Replace To Make Regular Bracket Sequence

Description

You are given string $s$ consists of opening and closing brackets of four kinds <>, {}, [], (). There are two types of brackets: opening and closing. You can replace any bracket by another of the same type. For example, you can replace < by the bracket {, but you can’t replace it by ) or >.

The following definition of a regular bracket sequence is well-known, so you can be familiar with it.

Let’s define a regular bracket sequence (RBS). Empty string is RBS. Let $s_{1}$ and $s_{2}$ be a RBS then the strings <$s_{1}$>$s_{2}$, {$s_{1}$}$s_{2}$, [$s_{1}$]$s_{2}$, ($s_{1}$)$s_{2}$ are also RBS.

For example the string “[[(){}]<>]” is RBS, but the strings “[)()” and “][()()” are not.

Determine the least number of replaces to make the string $s$ RBS.

Input

The only line contains a non empty string $s$, consisting of only opening and closing brackets of four kinds. The length of $s$ does not exceed $10^{6}$.

Output

If it’s impossible to get RBS from $s$ print Impossible.

Otherwise print the least number of replaces needed to get RBS from $s$.

Examples

Input

[<}){}

Output

2

Input

{()}[]

Output

0

Input

]]

Output

Impossible