⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡾⠋⠉⠉⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣫⠶⠒⢺⡄⠀⠈⠟⠷⣤⣠⠤⠞⠛⠛⠶⡤⠤⠶⠚⠋⣉⣹⠿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡏⠛⠒⠛⠋⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⡄⠀⠀⣀⣳⡄⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡽⢽⡿⣠⠗⠒⠋⠁⢸⣹⡆⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⣷⣾⡺⣥⣀⡀⢀⣾⣿⠷⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠉⠓⠯⢿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    

⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡾⠋⠉⠉⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣫⠶⠒⢺⡄⠀⠈⠟⠷⣤⣠⠤⠞⠛⠛⠶⡤⠤⠶⠚⠋⣉⣹⠿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡏⠛⠒⠛⠋⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⡄⠀⠀⣀⣳⡄⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡽⢽⡿⣠⠗⠒⠋⠁⢸⣹⡆⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⣷⣾⡺⣥⣀⡀⢀⣾⣿⠷⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠉⠓⠯⢿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀