human
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.
Using python3 can you solve the prior task?

What is a the Python program you requested?
assistant
#Here is the Python program you requested.

def main():
    t = int(input())
    for i in range(t):
        c = int(input())
        s = set()
        k = 999999
        for j in map(int, input().split()):
            # s.add(j)
            s.add(abs(j))
            k = min(abs(j), k)
        if len(s) < c or k == 0:
            print("YES")
            continue
        m = list(s)
        k = 1 << c
        k += 1
        # print(m)
        flag = False
        for j in range(k):
            t = 0
            L = 0
            for h in range(c):
                if (1 << h) & j != 0:
                    t += m[h]
                    L += 1
            if t in s and L > 1:
                # print(t, bin(j))
                flag = True
                break
            s.add(t)
            # print(bin(j)[2::],": ", t, ' ', m, sep='')
        if flag:
            print("YES")
        else:
            print("NO")

# def main2():
#     md = 998244353
#     n = int(input())
#     m = []
#     xs = []
#     ys = []
#     res = 0
#     for i in range(n):
#         m.append(list(map(int, input().split())))
#         ys.append(m[-1][1])
#         m[-1].append(1)
#         res = max(m[-1][0] + 1, res) % md
#     m.sort()
#     ys.sort()
#     pos_y = 0
#     k = 0
#     # print(*ys)
#     # print(*m)
#     for i in range(n):
#         while pos_y < n and ys[pos_y] <= m[i][0]:
#             k += 1
#             pos_y += 1
#         m[i][3] += k
#         k -= 1
#     print(*m)
#     for i in range(n):
#         print(res, m[i])
#         if m[i][2] == 0:
#             res += m[i][3] // 2 * (m[i][0] - m[i][1])
#             res %= md
#         elif m[i][2] == 1:
#             res += (m[i][3] + 1) // 2 * (m[i][0] - m[i][1])
#             res %= md
#     print(res % md)

main()