Problem: Palindromic characteristics of string s with length |s| is a sequence of |s| integers, where k-th number is the total number of non-empty substrings of s which are k-palindromes.

A string is 1-palindrome if and only if it reads the same backward as forward.

A string is k-palindrome (k > 1) if and only if: 

  1. Its left half equals to its right half. 
  2. Its left and right halfs are non-empty (k - 1)-palindromes. 



The left half of string t is its prefix of length ⌊|t| / 2⌋, and right half — the suffix of the same length. ⌊|t| / 2⌋ denotes the length of string t divided by 2, rounded down.

Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times.

Input

The first line contains the string s (1 ≤ |s| ≤ 5000) consisting of lowercase English letters.

Output

Print |s| integers — palindromic characteristics of string s.

Examples

Input

abba


Output

6 1 0 0 


Input

abacaba


Output

12 4 1 0 0 0 0 

Note

In the first example 1-palindromes are substring «a», «b», «b», «a», «bb», «abba», the substring «bb» is 2-palindrome. There are no 3- and 4-palindromes here.

Solution (in JAVA):

Solution:
import java.util.*;
import java.lang.*;
import java.math.*;
import java.io.*;
 
/* spar5h */
 
public class codeforces implements Runnable { 
	
	public void run() {
		
		InputReader s = new InputReader(System.in);
		PrintWriter w = new PrintWriter(System.out);
		
		String str = s.next();
		int n = str.length();
		
		int[][] dp = new int[n][n];
		int[] count = new int[n + 1];
		
		//dp[size][start]
		
		Arrays.fill(dp[0], 1);
		count[1] = n;
		
		for(int i = 0; i < n - 1; i++) {
			
			if(str.charAt(i) == str.charAt(i + 1)) {
				
				dp[1][i] = 2; count[2]++;
			}
		}
		
		for(int l = 2; l < n; l++) {
			
			for(int i = 0; i < n - l; i++) {
				
				if(str.charAt(i) == str.charAt(i + l) && dp[l - 2][i + 1] > 0)
					dp[l][i] = dp[(l - 1) / 2][i] + 1;
				
				count[dp[l][i]]++;
			}
		}
		
		/*
		dp check abacaba
		 
		 for(int l = 0; l < n; l++) {
			 
			 for(int i = 0; i < n - l; i++)
				 w.println(l + " " + i + " " + dp[l][i]);
		 }
		 */
	
		for(int i = n - 1; i >= 1; i--) 	
			count[i] += count[i + 1];
		
		for(int i = 1; i <= n; i++)
			w.print(count[i] + " ");
		
		w.println();
		
		w.close();
	}
	
	static class InputReader
	{
		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 String nextLine()
		{
			BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
			String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
		}
		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 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 String readString() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = read();
			} 
			while (!isSpaceChar(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;
		}
	 
		public String next() 
		{
			return readString();
		}
		
		public interface SpaceCharFilter 
		{
			public boolean isSpaceChar(int ch);
		}
	}
    
	public static void main(String args[]) throws Exception
	{
		new Thread(null, new codeforces(),"codeforces",1<<26).start();
	}
	   
}