⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⡿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠋⠑⠋⠁⠀⠀⠀⠀⠉⠙⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠿⣿⡶⣤⣤⣴⣴⣟⠟⠛⠿⢷⣧⣦⣦⣤⣤⣶⡫⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⢹⣅⠀⠘⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⣤⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣨⢀⠀⠄⡀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠡⢰⣶⢷⣲⣂⣌⣤⣴⣾⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣴⣴⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢻⣟⠛⢿⣿⡟⠙⠛⠛⠻⠺⠟⠛⠛⢛⡛⠛⣛⠻⠟⠛⠛⠛⢻⣿⡟⠉⠉⠉⢀⣀⣀⣠⣤⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⢿⣿⣷⣄⠀⠀⢀⡀⠈⣿⠀⣸⣿⣿⡄⠀⠀⠀⠀⣠⣴⣿⣿⡟⢰⣿⡇⠀⣿⣷⠀⣿⣿⠇⢰⣄⠀⠈⠉⠛⢫⣿⠟⠁⠀⠀⠀⠀⠀⣠⣦⣄
⠀⠀⠀⠈⢻⣿⣿⣿⣆⣿⣿⣇⠀⠀⣿⣿⡿⣷⡀⢀⣴⡿⠟⣫⣿⡿⠃⢾⣿⡇⢠⣿⡏⢰⣿⡿⠀⠈⢿⣆⠀⢳⣴⡿⠁⠀⠀⣴⣶⡆⠀⣴⣿⣿⡟
⠀⠀⠀⠀⠀⢿⣿⡿⣿⣿⣿⣿⣷⣤⣿⢯⣼⣿⣷⣿⠋⠠⠾⠛⢁⣀⣰⣿⣿⣷⣾⣿⡇⣾⣿⠇⠀⠀⠘⣿⣦⣿⠟⢷⣄⢀⣾⣿⠋⢀⣼⣿⣿⠏⠀
⠀⠀⠀⠀⠀⠸⣿⣧⠙⢿⣿⠈⣿⣿⣿⠋⢹⣿⣿⣧⣠⣤⣶⣾⣿⣿⣿⣿⡏⠀⣿⡿⢠⣿⡟⠀⠀⠀⢠⣺⡿⠃⠀⠀⣹⣿⣿⡁⠀⣼⣻⣿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⢿⣿⡆⠈⠉⠀⠹⣛⠟⠀⡈⢻⣿⡟⠛⠛⢉⣾⣿⢿⣿⣿⠇⠀⣿⠃⢸⣿⠇⠀⠀⣠⣻⡿⠁⠀⣠⣾⠟⠋⠈⠻⣷⣿⣿⠏⠀⠀⠀
⠾⣿⣦⣄⡀⠀⠸⣯⣷⠀⠀⠀⠀⠉⠀⠸⣷⡄⢿⣿⠀⣰⣿⡿⠁⢸⣿⡟⠀⠀⠏⠀⣿⣿⠀⠀⣴⣿⡟⠁⠀⠰⠟⠁⠀⠀⠀⢠⣿⡾⡟⢷⣤⣀⠀
⠀⠈⠙⢿⣿⣦⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⠘⢋⣼⣿⡟⠀⢠⣟⣿⠁⠀⢠⠀⢰⣿⡇⠀⣼⣿⣿⠀⠀⣀⣀⣀⣠⣤⣤⣤⣾⣿⣿⣧⣶⣿⣿⣷
⠀⠀⠀⠀⠙⢿⣷⣼⣥⣾⠀⠀⠀⠀⠀⠀⠸⣿⣇⣾⣿⠏⠀⠀⣸⣧⡆⠀⠀⠀⠀⢸⣿⠀⣰⣿⣿⣷⣾⠿⠿⠟⠛⠛⠉⠉⢹⣿⣿⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣾⡏⠀⠹⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣠⣏⣿⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⡿⠁⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⣿⠇⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀