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.Scanner;
import java.util.Stack;

public class q3 
{

    public static void main(String args[])
    {
        Scanner s=new Scanner(System.in);
        String st=s.next();
        Stack<Character> c=new Stack<>();
        int an=0;
        for(int i=0;i<st.length();i++)
        {
            if(st.charAt(i)=='>' || st.charAt(i)=='}' || st.charAt(i)==')' || st.charAt(i)==']')
            {
                if(c.isEmpty())
                {
                    System.out.println("Impossible");
                    return;
                }
                else
                {
                    char c1=c.pop();
                    if(!match(c1,st.charAt(i)))
                        an++;
                }
            }
            else
                c.push(st.charAt(i));
        }
        if(c.isEmpty())
        System.out.println(an);
        else
            System.out.println("Impossible");
    }
    
    public static boolean match(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;
        
    }
}