Problem: The tycoon of a winery empire in Mondstadt, unmatched in every possible way. A thinker in the Knights of Favonius with an exotic appearance.

This time, the brothers are dealing with a strange piece of wood marked with their names. This plank of wood can be represented as a string of n characters. Each character is either a 'D' or a 'K'. You want to make some number of cuts (possibly 0) on this string, partitioning it into several contiguous pieces, each with length at least 1. Both brothers act with dignity, so they want to split the wood as evenly as possible. They want to know the maximum number of pieces you can split the wood into such that the ratios of the number of occurrences of 'D' to the number of occurrences of 'K' in each chunk are the same.

Kaeya, the curious thinker, is interested in the solution for multiple scenarios. He wants to know the answer for every prefix of the given string. Help him to solve this problem!

For a string we define a ratio as a:b where 'D' appears in it a times, and 'K' appears b times. Note that a or b can equal 0, but not both. Ratios a:b and c:d are considered equal if and only if a⋅ d = b⋅ c. 

For example, for the string 'DDD' the ratio will be 3:0, for 'DKD' — 2:1, for 'DKK' — 1:2, and for 'KKKKDD' — 2:4. Note that the ratios of the latter two strings are equal to each other, but they are not equal to the ratios of the first two strings.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 1000). Description of the test cases follows.

The first line of each test case contains an integer n (1 ≤ n ≤ 5 ⋅ 10^5) — the length of the wood.

The second line of each test case contains a string s of length n. Every character of s will be either 'D' or 'K'.

It is guaranteed that the sum of n over all test cases does not exceed 5 ⋅ 10^5.

Output

For each test case, output n space separated integers. The i-th of these numbers should equal the answer for the prefix s_{1},s_{2},...,s_{i}.

Example

Input


5
3
DDK
6
DDDDDD
4
DKDK
1
D
9
DKDKDDDDK


Output


1 2 1 
1 2 3 4 5 6 
1 1 1 2 
1 
1 1 1 2 1 2 1 1 3 

Note

For the first test case, there is no way to partition 'D' or 'DDK' into more than one block with equal ratios of numbers of 'D' and 'K', while you can split 'DD' into 'D' and 'D'.

For the second test case, you can split each prefix of length i into i blocks 'D'.

Solution (in JAVA):

Solution:
// created by 我不知道我是谁
import java.io.*;
import java.lang.reflect.Array;
import java.math.BigDecimal;
import java.util.*;
public class cp18{


    static class Reader {
        static BufferedReader reader;
        static StringTokenizer tokenizer;

        static void init(InputStream input) {
            reader = new BufferedReader(
                    new InputStreamReader(input));
            tokenizer = new StringTokenizer("");
        }

        static String next() throws IOException {
            while (!tokenizer.hasMoreTokens()) {
                //TODO add check for eof if necessary
                tokenizer = new StringTokenizer(
                        reader.readLine());
            }
            return tokenizer.nextToken();
        }

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

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

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



    static class Pair{
        int d;
        int k;
        // smallest form only

        public Pair(int d, int k){
            this.d=d;
            this.k=k;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair pair = (Pair) o;
            return d == pair.d && k == pair.k;
        }

        @Override
        public int hashCode() {
            return Objects.hash(d, k);
        }
    }




    public static void main(String[] args)  throws IOException {
        Reader.init(System.in);
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
        int t= Reader.nextInt();
        for (int tt = 0; tt <t ; tt++) {
            int n= Reader.nextInt();
            String s= Reader.next();
            HashMap<Pair, Integer>map= new HashMap<>();
            int cd=0;
            int ck=0;
            for (int i = 0; i <n ; i++) {
                if(s.charAt(i)=='D'){
                    cd++;
                }
                else{
                    ck++;
                }
                int c1=cd;
                int c2=ck;
                if(cd!=0 && ck!=0){
                    int gcd= gcd(cd,ck);

                    c1/=gcd;
                    c2/=gcd;
                }

                if(cd==0 || ck==0){
                    out.append((i+1)+" ");
                    if(cd==0){
                        map.put(new Pair(0,1),(i+1));
                    }
                    if(ck==0){
                        map.put(new Pair(1,0),i+1);
                    }}
                else{
//                System.out.println(map+" "+c1+" "+c2);
                    if(!map.containsKey(new Pair(c1,c2))){
                        out.append(1+" ");
                        map.put(new Pair(c1,c2),1);
                    }
                    else{
                        out.append((map.get(new Pair(c1,c2))+1)+" ");
                        map.put(new Pair(c1,c2),map.get(new Pair(c1,c2))+1);
                    }
                }
            }
            out.append("\n");




        }
        out.flush();
        out.close();
    }

    static int gcd(int a, int b){
        if(a==0){
            return b;
        }
        else{
            return gcd(b%a,a);
        }
    }

    public static boolean done(ArrayList<Long>arr){
        int x= arr.size();
        Set<Long>set= new HashSet<>();
        for (int i = 0; i <x ; i++) {
            long a= arr.get(i);
            set.add(a);
        }
        boolean done=true;
        for (int i = 0; i <x-1 ; i++) {
            for (int j = i+1; j <x ; j++) {
                long x1= arr.get(i);
                long x2= arr.get(j);
                if(!set.contains(Math.abs(x1-x2))){
                    return false;
                }
            }
        }
        return true;
    }




    static long power( long x, long y, long p)
    {

        long res = 1;


        x = x % p;

        if (x == 0) return 0;

        while (y > 0)
        {

            if((y & 1)==1)
                res = (res * x) % p;


            y = y >> 1;
            x = (x * x) % p;
        }
        return res;
    }


}