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.util.*;
import java.io.*;
import java.math.*;
import java.io.FileWriter; 
import java.io.IOException; 
public class cf{
 
    static class Pair{
        int x;
        int y;
        public Pair(int x,int y){
            this.x=x;
            this.y=y;
        }
    }
 
 
////////////////////////////////////**********Code-Start**********/////////////////////////////////////////////////    
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
          if (System.getProperty("ONLINE_JUDGE") == null) {
            try {
                System.setOut(new PrintStream(
                    new FileOutputStream("output.txt")));
                 sc = new InputReader(new FileInputStream("input.txt"));
            }
            catch (Exception e) {
            }
            solve();
         }
         else{
            sc = new InputReader(inputStream);
            pw = new PrintWriter(outputStream);
            solve();
            pw.close();
       }
       

    }
   // static ArrayList<ArrayList<Integer>> arr=new ArrayList<>();
   // static PriorityQueue<Integer> pq=new PriorityQueue<>();
    public static void solve() {
                int t=s(0);
                while(t-->0){
                  int n=s(0);
                  String s=s("s");
                  HashMap<String,Integer> map=new HashMap<>();
                  StringBuilder sb=new StringBuilder();
                  int a=0,b=0;
                  for(int i=0;i<n;i++){
                        if(s.charAt(i)=='D')
                           a++;
                        if(s.charAt(i)=='K')
                           b++;

                       int c=gcd(a,b);

                       String sp="";
                       sp=(a/c)+","+(b/c);
                       if(map.containsKey(sp)){
                        map.put(sp,map.get(sp)+1);
                       }      
                       else{
                        map.put(sp,1);
                       } 
                        sb.append(map.get(sp)+" ");
                  }
                  System.out.println(sb);
                  

                }

    }

   


 
     
////////////////////////////////////**********Code-End**********//////////////////////////////////////////////////
    
 
    // Arrays.sort(a,(c,b)->(c.x==b.x)?c.y-b.y:c.x-b.x); sort the array ont the basis of y if x1==x2
    // set precision --> String.format("%.df",ans);  
 
    static InputReader sc;
    static PrintWriter pw;
    static ArrayList<ArrayList<Integer>> adj;
    static int mod=1000000007;
    static int mod1= 998244353;
    static int max(int ...a){int m=a[0];for(int e:a)m=(m>=e)?m:e;return m;}
    static int min(int ...a){int m=a[0];for(int e:a)m=(m<=e)?m:e;return m;}
    static int abs(int a){return Math.abs(a);}
    static long max(long ...a){long m=a[0];for(long e:a)m=(m>=e)?m:e;return m;}
    static long min(long ...a){long m=a[0];for(long e:a)m=(m<=e)?m:e;return m;}
    static long abs(long a){return Math.abs(a);}
 
    static void subset(int a[],int n,ArrayList<Integer> arr){
        if(n==a.length){
            System.out.println(arr);
            return;
        }
        ArrayList<Integer> b=new ArrayList<>();
        ArrayList<Integer> c=new ArrayList<>();
        b.addAll(arr);
        c.addAll(arr);
        b.add(a[n]);
        subset(a,n+1,b);
        subset(a,n+1,c);
     }
 
 
    static boolean prime[];
    static int smallestFactor[];
    static ArrayList<Integer> allPrimes;
    static void sieveOfEratosthenes(int n)
    {
        prime = new boolean[n+1];
        smallestFactor = new int[n+1];
        allPrimes=new ArrayList<>();
        smallestFactor[1] = 1;
        for(int i=2;i<n;i++) {
            prime[i] = true;
            smallestFactor[i] = i;
        }
 
        for(int p = 2; p*p <=n; p++)
        {
            if(prime[p])
            {
                smallestFactor[p] = p;
                for(int i = p*p; i <= n; i += p) {
                    prime[i] = false;
                    smallestFactor[i] = Math.min(p,smallestFactor[i]);
                }
            }
        }

        for(int i=0;i<prime.length;i++){
            if(prime[i]){
                allPrimes.add(i);
            }
        }
 
    }
    // static void initial(int n){
    //    for(int i=0;i<=n;i++){
    //        arr.add(new ArrayList<>());
    //    }
    // }
     static int sum(int n){
      int sum=0;
      while(n!=0){
        sum+=n%10;
        n/=10;
      }
      return sum;
   }
     static void sort(ArrayList<Integer> brr){
        Collections.sort(brr);
    }
  static void Lsort(ArrayList<Long> arr){
        Collections.sort(arr);
    }
    static void sort(int[] arr){
        Arrays.sort(arr);
    }
     static void Lsort(long[] arr){
        Arrays.sort(arr);
    }
    static boolean isperfect(double number)    
    {   
        double sqrt=Math.sqrt(number);  
        return ((sqrt - Math.floor(sqrt)) == 0);   
    }   
 
    static boolean isPrime(long n){
        if(n<2){
            return false;
        }
        for(int i = 2; i*i<=n; i++){
            if(n%i==0){
                return false;
            }
        }
        return true;
    }
 static int lowerBound(int[] arr, int low, int high, long element) {
        int middle;
        while (low < high) {
            middle = low + (high - low) / 2;
            if (element > arr[middle])
                low = middle + 1;
            else
                high = middle;
        }
        if (low < arr.length && arr[low] < element)
            return -1;
        return low;
    }
 
   static  int upperBound(int[] arr, int low, int high, long element) {
        int middle;
        while (low < high) {
            middle = low + (high - low) / 2;
            if (arr[middle] > element)
                high = middle;
            else
                low = middle + 1;
        }
        if (low<arr.length &&arr[low] <= element)
            return -1;
        return low;
    }
 
    public static String sortString(String inputString) 
    { 
        char tempArray[] = inputString.toCharArray(); 
        Arrays.sort(tempArray); 
        return new String(tempArray); 
    } 
 
    public static int ask(int l, int r){
        System.out.println("? "+l+" "+r);
        System.out.flush();
        return sc.nextInt();
    }
    public static void swap(char []chrr, int i, int j){
        char temp=chrr[i];
        chrr[i]=chrr[j];
        chrr[j]=temp;
    }
    public static void swap(int []chrr, int i, int j){
        int temp=chrr[i];
        chrr[i]=chrr[j];
        chrr[j]=temp;
    }
    public static int countSetBits(int n){
        int a=0;
        while(n>0){
            a+=(n&1);
            n>>=1;
        }
        return a;
    }
    public static boolean isPowerOfTwo(long x){
        return x!=0 && ((x&(x-1)) == 0);
    }
   
    static int gcd(int a, int b)
    {
      if (b == 0)
        return a;
      return gcd(b, a % b);
    }
    public static int lcm(int a , int b )
    {
        int gc = gcd(a,b);
        return (a/gc)*b;
    }
    static long fast_pow(long base,long n,long M){
        if(n==0)
           return 1;
        if(n==1)
        return base;
        long halfn=fast_pow(base,n/2,M);
        if(n%2==0)
            return ( halfn * halfn ) % M;
        else
            return ( ( ( halfn * halfn ) % M ) * base ) % M;
    }
    static long modInverse(long n,long M){
        return fast_pow(n,M-2,M);
    }
    public static String reverse(String input)
    {
        StringBuilder str  = new StringBuilder("") ;
 
        for(int i =input.length()-1 ; i >= 0  ; i-- )
        {
            str.append(input.charAt(i));
        }
 
        return str.toString() ;
    }
    
    public static long nCr(int n,int k)
    {
        long ans=1L;
        k=k>n-k?n-k:k;
        int j=1;
        for(;j<=k;j++,n--)
        {
            if(n%j==0)
            {
                ans*=n/j;
            }else
            if(ans%j==0)
            {
                ans=ans/j*n;
            }else
            {
                ans=(ans*n)/j;
            }
        }
        return ans;
    }
    public static long kadanesAlgorithm(long[] arr)
    {
    
        if(arr.length == 0)return  0 ;
        
          long[] dp = new long[arr.length] ;
          
          dp[0] = arr[0] ;
          long max =  dp[0] ;
          
          
          for(int i = 1; i <  arr.length ; i++)
          {
                if(dp[i-1] > 0)
                {
                      dp[i] = dp[i-1] + arr[i] ;
                }
                else{
                      dp[i] = arr[i] ;
                }
                
                if(dp[i] >  max)max = dp[i] ;
                
          }
          
          return max  ;
      
    }
   
    private static int countDigits(int l) {
            if (l >= 1000000000) return 10;
            if (l >= 100000000) return 9;
            if (l >= 10000000) return 8;
            if (l >= 1000000) return 7;
            if (l >= 100000) return 6;
            if (l >= 10000) return 5;
            if (l >= 1000) return 4;
            if (l >= 100) return 3;
            if (l >= 10) return 2;
            return 1;
        }
 
        private static int countDigits(long l) {
            if (l >= 1000000000000000000L) return 19;
            if (l >= 100000000000000000L) return 18;
            if (l >= 10000000000000000L) return 17;
            if (l >= 1000000000000000L) return 16;
            if (l >= 100000000000000L) return 15;
            if (l >= 10000000000000L) return 14;
            if (l >= 1000000000000L) return 13;
            if (l >= 100000000000L) return 12;
            if (l >= 10000000000L) return 11;
            if (l >= 1000000000L) return 10;
            if (l >= 100000000L) return 9;
            if (l >= 10000000L) return 8;
            if (l >= 1000000L) return 7;
            if (l >= 100000L) return 6;
            if (l >= 10000L) return 5;
            if (l >= 1000L) return 4;
            if (l >= 100L) return 3;
            if (l >= 10L) return 2;
            return 1;
        }   
    public static int s(int n){
        return sc.nextInt();
    }
    public static long s(long n){
        return sc.nextLong();
    }
    public static String s(String n){
        return sc.next();
    }
    public static double s(double n){
        return sc.nextDouble();
    }
    public static void p(int n){
        pw.print(n);
    }
    public static void p(long n){
        pw.print(n);
    }
    public static void p(String n){
        pw.print(n);
    }
    public static void p(double n){
        pw.print(n);
    }
    public static void pln(int n){
        pw.println(n);
    }
    public static void pln(long n){
        pw.println(n);
    }
    public static void pln(String n){
        pw.println(n);
    }
    public static void pln(double n){
        pw.println(n);
    }
    public static void feedArr(long []arr){
        for(int i=0;i<arr.length;++i)
            arr[i]=sc.nextLong();
    }
    public static void feedArr(double []arr){
        for(int i=0;i<arr.length;++i)
            arr[i]=sc.nextDouble();
    }
    public static void feedArr(int []arr){
        for(int i=0;i<arr.length;++i)
            arr[i]=sc.nextInt();
    }
    public static void feedArr(String []arr){
        for(int i=0;i<arr.length;++i)
            arr[i]=sc.next();
    }
    public static String printArr(int []arr){
        StringBuilder sbr=new StringBuilder();
        for(int i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    public  static String printArr(long []arr){
        StringBuilder sbr=new StringBuilder();
        for(long i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    public static String printArr(String []arr){
        StringBuilder sbr=new StringBuilder();
        for(String i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    public static String printArr(double []arr){
        StringBuilder sbr=new StringBuilder();
        for(double i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
 
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}
 
 
// smallest lcm(a,b) => a+b=n will be n/smallPrimefactor ans n-n/smallestprimefactor.