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F. k-substrings
time limit per test
4 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a string s consisting of n lowercase Latin letters.

Let's denote k-substring of s as a string subsk = sksk + 1..sn + 1 - k. Obviously, subs1 = s, and there are exactly such substrings.

Let's call some string t an odd proper suprefix of a string T iff the following conditions are met:

  • |T| > |t|;
  • |t| is an odd number;
  • t is simultaneously a prefix and a suffix of T.

For evey k-substring () of s you have to calculate the maximum length of its odd proper suprefix.

Input

The first line contains one integer n (2 ≤ n ≤ 106) — the length s.

The second line contains the string s consisting of n lowercase Latin letters.

Output

Print integers. i-th of them should be equal to maximum length of an odd proper suprefix of i-substring of s (or  - 1, if there is no such string that is an odd proper suprefix of i-substring).

Examples
Input
15
bcabcabcabcabca
Output
9 7 5 3 1 -1 -1 -1
Input
24
abaaabaaaabaaabaaaabaaab
Output
15 13 11 9 7 5 3 1 1 -1 -1 1
Input
19
cabcabbcabcabbcabca
Output
5 3 1 -1 -1 1 1 -1 -1 -1
Note

The answer for first sample test is folowing:

  • 1-substring: bcabcabcabcabca
  • 2-substring: cabcabcabcabc
  • 3-substring: abcabcabcab
  • 4-substring: bcabcabca
  • 5-substring: cabcabc
  • 6-substring: abcab
  • 7-substring: bca
  • 8-substring: c