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

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

    static class TaskC {
        public void solve(int testNumber, Reader in, PrintWriter out) {
            char[] s = in.rl().toCharArray();
            ArrayDeque<Character> dq = new ArrayDeque<>();
            int ans = 0;
            for (int i = 0; i < s.length; i++) {
                if (s[i] == ')') {
                    if (dq.isEmpty()) {
                        out.println("Impossible");
                        return;
                    } else if (dq.peekLast() != '(') {
                        dq.pollLast();
                        ++ans;
                    } else {
                        dq.pollLast();
                    }
                } else if (s[i] == '}') {
                    if (dq.isEmpty()) {
                        out.println("Impossible");
                        return;
                    } else if (dq.peekLast() != '{') {
                        dq.pollLast();
                        ++ans;
                    } else {
                        dq.pollLast();
                    }
                } else if (s[i] == '>') {
                    if (dq.isEmpty()) {
                        out.println("Impossible");
                        return;
                    } else if (dq.peekLast() != '<') {
                        dq.pollLast();
                        ++ans;
                    } else {
                        dq.pollLast();
                    }
                } else if (s[i] == ']') {
                    if (dq.isEmpty()) {
                        out.println("Impossible");
                        return;
                    } else if (dq.peekLast() != '[') {
                        dq.pollLast();
                        ++ans;
                    } else {
                        dq.pollLast();
                    }
                } else {
                    dq.addLast(s[i]);
                }
            }
            if (!dq.isEmpty()) {
                out.println("Impossible");
                return;
            }
            out.println(ans);

        }

    }

    static class Reader {
        private BufferedReader in;

        public Reader(InputStream in) {
            this.in = new BufferedReader(new InputStreamReader(in));
        }

        public String rl() {
            try {
                return in.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

    }
}