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.FileNotFoundException;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Scanner;
import java.util.StringTokenizer;


public class CodeforcesC {

	/**
	 * @param args
	 * @throws IOException 
	 */
	public static void main(String[] args) throws IOException {
		Scanner in = new Scanner(System.in);
		String s = in.next();
		ArrayList<Character> st = new ArrayList<Character>();
		int ans = 0;
		for (int i = 0; i<s.length(); i++){
			char br = s.charAt(i);
			if (Bracket.isOpen(br)){
				st.add(br);
			} else {
				if (st.size()==0){
					System.out.println("Impossible");
					return;
				}
				if (Bracket.reverse(st.get(st.size()-1))==br){
					st.remove(st.size()-1);
				} else {
					st.remove(st.size()-1);
					ans++;
				}
			}
		}
		if (st.size()!=0){
			System.out.println("Impossible");
			return;
		}
		System.out.println(ans);
	}

}

class Bracket{
	static char reverse(char b){
		switch(b){
		case '(':{
			return ')';
		}
		case '{':{
			return '}';
		}
		case '[':{
			return ']';
		}
		case '<':{
			return '>';
		}
		}
		return ' ';
	}
	static boolean isOpen(char b){
		if (b=='('||b=='{'||b=='<'||b=='[') return true;
		return false;
	}
}