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.*;

public class C612 {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int ans = 0;
        boolean flag = true;
        String s = sc.nextLine();
        Stack<Character> stack = new Stack<>();
        for (Character c : s.toCharArray()) {
            if (stack.empty()) {
                if (c == ')' || c == '>' || c == '}' || c == ']') {
                    flag = !flag; break;
                }
                stack.push(c);
            } else {
                char ch = stack.peek();
                if (c == '(' || c =='{' || c == '<' || c == '[') {
                    stack.push(c);
                    continue;
                }
                if (ch == '{') {
                    if (c != '}') {
                        ans += 1;
                    }
                }
                if (ch == '<') {
                    if (c != '>') {
                        ans += 1;
                    }
                }
                if (ch == '[') {
                    if (c != ']') {
                        ans += 1;
                    }
                }
                if (ch == '(') {
                    if (c != ')') {
                        ans += 1;
                    }
                }
                stack.pop();
            }
        }
        System.out.println(flag ? (stack.empty() ? ans : "Impossible") : "Impossible");
    }
}