Functions $f$ and $g$ are quadratic, $g(x)=-f(80-x)$ and the graph of $g$ contains the vertex of the graph of $f$. The four $x$-intercepts on the two graphs have $x$-coordinates $x_1,x_2,x_3,x_4$ in increasing order, and $x_3-x_2=120$. Then $x_4-x_1=m+n\sqrt{p}$, where $m,n,p$ are positive integers, and $p$ is not divisible by the square of any prime. What is $m+n+p$?