⠀⠀⠀⠀⣨⣿⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣳⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⣰⣿⣿⣳⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡰⠀⠀⠀⠀⠀⠀⠀⣿⣿⠓⠀⠀⠀⠀⠀⢀⣼⣿⣿⣳⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⢀⣠⡰⠀⠀⠀⠀⠀⠀⣬⣿⣿⡿⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣳⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠰⠀⠀⠀⠀⣀⠰⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣠⣿⣿⣷⠀⠀⠀⣼⣿⣷⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⠰⠀⠀⠀⠀⣬⣿⣿⠐⠀⣨⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠰⠀⠀⠀⠀⣬⣿⣿⠐⠀⣠⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⣯⣿⠑⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⣸⣿⣿⣿⣿⠐⠀⠀⠀⠀⣬⣿⣿⣷⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠰⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡰⣠⣿⣿⣷⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⠑⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⠱⣀⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⠳⣀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣯⣿⠑⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣬⣿⣿⣷⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⠳⠀⠀⠀⣿⣿⣿⠑⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⠱⠀⠀⠀⣿⣿⣿⠳⣿⣿⣿⣿⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⠱⠀⠀⠀⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⠑⠀⠀⠀⠀⣮⣿⠐⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠀⠀⠀⣬⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⠀⣿⣿⣿⡿⠀⠀⢏⣿⣿⣷⠀⠀⠀⣿⣿⣿⣻⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⠀⠀⢏⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⡿⠏⣯⣿⣿⣿⠳⠀⠀⠀⠀⣮⣿⠁⠀⠀⠀⣌⣿⣿⠗⠀⠀⢎⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⣿⡿⠏⣏⣿⣿⣿⣷⠀⠀⠀⣬⣿⣿⡿⠀⠀⠀⣌⣿⣿⣿⠇⠀⠀⣯⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⡿⠏⣯⣿⣿⣿⠏⠎⡏⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⣾⣿⣿⣿⠓⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⢈⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⣿⣿⣿⠓⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣬⣿⣿⠀⠀⠀⠀⢎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠿⠀⠀⠀⣏⣿⣿⣿⠀⠀⠀⣬⣿⣿⣷⠀⠀⠀⣾⣿⣿⠿⠀⠀⠀⠈⣿⣿⣿⠑⠀⠀⣌⣿⣿⣿⠀⠀⠀⣿⣿⣿⠑⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⣀⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣬⣿⣿⡿⠀⠀⠀⠀⣎⣿⣿⠐⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⢈⣿⣿⣿⠀⠀⠀⠀⣎⣿⣿⠐⠀⠀⣿⣿⣿⣿⠓⠀⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⡿⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠁⠀⠀⠀⢈⣿⣿⣿⠑⠀⠀⣎⣿⣿⣷⠀⠀⠀⣿⣿⣿⠑⠀⠀⠀⠀⣯⣿⣿⡳⠀⠀⣬⣿⣿⠷⠀⠀⠀⣯⣿⣿⠳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣾⣿⣿⠳⠀⠀⠀⠀⣌⣿⣿⠱⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⣌⣿⣿⡿⠀⠀⠀⠀⣌⣿⣿⠱⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠐⠀⠀⠀⠀⣿⣿⣿⠳⠀⠀⣎⣿⣿⡿⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⣎⣿⣿⡷⠀⠀⣾⣿⣿⠳⠀⠀⠀⣎⣿⣿⡳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣉⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣿⣿⣿⠓⠀⠀⠀⠀⢈⣿⣿⠳⠀⠀⣿⣿⣿⣿⠓⠀⠀⠀⠀⣮⣿⣿⠷⠀⠀⠀⠀⢈⣿⣿⠳⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⡳⠀⠀⣬⣿⣿⡿⠀⠀⣈⣿⣿⣿⠀⠀⠀⠀⠀⣌⣿⣿⣿⠀⠀⣾⣿⣿⠳⠀⠀⠀⣎⣿⣿⡷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣿⣿⣿⠑⠀⠀⠀⠀⢈⣿⣿⡳⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⠳⠀⠀⠀⠀⢈⣿⣿⡳⠀⠀⣿⣿⣿⡷⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⣿⣳⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠐⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⣎⣿⣿⣷⠀⠀⣌⣿⣿⣿⠀⠀⠀⠀⠀⢌⣿⣿⣿⠀⠀⣿⣿⣿⠳⠀⠀⠀⣬⣿⣿⡷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣿⣿⣿⣱⣰⣰⣰⣰⣸⣿⣿⡳⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⣾⣿⣿⣳⣰⣰⣰⣰⣸⣿⣿⡳⠀⠀⣿⣿⣿⡷⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠁⠀⠀⠀⠀⣯⣿⣿⣷⠀⠀⣎⣿⣿⡿⠀⠀⣬⣿⣿⣿⠀⠀⠀⠀⠀⢌⣿⣿⣿⠀⠀⣯⣿⣿⠳⠀⠀⠀⣬⣿⣿⡷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⠀⠀⣿⣿⣿⡷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠐⠀⠀⠀⠀⣮⣿⣿⣷⠀⠀⣎⣿⣿⣷⠀⠀⣬⣿⣿⣿⠀⠀⠀⠀⠀⢌⣿⣿⣿⠀⠀⣯⣿⣿⠳⠀⠀⠀⣬⣿⣿⠷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠁⠀⠀⠀⠀⣮⣿⣿⣷⠀⠀⣬⣿⣿⡿⠀⠀⣬⣿⣿⣿⠀⠀⠀⠀⠀⢌⣿⣿⣿⠐⠀⣎⣿⣿⡳⠀⠀⠀⣮⣿⣿⠳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠱⠀⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠐⠀⠀⠀⠀⣮⣿⣿⡿⠀⠀⣎⣿⣿⡿⠀⠀⣮⣿⣿⣿⠀⠀⠀⠀⠀⣈⣿⣿⣿⠐⠀⣌⣿⣿⣿⠀⠀⠀⣿⣿⣿⠓⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⠀⣿⣿⣿⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣿⣿⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠐⠀⠀⠀⠀⣮⣿⣿⡿⠀⠀⣬⣿⣿⣷⠀⠀⣎⣿⣿⣿⠀⠀⠀⠀⠀⣈⣿⣿⣿⠁⠀⠈⣿⣿⣿⣳⣰⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣍⣿⣿⣿⠐⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⠀⣯⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣏⣿⣿⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠐⠀⠀⠀⠀⣮⣿⣿⡿⠀⠀⣬⣿⣿⣷⠀⠀⣎⣿⣿⣿⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠗⠀⣿⣿⣿⡳⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣿⣿⣿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⠀⣯⣿⣿⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣿⣿⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠐⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⣬⣿⣿⡿⠀⠀⣎⣿⣿⣿⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⣮⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣿⣿⣿⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⠀⣎⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⠷⠀⠀⣬⣿⣿⡿⠀⠀⣌⣿⣿⣿⠀⠀⠀⠀⠀⣌⣿⣿⣿⠀⠀⢈⣿⢟⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⢈⣿⣿⣿⠑⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣮⣿⣿⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⠀⣌⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠐⠀⠀⠀⠀⣿⣿⣿⠳⠀⠀⣬⣿⣿⡿⠀⠀⢈⣿⣿⣿⠐⠀⠀⠀⠀⣬⣿⣿⣿⠀⠀⣈⣿⠁⠀⠌⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⡷⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣌⣿⣿⣿⠀⠀⠀⠀⠀⠀⣬⠱⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⠀⢈⣿⣿⣿⠀⠀⠀⠀⠀⠀⣬⠱⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡳⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠁⠀⠀⠀⢀⣿⣿⣿⠓⠀⠀⣎⣿⣿⡿⠀⠀⠈⣿⣿⣿⠑⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⣌⣿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣎⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⢈⣿⣿⣿⠰⠀⠀⠀⠀⣈⣿⠱⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⣈⣿⠱⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⠱⠀⠀⠀⠀⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠱⠀⠀⠀⣬⣿⣿⣿⠀⠀⠀⣬⣿⣿⣷⠀⠀⠀⣿⣿⣿⣳⠀⠀⠀⢀⣿⣿⣿⠳⠀⠀⣌⣿⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⠱⠀⠀⠀⣿⣿⣿⠑⠀⠀⠀⣿⣿⣿⣿⠰⠀⠀⣸⣿⣿⠳⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⠀⠀⣮⣿⣿⣿⠰⠀⠀⣸⣿⣿⠳⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡰⠀⠀⣬⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⣿⠐⠀⣠⣿⣿⣿⣿⠀⠀⠀⣎⣿⣿⡿⠀⠀⠀⣎⣿⣿⣿⡱⠀⠀⣾⣿⣿⣿⠁⠀⠀⢌⣿⣿⣿⣿⣿⣿⣿⣷⣰⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣯⣿⣿⣷⠀⠀⠀⣿⣿⣿⠑⠀⠀⠀⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠀⠀⠀⣎⣿⣿⡿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢌⣿⣿⣿⠐⠀⠀⣿⣿⣿⠑⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣯⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣎⣿⣿⡿⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠀⠀⠀⣮⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣮⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣮⣿⣿⠓⠀⠀⠀⠀⣮⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⢌⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣌⣿⣿⡷⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⠀⠀⠀
⠀⠀⠀⠀⠀⠎⠁⠀⠀⠀⠀⠀⠈⠎⠇⠀⠀⠀⠈⠏⠃⠀⠀⠀⠀⠀⠀⠀⢏⣯⣿⡿⠏⠀⠀⠀⠀⠀⠀⠎⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣯⣿⡿⠏⠀⠀⠀⠀⠀⠀⠎⠇⠀⠀⠀⠀⠀⠀⠎⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣏⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠏⠃⠀⠌⣯⣿⠿⠁⠀⠀⠀⠀⠀⠀⠎⠇⠀⠀⠀⠀⠀⠀⠀⠎⣯⣿⣿⠿⠁⠀⠀⠀⠀⠀⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠏⠏⠏⠏⣏⣿⣿⣿⡷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠳⠀⠀⠀⠀⠀⠀⠌⣿⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠑⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠱⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡳⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠰⠀⠀⠀⠀⠀⣼⣿⣿⠷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣳⣰⣰⣸⣿⣿⣿⣿⠑⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀
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this is my (kieren's) awesome blog that I started because I have theories.
during the day I think lots about lasers, measurement and signals, so most of my theories are avbout these sorts of things
one day I will populate this website with my theories. The main one I am thinking lots about is about how we need a (hilbert) basis space to represent a signal, and how the corresponding 'element' of the hilbert space is kind of the essence of the information in the signal.
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Theories for blog posts (TBD!!! Come back soon)
- The Laplacian as an optimizer & computational caustics
- How to do water mass analysis from inter-satellite interferometry (GRACE Level1B data)
- linear algebra based signal processing: ghost imaging, computed tomography and compressive sensing .
- Hilbert spaces & functional analysis in physics & how to choose a basis space.
I'm going to write a list of all the concerts I go to this year
- [21st Jun 2026] Stereolab @ the Metro Theatre, Sydney
- [13th Jun 2026] Êlêctron 45Cc L=20nm W20nm - Lolo & Sosaku @ Theatre Royal, Hobart
- [12th Jun 2026] Sassy009 @ Altar bar, Hobart
- [11th Jun 2026] Danny Brown @ the Odeon, Hobart
- [ 9th Jun 2026] The Bats / TeeVee Repairmann @ the Polo, Canberra
- [16th May 2026] Cloud Ice Nine / Olivia's World / Angel Waste @ Gang Gang, Canberra
- [ 9th May 2026] Garage Sale + Fear of Horses @ the Lord Gladstone Hotel, Sydney
- [25th Apr 2026] R.M.F.C. @ Gang Gang, Canberra
- [23rd Apr 2026] Masayoshi Takanaka @ Horden Pavillion, Sydney
- [ 4th Apr 2026] Any Young Mechanic @ Vic on the Park, Sydney
- [19th Mar 2026] Institute / R.M.F.C / Negative Gear / Station Model Violence @ Oxford Art Factory, Sydney
- [26th Feb 2026] Puffer @ Gutwrench DIY Summer 5, Campbell Primary School Cola, Canberra
- [13th Feb 2026] Geese / Yung Lean & Bladee / Alex G / Chappell Roan @ Laneway Festival, Melbourne
- [10th Feb 2026] Folk Bitch Trio @ Fed Square, Melboure
- [ 9th Feb 2026] Cameron Winter @ the Forum, Melbourne
- [30th Jan 2026] R.M.F.C. / Silicone Prarie @ the Tote Hotel, Melbourne
- [24th Jan 2026] Twine / Clamm / Shit Fetish @ Blue Evening vol. 3, the Tote Hotel , Melbourne
- [24th Jan 2026] Silicone Prarie / Program @ the Tramway Hotel, Melbourne
- [18th Jan 2026] TeeVee Repairman @ Thornbury Bowls Club, Melbourne
What I'm reading atm: Brave New World by Aldous Huxley
Books I've Read this Year so Far:
- Saudade by Suneeta Peres da Costa. The brunt of this melodic, abrupt, plain, short novella was as a coming of age story, with Angola's independence and the downfall of Portuguese colonial influence forming a vauge periphery. I was compelled by the fragments of culture -in words and food - shared with my own, similarly distant, understanding of my heritage.
- The Tall Man by Chloe Hooper. (for Neighbourhood Book Club!) Matter-of-a-fact reporting (non-fiction creative) into Cameron Domadgee's death in custody and the subsequent legal process. Captivating exploration of the blurring between individuals and insitutional/systematic forces, and the failings of this intersection on indigenous Australians. left me feeling angry, and ashamed of my ignorance, about the degree of disparity in Australia. It does slip into a deficit narrative at times, reflective of its 2007 publish date.
- Tropic of Cancer by Henry Miller. Equal part mix of disgusting perversion and poetic insight. I found the perversion incredibly hard to get through - enough so that I will second guess myself in ever saying 'cunt' outloud again - but eventually the gratuity of the sex scenes kind of started to make sense as part of a broader exploration into the #HumanExperience? A founding text in the genre of plotline lacking, semi-autobiographical novels about self pitying broke artists living in big city - I would reccomend reading 'down and out in paris and london' instead.
- On the Calculation of Volume I by Solvej Balle. Time loop novel where a bookseller lives a year in repetition of the 18th of November. A meditation on the mechanics of a day and the intimacy of sharing a life with a partner. I interpreted it as a breakup allegory. I enjoyed the pace & writing buthave no fucking clue how you could want to read (or write) 6 more parts in the series.
- Call for the Dead by John le Carré. Eminent spy novel author's first spy novel about post WW2 soviet espionage. Entertaining and briefly thrilling but I don't think this genre is my cup of tea. I did like the political tone set (not being mean to the communists) and I will try read 'The Spy Who Came in from the Cold.
- The Passion According to G.H. by Clarice Lispector. Describes having a mental breakdown such that reading feels like drowning. Repetive/rythmic waves of existential crisis driven prose hold you down for pages on end, only ocassionaly relenting to give you a brief gasp for air - moments when the protagonist (seamlessly) reconnects with her surrounds and attempts to deal with a crushed cockroach.
- The Hour of The Star by Clarice Lispector. Novella narrating an impoverished woman's life. The narrator's manic, disparraging tone is - at times - empathetic out of disgust, acting as a social commentary on classism baked into upper-class Brasillians.
- Under the Eye of the Big Bird by Hiromi Kawakami. Collection of stories dealing with human extinction in a sci-fi, post-apocalyptic world. Calming, terse prose covers themes of love, hate and humanity.