A string a of length m is called antipalindromic iff m is even, and for each i (1 ≤ i ≤ m) a_i ≠ a_{m - i + 1}.

Ivan has a string s consisting of n lowercase Latin letters; n is even. He wants to form some string t that will be an antipalindromic permutation of s. Also Ivan has denoted the beauty of index i as b_i, and the beauty of t as the sum of b_i among all indices i such that s_i = t_i.

Help Ivan to determine maximum possible beauty of t he can get.

Input

The first line contains one integer n (2 ≤ n ≤ 100, n is even) — the number of characters in s.

The second line contains the string s itself. It consists of only lowercase Latin letters, and it is guaranteed that its letters can be reordered to form an antipalindromic string.

The third line contains n integer numbers b₁, b₂, ..., b_n (1 ≤ b_i ≤ 100), where b_i is the beauty of index i.

Output

Print one number — the maximum possible beauty of t.

Anti-Palindromize

Examples