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.*;
import java.util.ArrayDeque;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

@SuppressWarnings("WeakerAccess")
public class Main {

    final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

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

    void init() throws FileNotFoundException {
        if (ONLINE_JUDGE) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());

        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    public void run() {
        try {
            long t1 = System.currentTimeMillis();
            init();
            solve();
            out.close();
            long t2 = System.currentTimeMillis();
            System.err.println("Time = " + (t2 - t1));
        } catch (Exception e) {
            e.printStackTrace(System.err);
            System.exit(-1);
        }
    }


    public static final class Point implements Comparable<Point> {
        final int x;
        final int y;

        public Point(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public int compareTo(Point o) {
            int compare = Integer.compare(x, o.x);
            if (compare == 0) {
                return Integer.compare(y, o.y);
            }
            return compare;
        }

        @Override
        public String toString() {
            return "Point{" +
                    "x=" + x +
                    ", y=" + y +
                    '}';
        }
    }

    public void solve() throws IOException {

        String s = readString();

        ArrayDeque<Character> deq = new ArrayDeque<>();

        int ans = 0;

        Map<Character, Character> ideal = new HashMap<>();
        ideal.put('[', ']');
        ideal.put('{', '}');
        ideal.put('<', '>');
        ideal.put('(', ')');


        for (char c : s.toCharArray()) {
            switch (c) {
                case '[':
                case '{':
                case '<':
                case '(':
                    deq.push(c);
                    break;
                case ']':
                case '}':
                case '>':
                case ')':
                    if (deq.isEmpty()) {
                        out.println("Impossible");
                        return;
                    }
                    char temp = deq.pop();
                    char r = ideal.get(temp);
                    if (c != r) {
                        ans++;
                    }
            }
        }

        if (!deq.isEmpty()) {
            out.println("Impossible");
        } else {
            out.println(ans);
        }

    }


}