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 SolutionD { 
    static Random random;
 
    /* public static void main(String[] args){
        new Thread(null, new SolutionD (), "Main", 1<<26).start();
    } */
 
    public static void main(String[] args) {
        FastScanner in = new FastScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        random = new Random();
 
        // long timeStamp = System.currentTimeMillis();
        Solver solver = new Solver();
        solver.solve(in, out);
        out.close();
        // System.err.println("TIME: "+(System.currentTimeMillis()-timeStamp)+" ms");
    }
 
    /* ------------------------------------- START -------------------------------------------- */
    static class Solver {
        public void solve(FastScanner in, PrintWriter out) {
            int tests = in.nextInt();
            for(int cases = 0; cases < tests; cases++)
                solveOne(in, out);
        }

        private static void solveOne(FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            int[] ans = new int[n];
            String input = in.next();

            TreeSet<Integer> One = new TreeSet<>(), Zero = new TreeSet<>();

            for(int i = 0; i<n; i++){
                if(input.charAt(i) == '1')
                    One.add(i);
                else
                    Zero.add(i);
            }

            int cnt = 0;
            int nxt = 0;

            while(!One.isEmpty() || !Zero.isEmpty()){
                cnt++;
                while(ans[nxt] != 0) nxt++;
                int curChar = (input.charAt(nxt) == '0')? 0 : 1;
                Integer cur = -1;
                while(true){
                    if(curChar == 0) {
                        cur = Zero.higher(cur);
                        if(cur == null) break;
                        ans[cur.intValue()] = cnt;
                        Zero.remove(cur);
                    }
                    else{
                        cur = One.higher(cur);
                        if(cur == null) break;
                        ans[cur.intValue()] = cnt;
                        One.remove(cur);
                    }
                    curChar ^= 1;
                }
            }

            out.println(cnt);
            for(int x : ans){
                out.print(x);
                out.print(' ');
            }
            out.println();




        }
    }
    /* -------------------------------------- END --------------------------------------------- */
 
    /* Shuffle function to shuffle before Arrays.sort */
    static void shuffle(int[] arr){
        int swapTemp;
        for(int i = arr.length-1; i>= 1; i--){
            int pos = random.nextInt(i+1);
            if(pos == i) continue;
            {swapTemp = arr[i]; arr[i] = arr[pos]; arr[pos] = swapTemp;}
        }
    }
 
    /* Fast Input reader */
    static class FastScanner {
        BufferedReader reader;
        StreamTokenizer tokenizer;
        public FastScanner() {
            reader = new BufferedReader(new InputStreamReader(System.in));
            tokenizer = new StreamTokenizer(reader);
            tokenizer.resetSyntax();
            tokenizer.whitespaceChars(0, 32);
            tokenizer.wordChars(33, 126);
        }
        private void nextToken(){
            try{ tokenizer.nextToken(); }
            catch (Exception e) { e.printStackTrace(); }
        }
        String next() {
            nextToken();
            return tokenizer.sval;
        }
        int nextInt() {
            nextToken();
            return Integer.parseInt(tokenizer.sval);
        }
        long nextLong() {
            nextToken();
            return Long.parseLong(tokenizer.sval);
        }
        double nextDouble() {
            nextToken();
            return Double.parseDouble(tokenizer.sval);
        }
        String nextLine() {
            try{
                String string = reader.readLine();
                return string;
            } catch (Exception e) {
                e.printStackTrace();
                return "";
            }
        }
    }
}