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()
import math
ls=len(s)
ans=[0 for i in range(ls+1)]
dp=[[0 for i in range(ls+1)] for j in range(ls+1)]
for k in range(1,ls+1):
    for i in range(0,ls-k+1):
        j=k+i
        if s[i]!=s[j-1]:
            continue;
        if k==1:
            dp[i][j]=1
            ans[1]+=1
        elif k==2:
            dp[i][j]=2
            ans[2]+=1
        elif dp[i+1][j-1]!=0:
            dp[i][j]=dp[i][int(math.ceil(i+j)/2)]+1
            ans[dp[i][j]]+=1
for i in range(ls-1,0,-1):
    ans[i]+=ans[i+1]
for i in range(1,ls+1):
    print ans[i],