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.*;
import java.math.BigInteger;
import java.util.*;

public class Solution{
    public static void main(String[] args){
        try {
            PrintWriter out=new PrintWriter(System.out,true);
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            int t=Integer.parseInt(br.readLine());
            for(int i=0;i<t;i++) {
                int n=Integer.parseInt(br.readLine());
                String ss = br.readLine();
                int grp=1;
                ArrayList<Integer> o=new ArrayList<>(),z=new ArrayList<>();
                int[] arr=new int[n];
                int size=0;
                StringBuilder str=new StringBuilder("");
                for(int j=0;j<n;j++){
                    if(ss.charAt(j)=='1'){
                        if(z.size()==0){
                            arr[j]=grp++;
                        }else{
                            arr[j]=arr[z.get(0)];
                            z.remove(0);
                        }
                        o.add(j);
                    }else{
                        if(o.size()==0){
                            arr[j]=grp++;
                        }else{
                            arr[j]=arr[o.get(0)];
                            o.remove(0);
                        }
                        z.add(j);
                    }
                    size=Math.max(size,arr[j]);
                    str.append(arr[j]).append(" ");
                }
                out.println(size);
                out.println(str);


            }



            out.close();
        } catch (Exception e) {
            System.out.println("kkkk "+ e.getMessage());
        }

    }

    static boolean isPal(String s){
        StringBuilder str=new StringBuilder(s);
        str=str.reverse();
        String ss=String.valueOf(str);
        if (ss.equals(s)) {
            return true;
        }
        return false;
    }
    static int mod(int a,int b){
        if (a>b){
            return a-b;
        }
        return b-a;
    }
    static void shuffle(int[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            int temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }
    static int lcm(int a,int b){
        long c=a*b;
        return (int)(c/hcf(a,b));
    }
    static int hcf(int a,int b){
        if(a==0){
            return b;
        }
        if(b==0){
            return a;
        }
        if(a>b)
            return hcf(a%b,b);

        return hcf(a,b%a);
    }
    static void dfs(ArrayList<HashSet<Integer>> list,boolean[] vis,int i){
        vis[i]=true;
        Iterator<Integer> it=list.get(i).iterator();
        while(it.hasNext()){
            int u=it.next();
            if(!vis[u]){
                dfs(list,vis,u);
            }
        }
    }
    static int modInverse(int x,int m){
        return power(x,m-2,m);
    }
    static int power(int x, int y, int m)
    {
        if (y == 0)
            return 1;

        long p = power(x, y / 2, m) % m;
        p = (p * p) % m;

        return (int)((y%2==0)? p : (x*p)%m);
    }
    static class pair{
        int a,b;
        public pair(int a,int b){
            this.a=a;
            this.b=b;
        }
    }
}