Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.

There are n positive integers a_1, a_2, …, a_n on Bob's homework paper, where n is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least 2 numbers. Suppose the numbers are divided into m groups, and the sum of the numbers in the j-th group is s_j. Bob's aim is to minimize the sum of the square of s_j, that is $$$∑_{j = 1}^{m} s_j^2.$$$

Bob is puzzled by this hard problem. Could you please help him solve it?

Input

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

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 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 $$$∑_{i = j}^{m} s_j^2, where m$$$ is the number of groups.

Examples

Input


4
8 5 2 3


Output


164


Input


6
1 1 1 2 2 2


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.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;

public class force1 {
	static Long [][]memo;
	static int[]arr1,arr2,val;
	static int n,m;
	static long INF=(long)(1e16);
	static HashMap<Integer, Integer>hm1,hm2;
	static long dp(int i ,int j) {
		if(i>=n&&j>=m) {
			return 0;
		}
		if(i>=n)return INF;
		if(memo[i][j]!=null)return memo[i][j];
		long take=INF;
		long leave= INF;
		if(j<m&&arr1[i]==arr2[j]) {
			take=dp(i+1,j+1);
		}
		if(hm1.get(arr1[i])==null||!(j>hm1.get(arr1[i])&&j<hm2.get(arr1[i]))) {
			leave=dp(i+1,j);
		}
		if(leave!=INF)leave+=val[i];
		return memo[i][j]=Math.min(take, leave);
	}
	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader  br= new BufferedReader(new InputStreamReader( System.in));
		PrintWriter pw = new PrintWriter(System.out);
		Scanner sc =new Scanner(System .in);
		int n = sc.nextInt();
		Integer []x=new Integer[n];
		for(int i=0;i<n;i++) {
			x[i]=sc.nextInt();
		}
		Arrays.sort(x);
		long sum=0l;
		for(int i=0;i<n/2;i++) {
			sum+=(x[i]+x[n-1-i])*(x[i]+x[n-1-i]);
		}
		System.out.println(sum);
		
   }

}


