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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Stack;

public class ReplaceToMakeRegularBracketSequence {
	
	public static boolean check(char ch1, char ch2){
		if((ch1=='(' && ch2==')') || (ch1=='{' && ch2=='}') || (ch1=='[' && ch2==']') || (ch1=='<' && ch2=='>')){
			return true;
		}
		return false;
	}

	public static void main(String[] args) throws IOException {
		BufferedReader reader=new BufferedReader(new InputStreamReader(System.in));
		String str=reader.readLine();
		Stack<Character> stack=new Stack<>();
		int ans=0, i=0;
		while(i<str.length()){
			if(str.charAt(i)=='(' || str.charAt(i)=='{' || str.charAt(i)=='[' || str.charAt(i)=='<'){
				stack.push(str.charAt(i));
			}
			else{
				if(stack.isEmpty()){
					System.out.println("Impossible");
					return;
				}
				else{
					char ch=stack.pop();
					if(!check(ch, str.charAt(i))){
						ans++;
					}
				}
			}
			i++;
		}
		if(!stack.isEmpty()){
			System.out.println("Impossible");
		}
		else{
			System.out.println(ans);
		}
	}
}