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.io.*;
public class Main {
    static class Scan {
        private byte[] buf=new byte[1024];
        private int index;
        private InputStream in;
        private int total;
        public Scan()
        {
            in=System.in;
        }
        public int scan()throws IOException
        {
            if(total<0)
            throw new InputMismatchException();
            if(index>=total)
            {
                index=0;
                total=in.read(buf);
                if(total<=0)
                return -1;
            }
            return buf[index++];
        }
        public int scanInt()throws IOException
        {
            int integer=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n))
            {
                if(n>='0'&&n<='9')
                {
                    integer*=10;
                    integer+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            return neg*integer;
        }
        public double scanDouble()throws IOException
        {
            double doub=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n)&&n!='.')
            {
                if(n>='0'&&n<='9')
                {
                    doub*=10;
                    doub+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            if(n=='.')
            {
                n=scan();
                double temp=1;
                while(!isWhiteSpace(n))
                {
                    if(n>='0'&&n<='9')
                    {
                        temp/=10;
                        doub+=(n-'0')*temp;
                        n=scan();
                    }
                    else throw new InputMismatchException();
                }
            }
            return doub*neg;
        }
        public String scanString()throws IOException
        {
            StringBuilder sb=new StringBuilder();
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            while(!isWhiteSpace(n))
            {
                sb.append((char)n);
                n=scan();
            }
            return sb.toString();
        }
        private boolean isWhiteSpace(int n)
        {
            if(n==' '||n=='\n'||n=='\r'||n=='\t'||n==-1)
            return true;
            return false;
        }
    }
    public static void main(String args[]) throws IOException {
        Scan input=new Scan();
        StringBuilder ans=new StringBuilder("");
        int test=input.scanInt();
        for(int t=1;t<=test;t++) {
            int n=input.scanInt();
            String str=input.scanString();
            ans.append(solve(n,str)+"\n");
        }
        System.out.println(ans);
    }
    public static StringBuilder solve(int n,String str) {
        StringBuilder ans=new StringBuilder("");
        TreeSet<Integer> zero = new TreeSet<>(); 
        TreeSet<Integer> one = new TreeSet<>();
        for(int i=0;i<n;i++) {
            if(str.charAt(i)=='0') {
                zero.add(i);
            }
            else {
                one.add(i);
            }
        }
        int arr[]=new int[n];
        int cnt=1;
        while(!zero.isEmpty() && !one.isEmpty()) {
//            System.out.println(zero.peek()+" "+one.peek());
            if(zero.first()<one.first()) {
                int curr=0;
                int prev=-1;
                while(true) {
                    if(curr%2==0) {
                        if(zero.isEmpty()) {
                            break;
                        }
                        if(zero.higher(prev)==null) {
                            break;
                        }
                        int indx=zero.higher(prev);
                        arr[indx]=cnt;
                        prev=indx;
                        zero.remove(indx);
                    }
                    else {
                        if(one.isEmpty()) {
                            break;
                        }
                        if(one.higher(prev)==null) {
                            break;
                        }
                        int indx=one.higher(prev);
                        arr[indx]=cnt;
                        prev=indx;
                        one.remove(indx);
                    }
                    curr++;
                }
            }
            else {
                int curr=0;
                int prev=-1;
                while(true) {
                    if(curr%2==1) {
                        if(zero.isEmpty()) {
                            break;
                        }
                        if(zero.higher(prev)==null) {
                            break;
                        }
                        int indx=zero.higher(prev);
                        arr[indx]=cnt;
                        prev=indx;
                        zero.remove(indx);
                    }
                    else {
                        if(one.isEmpty()) {
                            break;
                        }
                        if(one.higher(prev)==null) {
                            break;
                        }
                        int indx=one.higher(prev);
                        arr[indx]=cnt;
                        prev=indx;
                        one.remove(indx);
                    }
                    curr++;
                }
            }
            cnt++;
        }
        while(!zero.isEmpty()) {
            int indx=zero.first();
            arr[indx]=cnt;
            zero.remove(indx);
            cnt++;
        }
        while(!one.isEmpty()) {
            int indx=one.first();
            arr[indx]=cnt;
            one.remove(indx);
            cnt++;
        }
        ans.append((cnt-1)+"\n");
        for(int i=0;i<n;i++) {
            ans.append(arr[i]+" ");
        }
        return ans;
    }
}