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 Main {
    static PrintWriter pw;
    static Scanner sc;
    static ArrayList<Integer>[] adj;
    static boolean[] visit;
    static HashSet<Pair> hash;
    static boolean[] arr;
    static Pair[] dp;
    static long ceildiv(long x, long y){ return (x+y-1)/y;}
    public static void main(String[] args) throws Exception {
        sc = new Scanner(System.in);
        pw = new PrintWriter(System.out);
        int t=sc.nextInt();
        while(t-->0){
            int n=sc.nextInt();
            char[] arr=sc.nextLine().toCharArray();
            int[] ans= new int[n];
            TreeSet<Integer> one= new TreeSet<Integer>(), zero= new TreeSet<Integer>();
            ans[0]=1;
            if(arr[0]=='0')
                zero.add(1);
            else
                one.add(1);
            int max=1;
            for(int i=1; i<n; i++){
                if(arr[i]!=arr[i-1]){
                    ans[i]=1;
                }else{
                    if(arr[i]=='0'){
                        if(one.isEmpty())
                            ans[i]=++max;
                        else
                            ans[i]=one.pollFirst();
                    }else{
                        if(zero.isEmpty())
                            ans[i]=++max;
                        else
                            ans[i]=zero.pollFirst();
                    }
                }
                if(arr[i]=='0'){
                    zero.add(ans[i]);
                    if(one.contains(ans[i]))
                        one.remove(ans[i]);
                }
                else{
                    one.add(ans[i]);
                    if(zero.contains(ans[i]))
                        zero.remove(ans[i]);
                }
            }
            pw.println(max);
            printArr(ans);
        }
        pw.close();
    }
    static int test(Integer[] arr, int sum){
        int ans=0;
        for(int i=0, j=arr.length-1; i<j; ){
            if(arr[i]+arr[j]>sum){
                j--;
            }else if(arr[i]+arr[j]<sum){
                i++;
            }else{
                ans++;
                i++;
                j--;
            }
        }
        return ans;
    }
    static Pair min(Pair a, Pair b){
        if(a.x>b.x)
            return b;
        if(a.x<b.x)
            return a;
        if(a.y>b.y)
            return b;
        return a;
    }
    static StringBuilder ans;
    static void printArr(int[] arr){
        for(int i=0; i<arr.length-1; i++)
            pw.print(arr[i]+" ");
        pw.println(arr[arr.length-1]);
    }
    static void printArr(long[] arr){
        for(int i=0; i<arr.length-1; i++)
            pw.print(arr[i]+" ");
        pw.println(arr[arr.length-1]);
    }
    static void printArr(Integer[] arr){
        for(int i=0; i<arr.length; i++)
            pw.print(arr[i]+" ");
        pw.println();
    }
    static void printArr(char[] arr){
        for(int i=0; i<arr.length; i++)
            pw.print(arr[i]);
        pw.println();
    }
    static void printArr(ArrayList list){
        for(int i=0; i<list.size(); i++)
            pw.print(list.get(i)+" ");
        pw.println();
    }
    static class Scanner {
        StringTokenizer st;
        BufferedReader br;
        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public int[] nextArr(int n) throws IOException {
            int[] arr = new int[n];
            for (int i = 0; i < arr.length; i++)
                arr[i] = nextInt();
            return arr;
        }
        public Integer[] nextsort(int n) throws IOException{
            Integer[] arr=new Integer[n];
            for(int i=0; i<n; i++)
                arr[i]=nextInt();
            return arr;
        }
        public Pair nextPair() throws IOException{
            return new Pair(nextInt(), nextInt());
        }
        public Pair[] nextPairArr(int n) throws IOException{
            Pair[] arr=new Pair[n];
            for(int i=0; i<n; i++)
                arr[i]=new Pair(nextInt(), nextInt());
            return arr;
        }
        public boolean ready() throws IOException {
            return br.ready();
        }
    }
    static class Pair implements Comparable<Pair>{
        int x;
        int y;
        public Pair(int x, int y) {
            this.x=x;
            this.y=y;
        }
        public int hashCode() {
            return this.x*1000+this.y;
        }
        public int compareTo(Pair p){
            return x+y-p.x-p.y;
        }
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (this.getClass() != obj.getClass()) {
                return false;
            }
            Pair p = (Pair) obj;
            return this.x==p.x && this.y==p.y;
        }
        public boolean equal(Pair p){
            if(this.x==p.x)
                return this.y==p.y;
            if(this.x==p.y)
                return this.y==p.x;
            else
                return false;
        }
        public Pair clone(){
            return new Pair(x, y);
        }
        public String toString(){
            return this.x+" "+this.y;
        }
    }
    static class Triple{
        boolean b;
        int x;
        int y;
        public Triple(boolean b, int x, int y){
            this.b=b;
            this.x=x;
            this.y=y;
        }
        public String toString(){
            return (b?1:2)+" "+(x+1)+" "+(y+1);
        }
    }
    static class decimal{
        int x;
        int dec;
        public decimal(String s){
            x=Integer.parseInt(s.substring(0, s.length()-3));
            dec=Integer.parseInt(s.substring(s.length()-2));
        }
        public decimal(int x, int dec){
            this.x=x;
            this.dec=dec;
        }
        public decimal plus(decimal a){
            return new decimal(this.x+a.x+(this.dec+a.dec)/100, (this.dec+a.dec)%100);
        }
        public decimal minus(decimal a){
            return new decimal(this.x-a.x-(this.dec>=a.dec?0:1), (this.dec+100-a.dec)%100);
        }
        public decimal min(decimal a){
            if(a.x>this.x)
                return this;
            if(this.x>a.x)
                return a;
            if(a.dec>this.dec)
                return this;
            return a;
        }
        public String toString(){
            return this.x+"."+this.dec;
        }
        public decimal clone(){
            return new decimal(this.x, this.dec);
        }
        public boolean equal(decimal a){
            return a.x==this.x && a.dec==this.dec;
        }
    }
}