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.BufferedReader;
import java.io.InputStreamReader;
import java.util.Stack;

public class Edu4B {
    public static void main(String[] args) throws Exception {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        char[] s = bf.readLine().toCharArray();
        Stack<Character> st = new Stack<>();
        int ans = 0;
        for (int i = 0; i < s.length; i++) {
            if (checkOpening(s[i])) {
                st.push(s[i]);
            } else if (st.isEmpty()) {
                System.out.println("Impossible");
                return;
            } else {
                char x = st.pop();
                if (!sameType(x, s[i]))
                    ans++;
            }
        }
        if (!st.empty()) {
            System.out.println("Impossible");
            return;
        } else {
            System.out.println(ans);
        }
    }

    private static boolean sameType(char c, char x) {
        return (c == '[' && x == ']') || (c == '<' && x == '>')
                || (c == '{' && x == '}') || (c == '(' && x == ')');
    }

    private static boolean checkOpening(char c) {
        return c == '[' || c == '<' || c == '{' || c == '(';
    }
}