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.File;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.Scanner;

public class Main {

	static Scanner sc = new Scanner(System.in);

	static String str;
	static ArrayList<String> list = new ArrayList<String>();
	static long counter = 0;
	
	public static void main(String[] args) {
		str = sc.next();
		
		for (int i = 0; i < str.length(); i++) {
			list.add(str.charAt(i)+"");
			if (list.size() == 1 || list.size() == 0) continue;
			
			String str1 = list.get(list.size() - 2);
			String str2 = list.get(list.size() - 1);
			
			int type1, type2;
			if (str1.equals("{") || str1.equals("[") || str1.equals("(") || str1.equals("<")) type1 = 1;
			else type1 = 2;
			
			if (str2.equals("{") || str2.equals("[") || str2.equals("(") || str2.equals("<")) type2 = 1;
			else type2 = 2;
			
			if (type1 == 1 && type2 == 2) {
				if (str1.equals("{") && !str2.equals("}")) counter++;
				if (str1.equals("[") && !str2.equals("]")) counter++;
				if (str1.equals("(") && !str2.equals(")")) counter++;
				if (str1.equals("<") && !str2.equals(">")) counter++;
				list.remove(list.size() - 1);
				list.remove(list.size() - 1);
				continue;
			}
		}
		
		if (list.size() != 0) {System.out.println("Impossible"); return;}
		
		System.out.println(counter);
	}
}