D. Array Differentiationtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a sequence of n integers a_1, \, a_2, \, \dots, \, a_n.Does there exist a sequence of n integers b_1, \, b_2, \, \dots, \, b_n such that the following property holds?  For each 1 \le i \le n, there exist two (not necessarily distinct) indices j and k (1 \le j, \, k \le n) such that a_i = b_j - b_k. InputThe first line contains a single integer t (1 \le t \le 20) — the number of test cases. Then t test cases follow.The first line of each test case contains one integer n (1 \le n \le 10).The second line of each test case contains the n integers a_1, \, \dots, \, a_n (-10^5 \le a_i \le 10^5).OutputFor each test case, output a line containing YES if a sequence b_1, \, \dots, \, b_n satisfying the required property exists, and NO otherwise.ExampleInput
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
NoteIn 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.
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

YES YES NO YES YES 
['bitmasks', 'brute force', 'constructive algorithms', 'dfs and similar', 'dp', 'graphs', 'math', '*1800']