⣿⠛⠛⠛⠛⠻⡟⠛⣿⠛⠻⣿⠛⠛⠛⠛⠛⢿⣟⠛⠛⠛⠛⠛⠛⠛⢛⣻⠿⠛⠛⠛⣿⡛⠛⠛⣛⣛⣟⣛⠛⠛⠛⣛⣻⣿⣟⠛⠛⠛⢻⠛⠛⢻⡟⠛⢿⡂ ⣿⠀⠀⠀⠀⠀⣿⠀⠈⢧⡀⠈⠻⡄⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⢼⠷⠞⠛⠋⠉⢠⡏⢀⡴⢟⡹⠋⢠⠏⠀⠀⠀⢸⠀⠀⠈⣷⠀⢸⡇ ⣿⠀⠀⠀⠀⢰⡟⠀⠀⢸⡇⠀⠀⢿⠀⠀⠀⠀⠀⠀⠈⠛⢶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⣰⠏⠀⢰⡏⠀⠀⠀⠀⢹⠀⠀⠀⣿⠀⢸⡇ ⣿⠀⠀⠀⠀⢸⣧⠀⠀⢸⠃⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⡏⠀⠀⢸⠀⠀⠀⠀⠀⡾⠀⠀⠀⣿⠀⢸⡇ ⣿⠀⠀⠀⠀⠀⣿⠀⠀⢸⡄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⣼⠀⠀⠀⠀⢰⠇⠀⠀⠀⡿⠀⢸⡇ ⣿⠀⣄⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠙⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⣿⠀⠀⠀⢀⡟⢀⡞⠀⣸⠃⣰⢸⡇ ⣿⢸⡿⣆⠀⠀⠸⣇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⡟⠀⠀⢀⡾⢁⡞⠀⢠⡏⣴⢿⢸⡇ ⣿⢸⡇⠹⣧⡀⠀⢻⡄⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⡼⣡⠞⠀⣠⣿⠟⠁⢸⢸⡇ ⣿⢸⡇⠀⠈⠻⢦⣌⣻⠀⠀⢷⣄⡀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⡇⠸⢄⣀⠀⠸⣇⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠁⠤⠶⠋⠁⠀⠀⣿⢸⡇ ⣿⠀⣿⠀⠀⠀⠀⠉⠋⠀⠀⠀⠈⠙⠲⠦⣤⣀⣀⣼⠃⠀⠀⠀⠀⠀⠐⣏⠃⠀⠀⢸⡄⠀⠻⣆⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸⡇ ⣿⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣀⡞⠁⠀⠀⠈⠓⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇ ⣿⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢸⡇ ⣿⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡆⠀⠀⢸⠛⢷⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⢸⡇ ⣿⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠷⠀⠀⢸⡆⠀⠹⣦⠀⠀⠀⠀⠀⠀⠓⡀⠀⢀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢸⡇ ⣿⣀⣤⠶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠸⣇⠀⠀⢸⡇⢀⠀⠀⠀⢀⠔⣡⣴⣟⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⢸⡇ ⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣠⠞⠁⠀⠈⠢⣀⠀⡐⠋⠉⠉⠉⠉⠙⠛⠻⠗⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⢸⡇ ⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣤⣄⠀⠀⠀⠁⢀⣀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⡇ ⣿⠈⠻⣦⡀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠇⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⡇ ⣿⠀⠀⠈⠙⢷⣤⡀⠀⠀⠀⠁⠁⠀⠢⡀⠀⠀⠙⢧⡀⢀⣠⡤⠶⡶⣤⣀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠐⢅⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠀⢸⡇ ⣿⣦⡀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠉⠉⢿⢦⡼⣅⠀⠉⠛⢦⣄⣤⠞⣱⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡡⠀⠀⢀⣠⣴⠞⠋⠁⠀⠀⠀⢸⡇ ⣿⠈⠻⣶⡾⠛⠙⠛⠶⢮⣝⡓⣦⠀⠀⠀⠘⡄⠀⠀⠀⠀⠘⣧⡾⠉⢧⡀⠀⢀⡼⢳⡞⡟⠀⠀⠀⠀⠀⠀⡴⠂⠉⠀⠀⣶⠚⠛⠉⠀⠀⠀⠀⠀⠀⢠⣿⡇ ⣿⠀⢠⡟⠀⠀⠀⠀⠀⠀⠈⢹⡏⠀⠀⠀⠀⠘⣄⡀⠀⠀⠀⠈⠳⣤⡈⠙⠒⠛⠁⢀⡿⠁⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⡿⢹⡇ ⣿⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡴⠞⠋⠉⠉⠛⠲⣤⣀⠀⠀⠉⠛⠒⠲⠴⠚⠁⠀⠀⠀⣀⣤⣾⣿⣶⣦⣤⡀⠀⠈⣿⠀⠀⠀⠀⠀⣀⣴⠟⠀⢸⡇ ⣿⣼⠃⠀⠀⠀⠀⠀⠀⠀⣴⠸⣧⠞⠋⠀⠀⠀⠀⠀⡠⠂⠈⢻⣿⣶⣤⣀⠀⠀⣀⣀⣤⣴⣶⣿⣿⣿⣿⡿⠁⠈⠛⠿⣦⠀⣏⣠⣤⣤⠴⠞⠋⠁⠀⠀⢸⡇ ⣿⡟⠀⠀⠀⣿⡀⠀⠀⣸⠃⠀⠋⠀⠀⠀⠀⢀⠠⠈⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠘⣿⠉⠙⠛⠶⢤⣄⡀⠀⠀⠀⢸⡇ ⣿⠇⠀⠀⠀⣿⠙⠲⠤⠏⠀⠀⠀⠀⠀⢀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠛⢶⡀⠀⢸⠃ ⣿⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢠⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠈⣿⠀⢸⡀ ⣿⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇ ⣿⣀⣀⣀⣀⣰⣟⣁⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣘⣆⣀⣀⣀⣀⣀⣀⣀⣿⣀⣸⡇ ⠉⠉⠉⠁⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣶⡀⢀⣶⠀⢀⣴⢶⣄⠀⢀⣴⢶⡄⢠⡆⠀⢰⡄⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⢧⡸⢹⠀⣾⡁⠀⣿⡇⣿⡇⠀⠀⢸⡿⠶⢾⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠷⠘⠃⠾⠄⠘⠳⠶⠛⠀⠘⠳⠶⠃⠸⠗⠀⠸⠇⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀