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.Scanner;

public class P612C {
  public static void main(String[] args) throws Exception {
    Scanner scanner = new Scanner(System.in);
    String str = scanner.next();
    char[] stack = new char[str.length()];
    int pos = 0;
    int res = 0;
    for (int i = 0; i < str.length(); i++) {
      char c = str.charAt(i);
      if (isOpen(c)) {
        stack[pos] = c;
        pos++;
      } else {
        if (pos == 0) {
          System.out.println("Impossible");
          return;
        }
        pos--;
        char prev = stack[pos];
        switch (c) {
          case ']':
            if (prev != '[') res++;
            break;
          case ')':
            if (prev != '(') res++;
            break;
          case '>':
            if (prev != '<') res++;
            break;
          case '}':
            if (prev != '{') res++;
            break;
        }
      }
    }
    if (pos > 0) {
      System.out.println("Impossible");
      return;
    }
    System.out.println(res);
  }

  private static boolean isOpen(char c) {
    return c == '[' || c == '{' || c == '<' || c == '(';
  }
}