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.InputStreamReader;
import java.nio.charset.Charset;
import java.util.*;

public class Main {

    private FastScanner scanner = new FastScanner();

    public static void main(String[] args) {
        new Main().solve();
    }

    private void solve() {
        String s = scanner.nextLine();

        int ans = 0, b = 0;
        LinkedList<Character> st = new LinkedList<>();


        for (int i = 0; i < s.length(); i++) {
            Character c = s.charAt(i);

            if (isClosed(c)) {
                if (st.isEmpty()) {
                    System.out.print("Impossible");
                    return;
                }

                Character t = st.pollLast();
                if (isClosed(t)) {
                    System.out.print("Impossible");
                    return;
                }

                if (!isSame(c, t)) {
                    ans ++;
                }
            } else {
                st.addLast(c);
            }
        }
        if (!st.isEmpty()) {
            System.out.print("Impossible");
            return;
        }
        System.out.print(ans);

    }

    boolean isClosed(Character c) {
        return c == ')' || c == ']' || c == '>' || c == '}';
    }

    boolean isSame(Character c1, Character c2) {
        return c1 == ')' && c2 == '(' || c1 == ']' && c2 == '[' || c1 == '>' && c2 == '<' || c1 == '}' && c2 == '{';
    }

    class FastScanner {
        BufferedReader reader;
        StringTokenizer tokenizer;

        FastScanner() {
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }

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

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

        Integer[] nextA(int n) {
            Integer a[] = new Integer[n];
            for (int i = 0; i < n; i++) {
                a[i] = scanner.nextInt();
            }
            return a;
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
    }
}