A beautiful binary matrix is a matrix that has ones on its edges and zeros inside.

Examples of four beautiful binary matrices.

Today, Sakurako was playing with a beautiful binary matrix of size $$$r \times c$$$ and created a binary string $$$s$$$ by writing down all the rows of the matrix, starting from the first and ending with the $$$r$$$-th. More formally, the element from the matrix in the $$$i$$$-th row and $$$j$$$-th column corresponds to the $$$((i-1)*c+j)$$$-th element of the string.

You need to check whether the beautiful matrix from which the string $$$s$$$ was obtained could be squared. In other words, you need to check whether the string $$$s$$$ could have been build from a square beautiful binary matrix (i.e., one where $$$r=c$$$).

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

The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$) — the length of the string.

The second line of each test case contains the string $$$s$$$ of length $$$n$$$. The string is always the result of writing out the strings of a beautiful matrix.

It is guaranteed that the sum of $$$n$$$ across all test cases does not exceed $$$2 \cdot 10^5$$$.
Output format:
Print "Yes", if the original matrix could have been square, and "No" otherwise.
Example Input 0:
5
2
11
4
1111
9
111101111
9
111111111
12
111110011111

Example Output 0:
No
Yes
Yes
No
No

Notes:
For the second test case, string 1111 can be obtained from the matrix:

$$$1$$$$$$1$$$$$$1$$$$$$1$$$

For the third test case, string 111101111 can be obtained from the matrix:

$$$1$$$$$$1$$$$$$1$$$$$$1$$$$$$0$$$$$$1$$$$$$1$$$$$$1$$$$$$1$$$

There is no square matrix in the fourth case, such that the string can be obtained from it.

Example input:
5
2
11
4
1111
9
111101111
9
111111111
12
111110011111


Example output:
No
Yes
Yes
No
No