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.*;

public class CF612C {
    static Map<Character, Character> oposite = new HashMap<>();
    public static void main(String[] args) {
        FastReader reader = new FastReader();
        String s = reader.next();
        oposite.put('>', '<');
        oposite.put('}', '{');
        oposite.put(']', '[');
        oposite.put(')', '(');

        Deque<Character> stack = new ArrayDeque<>(s.length() / 2);

        int change = 0;
        for (char c : s.toCharArray()) {
            if (isOpening(c)) {
                stack.push(c);
            } else {
                if (stack.size() == 0) {
                    System.out.println("Impossible");
                    return;
                }
                char onStack = stack.pop();
                change += isValid(onStack, c);
            }
        }
        if (stack.size() != 0) {
            System.out.println("Impossible");
            return;
        }

        System.out.println(change);
    }

    private static boolean isOpening(char c) {
        return c == '<' || c == '(' || c == '{' || c == '[';
    }

    private static int isValid(char stack, char current) {
        return  stack == oposite.get(current) ? 0 : 1;
    }

    public static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public 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;
        }
    }
}