human
Give me a the Python code you requested given the following:
You are given a sequence of n integers a_1,   a_2,   ...,   a_n.

Does there exist a sequence of n integers b_1,   b_2,   ...,   b_n such that the following property holds?

  * For each 1 ≤ i ≤ n, there exist two (not necessarily distinct) indices j and k (1 ≤ j,   k ≤ n) such that a_i = b_j - b_k. 

Input

The first line contains a single integer t (1 ≤ t ≤ 20) — the number of test cases. Then t test cases follow.

The first line of each test case contains one integer n (1 ≤ n ≤ 10).

The second line of each test case contains the n integers a_1,   ...,   a_n (-10^5 ≤ a_i ≤ 10^5).

Output

For each test case, output a line containing YES if a sequence b_1,   ...,   b_n satisfying the required property exists, and NO otherwise.

Example

Input

5
5
4 -7 -1 5 10
1
0
3
1 10 100
4
-3 2 10 2
9
25 -171 250 174 152 242 100 -205 -258

Output

YES
YES
NO
YES
YES

Note

In the first test case, the sequence b = [-9,   2,   1,   3,   -2] satisfies the property. Indeed, the following holds: 

  * a_1 = 4 = 2 - (-2) = b_2 - b_5.

  * a_2 = -7 = -9 - (-2) = b_1 - b_5.

  * a_3 = -1 = 1 - 2 = b_3 - b_2.

  * a_4 = 5 = 3 - (-2) = b_4 - b_5.

  * a_5 = 10 = 1 - (-9) = b_3 - b_1. 


In the second test case, it is sufficient to choose b = [0], since a_1 = 0 = 0 - 0 = b_1 - b_1.

In the third test case, it is possible to show that no sequence b of length 3 satisfies the property.
The above is tricky. Write me a correct solution in PYTHON3.
assistant
#Here is the Python code you requested.

import sys
input = sys.stdin.readline
def solve():
    n = int(input())
    a = list(map(int,input().split()))

    def possible(j,target):
        # is it possible to have a subset sum a[j...] = target?
        ans = set([0])
        for k in range(j,n):
            to = set()
            for x in ans:
                to.add(x-a[k])
                to.add(x+a[k])
            ans |= to
        return target in ans

    for i in range(n):
        target = a[i]
        if possible(i+1, target):
            print("YES")
            return
    print("NO")
    return

for nt in range(int(input())):
    solve()