There are n + 1 cities, numbered from 0 to n. n roads connect these cities, the i-th road connects cities i - 1 and i (i ∈ [1, n]).

Each road has a direction. The directions are given by a string of n characters such that each character is either L or R. If the i-th character is L, it means that the i-th road initially goes from the city i to the city i - 1; otherwise it goes from the city i - 1 to the city i.

A traveler would like to visit as many cities of this country as possible. Initially, they will choose some city to start their journey from. Each day, the traveler must go from the city where they currently are to a neighboring city using one of the roads, and they can go along a road only if it is directed in the same direction they are going; i. e., if a road is directed from city i to the city i + 1, it is possible to travel from i to i + 1, but not from i + 1 to i. After the traveler moves to a neighboring city, all roads change their directions to the opposite ones. If the traveler cannot go from their current city to a neighboring city, their journey ends; it is also possible to end the journey whenever the traveler wants to.

The goal of the traveler is to visit as many different cities as possible (they can visit a city multiple times, but only the first visit is counted). For each city i, calculate the maximum number of different cities the traveler can visit during exactly one journey if they start in the city i. 

Input

The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.

Each test case consists of two lines. The first line contains one integer n (1 ≤ n ≤ 3 ⋅ 10^5). The second line contains the string s consisting of exactly n characters, each character is either L or R.

It is guaranteed that the sum of n over all test cases does not exceed 3 ⋅ 10^5.

Output

For each test case, print n + 1 integers. The i-th integer should be equal to the maximum number of different cities the traveler can visit during one journey if this journey starts in the i-th city.

Example

Input


2
6
LRRRLL
3
LRL


Output


1 3 2 3 1 3 2
1 4 1 4
import java.io.*;
import java.math.BigInteger;
import java.util.*;
import java.util.concurrent.TimeUnit;

public class d1476 implements Runnable{
	
    public static void main(String[] args) {
    	try{
            new Thread(null, new d1476(), "process", 1<<26).start();
        }
        catch(Exception e){
            System.out.println(e);
        }
    }
	public void run() {
		FastReader scan = new FastReader();
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
		//PrintWriter out = new PrintWriter("file.out");
		Task solver = new Task();
		int t = scan.nextInt();
		//int t = 1;
		for(int i = 1; i <= t; i++) solver.solve(i, scan, out);
		out.close();
	}

	static class Task {
		static final int oo = Integer.MAX_VALUE;
		static final long OO = Long.MAX_VALUE;

		int[] left;
		int[] leftI;
		int[] right;
		int[] rightI;
		
		String s;
		public void solve(int testNumber, FastReader sc, PrintWriter out) {
			int N = sc.nextInt();
			s = sc.nextLine();
			
			
			left = new int[N+1];
			leftI = new int[N+1];
			right = new int[N+1];
			rightI = new int[N+1];
			
			for(int i = 0; i <= N; i++) {
				right[i] = dfs(i, false);
				rightI[i] = dfs(i, true);
				left[i] = dfsR(i, false);
				leftI[i] = dfsR(i, true);
			}
			
//			dbg(left);
//			dbg(leftI);
//			dbg(right);
//			dbg(rightI);
			
			for(int i = 0; i <= N; i++) {
				int L = left[i];
				int R = right[i];
				
				if( (L % 2 == 1 && right[i-L+1] >= L) || (L % 2 == 0 && rightI[i-L+1] >= L) || (R % 2 == 1 && left[i+R-1] >= R) || (R % 2 == 0 && leftI[i+R-1] >= R)) {
					out.print(L + R - 1 + " ");
				} else {
					out.print(Math.max(L, R) + " ");
				}
			}
			out.println();
		}
		
		public int dfs(int i, boolean flipped) {
			int count = 1;
			if(i >= left.length-1)
				return count;
			if(flipped) {
				if(rightI[i] != 0)
					return rightI[i];
				if(s.charAt(i) == 'L')
					count += dfs(i+1, !flipped);
				rightI[i] = count;
			} else {
				if(right[i] != 0)
					return right[i];
				if(s.charAt(i) == 'R')
					count += dfs(i+1, !flipped);
				right[i] = count;
			}
			return count;
		}
		
		public int dfsR(int i, boolean flipped) {
			int count = 1;
			if(i <= 0)
				return count;
			if(flipped) {
				if(leftI[i] != 0)
					return leftI[i];
				if(s.charAt(i-1) == 'R')
					count += dfsR(i-1, !flipped);
				leftI[i] = count;
			} else {
				if(left[i] != 0)
					return left[i];
				if(s.charAt(i-1) == 'L')
					count += dfsR(i-1, !flipped);
				left[i] = count;
			}
			return count;
		}
		
	}
	static long modInverse(long N, long MOD) {
		return binpow(N, MOD - 2, MOD);
	}
	static long modDivide(long a, long b, long MOD) {
		a %= MOD;
		return (binpow(b, MOD-2, MOD) * a) % MOD;
	}
	static long binpow(long a, long b, long m) {
		a %= m;
		long res = 1;
		while (b > 0) {
			if ((b & 1) == 1)
				res = res * a % m;
			a = a * a % m;
			b >>= 1;
		}
		return res;
	}
	static int[] reverse(int a[]) 
    { 
        int[] b = new int[a.length]; 
        for (int i = 0, j = a.length; i < a.length; i++, j--) { 
            b[j - 1] = a[i]; 
        } 
        
        return b;
    }
	static long[] reverse(long a[]) 
    { 
        long[] b = new long[a.length]; 
        for (int i = 0, j = a.length; i < a.length; i++, j--) { 
            b[j - 1] = a[i]; 
        } 
        
        return b;
    }
	
	static void shuffle(Object[] a) {
		Random get = new Random();
		for (int i = 0; i < a.length; i++) {
			int r = get.nextInt(a.length);
			Object temp = a[i];
			a[i] = a[r];
			a[r] = temp;
		}
	}
	
	static void shuffle(int[] a) {
		Random get = new Random();
		for (int i = 0; i < a.length; i++) {
			int r = get.nextInt(a.length);
			int temp = a[i];
			a[i] = a[r];
			a[r] = temp;
		}
	}
	static void shuffle(long[] a) {
		Random get = new Random();
		for (int i = 0; i < a.length; i++) {
			int r = get.nextInt(a.length);
			long temp = a[i];
			a[i] = a[r];
			a[r] = temp;
		}
	}
	
	static class tup implements Comparable<tup>, Comparator<tup>{
		int a, b;
		tup(int a,int b){
			this.a=a;
			this.b=b;
		}
		public tup() {
		}
		@Override
		public int compareTo(tup o){
			return Integer.compare(b,o.b);
		}
		@Override
		public int compare(tup o1, tup o2) {
			return Integer.compare(o1.b, o2.b);
		}
		
		@Override
	    public int hashCode() {
			return Objects.hash(a, b);
	    }
 
	    @Override
	    public boolean equals(Object obj) {
	    	if (this == obj)
                return true;
	    	if (obj == null)
                return false;
	    	if (getClass() != obj.getClass())
                return false;
	    	tup other = (tup) obj;
	    	return a==other.a && b==other.b;
	    }
	    
	    @Override
	    public String toString() {
	    	return a + " " + b;
	    }
	}

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		public FastReader(String s) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(new File(s)));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

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

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

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
		
		int[] readArray(int size) {
			int[] a = new int[size];
			for(int i = 0; i < size; i++) {
				a[i] = nextInt();
			}
			return a;
		}
		
		long[] readLongArray(int size) {
			long[] a = new long[size];
			for(int i = 0; i < size; i++) {
				a[i] = nextLong();
			}
			return a;
		}
	}
	
	static void dbg(int[] arr) {
		System.out.println(Arrays.toString(arr));
	}
	static void dbg(long[] arr) {
		System.out.println(Arrays.toString(arr));
	}
	static void dbg(boolean[] arr) {
		System.out.println(Arrays.toString(arr));
	}

	static void dbg(Object... args) {
        for (Object arg : args)
            System.out.print(arg + " ");
        System.out.println();
    }
}