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.Scanner;
import java.util.Stack;

/**
 * Created by gusak on 25.12.2015.
 */
public class C {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        String input = sc.next();
        int[] full = sequenceToArray(input);
        int[] simplified = simplify(full);
        if (isValid(simplified)) {
            System.out.println(price(full));
        } else {
            System.out.println("Impossible");
        }
    }

    public static int bracketToInt(char bracket) {
        switch (bracket) {
            case '<':
                return -4;
            case '{':
                return -3;
            case '[':
                return -2;
            case '(':
                return -1;
            case ')':
                return 1;
            case ']':
                return 2;
            case '}':
                return 3;
            case '>':
                return 4;
        }
        return 0;
    }

    public static int[] sequenceToArray(String sequence) {
        int[] out = new int[sequence.length()];
        int index = 0;
        for (char cur: sequence.toCharArray()) {
            out[index++] = bracketToInt(cur);
        }
        return out;
    }

    public static int[] simplify(int[] sequence) {
        int[] out = new int[sequence.length];
        for (int i = 0; i < sequence.length; i++) {
            out[i] = (int) Math.signum(sequence[i]);
        }
        return out;
    }

    public static boolean isValid(int[] simplified) {
        int balance = 0;
        for (int cur: simplified) {
            balance += cur;
            if (balance > 0) {
                return false;
            }
        }
        return (balance == 0);
    }

    public static int price(int[] sequence) {
        int answer = 0;
        Stack<Integer> openBrackets = new Stack<>();
        for (int cur: sequence) {
            if (cur < 0) {
                openBrackets.push(cur);
            } else {
                if (openBrackets.pop() != -1 * cur) {
                    answer++;
                }
            }
        }
        return answer;
    }
}