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.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.Scanner;
import java.util.Stack;


public class C612 {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner in = new Scanner(System.in);
		String s = in.nextLine();
		in.close();
		Stack<Character> stk = new Stack<>();
		List<Character> openBrackets = Arrays.asList('<', '{', '(', '[');
		HashMap <Character, Character> hm = new HashMap<>(4);
		hm.put('>', '<');
		hm.put('}','{');
		hm.put(']', '[');
		hm.put(')', '(');
		int changes = 0;
		for (int i = 0; i<s.length(); i++) {
			Character c = s.charAt(i);
			if (openBrackets.contains(c)) {
				stk.add(c);
			} else {
				if (stk.empty()) {
					System.out.println("Impossible");
					return;
				}
				Character open = stk.pop();
				if (hm.get(c) != open) {
					changes++;
				}
			}
		}
		if (stk.empty()){
			System.out.println(changes);
		} else {
			System.out.println("Impossible");
		}
	}

}