⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠈⠻⠶⡴⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠁⠀⠈⠀⠀⠀⠻⠷⠶⣦⣀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠆⠀⠀⠀⠀⢀⣹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⢶⣶⡄⠀⠀⣀⣀⣀⣤⣼⠟⠀⠀⠀⠀⠀⠘⣿⣡⣀⣄⣠⡀⠀⢺⣽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⢀⣼⣿⣭⡽⠯⠶⠶⠶⠶⠶⠶⠶⠶⠶⠮⣭⣥⣹⣿⡄⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⣀⡼⠋⠈⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣴⡯⠁⠀⠀⠀⠀⠀⣀⣠⠿⠛⣳⢾⣶⡀⠀⠉⠛⠻⠶⠦⡤⢤⠴⠶⣾⡗⠒⠛⠻⢴⣤⡀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⢠⣴⠟⢁⣴⣾⣿⣿⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢱⣶⣶⣦⡀⠉⠻⣆⡀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⢀⣿⠃⢀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⡄⠀⢙⡦⠀⠀⠀⠀⠀⢻⡿⢶⣤⡀⠀⠀
⠀⢀⣠⣰⣿⡿⠀⠀⠀⠀⠀⠀⢾⣟⠀⠈⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⠇⠀⣨⣷⡀⠀⠀⠀⠀⠸⣷⠈⠛⠷⣦⡀
⣴⡟⠋⢉⣾⠁⠀⠀⠀⠀⠀⠀⣬⡟⠿⠿⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⡾⢿⣵⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢸⡇
⣯⣄⠀⢸⣏⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⡇⢀⣤⡿⠃
⠀⠙⠿⣾⣧⠀⠀⠀⠀⠀⠀⠰⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡿⠟⠋⠀⠀
⠀⠀⠀⢨⣷⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⣽⠃⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⢀⣀⠀⠀⢀⣀⣤⣴⠾⣿⡿⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢽⣦⡀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠈⠛⠷⢾⣟⠛⠉⠀⠀⠸⠇⠀⠀⠈⣹⡿⠲⠶⢶⠟⠀⣴⠟⠁⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⢠⣤⣄⡀⢈⡏⠓⢤⣄⠀⠀⠀⠙⣷⣄⣀⠀⠀⢀⣀⣤⣾⠟⠁⠀⠀⣀⣤⡼⠁⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠛⠀⠈⠉⠉⠁⠀⢈⣹⡿⠷⣦⣤⣀⣉⡛⠛⠛⢛⣛⣉⣠⣤⣶⢾⣿⡋⣸⡇⢀⣤⣤⡀⠀⣠⠾⣗⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢴⣿⣧⡄⠀⠀⠀⠀⠀⠀⣠⣾⡋⢦⣵⠁⠈⠻⢿⣛⣀⣀⣙⣻⡟⠁⠀⢳⢎⡜⣷⡛⠞⠛⠁⠈⠛⠛⠁⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠂⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⢻⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⣸⡷⠿⠟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⣀⣄⠀⠀⠉⠉⢻⣇⡀⣀⢀⡀⠀⠀⠀⣀⣀⣀⡀⣀⣠⣿⠋⠉⠁⢀⣤⣆⡀⠀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣦⣴⡿⠛⠿⢶⣤⣤⣨⣷⣶⣠⣇⣮⣝⣺⣱⣡⣲⣬⣴⣢⣼⣧⡴⡲⠟⠛⠉⠙⠷⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠉⠛⠿⣿⠟⠉⠉⠉⠉⠛⠿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀