⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⡈⠐⠠⢁⠂⠐⢀⣾⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠿⣷⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠠⢁⠂⠄⠀⣛⠀⡟⢁⣠⣄⠀⠀⠀⠙⢻⡟⠉⠀⠀⢀⣴⣦⣬⠃⣬⣅⠀⢂⠐⡀⢂⠐⠠⠀⠄⠠⠀⠄⠠⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡁⢂⠈⠀⠾⡛⢱⡿⢿⣿⣿⣿⣦⣄⣠⣼⣷⣤⣤⣶⠿⠿⢿⣟⠆⢉⡛⠆⠀⢂⠐⠠⠈⠄⠡⠈⠄⠡⢈⠐⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡐⢀⠂⢠⣾⡟⣸⣰⡿⠁⠀⠀⠙⣿⡇⣿⣿⠸⣿⠁⢀⣀⣀⣙⡸⠎⢿⡆⠀⠂⠌⠠⠁⠌⠠⠁⠌⡐⢀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠟⡸⢛⣤⣼⣿⣿⣿⣤⣼⠇⣿⣿⠀⢧⣿⣿⣿⣿⣿⣿⣧⣄⠃⠀⢃⠘⡀⢃⠘⡀⠃⠄⠠⢀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢂⠡⠈⠄⢈⡾⠋⢹⣿⣿⣿⣿⡟⢡⣴⣿⣿⣷⣦⡙⢿⣿⣿⣿⣿⠀⠙⠀⠈⡀⢂⠐⡀⠂⠄⠡⢈⠐⡀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠄⢂⠡⠀⢸⠀⠀⢸⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⡇⠸⢿⣿⣿⡟⠀⠀⠀⠀⡐⢀⠂⠄⠡⢈⠐⡀⢂⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠄⡐⠠⠀⠀⠀⠀⠙⠋⠉⠀⠀⠉⠉⠙⠛⠋⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠐⠠⠈⠄⡁⢂⠐⡀⠂⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⠐⠠⠁⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⠀⠀⢀⠂⠌⠠⢁⠂⡐⢀⠂⠄⠡⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠈⠄⠡⢈⠐⡀⠸⣿⣦⡀⠀⠀⠛⠒⠚⠛⠛⠛⠛⠀⢀⣴⣿⠃⠀⠌⡀⠂⠌⡐⢀⠂⡐⠠⠈⠄⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠡⢈⠐⡀⠂⠄⠀⢻⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣶⣾⣿⣿⡿⠀⠐⠠⢀⠁⢂⠐⡀⠂⠄⠡⢈⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡐⢀⠂⠄⠡⠈⠄⠘⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⠃⠀⠌⡐⠠⠈⠄⠂⠄⠡⢈⠐⠠⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠈⠄⠡⢈⠐⠀⠀⠙⠃⣿⣿⣿⣿⣿⣿⣿⣿⡗⠋⠀⣤⠀⠀⠀⠡⠈⠄⠡⢈⠐⠠⠈⠄⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠄⠡⠈⠄⡁⠂⠀⠀⣤⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠇⣠⣾⣿⠀⣰⠀⠀⠀⣈⡀⠀⠈⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡈⠄⠁⠂⠀⠀⠀⠀⢻⣿⣷⠬⠉⠉⠉⠉⠉⠉⠀⠚⢿⣿⣿⢀⣿⡀⠀⠀⢹⣿⣿⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢸⣧⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣾⣿⡇⠀⠁⠀⢻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣟⡿⠀⠀⠀⠀⣿⣿⣦⠘⣿⣶⠖⣠⠆⠀⠀⢳⣤⡙⢿⣟⣼⣿⣿⡇⠀⠐⡀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀⢿⣿⣿⣷⣌⣿⣾⠏⠀⡀⠀⠸⡿⠿⠾⠿⠿⠿⠿⠷⠀⠀⠄⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⡄⣴⠀⠀⡄⠐⠀⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⢀⠀⠠⠀⠄⢂⠐⠠⢈⠐⡈⠐⡀⢂⠐⠘⢷⡭⠂⠄⡁⢂⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠐⠠⠈⡐⠠⠈⠄⠡⠈⠄⡈⠐⡀⠂⠄⠡⠐⠠⠨⠄⠆⠠⠌⠠⠐⠠⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⠿⠿⠀⣼⡿⠿⣿⡆⢠⣿⠿⢿⣷⠀⣼⡿⠿⣿⡆⢸⣿⠀⣿⡿⠿⠿⠀⠾⢿⣿⠿⠇⠘⣿⡄⣰⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣧⣤⡄⠀⢿⣧⣤⣤⡁⢨⣿⠀⢀⣿⠀⣿⡇⠀⠀⠁⢸⣿⠀⣿⣧⣤⡄⠀⠀⢸⣿⠀⠀⠀⠘⢿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡏⠁⠁⠀⣤⣍⣈⣿⡇⢸⣿⣀⣀⣿⠀⣿⣇⣀⣤⡄⢸⣿⠀⣿⣇⣉⣀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠙⠛⠛⠛⠁⠀⠛⠛⠛⠋⠀⠘⠛⠛⠛⠁⠘⠛⠀⠛⠛⠛⠛⠀⠀⠘⠛⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀