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.FileNotFoundException;
import java.io.FileReader;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.lang.StringBuilder;

public class Main {

    public static void main(String[] args) throws IOException{
        
        InputReader reader = new InputReader();
        String input = reader.nextLine();

        CharStack stack = new CharStack();
        boolean flag = true;
        int counter = 0;

        for(int i = 0; i < input.length() && flag; i++) {
            char c = input.charAt(i);
            if(isOpen(c)) {
                stack.push(c);
            } else {
                if(stack.isEmpty()) {
                    flag = false;
                } else {
                    if(stack.peek() == getOpposite(c)) { //if last one is the same
                        stack.pop();
                    } else if(isOpen(stack.peek())) { //trying to change
                        stack.pop();
                        ++counter;
                    } else {
                        stack.push(c);
                    }
                } 
            }
        }

        if(!flag || !stack.isEmpty()) {
            System.out.println("Impossible");
        } else {
            System.out.println(counter);
        }
        
    }

    public static char getOpposite(char c) {
        if(c == ']') return '[';
        else if(c == '}') return '{';
        else if(c == ')') return '(';
        else return '<';

    }

    public static boolean isOpen(char c) {
        return c == '[' || c == '{' || c == '<' || c == '(';
    }
}

class CharStack {
    
    private StringBuilder sb = new StringBuilder();

    public void push(char c) {
        sb.append(c);
    }

    public char pop() {
        char last = sb.charAt(sb.length() - 1);
        sb.setLength(sb.length() - 1);
        return last;
    }

    public boolean isEmpty() {
        return sb.length() == 0;
    }

    public char peek() {
        return sb.charAt(sb.length() - 1);
    }

}
class InputReader{
    private BufferedReader reader;
    private StringTokenizer tokenizer;

    public InputReader() {
        tokenizer = null;
        reader = new BufferedReader(new InputStreamReader(System.in));
    }

    public InputReader(String fileName) throws FileNotFoundException{
        tokenizer = null;
        reader = new BufferedReader(new FileReader(fileName));
    }

    public String nextLine() throws IOException{
        return reader.readLine();
    }

    public String next() {
        while ( tokenizer == null || !tokenizer.hasMoreTokens() ) {
            try {
                tokenizer = new StringTokenizer(nextLine());
            } catch( IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }

    public long nextLong() {
        return Long.parseLong(next());
    }
}