2025 AIME I Problem 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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.