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 CF612C{ 
  public static int index;
  public static void main(String[] args)throws IOException, Exception {
    InputReader in = new InputReader(System.in);
    PrintWriter pw = new PrintWriter(new OutputStreamWriter(System.out));
    String s = in.nextLine();
    Stack<Character> open = new Stack<Character>();
    // Queue<Character> close = new LinkedList<Character>();
    int len = s.length(),o = 0, c1 = 0;
    long count = 0;
    for(int i = 0; i < len; i++){
      char c = s.charAt(i);
      if( c == '<' || c == '{' || c == '[' || c == '(')
        o++;
      else 
        c1++;
    }
    if( o != c1){
      System.out.println("Impossible");
      return;
    }
//    try{
    for(int i = 0; i < len; i++){
      char c = s.charAt(i);
      if( c == '<' ) open.add('>');
      else if( c == '{' ) open.add('}');
      else if( c == '[' ) open.add(']');
      else if( c == '(' ) open.add(')');
      else{
        if(open.isEmpty()){ 
          System.out.println("Impossible");
          return;
        }
        else{
          if (c != open.peek()) count++;
          open.pop();
        }
      }
      
    }
////    }
//    catch(Exception e){
//      System.out.println("Impossible");
//    }
    pw.println(count);
    
    pw.close();
  }
  
  static class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;
    
    public InputReader(InputStream stream) {
      reader = new BufferedReader(new InputStreamReader(stream));
      tokenizer = null;
    }
    
    public String next() {
      
      try {
        while (tokenizer == null || !tokenizer.hasMoreTokens())
          tokenizer = new StringTokenizer(reader.readLine());
      } catch (IOException e) {
        return null;
      }
      
      return tokenizer.nextToken();
    }
    
    public String nextLine() {
      String line = null;
      try {
        tokenizer = null;
        line =  reader.readLine();
      } catch (IOException e) {
        throw new RuntimeException(e);
      }
      return line;
    }
    
    public int nextInt() {
      return Integer.parseInt(next());
    }
    
    public double nextDouble() {
      return Double.parseDouble(next());
    }
    
    public long nextLong() {
      return Long.parseLong(next());
    }
    public boolean hasNext(){
      try {
        while (tokenizer == null || !tokenizer.hasMoreTokens())
          tokenizer = new StringTokenizer(reader.readLine());
      } 
      catch (Exception e) {
        return false;
      }
      
      return true; 
      
    }
  }
}