PerMEXuation

 You are given an integer 

N$N$ and a (0$0$-indexed) binary string A$A$ having length N+1$N+1$.

Find any permutation P$P$ of 0,1,2,...,N−1$0,1,2,...,N-1$ (or determine that it does not exist) that satisfies the following conditions for all i$i$ (0≤i≤N$0\le i\le N$):

• if Ai=0$A_i=0$: No contiguous segment of P$P$ has mex$\mathtt{\text{mex}}$ equal to i$i$
• if Ai=1$A_i=1$: There exists at least one contiguous segment of P$P$ that has mex$\mathtt{\text{mex}}$ equal to i$i$

If multiple permutations exist that satisfy the given conditions, print any.

Note: mex$\mathtt{\text{mex}}$ of a segment is the smallest non-negative number that does not occur in that segment.

Input Format

• The first line contains the number of test cases T$T$. Description of the test cases follows.
• The first line of each test case contains a single integer N$N$.
• The second line of each test case contains the binary string A$A$ of length N+1$N+1$.

Output Format

For each test case print :

• Yes$\mathtt{\text{Yes}}$ if there exists a permutation P$P$ that satisfies the conditions described in the statement, followed by the permutation P$P$ in the next line (If multiple permutations exist that satisfy the given conditions, print any).
• No$\mathtt{\text{No}}$ otherwise.

You may print each character of Yes$\mathtt{\text{Yes}}$ and No$\mathtt{\text{No}}$ in uppercase or lowercase (for example, yes$\mathtt{\text{yes}}$, yEs$\mathtt{\text{yEs}}$, YES$\mathtt{\text{YES}}$ will be considered identical).

Constraints

• 1≤T≤104$1\le T\le {10}^4$
• 2≤N≤3⋅105$2\le N\le 3\cdot {10}^5$
• |A|=N+1$|A|=N+1$
• It is guaranteed that the sum of N$N$ over all test cases does not exceed 3⋅105$3\cdot {10}^5$.

Sample Input 1 

4
2
111
5
110100
5
110101
7
11100111

Sample Output 1 

Yes
0 1
No
Yes
0 2 1 4 3
Yes
0 1 3 4 2 5 6

Explanation

Test case-1: One of the possible permutations satisfying the given conditions is [0,1$0,1$] because:

• mex([1])=0$\mathtt{\text{mex}}([1])=0$. Therefore the condition is satisfied for i=0$i=0$.
• mex([0])=1$\mathtt{\text{mex}}([0])=1$. Therefore the condition is satisfied for i=1$i=1$.
• mex([0,1])=2$\mathtt{\text{mex}}([0,1])=2$. Therefore the condition is satisfied for i=2$i=2$.

Test case-2: It can be proven that no permutation exists that satisfies the given conditions.

Test case-3: One of the possible permutations satisfying the given conditions is [0,2,1,4,3$0,2,1,4,3$] because:

• mex([2])=0$\mathtt{\text{mex}}([2])=0$. Therefore the condition is satisfied for i=0$i=0$.
• mex([0,2])=1$\mathtt{\text{mex}}([0,2])=1$. Therefore the condition is satisfied for i=1$i=1$.
• There does not exist any segment with mex=2$\mathtt{\text{mex}}=2$. Therefore the condition is satisfied for i=2$i=2$.
• mex([0,2,1])=3$\mathtt{\text{mex}}([0,2,1])=3$. Therefore the condition is satisfied for i=3$i=3$.
• There does not exist any segment with mex=4$\mathtt{\text{mex}}=4$. Therefore the condition is satisfied for i=4$i=4$.