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.util.*;
import java.io.*;

public class Main {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;
        FastReader() { 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;
        }
    }


    public static void main(String[] args) throws IOException {
        FastReader ip = new FastReader();
        OutputStream output = System.out;
        PrintWriter out = new PrintWriter(output);
        String s=ip.nextLine();
        Stack<Character> stack=new Stack<>();
        int count=0;
        boolean impossible=false;
        for(int i=0;i<s.length();i++){
            char c=s.charAt(i);
            if(c=='<' || c=='(' || c=='{' || c=='['){
                stack.add(c);
            }else{
                if(stack.isEmpty()){
                    impossible=true;
                    break;
                }else {
                    if ((stack.peek()=='<' && c=='>') || (stack.peek()=='(' && c==')') || (stack.peek()=='{' && c=='}') || (stack.peek()=='[' && c==']') ) {
                        stack.pop();
                    } else {
                        stack.pop();
                        count++;
                    }
                }
            }
        }
        if(impossible || !stack.isEmpty()){
            out.println("Impossible");
        }else{
            out.println(count);
        }
        out.close();
    }
}