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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.*;
import java.math.*;
public class Main {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
    //class  Declaration

    static class pair implements Comparable < pair > {
        long x;
        long y;

        
        pair(long i, long j) {
            x = i;
            y = j;
            


        }
        public int compareTo(pair p) {
            if (this.x != p.x) {
                return Long.compare(this.x,p.x);
            } else {
                return Long.compare(this.y,p.y);
            }
        }
        public int hashCode() {
            return (x + " " + y).hashCode();
        }
        public String toString() {
            return x + " " + y;
        }
        public boolean equals(Object o) {
            pair x = (pair) o;
            return (x.x == this.x && x.y == this.y);
        }
    }
    // int[] dx = {0,0,1,-1};
    // int[] dy = {1,-1,0,0};
    // int[] ddx = {0,0,1,-1,1,-1,1,-1}; 
    // int[] ddy = {1,-1,0,0,1,-1,-1,1};

int inf = (int) 1e9 + 9;
long biginf  = (long)1e17 + 7 ;
long mod =  (long)1e9 + 7;  

void solve() throws Exception {
    int T=ni();
    while(T-->0){
     int n=ni();
     char[] s = ns().toCharArray();
    LinkedList<Integer> oneEnd  = new LinkedList<>();
    LinkedList<Integer> zeroEnd  = new LinkedList<>();
    int[] ans = new int[n];
    int maxans = 0 ;
    for(int i=0;i<n;++i){
        if(s[i]=='0'){
            if(oneEnd.size()>0){
                ans[i]=oneEnd.pollLast();
                zeroEnd.add(ans[i]);
            }
            else{
                maxans++;
                zeroEnd.add(maxans);
                ans[i]= maxans;

            }
        }
        else{

            if(zeroEnd.size()>0){
                ans[i] = zeroEnd.pollLast();
                oneEnd.add(ans[i]);
            }
            else{
                maxans++;
                oneEnd.add(maxans);
                ans[i]=maxans;
            }
        }
    }
    pn(maxans);
    for(int i=0;i<n;++i){
        p(ans[i]+" ");
    }
    pn("");
  
    }
}




long pow(long a, long b) {
        long result = 1;
        while (b > 0) {
            if (b % 2 == 1) result = (result * a) % mod;
            b /= 2;
            a = (a * a) % mod;
        }
        return result;
    }


    void print(Object o) {
        System.out.println(o);
        System.out.flush();
    }



    long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
    void run() throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);

        long s = System.currentTimeMillis();
        solve();
        out.flush();
        if (!INPUT.isEmpty()) tr(System.currentTimeMillis() - s + "ms");
    }


    public static void main(String[] args) throws Exception {
        new Main().run();
    }

    //output methods
    private void pn(Object o) {
        out.println(o);
    }
    private void p(Object o) {
        out.print(o);
    }
    private ArrayList < ArrayList < Integer >> ng(int n, int e) {
        ArrayList < ArrayList < Integer >> g = new ArrayList < > ();
        for (int i = 0; i <= n; ++i) g.add(new ArrayList < > ());

        for (int i = 0; i < e; ++i) {
            int u = ni(), v = ni();
            g.get(u).add(v);
            g.get(v).add(u);
        }

        return g;
    }

    private ArrayList < ArrayList < pair >> nwg(int n, int e) {
        ArrayList < ArrayList < pair >> g = new ArrayList < > ();
        for (int i = 0; i <= n; ++i) g.add(new ArrayList < > ());

        for (int i = 0; i < e; ++i) {
            int u = ni(), v = ni(), w = ni();
            g.get(u).add(new pair(w, v));
            g.get(v).add(new pair(w, u));
        }

        return g;
    }


    //input methods
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;


    private int readByte() {
        if (lenbuf == -1) throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) return -1;
        }
        return inbuf[ptrbuf++];
    }




    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }
    private int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b));
        return b;
    }

    private double nd() {
        return Double.parseDouble(ns());
    }
    private char nc() {
        return (char) skip();
    }

    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++) map[i] = ns(m);
        return map;
    }

    private int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = ni();
        return a;
    }

    private int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private void tr(Object...o) {
        if (INPUT.length() > 0) System.out.println(Arrays.deepToString(o));
    }
    void watch(Object...a) throws Exception {
        int i = 1;
        print("watch starts :");
        for (Object o: a) {
            //print(o);
            boolean notfound = true;
            if (o.getClass().isArray()) {

                String type = o.getClass().getName().toString();
                //print("type is "+type);
                switch (type) {
                    case "[I":
                        {
                            int[] test = (int[]) o;
                            print(i + " " + Arrays.toString(test));
                            break;
                        }
                    case "[[I":
                        {
                            int[][] obj = (int[][]) o;

                            print(i + " " + Arrays.deepToString(obj));
                            break;
                        }
                    case "[J":
                        {

                            long[] obj = (long[]) o;
                            print(i + " " + Arrays.toString(obj));
                            break;
                        }
                    case "[[J":
                        {

                            long[][] obj = (long[][]) o;
                            print(i + " " + Arrays.deepToString(obj));
                            break;
                        }
                    case "[D":
                        {

                            double[] obj = (double[]) o;
                            print(i + " " + Arrays.toString(obj));
                            break;
                        }
                    case "[[D":
                        {

                            double[][] obj = (double[][]) o;
                            print(i + " " + Arrays.deepToString(obj));
                            break;
                        }
                    case "[Ljava.lang.String":
                        {

                            String[] obj = (String[]) o;
                            print(i + " " + Arrays.toString(obj));
                            break;
                        }
                    case "[[Ljava.lang.String":
                        {

                            String[][] obj = (String[][]) o;
                            print(i + " " + Arrays.deepToString(obj));
                            break;
                        }
                    case "[C":
                        {
                            char[] obj = (char[]) o;
                            print(i + " " + Arrays.toString(obj));
                            break;
                        }
                    case "[[C":
                        {

                            char[][] obj = (char[][]) o;
                            print(i + " " + Arrays.deepToString(obj));
                            break;
                        }



                    default:
                        {
                            print(i + " type not identified");
                            break;
                        }
                }
                notfound = false;

            }
            if (o.getClass() == ArrayList.class) {
                print(i + " al: " + o);
                notfound = false;
            }
            if (o.getClass() == HashSet.class) {
                print(i + " hs: " + o);
                notfound = false;
            }
            if (o.getClass() == TreeSet.class) {
                print(i + " ts: " + o);
                notfound = false;
            }
            if (o.getClass() == TreeMap.class) {
                print(i + " tm: " + o);
                notfound = false;
            }
            if (o.getClass() == HashMap.class) {
                print(i + " hm: " + o);
                notfound = false;
            }
            if (o.getClass() == LinkedList.class) {
                print(i + " ll: " + o);
                notfound = false;
            }
            if (o.getClass() == PriorityQueue.class) {
                print(i + " pq : " + o);
                notfound = false;
            }
            if (o.getClass() == pair.class) {
                print(i + " pq : " + o);
                notfound = false;
            }

            if (notfound) {
                print(i + " unknown: " + o);
            }
            i++;
        }
        print("watch ends ");
    }

}