⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣆⡀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠂⠁⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⣀⣤⣤⣶⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠑⠈⢹⣿⡟⢵⣾⣽⡈⠫⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠈⣛⣫⣤⣈⣛⣶⣾⣶⣶⡶⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠐⠝⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⡈⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⡏⡍⢯⡻⢿⡟⢻⣄⣹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⡀⠀⢸⣿⣿⣿⣿⠟⣻⡙⡏⠘⢸⡅⠢⠈⠻⠷⠔⠛⠛⢛⢻⡿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⠀⢼⣿⣿⣿⡿⡶⠋⠰⠉⠐⡀⠈⢢⣄⠀⠀⢠⠊⣩⡝⢉⣉⠫⣜⠝⢿⣦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇⠄⣿⣿⣿⠿⠃⠁⠀⠀⠀⠘⠁⠀⠀⣿⡀⡇⡸⢸⣿⡇⢧⣸⡇⣿⡇⢸⣿⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡄⠐⠿⢋⡥⢖⢩⣥⣤⡑⣤⡀⡀⢡⢀⣿⣿⣮⡣⠢⢈⡛⠠⠄⠂⢉⠂⣾⣿⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢀⠜⣵⢠⠖⢦⠘⣿⡿⢠⡇⠀⠠⠀⣼⣿⣿⣷⡔⣖⠨⡤⣭⣤⣄⠃⠝⣿⣿⣿⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⡏⣸⣿⡘⠗⠋⡀⡫⡰⡱⢡⡧⠀⠸⣿⣿⣿⣿⣿⣆⢠⡀⠁⠉⢻⣷⣄⢊⣿⣿⣿⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠻⢀⠻⠿⠛⠛⡉⠊⢂⡴⣣⣿⣧⠀⠀⠹⣿⣿⣿⣿⣿⡌⣳⢦⣄⠀⠉⢿⡆⠘⢿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣁⣀⣀⠀⢹⡅⣾⣿⣿⣿⣿⣿⣥⠀⠀⡋⠸⣿⣿⣿⣿⠹⠿⢍⠓⠀⠀⢿⠀⢨⡿⢿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⢿⡿⣿⣿⣿⣿⣿⣄⠀⡇⣿⣿⣿⣿⣿⣿⠛⠁⣹⡇⠄⠻⣿⠿⠟⠀⠀⣾⣿⣦⡀⠈⠦⠴⠁⢼⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢸⠁⣙⣿⣿⣿⣿⣿⠀⠇⣿⣿⣿⣿⣿⠏⣰⡆⠙⠁⠀⠄⠉⣀⠠⠀⢠⡿⠛⣛⠇⠀⡀⠀⢀⣾⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠐⠉⣿⣿⣿⣿⡀⡆⣿⣿⣿⣿⡏⣸⣿⣿⣤⡀⠀⣤⢀⠀⠶⠖⣫⣴⡟⠉⢻⣦⠣⠁⣦⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠐⠟⢿⠿⣇⢀⡛⠟⠈⡌⢠⣿⣿⠟⣋⣩⣥⣤⣤⣶⣾⠿⠛⡉⣶⣽⡤⢁⡁⡄⠭⢿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠈⡀⠀⠀⢀⣾⣿⢁⡾⠋⡀⣄⣤⢠⣤⣰⡠⣿⣿⡜⣯⢅⢰⣇⠁⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢧⣀⠀⠀⠀⡀⡀⠀⠀⠀⢸⣿⡇⣾⠁⣼⣇⣿⣿⡟⠿⠿⠃⣩⣷⡆⢨⢸⢸⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢑⢄⠀⠹⡑⡀⠈⣚⠸⣿⠠⠃⣄⢫⡋⠘⣷⠷⠶⠶⠿⢛⣫⠤⢟⠔⢰⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠃⠀⢄⢃⡁⢥⣤⣀⠻⠟⢿⡾⣷⣇⠿⡿⠋⠛⠈⣀⣴⣾⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠈⠻⣿⣦⣀⠒⠀⠂⢁⣠⣄⣤⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀