Circular Spanning Tree

Description:

Input:

The input consists of multiple test cases. The first line contains a single integer $$$t$$$ $$$(1 \leq t \leq 2\cdot 10^4)$$$  — the number of test cases. Description of the test cases follows.

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

The second line of each test case contains a binary string $$$s$$$ of length $$$n$$$.

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

Output:

For each test case, if there does not exist a tree that satisfies the given conditions, then output "NO" (without quotes), otherwise output "YES" followed by the description of tree.

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

If there exists a tree, then output $$$n - 1$$$ lines, each containing two integers $$$u$$$ and $$$v$$$ $$$(1 \leq u,v \leq n, u \neq v)$$$ denoting an edge between $$$u$$$ and $$$v$$$ in the tree. If there are multiple possible answers, output any.

Sample Input:

3
4
0110
2
10
6
110110

Sample Output:

YES
2 1
3 4
1 4
NO
YES
2 3
1 2
5 6
6 2
3 4

Note:

In the first test case, the tree looks as follows:

In the second test case, there is only one possible tree with an edge between $$$1$$$ and $$$2$$$, and it does not satisfy the degree constraints.

In the third test case,

The tree on the left satisfies the degree constraints but the edges intersect internally, therefore it is not a valid tree, while the tree on the right is valid.