠿⢇⣼⠛⠉⠙⣿⡻⣿⣿⣏⡼⠃ ⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⠀⠰⣾⡻⠿⠿⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠉⠉⠉⠁ ⠀⠀⠀⠀⢚⣷⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣷⣖⠀⠸⡇ ⠀⠀⠀⠶⢿⣿⣿⡽⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⣿⣿⣗⡸⠃ ⠀⠀⢠⣤⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣉⠙⠛⠉ ⠀⠀⠀⡀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⣒⠛⢿⡆ ⠀⠀⠛⣷⣠⣹⡇⠀⠀⠀⠀⠀⠀⠀⣷⡀⣴⣿⣆⡈ ⠀⡴⢿⣿⣯⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢣⣿⣿⣿⡥ ⠀⣀⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣍⣉⠉ ⠀⠀⠉⢿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠁⠰⠟⢷⡄ ⠰⢶⣄⣸⣿⠆⠀⠀⠀⠀⠀⠀⢸⣇⠀⠴⣿⣀⠀⠇ ⢲⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡥ ⠙⢁⣹⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⣃⣁⡀ ⠀⠀⠁⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⢠⡞⠉⠒⠾⠽⠆ ⠀⠀⠰⣶⣀⣼⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⡀ ⠀⠐⠖⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣇⣀ ⠀⠈⠙⠋⣈⣧⡄⢀⡀⠀⠀⠀⠀⠀⠀⠉⠛⣻⡟⠫⠯⠽⠷⠆ ⠀⠀⠀⠀⠈⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⣿⡁⠠⣶⣦⢀⡀ ⠀⠀⠀⠀⠀⠘⢳⣄⣼⣿⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⣾⣿⣿⡿⢃⣴⠒⠃ ⠀⠀⠀⠀⣙⢓⢺⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠙⣾⠅⠀⣠⣦⠀⣀⠀⠀⠀⣤⠶⠀⡀ ⠀⠀⠀⠀⠀⠉⠉⠁⣴⠾⠛⠘⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣭⣿⣷⣿⣧⣤⣿⠀⢠⣤⡉⠀⣤⡄⢀⣼⠀⢠⣤⡀⠀⣠⡀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠟⠋⠀⠙⣿⣦⣉⣹⣷⣶⣿⠓⠚⣿⣦⣤⣾⣿⣾⣿⣿⡇⠀⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠟⠁⠀⠀⠈⠛⠻⠿⠿⠛⠹⣿⣆⣔⣿⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠿⠿⠙⣷⡶⠛⠛⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⢠⣤⡀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠏⠁⠀⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣉⣿⣿⣾⡿⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠸⣷⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⣼⠿⠏⠀⣴⠟⠉⠀⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣷⣶⣿⡿⣂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠸⢿⣧⣀⣼⠇⠀⠀⣠⡴⠞⠲⢶⣄⠀⠀⠀⠀⠀⣀⢀⣀⣀⠀⠀⣠⡾⠋⠉⠈⠛⢿⡝⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠶⠾⠿⣿⡿⠦⣤⣸⡟⠀⣄⣤⠀⢹⣧⠀⠀⢰⡾⠋⠈⢿⠿⣷⡄⣿⡅⠀⣶⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⢿⢠⣬⣿⣿⣶⣾⣿⣿⣿⣿⡇⣼⣿⣿⡂⢻⣿⣿⣟⡠⣿⣿⢟⡽⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣯⣿⠽⠟⠁⠀⠀⠹⣔⠾⠿⠿⢟⣱⠏⠉⠈⠛⠒⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠿⠻⠿⢿⣿⣿⣿⣷⣦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠨⠉⠋⢽⣿⠋⢹⣧⠀⠀⠀⣸⡟⠲⣾⠛⠷⡿⠗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⢿⣿⠉⢟⣶⣷⣦⣤⣿⣿⣷⣾⡟⠀⠀⠀⢿⣇⣰⣿⣿⣆⠀⣵⣀⣤⣤⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⣾⣿⣦⣼⠇⠈⠻⣿⣿⣿⣿⣯⣤⣤⣀⣀⣈⣿⣿⣿⣿⣿⡿⢿⡇⠋⣿⡟⠛⢣ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣖⣦⠋⠙⢻⣿⣿⣟⡋⠀⢠⣶⣧⣽⣿⣷⡄⠀⠀⠉⣩⣭⣯⣭⡉⠉⠁⠀⢸⣇⣀⣿⣧⡀⣼ ⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⣿⡀⠀⣿⠀⣰⠾⢿⣿⡿⠿⣶⣏⠀⢸⣿⡏⠉⣿⣶⣶⡾⠛⢻⣿⠿⠿⣆⠀⠀⠀⠙⠻⠿⠿⠟⢿⣶⣤⣤⣤⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏⠀⣏⡀⢸⣿⣆⢀⣿⠻⢿⣿⣿⣿⡿⠋⠉⠉⣷⣤⣼⣿⣆⣤⣿⣦⣶⣶⣶⣶⣄⠀⠀⢠⡿⠉⢻⣿⠛⢷⡀ ⠀⠀⠀⠀⣀⣀⣠⣎⠔⠉⢻⣿⣿⣿⣿⣿⡷⣿⣿⣿⠟⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⢹⡏⠀⣿⣟⠁⠹⡆⠀⠘⢿⣤⣼⣿⣦⣾⠁ ⠀⠀⢠⡾⠿⣿⡿⠛⣦⢰⣋⠉⣿⣇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣿⣿⢢⠴⣇⡀⠀⠈⠛⠿⠿⢫⠈ ⠀⠀⢸⣀⣀⣿⣇⣀⣿⠋⢿⣿⣿⣿⣶⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣿⣿⣛⣻⣿⣦⠀⠀⠀⣠⣷⣿⣷⣶⣄ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣾⣿⣟⣻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⣯⠀⢩⡇⠀⠀⣿⠀⢘⣿⠁⠙⡇ ⠀⠀⠀⠀⡏⠋⠀⣿⠀⢹⣿⠁⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣿⣿⣷⡾⠁⠀⠀⠻⣦⣾⣿⣷⡶⠁ ⠀⣠⣶⣿⣿⣶⡄⢿⣦⣼⡿⢶⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣙⣀⠀⠀⠀⠀⠈⠉⢻⠋⠁ ⣼⠀⠀⣿⠉⠉⣿⠀⣙⣏⣽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣦⠀⠀⠀⠀⣠⣴⣄⡀ ⠸⣶⣾⣿⣷⣾⣿⣿⠿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⣹⣯⠉⢹⡆⠀⢠⣾⠿⣿⡿⠛⢷⡀ ⠀⠈⠛⠛⡟⠋⢿⡇⢀⣿⣇⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠁⠀⢸⣿⣤⣿⣧⡀⢨⠇ ⠀⠀⠀⣀⣧⣀⠘⢿⣻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡉⠁⠀⠀⠀⠀⠛⢿⡿⢿⠟⠋ ⠀⡠⠾⢿⣿⣿⣿⣆⠈⢹⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣷⣀⠀⠀⠀⠀⠀⠀⠃ ⠀⣇⠀⣠⣿⣄⣨⣿⣰⣿⣿⣿⡿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⢻⡿⠛⢛⣇⠀⢀⣴⣾⣿⣿⣦⡀ ⠀⠘⠿⣿⣿⣿⡿⠋⣟⡀⢸⣿⡄⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣾⣿⣦⣼⡇⠀⣼⡏⠉⣿⡏⠉⢳ ⠀⠀⠀⠀⠈⠀⢳⡀⠘⣿⣿⣿⣿⣿⡇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⠿⠋⠀⠀⢻⣿⣶⣿⣷⣤⡞ ⠀⠀⠀⠀⠀⢠⡿⣿⣿⣿⣿⡉⢻⣿⡿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢉⢻⡉⠙⣿⠀⠀⠀⠀⠀⡽⠛⠟⠛⠉ ⠀⠀⠀⠀⠀⡇⠀⢹⣿⠀⢈⣷⢸⣇⠀⣸⣿⠀⣸⡇⠀⣠⣴⣶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡾⢿⣿⣷⣶⣟⣠⣾⣿⣿⣷⣧ ⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣾⠟⠈⠻⣿⣿⣿⣿⣿⣷⣶⡟⠁⢹⣿⠋⣹⣧⡀⠀⣴⢾⣿⣿⣷⣶⣾⣿⣿⣿⣿⣕⣻⣿⣟⠋⢼⣿⡛⢻⣿⠋⢻⡆ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠳⣤⣤⣬⣭⣍⠉⠀⠀⠈⣷⣤⣿⣿⣷⣿⡿⠿⣿⡇⠀⣿⣿⣿⡏⠀⢹⣿⠀⠈⣿⣿⡿⠽⣷⣸⣿⣵⣾⣿⣷⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠙⣿⡿⠻⣷⡀⠀⠀⠈⠛⠛⠛⠛⠋⠀⠀⢘⣷⣾⣿⣿⡿⢻⣿⣿⣿⣷⣾⣿⣼⣧⠀⢸⡟⠉⠛⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣿⣷⣤⣿⣇⠀⢀⣤⣶⣶⣦⣄⠀⢀⣴⠿⣿⣿⠿⢯⡴⠋⠉⠛⠛⠙⢿⣿⣿⣿⡿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⠟⠛⠿⣾⡟⠛⢻⣿⠛⢻⣧⣸⡇⢀⣸⣷⡀⢘⡇⠀⠀⠀⠀⠀⠀⠈⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⣠⣾⣿⣧⢿⣯⠙⢿⣿⣿⣿⣿⠿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠁⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀ ⣠⣤⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠉⠀⠉⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠈⠉⠻⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⢀⡾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⡾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢀⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⢸⠀⠀⠀⢀⣠⠴⠾⠛⠛⢻⡶⢶⣞⠛⠛⠷⠶⣤⣀⠀⠀⠀⠸⡇⠀⠀⡴⠏⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣾⣄⠀⣠⠋⠁⢀⣠⠤⢶⡿⢤⣤⠿⡶⠤⢤⡀⠀⠉⠣⡀⢀⣴⣧⣤⡟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠾⣿⣿⣶⣦⣤⣤⣤⣿⣿⣿⣿⣿⣇⣠⣤⣾⣧⣤⣸⡀⢸⡇⠀⡇⣠⣤⣿⣧⣄⣀⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣶⣾⣿⠷⠦⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⣴⠶⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠈⣿⢷⣴⣧⣼⢹⡏⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠶⣦⠈⠹⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣿⠀⠀⣠⡶⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣿⣿⠿⠿⣿⣿⣷⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢶⣄⠀⠀⢿⣇⠀⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣄⣸⡏⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⢹⣧⣀⣾⣿⣾⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⠙⣆⣠⠊⢹⡿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⡿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣆⡀⢀⣿⣤⡞⠻⣤⣿⣅⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⣿⡿⠛⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⣿⣀⣠⣼⣿⣿⣿⣿⣿⡿⢿⣿⠋⠉⢹⡿⠀⠀⠻⣟⠉⠉⢻⣿⠿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣿⡟⢻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢈⣿⠛⠛⠙⣿⢿⣿⠋⢹⣇⠀⠈⠙⠛⠋⠀⠀⠀⠀⠈⠛⠛⠉⠁⠀⣿⠉⢻⣿⢿⣿⠛⠛⠛⣿⡁⣸⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠷⠶⠞⠁⣾⠋⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⢻⡆⠘⠳⠶⠾⠿⠟⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠻⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⢳⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⠛⣆⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠊⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⣀ ⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀ ⢠⣶⣾⣿⣿⣿⣇⣀⣀⡤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⣦⣄⣀⣠⣿⣿⣿⣿⣶⣶ ⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⡇ ⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀ ⢀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠶⠶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠶⠶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⠛⠿⠿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⡿⠿⠿⠛⠋

⠀⠀⠀⠀ ⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠈⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡜⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⣀⡇⠀⣠⠖⠛⢉⣿⢒⣟⡙⠛⠲⢄⠀⢸⣇⡠⠊ ⠀⠀⠀⠀⠀⠀⠀⣠⠴⣶⣶⣤⣤⣼⣿⣿⣷⣇⣴⡯⣬⡇⡟⢹⣨⢽⣦⣀⣷⣿⣿⣧⣠⣤⣴⣶⡶⢤⡀ ⠀⠀⠀⠀⠀⠀⣾⢡⡞⠉⣩⣽⣿⣿⣿⣿⣿⣿⣃⣀⣸⣿⣿⣷⣧⣀⣘⣿⣿⣿⣿⣿⣿⣿⣭⡉⢹⣦⢹⡆ ⠀⠀⠀⠀⠀⠀⠹⣿⣷⣼⣁⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⢀⣿⣼⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⡿⠿⣿⣿⣿⣿⣯⣉⣹⣬⠷⣴⣏⣉⣿⣿⣿⣿⣿⡿⠻⣿⣿⡿⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢹⣧⡼⣿⣿⡿⡟⠻⠏⡩⠋⠀⠹⢍⠩⠟⢻⢿⣿⣿⢷⣤⡿⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠴⠋⡟⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⡏⠢⠴⠿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⡷⠀⠀⠀⠱⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⠈⡧⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠓⢀⡀ ⠀⣀⣤⣤⡄⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣀⠀⠀⣤⣤⣄⣀ ⢸⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⠆ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁ ⠀⢀⣀⣀⣠⣤⣤⣄⣀⣀⣀⣤⡤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠤⣤⣀⣀⣀⣀⣤⣤⣤⣀⣀⣀⡀ ⢰⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣷⠄ ⠀⠉⠛⠛⠻⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠟⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀ ⠀⠀⣀⣠⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠙⣷ ⢠⣾⠋⠁⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢸⡇ ⣿⡏⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⣸ ⠘⣧⡀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠟⠛⠓⠶⣤⣄⡀⠀⢠⡾⢶⣸⡇⠀⠀⠀⠀⠀⠀⣰⠏ ⠀⠈⠻⢦⣀⡀⠀⠀⣾⣴⡿⢷⡄⣠⣤⣤⣀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⣼⣇⠈⢿⣿⡀⠀⠀⠀⣠⡴⠋ ⣠⡶⠶⠶⠾⣿⣾⣶⣿⣿⣇⣾⣿⡋⠀⠀⠙⣇⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦⣾⣿⣷⣤⣶⣿⣅⡀ ⠙⠷⠶⢶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⠾⠏⠀⠀⠀⠙⠶⢤⣤⣤⣤⣤⢴⣶⣾⡿⣿⣿⣿⣿⣿⣿⣿⣉⣠⣬⡿ ⢀⣤⡶⠛⢻⣿⣿⣿⣿⣿⣿⣿⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣡⣤⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⣤⣄⡀ ⢿⣿⣤⣴⠟⣿⣿⣿⣿⡿⠿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣽⠞⠋⠿⣿⣿⡻⣿⣿⣦⡀⠀⠀⠉⠙⠳⣦⡀ ⠀⠉⠉⠁⠀⠉⠉⢹⣿⠀⠀⠈⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⢻⣿⣷⣿⣧⠙⢷⣄⠀⠀⠀⠀⠨⣿⣶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⣦⣄⣀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠹⣯⠉⠁⠀⠀⠉⠳⣄⡀⠀⠀⠈⠙⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠈⠙⢷⣤⣀⠀⠈⢻⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠈⠙⠿⠶⠾⢿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣠⣤⡀⠀⠀⠀⢸⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⣸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠉⠛⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣷⣶⣿⣶⣿⡆⠀⠀⠀⠀⠀⠸⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠻⠿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⠀⠀⠀⠀⠀⠈⠿⠟⠀⠀⠀⠀⠀⢀⣶⣤⣿⣶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⡿⠿⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀ ⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⠉⠉⠉⠻⣧⡀ ⠀⢀⣴⡾⠟⠋⠉⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⢹⡇ ⠀⣿⡿⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃ ⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠉⠉⠙⠛⠳⢶⣤⣀⠀⢰⡟⠻⣧⣿⡄⠀⠀⠀⠀⠀⠀⢀⣼⠇ ⠀⠀⠀⠙⢷⣄⣀⠀⠀⠀⣾⣧⣿⠻⣷⠀⣠⣤⣤⣄⡀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣼⣧⡀⠹⣿⣷⠀⠀⠀⠀⢀⣤⠞⠃ ⠀⣠⣶⠶⠶⣾⣽⣷⣶⣶⣿⣿⣿⣠⣿⣾⡋⠀⠀⠈⢻⡀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⣿⣿⣷⣠⣴⣾⣋⣁ ⠀⠿⣦⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣤⣾⠇⠀⠀⠈⠻⢦⣄⣀⣀⣀⣀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⣉⣹⣷ ⠀⠀⢀⣩⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢩⣿⠟⠋⢉⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣋⠁ ⠀⣴⣿⠋⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠶⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠉⠉⠛⠷⢦⣄⡀ ⠈⠿⣿⣶⠿⠋⠹⣿⣿⣿⣿⡟⠙⠻⢿⣏⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠉⢿⣿⣷⡘⣿⡟⢿⣦⠀⠀⠀⠀⠀⠉⠻⣶⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠉⠛⠿⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⠙⢷⣄⠀⠀⠀⠀⠀⠲⣿⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⣶⣤⣄⡀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣎⠉⠁⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠈⠻⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⣦⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣀⠀⠀⠈⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣶⣤⣤⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢻⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣶⣿⣶⣄⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⡷⣄⠀⣠⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠙⠛⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣸⣶⣾⣿⣶⣿⡆⠀⠀⠀⠀⠀⠀⠘⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⠋⠁⠀⠀⠀⠀⢀⡀⠀⢸⣇⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣇⣤⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⡿⠿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀ ⢀⡤⠴⠤⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣄⡀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣿⣿⣇⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠸⣿⣿⣿⣿⣿⣧⣠⠶⢶⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠉⠛⠳⣿⣿⣿⣿⣿⣿⣅⣴⡟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⢶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠟⠉⢻⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⣠⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢦⣴⠟⣹⣿⠟⢻⡛⣹⠋⣿⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢿⣿⡎⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣤⣀⣈⣿⣶⡞⠂⢰⣶⣧⣤⣤⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣷⣶⣾⢛⣿⠉⠀⠈⠉⠻⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⣠⣦⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⣦⡀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣬⠄⠀⣰⣟⣀⣠⣄⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣙⣷⣄⡈⠉⣸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⣤⣴⣾⣿⠟⠉⠉⠉⠙⢷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⡀⠀⠈⠙⢿⣟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣽⣿⡀⠀⠀⣿⠁⠀⢠⣶⣶⡄⢸⡇ ⠀⠀⢀⣀⣤⣤⣤⣀⡀⢸⣄⣸⣿⣷⣠⣤⣄⣻⠞⠉⠀⢲⣿⣿⣿⣿⣿⣿⣿⣤⣄⠙⣦⣀⣿⣦⣤⣿⣿⣿⣷⣾⣇⣀⣀⣀⣀ ⢀⡴⠋⠁⠀⠀⠀⠉⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣾⣾⢛⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠉⠙⠲⣤⡀ ⣾⠁⠀⠀⢀⣤⣶⣤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣷⣶⣦⣄⠀⠀⠀⠻⡆ ⢻⡄⠀⠀⢸⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣿ ⠀⠹⢦⣄⣀⢀⣼⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣰⠏ ⠀⠀⠀⠈⠉⠉⠹⣯⣿⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣹⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓⠶⠶⠶⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⢹⡿⢿⣿⣿⣷⡿⠻⣶⣄⣀⣛⢻⣿⣿⣿⣽⣿⣿⠉⣩⣾⠏⠉⠙⣿⣿⣿⣿⠇⠈⠙⠛⣿ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⢷⣀⣹⡇⣿⣤⡤⠶⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⢶⣽⣏⠉⠀⠀⠀⠀⠀⡟ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⣀⠀⣛⣻⣽⠟⠁⣠⣤⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣼⠇⠀⠀⠈⠻⣷⣄⣀⣀⣠⡾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⣹⠃⠀⠀⢿⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣤⡀⠀⠀⠀⢻⡍⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠈⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢻⣶⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢤⣤⣤⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⠻⠾⠛⠀⠀⣼⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⣄⣀⣀⣠⠼⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢰⣿⣿⡆⢈⣏⠀⠀⠀⠈⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⠿⣿⣿⣿⣿⣿⢿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣌⡻⣷⣤⣬⣿⣿⣿⣷⠞⣀⣤⣤⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠈⠹⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠾⣻⣿⣿⣿⣿⣿⡿⠻⣿⢶⣤⣤⣼⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣼⣿⣿⣿⠙⣧⡀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡏⠛⠻⡄⠀⠙⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠴⠃

⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀ ⠀⢠⣶⠿⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⠻⣧⡀ ⢠⣿⠁⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⢸⡇ ⢸⣿⡀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⠀⠙⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⣸⡇ ⠈⢿⣧⡀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⣠⣤⣤⡀⠀⣾⡏⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⣀⠀⠀⣿⡀⢠⣶⣶⡄⠀⠀⣾⠇⠀⠀⠀⠀⣰⣿⠃ ⠀⠈⠻⣿⣤⣀⠀⠀⠀⠘⣿⣆⠀⢰⣿⡉⣿⣷⣴⣿⣿⣴⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣷⣿⣇⣸⣧⠀⣸⡿⠀⠀⢀⣠⣾⠿⠃ ⠀⠀⠀⠈⠙⠛⠿⣶⣦⣤⣿⣿⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣟⣻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠿⠛⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⠶⠶⠶⠦⣤⣤⣤⣀⣠⣤⣶⠶⠒⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠶⠶⠖⠲⣶⣶⣿⣿⣿⣿⣶⣾⣟⠙⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣀⣴⣾⣿⡿⠛⠉⠉⠛⠿⢿⣿⣿⣦⣄⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⡿⠿⠟⢿⣿⣿⣯⣿⠏⠙⢿⣷⣤⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣥⣸⣿⣿⣿⡟⠉⠛⢿⣿⡿⠟⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠈⣿⡿⠿⠛⠀⢀⣴⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠻⢿⣿⣿⣿⣿⡇⠀⠀⠀⢹⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣀⣀⣤⣼⣿⠇⠀⣀⣾⣿⠟⠉⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠉⠛⢿⣿⣿⣦⣤⣴⣿⡧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣍⣙⣛⣻⣿⡋⣠⣼⡿⠛⠁⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣧⡾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣽⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣶⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣠⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠁

⠀⠀⠀⠀⠀⠀⠀ ⣠⣿⡿⠟⠛⠛⠻⣿⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⣤⣀⠀⢸⣿⣿⠁⠀⠀⠀⠀⢸⣿⣿⡆⠀⣠⣤⣴⣦⣤⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠋⠉⠉⠛⢿⣿⣿⣿⣿⡀⣀⣤⣤⡀⣸⣿⣿⣿⣿⡿⠋⠉⠉⠙⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣹⣿⣿⣦⡀⠀⠀⠀⠙⣿⣿⢿⠿⢿⣿⣿⡿⠿⣿⣿⠿⠋⠀⠀⠀⢀⣴⣿⣿⣏⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠿⠟⠛⠛⠛⠿⢿⣿⣿⣿⣿⣶⣶⣤⣤⣿⣿⣰⣤⣼⣿⣿⣧⣤⣿⣿⣦⣤⣤⣶⣶⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠿⠿⣿⣶⣶⣤⡀ ⠀⠀⢀⣴⣾⡿⠛⠋⠁⢀⣠⣴⣶⣶⣶⣶⣶⣾⣿⣿⠛⢻⣿⣿⡛⠛⣿⣿⣟⠛⢻⣿⣿⡛⢙⣿⣿⣿⠛⢻⣿⣿⡛⠛⣿⣿⣷⣶⣶⣶⣶⣶⣦⣄⠀⠈⠙⠻⢿⣷⣄ ⠀⢀⣾⣿⠏⠀⠀⢀⣶⣿⡿⠋⠉⠀⢀⣀⣀⣿⣿⣿⠿⢿⣿⣿⠿⠿⣿⣿⡿⠿⢿⣿⣿⡿⠿⣿⣿⡿⠿⢿⣿⣿⠿⠿⣷⣿⣿⣀⡀⠀⠀⠉⠛⢿⣿⣦⡀⠀⠀⢻⣿⣧⡄ ⢀⣾⣿⡏⠀⠀⢀⣿⣿⡟⠀⠀⣠⣾⣿⡿⠿⣿⣿⣤⣤⣼⣿⣿⣤⣤⣿⣿⣷⣤⣼⣿⣿⣧⣤⣿⣿⣧⣤⣼⣿⣿⣤⣤⣿⣿⣿⠿⢿⣿⣶⡀⠀⠀⢻⣿⣷⡀⠀⠀⣿⣿⣷ ⠀⢻⣿⣧⠀⠀⠈⢿⣿⣧⠀⠀⠘⠿⢿⣷⣶⣿⣿⣿⠛⢻⣿⣿⡛⠛⣿⣿⣟⠛⢻⣿⣿⡟⢛⣿⣿⣟⠛⢻⣿⣿⠛⠛⣿⣿⣿⣶⣾⡿⠟⠁⠀⢀⣾⣿⡿⠁⠀⢀⣿⣿⡿⠁ ⠀⠈⢻⣿⣧⡀⠀⠀⠙⢿⣿⣦⣤⣀⣀⣀⣀⣿⣿⣿⠿⢿⣿⣿⠿⠿⣿⣿⣿⠿⢿⣿⣿⡿⢿⣿⣿⡿⠿⢿⣿⣿⠿⠿⣿⣿⣿⣀⣀⣀⣀⣤⣴⣿⡿⠋⠀⠀⢀⣾⣿⡟⠁ ⠀⠀⠀⠙⠿⣿⣶⣤⣀⠀⠈⠉⠛⠛⠛⠛⠻⢿⣿⣿⣤⣼⣿⣿⣤⣤⣿⣿⣧⣤⣼⣿⣿⣧⣴⣿⣿⣧⣤⣼⣿⣿⣤⣤⣿⣿⡿⠿⠿⠿⠛⠛⠋⠁⠀⣀⣠⣶⣿⡿⠋ ⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⡿⠿⠟⠛⠛⣿⣿⡟⠛⢻⣿⣿⡟⢻⣿⣿⡟⠛⠛⠿⠿⣿⣿⣿⣿⣷⣶⣶⣦⣶⣶⣶⣾⠿⠿⠟⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠿⢿⣿⣿⠿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠹⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣤⣤⣤⣾⣿⠿⢿⣿⣿⠀⠀⠉⠁⠀⢸⣿⣿⠿⢿⣿⣦⣀⣠⣴⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠸⣿⣿⡀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠉⠛⠛⠛⠋⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠶⠶⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠙⢷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⣽⠁⠀⠀⢸⡧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⣿⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠘⣿⣿⡻⣆⠀⠀⣯⠀⠀⠀⣼⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⢻⢹⣇⠙⢷⡀⢿⠀⠀⢰⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢹⡆⠀⠀⠀⣀⣀⣘⣇⣿⣆⠀⠳⣼⡇⢀⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣿⣤⡾⣻⡿⠛⠛⢻⣿⣿⣧⡀⠹⣿⣼⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⠿⣄⡀⠀⠈⢿⡟⢯⣳⣄⢸⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢡⣿⣿⣿⣿⡺⢽⣷⣤⣸⣷⡈⢷⣹⣿⣍⣷⣶⠀⠀⠀⠀⠀⠀⠀⣾⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣴⠟⠁⢹⣯⣿⣿⣾⠛⠛⢻⣿⣿⣟⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢳⣾⡟ ⠀⠀⠀⠀⠀⠀⠀⣤⣟⣾⠋⣠⡶⠛⠙⣷⣹⣿⣷⣄⣼⡇⠻⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⡿⠋⠀⣀⣠⣼⣿⣿⣿⣿⣿⣇⢠⣿⣇⣿⢸⡿⢿⣼⣿⢳⣴⣿⣿⠇ ⢰⣤⡀⠀⠀⢸⣶⣿⣿⣿⣿⣿⡛⠋⠉⠀⠀⠻⣿⣾⣿⣿⣿⣿⣻⣿⣾⡇⠈⣿⣿⣿⣿⣿⡟ ⠀⠻⡟⢷⣄⣸⡿⣿⡇⠈⢻⣿⣿⣆⠀⢀⣀⣀⣽⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣶⣶ ⠀⠀⠈⠷⣝⣿⣿⡿⣿⣦⣄⡿⣿⣿⣿⣿⣛⣿⣯⣿⣿⣿⠷⠿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡷⠟⢻⡆ ⠀⠀⠀⠀⣹⢿⣿⡿⣿⣿⣧⣳⡈⢻⣮⠻⣿⣧⣾⢻⣿⣿⣧⡀⢨⡿⣿⣿⣿⣿⡿⣿⠉⠀⠀⠀⣿ ⠀⠀⠸⣿⣯⣄⣿⣷⣌⠻⣿⣷⣷⠀⠙⣿⣯⣿⢿⣾⣿⠃⠹⣿⡟⠀⣯⣿⠟⣿⣷⡟⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠘⣷⣍⣻⣿⡌⠳⣬⣻⣿⣿⣾⡟⢻⣿⡀⢻⣿⣦⣤⣿⣷⡞⢻⠀⣼⣿⣿⣇⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⢧⠉⠻⣯⣿⣶⣦⣝⣿⣿⢿⣿⣿⣯⡻⣿⡇⢨⣿⣿⣿⡷⢸⣼⣿⠏⣿⣿⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⠘⢆⠀⠘⣟⠿⣿⣿⣿⣿⣿⣿⣿⣭⣻⣿⣿⣿⡥⠤⠿⣿⣿⡏⠀⣸⡏⣿⠀⠀⠀⣰⡏ ⠀⠀⠀⠀⠀⠈⢳⡀⠹⡄⢼⡿⠿⣿⣿⣯⣿⣿⣿⣿⣟⠉⣿⣷⣾⣿⣿⣇⣴⠏⣸⡟⠀⠀⣰⠟ ⠀⠀⠀⠀⠀⠀⢨⡟⢶⣿⣿⣤⣤⠬⣭⣿⣿⣿⣿⡿⣿⢿⣏⠙⢷⣌⣼⣿⣷⢿⣿⡇⢀⡼⠋ ⠀⠀⠀⠀⠀⢀⣠⣷⣾⣽⣿⣄⢀⣴⡿⠋⠉⢻⣿⣿⣮⣳⣿⣿⣾⣻⣿⡟⢡⣾⣿⡵⠏⠁ ⠀⠀⠀⣀⡴⠋⠁⢄⠙⢻⣿⣿⣿⣿⣤⣀⡀⢨⣿⣮⡿⣿⣿⣿⣾⣛⣿⣿⣿⠿⠋ ⠀⠀⣴⠋⠀⠀⠀⠀⠑⢄⣙⡓⠿⣿⣿⣿⠿⢿⣿⣽⣷⣽⣿⣿⣿⣿⣿⠋⠛⠃ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⡿⣷⣾⡷⣶⣾⣿⣿⣿⣾⢿⣿⣦⣀ ⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣻⣿⠉⣀⣴⠟⢻⣿⣿⠗⠿⠿⣿⣿⣶⣶⣤⣄⣀⡀ ⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣾⠛⠀⠀⠀⢉⡿⣦⡀⠀⠈⠳⣄⠉⠉⠛⠛⠿⠦ ⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠚⠛⠋⠉⠰⠿⠛⣟⠻⠀⠀⠀⠀⣸⠇⠈⠻⢶⣄⠀⠙⢧⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠙⠻⢦⣌⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣠⡞⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣴⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⠞⢹⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣀⣠⣀⣀⣀⣀⣀⡀⢰⣿⠟⠁⠀⣿⣿⣀⣀⣀⣠⣀⣤⣤⣤⣤⣤⣤⣤⣤⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⣛⣿⣿⡿⠟⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠿⠛⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠿⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⢀⣠⣴⣶⣤⠀⠀⢰⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣁⣠⣤⣶⣿⠿⠻⣿⣝⣷⡀⣿⣿ ⠀⠀⠀⠀⢀⣠⣾⣿⣷⣿⡿⠟⠛⠉⠀⠀⠀⠙⣿⣿⣵⣿⠇ ⠀⠀⠀⣴⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡟ ⢀⣴⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁ ⠉

⠀ ⢀⣤⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀ ⠀⠀⠀⠀⣰⣿⡏⠀⠈⠙⠻⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠟⠻⢿⣶⡀ ⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⠀⠙⢷⡀⠀⢀⣠⣶⣾⠿⠿⠿⢿⣿⣦⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⢠⣿⠟⠉⠀⠀⠀⠀⢸⣿⣿ ⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⢠⣿⠟⠋⠉⠉⠉⠙⠛⠻⢷⣦⣤⣴⣿⣥⣤⣤⣤⣤⣤⣶⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠙⣿⣿⣷⣄⡀⠀⠀⠀⠀⢀⣾⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⢿⣿⣟⠛⠛⠛⠛⠛⠋⠁ ⠀⢠⣴⡆⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⢹⡟⠿⣿⣿⣿⣷⣶⣶⡿⠏⠀⠀⠀⠘⢿⣦⣄⣀⣀⣤⣴⣾⣿⣿⢟⣿⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣀ ⢰⣿⣿⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠈⣷⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠁⣼⠇⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⢻⣿⣦ ⠘⢿⣿⣷⣤⣤⣼⡿⢿⠁⠀⢀⣤⣶⡿⠿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣤⣤⣤⣀⠀⠀⠈⠻⣷⣤⣀⣀⣀⣠⣾⣿⣿ ⠀⠀⠉⣿⣟⠉⠁⢇⣸⠀⢀⣿⣿⠀⢀⣰⠟⠉⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠟⣿⡍⠉⠙⢻⣷⣄⠀⠀⡜⢻⡿⠿⠿⠿⠿⠛⠁ ⠀⠀⠀⢋⠈⢃⠀⠈⢿⡇⠘⠿⣿⠿⠟⠁⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠈⠻⣶⣶⣾⣿⣿⠀⢰⣇⡘ ⠀⠀⠀⠈⣦⣾⡀⠀⢸⣷⡀⠀⠀⠀⠀⠀⣠⣴⣶⠿⢿⣿⣿⣿⣷⣦⡀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣷⣦⣤⣀⠀⠀⠀⠉⠉⠉⠁⠀⣸⣿⠃⠀⠀⠀⠀⣠⡀⠀⢠⣀ ⠀⠀⠀⠀⠈⠹⣷⡀⠘⡋⠹⠀⠀⠀⢠⣾⡟⠁⠀⠀⣼⠏⠀⠙⠻⣿⣿⡄⢀⣾⣿⣿⠟⠛⠹⣿⡉⠉⠙⠻⣷⣦⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⣤⣄⣤⣿⠷⠶⢾⣯⣀⣤⣄ ⠀⠀⠀⠀⠀⠀⣿⠛⣆⢧⣴⡇⠀⠀⢸⣿⣇⣀⣠⡾⠋⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠁⠀⠀⠀⠙⢧⣀⠀⠀⢸⣿⡇⠀⠀⠀⢀⡇⢹⠃⢀⣀⣸⡟⠻⣷⡄⠀⣠⣿⠿⣿⡁ ⠀⠀⠀⠀⠀⠀⠘⢄⣸⡆⢹⣧⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠟⣃⠀⠀⠀⢸⣧⡇⠀⠺⢿⡿⠀⠀⣹⣿⣟⢿⠁⠀⢸⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠙⢿⣧⠀⠀⠀⠀⠀⣀⡀⠀⣾⣆⣠⣿⣧⣤⣿⣿⢋⣤⡄⣤⣾⣿⣶⠿⠿⣿⣿⣿⣷⣦⣼⣿⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⠀⠀⠉⠓⠢⢤⣄⣀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣹⣯⣻⣦⡀⠀⣿⡟⠀⠀⣩⣿⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣿⣿⣿⣿⣿⣿⠉⠀⠀⢀⣏⢹⢻⣿⣿⣿⣿⣿⣿⡟⢻⣶⣿⣷⣶⡿⡻⠿⢦⣤⡀⢀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠏⠉⢻⣿⣷⡄⢀⣾⡿⣿⣿⣿⠿⢿⣿⣿⣿⠃⠘⠛⠀⣨⡿⣻⣿⣶⣾⣿⣷⣾⣿⣇⣠⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢹⣿⣿⣿⡷⢀⠀⢻⣿⣿⣿⣿⠛⠛⠛⠛⢿⣿⣿⣿⣤⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⡏⠀⠀⠀⠀⣸⣿⢏⣽⣯⡻⣿⡅⠀⠀⠀⠈⣿⣿⣿⣤⡾⣿⣿⣿⠟⠙⢿⣦⡀⠀⣠⣾⡿⠻⣿⣿⣏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣷⣤⣶⣾⣿⣿⣿⣿⠿⢿⣳⣿⣿⣦⣄⣀⣀⣿⣿⣿⣿⣵⣿⣿⡏⠀⠀⢘⣿⣿⣿⣿⡏⠀⠀⢹⣿⣿⡿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡟⠛⡿⠋⠙⣿⣿⣿⠿⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣧⣴⣶⣿⣿⣿⣿⣿⣷⣤⣀⣸⣿⣿⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⠁⠒⣦⣤⣤⡖⠛⣹⣿⣿⣿⡧⠚⠁⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⣸⣿⣿⣿⣤⠸⠿⢿⣿⣿⡋⠁⠀⠈⣿⡟⠉⠉⠙⢻⣿⣿⣿⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠛⠛⠛⠻⠾⠛⠛⣿⣿⣿⣦⣤⣀⠀⣿⣿⡏⠀⠀⣀⣤⣾⣿⣿⣟⠉⠉⠀⢠⣾⣿⣿⣿⣦⣀⣀⣿⡇⠀⣀⣴⣿⣿⡟⠻⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠻⠃⠀⠀⠀⠁⢀⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠉⢻⣿⠿⣿⣿⠿⣿⣿⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⠏⢹⣿⡏⠙⡿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠛⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⡀⣰⡄⣠⡄⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣦⡀⣷⣀⣾⣀⣴⠀⣤⠀⣤ ⠀⠀⠀⠀⠀⠀⠀⢠⣄⢸⣦⣼⣷⣿⣷⣿⣷⣿⣷⣿⣧⣾⣁⣴⠀⠀⠀⠀⠀⢀⡀⢳⣦⣿⣴⣿⣿⣿⣿⠿⢿⣿⣾⣿⣾⣯⣤⡄ ⠀⠀⠀⠀⠀⠀⢷⣦⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠉⠉⠛⠻⣿⣿⣦⣄⣠⣤⣤⣄⣿⣿⢿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⡄ ⠀⠀⠀⢤⣀⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⡿⠃⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄ ⠀⠀⢤⣬⣿⣿⠛⢿⣿⣦⣄⢀⣠⣤⣶⣶⣶⣶⣦⣤⣀⢀⣴⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⡟⠁ ⠀⢤⣤⣿⡿⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⣤⣄⡀⢀⣤⣴⣿⣿⣿⣿⣿⠏ ⠰⢶⣾⣿⠁⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢻⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠸⣿⣟⠋ ⠴⣶⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣧⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣋⠁ ⠴⢾⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⡛⠉ ⠴⠾⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢰⣿⣿⡉⠁ ⠠⠾⢿⣿⡀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣾⣿⣍⠉ ⠀⠴⠿⣿⣷⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢉⣹⣿⣿⣿⣿⣿⠀⠈⠙⠿⣿⣿⣿⠋⠉⠙⣿⣿⣆⠀⠀⠀⠀⢀⣾⣿⣯⡉⠁ ⠀⠀⠼⠛⣻⣿⣶⣿⡿⠛⠁⠀⠉⠉⠛⠿⣿⣿⣿⠋⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣾⣿⣿⣦⠀⠀⠘⣿⣿⣆⠀⢀⣠⣿⡿⠋⠀⠁ ⠀⠀⠀⠘⠉⠙⢿⣿⣄⣀⠀⠀⠀⠀⢉⣻⣿⡿⠁⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⣿⣿⣷⣿⣿⠛⠧ ⠀⠀⠀⠀⠀⠀⢰⠟⢻⣿⣿⣶⣦⣄⣹⣿⣿⣅⣠⣴⣶⣾⣿⣿⣿⣿⣿⠿⡿⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⠿⡏⠉⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⢿⣿⣿⣿⡿⠟⠛⠻⢿⠹⣿⣿⣿⣏⠙⠀⣠⡀⠀⠛⣛⣿⣇⢻⠋⡿⠛⣿⣿⣿⡿⠋⠈⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⡥⠀⢾⣿⣿⡆⠈⣛⣿⡟⠀⠀⠀⠀⢻⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⣿⣿⡀⠀⠀⠀⣰⣿⣿⣿⣶⠖⣠⠉⠀⢤⣌⣿⡿⠁⠀⠀⠀⠀⣼⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣇⢀⣤⣾⣿⣿⠿⠿⣿⣿⣿⣼⣷⣼⣿⣿⣇⠀⠀⠀⠀⢠⣿⣿⣧⠀⣆⢀⣤⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⣷⡀⠀⣴⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣦⣤⣀⣀⣀⣀⣀⣀⣠⣴⣾⣿⡿⠛⠁⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠉⢉⣿⣿⣿⣿⣿⣿⠿⣏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⠋⢿⠋⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⣠⠀⠀⠀⠀⠀⣤⣽⣷⣿⣾⣧⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⠿⠛⠛⠛⠉⠉⠛⠛⠛⠿⣿⣷⣦⣀⠀⣠⣸⣶⣿⠿⢿⣿⣿⣯⣴⢀⡒⣾⣿⡏⠉⢻⣿⣷⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣷⣿⡟⠁⠀⠀⢸⣿⡇⠉⠻⣿⣿⣿⣿⣷⣴⣿⣿⡟⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⢀⣻⣿⣿⣷⡀⠀⣠⣿⣿⡇⠀⠀⠙⣿⡿⠿⠟⡿⠻⠏⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⢀⣴⡿⠁⣀⣈⣻⣿⣼⣿⣿⣾⣿⣉⣿⣇⡀⠀⠀⣿⣟⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⡉⣻⣿⣿⣷⣀⣨⣿⣏⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⣀⣀⣠⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⠿⠛⠛⠋⠉⠉⠰⢻⣿⣦⣼⣿⡿⠿⠟⠻⢿⣿⣿⣯⡁ ⠀⢠⣄⣶⣤⣆⣀⣀⣀⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣿⣷⡿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⢿⡟⠛⣿⣯⡄ ⠰⣾⣿⠟⠛⢿⣿⣿⣿⡿⠿⢿⣿⣿⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⣿⣿⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣯⣄⣀⣤⣽⣿⠧ ⠰⢿⣿⣄⠀⣸⣿⡧⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢯⣼⣿⣿⣿⡿⠿⠛⠛⠋⠉⠙⠻⠿⣿⣿⣿⣿⡿⡟⠁⠀⠀⣸⣿⠳ ⠀⠘⠻⣿⢻⣿⣿⣷⣄⠀⠀⠀⠸⣿⣦⠀⠀⠀⠀⠀⠀⣰⡿⠳⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣇⡄⢀⣰⣿⡟⠃ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⡀⠀⠀⠘⢿⣧⡄⠀⠀⠀⣴⠟⠙⢿⣿⣿⠏⠀⠀⠀⢠⠖⠒⠋⠉⠒⢄⡀⠀⠀⠘⣿⣿⣿⣿⣿⢻⠇⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣆⠀⠀⠀⠹⣿⣶⣶⣾⣏⠀⣙⣿⣿⣿⠀⠀⠀⢰⠁⠀⠀⣀⡀⠀⠀⢱⠀⠀⠀⢸⣿⣿⣷⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⡀⠀⠀⠀⠙⠿⣿⣿⣤⣙⣿⣿⣧⠀⠀⠀⢯⠀⠀⠀⠻⠇⠀⠀⢀⠇⠀⠀⢠⣿⣿⣷⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣠⣦⣰⣆⣼⣙⣻⣿⣿⣿⣿⡀⠀⠀⠈⢦⡀⠀⠀⠀⠀⢀⠞⠀⠀⠀⣼⣿⣿⡟⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣟⠉⢹⠟⠿⣷⣾⣿⣿⣿⣷⡄⠀⠀⠀⠈⠑⠒⠒⠈⠁⠀⠀⢀⣼⣿⣿⣿⣛⡃⣤⣄⣴⣠⣦⣀⡄⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⡿⠹⣿⣿⣦⣼⡀⠀⠈⢻⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣷⣿⣵⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⠁⠀⢈⣿⠋⢉⣿⠀⠀⠀⣿⣧⡏⢹⠿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⢼⠏⠉⠻⢿⣿⣟⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡶⠖⠛⠛⠿⠾⠿⣤⠀⢠⣿⠷⠀⠀⠐⠛⢹⡟⣿⢿⣿⢿⣿⢿⡏⠻⠋⣽⣿⣿⡟⠷⣤⡀⠀⢀⣠⡟⠀⠀⠀⠈⢿⣿⣯⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣤⡀⠀⠀⠀⠀⢈⣻⣿⠻⠆⠀⠀⠀⠀⠀⠀⠈⠀⠉⠈⠃⠀⠀⠀⠀⢶⣿⣿⠀⠀⠈⠙⣿⡟⠛⢿⣷⣀⣀⣄⣸⣿⣷⠦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠿⣿⣶⣶⣾⡟⠿⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠀⠀⠀⢀⣿⣷⣤⣾⡟⠉⠉⠉⢈⣿⡿⠦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣦⣠⠶⠋⠀⠉⠛⢷⠀⠀⠀⢀⣼⣿⡟⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣷⣄⡀⠀⠀⠀⠘⣧⣀⣴⣾⣿⣏⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠾⢻⣿⣿⣿⣷⣶⣾⣿⡿⣿⠻⠇⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠉⠿⠹⠏⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⠶⠲⢾⣿⠗⠶⢤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡏⠀⠀⠀⢸⡿⠀⠀⠀⠉⣷⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⣴⣤⣼⣿⣷⣄⡀⠀⢸⣇⠀⢀⣤⣶⠿⢿⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⣠⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⠉⠀⠀⠈⣯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⢀⡗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠛⠿⣿⣏⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⢠⣤⡄⠀⠀⠀⣠⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⣻⣿⣷⣿⣿⣾⣿⡏⠉⠛⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣾⣿⣿⠿⢿⣿⣿⣿⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣇⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡀⣀⣿⣿⣿⣿⣿⣶⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⠿⠿⢿⣿⣿⣿⠁⠀⣻⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠙⢿⣷⣾⣿⣿⣿⣤⣄ ⠀⠀⠀⢀⣀⣶⡴⠿⠒⠻⢿⣿⣿⣿⣿⣿⣿⣿⣤⡀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠿⣿⡟⠛ ⠀⠀⣤⡼⢿⣅⠀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠈⠁⢹⣿⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣀⣠⣿⡇ ⠀⣶⡟⠁⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣄⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⢵⡆ ⠠⣾⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣧⡀⣀⣿⣿⣿⣷⣾⣿⣿⣿⠃⠈⢹⣿⡿⠋⠉ ⢠⣾⡶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠿⠿⠛⢿⣿⣿⣿⣟⠀⠀⣿⣿⣿⣷⣶⣿⣿⡁ ⠀⢸⣧⠀⠀⠹⣿⣿⣿⣿⣿⣿⡏⠀⢠⡟⠿⠋⢈⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⠀⠈⠁⠀⠀⠀⠀⠉⣿⣿⠿⠷⢾⣿⣿⡿⠟⠉⠉⠛ ⠀⠀⠺⠷⣄⡀⣸⠏⠉⠉⠁⠀⢻⣶⡟⠛⠀⠀⠀⠉⠛⠀⠸⠿⠿⠃⠘⠿⠿⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⠛⠁ ⠀⠀⠀⠈⠛⢹⡿⢶⡶⢶⣶⠻⠯⠈⠁ ⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣦⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⡿⠋⠉⠉⠉⠙⠻⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⠀⣤⣀⣾⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣷⣶⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⣀⣠⣶⣴⣷⣶⣶⣄⣨⣿⣿⣿⣦⡀⠀⠀⠀⢀⣤⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠓ ⠀⢠⣴⣿⠟⠛⠿⣿⡟⠉⠻⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡿⠃⠀⠿⢿⣿⣿⣿⣿⡟⠃ ⢠⣾⡿⠁⠀⣠⣶⣾⣷⣦⡀⠀⢻⣿⡿⠋⠹⠿⣿⣿⣿⣿⣿⣷⣼⣇⣼⣸⣿⢙⡋⠉⠁ ⣼⣿⣷⣄⢸⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⠆⠰⣤⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣷⣿⣤⡖ ⢸⣿⣿⠋⠻⣿⣿⣿⣿⣿⠟⠉⢻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣟⣤ ⠀⢿⣿⣦⡀⠉⠛⣿⡿⠋⠀⢀⣼⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡖ ⠀⠀⠸⠿⣿⣶⣾⣿⣿⣶⣾⣿⡿⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠂ ⠀⠀⠀⠀⠘⠉⠙⠛⠛⠛⠋⠁⠐⠺⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣉⣠⣤⣴⣶⣶⣤⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠟⠛⠛⠻⢿⣿⣿⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠍⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⣀⣠⣴⣾⣿⣿⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠁⠀⠀⠀⠁⠸⠋⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣀⣀⣀⣀⣤⣴⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣥⣾⡿⠟⢫⡿⠁⠁⠀⠈⠛⢿⣿⡿⠿⠿⣿⠿⠿⠿⠛⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⣀⠀⠀⢀⣀⣤⣾⡿⠟⠁⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⢻⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠿⠟⠻⠿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⠚⠉⠉⠙⠷⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡏⠀⠀⠀⢀⣴⣿⠟⠛⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣤⣤⣶⣿⠟⠁⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣤⣀⡀⠀⢀⣀⣴⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⡿⠿⠿⠟⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣀⠀⠀⣀⣀⣤⡾⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣀⡀⠀⣀⣀⣤⣤⣤⣀ ⣀⣀⣤⣾⣿⣿⣷⣄⣶⣿⣧⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣆⣶⣤⡄⣀⣤⣤⣀ ⣿⣿⣿⣿⡁⠀⣹⣿⣿⣿⣿⣿⣷⣄⣴⣿⣿⣿⣿⣿⣿⣧⣠⣾⣿⣿⣿⣿⣿⣿⠟⠻⣿⣷⡀ ⣿⠿⢿⣿⣷⣾⣿⠟⠘⠛⠋⠈⠛⠛⠛⠉⠁⠀⠀⠈⠉⠛⠛⠛⠁⠻⠿⠏⣿⣷⣄⣠⣿⣿⣿⣶⣤⣄⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⣿⣿⣿⣿⠿⣿⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣇⢀⣨⣿⣇⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⢿⣿⣿⣿⡦⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⢿⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⣠⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣦⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠻⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⣠⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣾⡿⠿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⢀⣼⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠉⢻⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢿⣷⣶⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣴⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡟⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⢙⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣾⣿⣿⣿⡿⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡏⠈⠛⣿⡏⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣶⣿⡿⠃ ⣿⣶⣾⣿⣿⣿⣷⣆⢠⣤⣄⢀⣤⣤⣤⣀⡀⠀⠀⠀⣀⣤⣤⣤⡀⣴⣶⡖⣿⡿⠛⠛⢿⣿⣿⠿⠛⠛⠉⠉ ⣿⣿⣿⣿⠁⠀⣹⣿⣿⣿⣿⣿⡿⠋⠻⣿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣷⣿⣷⣤⣴⣿⡿⠁ ⠉⠙⠛⠿⣿⣿⡿⠏⠿⣿⡟⣿⣷⣤⣴⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⠏⠿⠛⠛⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⣒⣲⣶⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣖⣲⣶⣤⣴⣖⣒⣋⣭⣵⣾⢋⠔⢲⣌⢻⣷⠀⣿⣶⣶⡄⢀⣤⣶⣶⣦⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢩⠔⢪⡙⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⠟⣸⡿⢠⣿⣿⡿⢠⣿⠏⡥⠒⢍⠳⣝⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡀⣿⣇⠳⣿⣿⠇⣿⣿⡯⠝⠒⠒⠚⠿⢿⣶⣶⣾⠟⠁⠘⠛⠻⠧⠸⣿⡜⢿⣿⡿⢠⣿⣷⣭⡲⢄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣤⡈⠻⣿⣿⣷⡘⠻⣷⣦⣴⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣶⣿⡿⢿⣿⣿⣷⣮⣽⣒⣢⠤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⢞⢭⣭⡙⣿⣆⢹⡿⠟⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠬⣻⣿⣿⠟⣩⣭⡙⢾⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢣⣇⢸⣿⣿⡇⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⣀⣤⣴⣶⡿⢛⣙⢻⣆⢠⣤⣀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠸⣿⣿⡿⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣱⣿⣿⣷⣬⣭⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⢠⡿⢉⣭⣙⣿⣿⣿⣿⣿⣇⠙⠟⣣⡿⢸⣿⡟⣴⡟⣩⣍⢻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠻⣷⣬⣭⣶⡿⠋⣠⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣾⣿⣿⢛⡿⠛⠉⠁⠀⠀⠀⢀⣀⡀⠠⣾⣷⡜⣷⣌⣛⣱⡿⠛⠉⠉⠉⠙⠛⠛⠛⠁⠈⠉⠁⠹⣧⣙⣋⣼⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠈⠉⠉⠡⣤⣾⣿⣿⠿⠆ ⠀⠀⠀⠀⠀⠀⣠⢞⣯⣾⣿⣿⣿⡳⠋⠀⠀⠀⠀⠀⠀⣴⠟⣻⡻⣷⡹⡿⠟⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠿⣿⣿⡟⣛⡛⣷⡀⠀⠀⠀⠀⠀⠈⢻⠟⢁⣴⣶⣶⣶⣤⡀ ⠀⠀⠀⠀⠀⣼⡵⢩⣶⣶⡌⣿⣿⠃⠀⠀⠀⠀⠀⢀⣼⣿⡘⠿⢃⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠻⠟⣼⠇⠀⠀⠀⠀⠀⠀⠀⢠⣿⢋⣴⡒⢌⢻⢳ ⠀⠀⠀⠀⠀⢿⣧⠸⢿⣿⠇⣾⡿⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢠⣶⠿⣶⣾⣿⣿⣏⣸⣿⢸⣿⢠⡶⢶⣦⡀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣫⣾⣿⡦⠀⠀⠀⠀⠀⢸⣿⡘⢿⣿⠜⣸⣾⡀ ⠀⠀⠀⠀⢀⡈⠻⢿⣶⣶⡾⠟⠁⠀⠀⢀⣴⠾⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣠⣄⠰⣿⡜⢷⣶⠟⠋⠉⠉⠙⠋⠁⠈⠁⠘⢷⣾⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠙⠟⣫⣴⠶⣦⣄⠀⠀⠀⠙⢿⣶⣶⣾⣿⡇⡇ ⠀⠀⠀⠀⣼⣿⣷⣦⣤⠀⠀⠀⠀⠀⠀⣿⠣⣶⣦⢹⡟⠀⠀⠀⠀⠀⢀⣾⣏⣙⣷⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣏⣨⣿⠄⠀⠀⠀⠀⠀⠀⣿⢠⣶⡦⣿⡆⠀⠀⠀⠀⠙⢿⢿⣿⣿⡹⡄ ⠀⠀⠀⠘⠛⠻⠿⣿⡏⠀⠀⠀⠀⠀⠀⠹⢷⣬⣴⠿⠃⠀⠀⠀⢀⣴⣿⣿⠟⠋⠁⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣴⡶⢤⣀⠀⠀⠀⠀⠀⠙⠋⢵⣿⠆⠀⠀⠀⠀⠀⠻⣦⣭⣶⣿⡇⠀⠀⠀⠀⠀⠘⡜⣿⣿⣧⣳⡀ ⠀⢀⣴⣿⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⣼⣿⣶⡦⠀⠀⠀⠀⠀⢰⡿⠻⣿⠃⠀⠀⠀⠀⣀⣴⣾⣿⣧⣭⡿⠛⠛⠿⣤⣴⣿⣷⣦⣄⠀⠀⠀⠀⠀⣼⡟⢻⣧⠀⠀⠀⠀⠈⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⣧⣿⣿⠿⣷⡱⣄ ⢀⡿⡟⡔⢲⣶⡌⣿⡆⠀⠀⠀⢀⣠⣤⣭⡙⠁⠀⠀⠀⠀⠀⣌⡛⠞⠋⠀⠀⠀⢀⣼⡁⢈⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⠈⣷⡄⠀⠀⠀⠘⢿⣾⣿⡀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⢠⣿⡏⣴⣶⠲⠹⡘⡆ ⠀⢇⣧⠳⠾⠿⣁⣿⠇⠀⠀⠀⣾⢋⣴⣌⢻⡆⠀⠀⠀⠀⣀⣛⠻⠀⠀⠀⠀⢀⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⣿⡄⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⣿⢩⣴⡌⣿⡄⠀⠀⠘⣿⣇⠻⠿⠶⣰⣿⠇ ⠀⢸⣸⣿⣿⣿⣿⠏⠀⠀⠀⠀⢻⣦⣉⣡⡾⠃⠀⠀⠀⢰⣟⢙⣷⠀⠀⠀⠀⡞⠙⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠹⡄⠀⠀⠀⢸⣟⢙⣷⠀⠀⠀⠀⢿⣮⣛⣡⡿⠁⠀⠀⠀⠈⠻⢿⣿⣿⠿⠋ ⠀⠀⡏⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⣿⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⡇⠀⠀⠀⠈⣛⣛⡁⠀⠀⠀⠀⠀⣬⣭⣭⡄⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆ ⠀⠀⣇⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡇⠀⠀⠀⠀⣛⣛⡃⠀⠀⠀⠀⠀⠻⠿⠿⠇⠀⠀⠀⠀⠀⢸⡿⠿⠿⣿⡇ ⠀⢸⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⣸⡿⢛⡻⣷⡀⠀⠀⠀⢸⣟⢙⣿⠀⠀⠀⠀⣇⣀⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣨⠇⠀⠀⠀⢸⣟⢙⣷⠀⠀⠀⠀⣴⠞⣛⠻⣦⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⡀ ⠀⡞⡞⣩⣤⣬⠙⣿⡄⠀⠀⠀⣿⡐⠿⠗⣸⡇⠀⠀⠀⠈⢛⣛⣧⠀⠀⠀⠀⠘⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⣿⠘⠿⠗⣿⠇⠀⠀⢀⣾⡟⣡⣤⢬⢻⣿⡄ ⠀⣧⣇⢿⣿⣿⢃⣿⡇⠀⠀⠀⠈⠻⠶⠟⢋⠀⠀⠀⠀⠀⠀⠛⣫⣤⣄⠀⠀⠀⠘⢟⠋⢙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⣿⠏⠀⠀⠀⢀⣴⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣶⣿⠋⠀⠀⠀⠘⣿⡇⢿⣿⡸⢡⢇⠇ ⠀⠘⢿⣶⣦⣶⡿⠟⠀⠀⠀⠀⠀⠀⢾⣿⣿⠧⠀⠀⠀⠀⠀⢸⣯⣨⣿⡀⠀⠀⠀⠈⠑⠿⣿⣿⡶⣒⣦⣤⣠⣤⢆⣶⣾⣿⡿⠒⠁⠀⠀⠀⠀⢿⣏⣸⡿⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⡿⣿⣶⣦⣶⢫⠎ ⠀⠀⠀⢈⣉⣭⣴⣶⡆⠀⠀⠀⠀⠀⠈⢩⣴⠶⠶⣤⡀⠀⠀⠀⠉⠻⣿⣷⣤⣀⠀⠀⠀⠀⠈⠙⠲⠭⠾⠿⠿⠿⠯⠟⠛⠁⠀⠀⠀⠀⣀⣀⠸⣶⡍⠉⠁⠀⠀⠀⣠⡾⠿⢿⣿⡏⠀⠀⠀⠀⠀⢀⢇⣿⣿⡿⣳⠃ ⠀⠀⠀⠈⢿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⣿⡁⣾⡦⢹⣇⠀⠀⠀⠀⠀⠘⣿⣟⢛⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⢛⣷⠈⠀⠀⠀⠀⠀⠀⣿⠰⣿⡦⣿⡇⠀⠀⠀⠀⢀⣾⣾⣿⣿⢣⠇ ⠀⠀⠀⠀⠘⠉⣡⣶⣶⣶⣶⣄⠀⠀⠀⠘⢷⣾⣶⣿⣿⡄⠀⠀⠀⠀⠀⠈⠛⠛⢡⣿⢇⣴⢶⣤⡀⠀⠀⢀⡀⠀⠀⠀⢠⣶⣶⣾⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⢀⣤⡹⢷⣶⡾⠟⠀⠀⠀⣀⣴⣿⣿⣿⣿⡏⡏ ⠀⠀⠀⠀⠀⣼⡿⢡⣶⣶⡌⢿⣧⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠈⠸⣷⣴⣿⣿⣿⣿⡟⢛⣷⢸⣷⠸⣧⣼⠟⠋⠀⠀⠀⠀⠀⠀⣀⣤⣄⡻⢿⣿⠖⠀⠀⠀⠀⠀⢰⣿⢋⣴⣶⣌⢻⣷⠃ ⠀⠀⠀⠀⠀⢿⣧⡸⢌⡿⢇⣾⣿⡀⠀⠀⠀⠀⠀⠈⢿⣿⢋⣽⡝⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠟⠋⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣾⢏⣭⣍⢻⡄⠉⠀⠀⠀⠀⠀⠀⠸⣿⡘⢿⣿⠟⣸⣸ ⠀⠀⠀⠀⠀⠈⠳⢝⡶⣶⣿⣿⣯⣣⡀⠀⠀⠀⠀⠀⠈⢿⣌⣛⣡⣾⢣⣦⣄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⣿⣿⣆⣙⣋⣾⠃⠀⠀⠀⠀⠀⠀⣴⣄⡙⢿⣶⣶⣾⠿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⡻⣿⣿⣷⣝⣦⣀⡀⠀⠀⠀⠀⠉⠉⠉⠱⣿⣿⢃⣾⢛⣙⠻⣦⣀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⡀⢠⡾⢋⡙⢿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣦⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⢻⣿⣿⣿⠿⠿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠁⠸⣧⡘⠿⢣⣿⣿⣿⣿⣿⡟⣩⣭⡹⣧⢹⣿⣇⢿⣇⠻⠟⣸⡿⠛⠁⠀⠀⠀⠀⠀⠀⣰⣾⠿⠿⢿⣶⡌⠻⡿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡹⡟⢰⣾⣿⡆⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠻⠿⢿⣧⣙⣛⣱⡟⠸⠿⠛⠀⠙⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢡⣾⣿⢦⢹⣿⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡑⣜⠤⠽⣃⣾⡟⢰⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣻⣿⣿⣌⠻⠯⢊⡼⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠿⡿⠿⠋⣠⣿⣿⣿⢃⣴⣾⡿⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠿⣿⣿⣿⣶⣿⣿⣿⡿⢟⣛⡭⠵⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⠃⣾⡟⣱⣾⣶⡌⣿⣿⣦⠤⣄⣀⣠⣤⣶⣾⣷⣶⣄⠀⢀⣠⣤⡄⢰⣿⢋⣶⣶⣦⠹⣿⣿⢟⣫⠗⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡱⠭⠽⢃⣿⣿⣿⣿⣿⣷⣶⣿⢩⣶⣶⣌⢻⣧⠘⣿⣿⣧⠸⣿⣌⠿⠭⠜⣠⢟⠕⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣒⣺⡿⠿⠿⢟⣛⣛⡿⢿⣿⡘⢏⣩⠟⣸⡿⠀⣿⣿⣿⠆⠙⠿⢿⣶⡿⠗⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢭⣓⣶⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⠀⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣦⡀⢀⣰⣿⣿⣷⣶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠿⠿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡿⠃ ⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⠈⠙⠻⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣤⡀ ⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣶⣦⣤⣤⣤⣴⣶⣶⣾⣿⣶⣦⣴⣾⣿⠿⠛⠉⠁⠰⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠟⠛⣿⣿⣿⣿⣿⣿⣍⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠈⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠛⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈ ⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠁⠀⠀⠀⠸⣿⠻⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡇ ⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠀⠀⠀⠀⠀⠀⢿⡆⠀⠉⠛⠛⠿⠿⠿⠿⠿⠛⠋⠉⠛⠻⢿⡿⠁⠀⠀⠙⠿⠟⠛⠉ ⢸⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀ ⠘⣿⣿⣿⣿⣦⣤⣤⣤⣶⣿⠿⠋⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄ ⠀⠈⠛⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⣠⣾⣿⠋⠉⠉⠉⣹⡿⠛⠿⣿⣿⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣄⣀⣤⣾⠟⠁⠀⠀⠈⠻⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠉⠉⠀⣿⡿⠙⠛⢿⣿⣿⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠙⢿⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀ ⠀⠀⠀⠀⠀⢠⣶⣤⣼⣿⣶⣾⣿⣧⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣤⣤⣾⣿⣿⣿⣷⣤⣤⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⢀⣿⣿⡀⢀⣶⣦ ⠀⠀⠀⢴⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣴⣦ ⠀⢠⣶⣾⣿⣿⡿⠋⠉⠀⠀⠀⠀⠉⠛⢿⣿⣿⣶⣶⡀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠿⠛⠛⠛⠛⠿⣿⣿⣿⣿⡋ ⠀⣀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣏⣀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢾⣿⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿ ⠘⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇ ⢠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠇ ⠀⢉⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣏⡁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡀ ⠀⠘⠟⢿⣿⣿⣷⣤⣀⡀⠀⠀⢀⣀⣴⣿⣿⣿⠟⠿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠟⣿⣿⣿⣷⣦⣤⣤⣴⣾⣿⣿⣿⠟⠿⡿⠂ ⠀⠀⠀⠻⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠻⣿⣿⣿⣿⣿⣿⠟⢿⣿⣆ ⠀⠀⠀⠀⠀⠘⠛⠋⢹⣿⠟⢻⣿⡏⠻⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠻⣿⣿⣿⠟⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⣿⠇⠈⣿⣿⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄ ⠀⠀⠀⠀⣤⣦⣄⠀⠀⢸⣿⣿⡆⠀⢀⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣷⣦⣀⣸⣿⣿⣿⣇⣀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣴⣿⣿⣿⣿⣦⣀⡀⣀⣄ ⠀⠀⠀⠀⢻⣿⣿⣷⣾⣿⣿⣿⣿⣶⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄ ⠀⣀⣀⣀⣠⣿⣿⡿⠟⠛⠉⠉⠛⠿⣿⣿⣿⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣿⣿⡿⠋⠁⠀⠀⠀⠉⠛⢿⣿⣿⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠟⠉⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⠁ ⠰⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⣀ ⠀⠀⠙⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇ ⠀⣠⣴⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠇ ⠘⠿⠿⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏ ⠀⠀⠀⠀⢈⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣶⣦⣤⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣷⣦⣄⣀⣀⣠⣤⣾⣿⣿⣿⣿⣄ ⠀⠀⠀⠀⣾⣿⡿⠛⠛⢿⣿⣿⡿⠛⠻⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠿⢿⣿⣿⣿⡿⠿⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠟⠁ ⠀⠀⠀⠀⠈⠉⠀⠀⠀⠸⣿⣿⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⣿⣿⣿⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⠀⠀⠀⠀⠀⢀⣤⣄⣀⣠⣾⣷⣄⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⣸⣿⣇⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤ ⠀⠀⢀⣀⣀⣼⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢰⣿⣿⡆⠀⠀⢀⣤⣤⡀ ⠀⠀⢺⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⡿⠟⠛⠛⠛⠻⢿⣿⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣤⣾⣿⣿⣷⣤⣴⣿⣿⡿⠁ ⢠⣶⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟⠛⠛⠻⢿⣿⣿⣿⠁ ⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⢀⣤⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⣶⣶⣶⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣶⣶⣶⡄ ⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡄⠀⠀⠀⠀⠘⠻⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠛⠋⠁ ⠻⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠃⠀⠀⠀⠀⢀⣴⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡀ ⠀⣸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⠀⠈⠛⠛⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣷⣤⣀⣀⣠⣴⣿⣿⣿⣿⣿⣦⡀ ⠀⠙⠿⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠛⠛⠁ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠈⢻⣿⣿⡄ ⠀⠀⠀⠀⠀⠁⠀⠹⠿⡿⠛⠻⢿⠿⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠘⣿⡟⠉⢻⣿⠇⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠙⠛⠃

⠀⠀⠀⠀ ⢠⣤⡄ ⠀⠀⠀⣀⣤⡀⠀⠀⠀⣿⣿⣷⠀⠀⠀⢀⣤⡀ ⠀⠀⠀⠻⣿⣿⣶⣤⣴⣿⣿⣿⣦⣤⣶⣿⣿⠏ ⠀⠀⠀⠀⢹⣿⣿⣿⠿⠛⠛⠛⠿⣿⣿⣿⡏ ⣤⣤⣴⣶⣾⣿⡟⠁⠀⠀⠀⠀⠀⠈⢻⣿⣷⣶⣶⣶⣦ ⠛⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠿⠛ ⠀⠀⠀⢸⣿⣿⣄⣠⣴⣶⣶⣶⣶⣦⣴⣿⣿⡇ ⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣶⣦⣄ ⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⣠⣶⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠻⣿⣿⣯⠛⢿⣿⣿⣦⣶⣦⣤⠾⠛⠁⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⣿⠿⠀⣀⣽⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠏ ⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁ ⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⣿⡟⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁ ⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠸⣿⣿⣿⡆⠉⠙⠛⠛⠛⠋⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣄⣀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⣿⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⣿⣿⣿⣿⣦⣠⣿⣿⡿⠋⠸⣿⣿⣇⠘⣿⣿⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢹⣿⣿⣇⠀⠈⠙⢿⣿⣿⣿⡿⠀⠀⠀⢻⣿⣿⠀⠘⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠈⢿⣿⣿⡀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⢸⣿⡿⠀⠀⢹⣿⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠈⢿⣿⣧⡀⠀⠀⠀⣿⣿⣷⠀⠀⠀⣸⣿⠇⠀⠀⠀⢿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠙⢿⣷⣄⡀⢠⡿⠁⠙⠷⣤⣴⡿⠋⠀⠀⣠⣄⠸⣿⣿⣿⣇⠀⢀⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣿⣿⠟⣿⣿⣿⣿⠙⢿⣿⣷⣤⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⠁⠀⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⠗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⠀⠀⣿⣿⣿⣿⠀⠀⢸⣿⣿⣅ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣄⠀⣿⣿⣿⣿⠀⢀⣼⣿⣿⣿⡗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⣿⣿⣷⣿⣿⣿⣿⣴⣿⣿⣟⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠿⣿⣿⣿⣿⠿⢿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⣿⣿⣿⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟