Problem: You are given a binary string s consisting of n zeros and ones.

Your task is to divide the given string into the minimum number of subsequences in such a way that each character of the string belongs to exactly one subsequence and each subsequence looks like "010101 ..." or "101010 ..." (i.e. the subsequence should not contain two adjacent zeros or ones).

Recall that a subsequence is a sequence that can be derived from the given sequence by deleting zero or more elements without changing the order of the remaining elements. For example, subsequences of "1011101" are "0", "1", "11111", "0111", "101", "1001", but not "000", "101010" and "11100".

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.

The first line of the test case contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of s. The second line of the test case contains n characters '0' and '1' — the string s.

It is guaranteed that the sum of n does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).

Output

For each test case, print the answer: in the first line print one integer k (1 ≤ k ≤ n) — the minimum number of subsequences you can divide the string s to. In the second line print n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ k), where a_i is the number of subsequence the i-th character of s belongs to.

If there are several answers, you can print any.

Example

Input


4
4
0011
6
111111
5
10101
8
01010000


Output


2
1 2 2 1 
6
1 2 3 4 5 6 
1
1 1 1 1 1 
4
1 1 1 1 1 2 3 4 

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.lang.reflect.Array;
import java.util.*;
import java.util.function.BiFunction;
import java.util.jar.JarOutputStream;
import java.util.Comparator;



public class Main {

    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        int cases = Reader.nextInt();

        for(int p=0;p<cases;p++){
            int n=Reader.nextInt();
            String s=Reader.nextLine();
            Stack<Integer> res0 = new Stack<>();
            Stack<Integer> res1 = new Stack<>();
            int[] res=new int[n];
            //ArrayList<String> seq = new ArrayList<>();
            int max=0;
            for(int i=0;i<s.length();i++){
                if(s.charAt(i)=='0'){
                    if(res1.isEmpty()){
                        max++;
                        res[i]=max;
                        res0.push(max);
                    }
                    else{
                        int index = res1.pop();
                        res0.push(index);
                        res[i]=index;
                    }
                }
                else{
                    if(res0.isEmpty()){
                        max++;
                        res[i]=max;
                        res1.push(max);
                    }
                    else{
                        int index = res0.pop();
                        res1.push(index);
                        res[i]=index;
                    }
                }
            }

            System.out.println(max);
            for(int i=0;i<n;i++){
                System.out.print(res[i]+" ");
            }
            System.out.println();
        }
    }

}


class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }

    /** get next word */
    static String nextLine() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                    reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( nextLine() );
    }
    static long nextLong() throws IOException {
        return Long.parseLong(nextLine());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble( nextLine() );
    }

    static float nextFloat() throws IOException {
        return Float.parseFloat( nextLine() );
    }
    static int[] nextIntArray(int length) throws IOException {
        int[] arr = new int[length];
        //System.out.println(length);
        for (int i=0; i<length; i++) {
            arr[i] = Integer.parseInt( nextLine() );
            //System.out.println(arr[i]);
        }
        //System.out.println(arr);
        return arr;
    }
    static long[] nextLongArray(int length) throws IOException {
        long[] arr = new long[length];
        for (int i=0; i<length; i++) {
            arr[i] = Long.parseLong( nextLine() );
        }
        return arr;
    }

}