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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Stack;
import java.util.StringTokenizer;

public class Main {

    public static void main(String[] args) {
	    String s = new InputReader(System.in).next();

        int ans = 0;
        Stack<Character> st = new Stack<>();
        for (int i = 0; i < s.length(); ++i) {
            char ch = s.charAt(i);
            if (ch ==  '[' || ch == '<' || ch == '(' || ch == '{') {
                st.push(ch);
                continue;
            }
            if (st.empty()) {
                ans = -1;
                break;
            }

            char t = st.pop();
            if (t == '[' && ch == ']' ||
                t == '<' && ch == '>' ||
                t == '(' && ch == ')' ||
                t == '{' && ch == '}') {
                //  ok
            }
            else {
                ++ans;
            }
        }

        if  (!st.empty()) {
            ans = -1;
        }
        if (ans < 0) System.out.println("Impossible");
        else System.out.println(ans);
    }
}


class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

}