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.ArrayList;
import java.util.Scanner;


public class C {
    public static void main(String args[]){
        Scanner sc = new Scanner(System.in);
        String s = sc.nextLine();
        char[] op = {'{', '<', '[', '('};
        char[] cl = {'}', '>', ']', ')'};
        ArrayList<Character> need = new ArrayList<Character>();
        boolean good = true;
        int ret = 0;
        int i = 0;
        while(i < s.length() && good){
            if(s.charAt(i) == '{' || s.charAt(i) == '<' || 
                    s.charAt(i) == '[' || s.charAt(i) == '('){
                for(int j = 0; j < 4; j++){
                    if(s.charAt(i) == op[j]) need.add(cl[j]);
                }
            }
            else{
                if(need.size() == 0){
                    good = false;
                }
                else{
                    if(s.charAt(i) != need.get(need.size()-1)){
                        ret++;
                    }
                    need.remove(need.size()-1);
                }
            }
            i++;
        }
        if(!good || need.size() > 0) System.out.println("Impossible");
        else                         System.out.println(ret);
    }
}