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.IOException;
import java.io.InputStreamReader;
import java.util.InputMismatchException;
import java.util.Stack;
import java.util.StringTokenizer;

public class Main {

    public static void main(String[] args) {
        QuickScanner scanner = new QuickScanner();
        String str = scanner.next();
        int replaces = findReplacement(str);
        if (replaces == -1) {
            System.out.println("Impossible");
        }
        else {
            System.out.println(replaces);
        }
    }

    public static int findReplacement(String str) {
        Stack<Character> stack = new Stack<>();

        int replaces = 0;
        for (int i = 0; i < str.length(); i++) {
            char ch = str.charAt(i);
            if (isOpeningBrace(ch)) {
                stack.push(ch);
            }
            else if (isClosingBrace(ch)) {
                if (stack.isEmpty()) {
                    return -1;
                }

                Character opening = stack.pop();
                char closingBrace = getClosingBrace(opening);
                if (closingBrace != ch) {
                    replaces++;
                }
            }
        }
        return !stack.isEmpty() ? -1 : replaces;
    }

    public static boolean isOpeningBrace(char ch) {
        return ch == '<' || ch == '{' || ch == '[' || ch == '(';
    }

    public static boolean isClosingBrace(char ch) {
        return ch == '>' || ch == '}' || ch == ']' || ch == ')';
    }

    public static char getClosingBrace(char ch) {
        if (ch == '<') {
            return '>';
        }
        if (ch == '{') {
            return '}';
        }
        if (ch == '[') {
            return ']';
        }
        if (ch == '(') {
            return ')';
        }
        return '0';
    }

    private static class QuickScanner {
        BufferedReader in;
        StringTokenizer token;

        public QuickScanner() {
            this.in=new BufferedReader(new InputStreamReader(System.in));
            this.token=new StringTokenizer(""," \n\t");
        }

        public boolean hasNext() {
            while(!token.hasMoreTokens()) {
                try {
                    String s=in.readLine();
                    if(s==null) return false;
                    token=new StringTokenizer(s," \n\t");
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
            }
            return true;
        }

        public String nextLine() {
            try {
                return in.readLine();
            } catch (IOException e) {
                throw new InputMismatchException();
            }
        }

        public String next() {
            hasNext();
            return token.nextToken();
        }

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