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 PanlidromicCharacteristics(string):
  n = len(string)
  res = [[0 for i in range (n)] for j in range (n)]
  count = [0 for i in range (n + 1)]
  # for i in range (n):
  #   res[i][i] = 1
  #   count[1] += 1
  
  for length in range (1, n + 1):
    for i in range (n-length + 1):
      j = i + length - 1
      if length == 1:
          res[i][j] = 1
      elif length == 2 and string[i] == string[j]:
          res[i][j] = 2
      elif string[i] == string[j] and res[i + 1][j - 1] > 0:
        res[i][j] = res[i][i + length//2 - 1]  + 1        
      count[res[i][j]] += 1
      
  # k-palindrome is also a (k - 1)-palindrome
  for i in range (len(count) - 1, 0, -1):
    count[i - 1] += count[i]
  for i in range (1, len(count)):
    print(count[i], end = " ")
  return 
  
string = input()
PanlidromicCharacteristics(string)