CF1552D Array Differentiation

You 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 $ .

The 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 $ ).

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

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.