[Solution] 3SUM Closure Codeforces Solution

[Solution] 3SUM Closure Codeforces Solution | Codeforces Problem Solution 2022

C. 3SUM Closure

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given an array a$a$ of length n$n$. The array is called 3SUM-closed if for all distinct indices i$i$, j$j$, k$k$, the sum ai+aj+ak$a_i+a_j+a_k$ is an element of the array. More formally, a$a$ is 3SUM-closed if for all integers 1≤i<j<k≤n$1\le i<j<k\le n$, there exists some integer 1≤l≤n$1\le l\le n$ such that ai+aj+ak=al$a_i+a_j+a_k=a_l$.

Determine if a$a$ is 3SUM-closed.

Input

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

The first line of each test case contains an integer n$n$ (3≤n≤2⋅105$3\le n\le 2\cdot {10}^5$) — the length of the array.

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The second line of each test case contains n$n$ integers a1,a2,…,an$a_1,a_2,\dots ,a_n$ (−109≤ai≤109$-{10}^9\le a_i\le {10}^9$) — the elements of the array.

It is guaranteed that the sum of n$n$ across all test cases does not exceed 2⋅105$2\cdot {10}^5$.

Output

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

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 otherwise.

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