⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠫⠗⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡔⠠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⣀⢀⠀⠀⠀⠀⠀⡇⠀⠠⢀⡖⡰⠠⠀⠀⣀⠵⠁⠀⠀⠀⠀⠀⠸⠚⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡡⡔⢆⠀⠀⠀⢸⣇⠀⢀⢸⠃⢷⡖⢠⢾⡏⠀⠀⡀⠀⠀⢰⣱⡉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡌⣇⡁⠑⢚⡘⢷⣿⠞⠀⠀⠱⣪⡘⡇⢀⠎⡴⢖⡉⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠱⡌⠛⡚⠿⠼⠚⠉⠀⠀⢠⠐⠈⠉⠛⢀⠈⠀⡟⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠄⠑⠨⠀⠄⠀⠀⠀⡠⠀⠣⣼⠔⠀⢄⠀⠀⠀⢠⣷⠖⢓⡶⠶⠢⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⣷⠶⠾⣻⡇⠀⠀⠀⠘⢥⠀⠀⢻⠀⠀⣠⠃⠀⠀⠀⠻⣷⠏⠀⣀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠤⠀⠀⠀⠀⠀⡠⣄⣀⠀⠤⠘⢁⣮⠟⠀⠀⠀⠀⠀⠈⠑⢄⣸⣠⠚⠁⠀⠀⠀⠀⠀⠙⠨⠥⢤⣏⡀⢀⡀⠀⢀⢀⠀⢀⠀⠀
⠀⠀⠠⠞⢹⢦⡰⠀⡖⠄⢍⣓⠷⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⣨⢿⣅⠀⠀⠀⠀⠀⠀⠀⢁⣠⠼⡟⠦⣅⣱⡂⠺⠉⠱⠴⠂⢠⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡄⢈⣉⠩⠴⣄⠀⠀⠀⠀⠀⣠⠞⠀⣼⠀⠑⢄⠀⠀⠀⠀⠀⡼⠧⣬⣄⠈⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠂⠁⣠⠿⣆⠀⠀⠀⠸⡅⠀⠀⢾⠀⠀⢠⠇⠀⠀⠀⣰⡷⠚⠛⡻⢦⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣴⣜⡁⠘⡟⠀⠀⠀⠀⠈⠢⡀⢿⢀⠔⠁⠀⠀⠀⠀⢹⣓⠤⡠⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢳⠇⣠⢴⣦⣄⡀⠀⠈⠛⠁⠀⠀⣀⣴⡶⠶⢦⠙⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⡠⡴⠟⢋⠌⢻⠋⡟⠿⣦⠀⢰⢻⠻⣍⢁⠁⠀⠀⢂⢙⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢈⠋⠃⠐⠈⢁⠀⣸⠔⠀⠀⢸⡗⣼⠘⡀⠉⣷⠁⠈⠀⠀⢑⠉⢥⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⡐⠃⠀⠀⠀⠀⡠⠚⠁⠈⠉⠀⡐⠰⠇⠈⠠⠀⡘⠈⠀⠀⠀⠠⠩⠀⠀⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢧⠟⠆⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀