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 com.sun.source.tree.Tree;

import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;

/**
 * @author Mubtasim Shahriar
 */

public class DuKeya {

    public static void main(String[] args) {

        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader sc = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
		int t = sc.nextInt();
//        int t = 1;
        while (t-- != 0) {
            solver.solve(sc, out);
        }
        out.close();

    }

    static class Solver {
        public void solve(InputReader sc, PrintWriter out) {
            int n = sc.nextInt();
            char[] carr = sc.next().toCharArray();
            int[] arr = new int[n];
            for(int i = 0; i < n; i++) arr[i] = carr[i]=='D' ? 1 : 0;
            TreeMap<Integer, TreeMap<Integer, Integer>> map = new TreeMap<>();
            int cnt1 = 0;
            int cnt0 = 0;
            long[] ans = new long[n];
            for(int i = 0; i < n; i++) {
                int now = arr[i];
                if(now==1) cnt1++;
                else cnt0++;
                int nowGcd = getGcd(cnt1,cnt0);
                int cnt1less = cnt1/nowGcd;
                int cnt0less = cnt0/nowGcd;
                boolean found = false;
                if(map.containsKey(cnt1less)) {
                    TreeMap<Integer,Integer> cnt0map = map.get(cnt1less);
                    if(cnt0map.containsKey(cnt0less)) {
                        found = true;
                        int lastIdx = cnt0map.get(cnt0less);
                        ans[i] = ans[lastIdx]+1;
                    }
                }
                putt(map,cnt1less,cnt0less,i);
                if(!found) ans[i] = 1;
            }
            for(int i = 0 ; i < n; i++) {
                if(i>0) out.print(" ");
                out.print(ans[i]);
            }
            out.println();
        }

        private void putt(TreeMap<Integer, TreeMap<Integer, Integer>> map, int cnt1less, int cnt0less, int i) {
            if(!map.containsKey(cnt1less)) map.put(cnt1less,new TreeMap<>());
            TreeMap<Integer,Integer> cnt1map = map.get(cnt1less);
            cnt1map.put(cnt0less,i);
        }

        private int getGcd(int a, int b) {
            return b==0 ? a : getGcd(b,a%b);
        }

    }

    static void sort(int[] arr) {
        Random rand = new Random();
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int idx = rand.nextInt(n);
            if (idx == i) continue;
            arr[i] ^= arr[idx];
            arr[idx] ^= arr[i];
            arr[i] ^= arr[idx];
        }
        Arrays.sort(arr);
    }

    static void sort(long[] arr) {
        Random rand = new Random();
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int idx = rand.nextInt(n);
            if (idx == i) continue;
            arr[i] ^= arr[idx];
            arr[idx] ^= arr[i];
            arr[i] ^= arr[idx];
        }
        Arrays.sort(arr);
    }

    static void sortDec(int[] arr) {
        Random rand = new Random();
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int idx = rand.nextInt(n);
            if (idx == i) continue;
            arr[i] ^= arr[idx];
            arr[idx] ^= arr[i];
            arr[i] ^= arr[idx];
        }
        Arrays.sort(arr);
        int l = 0;
        int r = n - 1;
        while (l < r) {
            arr[l] ^= arr[r];
            arr[r] ^= arr[l];
            arr[l] ^= arr[r];
            l++;
            r--;
        }
    }

    static void sortDec(long[] arr) {
        Random rand = new Random();
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int idx = rand.nextInt(n);
            if (idx == i) continue;
            arr[i] ^= arr[idx];
            arr[idx] ^= arr[i];
            arr[i] ^= arr[idx];
        }
        Arrays.sort(arr);
        int l = 0;
        int r = n - 1;
        while (l < r) {
            arr[l] ^= arr[r];
            arr[r] ^= arr[l];
            arr[l] ^= arr[r];
            l++;
            r--;
        }
    }

    static class InputReader {
        private boolean finished = false;

        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

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

        public int peek() {
            if (numChars == -1) {
                return -1;
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    return -1;
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar];
        }

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

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

        public String nextString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private String readLine0() {
            StringBuilder buf = new StringBuilder();
            int c = read();
            while (c != '\n' && c != -1) {
                if (c != '\r') {
                    buf.appendCodePoint(c);
                }
                c = read();
            }
            return buf.toString();
        }

        public String readLine() {
            String s = readLine0();
            while (s.trim().length() == 0) {
                s = readLine0();
            }
            return s;
        }

        public String readLine(boolean ignoreEmptyLines) {
            if (ignoreEmptyLines) {
                return readLine();
            } else {
                return readLine0();
            }
        }

        public BigInteger readBigInteger() {
            try {
                return new BigInteger(nextString());
            } catch (NumberFormatException e) {
                throw new InputMismatchException();
            }
        }

        public char nextCharacter() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            return (char) c;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E') {
                    return res * Math.pow(10, nextInt());
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E') {
                        return res * Math.pow(10, nextInt());
                    }
                    if (c < '0' || c > '9') {
                        throw new InputMismatchException();
                    }
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public boolean isExhausted() {
            int value;
            while (isSpaceChar(value = peek()) && value != -1) {
                read();
            }
            return value == -1;
        }

        public String next() {
            return nextString();
        }

        public SpaceCharFilter getFilter() {
            return filter;
        }

        public void setFilter(SpaceCharFilter filter) {
            this.filter = filter;
        }

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

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

        public int[] nextSortedIntArray(int n) {
            int array[] = nextIntArray(n);
            Arrays.sort(array);
            return array;
        }

        public int[] nextSumIntArray(int n) {
            int[] array = new int[n];
            array[0] = nextInt();
            for (int i = 1; i < n; ++i) array[i] = array[i - 1] + nextInt();
            return array;
        }

        public long[] nextLongArray(int n) {
            long[] array = new long[n];
            for (int i = 0; i < n; ++i) array[i] = nextLong();
            return array;
        }

        public long[] nextSumLongArray(int n) {
            long[] array = new long[n];
            array[0] = nextInt();
            for (int i = 1; i < n; ++i) array[i] = array[i - 1] + nextInt();
            return array;
        }

        public long[] nextSortedLongArray(int n) {
            long array[] = nextLongArray(n);
            Arrays.sort(array);
            return array;
        }
    }


}