A13049. Grow The Tree

Gardener Alexey teaches competitive programming to high school students. To congratulate Alexey on the Teacher's Day, the students have gifted him a collection of wooden sticks, where every stick has an integer length. Now Alexey wants to grow a tree from them.

The tree looks like a polyline on the plane, consisting of all sticks. The polyline starts at the point $(0, 0)$ . While constructing the polyline, Alexey will attach sticks to it one by one in arbitrary order. Each stick must be either vertical or horizontal (that is, parallel to $OX$ or $OY$ axis). It is not allowed for two consecutive sticks to be aligned simultaneously horizontally or simultaneously vertically. See the images below for clarification.

Alexey wants to make a polyline in such a way that its end is as far as possible from $(0, 0)$ . Please help him to grow the tree this way.

Note that the polyline defining the form of the tree may have self-intersections and self-touches, but it can be proved that the optimal answer does not contain any self-intersections or self-touches.

The first line contains an integer $n$ ( $1 \le n \le 100\,000$ ) — the number of sticks Alexey got as a present.

The second line contains $n$ integers $a_1, \ldots, a_n$ ( $1 \le a_i \le 10\,000$ ) — the lengths of the sticks.

Print one integer — the square of the largest possible distance from $(0, 0)$ to the tree end.

The following pictures show optimal trees for example tests. The squared distance in the first example equals $5 \cdot 5 + 1 \cdot 1 = 26$ , and in the second example $4 \cdot 4 + 2 \cdot 2 = 20$ .