⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢫⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠹⣎⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠘⣧⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⢷⡽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠹⣎⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠹⣮⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⡀⠀⠀⠀⠙⣯⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇⠀⠀⠀⠀⠹⣏⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠸⣧⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠇⠀⠀⠀⠀⠹⣎⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠆⠀⠀⠀⠀⠀⢻⡜⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡿⡸⣿⣆⠀⠀⠀ ⠀⠀⢀⣿⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡇⠀⢸⣧⢻⣿⡀⠀⠀ ⠀⠀⣼⣿⢱⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢰⠁⠀⠀⠿⡜⣿⣧⠀⠀ ⠀⢰⣿⡇⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡌⠀⠀⠀⢠⢣⢻⣿⡆⠀ ⠀⣿⣿⢱⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⡜⠀⠀⠀⠀⢸⢸⠘⣿⣧⠀ ⢸⣿⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠋⠀⠀⠀⠀⠀⢸⢸⠀⣿⣿⡀ ⢸⣿⡇⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⡇ ⣿⣿⣷⢸⡀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⠄⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⢠⣿⣿⡇ ⢻⣿⣿⡄⢃⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠃⣼⣿⣿⡇ ⢸⣿⣿⣷⡈⢦⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠆⣸⣿⣿⡿⠀ ⠈⢿⣿⣿⣷⣤⣷⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠋⣸⣿⣿⣿⠇⠀ ⠀⠈⢿⣿⣿⣿⣮⡪⣢⡀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⢀⠜⢁⣾⣿⣿⣿⠏⠀⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣾⡺⣶⣄⡀⠀⠀⠉⠓⠂⠤⠤⠤⠤⠤⠄⠒⠉⠀⠀⢀⠔⢁⣴⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣝⡯⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⢁⣴⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣬⣅⡉⠙⠒⠒⠀⠀⠒⠒⠉⣀⣤⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉