Problem: 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 s1 and s2 be a RBS then the strings <s1>s2, {s1}s2, [s1]s2, (s1)s2 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 106.

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

[&lt;}){}


Output

2

Input

{()}[]


Output

0

Input

]]


Output

Impossible

Solution (in JAVA):

Solution:
import java.util.*;


public class practice {
    public static void main(String args[])
    {
        Scanner scan = new Scanner(System.in);
        String s=scan.nextLine();
        Stack<Character>ms=new Stack<>();
        int counter=0, n=s.length();
        for(int index=0; index<n; index++)
        {
            char c=s.charAt(index);
            if(c=='(' || c=='[' || c=='{' || c=='<')
                ms.push(c);
            else
            {
                if(ms.empty()==true)
                {
                    System.out.println("Impossible");
                    return;
                }
                else
                {
                    char d=ms.peek();
                    if(c==')' && d!='(')
                        counter++;
                    else if(c=='}' && d!='{')
                        counter++;
                    else if(c==']' && d!='[')
                        counter++;
                    else if(c=='>' && d!='<')
                        counter++;
                    ms.pop();
                }
            }

        }
        if(ms.empty()!=true)
            System.out.println("Impossible");
        else
            System.out.println(counter);
        return;
    }
}