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.Scanner;
import java.util.Stack;

public class Educational4C {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        String s=sc.nextLine();
        char []c=s.toCharArray();
        Stack st=new Stack();
        int now=0;
        boolean judge=false;
        for(int i=0;i<s.length();i++){
            if(c[i]=='['||c[i]=='{'||c[i]=='('||c[i]=='<')
                st.push(c[i]);
            else{
                if(!st.isEmpty()){
                    char tem=(char) st.pop();
                    if((tem=='<'&&c[i]=='>')||(tem=='('&&c[i]==')')||(tem=='['&&c[i]==']')||(tem=='{'&&c[i]=='}')){
                        
                    }
                    else
                        now++;
                }
                else{
                    judge=true;
                    break;
                }
            }   
        }
        if(!st.isEmpty()||judge)
            System.out.println("Impossible");
        else
            System.out.println(now);
    }
}