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