C. Can I Square?
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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).

Example
Input
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
Output
YES
YES
NO
YES
NO
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.