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.*;
import java.lang.*;
public class Branches{
	public static void main(String args[]){
	        Scanner in = new Scanner(System.in);
	        String exp = in.next();
	        int ans = 0;
	        Stack<Character> o = new Stack<>();
	        for(int i = 0;i<exp.length();i++){
	            char b  = exp.charAt(i);
	            if(b == '{' || b == '[' || b == '(' || b=='<'){
	                o.push(b);
	                continue;
	            } 
	            if(o.isEmpty() && (b == '}' || b == ')' || b == ']' || b == '>')){
	                System.out.println("Impossible");
	                return;
	            }
	            char a = o.pop();
	            if((b == '}' && a == '{') || (b == ']' && a == '[') || (b == '>' && a == '<') || (b == ')' && a == '(')){
	                continue;
	            }
	            ans++;
	        }
	        if(!o.isEmpty()){
	            System.out.println("Impossible");
	            return;
	        }
	        System.out.println(ans);
	}
}