⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣦⣶⣴⣶⣦⡴⠵⠾⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣴⣶⣿⣿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣷⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠤⠄⢀⡈⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣠⡾⠟⠋⠁⠀⠀⠀⠀⠀⢀⠠⠀⠂⠁⠀⠀⢀⠔⠀⠀⠂⠀⠐⠈⢽⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢐⣦⣦⠼⠞⠁⠀⠀⠀⠀⠀⠀⠀⢂⣤⡬⠤⠤⠤⢤⣄⣀⠜⣣⡄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⢀⡤⣂⡵⠚⠉⠆⠀⠀⠀⢠⠏⠉⠉⠛⢾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⣤⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⢭⡞⠉⠀⠀⣰⣀⣤⣄⣀⡸⠤⠤⠤⠀⠒⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢏⣶⠋⠀⣀⡴⠚⠉⣀⣀⣤⣤⣼⣶⣄⠀⠀⠀⠀⣿⡿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣾⠃⠀⣰⣯⣴⣾⣿⣿⣿⣿⣿⣻⣻⢿⣆⢠⠀⠴⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀ ⠨⠀⠀⠀⠰⡱⣱⣿⣿⣿⠻⠙⣠⣤⣧⡡⡫⠴⠀⠀⠀⠀⠀⡐⠇⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⡟⠀⢠⣿⣿⣿⣿⣿⣯⡯⢕⣿⣿⣿⣿⣚⣿⠁⠀⠀⠀⠙⣯⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⣇⢿⣿⣿⣿⠯⢕⣾⣿⣿⣿⣿⣒⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠸⣿⠿⠟⠻⠉⠁⠀⠈⣣⣿⣿⣿⣻⠇⠀⠀⠀⠀⡐⠆⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⢀⢠⣿⡄⠀⠀⡀⠀⠀⢠⣎⣿⣿⡿⠃⠀⠀⠀⢀⣸⠇⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⣆⠈⠓⡙⢦⣀⢧⠀⢒⠫⢳⠿⢃⠄⠀⠀⠀⣠⡾⣃⡀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠈⣿⣿⣿⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠘⢷⠀⠀⠀⠈⠀⠀⠈⢹⡀⣠⣄⠄⠀⠀⣾⢎⣽⣿⣷⡀⠀⠀⠀⠀⣠⣴⣿⡷⡄⠀⠛⣿⣿⣿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢱⡄⢠⠀⠀⠀⠀⠀⢷⣷⣾⣦⠐⣃⣴⡿⣿⣿⣿⣿⣆⡀⠀⢸⣿⣽⣿⣿⣿⠀⠐⡻⣟⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠐⣹⣶⣤⣐⣀⣀⢐⣸⣟⣭⣴⠾⠛⠁⣀⠈⠻⠿⠛⣛⣉⣩⣿⣿⣾⡿⠟⠛⠀⠐⢧⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⢌⡵⣻⣿⡌⢉⣉⠉⢭⣛⣐⣦⣬⣿⣶⣿⡶⠖⠻⢿⣿⡻⣯⠉⠉⠉⠁⠀⠀⠀⡨⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⠿⢗⣛⣧⣭⣭⣶⣶⣿⡿⠿⠿⠛⣿⣏⣩⣅⠀⠀⠀⠀⠀⠛⢿⣿⣷⡀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣴⠶⠖⠒⠒⠙⠛⠉⠉⠙⠿⣿⣦⡀⠀⠈⠛⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⠻⡟⠟⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠤⠀⢈⣛⠻⠿⣿⣿⡷⠂⠤⠤⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀