Peragrams

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.”

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

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 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 |