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 PYTHON):

Solution:
s = raw_input()
n = len(s)
res = [0] * (n + 1)
dp = [[0] * n for _ in xrange(n)]

for l in xrange(1, n + 1):
    for i in xrange(n - l + 1):
        j = i + l - 1
        if l == 1:
            dp[i][j] = 1
            continue
        if s[i] == s[j] and (l == 2 or dp[i + 1][j - 1] > 0):
            dp[i][j] = 1
        else:
            continue
        sub_l = l / 2
        if dp[i][i + sub_l - 1] > 0:
            dp[i][j] = dp[i][i + sub_l - 1] + 1

for i in xrange(n):
    for j in xrange(n):
        res[dp[i][j]] += 1

for i in xrange(n - 1, 0, -1):
    res[i] += res[i + 1]

print ' '.join(map(str, res[1:]))