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.HashSet;
import java.util.Vector;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main
{
    public static void main(String[] args)
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD
    {
        public void solve(int testNumber, Scanner in, PrintWriter out)
        {
            int T = in.nextInt();
            while (T-- > 0)
            {
                solve(in, out);
            }
        }

        private void solve(Scanner in, PrintWriter out)
        {
            int N = in.nextInt();
            String S = in.next();

            int nSequences = 1;
            Stack<Sequence> allEndWithZero = new Stack<>();
            Stack<Sequence> allEndWithOne = new Stack<>();

            int idx = 0;
            for (char c : S.toCharArray())
            {
                if (c == '0')
                {
                    if (!allEndWithOne.isEmpty())
                    {
                        Sequence one = allEndWithOne.pop();
                        one.indices.add(idx);
                        allEndWithZero.push(one);
                    } else
                    {
                        Sequence zero = makeNew(nSequences);
                        nSequences++;
                        zero.indices.add(idx);
                        allEndWithZero.add(zero);
                    }
                } else if (c == '1')
                {
                    if (!allEndWithZero.isEmpty())
                    {
                        Sequence zero = allEndWithZero.pop();
                        zero.indices.add(idx);
                        allEndWithOne.push(zero);
                    } else
                    {
                        Sequence one = makeNew(nSequences);
                        nSequences++;
                        one.indices.add(idx);
                        allEndWithOne.add(one);
                    }
                } else
                    throw new IllegalArgumentException();
                idx++;
            }
            int location[] = new int[S.length()];

            while (!allEndWithOne.isEmpty())
            {
                Sequence s = allEndWithOne.pop();
                for (int i : s.indices)
                {
                    location[i] = s.id;
                }
            }
            while (!allEndWithZero.isEmpty())
            {
                Sequence s = allEndWithZero.pop();
                for (int i : s.indices)
                {
                    location[i] = s.id;
                }
            }
            out.println(nSequences - 1);
            CPUtils.printIntArray(location, out);
            out.println();
        }

        Sequence makeNew(int nSequences)
        {
            Sequence sequence = new Sequence();
            sequence.id = nSequences;
            return sequence;
        }

    }

    static class CPUtils
    {
        public static void printIntArray(int[] array, PrintWriter out)
        {
            StringBuilder stringBuilder = new StringBuilder();
            for (int i = 0; i < array.length; i++)
            {
                stringBuilder.append(array[i] + " ");
            }
            out.print(stringBuilder.toString());
        }

    }

    static class Sequence
    {
        int id;
        Set<Integer> indices = new HashSet<>();

    }
}