⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠛⠷⠿⡟⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠛⠛⡛⠷⣴⣦⣈⠻⡟⠻⠒⠚⣋⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣫⣥⠦⢭⣉⡉⠛⢷⣿⠻⣿⣾⢁⣶⡇⣼⣏⠁⠉⢿⢻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣟⣥⣀⡀⢈⣹⣷⣼⣟⢦⡙⢻⣿⠀⣿⣿⣭⣂⣀⣙⣛⣧⣌⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⢿⡟⣷⡁⠸⢿⣽⣿⣿⣆⣿⡄⠹⡆⢻⣿⣿⣯⣄⣀⣈⡛⣿⣷⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⠟⠉⣽⣿⣾⣿⣤⣤⡻⣿⣿⣿⠈⢃⣄⠀⠈⠀⠙⣻⣿⢭⣤⣭⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⡂⣶⣿⣿⣿⣿⢹⢽⣿⣿⣿⣿⡄⠀⡱⠄⠀⠀⠀⠘⢿⣦⠤⣬⣿⣿⣿⣿⣷⣝⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⠋⠀⢷⣿⣿⠟⠁⠈⠈⠛⠻⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⡙⣒⠾⣿⣟⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⡿⢿⡆⠀⠀⠀⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢝⡮⣝⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢾⣿⣿⣓⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣝⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠻⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡏⠁⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠁⠀⠀⡀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠢⡀⠀⠈⢿⣿⣿⡇⢠⣄⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠛⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡰⠤⠂⠀⠀⠑⠄⠀⠈⢿⢻⣇⠸⡌⣧⠀⡅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⡇⠸⣿⠀⠀⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣭⣯⣭⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠫⢺⠁⢳⡾⢀⠁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠱⡀⡿⢼⠛⠲⠾⢛⣿⣿⣤⣤⣄⠀⠀⢠⢰⣾⣿⣟⠹⠿⠿⠚⠙⠃⠀⠀⠀⠀⢐⠀⢸⠀⠞⠀⠈⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡖⢹⣶⣴⣞⠻⣯⡿⢻⣿⢿⠀⠀⠀⠊⠛⠉⠀⠐⠂⠐⢊⡁⠀⠀⠀⠀⠂⢠⠀⢸⠀⠂⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠉⠋⠲⣤⠤⡖⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢠⠀⡇⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⠒⠠⠄⢠⠎⠀⡾⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠐⠁⠀⠰⡃⠀⠀⠀⠀⡴⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣠⣼⣇⠉⠢⣄⣀⠀⠀⠀⠀⢆⠁⠀⠀⡸⣸⣄⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢀⡏⠘⣦⣤⠤⢠⠞⠉⢥⠟⠀⠀⠀⠑⡍⠒⠀⡇⠈⣇⠀⠀⡇⡟⣿⢿⡜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⣠⠞⠀⠀⠈⠛⣿⣯⣀⣠⠁⠀⠀⢀⣴⣾⡼⠀⣀⡆⠀⢹⠀⡸⠀⠀⢿⣷⡇⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘⡁⢀⣀⡄⠄⠀⢀⣙⣋⣤⣶⣾⡿⢟⡽⠋⠁⠀⣭⠇⠀⡜⣴⠃⠀⠀⢘⣿⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢣⠈⠿⠿⣗⠛⠛⠛⠉⣉⣀⣤⣶⠏⠀⠀⠀⢈⠟⠀⠀⣿⠃⠀⠀⠆⣸⡏⠀⠀⠀⠀⠹⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣬⢣⡀⠀⠈⠻⠿⠿⢛⣋⡻⠋⠀⠀⠀⠀⠀⢏⡄⢀⡾⠁⠀⠀⢀⡗⢻⠃⠀⠀⠀⠀⠀⡟⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠝⠈⠱⣽⡄⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣀⡄⢋⣴⠟⠁⠀⠀⠀⢸⣇⡟⠀⠀⠀⠀⠀⢀⣟⠀⠀⠀⠀⠈⠙⠳⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⢀⠂⠀⠀⢀⢇⢻⣦⠀⠀⠀⠀⠀⠀⠀⢀⡦⠂⣈⡴⠏⡅⠀⠀⣺⠁⠀⠘⡿⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠤⠖⠋⠁⠀⠀⠀⠀⣠⠃⠀⠀⠀⢸⠘⣯⣿⣷⠦⣷⣲⣶⣞⣧⣶⠶⣞⠋⠀⠞⠀⠀⠀⣰⠆⠀⣼⠃⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡇⢸⣸⠋⣿⠀⠀⠈⠙⣻⣿⠿⠲⠇⠀⠀⠀⠀⠀⡸⠃⠀⣠⠃⠀⠀⠀⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠌⣿⠀⢻⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⡆⠀⠀⠃⠀⣠⠃⠀⠀⠀⠀⠀⠈⠑⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⣾⣲⠦⠀⢈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢁⣠⡤⠶⣿⣥⡀⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⠟⠟⠿⣭⣻⢦⣐⠵⣄⠀⠀⠀⠀⠀⠀⢰⣭⠖⠛⢛⡿⢋⣠⠟⠳⠦⣄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠾⠵⠒⠂⠀⠀⠘⠰⠝⢷⣌⡢⣀⠀⠀⠀⠀⣸⠁⡠⠞⣉⡴⠋⠀⠀⠀⠀⠉⠙⠦⣄⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠺⣷⣄⢀⣴⡵⣋⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣫⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⢻⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢙⡦⠵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀