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 ReplaceToMakeRegularBracketSequence {

	public static boolean isOpen(char c){
		return c == '(' || c == '[' || c == '{' || c == '<';
	}
	
	public static boolean isMatched(char open, char closed){
		return (open == '(' && closed == ')')
				|| (open == '[' && closed == ']') 
				|| (open == '{' && closed == '}')
				|| (open == '<' && closed == '>');
	}
	
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		char[] inputLine = s.next().toCharArray();
		
		int indicator = 0;
		boolean possible=true;
		int result=0;
		
		for(int i = 0; i < inputLine.length; i++)	{
			if(isOpen(inputLine[i])){
				indicator ++;
			}
			else {
				indicator--;
			}
			if (indicator < 0){
				possible = false;
				break;
			}
		}
		
		if (indicator!=0 || !possible){
			System.out.println("Impossible");
			s.close();
			return;
		}
		
		Stack<Character> stack = new Stack<>();
		for(int i = 0; i < inputLine.length; i++){
			if (isOpen(inputLine[i])){
				stack.add(inputLine[i]);
			}
			else{
				char closed = inputLine[i];
				if (!isMatched(stack.pop(),closed)){
					result++;
				}
			}
		}
		System.out.println(result);
		
		s.close();

	}

}