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.io.PrintWriter;
import java.util.HashMap;
import java.util.Scanner;

/**
 * Created by ProDota2 on 25.12.2015.
 * name of project code
 **/
public class Main {
    public static class Stack{
        char mas[] = new char[10000000];
        int top = 0;
        public void print(){
            for(int i = 0;i < top;i++){
                System.out.print(mas[i]);
            }
        }
        public Stack(){
        }
        void put(char a){
            mas[top++] = a;
        }
        char getTop(){
            return mas[top - 1];
        }
        void pop(){
            top--;
        }
        int size(){
            return top;
        }
    }
    public static boolean type(char a){
        return (a == '{' || a == '(' || a == '<' || a == '[');
    }
    public static void main(String argc[]) {
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        String s = in.next();
        Stack stack = new Stack();
        int ans = 0;
        for(int i = 0;i < s.length();i++){
            if(stack.size() == 0){
                stack.put(s.charAt(i));
            }else{
                if(type(stack.getTop()) != type(s.charAt(i)) && type(stack.getTop())){
                    if(!equals(stack.getTop() , s.charAt(i))){
                        ans++;
                    }
                    stack.pop();
                }else{
                    stack.put(s.charAt(i));
                }
            }
        }
        if(stack.size() != 0 || s.length() % 2 == 1)
            out.print("Impossible");
        else
            out.print(ans);
        out.close();
    }
    public static boolean equals(char a , char b){
        if(a == '{' && b == '}')
            return true;
        if(a == '[' && b == ']')
            return true;
        if(a == '<' && b == '>')
            return true;
        if(a == '(' && b == ')')
            return true;
        return false;
    }
}