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.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Stack;
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;
        InputReader in = new InputReader(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, InputReader in, PrintWriter out) {
            String s = in.next();
            int left = 0;
            for (int i = 0; i < s.length(); i++) {
                switch (s.charAt(i)) {
                    case '(':
                    case '{':
                    case '[':
                    case '<':
                        left++;
                        break;
                    default:
                        if (left > 0) left--;
                        else {
                            out.println("Impossible");
                            return;
                        }
                }
            }
            if (left > 0) {
                out.println("Impossible");
                return;
            }
            int ans = 0;
            Stack<Character> ch = new Stack<>();
            for (int i = 0; i < s.length(); i++) {
                switch (s.charAt(i)) {
                    case '>':
                        if (ch.pop() != '<') ans++;
                        break;
                    case '}':
                        if (ch.pop() != '{') ans++;
                        break;
                    case ')':
                        if (ch.pop() != '(') ans++;
                        break;
                    case ']':
                        if (ch.pop() != '[') ans++;
                        break;
                    default:
                        ch.push(s.charAt(i));
                }
            }
            out.println(ans);
        }

    }

    static class InputReader {
        private StringTokenizer tokenizer;
        private BufferedReader reader;

        public InputReader(InputStream inputStream) {
            reader = new BufferedReader(new InputStreamReader(inputStream));
        }

        private void fillTokenizer() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (Exception e) {
                    throw new RuntimeException(e);
                }
            }
        }

        public String next() {
            fillTokenizer();
            return tokenizer.nextToken();
        }

    }
}