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.*;

/**
 * Created by jiaweizhang on 2/29/16.
 */
public class Brackets {
    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);

        String str = sc.nextLine();

        int num = 0;

        Stack<Character> s = new Stack<Character>();
        for (int i = 0; i < str.length(); i++) {
            if (str.charAt(i) == '<') {
                s.push('>');
            } else if (str.charAt(i) == '{') {
                s.push('}');
            } else if (str.charAt(i) == '[') {
                s.push(']');
            } else if (str.charAt(i) == '(') {
                s.push(')');
            } else {
                if (s.empty()) {
                    System.out.println("Impossible");
                    return;
                }
                //System.out.println(s);

                if (s.peek() != str.charAt(i)) {
                    num++;
                }
                s.pop();
            }
        }

        if (!s.empty()) {
            System.out.println("Impossible");
            return;
        }

        System.out.println(num);

    }
}