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.beans.Visibility;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;

public class Main implements Runnable{
		
		 public static void main(String[] args) throws IOException {
			new Thread(null , new Main(),"Main", 1<<26).start();
			
		 }
		 
		 
		public void run(){
			try {
			PrintWriter out = new PrintWriter(System.out);
			MyScanner sc = new MyScanner();
			solve(out, sc);
			out.flush();
			out.close();
			}
			catch (Exception e) {
				e.printStackTrace();
				
			}
		}
	
		
		
		
		
		void solve(PrintWriter out, MyScanner sc) throws IOException{	
			
			String s = sc.next();
			Stack<Character> stack = new Stack<>();
			int min = 0;
			for(int i = 0 ; i < s.length(); ++i) {
				Character c = s.charAt(i);
				if("[(<{".indexOf(c) >= 0) { stack.push(c);}
				else {
					if(stack.size() == 0) {
						out.print("Impossible");return;
					}else {
						Character cc = stack.pop();
						if("]}>)".indexOf(cc) != -1) {
							out.println("Impossible"); return;
						}else {
							if((cc == '(' && c == ')') || (cc == '{' && c == '}') || (cc == '[' && c == ']') || (cc == '<' && c == '>')) {
								continue; 
							}
							else ++min;
						}
					}
				}
			}
			if(stack.size() == 0) out.println(min); 
			else out.println("Impossible");
		
		
			
}
		
		
		
}
		

class MyScanner {
    BufferedReader br;
    StringTokenizer st;

    public MyScanner() {
       br = new BufferedReader(new InputStreamReader(System.in));
    }

    String next() {
        while (st == null || !st.hasMoreElements()) {
            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());}

    String nextLine(){
        String str = "";
	  try {
	     str = br.readLine();
	  } catch (IOException e) {
	     e.printStackTrace();
	  }
	  return str;
    }
    

}