## Mexes

Points: 100 (partial)
Time limit: 1.0s
Memory limit: 256M

Author:
Problem type

Given an integer $$n$$ and a binary string $$a$$ of $$n+1$$ characters, find the lexicographically smallest permutation $$P$$ of $${0,1,2,...,n-1}$$ that satisfies the following conditions for all $$i$$ $$0 \leq i \leq n$$ :

if $$a_i = 0$$ : No contiguous segment of $$P$$ has mex equal to $$i$$

if $$a_i = 1$$ : there exists at least one contiguous segment of $$P$$ that has mex equal to $$i$$

#### Input Specification

The first line contains the number of test cases $$t$$ $$(1\leq t \leq 10^4)$$. Description of the test cases follows.

The first line of each test case contains a single integer $$n$$ $$(3 \leq n \leq 3.10^5)$$

The second line of each test case contains the binary string $$a$$ of size equal to $$n+1$$.

It is guaranteed that the sum of $$n$$ over all test cases does not exceed $$3.10^5$$.

#### Output Specification

For each test case print (case sensitive):

• "Yes" if there exists a permutation P that satisfies the conditions described in the statement,followed by the permutation P on a separate line.
• "No" otherwise.

#### Sample input

1
7
00100110

#### Sample output

No

#### Scoring

\begin{array}{|c|c|c|} \hline \text{Group} & \text{Points} & \text{Constraints} \cr \hline 1 & 20 & 3 \leq n \leq 8 \cr \hline 2 & 45 & \text{Sum of $$n$$ over all test cases does not exceed 5000} \cr \hline 3 & 35 & \text{ No additional constraints } \cr \hline \end{array}