⠀⠀⠀⠀⠀⢀⣿⠃⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣷⠀⠀⠀⠈⢿⣿⠈⠅⠀⠀⠀⢀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣏⡾⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⣒⠊⢩⣶⡀⠀⠀⠸⡆⠀⠀⠀⠈⢿⢰⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⢰⡄⣿⣿⠞⠁⠀⢲⢰⣿⠟⣽⣿⣿⣿⣿⠀⢸⣿⣿⡄⠀⠀⢣⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠰⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣾⣾⣿⣯⣀⣀⡀⣿⣿⢛⣄⠙⣿⣿⣿⣿⠀⢸⢹⣿⡿⠆⠀⠸⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⡅⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣇⡀⠀⠀⠀⠉⠈⠙⠺⣿⣿⣿⣿⡿⢸⣿⣦⣽⣿⣿⡇⠀⠈⠈⣡⠔⢸⣦⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⡇⢈⢡⣿⣿⣿⣿⠃⣠⣔⡉⠘⣠⣿⠉⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣿⡏⠀⢀⡀⠀⠀⠀⢀⢆⠈⠉⠍⠃⠋⣔⠾⣿⣿⣟⣵⣾⣿⡏⠁⣴⣿⣿⠀⢿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠅⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠻⣿⣶⣄⡀⠉⠐⢲⣿⣷⡀⠈⠂⠀⢠⣅⣬⢝⣿⣿⣿⣿⡿⢁⣼⣿⣿⣿⠀⡸⠁⠃⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣄⣸⣿⣿⣿⣦⣄⡢⣦⡈⢡⣾⡿⠈⠛⣫⠑⢺⣿⡟⠸⡏⠀⠀⠀⢠⠀⠀⠀⠈⠀⠀⠀⠀⢰⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠉⠒⠒⠚⣋⣥⣔⠀⠟⣴⡇⠋⣠⠀⠀⠈⡆⠀⠀⠀⡄⠀⠀⠀⠰⠀⠀⡇⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡉⠉⠛⠿⢿⡿⠃⢀⡀⣤⢰⣾⣿⣿⣿⡿⣶⢘⣿⣷⣿⣿⣥⡄⠀⣷⡀⠀⢀⡃⠀⠀⠀⠀⠀⠀⡇⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡀⣀⡔⠐⠋⠉⠁⠈⠁⢰⣖⣿⣿⣿⣿⢀⣿⣿⣽⣿⣿⠇⠀⢹⣿⠀⢸⡇⠀⠀⠀⡄⠀⢀⣵⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣹⣾⡆⠀⠈⢻⣿⣿⣟⣿⣿⣿⣿⣻⡈⣿⣿⣿⣯⣶⡆⠀⢸⡏⠀⢸⠆⠀⠀⠀⢁⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⣿⢷⠀⠀⠙⣿⣿⣿⣿⡷⣿⣿⣿⣿⢸⣿⣿⣿⣿⠃⡰⢸⡇⠀⢸⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⣤⡀⠀⢹⠟⣛⣷⣿⣿⣗⣿⠇⣰⣿⣿⣿⣡⣾⠃⠀⡇⠀⢸⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⡀⢀⠤⣿⣿⣿⣿⣿⠀⣶⣿⣿⣿⢟⡡⠀⠀⡇⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⡆⠀⡿⣹⣿⡿⣷⠆⣽⡿⡏⣠⡞⠁⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⣿⣅⠐⠁⣿⣿⣷⣿⡄⢿⣿⣾⠏⠀⢀⣴⡿⠋⠁⠀⢀⠄⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠩⢧⣷⣶⣯⣿⣿⣿⣹⢸⣿⣃⡤⠾⠛⠋⠀⢀⡄⠂⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣧⣤⣀⠀⢻⣿⣿⣿⣿⣿⣿⡟⠞⠁⠀⠀⠀⢀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣷⢻⣿⣿⢔⣿⣿⣿⡿⠿⠋⢀⣠⣤⣤⡴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀