⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣤⠖⠛⠉⠉⠉⠉⠉⠙⠒⠦⣿⣏⣀⠀⠀⠀⠀ ⠀⠀⣠⠞⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⡄⠀⠀ ⠀⢰⣯⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⠀⠀ ⠀⠈⣇⢀⢠⠇⠀⣶⡶⠄⠀⠀⠀⢠⣶⡶⠀⠀⣸⣀⣼⠟⠀⠀ ⠀⠀⠙⠛⠾⡆⠀⠙⠛⠃⠀⠀⠀⠀⠙⠋⠀⠀⣹⠟⠁⠀⠀⠀ ⢀⡴⠚⠉⠛⢿⠀⠀⠀⠀⢿⣿⠆⠀⠀⠀⠀⢀⣿⠋⠉⠉⢳⡄ ⢾⡀⡄⠀⣄⡼⠻⢧⠤⣤⠤⠤⣤⣠⣦⣾⠶⠞⢿⣤⡄⣠⣀⡷ ⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠹⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠾⠛⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠛⠷⣶⣼⣿⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠛⠉⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠉⠙⠛⢶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣧⠀⠀⠀⠀ ⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢿⡇⠀⠀⠀ ⠀⠀⠹⣿⡎⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⡆⠀⠀⣆⣿⡇⠀⠀⠀ ⠀⠀⠀⣿⡀⠀⡀⠀⣿⠁⠀⢠⣾⣿⡿⠆⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠆⠀⠀⠀⢈⣿⠀⣄⣾⡿⠁⠀⠀⠀ ⠀⠀⠀⠘⣿⣧⣇⢀⣇⠀⠀⠘⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠖⠀⠀⠀⢸⣿⣷⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⠻⣿⣆⡀⠀⠀⠉⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⣿⠁⣀⣀⣀⠀⠀⠀⠀ ⠀⢀⣠⡶⠾⠛⠓⠶⣿⡟⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠋⠉⠛⠻⣦⡀⠀ ⢀⣾⠋⠀⠀⠀⠀⠀⠘⣿⣠⣄⡀⠀⠀⠀⠀⠛⠿⠟⠁⠀⠀⠀⠀⠀⡀⡀⠀⣴⣾⡏⠀⠀⠀⠀⠀⠈⣿⡄ ⢸⣯⠀⢠⠀⠀⢀⣄⣠⣿⠿⢿⣷⣤⣦⣀⣤⣤⣤⣤⣀⣀⣀⣼⣆⣼⣷⣿⡾⠿⢿⣧⣀⣦⠀⠀⣤⠀⣸⡧ ⠘⠿⣷⣾⣷⣤⠾⠿⠛⠁⠀⠀⠀⠁⠀⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠛⠻⠷⠾⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⢷⣦⣤⣀⡹⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠉⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣽⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⡏⣤⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⡀⠀⠀⢤⢠⣼⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⣴⡾⠁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠈⣇⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⡀⣀⠀⢠⣿⠃⠀⠀⢀⣾⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡷⠀⠀⠀⠀⠀⢸⣿⠀⢠⣠⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣷⣇⣽⠀⢈⡏⠀⠀⠀⠸⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⣤⠥⠀⠀⠀⠀⣿⣿⣧⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠿⣿⣧⣾⣿⡄⠀⠀⠀⠙⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⢸⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡇⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣼⣿⣀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣾⠿⠛⠛⠻⢷⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠋⠉⠉⠉⠛⢿⣦⡀⠀⠀ ⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠙⣿⡆⢀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀ ⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⣷⣧⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢠⡾⣠⣇⣠⣿⣿⣿⡇⠀⢀⠀⠀⠀⢀⠀⠀⢹⣷⠀ ⣿⣷⡀⠀⣷⠀⠀⠀⣼⣦⣴⣿⠏⠙⠻⠿⣷⡿⠷⣶⣶⡾⠿⠿⠷⢶⣶⣦⣤⣾⣿⣷⣿⣿⠿⠿⠛⠛⠙⠻⣿⣤⣾⣇⠀⢀⣸⣇⣀⣼⣿⠃ ⠘⢿⣿⣾⣿⣷⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠟⠛⠛⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠉⣧⣀⡠⠤⠤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡤⠒⡻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⣀⣠⠖⠀⠀⠀⠀⡞⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⡤⠚⠁⣠⠎⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡴⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⢠⠊⠙⢆⠀⠀⠀⠀⠀⠀⢀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⢀⣀⣀⠑⠲⠚⠀⠀⠀⠀⠀⠀⢇⣀⣀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⠳⡶⠋⠑⠢⡔⠺⢿⣿⣿⣧⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠁⡜⠀⠀⠀⠀⠘⡆⠀⠙⢻⡗⠈⢱⣶⣶⣭⡍⠓⢦⣠⣾⠿⠛⢛⡏⠉⠉⠉⠉⠉⠫⡑⠲⢄⡈⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠀⢠⠉⠓⠦⠤⠴⠚⠁⠀⠀⠀⠙⢄⠀⠙⡟⠋⢀⠴⠊⠁⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⡧⢤⠀⠙⢮⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⠘⢧⡔⠁⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⠤⠔⡞⠁⡜⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⢠⠇⠀⠀⢠⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⡀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⢀⠎⠀⠀⣠⠎⢸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡇⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⢠⡯⠤⠶⠊⠁⡠⢚⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢻⠯⣓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢴⠞⠁⠀⠀⠀⠀⠘⠁⠀⠀⡰⠊⡰⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⠀⠈⢱⠢⢌⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠤⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⡹⠀⠀⠀⠀⠀⢀⣀⠤⠒⢻⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⡸⠀⣿⢀⠆⠀⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠹⡄⠀⠉⠀⠀⠀⣀⠀⠀ ⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠇⡼⢳⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⡏⢀⣀⡀⠀⠀⢹⣤⠔⠊⠉⠉⠉⠉⠒ ⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣴⠃⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠒⢿⡖⠓⠒⣤⠄⠀⠀ ⠀⢠⠏⠀⠀⠀⠀⠀⠀⠐⣿⠀⠸⣦⠘⡄⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⣼⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠙⢦⠀ ⢠⠃⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠃⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢳⡄⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠶⠖⠶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠇⠀⠀⠀⠀⢀⣀⡀⠀⣀⡀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣤⣴⣾⣿⣿⣿⡏⠉⠻⢇⠀⠀⠀⠀⢰⡀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢀⡟⠹⣿⣿⣿⣿⠇⠀⠀⠀⠁⠀⠀⠀⠈⡇⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⢠⡄⠀⠘⠁⠀⠈⠛⢿⡋⠀⠀⠀⠀⣼⡀⠀⠀⠀⣿⢀⣤⣄⣬⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠏⠈⣷⠀⠀⠀⠀⠀⢠⣿⣿⣶⣤⣴⣾⣿⡇⠀⠀⢀⣿⡟⠀⠌⠀⠐⢻⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡄⠀⠸⣶⣶⣿⣿⢿⡟⠉⣽⣿⡿⠃⠀⢠⣿⠉⠁⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⣇⠀⠀⠙⠿⣿⠃⢸⠃⢀⡿⠋⠁⠀⠀⠘⢻⡀⠀⠠⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣨⡷⠾⠷⠿⣤⣀⠀⢠⡏⢠⠟⢀⡼⠁⣀⣠⠴⠂⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠙⢷⡈⠛⠶⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀ ⠚⠓⠒⠒⠒⢿⡀⠀⠀⠀⠀⠀⠀⣸⠟⠒⠒⠒⠛⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠓⠒⠒⠒⠒⠒⠒⠛⠒⠒⠒⠚⠻ ⠀⠀⠀⠀⠀⠈⠙⠛⠦⠴⠦⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡐⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢀⣇⠤⠤⠐⠒⠠⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠜⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⡦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠓⠒⠀⠐⠚⠳⢄⣀⠀⠀⠀⠀⠀⠀⠀ ⡎⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡛⠒⢤⡀⠀⠀ ⡇⠀⢠⠀⠀⢀⡴⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠇⠀⢳⡀⠀ ⢸⠀⠈⣧⠀⣸⠁⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢧⠀ ⠀⢣⠀⠘⠷⣽⠀⠀⠀⠀⢸⡀⢀⠊⣷⡀⠀⠀⠀⠀⠀⣎⣷⣼⢠⠀⠀⠸⠀ ⠀⠀⠑⢄⠈⢺⡄⠀⠀⠀⢸⢃⠀⠻⠟⠁⠀⠀⢤⠄⠀⠙⠋⢹⣌⢆⠀⢠⠀ ⠀⠀⠀⠀⠉⠉⠙⢄⡀⢀⡞⠢⡢⡀⠀⠀⣠⠤⠐⠀⢢⡀⢀⡴⠀⠉⠛⠁⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠦⣘⣛⣷⣾⠁⢠⠀⠀⠠⡈⢱⠁⠀⡴⠶⢦⡀ ⠀⠀⠀⠀⣾⢾⡏⢰⣆⡄⠀⠀⠀⡸⠖⣓⠒⢧⡀⣠⡶⠉⠛⠀⠘⣇⣻⣽⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣇⠀⠫⣉⡿⠣⣀⣱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣠⣀⣀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢿⣥⠀⠀⠉⣿⣿⣿⡀⠀⠀⠸⣇⣀⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡈⠉⠀⠀⠈⠿⠆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠡⡌⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠒⠒⠒⠒⠢⠤⠴⠒⠒⠊⠉⠛⠀⠿⠢⡈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠴⠊⠉⢀⣀⠠⠤⢄⣀⠀⠀⢳⠉⠻⢲⠆⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠘⠬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⠀⣠⠞⠁⠀⠀⠀⠀⠈⠷⣄⠀⢳⡴⠓⠂⠉⠂⠀⠐⣏⠀⠈⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⢀⠎⠀⠀⠀⠀⠀⠈⣻⠆⢈⡇⠀⠀⠐⠁⢀⡀⣠⣤⠦⣧⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡟⢠⡏⠀⢀⣴⣄⡀⠠⣤⣿⣄⣼⠀⠉⠉⠿⢿⡿⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣧⠀⠃⣄⠸⢿⣿⣿⠟⠋⠀⠀⡇⠀⠀⠲⣤⢾⡟⠒⣶⠴⠃⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣰⡋⠉⢳⡀⠀⠀⠀⠀ ⠀⠀⣹⢄⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠸⢄⣀⡶⠋⠀⠀⠀⠀⠀⠀⠀⣠⢟⣿⠀⠀⠀⢸⡗⣿⡟⣉⣷⠀⠀⠀ ⠀⣼⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢁⡽⢩⠀⠀⠀⠘⠿⢿⣦⡿⠁⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠦⣄⣀⣀⣀⣀⣀⡤⠴⢛⢱⡶⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⠒⠯⠭⠥⠤⠤⠤⠖⠚⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉ ⠀⡇⠀⠀⠀⠀⠀⢳⣤⣀⠀⠀⠄⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⠀⠀⠀⢀⡴⠁⠀⠘⡗⢄⡀⠀⢻⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣀⣤⠞⠀⢠⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⡼⠀⡄⠀⠀⡞⠀⠀⠀⠀⡇⠀⠈⡷⠺⡇⠀⠀⠀⠀⠀⡞⣡⣤⣤⠴⡾⣿⠁⠀⠀⡞⠀⢠⣾⣷⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⢀⡞⠀⠀⠀⠀⠀⠹⣄⣀⣧⠀⢹⡀⠀⠀⠀⢰⠋⠉⠀⠀⠀⠀⠹⡄⠀⠀⡇⠀⠀⢻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠙⢆⣘⣾⡦⠀⣀⢀⡀⠀⠀⡈⠉⠁⠀⠀⣇⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠷⡀⢠⣙⣦⠀⠀⠀⢹⣧⣤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠃⠀⠀⠀⠀⢹⡈⠀⠀⢳⡀⢠⣤⣤⣤⡤⠄⠀⠈⠻⣟⠉⡀⠛⠉⠈⠛⠛⠉⠀⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠿⠿⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠋⢧⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⡤⠞⠓⠉⠉⠉⠀⠉⠉⠉⠛⠉⠉⠙⠒⠶⣤⡀⠀⠀⠀⣠⠶⠋⠁⣴⠊⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣠⠞⠉⠀⠀⠀⠀⠀⣸⣥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣴⠋⠁⠀⣠⠞⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡴⠃⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⢀⡴⠒⠳⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⢯⣷⡀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡶⠉⠁⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⣀⣀⠀⠀⠀⠀⣤⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⠉⢻⡞⠁⠀⠉⠳⣍⠙⠿⣿⣿⣿⣿⡆⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣴⣶⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡿⠁⢠⠟⠀⠀⠀⠀⠀⠈⢧⠀⠀⠙⢻⡭⠆⠈⠁⣶⣶⣶⣦⣬⠉⠳⢤⣀⣼⣿⡿⠿⠛⣻⠉⠉⠉⠉⠉⠉⠉⠹⣍⠙⠲⢤⡀⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠁⠀⡞⠲⢦⣀⠀⢀⣠⡴⠟⠀⠀⠀⠀⠙⢦⠀⠀⠻⢿⡿⠟⠃⠀⣀⠴⠋⠁⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠉⠳⣌⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⠃⠀⠀⡇⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⣸⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⢹⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⡃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠉⠉⣳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠶⠶⠒⠋⣹⠁⠀⡞⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⢠⠇⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⢠⠎⠀⠀⠀⢀⡾⠉⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠘⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⢠⠏⠐⣀⣠⠾⠋⠀⣠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⢳⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢠⣿⠛⠫⠉⠁⠀⣠⠞⢡⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠈⡏⠳⣌⠙⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⢒⡟⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣐⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⢠⡇⠀⠀⠙⡶⢤⣈⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣁⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠈⡇⠀⠀⣸⠃⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠒⠛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⡇⠀⣰⠋⠀⠀⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡠⡴⠚⠋⠁⠀⠘⣧⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢠⠃⢠⡿⠀⡼⠀⠀⠀⠉⠳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⡧⠀⠀⠀⠀⠀⠘⢧⡀⠀⠈⠀⢀⣀⣀⣤⣀⠀⠀ ⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢸⢀⡟⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣀⣀⡀⠀⠀⠨⣷⣤⠖⠋⠁⠀⠀⠀⠈⠉⠓ ⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⡀⣸⠃⢸⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠉⠉⠉⠉⠛⠶⢭⣷⡦⠦⠤⢤⣀⡀⠀⠀⠀ ⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢠⣷⡇⠀⢘⣆⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢷⡀⠀⠈⠓⢯⣄⠀⠀ ⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡇⠀⠘⣿⣇⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⢀⣼⢣⡀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠲⢤⡀⠀⠉⢳⡀ ⡀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠀⠀⠀⠘⣟⣦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⡾⡟⠚⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢹⣆⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢳⡀⠠⠄⠀⠀⣀⡀⠀⠀⢀⠄⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⡔⠁⠀⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢎⡠⠊⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠠⠎⠀⠀⠰⣈⡆⠀⠀⠀⡠⠠⡀⠀⠀⠀⠉⠲⢼⠀⠀⠀⠀⠀ ⠀⠀⢀⡜⡧⠒⠠⡰⢾⣷⠄⠀⠀⣀⠀⠈⣩⣤⡀⣀⣀⡀⡀⠀⢃⠀⠀⠀⠀ ⠀⠀⡜⢠⠡⠀⠠⠔⠀⠘⢅⠘⡿⠃⡨⠚⠉⢡⠃⠀⠀⠀⢡⡉⠢⣃⠀⠀⠀ ⠀⠘⡆⢸⠀⠀⠀⠀⠀⠀⠀⠆⡳⠀⠀⠀⠀⠀⠑⠂⠐⠺⠁⠆⠀⢸⠀⠀⠀ ⠀⠀⢣⠀⢆⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠜⢀⡠⢋⡀⠀⠀ ⠀⠀⠘⠀⠀⠙⠶⡠⢀⠀⠀⠀⠀⠀⠀⢀⠀⡤⠊⠀⠀⠘⠉⢁⢐⠕⠁⠀⠀ ⠀⠀⢀⠃⠀⠐⠀⠸⠑⠂⠀⠀⠀⠀⠀⠤⢰⠁⠀⠀⠀⣀⢤⠒⠁⠀⠀⠀⠀ ⠀⠀⠌⠀⠀⢠⢠⣇⠂⠁⠂⠀⠀⠀⠀⠀⡌⠀⠀⠀⡇⠀⠀⠡⡀⣁⠀⠤⢀ ⠀⡜⠀⠀⠀⢨⠇⡏⡄⠀⠀⠀⠀⠀⡠⢀⠁⠀⠀⠀⠇⠉⠀⠒⠹⡒⠠⡄⠀ ⡘⠀⠀⠀⠀⣸⠀⢹⡜⠀⠀⠀⠀⠊⢀⡾⠀⠀⠀⢀⠀⠀⠀⠀⠀⢱⠢⡈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠎⢀⣠⣴⣶⡖⠲⡂⠀⠀⡄⠈⢢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠋⠀⡼⠙⢿⣿⠃⠀⠈⡀⠀⢸⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠘⡄⠀⡀⢀⣿⣦⣤⣾⡇⠀⣸⡞⠉⠉⠳⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⢃⠀⢣⠀⠻⣿⠋⡇⢸⠟⠁⠐⢇⠀⠀⠐⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⢀⠜⠚⠚⠢⡄⢮⣘⣠⠧⠄⠂⠀⠘⡄⠀⠀⠀⠸⡀⠀⠀⠀ ⠐⠒⠒⠺⣀⠀⠀⢀⡸⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠓⠒⠒⠂ ⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠃⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡏⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⠠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡄⣠⣿⠤⠶⠒⠒⠋⠉⠉⠙⠓⠲⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣋⣠⠤⠤⠤⣤⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡛⢻⠶⣤⣀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⡄⠈⠙⣧⠀⠀⠀ ⡇⠀⠀⠀⣆⠀⠀⠀⠀⣠⣾⠏⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠇⠀⠀⠘⣧⠀⠀ ⢻⡄⠀⠀⢻⣆⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⣇⠀ ⠘⣧⡀⠀⠈⣿⣦⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣿⢀⠀⠀⠀⠀⢿⡀ ⠀⠘⣧⡀⠀⠘⢟⢷⣼⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⡞⠉⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⣸⣷⣴⣿⢸⠀⠀⠀⠀⠸⡇ ⠀⠀⠘⢷⡀⠀⠀⠢⣹⣇⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠈⣷⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢹⣿⠈⣇⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠙⢦⣀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⣿⠻⡄⠀⠈⠛⠋⠁⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠁⠀⠈⣿⣧⣘⣦⠀⠀⢠⠇ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠻⣆⠀⠀⠀⠀⢰⣿⣧⡘⢦⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠤⢶⡀⠀⠀⠀⢀⡾⠀⠉⠛⠻⠛⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠶⠻⣇⠀⠙⢶⣿⣦⣤⡀⠀⡴⠻⡇⠀⠀⠀⠀⠀⠙⠶⣤⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣙⣛⣻⣿⣿⠃⠀⠀⡄⠀⠀⠀⠘⣄⠀⠈⣿⠁⠀⠀⣠⠞⢿⠟⣶⡄ ⠀⠀⠀⠀⠀⠀⣠⣿⣤⣶⡖⠠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠉⣟⣩⣥⣿⢤⣤⣼⠀⠀⠀⠰⣄⣼⠳⢼⡿⠀⠀⠀⣿⠖⢾⡷⢻⣿ ⠀⠀⠀⠀⠀⠀⠻⠏⣩⣿⣯⣀⣿⠿⠤⠇⠀⠀⠀⠀⠀⢰⠋⠉⠀⣶⣤⣀⣙⣷⡀⠐⠿⣟⠁⠀⠀⠀⠀⠀⠀⠙⠦⢾⣿⠾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⡀⠀⠀⠢⡁⢈⣿⡾⢧⣀⠀⢈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⢿⠟⠒⠲⠶⠟⠚⠉⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣧⠀⠨⠿⠧⠀⠐⢧⠄⠠⣄⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡎⡢⢄⠀⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠄⠀⣀⡀⠀⠸⠩⣍⠉⠒⠈⠉⠈⠁⠋⢪⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢠⠊⠁⠀⠀⠑⣄⢱⠚⠀⠀⠀⠇⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⡎⢀⣦⣀⣤⠧⡜⠐⠲⢶⡞⠉⡁⠁⠀⠀⠀⡆⠀⠀⣀⡀⠀⠀⠀ ⠀⠀⣇⡉⠪⠟⠋⠁⠀⢇⠀⠑⣝⣠⠏⠁⠀⠀⠀⡰⡇⠀⠘⣤⡽⣢⠀⠀ ⠀⠰⠈⠀⠀⠀⠀⠀⠀⠈⢢⣀⠀⠀⠀⠀⣀⡠⣊⠜⡀⠀⠀⠛⠓⠃⠀⠀ ⠀⠠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠛⠉⠉⠉⠐⠊⠁⠀⠅⠀⠀⠀⠀⢸⣿⡇ ⠀⢰⠀⠀⠀⣠⣀⠀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⡆⡀⠀⠎⠀⠘⠑⢠⢰⠀⠀⠀⠠⢃⣀⣠⡴⠊⢰⠀⣠⣤⣄⠀⠀⠀⠀ ⠰⡄⢁⡎⠀⠀⠀⠣⠼⠀⠃⠀⠀⠎⠉⠁⠀⢱⠀⢠⠀⠹⠿⠟⠀⠀⠀⠀ ⠀⠈⠈⠁⠘⠒⠒⠚⠀⠀⠸⡀⠈⡄⢠⠤⠤⠀⠑⠗⠃⠒⠒⠛⠛⠀⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠶⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠛⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠃⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠘⡀⠀⣴⣠⣾⣿⣿⣿⣿⣿⡄⠉⠻⢯⡀⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠘⣿⢹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠙⡂⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣾⠁⠀⠻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⢸⡆⠀⠀⠋⠀⠀⠀⠈⠉⢻⣏⠀⠀⠀⠀⠀⢠⣾⡆⠀⠀⠀⠀⢸⡇⣠⣶⣦⣴⠾⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠈⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣤⣴⣶⣿⣿⣿⠀⠀⠀⠀⣸⣧⡏⠀⣆⠀⠆⠐⢹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢻⡆⠀⠀⢰⣦⣤⣴⣿⣿⣿⣿⡿⠛⢛⣿⣿⣿⡏⠀⠀⠀⣾⠟⠽⠃⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣷⠀⠀⠈⢿⣿⣿⣿⡿⠁⣿⠁⠀⣾⣿⡿⠋⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣀⠀⢻⡀⠀⠀⠀⠙⠻⣿⠁⢀⡏⠀⢀⣿⠋⠀⠀⠀⠀⠀⠈⠘⣧⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⠶⠶⠾⣧⣄⡀⠀⠀⢸⠃⢠⡾⠃⢀⣾⠃⠀⢀⣠⡴⠖⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡏⠁⠀⠀⠀⠀⠀⠈⠻⣷⡀⠸⢷⣤⣤⣴⠿⠷⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⣄⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣦⣀⣀⣠⣠⣄⣄⣄⣀⣀⣀⣠⣀⣀⣀⣀⣀⣿⣧⣄⣀⣀⣀⣀⣀⣀⣀⣀⣿⣄⣀⣀⣀⣠⣤⣤ ⠈⠉⠉⠉⠉⠉⠉⢿⣄⣀⡀⠀⠀⠀⠀⠀⣀⣴⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠶⠶⠶⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀