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;


public class Main {

    static boolean isle(char x) {
        return x == '(' || x == '<' || x == '[' || x == '{';
    }

    static int cal(char x, char y) {
        if (x == '(' && y == ')') return 0;
        if (x == '[' && y == ']') return 0;
        if (x == '{' && y == '}') return 0;
        if (x == '<' && y == '>') return 0;
        return 1;
    }

    static int work(char[] in) {
        int length = in.length;
        Stack<Integer> st = new Stack<>();
        int answer = 0;
        for (int i = 0; i < length; i++) {
            char x = in[i];
            if (isle(x)) st.push(i);
            else {
                if (st.empty()) return -1;
                int y = st.peek();
                st.pop();
                answer += cal(in[y], in[i]);
            }
        }
        if (!st.empty()) return -1;
        return answer;
    }

    public static void main(String[] args) {
        Scanner scn = new Scanner(System.in);
        char[] input = scn.next().toCharArray();
        scn.close();
        int a = work(input);
        if(a>=0) System.out.println(a);
        else System.out.println("Impossible");
    }
}