You are given string s consists of opening and closing brackets of four kinds \neq , {}, [], (). 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 \lt by the bracket {, but you can't replace it by ) or \gt .

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 s1 and s2 be a RBS then the strings \lt s1 \gt s2, {s1}s2, [s1]s2, (s1)s2 are also RBS.

For example the string "[[(){}] \neq ]" 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 106.

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

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