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 Main {
  static int n;
  static String s;
  static char[] str;

  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);

    s = sc.next();
    n = s.length();
    str = s.toCharArray();

    char[] stack = new char[n];
    int sp = 0;
    int count = 0;
    for(int i = 0; i < n; i++){
      if(str[i] == '(' || str[i] == '<' || 
        str[i] == '{' || str[i] == '['){
        if(sp + 1 >= n){
          System.out.println("Impossible");
          return;
        }
        stack[sp++] = str[i];
      }
      else{
        if(sp - 1 < 0){
          System.out.println("Impossible");
          return;
        }
        char ch = stack[--sp];
        if(ch == '(' && str[i] != ')'){
          ++count;
        }
        else if(ch == '<' && str[i] != '>'){
          ++count;
        }
        else if(ch == '{' && str[i] != '}'){
          ++count;
        }
        else if(ch == '[' && str[i] != ']'){
          ++count;
        }
      }
    }

    if(sp != 0){
      System.out.println("Impossible");
    }
    else{
      System.out.println(count);
    }
  }
}