Peragrams

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Photo by Ross Beresford

Per recently learned about palindromes. Now he wants to tell us about it and also has more awesome scientific news to share with us.

“A palindrome is a word that is the same no matter whether you read it backward or forward”, Per recently said in an interview. He continued: “For example, add is not a palindrome, because reading it backwards gives dda and it’s actually not the same thing, you see. However, if we reorder the letters of the word, we can actually get a palindrome. Hence, we say that add is a Peragram, because it is an anagram of a palindrome”.

Per gives us a more formal definition of Peragrams: “Like I said, if a word is an anagram of at least one palindrome, we call it a Peragram. And recall that an anagram of a word $w$ contains exactly the same letters as $w$, possibly in a different order.”

Task

Given a string, find the minimum number of letters you have to remove from it, so that the string becomes a Peragram.

Input

Input consists of a string on a single line. The string will contain at least $1$ and at most $1\, 000$ characters. The string will only contain lowercase letters a-z.

Output

Output should consist of a single integer on a single line, the minimum number of characters that have to be removed from the string to make it a Peragram.

Sample Input 1 Sample Output 1
abc
2
Sample Input 2 Sample Output 2
aab
0