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.InputStreamReader;
import java.util.HashMap;
import java.util.Scanner;
import java.util.Stack;

public final class ReplaceToMakeRegularBRacketSequenceCF {
    public static void main(String[] args) throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        String s=br.readLine();
        if(isPossible(s)){
            Stack<Character> stack=new Stack<>();
            int res=0;
            for(int i=0;i<s.length();i++){
                if(s.charAt(i)=='(' || s.charAt(i)=='{' || s.charAt(i)=='[' || s.charAt(i)=='<' ){
                    stack.add(s.charAt(i));
                }else{
                    char ch=stack.pop();
                    if( (s.charAt(i)==')' && ch=='(') || (s.charAt(i)=='}' && ch=='{') ||(s.charAt(i)==']' && ch=='[') ||(s.charAt(i)=='>' && ch=='<') ){
                        continue;
                    }else
                        res++;
                }
            }
            System.out.println(res);
        }else
            System.out.println("Impossible");
    }

    private static boolean isPossible(String s) {

        int open=0,close=0;
        for(int i=0;i<s.length();i++){
            if(s.charAt(i)=='(' || s.charAt(i)=='{' || s.charAt(i)=='[' || s.charAt(i)=='<' ){
                open++;
            }else
                close++;
            if(open<close)
                return false;
        }
            if(open==close) return true;
            else return false;
    }
}