You are given a regular $$$N$$$-sided polygon. Label one arbitrary side as side $$$1$$$, then label the next sides in clockwise order as side $$$2$$$, $$$3$$$, $$$\dots$$$, $$$N$$$. There are $$$A_i$$$ special points on side $$$i$$$. These points are positioned such that side $$$i$$$ is divided into $$$A_i + 1$$$ segments with equal length.

For instance, suppose that you have a regular $$$4$$$-sided polygon, i.e., a square. The following illustration shows how the special points are located within each side when $$$A = [3, 1, 4, 6]$$$. The uppermost side is labelled as side $$$1$$$.

$\text{[math]}$

You want to create as many non-degenerate triangles as possible while satisfying the following requirements. Each triangle consists of $$$3$$$ distinct special points (not necessarily from different sides) as its corners. Each special point can only become the corner of at most $$$1$$$ triangle. All triangles must not intersect with each other.

Determine the maximum number of non-degenerate triangles that you can create.

A triangle is non-degenerate if it has a positive area.

Input

The first line consists of an integer $$$N$$$ ($$$3 \leq N \leq 200\,000$$$).

The following line consists of $$$N$$$ integers $$$A_i$$$ ($$$1 \leq A_i \leq 2 \cdot 10^9$$$).

Output

Output a single integer representing the maximum number of non-degenerate triangles that you can create.

Note

Explanation for the sample input/output #1

One possible construction which achieves maximum number of non-degenerate triangles can be seen in the following illustration.

$\text{[math]}$

Explanation for the sample input/output #2

One possible construction which achieves maximum number of non-degenerate triangles can be seen in the following illustration.

$\text{[math]}$

Triangle Construction

Examples