Ksyusha has a string and she enjoys rearranging its letters. She is curious to find out how many distinct palindromes she can create by rearranging the letters of .
A palindrome is a string that reads the same forwards and backwards. For example, the string "ded" is a palindrome.
The input consists of a single line containing the string , where
and consists only of lowercase Latin letters.
Output a single integer representing the number of unique palindromes Ksyusha can form by rearranging the letters of the string .
Example 1
A string x = x_1x_2\ldots x_p is considered lexicographically smaller than a string y = y_1y_2\ldots y_q if either p < q and x_1 = y_1, x_2 = y_2, ..., x_p = y_p, or there exists an index (r < p, r < q) such that x_1 = y_1, x_2 = y_2, ..., x_r = y_r and x_{r+1} < y_{r+1}. The characters of the strings are compared according to their ASCII values.