Calin has $n$ buckets, the $i$-th of which contains $a_i$ wooden squares of side length $1$.

Can Calin build a square using all the given squares?

Input

The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($1 \leq n \leq 2 \cdot 10^5$) — the number of buckets.

The second line of each test case contains $n$ integers $a_1, \ldots, a_n$ ($1 \leq a_i \leq 10^9$) — the number of squares in each bucket.

The sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.

Output

For each test case, output "YES" if Calin can build a square using all of the given $1 \times 1$ squares, and "NO" otherwise.

You can output the answer in any case (for example, the strings "yEs", "yes", "Yes" and "YES" will be recognized as a positive answer).

Note

In the first test case, Calin can build a $3 \times 3$ square.

In the second test case, Calin can build a $4 \times 4$ square.

In the third test case, Calin cannot build a square using all the given squares.

Samples

5
1
9
2
14 2
7
1 2 3 4 5 6 7
6
1 3 5 7 9 11
4
2 2 2 2

YES
YES
NO
YES
NO