⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⡿⠍⠁⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⢁⣤⡷⢿⠛⠛⠛⠳⠲⠦⣤⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⣾⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⡏⡛⠉⢻⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣇⡄⠀⣸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡗⠁⠀⢰⣾⣶⣀⡠⣀⣀⡀⠀⠀⠀⠀⠀⣽⣕⣶⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠈⣽⠁⢠⣶⠈⢣⣤⣯⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣧⡄⠀⠀⠋⢦⠉⣙⣀⡜⠛⠛⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠿⠦⣄⣀⢀⠀⠀⠀⠀⠀⠀⡀⣼⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡣⠒⣄⠀⠉⠙⢛⠳⠶⠶⠶⢾⡛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡃⠀⠈⠓⠺⠈⠀⠀⣸⣖⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡅⠀⠀⠀⠀⠀⠀⠈⠹⣶⢮⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣐⣿⡟⣯⠀⠀⣴⡾⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠛⠷⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣤⣶⣾⣿⠿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⡿⣻⡷⡀⠁⠀⠬⠛⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⣿⡯⠛⠀⠀⣠⣀⣠⣤⣾⣿⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⡁⢀⣴⣶⣽⣿⠟⡛⠋⠉⠉⠉⠉⠙⠛⠛⠿⣶⣦⣄⠀⠀⠀⠀⣀⣀⣄⣀⠀⠀⠀⠀ ⠀⠀⠻⣷⣽⣾⠿⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⣴⡿⢟⣿⡻⠛⣿⣦⡄⠀ ⠀⠀⣠⣾⣯⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣶⣬⠀⠀⠀⠸⠻⣿⡄ ⠀⣴⣿⠣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⣂⡄⠀⠀⠐⣿⡇ ⢸⡿⢿⠇⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣽⣿⢸⠀⠀⣸⣿⡇ ⣿⣧⠀⠀⠀⠀⢴⣽⣿⣿⣷⣀⣀⣀⣀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣮⣻⣿⡿⠏⠀ ⣿⣏⠀⠀⠀⠀⠈⠚⠛⢻⣵⠋⠉⢀⣈⡉⠛⢿⡀⠔⡢⡶⡄⠀⠀⠀⠀⠘⢿⣿⠉⠉⠀⠀⠀ ⢿⣗⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⢀⣘⣿⠟⠀⠀⣷⣾⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠈⢿⣿⡂⡀⠀⠀⠀⠀⢹⠳⣀⡘⠋⠻⠇⠀⢀⡯⠿⠿⠿⠁⠀⠀⠀⠀⢐⣼⡟⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣤⡄⡀⠀⠀⠀⠛⠛⠓⠒⠤⠴⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡟⣟⡿⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⠣⠀⢏⠀⠈⠙⠻⠿⣶⣷⣶⣀⣄⡀⢀⠀⡀⢀⣀⣤⡪⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡯⠊⡉⢣⣤⠀⠀⠀⠀⢈⠉⣹⢽⠻⠿⠿⠿⠿⠿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡇⠀⠀⠈⠛⢶⣤⣴⡴⠞⠉⠙⠁⠀⣤⣆⣴⠀⠈⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⡝⣀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⣿⣿⡾⡀⢀⠀⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⣿⣿⣿⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡃⠀⠠⣴⣴⣤⣢⣤⠀⠀⠀⠀⠀⢠⣥⣿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣔⡔⣁⣼⣿⡟⢻⣷⠀⠀⠀⣠⣾⣿⣿⣷⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠻⠟⠋⠀⢸⣷⣂⣀⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀