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.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Reader;
import java.util.Stack;
import java.util.StringTokenizer;

// Educational Codeforces Round 4
// Replace To Make Regular Bracket Sequence
public class Problem_612_C {
    

    public static void main(String[] args)
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        PrintWriter out = new PrintWriter(outputStream);
        Problem_612_C solver = new Problem_612_C();
        solver.solve(1, new InputStreamReader(inputStream), out);
        out.close();
    }

    public void solve(int test, Reader input, PrintWriter out)
    {
        MyScanner in = new MyScanner(input);
        
        char[] s = in.next().toCharArray();
        
        Stack<Character> stack = new Stack<>();
        
        int res = 0;
        
        for(char c : s) {
          switch(c) {
          case '<':
          case '[':
          case '{':
          case '(':
            stack.push(c);
            break;
          case '>':
          case ']':
          case '}':
          case ')':
            if(stack.empty()) {
              out.println("Impossible");
              return;
            }
            char top = stack.pop();
            if((top == '<' && c == '>') ||
                (top == '[' && c == ']') ||
                (top == '(' && c == ')') ||
                (top == '{' && c == '}'))
              continue;
            else
              res++;
          }
        }
        if(!stack.empty()) out.println("Impossible");
        else out.println(res);
    }

    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner(Reader reader) {
            br = new BufferedReader(reader);
        }

        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());
        }
        
        int[] nextIntArray(int n)
        {
            int[] r = new int[n];
            for(int i = 0; i < n; i++)
                r[i] = nextInt();
            return r;
        }

        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;
        }

    }
    //--------------------------------------------------------

}