⠀⢀⣤⡤⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⠃⠁⠀⠁⠈⠳⠿⡂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⢠⡀⠀ ⣾⠟⠀⠀⠀⠀⠀⠀⠃⠈⠰⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡾⠿⢛⠾⠀⠀⠀⠸⣧⠀ ⢻⣶⠀⠠⡄⠀⠀⠀⠀⠀⠀⠘⠀⢿⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄ ⠀⢹⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡨⢵⢦⡀⠀⠀⠀⣀⣀⣀⡀⠀⢴⠶⠶⣶⣶⠦⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃ ⠀⠀⢷⡀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⠻⣿⣟⠑⢀⠀⠀⠘⣦⡆⠀⠃⠉⠻⡀⠀⡄⠢⠉⠩⠓⢲⣤⣤⣴⣿⣿⣛⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀ ⠀⠀⠀⢧⣢⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠥⢌⡉⠉⠳⠄⠀⢠⡾⠋⣁⠂⡀⠀⠀⠀⡀⠙⢦⠀⠐⠈⠑⠻⠛⠉⠻⣿⣗⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡾⠁⠀⠀ ⠀⠀⠀⠈⢇⠀⠈⠳⣄⡀⠀⡀⠚⠉⢀⣤⠤⠀⠀⠀⠤⠐⠊⠀⢉⣿⡤⠀⢀⡄⠀⢀⠈⠀⢴⣿⡓⠲⢄⡀⠀⠀⠀⠉⠉⠛⠷⣤⡀⠀⡀⠀⠀⠀⠀⠠⢀⡼⠁⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣤⠀⠈⠳⠞⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣛⠁⠀⢀⣻⠀⣤⠈⣇⠀⠀⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⢀⡴⠛⢉⣡⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⡇⠀⢰⠟⠁⠀⣥⠀⠈⠳⡄⠀⢳⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⢺⡁⣀⠀⣼⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠈⣧⠀⠆⠀⢰⠀⡾⠃⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⢿⣥⣄⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢹⡇⠀⠘⠀⠀⠃⠀⠐⢃⡀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠤⢄⢠⠀⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣏⠀⣀⣀⣤⣤⣴⣾⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠈⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡿⠚⠓⠀⣽⠁⠀⣾⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡛⠛⠿⣶⡶⣤⣀⣻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⠀⠄⠀⠀⢹⣦⠘⣿⣿⣟⣿⣿⣿⡇⣻⣦⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⡄⢀⣿⠀⠘⠙⠿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠂⠀⠀⠻⣦⡘⢿⣿⣿⣿⠟⠐⣻⣿⣷⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡜⣿⣿⣿⣿⣿⡟⠀⣼⠏⠀⠀⢀⠀⠹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠂⢠⠀⠀⡀⠀⠀⠈⠛⢶⣤⣤⣤⣶⠾⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⢀⣼⣿⣿⣷⣤⣌⠻⠿⠿⢋⣠⡾⠋⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠘⢤⡀⠨⣅⡀⢀⣀⣀⣀⣀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⣴⠶⠋⠈⢳⣄⠀⠆⠠⢿⣿⣿⣇⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢀⠄⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠙⠦⠀⠀⠀⠁⠉⠁⠀⠀⠀⢠⣿⡿⠁⣶⠇⣠⣾⠋⣠⡀⣀⠀⠙⣷⣈⣷⣄⠻⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠘⠳⠤⣤⣀⠀⠀⠀⠀⠀⠀⢀⡰⠟⠿⠥⢸⡿⣾⡇⣿⠀⠉⠋⠋⠀⢠⣿⣿⣟⣿⠀⠻⣽⣧⠀⠀⠀⠀⠀⠠⢀⣠⠴⠞⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠈⠀⠀⠀⠀⠀⢁⣿⣇⣿⣶⣄⠀⢀⣠⣿⣿⣼⣏⠛⡍⠀⠉⠘⠶⠀⠀⠀⠀⠀⠉⠀⠰⠶⠒⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣯⣬⡟⢓⠻⣿⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⣧⢹⣧⣠⣼⡿⣭⡖⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠗⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⣸⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢎⠐⢄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢀⡤⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢷⠄⡉⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢋⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⡀⠆⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣠⣿⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠠⢄⣀⠘⠦⢀⠀⠀⠀⠀⣀⣀⣴⠾⠿⠿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⠀⢀⡠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠠⠖⠋⠤⠄⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠠⠄⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀