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.LinkedList;

import java.util.StringTokenizer;



public class Task11 {
    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        FastScanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }

        String nextLine() {
            try {
                return br.readLine();
            } catch (IOException e) {
                return null;
            }
        }

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

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

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

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

    }
    public static void main(String[] args) {

        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        String IMPOSSIBLE = "Impossible";

        char[] c = in.nextLine().toCharArray();
        int n = c.length;
        char[] s = new char[n];
        int t = -1;
        String p = "[](){}<>";
        int r = 0;
        for ( char d : c ) {
            int i = p.indexOf( d );
            if ( i % 2 == 0 ) {
                s[++ t] = d;
            } else if ( t < 0 ) {
                t = -10;
                break;
            } else {
                r += ( ( i ^ 1 ) == p.indexOf( s[t] ) ) ? 0 : 1;
                t --;
            }
        }
        out.println( t == -1 ? r : IMPOSSIBLE );
        out.close();
    }
}