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Given `N`

, consider a convex `N`

-sided polygon with vertices labelled
`A[0], A[i], ..., A[N-1]`

in clockwise order.

Suppose you triangulate the polygon into `N-2`

triangles. For each triangle,
the value of that triangle is the **product** of the labels of the
vertices, and the *total score* of the triangulation is the sum of these values over
all `N-2`

triangles in the triangulation.

Return the smallest possible total score that you can achieve with some triangulation of the polygon.

**Example 1:**

Input:[1,2,3]Output:6Explanation:The polygon is already triangulated, and the score of the only triangle is 6.

**Example 2:**

Input:[3,7,4,5]Output:144Explanation:There are two triangulations, with possible scores: 3*7*5 + 4*5*7 = 245, or 3*4*5 + 3*4*7 = 144. The minimum score is 144.

**Example 3:**

Input:[1,3,1,4,1,5]Output:13Explanation:The minimum score triangulation has score 1*1*3 + 1*1*4 + 1*1*5 + 1*1*1 = 13.

**Note:**

`3 <= A.length <= 50`

`1 <= A[i] <= 100`

All contents and pictures on this website come from the Internet and are updated regularly every week. They are for personal study and research only, and should not be used for commercial purposes. Thank you for your cooperation.