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:
/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

//package Educational4;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Stack;
/**
 *
 * @author Sourav Kumar Paul
 */
public class SolveC {
    public static void main(String[] args) throws IOException{
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        Stack<Character> stack = new Stack();
        String text = reader.readLine();
        // <>  :  0
        // {}  :  1
        // []  :  2
        // ()  :  3
        int open[] = new int[4];
        int close[] = new int[4];
        boolean flag = false;
        for(int i=0; i<text.length() && !flag; i++)
        {
           char c = text.charAt(i);
           if(c == '<' || c== '{' || c == '[' || c== '(')
           {
               stack.push(c);
               if(c == '<' )
                   open[0]++;
               else if(c== '{')
                   open[1]++;
               else if(c == '[' )
                   open[2]++;
               else
                   open[3]++;
           }
           else if(c == '>' || c== '}' || c == ']' || c== ')')
               if(stack.isEmpty() )
               {
                   flag = true;
                   break;
                   
               }
               else 
               {
                   char x = stack.pop();
                   if(x == '<' && c=='>' )
                   open[0]--;
               else if(x== '{' && c=='}')
                   open[1]--;
               else if(x == '[' && c==']' )
                   open[2]--;
               else if(x== '(' && c == ')')
                   open[3]--;
                else
               {
                   if(c == '>' )
                   close[0]++;
                    else if(c== '}')
                   close[1]++;
                    else if(c == ']' )
                   close[2]++;
                    else
                   close[3]++;
               }
                    
                   
               }
        }
        long count =0;
        if(!stack.isEmpty() || flag)
        {
            System.out.println("Impossible");
            
        }
        else
        {
            for(int i=0; i<4; i++)
                count += close[i];
            System.out.println(count);
        }
    }
}