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.*;
public class Codeforces {
	static Scanner sc;
	static PrintWriter out;
	static final long oo = (long) 1e16;
	static final int mod = 1_000_000_007;
	public static void main(String[] args) throws Exception{
		// TODO Auto-generated method stub
		sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		int t = sc.nextInt();
		while(t-->0)
			solve();
		out.flush();
	}
	static long pow(long a,int n) {
	    long res=1;
	    while (n>0) {
	        if ((n-n/2*2)==1) {
	            res=res*a % mod;
	        }
	        a=a*a % mod;
	        n>>=1;
	    }
	    return res % mod;
	}

	static void solve() throws Exception{
		int n = sc.nextInt();
		String s = sc.nextLine();
		LinkedList<Integer> zeros = new LinkedList<>();
		LinkedList<Integer> ones = new LinkedList<>();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			char c = s.charAt(i);
			int j = zeros.size()+ones.size();
			if(c == '0')
			{
				if(ones.isEmpty())
					zeros.add(j);
				else {
					j = ones.removeLast();
					zeros.add(j);
				}
			}
			else
			{
				if(zeros.isEmpty())
					ones.add(j);
				else {
					j = zeros.removeLast();
					ones.add(j);
				}
			}
			a[i] = j; 
		}
		out.println(zeros.size()+ones.size());
		for(int i:a)
			out.printf("%d ", i+1);
		out.println();
	}
	
	static int minArr(int[] a) {
		int min = (int) 1e9;
		for(int i:a) {
			min = Math.min(min, i);
		}
		return min;
	}
	static int maxArr(int[] a) {
		int max = -1;
		for(int i:a) {
			max = Math.max(max, i);
		}
		return max;
	}

	static class Scanner{
		private BufferedReader br;
		private StringTokenizer st;
		public Scanner(InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
		}
		public Scanner(String filename) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(filename));
		}
		public String next() throws IOException{
			while(st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public String nextLine() throws IOException {
			return br.readLine();
		}
		public int nextInt() throws IOException{
			return Integer.parseInt(next());
		}
		public long nextLong() throws IOException{
			return Long.parseLong(next());
		}
		public double nextDouble() throws IOException{
			return Double.parseDouble(next());
		}
		public int[] inArr(int n) throws Exception{
			int a [] = new int[n];
			for(int i=0;i<n;i++) {
				a[i] = Integer.parseInt(next());
			}
			return a;
		}
	}
}