A10073. Replace To Make Regular Bracket Sequence

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.

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 $10^{6}$ .

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

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