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.*;
public class replacetomakeregularbracketsequence
{
  public static void main(String args[])
  {
     Scanner in=new Scanner(System.in);
     String str=in.nextLine();
     int l=str.length();
     int i,top=-1,c=0;char ch;
     char s[]=new char[l];
     for(i=0;i<l;i++)
     {
         ch=str.charAt(i);
         if(ch=='[' || ch=='<' || ch=='{' || ch=='(')
         {
             top=top+1;
             s[top]=ch;
            }
         else
         {
             if(top==-1)
             {
                 System.out.println("Impossible");
                 System.exit(0);
                }
             else if((ch==')' && s[top]=='(') ||(ch=='>' && s[top]=='<') ||(ch=='}' && s[top]=='{') ||(ch==']' && s[top]=='['))
                 top=top-1;
             else
             {
                 top--;
                 c++;
                }
            }
        }
       if(top==-1)
        System.out.println(c);
       else
        System.out.println("Impossible");
    }
}