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

Let's denote k-substring of s as a string subs_k = s_ks_k + 1..s_{n + 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.

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).