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.Scanner;
import java.util.Stack;

public class Main {

	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);
		
		Stack<Character> st = new Stack<Character>();
		
		String s = sc.next();
		
		boolean bo = true;
		
		int count = 0;
		
		for(int i=0;i<s.length();i++)
		{
			switch(s.charAt(i))
			{
				case '>':
					if(st.isEmpty()){
						bo = false;
						break;
					}
					if(st.pop()!='<'){
						count++;
						break;
					}
					break;
				case '}':
					if(st.isEmpty()){
						bo = false;
						break;
					}
					if(st.pop()!='{'){
						count++;
						break;
					}
					break;
				case ']':
					if(st.isEmpty()){
						bo = false;
						break;
					}
					if(st.pop()!='['){
						count++;
						break;
					}
					break;
				case ')':
					if(st.isEmpty()){
						bo = false;
						break;
					}
					if(st.pop()!='('){
						count++;
						break;
					}
					break;
				default: 
					st.push(s.charAt(i));
			}
		}
		
		if(!bo || !st.isEmpty())
			System.out.println("Impossible");
		else 
			System.out.println(count);
	}

}