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.HashMap;
import java.util.Scanner;
import java.util.Stack;

/**
 * Created by naveen on 23-Dec-15.
 */
public class Test1 {
    public static void main(String[] args) {
        Scanner scn = new Scanner(System.in);

        String str = scn.nextLine();

        int count = 0;

        Stack<Character> stBarces = new Stack<>();
        HashMap<Character, Character> closeMap = new HashMap<>(4);

        closeMap.put('>', '<');
        closeMap.put('}', '{');
        closeMap.put(']', '[');
        closeMap.put(')', '(');

        boolean flag = true;

        for (int i = 0; i < str.length(); i++) {
            char ch = str.charAt(i);

            if( ch == '<'
                || ch == '{'
                || ch == '['
                || ch == '(' )
                stBarces.push(ch);
            else if(!stBarces.empty())
            {
                char top = stBarces.peek();
                char match = closeMap.get(ch);

                if(top != match)
                {
                    count++;
                }
                stBarces.pop();
            }
            else
                flag = false;
        }

        if(!flag)
            System.out.println("Impossible");
        else if(stBarces.empty())
            System.out.println(count);
        else
            System.out.println("Impossible");

    }
}