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.util.LinkedList;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class tmp {
    public static void main(String [] args) throws Exception{
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(in.readLine());
        StringBuilder sb = new StringBuilder();
        
        HashMap<Character, Character> map = new HashMap();
        map.put(']', '['); map.put('}', '{'); map.put('>', '<'); map.put(')', '(');
        Stack<Character> open = new Stack();
        String s = st.nextToken();
        int out = 0;
        char c, t;
        for(int i=0; i<s.length(); i++){
            c = s.charAt(i);
            if(!map.containsKey(c))
                open.push(c);
            else{
                t = map.get(c);
                if(!open.isEmpty()){
                    if(t != open.pop()) out++;
                }else{
                    System.out.println("Impossible");
                    System.exit(0);
                }
            }
        }
        if(open.isEmpty())
            System.out.println(out);
        else
            System.out.println("Impossible");
        
        
        
        
        
        
        
     
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
    }

    
    
    
    
    
    

    
    
    
    
    


    
    
    
    
}

class Pair implements Comparable<Pair>{
    int x,h;
    
    public Pair(int fi, int ti){
        x = fi;
        h = ti;
    }
    
    public int compareTo(Pair p){
        return x < p.x ? -1 : (x == p.x ? (h < p.h ? -1 : 1) : 1);
    }
}