3SUM Closure

Description:

Input:

The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 1000$$$) — the number of test cases.

The first line of each test case contains an integer $$$n$$$ ($$$3 \leq n \leq 2 \cdot 10^5$$$) — the length of the array.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$-10^9 \leq a_i \leq 10^9$$$) — the elements of the array.

It is guaranteed that the sum of $$$n$$$ across all test cases does not exceed $$$2 \cdot 10^5$$$.

Output:

For each test case, output "YES" (without quotes) if $$$a$$$ is 3SUM-closed and "NO" (without quotes) otherwise.

You can output "YES" and "NO" in any case (for example, strings "yEs", "yes" and "Yes" will be recognized as a positive response).

Sample Input:

4
3
-1 0 1
5
1 -2 -2 1 -3
6
0 0 0 0 0 0
4
-1 2 -3 4

Sample Output:

YES
NO
YES
NO

Note:

In the first test case, there is only one triple where $$$i=1$$$, $$$j=2$$$, $$$k=3$$$. In this case, $$$a_1 + a_2 + a_3 = 0$$$, which is an element of the array ($$$a_2 = 0$$$), so the array is 3SUM-closed.

In the second test case, $$$a_1 + a_4 + a_5 = -1$$$, which is not an element of the array. Therefore, the array is not 3SUM-closed.

In the third test case, $$$a_i + a_j + a_k = 0$$$ for all distinct $$$i$$$, $$$j$$$, $$$k$$$, and $$$0$$$ is an element of the array, so the array is 3SUM-closed.