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:
s = input()

size = len(s)

dp = [[0 for l in range(size)] for li in range(size)]

ans = [0]*(size+1)

for i in range(1, size+1):
    if i == 1:
        for j in range(0, size):
            dp[j][j] = 1
            ans[1] += 1
    elif i == 2:
        for j in range(0, size-1):
            if s[j+1] == s[j]:
                dp[j][j+1] = 2
                ans[1] += 1
                ans[2] += 1
            else:
                dp[j][j+1] = 0
    else:
        for j in range(0, size-i+1):
            if s[j] != s[j+i-1] or dp[j+1][j+i-2] == 0:
                dp[j][j+i-1] = 0
            else:
                dp[j][j+i-1] = dp[j][int((j+j+i-2)/2)] + 1
                for p in range(1, dp[j][j+i-1]+1):
                    ans[p] += 1

for i in range(1, size):
    print(ans[i], end="")
    print(" ", end="")
print(ans[size])