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.*;
import java.util.*;


public class Main {
	public static void main(String args[]){
		Scanner in = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		String s = in.next();
		int l = s.length();
		int count = 0;
		ArrayList<Character> list = new ArrayList<Character>();
		for(int i =0;i<l;i++){
			char t = s.charAt(i);
			if(t=='['||t=='('||t=='{'||t=='<'){
				list.add(t);
			}else{
				boolean p = false;
				char tx = 'a';
				if(list.size()>0){
					tx = list.get(list.size()-1);
					list.remove(list.size()-1);
				}else{
					System.out.print("Impossible");
					System.exit(0);
				}
				if(!p){
					if(tx!='(' & t==')'){
							p=true;
					}
					if(tx!='[' & t==']'){
						p=true;
					}
					if(tx!='{' & t=='}'){
						p=true;
					}
					if(tx!='<' & t=='>'){
						p=true;
					}
				}
				if(p){
					count++;
				}
			}
		}
		if(list.size()>0){
			System.out.print("Impossible");
			System.exit(0);
		}
		out.print(count);
		out.close();
	}
}