You are given a set S of n elements. Do you know how many subsets the set has? It is 2ⁿ where n is the number of elements in S.

For example, consider a set S of 3 elements. S = {1, 2, 3} so S has 2³ = 8 subsets. They are {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}, { }. Here { } is empty set.

In the above example number of subsets of S having at most 2 elements excluding empty set are {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}.

Find subsets which have at most 2 elements excluding empty set in which each element of S must belong to a single a subset i.e. if we take subset for example {1} then we can’t take other subsets containing element 1. Now sum the product of the subsets containing 2 elements with the value of subsets containing single element. Your target will be maximizing this sum.

For example consider a set S= {1, 2, 3, 4, 5, 6}. So the subsets of S having at most 2 elements excluding the empty set are {1}, {2}, {3}, {4}, {5}, {6}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, {2, 3}, {2, 4}, {2, 5}, {2, 6}, {3, 4}, {3, 5}, {3, 6}, {4, 5}, {4, 6}, {5, 6}.

Now we can take subsets of {5, 6}, {4, 3} and {1, 2} which contains all 6 elements of S then total sum  will be = (5 * 6) + (4 * 3) + (1 * 2) = 44. On the other hand if we take subsets of {5, 6}, {4, 3} and {1} and {2} then total sum will be (5 * 6) + (4 * 3) + 1 + 2 = 45 which is greater than the previous one.

Input

The first line of the input will be an integer T to represent the number of test cases. For each case there will be two lines. The first line contains integer n — the number of distinct elements in the given set S. The second line contains n integers s_i (i = 1, 2 ... n) — the elements of the S.

Output

In a single line, output the maximum sum.

Constraints

• 1 ≤ T ≤ 100
• 1 ≤ n ≤ 100
• -10000 ≤ s_i ≤ 10000

Example

Input:
2
6
1 2 3 4 5 6
3
1 2 3

Output:
45
7