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:
//      これを翻訳している間、あなたはあなたの人生のいくつかの貴重な瞬間を無駄にしました
//  DO something instead of nothing

import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;


public class Solution {

    static PrintWriter fop = new PrintWriter(System.out);









    public static void main(String[] args) {
        FastScanner fsca = new FastScanner();


        int t = fsca.nextInt();
        while (t-- > 0) {
            int n = fsca.nextInt() ;
            char a[] = fsca.next().toCharArray() ;

            ArrayDeque<Integer> one = new ArrayDeque<>();
            ArrayDeque<Integer> zero = new ArrayDeque<>();
            int tt[] = new int[n] ;
            int cnt = 0 ;

            for (int i = 0; i <n ; i++) {
                char temp = a[i] ;
                if (temp == '0'){
                    if (zero.isEmpty()){
                        cnt++ ;
                        tt[i] = cnt ;
                        one.addLast(cnt);
                    }
                    else {
                        int curr = zero.removeFirst() ;
                        tt[i] = curr ;
                        one.addLast(curr);
                    }
                }
                else {
                    if (one.isEmpty()){
                        cnt++ ;
                        tt[i] = cnt ;
                        zero.addLast(cnt);
                    }
                    else {
                        int curr = one.removeFirst() ;
                        tt[i] = curr ;
                        zero.addLast(curr);
                    }


                }


            }
            fop.append(cnt + "\n") ;
            print(tt , n);
            fop.append("\n") ;
        }












        fop.flush();
        fop.close();


    }
    /*-----------------------------------------------------------------------------------------------------------------------------------------------*/


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

    ;

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


    static final Random random = new Random();

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


    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[][] readMat(int n, int m) {
            int a[][] = new int[n][m];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    a[i][j] = nextInt();
            return a;
        }

        char[][] readCharMat(int n, int m) {
            char a[][] = new char[n][m];
            for (int i = 0; i < n; i++) {
                String s = next();
                for (int j = 0; j < m; j++)
                    a[i][j] = s.charAt(j);
            }
            return a;
        }


        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        long[] readLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }

    static void print(int a[], int n) {
        for (int i = 0; i < n; i++)
            fop.append((a[i]) + " ");
        // fop.append("\n") ;
    }

    static void print(long a[], int n) {
        for (int i = 0; i < n; i++)
            fop.append((a[i]) + " ");
        // fop.append("\n") ;
    }
}