⠀⠀⠀⠀⣨⣿⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣳⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⣰⣿⣿⣳⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡰⠀⠀⠀⠀⠀⠀⠀⣿⣿⠓⠀⠀⠀⠀⠀⢀⣼⣿⣿⣳⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⢀⣠⡰⠀⠀⠀⠀⠀⠀⣬⣿⣿⡿⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣳⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠰⠀⠀⠀⠀⣀⠰⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣠⣿⣿⣷⠀⠀⠀⣼⣿⣷⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⠰⠀⠀⠀⠀⣬⣿⣿⠐⠀⣨⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠰⠀⠀⠀⠀⣬⣿⣿⠐⠀⣠⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⣯⣿⠑⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⣸⣿⣿⣿⣿⠐⠀⠀⠀⠀⣬⣿⣿⣷⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠰⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡰⣠⣿⣿⣷⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⠑⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⠱⣀⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⠳⣀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣯⣿⠑⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣬⣿⣿⣷⠀⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣼⣿⣿⣿⠳⠀⠀⠀⣿⣿⣿⠑⠀⠀⠀⣬⣿⣿⣿⣿⣿⣿⣿⣿⠱⠀⠀⠀⣿⣿⣿⠳⣿⣿⣿⣿⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⠱⠀⠀⠀⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⠑⠀⠀⠀⠀⣮⣿⠐⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠀⠀⠀⣬⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⠀⣿⣿⣿⡿⠀⠀⢏⣿⣿⣷⠀⠀⠀⣿⣿⣿⣻⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⠀⠀⢏⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⡿⠏⣯⣿⣿⣿⠳⠀⠀⠀⠀⣮⣿⠁⠀⠀⠀⣌⣿⣿⠗⠀⠀⢎⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⣿⡿⠏⣏⣿⣿⣿⣷⠀⠀⠀⣬⣿⣿⡿⠀⠀⠀⣌⣿⣿⣿⠇⠀⠀⣯⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⡿⠏⣯⣿⣿⣿⠏⠎⡏⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⣾⣿⣿⣿⠓⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⢈⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⣿⣿⣿⠓⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣬⣿⣿⠀⠀⠀⠀⢎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠿⠀⠀⠀⣏⣿⣿⣿⠀⠀⠀⣬⣿⣿⣷⠀⠀⠀⣾⣿⣿⠿⠀⠀⠀⠈⣿⣿⣿⠑⠀⠀⣌⣿⣿⣿⠀⠀⠀⣿⣿⣿⠑⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⣀⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣬⣿⣿⡿⠀⠀⠀⠀⣎⣿⣿⠐⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⢈⣿⣿⣿⠀⠀⠀⠀⣎⣿⣿⠐⠀⠀⣿⣿⣿⣿⠓⠀⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⡿⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠁⠀⠀⠀⢈⣿⣿⣿⠑⠀⠀⣎⣿⣿⣷⠀⠀⠀⣿⣿⣿⠑⠀⠀⠀⠀⣯⣿⣿⡳⠀⠀⣬⣿⣿⠷⠀⠀⠀⣯⣿⣿⠳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣾⣿⣿⠳⠀⠀⠀⠀⣌⣿⣿⠱⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⣌⣿⣿⡿⠀⠀⠀⠀⣌⣿⣿⠱⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠐⠀⠀⠀⠀⣿⣿⣿⠳⠀⠀⣎⣿⣿⡿⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⣎⣿⣿⡷⠀⠀⣾⣿⣿⠳⠀⠀⠀⣎⣿⣿⡳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣉⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣿⣿⣿⠓⠀⠀⠀⠀⢈⣿⣿⠳⠀⠀⣿⣿⣿⣿⠓⠀⠀⠀⠀⣮⣿⣿⠷⠀⠀⠀⠀⢈⣿⣿⠳⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⡳⠀⠀⣬⣿⣿⡿⠀⠀⣈⣿⣿⣿⠀⠀⠀⠀⠀⣌⣿⣿⣿⠀⠀⣾⣿⣿⠳⠀⠀⠀⣎⣿⣿⡷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣿⣿⣿⠑⠀⠀⠀⠀⢈⣿⣿⡳⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⠳⠀⠀⠀⠀⢈⣿⣿⡳⠀⠀⣿⣿⣿⡷⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⣿⣿⣳⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠐⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⣎⣿⣿⣷⠀⠀⣌⣿⣿⣿⠀⠀⠀⠀⠀⢌⣿⣿⣿⠀⠀⣿⣿⣿⠳⠀⠀⠀⣬⣿⣿⡷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣿⣿⣿⣱⣰⣰⣰⣰⣸⣿⣿⡳⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⣾⣿⣿⣳⣰⣰⣰⣰⣸⣿⣿⡳⠀⠀⣿⣿⣿⡷⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠁⠀⠀⠀⠀⣯⣿⣿⣷⠀⠀⣎⣿⣿⡿⠀⠀⣬⣿⣿⣿⠀⠀⠀⠀⠀⢌⣿⣿⣿⠀⠀⣯⣿⣿⠳⠀⠀⠀⣬⣿⣿⡷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⠀⠀⣿⣿⣿⡷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠐⠀⠀⠀⠀⣮⣿⣿⣷⠀⠀⣎⣿⣿⣷⠀⠀⣬⣿⣿⣿⠀⠀⠀⠀⠀⢌⣿⣿⣿⠀⠀⣯⣿⣿⠳⠀⠀⠀⣬⣿⣿⠷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠁⠀⠀⠀⠀⣮⣿⣿⣷⠀⠀⣬⣿⣿⡿⠀⠀⣬⣿⣿⣿⠀⠀⠀⠀⠀⢌⣿⣿⣿⠐⠀⣎⣿⣿⡳⠀⠀⠀⣮⣿⣿⠳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠱⠀⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠐⠀⠀⠀⠀⣮⣿⣿⡿⠀⠀⣎⣿⣿⡿⠀⠀⣮⣿⣿⣿⠀⠀⠀⠀⠀⣈⣿⣿⣿⠐⠀⣌⣿⣿⣿⠀⠀⠀⣿⣿⣿⠓⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⠀⣿⣿⣿⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣿⣿⣿⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠐⠀⠀⠀⠀⣮⣿⣿⡿⠀⠀⣬⣿⣿⣷⠀⠀⣎⣿⣿⣿⠀⠀⠀⠀⠀⣈⣿⣿⣿⠁⠀⠈⣿⣿⣿⣳⣰⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣍⣿⣿⣿⠐⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⠀⣯⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣏⣿⣿⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠐⠀⠀⠀⠀⣮⣿⣿⡿⠀⠀⣬⣿⣿⣷⠀⠀⣎⣿⣿⣿⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠗⠀⣿⣿⣿⡳⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣿⣿⣿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⠀⣯⣿⣿⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣿⣿⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠐⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⣬⣿⣿⡿⠀⠀⣎⣿⣿⣿⠀⠀⠀⠀⠀⣈⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⣮⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣿⣿⣿⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⠀⣎⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⠷⠀⠀⣬⣿⣿⡿⠀⠀⣌⣿⣿⣿⠀⠀⠀⠀⠀⣌⣿⣿⣿⠀⠀⢈⣿⢟⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⢈⣿⣿⣿⠑⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣮⣿⣿⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⠀⣌⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠐⠀⠀⠀⠀⣿⣿⣿⠳⠀⠀⣬⣿⣿⡿⠀⠀⢈⣿⣿⣿⠐⠀⠀⠀⠀⣬⣿⣿⣿⠀⠀⣈⣿⠁⠀⠌⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⡷⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣌⣿⣿⣿⠀⠀⠀⠀⠀⠀⣬⠱⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⠀⢈⣿⣿⣿⠀⠀⠀⠀⠀⠀⣬⠱⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡳⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⠁⠀⠀⠀⢀⣿⣿⣿⠓⠀⠀⣎⣿⣿⡿⠀⠀⠈⣿⣿⣿⠑⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⣌⣿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣎⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⢈⣿⣿⣿⠰⠀⠀⠀⠀⣈⣿⠱⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⣈⣿⠱⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣿⠱⠀⠀⠀⠀⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠱⠀⠀⠀⣬⣿⣿⣿⠀⠀⠀⣬⣿⣿⣷⠀⠀⠀⣿⣿⣿⣳⠀⠀⠀⢀⣿⣿⣿⠳⠀⠀⣌⣿⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⠱⠀⠀⠀⣿⣿⣿⠑⠀⠀⠀⣿⣿⣿⣿⠰⠀⠀⣸⣿⣿⠳⠀⠀⣿⣿⣿⡳⠀⠀⠀⠀⠀⠀⣮⣿⣿⣿⠰⠀⠀⣸⣿⣿⠳⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡰⠀⠀⣬⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⣿⠐⠀⣠⣿⣿⣿⣿⠀⠀⠀⣎⣿⣿⡿⠀⠀⠀⣎⣿⣿⣿⡱⠀⠀⣾⣿⣿⣿⠁⠀⠀⢌⣿⣿⣿⣿⣿⣿⣿⣷⣰⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣯⣿⣿⣷⠀⠀⠀⣿⣿⣿⠑⠀⠀⠀⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠀⠀⠀⣎⣿⣿⡿⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢌⣿⣿⣿⠐⠀⠀⣿⣿⣿⠑⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣯⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⠷⠀⠀⠀⠀⣯⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣎⣿⣿⡿⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀
⠀⠀⠀⠀⣮⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠑⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣮⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣮⣿⣿⠓⠀⠀⠀⠀⣮⣿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⢌⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣌⣿⣿⡷⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⠀⠀⠀
⠀⠀⠀⠀⠀⠎⠁⠀⠀⠀⠀⠀⠈⠎⠇⠀⠀⠀⠈⠏⠃⠀⠀⠀⠀⠀⠀⠀⢏⣯⣿⡿⠏⠀⠀⠀⠀⠀⠀⠎⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣯⣿⡿⠏⠀⠀⠀⠀⠀⠀⠎⠇⠀⠀⠀⠀⠀⠀⠎⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣏⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠏⠃⠀⠌⣯⣿⠿⠁⠀⠀⠀⠀⠀⠀⠎⠇⠀⠀⠀⠀⠀⠀⠀⠎⣯⣿⣿⠿⠁⠀⠀⠀⠀⠀⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠏⠏⠏⠏⣏⣿⣿⣿⡷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠳⠀⠀⠀⠀⠀⠀⠌⣿⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠑⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠱⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡳⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠰⠀⠀⠀⠀⠀⣼⣿⣿⠷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣳⣰⣰⣸⣿⣿⣿⣿⠑⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠎⠇⠇⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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.
I'm going to write a list of all the concerts I go to this year
- [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
Books I've Read this Year so Far:
- 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.