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.util.*;
import java.lang.*;
public class Codechef {
	PrintWriter out;
    StringTokenizer st;
    BufferedReader br;
 	
 	class Pair implements Comparable<Pair>
	{
	    int f;
	    int s;
 
	    Pair(int t, int r) {
	       f = t;
	       s = r;
	    }
	    public int compareTo(Pair p)
	    {
	    	if(this.f!=p.f)
	    		return this.f-p.f;
 
	    	return this.s-p.s;
	    }
 	}
 // 	class Sort implements Comparator<String> 
	// { 
	//     public int compare(String a, String b) 
	//     { 
	//     	return (a+b).compareTo(b+a);
	//     } 
	// }
 
	String ns() {
        while (st == null || !st.hasMoreElements()) {
 
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
 
    String nextLine() throws Exception {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            throw new Exception(e.toString());
        }
        return str;
    }
 
    int nextInt() {
        return Integer.parseInt(ns());
    }
 
    long nextLong() {
        return Long.parseLong(ns());
    }
 
    double nextDouble() {
        return Double.parseDouble(ns());
    }
	
	int upperBound(long a[],long key)
	{
		int l=0,r=a.length-1;
		int i=-1;
 
		while(l<=r)
		{
			int mid=(l+r)/2;
 
			if(a[mid]<key)
				l=mid+1;
 
			else{
				i=mid;	
				r=mid-1;
			}
			
		}
		return i;
	}
	int lowerBound(Pair[] a , long key)
	{
		int l = 0, r = a.length- 1;
		int i = -1;
 	
		while(l<=r)
		{
			int mid=(l+r)/2;
 
			if(a[mid].f<key)
			{
				i=mid;
				l=mid+1;	
			}
 
			else
				r=mid-1;
			
		}
		return i;
	}
 
	long power(long x,long y)
	{
	    long ans=1;
	    
	    while(y!=0)
	    {
	        if(y%2==1) ans=(ans*x)%mod;
	        x=(x*x)%mod;
	        y/=2;
	    }
	    return ans%mod;
	}
	
 
	int mod= 1000000007;
	long gcd(long x ,long y)
	{
		if(y==0)
			return x;
		return gcd(y,x%y);
	}
 
	// ArrayList<Integer> a[];
	// TreeMap<Integer, Long> map;
	// int vis[];
	// long d[];
	// void dfs(int ver, int m)
	// {
	// 	map.put(ver, d[m % 3]);
	// 	for(int v : a[ver])
	// 	{
	// 		if(vis[v] == 0){
	// 			vis[v] = vis[ver] + 1;
	// 			dfs(v, m + 1);
	// 		}
	// 	}
	// }
 
 	int countSetBits(long n) 
    { 
        int count = 0; 
        while (n > 0) { 
            n &= (n - 1); 
            count++; 
        } 
        return count; 
    }

	void solve() throws IOException{
		int t = nextInt();
		while(t --> 0)
		{
			int n = nextInt();
			char c[] = ns().toCharArray();
			int a[] = new int[n];
			LinkedHashSet<Integer> set = new LinkedHashSet<>();
			for(int i = 0; i < n; i++)
				set.add(i);

			int cnt = 1,s = 0;
			boolean ok = true;
			while(!set.isEmpty()){
				ok = true; 
				int size = set.size();
				Iterator<Integer> itr = set.iterator();
				while(itr.hasNext())
				{
					int i = itr.next();
					if(ok)
					{
						ok = false;
						itr.remove();
						s = i;
						a[s] = cnt;
					}
					if(c[i] != c[s])
					{
						itr.remove();
						a[i] = cnt;
						s = i;
					}
				}
				cnt++;
				if(size - set.size() < 3)
					break;
			}
			ok = true;
			int k = cnt;
			//out.println(k +" " + cnt);
			Iterator<Integer> itr = set.iterator();
			while(itr.hasNext())
			{
				int i = itr.next();
				if(ok)
				{
					ok = false;
					s = i;
				}
				if(c[s] == c[i]){
					a[i] = k++;
					itr.remove();
				}
				else
					break;
			}

			ok = true;
			for(int i : set)
			{
				if(ok)
				{
					ok = false;
					s = i;
				}
				if(c[s] == c[i])
					a[i] = cnt++;
				else
					break;
			}
			out.println(Math.max(k, cnt) - 1);
			for(int i = 0; i < n; i++)
				out.print(a[i] + " ");
			out.println();
		}	
	}
	
	
    void run() throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
		solve();
		out.flush();
 
		out.close();
	}
 
	public static void main(String args[]) throws IOException {
		new Codechef().run();
	}
}