You are given a string ~A~. You want to remove the most number of characters to make the string a palindrome.

A palindrome is defined as a string of length greater than or equal to ~1~ that is the same forwards as it is backwards.

Input Specification

The first line will contain the string ~A~ ~(1 \le |A| \le 10^5)~. ~A~ is guaranteed to only contain lowercase alphabetical characters.

Output Specification

Print the maximum number of characters that can be removed to make the string a palindrome.

Sample Input

jsumabatroooheart

Sample Output

16