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.*;
public final class replace_to_make_regular
{
    static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	static FastScanner sc=new FastScanner(br);
    static PrintWriter out=new PrintWriter(System.out);
	static Stack<Character> s1;
	
	static boolean isOpen(char ch)
	{
		if(ch=='{' || ch=='[' || ch=='(' || ch=='<')
		{
			return true;
		}
		return false;
	}
	
	static boolean isMatch(char a,char b)
	{
		if(a=='{' && b=='}')
			return true;
		if(a=='(' && b==')')
			return true;
		if(a=='[' && b==']')
			return true;
		if(a=='<' && b=='>')
			return true;
		return false;
	}
	
	@SuppressWarnings("unchecked")
	public static void main(String args[]) throws Exception
	{
		char[] a=sc.next().toCharArray();
		s1=new Stack<Character>();
		int res=0;boolean ans=true;
		for(int i=0;i<a.length;i++)
		{
			if(isOpen(a[i]))
			{
				s1.push(a[i]);
			}
			else
			{
				if(s1.size()>0)
				{
					char elem=s1.pop();
					if(!isMatch(elem,a[i]))
					{
						res++;
					}
				}
				else
				{
					ans=false;
					break;
				}
			}
		}
		if(s1.size()==0)
		{
			out.println((ans)?res:"Impossible");
		}
		else
		{
			out.println("Impossible");
		}
		out.close();
	}
}
class FastScanner
{
    BufferedReader in;
    StringTokenizer st;

    public FastScanner(BufferedReader in) {
        this.in = in;
    }
	
    public String nextToken() throws Exception {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }
	
	public String next() throws Exception {
		return nextToken().toString();
	}
	
    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }
}