Lunar New Year and Number Division

Description:

Input:

The first line contains an even integer $$$n$$$ ($$$2 \leq n \leq 3 \cdot 10^5$$$), denoting that there are $$$n$$$ integers on Bob's homework paper.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \leq a_i \leq 10^4$$$), describing the numbers you need to deal with.

Output:

A single line containing one integer, denoting the minimum of the sum of the square of $$$s_j$$$, which is $$$$$$\sum_{i = j}^{m} s_j^2,$$$$$$ where $$$m$$$ is the number of groups.

Sample Input:

4
8 5 2 3

Sample Output:

164

Sample Input:

6
1 1 1 2 2 2

Sample Output:

27

Note:

In the first sample, one of the optimal solutions is to divide those $$$4$$$ numbers into $$$2$$$ groups $$$\{2, 8\}, \{5, 3\}$$$. Thus the answer is $$$(2 + 8)^2 + (5 + 3)^2 = 164$$$.

In the second sample, one of the optimal solutions is to divide those $$$6$$$ numbers into $$$3$$$ groups $$$\{1, 2\}, \{1, 2\}, \{1, 2\}$$$. Thus the answer is $$$(1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27$$$.