⠀⠀⠀⠀⠀⠀⣀⣤⠶⠓⠛⠛⠛⠛⠓⠲⠶⠤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠟⠀⠠⠀⠀⠀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢋⣤⡴⠶⠶⠶⣤⡿⠋⠉⠈⠉⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡶⠛⠁⠀⠀⢠⣾⠏⠀⠀⠀⠀⣸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠇⠀⠠⠀⣴⣿⡏⠀⠀⠀⠂⢠⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀ ⣿⠀⠀⢰⣿⣿⡿⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀ ⢸⡆⠀⢸⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢻⡄⠀⠀⠀ ⠈⣷⡀⠀⢿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⣼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠁⠀⠀⠀ ⠀⠈⢷⡄⠈⢿⣿⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀ ⠀⠀⠈⠻⣧⣤⡿⢷⣄⠀⠀⠀⠀⠹⣿⣿⣿⡿⠃⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀ ⠀⠀⠰⠇⢹⡆⠀⠀⢹⣷⣦⣄⣀⣀⣹⣿⣿⡁⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⢹⡆⠀⠀ ⠀⠀⠀⠀⠸⣧⠀⠀⠀⠻⣦⣉⣉⣭⡍⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⠸⣇⠀⠀ ⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀ ⠀⠀⠀⠀⠀⠀⠙⣇⠀⢀⣴⡶⠶⢦⣤⣄⣀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⢻⡄⠀⠀⠀⠀⠀⠈⢻⡄ ⠀⠀⠀⠀⠀⠀⠀⠻⠶⠟⠉⠻⢷⣄⡀⠈⠉⠙⠳⠶⠾⢷⣄⠀⠀⠀⠀⣼⠏⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢶⣄⣀⠀⠀⠀⠉⠀⢀⣀⡾⠃⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠐⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠶⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⢸⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣠⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⡾⠟⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢠⡿⣷⡄⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⣽⠁⠈⣿⡆⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⢀⠀⣰⡇⠀⠀⠈⢿⣄⠀⠀⠀⢸⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠻⣦⡀⢀⣾⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠛⠛⠈⠀⠀⠀⠀⠀⠀⠀⠋⡾⣠⣆⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⣾⢀⡀⣦⠻⠀⠀⠀⠀⠀⡟⣰⠀⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡏⢸⠀⠀⠀⣄⢿⠈⠀⠀⡇⣰⠀⢀⠀⠀⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⡆⣿⠈⠁⣽⠀⠀⠀⠀⠀⠆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⡄⣷⡿⢠⠀⠀⠀⠀⠀⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣹⠟⡾⣤⣦⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⣠⣀⣦⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣾⢀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⢸⠀⠀⠀⡆⢻⠀⠀⠀⠀⠀⠀⠀⠀⠏⣼⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⣧⠸⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⡄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠳⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠐⠀⠀⠀⠀⠀⣧⠘⠀⠀⠀⠀⠀⠃⡾⣀⢀⠀⠉⠀⠀⠀⣀⣄⢶⠶⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠈⠀⠀⠀⠀⠀⠀⣿⠈⠀⠀⠀⠏⣼⠀⠀⠀⠀⣄⢷⠾⠶⠳⠙⠉⠈⡀⣄⢷⠻⠉⠟⠶⠻⠀⠀⠀⠀⠀⠀⠀ ⡄⢻⠈⠀⠀⠀⠀⠀⡄⢻⠀⠀⠟⣼⠀⠀⠀⠀⠀⠀⠀⣆⠻⠀⠀⣀⣄⣤⢦⠶⡶⣴⢀⠀⣇⠙⠀⠀⠀⠀⠀⠀ ⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⡟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⠀⠀⠀⠀⠀⠀⠁⡿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⣧⠹⠀⠀⠀⠀⠀ ⠀⠀⣇⠸⢀⠀⠀⠁⠟⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡍⣭⣉⣉⣦⠻⠀⠀⠀⣧⠸⠀⠀⠀⠀ ⠀⠀⡆⢹⠀⠀⠄⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠰⡁⣿⣿⣹⣀⣀⣄⣦⣷⢹⠀⠀⡆⢹⠇⠰⠀⠀ ⠀⠀⠀⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣰⠃⡿⣿⣿⣿⠹⠀⠀⠀⠀⣄⢷⡿⣤⣧⠻⠈⠀⠀ ⠀⠀⠀⡄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣰⠀⡿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⡀⣿⢿⠈⡄⢷⠈⠀ ⠀⠀⠀⠁⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣼⠀⡇⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⣧⣿⢿⠀⡀⣷⠈ ⠀⠀⠀⡄⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⡇⣿⣿⢸⠀⡆⢸ ⠀⠀⠀⠀⡄⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⢐⠀⠀⠀⠀⡿⣿⣿⢰⠀⠀⣿ ⠀⠀⠀⠀⠀⡀⣷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⢀⠀⠀⠀⠃⣿⣿⣼⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⣄⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⢠⠂⠀⠀⠀⡏⣿⣴⠀⠠⠀⠇⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣸⠀⠀⠀⠀⠏⣾⢠⠀⠀⠁⠛⡶⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⠉⠈⠉⠋⡿⣤⠶⠶⠶⡴⣤⢋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣤⣤⣀⠀⠀⠀⠠⠀⠟⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢦⠳⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣴⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢶⠻⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⡾⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⢤⠤⠶⠲⠓⠛⠛⠛⠛⠓⠶⣤⣀⠀⠀⠀⠀⠀⠀