CF1248B.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.

园丁阿列克谢正在为高中生讲授竞赛编程课程。为了庆祝教师节，学生们送给他一捆木棍作为礼物，每根木棍的长度均为整数。现在阿列克谢想用这些木棍“种”出一棵树。

这棵树在平面上表现为一条由所有木棍构成的折线。该折线起始于点 $(0, 0)$。在构造折线的过程中，阿列克谢将按任意顺序逐根添加木棍。每根木棍必须严格竖直或水平（即分别平行于 $OY$ 轴或 $OX$ 轴）。不允许两根相邻的木棍同时为水平方向或同时为竖直方向。参见下方图示以进一步理解。

阿列克谢希望构造出一条折线，使其终点距离原点 $(0, 0)$ 尽可能远。请帮助他以这种方式“种”出这棵树。

注意：定义树形状的折线允许自相交或自接触；但可以证明，最优解中不会出现任何自相交或自接触。

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.

第一行包含一个整数 $n$（$1 \le n \le 100\,000$）—— Alexey 收到的木棍数量。

第二行包含 $n$ 个整数 $a_1, \ldots, a_n$（$1 \le a_i \le 10\,000$）—— 各木棍的长度。

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

输出一个整数——树的末端到点 $(0, 0)$ 的最大可能距离的平方。

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 $4 \cdot 4 + 2 \cdot 2 = 20$.

以下图片展示了示例测试的最优树。第一个示例中的平方距离为 $5 \cdot 5 + 1 \cdot 1 = 26$，第二个示例中为 $4 \cdot 4 + 2 \cdot 2 = 20$。