Problem G
Peragrams
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 |
