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 P612C {

  private static void solve() {
    char[] s = next().toCharArray();

    Stack<Character> stack = new Stack<>();
    int ans = 0;
    boolean valid = true;
    for (int i = 0; i < s.length && valid; i++) {
      char c = s[i];
      if (c == '(' || c == '{' || c == '[' || c == '<') {
        stack.push(c);
      } else {
        if (stack.isEmpty()) {
          valid = false;
        } else {
          Character sc = stack.pop();
          if ((c == '}' && sc != '{') || (c == ']' && sc != '[') || (c == ')' && sc != '(') || (c == '>' && sc != '<')) {
            ans++;
          }
        }
      }
    }

    valid &= stack.isEmpty();
    System.out.println(valid ? String.valueOf(ans) : "Impossible");
  }

  private static void run() {
    br = new BufferedReader(new InputStreamReader(System.in));
    out = new PrintWriter(System.out);

    solve();

    out.close();
  }

  private static StringTokenizer st;
  private static BufferedReader br;
  private static PrintWriter out;

  private static String next() {
    while (st == null || !st.hasMoreElements()) {
      String s;
      try {
        s = br.readLine();
      } catch (IOException e) {
        return null;
      }
      st = new StringTokenizer(s);
    }
    return st.nextToken();
  }

  private static int nextInt() {
    return Integer.parseInt(next());
  }

  private static long nextLong() {
    return Long.parseLong(next());
  }

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