Lunar New Year and Number Division

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

There are n positive integers a1,a2,…,an 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 sj. Bob's aim is to minimize the sum of the square of sj, that is

\sum j = m .

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), denoting that there are n integers on Bob's homework paper.

The second line contains n integers a1,a2,…,an (1≤ai≤10), 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 sj, which is

\sum i = m

where m is the number of groups.

Examples

Input

4
8 5 2 3

Output

Input

6
1 1 1 2 2 2

Output

27

Solution

n = int(input())

a = list(map(int, input().split()))

a.sort()

ans = 0

for i in range(n // 2):

pair_sum = a[i] + a[n - 1 - i]

ans += pair_sum * pair_sum

print(ans)

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