⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣤⣶⡾⠿⠛⠛⠛⢂⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢣⠀⠀⣼⡿⠋⠁⠀⢀⡄⢀⣤⢠⣿⣟⣛⢶⣄⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⢆⣼⠋⠀⣄⠘⣿⡘⣿⢼⡏⢹⣿⣼⡟⠻⡏⢢⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣣⠀⠚⣼⣿⣇⢻⡗⣿⢺⠇⣿⢠⡏⣼⡇⠸⣖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢏⣒⣾⡟⢹⣿⠸⡇⣿⠈⠀⣿⣾⢰⣿⡧⠠⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⣿⡏⠀⣼⣿⢂⡇⣿⢰⠀⡇⣿⢸⠋⠰⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡓⣬⣵⣿⣿⣿⣻⡇⡇⢸⠀⣇⣿⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣻⠾⢿⣿⣿⣟⠁⠁⠀⠀⠈⠈⠓⢻⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣀⣀⣄⣀⣀⣤⣤⣆⡠⣀⣀⠀⢁⣾⣯⣝⣹⣻⡷⠿⢻⣶⡶⣶⣶⣶⣦⡘⣿⣇⣄⡀⢀⣀⣀⠀⣀⣀⡀⠀⠀⠀⠀⢀⢀
⠛⠉⠉⢹⢭⣭⣽⣯⣿⣿⣿⣷⣷⠌⡏⣿⣿⡇⣿⣵⣾⣿⣿⣿⣿⣷⣿⣿⣷⢿⣿⣟⣛⣽⠓⡺⠿⣿⣿⠛⠻⣛⣛⣯⣿⣿
⣄⢀⡏⠉⠉⠙⡏⠉⠽⠏⠁⠈⠻⡅⠀⣿⣿⣷⠛⣿⢿⠻⢿⣿⣿⣻⣿⣿⣿⡞⢫⡟⣛⣽⠿⠟⠛⠛⠛⠻⣋⣽⠽⠿⢿⢿
⡋⠁⠀⠀⠀⢀⡗⠲⠦⢄⣉⣡⣬⡃⢀⣿⣿⡇⣀⣿⣟⣳⠾⣛⡯⢿⣿⣿⣿⡏⢼⣷⣿⣷⣶⢶⣶⣶⣿⣿⣿⢿⣻⣯⠽⠿
⠀⠀⠀⠀⣀⣤⣀⣤⣄⠀⠈⠉⠩⡄⢸⣿⣿⡗⢨⣿⣿⠛⢋⡉⠀⢿⣿⣿⡿⡧⠘⠋⢉⣉⠭⠉⠉⠉⠀⠀⠀⠉⠁⠀⠀⠀
⠀⠀⠂⠒⠂⠒⠒⠒⣒⣂⣤⡶⠾⠧⠼⠿⢿⡇⡰⣿⡿⡧⠤⠤⣖⣾⣯⣿⣿⣶⣴⣶⣶⣲⣶⣶⣒⣶⣶⣦⣶⣶⣶⣶⡶⣤
⠉⠀⠀⠀⠀⠐⠓⢒⠉⣤⠤⠀⠀⠀⠀⠀⠀⡀⠋⠀⠀⠑⠒⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠐⠒⠛⠛⠻⠟⠻⠿⢿
⣀⣀⣀⠀⠀⠀⣀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⠤
⣭⣥⡤⣤⣶⣶⢲⣒⣊⡀⣀⣀⡀⠀⠀⠠⠤⣤⠤⣤⣤⢴⡶⠶⠾⡭⠭⢅⣠⣀⣀⣀⣀⣀⣈⡥⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀