You are given an integer (n) and a binary string(^{\text{∗}}) (s) of length (n). For a permutation(^{\text{†}}) (p) of length (n) and an integer (x), we define (\text{find}(x)) as in the following pseudocode: We call an integer (x) ((1\le x\le n)) stable if and only if (\text{find}(x)) is always not undefined and (p_{\text{find}(x)}=x) always holds, no matter how the value of (m) is selected in the process of the pseudocode. You have to construct a permutation (p) of length (n), such that: For each (1\le i\le n), the integer (i) is stable if and only if (s_i=\mathtt{1}). Or determine that no such permutation exists. (^{\text{∗}})A binary string is a string where each character is either (\mathtt{0}) or (\mathtt{1}). (^{\text{†}})A permutation of length (n) is an array consisting of (n) distinct integers from (1) to (n) in arbitrary order. For example, (2,3,1,5,4) is a permutation, but (1,2,2) is not a permutation ((2) appears twice in the array), and (1,3,4) is also not a permutation ((n=3) but there is (4) in the array). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains a single integer (n) ((2\le n \le 2\cdot 10^5)) — the length of the permutation. The second line contains the binary string (s) of length (n) ((s_i=\mathtt{0}) or (\mathtt{1})). It is guaranteed that the sum of (n) over all test cases does not exceed (2\cdot 10^5). For each test case: If no such permutation exists, print " NO " in the only line of output. Otherwise, print " YES " in the first line of output. Then output (n) distinct integers (p_1, p_2, \ldots, p_n) ((1\le p_i\le n)) in the second line — the permutation you constructed. You can output the t