Migrated from Lutece 2843 Kanade Loves Symmetry

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Description

Kanade really loves symmetrical things, like squares, circles, and the substring ana in her name.

Now she has a string that only contains lowercase letters. She would like two swap two adjacent letters several times, to make this string be a palindrome. A palindrome is a string that reads the same backward as forward. madam is a palindrome, while kanade is not a palindrome.

She would like to know the minimum time(s) of the swap operation that will be performed to make this string a palindrome.

Input

Only one line. The only line contains only one string, consisting of $n\ (1\le n\le 10^5)$ lowercase letters.

Output

Output the minimum time(s) in one line. If the string can't be a palindrome, please output Impossible.

Samples

aaaab

2

kanade

Impossible

ana

0

Note

In Sample 1, the swap operations are done as follows.

$$\texttt{aaaab}\to \texttt{aaaba} \to \texttt{aabaa} $$

In Sample 3, she doesn't need to do the swap operation. So just output $0$.

Resources

The 18th UESTC Programming Contest Preliminary