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.*;
import java.util.*;
import java.lang.*;
import java.math.BigInteger;


public class Main
{
    
    public static void main(String args[]) throws FileNotFoundException, IOException
    {
        //Scanner in =new Scanner(new FileReader("input.txt"));
        //PrintWriter out = new PrintWriter(new FileWriter("output.txt"));
        //Scanner in=new Scanner(System.in);
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out=new PrintWriter(System.out);
        
        String s=br.readLine();
        char stack[]=new char[1000001];
        int n=0;
        int ans=0;
        for(int i=0;i<s.length();i++)
        {
            if(s.charAt(i)=='{' || s.charAt(i)=='[' || s.charAt(i)=='<' || s.charAt(i)=='(')
            {
                stack[n]=s.charAt(i);
                n++;
            }
            else if(n==0)
            {
                out.print("Impossible");
                out.close();
                return ;
            }
            else if(s.charAt(i)=='}')
            {
                if(stack[n-1]!='{')
                    ans++;
                n--;
            }
            else if(s.charAt(i)==']')
            {
                if(stack[n-1]!='[')
                    ans++;
                n--;
            }
            else if(s.charAt(i)=='>')
            {
                if(stack[n-1]!='<')
                    ans++;
                n--;
            }
            else if(s.charAt(i)==')')
            {
                if(stack[n-1]!='(')
                    ans++;
                n--;
            }
        }
        if(n==0)
        out.print(ans);
        else out.print("Impossible");
        
	out.close();
    }
    public static Integer ni(String s)
    {
        return Integer.parseInt(s);
    }
    public static BigInteger nb(String s)
    {
        return BigInteger.valueOf(Long.parseLong(s));
    }
    public static Long nl(String s)
    {
        return Long.parseLong(s);
    }
    public static Double nd(String s)
    {
        return Double.parseDouble(s);
    }
}