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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.FilterInputStream;
import java.util.Vector;
import java.io.BufferedInputStream;
import java.util.HashMap;
import java.util.Stack;
import java.io.InputStream;

/**
 * @author khokharnikunj8
 */

public class Main {
    public static void main(String[] args) {
        new Thread(null, new Runnable() {
            public void run() {
                new Main().solve();
            }
        }, "1", 1 << 26).start();
    }

    void solve() {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        ScanReader in = new ScanReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        EReplaceToMakeRegularBracketSequence solver = new EReplaceToMakeRegularBracketSequence();
        solver.solve(1, in, out);
        out.close();
    }

    static class EReplaceToMakeRegularBracketSequence {
        HashMap<Character, Character> map;

        public void solve(int testNumber, ScanReader in, PrintWriter out) {
            map = new HashMap<>();
            map.put('{', '}');
            map.put('(', ')');
            map.put('<', '>');
            map.put('[', ']');
            String s = in.scanString();
            Stack<Character> stack = new Stack<>();
            boolean flag = true;
            int ans = 0;
            for (int i = 0; i < s.length(); i++) {
                if (s.charAt(i) == '(' || s.charAt(i) == '{' || s.charAt(i) == '[' || s.charAt(i) == '<')
                    stack.push(s.charAt(i));
                else if (stack.size() == 0) flag = false;
                else if (map.get(stack.pop()) != s.charAt(i)) ans++;

            }
            if (!stack.isEmpty()) flag = false;
            if (flag) out.println(ans);
            else out.println("Impossible");
        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int index;
        private BufferedInputStream in;
        private int total;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (index >= total) {
                index = 0;
                try {
                    total = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (total <= 0) return -1;
            }
            return buf[index++];
        }

        public String scanString() {
            int c = scan();
            if (c == -1) return null;
            while (isWhiteSpace(c)) c = scan();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = scan();
            } while (!isWhiteSpace(c));
            return res.toString();
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

    }
}