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.InputStreamReader;
import java.io.IOException;
import java.util.InputMismatchException;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.util.ArrayDeque;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        QuickScanner in = new QuickScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }
}

class TaskC {
    String chrOpen="<{[(";
    String chrClose=">}])";
    public void solve(int testNumber, QuickScanner in, PrintWriter out) {
        ArrayDeque<Integer> q = new ArrayDeque<Integer>();
        String s=in.next();
        int res=0;
        for(int i=0;i<s.length();i++)
        {
            int iOpen=chrOpen.indexOf(s.charAt(i));
            int iClose=chrClose.indexOf(s.charAt(i));
            if(iOpen!=-1)
            {
                q.addLast(iOpen);
            }
            else if(iClose!=-1)
            {
                if(q.isEmpty())
                {
                    out.println("Impossible");
                    return;
                }
                if(q.pollLast()!=iClose)
                    res++;
            }
            else
                throw new RuntimeException();
        }
        if(q.size()!=0)
            out.println("Impossible");
        else
            out.println(res);
    }
}

class QuickScanner {
    BufferedReader in;
    StringTokenizer token;
    String delim;
    public QuickScanner(InputStream inputStream)
    {
        this.in=new BufferedReader(new InputStreamReader(inputStream));
        this.delim=" \n\t";
        this.token=new StringTokenizer("",delim);
    }

    public boolean hasNext()
    {
        while(!token.hasMoreTokens())
        {
            try {
                String s=in.readLine();
                if(s==null) return false;
                token=new StringTokenizer(s,delim);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
        }
        return true;
    }

    public String next()
    {
        hasNext();
        return token.nextToken();
    }

}