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:
For evey k-substring () of s you have to calculate the maximum length of its odd proper suprefix.
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.
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).
15
bcabcabcabcabca
9 7 5 3 1 -1 -1 -1
24
abaaabaaaabaaabaaaabaaab
15 13 11 9 7 5 3 1 1 -1 -1 1
19
cabcabbcabcabbcabca
5 3 1 -1 -1 1 1 -1 -1 -1
The answer for first sample test is folowing:
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