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;
import java.util.Stack;

//import edu.princeton.cs.algs4.Stack;

public class ReplacetoMakeRegularBrackets {

	public static void main(String[] args) {
		// TODO Auto-generated method stub

		Scanner input= new Scanner(System.in);
		Stack<Character> s = new Stack<Character>();
		char[] str =  input.next().toCharArray();
	  
		int counter=0;
		for(int i=0; i<str.length;i++){
			if(str[i]=='<'||str[i]=='{' || str[i]=='('|| str[i]=='['){
				s.push(str[i]);
			}
			else{
				
				   if(s.isEmpty()){
					   System.out.println("Impossible");
					   return;
				   }
				if((str[i]==']' && s.peek()=='[') || (str[i]=='}' && s.peek()=='{') || (str[i]==')'&& s.peek()=='(') || (str[i]=='>' && s.peek()=='<')){
					s.pop();
				//	System.out.println("fd");
				}
				else{
					counter++;
					//System.out.println(str[i]+" "+s.peek());
					s.pop();
				}
			}
		}
		if(s.isEmpty()){
			System.out.println(counter);
		}
		else{
			System.out.println("Impossible");
		}
	
	}

}