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 PYTHON3):

Solution:
def palindromic_characteristics(s):
	n = len(s)
	palindrome_level = [[0 for _ in range(n)] for _ in range(n)]
	palindrome_level_count = [0 for _ in range(n + 1)]

	for i in range(n):
		j = i
		while i >= 0 and j < n and s[i] == s[j]:
			palindrome_level[i][j] = 1
			i, j = i - 1, j + 1
	
	for i in range(n-1):
		j = i + 1
		while i >= 0 and j < n and s[i] == s[j]:
			palindrome_level[i][j] = 1
			i, j = i - 1, j + 1

	for i in range(n):
		for j in range(i, n):
			if palindrome_level[i][j] > 0:
				mid = (i + j) // 2 + (i + j) % 2
				if i <= mid-1: palindrome_level[i][j] = palindrome_level[i][mid-1] + 1

				palindrome_level_count[palindrome_level[i][j]] += 1
	
	for i in range(n-1, 0, -1): palindrome_level_count[i] += palindrome_level_count[i+1]
	return palindrome_level_count[1:]

s = input()
print(' '.join(map(str, palindromic_characteristics(s))))