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.ArrayList;
import java.util.Scanner;

public class CodeForces132 {
  public static void main(String argv[]) {
    Scanner scanner = new Scanner(System.in);
    
    String s1 = scanner.nextLine();
    char[] ch = s1.toCharArray();
    
    boolean impossible = false;
    int left = 0;
    int right = 0;

    ArrayList<char[]> start = new ArrayList<>();
    ArrayList<char[]> fin = new ArrayList<>();
    
    for(int i = 0; i < ch.length; i++) {
      if(ch[i] == '{') {
        char[] char1 = new char[2];
        char1[0] = '{';
        start.add(char1);
        left++;
      } 
      else if(ch[i] == '(') {
        char[] char1 = new char[2];
        char1[0] = '(';
        start.add(char1);
        left++;
      }
      else if(ch[i] == '<') {
        char[] char1 = new char[2];
        char1[0] = '<';
        start.add(char1);
        left++;
      }
      else if(ch[i] == '[') {
        char[] char1 = new char[2];
        char1[0] = '[';
        start.add(char1);
        left++;
      }
      else if(start.size() == 0) {
        impossible = true;
        break;
      }
      else if(ch[i] == '}') {
        char[] char1 = start.get(start.size() - 1);
        char1[1] = '}';
        fin.add(char1);
        start.remove(start.size() - 1);
        right++;
      }
      else if(ch[i] == ')') {
        char[] char1 = start.get(start.size() - 1);
        char1[1] = ')';
        fin.add(char1);
        start.remove(start.size() - 1);
        right++;
      }
      else if(ch[i] == ']') {
        char[] char1 = start.get(start.size() - 1);
        char1[1] = ']';
        fin.add(char1);
        start.remove(start.size() - 1);
        right++;
      }
      else if(ch[i] == '>') {
        char[] char1 = start.get(start.size() - 1);
        char1[1] = '>';
        fin.add(char1);
        start.remove(start.size() - 1);
        right++;
      }
      if(right > left) {
        impossible = true;
        break;
      }
    }
    
    if(right != left) {
      impossible = true;
    }
    
    int total = 0;
    
    for(int i = 0; i < fin.size(); i++) {
      if(fin.get(i)[1] - (fin.get(i)[0]) != 1 && fin.get(i)[1] - (fin.get(i)[0]) != 2) {
        total++;
      }
    }
    
    if(impossible) {
      System.out.println("Impossible");
    } else {
      System.out.println(total);
    }
    
    scanner.close();
  }
}