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 $a_i = b_j - b_k$.

给你一个长度为 $n$ 的整数序列 $a_1, \, a_2, \, \dots, \, a_n$。

是否存在一个长度为 $n$ 的整数序列 $b_1, \, b_2, \, \dots, \, b_n$，使得以下性质成立？

• 对每个 $1 \le i \le n$，均存在两个（不一定互异）下标 $j$ 和 $k$（满足 $1 \le j, \, k \le n$），使得 $a_i = b_j - b_k$。

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 $a_1, \, \dots, \, a_n$ ($-10^5 \le a_i \le 10^5$).

第一行包含一个整数 $t$（$1 \le t \le 20$）—— 表示测试用例的数量。随后是 $t$ 个测试用例。

每个测试用例的第一行包含一个整数 $n$（$1 \le n \le 10$）。

每个测试用例的第二行包含 $n$ 个整数 $a_1, \, \dots, \, a_n$（$-10^5 \le a_i \le 10^5$）。

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.

对于每个测试用例，如果存在满足要求性质的序列 $b_1, \, \dots, \, b_n$，则输出一行 YES；否则输出 NO。

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.

在第一个测试用例中，序列 $b = [-9, \, 2, \, 1, \, 3, \, -2]$ 满足该性质。事实上，以下等式成立：

• $a_1 = 4 = 2 - (-2) = b_2 - b_5$；
• $a_2 = -7 = -9 - (-2) = b_1 - b_5$；
• $a_3 = -1 = 1 - 2 = b_3 - b_2$；
• $a_4 = 5 = 3 - (-2) = b_4 - b_5$；
• $a_5 = 10 = 1 - (-9) = b_3 - b_1$。

在第二个测试用例中，只需选择 $b = [0]$ 即可，因为 $a_1 = 0 = 0 - 0 = b_1 - b_1$。

在第三个测试用例中，可以证明：不存在长度为 $3$ 的序列 $b$ 满足该性质。