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.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.Map;
import java.util.Queue;
import java.util.Stack;
import java.util.StringTokenizer;
public class cfvc12
{
	static BufferedReader reader;
    static StringTokenizer tokenizer;
    static void init(InputStream input) 
    {
        reader = new BufferedReader( new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }
    static String next() throws IOException
    {
        while ( ! tokenizer.hasMoreTokens() )
        {
            tokenizer = new StringTokenizer(reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static long nextInt() throws IOException 
    {
        return Long.parseLong( next() );
    }
	static PrintWriter writer;
	static void outit(OutputStream outputStream)
	{
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
	}
	static void print(Object...objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	static void println(Object...objects) {
		print(objects);
		writer.println();
	}

	static void close() {
		writer.close();
	}

	static void flush() {
		writer.flush();
	}
    public static void main(String [] args) throws IOException
    {
    	init(System.in) ;
    	outit(System.out) ;
//    	int t = (int) nextInt() ;
//    	for(int i = 0 ; i<t ; i++)
    	output() ;
        flush();
        close();
    }
    public static void output( ) throws IOException
    {
    	String s = next() ;
    	Stack<Character> st = new Stack<Character>() ;
    	int ans = 0 ;
    	boolean check = true ;
    	for(int i = 0 ; i<s.length(); i++)
    	{
    		if(s.charAt(i)=='<')
    		{
    			st.push('>') ;
    		}
    		else if(s.charAt(i)=='(')
    		{
    			st.push(')') ;
    		}
    		else if(s.charAt(i)=='{')
    		{
    			st.push('}') ;
    		}
    		else if(s.charAt(i)=='[')
    		{
    			st.push(']') ;
    		}
    		else
    		{
    			if(!st.isEmpty())
    			{
    			if(s.charAt(i)!=st.pop())
    			{
//    				println(s.charAt(i)) ;
    				ans++ ;
    			}
    			}
    			else
    			{
    				check = false ;
    				break ;
    			}
    		}
    	}
    	if(!st.isEmpty())
    	{
    		check = false ;
    	}
    	if(check)
    	{
    	println(ans) ;
    	}
    	else
    	{
    		println("Impossible") ;
    	}
    }
}