⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⡿⢿⠿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⡠⠀⢀⠠⢀⣾⣿⠟⠁⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⡄⣾⣿⡗⠚⢉⠑⡀⠂⢤⣿⣿⠋⢈⠁⠒⠀⡉⢈⠱⣢⣴⣾⠿⠿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢀⠇⠇⣸⣿⡗⡀⠐⠂⡠⢀⠡⠈⠟⠃⡈⠀⠄⡁⢂⠐⣤⣿⡿⢋⠁⡐⢂⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⣶⣿⡿⠛⠀⠀⠀⠀⠀⢸⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢰⠈⠀⢾⣿⡆⢃⣸⣤⣶⣶⣶⣶⣬⣤⣁⠌⢀⠐⡀⢿⣿⠏⠐⠠⠐⠠⢀⠂⠄⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠁⠀⠀⠀⡆⠠⢈⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⣿⣇⢠⢀⠡⢀⢩⣴⣿⣿⠟⠛⠛⠛⠛⠿⢿⣿⣿⣦⡐⠠⠀⢁⠐⡈⠐⡈⠄⢂⠠⠈⡐⠠⠀⢆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠲⠞⠃⠇⣸⣿⣟⠂⠀⠀⠀⠀⠀⠀⠠⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣀⠐⠠⠨⣿⣧⡸⢀⠰⢠⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡑⡀⢂⠀⡁⠂⠐⢀⠂⡐⢡⣼⣶⣿⣿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠐⠁⡐⢀⠂⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣧⡄⢂⠡⠐⡙⠿⡗⠀⢢⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⢀⠂⠄⠁⠌⡀⢰⣾⣿⠟⠛⠁⠄⠠⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡀⠄⠀⠒⢐⣠⣤⣆⣿⣿⠂⠀⠀⠀⠀⢀⠆⣸⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡆⣡⠠⠁⠌⢀⠁⣾⣿⡷⠂⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠂⠌⡐⠄⠠⠉⠩⢁⠐⡈⠂⠌⠠⢁⢈⣣⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠣⣈⠛⡛⠻⢿⣿⣦⠀⠀⠀⠀⡆⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⡻⠿⠀⢀⠂⡈⠄⢸⣿⡿⠀⠀⠀⠀⠀⢻⣿⣇⠠⠀⠀⠀⠀⠀⢸⣿⣿⠈⠐⠠⠀⢂⠡⠈⡐⠀⠂⠄⠡⢈⢐⣠⣠⣄⣄⣀⣀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠑⢂⣶⣿⡿⠟⠛⠁⠀⠀⠰⠀⣾⣿⣧⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣧⣤⣒⡀⠖⠠⠤⢊⣿⣿⠃⠀⠀⠀⠀⠄⣹⣿⣯⠂⠡⠠⡀⠀⠀⢸⣿⣿⠈⠠⠁⠂⠄⠂⢁⡐⠈⠄⡁⢶⣿⡿⠿⠟⠻⠛⠟⠿⣿⡦⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠐⣿⠿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⢿⣿⣶⣬⣶⣿⡿⠃⠀⠀⠀⠀⠀⢀⣿⣿⠅⢀⠂⢁⠀⠀⠀⢸⣿⣿⠀⡁⠂⠁⠌⡐⠀⡀⠂⡁⠠⠂⠄⡐⢂⢈⠐⠠⠀⠀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣶⣤⣦⠈⠁⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣯⡄⠀⠀⠀⠀⠤⢁⣼⣿⣧⣤⣂⠈⠄⠀⠀⠀⣼⣿⡿⠄⠠⠁⠌⠐⡀⠂⠄⢁⠈⡀⠌⢀⠁⠂⠄⢊⠀⠅⠠⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡿⠃⠀⠀⠀⠀⣰⣿⡿⠟⠍⣿⡿⠆⠀⠀⠀⣸⣿⣿⠃⢀⠂⠌⠠⠁⡀⠂⠌⢀⠂⠄⢈⠂⠠⢁⠈⠄⡈⠠⠁⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣶⡤⠀⠤⠤⢀⣼⣿⣿⠇⢂⠠⠐⠠⠁⢂⠐⠠⢈⠀⡐⠈⡀⠤⠁⠠⠌⡀⠄⡁⠂⠁⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠁⠀⠀⠀⣠⣾⣿⡿⠁⡐⢀⠂⠄⡡⠐⠠⠐⢀⠂⠠⠐⡀⠄⡀⠂⠁⢾⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⠋⢁⠐⡀⠢⢀⠂⡀⠂⡁⠐⡀⠂⢁⠐⢀⠐⡀⠡⢈⠠⠀⠄⡈⠉⣉⠛⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠟⠋⢀⠐⡀⠂⡀⠁⠄⡐⠀⡁⠄⢁⠠⠁⠠⠈⡀⠐⠠⠐⠀⠄⡈⠄⠠⠁⢸⠀⠀⠀⠉⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣦⣤⣠⡀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡠⢂⠠⠄⠁⠄⠉⠄⠠⠁⠄⡈⢀⠐⡈⢀⠡⠐⠈⠄⢂⠁⢂⠐⢀⠡⢀⢹⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠛⠻⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⡄⢂⠈⡐⠈⡐⠈⠄⡁⢂⠰⠀⡐⠠⠀⠂⠄⢁⠂⠄⡈⠠⠐⠂⠄⠂⢸⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣾⣿⣿⣿⣿⣿⣿⣿⣶⡀⢿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠆⡀⠁⡀⠁⠆⠰⠀⡀⠁⢀⠀⢁⠈⠀⠆⠰⢀⠰⠀⢆⣿⣶⣿⣶⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠛⠀⠀⠀⠀⠹⢿⣿⣆⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡿⠛⣀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠁⠢⠄⣁⠠⢁⠠⠁⡁⠐⠁⠠⢈⠀⠂⡁⢈⠐⠠⠀⠌⠠⢉⠙⡙⠻⢿⣿⣦⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠿⠿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢨⣿⣿⡆⠀⠀⣀⠐⠒⢂⠀⡄⠀⠀⠀⣴⣿⣿⣿⠟⠻⠿⢿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣴⣤⣤⣂⡄⠠⠁⡄⠘⢀⠁⢂⠠⢁⠀⢂⠈⠄⠡⠐⡀⠂⡐⢀⡑⠀⠹⣿⣧⠄
⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⣂⠉⣿⣿⣿⣿⣶⣾⣿⣶⣬⣤⣾⣿⣿⡇⢀⡃⠄⡉⢁⠂⠄⠘⡄⠀⣾⣿⣿⣿⠃⢀⠀⠀⠀⠉⣻⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⠉⠛⠛⠻⠿⣿⡧⠐⠀⠂⠌⡀⠄⠂⠌⠀⠆⢈⠐⠠⠐⠠⠐⠠⢸⠀⠀⠀⠃⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⣶⣿⠏⣡⡓⡜⢿⣿⣿⣯⣍⣛⣛⣿⣿⣿⣿⠟⠀⠆⠠⠐⡀⢂⠄⠈⢄⢻⠀⣿⣿⣿⣿⣦⣤⣤⣤⡀⠀⢈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠒⠈⠄⡁⠄⡀⠂⠌⠠⢈⠠⢀⠂⠄⠁⠆⢁⠂⠈⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣡⣤⣶⣷⠀⠀⠀⠀⠀⠀⣾⡿⢏⣥⣾⣿⢯⣵⣶⢩⡛⠻⠿⣿⢿⡿⠿⠟⠉⠀⡀⠸⡄⠡⠰⠄⢀⠈⡄⠀⠈⠻⣿⣿⣿⣛⠛⠿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠘⡀⠂⠠⠐⢀⠡⠀⡁⠄⡐⠠⣾⣶⣿⣶⣦⣌⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠘⢃⡦⠿⣟⢵⣿⣿⢳⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠘⢀⣶⣾⡄⠀⣠⣄⠀⠀⠈⠻⢿⣿⣿⣶⣶⣿⣿⣿⣿⠏⡠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣶⣄⠀⠀⠐⡀⢁⠂⢁⠂⡀⠡⠀⢂⠀⠂⠌⠁⡉⠉⠛⠿⣿⣦⡀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⣘⣌⡙⡰⣙⠿⢃⡀⢀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⣾⣿⣿⣄⣴⣿⡇⠀⠀⠀⠀⠀⣈⠩⠛⠛⣟⣿⠩⢆⣬⡱⢂⡜⡱⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⠂⢀⠐⠠⠈⠄⡐⢀⠡⠁⢂⠡⠈⠄⠂⠄⡈⠀⠀⠈⢿⡿⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢄⠐⢤⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠉⠃⣈⣀⣿⣷⣄⠀⠀⠀⠀⠀⠈⠉⠀⠉⠙⢿⣿⣿⠿⠟⢿⣷⡄⠀⠠⠀⣼⣿⣀⠘⣽⣿⠟⣱⣾⡿⣳⣿⣟⣿⡷⡵⠀⠀⠀⣂⣤⣤⡀⠀⠀⠀⠀⠉⠄⠠⠁⠢⠁⠔⡀⠄⠂⡈⠀⠄⠂⠌⡐⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠏⠀⠀⣠⡁⠀⠀⠀⠀⠄⢊⣠⣾⣿⡿⠟⢛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⢁⡀⠀⠀⠀⠀⠀⢀⢹⣿⣿⠿⣿⣾⣭⡞⠻⢟⠡⢿⠿⣘⠻⢱⡷⠀⠀⠀⠘⠻⢿⣿⣯⡀⠀⠀⠀⠚⠀⠌⠐⡈⠀⠄⡐⠠⢀⡑⠈⡐⠠⢀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠈⢹⣿⣆⡀⠀⠈⣠⣿⣿⠟⠋⠀⠸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣮⠙⢿⣿⣿⡈⠾⠘⠢⢅⡪⠻⠁⠀⠀⠀⠀⠀⠀⠛⢿⣿⡆⠀⠀⠌⡐⠈⠠⢀⠁⠂⠄⠲⣿⣿⣷⣄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠁⠀⠀⠀⠀⠀⠻⣿⣷⣆⣰⣿⡿⠁⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣾⣿⠋⠀⠀⠀⠙⣿⣿⣤⠈⠉⠁⠀⠀⠀⠀⠀⠀⣴⣦⡄⠀⠘⢿⣿⠠⢀⠡⠀⢂⠁⢂⠈⡐⠠⠐⠀⡙⢿⣿⣧⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡁⠀⠀⠠⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣤⡀⠀⠀⠀⠀⠻⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⠠⡐⠀⠄⠘⠀⠌⡀⢂⠐⠠⠁⠂⠠⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⢿⣿⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀⠀⠀⠈⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⡃⠈⡐⠀⠌⠐⡈⠄⠂⡐⣀⠘⠂⡌⢀⠡⢸⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⢿⡦⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠁⡐⠀⠌⠠⢁⠐⡀⠁⠲⢿⣿⣧⡄⠂⠀⢲⠀⠀⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣅⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠺⠏⠀⠀⠀⠀⠰⠀⣶⣴⠂⡀⠡⠐⡀⠐⡈⠄⡁⠂⢂⠀⠆⠡⢀⠹⣿⣿⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣧⠐⠠⢁⠐⠠⠐⠠⠐⢡⣾⣶⡈⠐⡀⠂⢸⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⡠⠐⡀⠈⢄⣇⡰⠁⠠⠙⣿⣷⠁⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀HTTP 404⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠐⡀⢁⢻⣿⡆⠄⠁⠂⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀not⠀found⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃⠠⢁⠐⠠⢸⣿⡏⠙⠒⠀⢺⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣴⣿⡿⠏⠀⠑⠢⢄⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⣢⠀⠀⠀⠀⠀⠀⠰⢀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣶⡆⠀⠀⠆⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⡙⢅⠀⠀⠀⣿⣿⣠⠀⠀⠀⢀⣶⣴⣤⣤⣤⣤⣤⣴⣶⣷⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⠤⠀⠀⢸⣿⡿⠃⡀⠀⢻⣿⡟⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢿⣷⣿⣶⣿⡿⣿⣿⣿⣦⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀