Hexagon

Problem Description

Given the lengths of the six sides of a hexagon in clockwise order, where all six interior angles are $120^{\circ}$, find the number of equilateral triangles with side length of $1$ that the hexagon can be divided into. Ensure that the hexagon can be divided into several equilateral triangles with side length of $1$.

1 1 1 1 1 1

6

1 2 1 2 1 2

13

3 4 2 6 1 5

67

Data Range

Let the side lengths be $a_1...a_n$. For all data, $1\le a_i\le 1000$.

Hints

Example 1: Example 2: Example 3: