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:
import java.io.*;
import java.util.*;
import java.lang.*;


public class Main{

    public void solve () throws IOException  {

        InputReader in = new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int t = in.nextInt();
        while(t-- > 0){
            int n = in.nextInt();
            char s[] = in.nextLine().toCharArray();
            int totalD = 0;
            HashMap<Pair , Integer> hm = new HashMap<>();
            for(int i = 0 ; i < n ; i++){
                if(s[i] == 'D'){
                    totalD ++;
                }
                int totalK = i + 1 - totalD;
                if(totalK == 0){
                    int val = hm.get(new Pair(n + 1 , n + 1)) == null ? 0 : hm.get(new Pair(n + 1 , n + 1));
                    hm.put(new Pair(n + 1 , n + 1) , val + 1);
                    pw.print((val + 1)+" ");
                }else if(totalD == 0){
                    int val = hm.get(new Pair(0, 0)) == null ? 0 : hm.get(new Pair(0 , 0));
                    hm.put(new Pair(0 , 0) , val + 1);
                    pw.print((val + 1)+" ");
                }
                else{
                    int gcd = GCD(totalD , totalK);
                    Pair p = new Pair(totalD / gcd , totalK / gcd);
                    int val = hm.get(p) == null ? 0 : hm.get(p);
                    hm.put(p , val + 1);
                    pw.print((val + 1)+" ");
                }
            }
            pw.println();
        }
        pw.flush();
        pw.close();
    }

    public int GCD(int x , int y){
        if(y == 0){
            return x;
        }else{
            return GCD(y , x % y);
        }
    }

    public void debug(Object...o){
        System.out.println(Arrays.deepToString(o));
    }

    public static class Pair implements Comparable<Pair>{
        int x;
        int y;
        public Pair(int x , int y){
            this.x = x;
            this.y = y;
        }

        @Override
        public int compareTo(Pair o) {
            if(o.x > x) return  -1;
            if(o.x < x) return  1;
            return Integer.compare(y, o.y);
        }

        @Override
        public boolean equals(Object o){
            if(o instanceof Pair){
                Pair p = (Pair)o;
                return p.x == x && p.y == y;
            }
            return false;
        }

        @Override
        public String toString(){
            return x+" "+y;
        }

        @Override
        public int hashCode(){
            return Integer.hashCode(x) * 31 + Integer.hashCode(y);
        }
    }

    public static void main(String[] args) throws Exception {


        new Thread(null,new Runnable() {
            public void run() {
                try {
                    new Main().solve();
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
        },"1",1<<26).start();


    }

    static class InputReader
    {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }
        public int snext()
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars)
            {
                curChar = 0;
                try
                {
                    snumChars = stream.read(buf);
                }
                catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt()
        {
            int c = snext();
            while (isSpaceChar(c))
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c))
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n)
        {
            int a[] = new int[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = nextInt();
            }
            return a;
        }

        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c))
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public String nextLine()
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c)
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c)
        {
            return c == '\n' || c == '\r' || c == -1;
        }

        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }

}