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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

public class First {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        int t;
        t = in.nextInt();
        //t = 1;
        while (t > 0) {
            solver.call(in,out);
            t--;
        }
        out.close();
    }

    static class TaskA {
        public void call(InputReader in, PrintWriter out) {
            int n, a = 0;
            n = in.nextInt();

            char[] arr = in.next().toCharArray();
            int[] ans = new int[n];

            LinkedList<Integer> zeros = new LinkedList<>();
            LinkedList<Integer> ones = new LinkedList<>();

            for (int i = 0; i < n; i++) {
                if(arr[i]=='0'){
                    if(ones.size()==0){
                        a++;
                        ans[i] = a;
                    }
                    else{
                        ans[i] = ones.getFirst();
                        ones.remove(0);
                    }
                    zeros.add(ans[i]);
                }
                else{
                    if(zeros.size()==0){
                        a++;
                        ans[i] = a;
                    }
                    else{
                        ans[i] = zeros.getFirst();
                        zeros.remove(0);
                    }
                    ones.add(ans[i]);
                }
            }

            out.println(a);

            for (int i = 0; i < n; i++) {
                out.print(ans[i]+" ");
            }

            out.println();

        }
    }

    static int gcd(int a, int b)
    {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    static int lcm(int a, int b)
    {
        return (a / gcd(a, b)) * b;
    }

    static class answer implements Comparable<answer>{
        int a,b;

        public answer(int a, int b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public int compareTo(answer o) {
            return this.a - o.a;
        }
    }

    static class arrayListClass {
        ArrayList<Integer> arrayList2 ;

        public arrayListClass(ArrayList<Integer> arrayList) {
            this.arrayList2 = arrayList;
        }
    }

    static long gcd(long a, long b)
    {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    static void sort(long[] a) {
        ArrayList<Long> l=new ArrayList<>();
        for (long i:a) l.add(i);
        Collections.sort(l);
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }

    static final Random random=new Random();

    static void shuffleSort(int[] a) {
        int n=a.length;
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n), temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong(){
            return Long.parseLong(next());
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }

    }
}