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 problem612C {
    public static void main(String[] args) {
        Scanner aka = new Scanner(System.in);
        Stack<Character> stack = new Stack<>();
        String inp = aka.nextLine();
        int count = 0;
        for (int i = 0; i < inp.length(); i++) {
            switch(inp.charAt(i)) {
                case '[':
                case '{':
                case '<':
                case '(':
                    stack.push(inp.charAt(i));
                    break;
                case ']':
                    if (stack.empty()) {
                        System.out.print("Impossible");
                        return;
                    }
                    if (stack.pop() != '[')
                        count++;
                    break;
                case '}': if (stack.empty()) {
                    System.out.print("Impossible");
                    return;
                    }
                    if (stack.pop() != '{')
                        count++;
                    break;
                case '>': if (stack.empty()) {
                    System.out.print("Impossible");
                    return;
                    }
                    if (stack.pop() != '<')
                        count++;
                    break;
                case ')': if (stack.empty()) {
                        System.out.print("Impossible");
                        return;
                    }
                    if (stack.pop() != '(')
                        count++;
                    break;
            }
        }
        if (stack.empty()) {
            System.out.print(count);
        } else {
            System.out.print("Impossible");
        }
    }
}