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.Scanner;

public class C {

    static void solve() throws IOException {
        char[] c = in.readLine().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" );
    }

    static BufferedReader in;
    static PrintWriter out;

//    static int nextInt() throws IOException {
//        in.nextToken();
//        return ( int ) in.nval;
//    }

    public static void main( String[] args ) throws IOException {
        in = new BufferedReader( new InputStreamReader( System.in ) );
        out = new PrintWriter( System.out );
        solve();
        out.close();
    }
}