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.io.PrintWriter;
import java.util.Stack;
import java.util.StringTokenizer;

public class ProblemC {
    private char[] open = { '<', '{', '[', '(' };
    private char[] close = { '>', '}', ']', ')' };

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

        new ProblemC().solve(in, out);

        out.close();
    }

    public void solve(InputReader in, PrintWriter out) {
        String s = in.nextLine();

        Stack<Character> stack = new Stack<Character>();

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

            boolean openFound = false;
            for (int j = 0; j < 4; j++) {
                if (c == open[j]) {
                    stack.add(c);

                    openFound = true;
                }
            }

            if (!openFound) {
                if (stack.size() > 0) {

                    for (int j = 0; j < 4; j++) {
                        if (c == close[j]) {
                            char top = stack.peek();

                            if (top != open[j]) {
                                result++;
                            }

                            stack.pop();
                        }
                    }
                } else {
                    out.println("Impossible");

                    return;
                }
            }
        }

        if (stack.size() != 0) {
            out.println("Impossible");
        } else {
            out.println(result);
        }
    }

    class Pas implements Comparable<Pas> {
        int f;
        int t;

        Pas(int f, int t) {
            this.f = f;
            this.t = t;
        }

        @Override
        public int compareTo(Pas p) {
            return f - p.f;
        }
    }

    static class InputReader {
        public BufferedReader br;
        public StringTokenizer st;

        public InputReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

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

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}