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.*;
import java.io.*;

public class ForProblems {

    Random rnd = new Random();

    void solve() throws IOException {

        String str = readString();
        Stack<Character> a = new Stack<Character>();

        int ans = 0;
        boolean flag = true;
        for (int i = 0; i < str.length(); ++i) {

            char tmp = str.charAt(i);
            if (tmp == '(' || tmp == '{' || tmp =='[' || tmp == '<') {

                a.add(tmp);
            } else {

                if (a.size() == 0) {

                    flag = false;
                    break;
                } else {

                    char rem = a.pop();
                    if (!((tmp == ')' && rem == '(') || (tmp == '}' && rem == '{') || (tmp == ']' && rem == '[') || (tmp == '>' && rem == '<'))) {
                        ++ans;
                    }
                }
            }
        }

        if (flag && a.size() == 0)
            out.print(ans);
        else
            out.print("Impossible");

    }

    final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    public static void main(String[] args){
        new ForProblems().run();
    }

    public void run() {
        try {
            long timeBegin = System.currentTimeMillis();
            Locale.setDefault(Locale.US);

            init();
            solve();

            out.close();

            long timeEnd = System.currentTimeMillis();
            System.err.println("Time = " + (timeEnd - timeBegin));
        } catch (Exception e) {
            e.printStackTrace(System.err);
            System.exit(-1);
        }
    }

    String readString() throws IOException {
        while(!tok.hasMoreTokens()){
            try{
                tok = new StringTokenizer(in.readLine());
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    void init() throws FileNotFoundException {
        Locale.setDefault(Locale.US);

        if (ONLINE_JUDGE) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }
    }
}