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 {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        Skobka skb = new Skobka();
        PrintWriter out = new PrintWriter(outputStream);
        String line = in.readLine();
        Stack<Character> st = new Stack<Character>();
        int ans = 0;
        boolean allisok = true;
        for(int i = 0; i < line.length(); i++){
            if(skb.isOpen(line.charAt(i))){
                st.push(line.charAt(i));
            }
            else {
                if(st.isEmpty()){                                                   //N
                    System.out.print("Impossible");
                    allisok = false;
                    break;
                }
                if(line.charAt(i) == '>' && st.peek() == '<' || line.charAt(i) == ')' && st.peek() == '(' ||
                        line.charAt(i) == ']' && st.peek() == '[' || line.charAt(i) == '}' && st.peek() == '{'){
                    st.pop();
                }
                else {
                    st.pop();
                    ans++;
                }
            }
        }
        if(allisok == true && !st.isEmpty()){
            System.out.print("Impossible");
            allisok = false;
        }
        if(allisok){System.out.print(ans);}

    }


    static class Skobka {
        public boolean isOpen(char x) {
            if (x == '<' || x == '(' || x == '{' || x == '[') {
                return true;
            } else return false;
        }

        public boolean isClose(char x) {
            if (x == '>' || x == ')' || x == '}' || x == ']') {
                return true;
            } else return false;
        }
    }


    static class InputReader {
        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public int[] nextIntArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++) {
                array[i] = nextInt();
            }
            return array;
        }

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

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(readLine());
            }
            return tokenizer.nextToken();
        }

        public String readLine() {
            String line;
            try {
                line = reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return line;
        }
    }
}