Question 14
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 $m + n + p.$