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

public class BinaryStringToSubseq
{
	public static void solve() throws IOException
    {
		int n=ni();
		String s=new String(nln());
		Stack<Integer> one=new Stack<>();
		Stack<Integer> zero=new Stack<>();
		int sub=1;
		int a[]=new int[n];
		for(int i=0;i<n;i++)
		{
			if(s.charAt(i)=='0')
			{
				if(one.isEmpty())
				{
					zero.push(sub);
					a[i]=sub;
					sub++;
				}
				else
				{
					int k=one.pop();
					a[i]=k;
					zero.push(k);
				}
			}
			else
			{
				if(zero.isEmpty())
				{
					one.push(sub);
					a[i]=sub;
					sub++;
				}
				else
				{
					int k=zero.pop();
					a[i]=k;
					one.push(k);
				}
			}
		}
		pln(sub-1);
		for(int i=0;i<n;i++)
			p(a[i]+" ");
		pln("");
	}
	static AnotherReader sc;
    static PrintWriter out;
	public static void main (String[] args) throws java.lang.Exception
	{
		boolean oj = true;
        if(oj){sc=new AnotherReader();out=new PrintWriter(System.out);}
        else{sc=new AnotherReader(100);out=new PrintWriter("output.txt");}
        int t=1;
		t=ni();
		long s = System.currentTimeMillis();
        while(t-->0)
			solve();
		//pln(((System.currentTimeMillis() - s)/1000.0) + "s");
		out.flush();out.close();  
	}
	static void pln(Object o){out.println(o);}
    static void p(Object o){out.print(o);}
    static void pni(Object o){out.println(o);out.flush();}
    static int ni()throws IOException{return sc.nextInt();}
    static long nl()throws IOException{return sc.nextLong();}
    static double nd()throws IOException{return sc.nextDouble();}
    static String nln()throws IOException{return sc.nextLine();}
    static int[] nai(int N)throws IOException{int[]A=new int[N];for(int i=0;i!=N;i++){A[i]=ni();}return A;}
    static long[] nal(int N)throws IOException{long[]A=new long[N];for(int i=0;i!=N;i++){A[i]=nl();}return A;}
    static long gcd(long a, long b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int gcd(int a, int b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));}
	static boolean isPowerOfTwo (int x) throws IOException{ return x!=0 && ((x&(x-1)) == 0);} //1000(8) & 1111(7)==0
	static boolean isPrime2(long n)throws IOException{ return BigInteger.valueOf(n).isProbablePrime(1);}
	static BigInteger factorial(long n) throws IOException{BigInteger res = BigInteger.ONE;for(long i=1;i<=n;i++)res = res.multiply(BigInteger.valueOf(i)); return res;}
	static boolean isPrime(long n){if(n<2)return false;if(n==2 || n==3)return true;for(int i=1;i*i<=n;i++){long a=6*i+1;long b=6*i-1;if(n%a==0 || n%b==0)return false;}return true;}
	static int mod=(int)(1e9)+7;
	public static long mod(long x){return ((x%mod)+mod)%mod;}
	public static long add(long a,long b){return mod(mod(a)+mod(b));}
	public static long mul(long a,long b){return mod(mod(a)*mod(b));}
	
    static class AnotherReader{BufferedReader br; StringTokenizer st;AnotherReader()throws FileNotFoundException{br=new BufferedReader(new InputStreamReader(System.in));}AnotherReader(int a)throws FileNotFoundException{br = new BufferedReader(new FileReader("input.txt"));}String next()throws IOException{while (st == null || !st.hasMoreElements()) {try{st = new StringTokenizer(br.readLine());}catch (IOException  e){e.printStackTrace(); }}return st.nextToken();}int nextInt() throws IOException{return Integer.parseInt(next());}long nextLong() throws IOException{return Long.parseLong(next());}double nextDouble()throws IOException {return Double.parseDouble(next()); }String nextLine() throws IOException{ String str = "";try{str = br.readLine();}catch (IOException e){e.printStackTrace();} return str;}} 
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
}