Question 137
Let $ABCDE$ be a convex pentagon with $AB = 14$, $BC = 7$, $CD = 24$, $DE = 13$, $EA = 26$, and $\angle B = \angle E = 60^\circ$. For each point $X$ in the plane, define $f(X) = AX + BX + CX + DX + EX$. The least possible value of $f(X)$ can be expressed as $m + n\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.