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.ArrayList;
import java.util.LinkedList;
import java.util.List;
import java.util.Scanner;

public class C {
	String s;
	void readInput() throws NumberFormatException, IOException{
		//BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		Scanner sc = new Scanner(System.in);
		s = sc.nextLine();
	}
	
	void solve(){
		if (s.length()%2==1)
		{
			System.out.println("Impossible");
			return;
		}
		
		int ch = 0;;
		int v = 0;
		int vs[] = new int[4];
		int mins[] = new int[4];
		LinkedList<Integer> prevs = new LinkedList<Integer>();
		for(int i=0; i<s.length(); i++){
			char c = s.charAt(i);
			int ss = 1;
			if (c == '<' || c == '{' || c == '[' || c == '('  )
				ss = 1;
			else if (c == '>' || c == '}' || c == ']' || c == ')'  ){
				ss = -1;				
			}
									
			int j = 0;
			if (c == '<' || c=='>')
				j = 0;
			if (c == '{' || c=='}')
				j = 1;
			if (c == '[' || c==']')
				j = 2;
			if (c == '(' || c==')')
				j = 3;
			
			v += ss;
			if (v<0){
				System.out.println("Impossible");
				return;
			}
			
			vs[j] += ss;
			if (ss == -1){
				if(prevs.getLast()!=j){			
					vs[j]++;
					vs[prevs.getLast()]--;
					prevs.removeLast();
					ch ++;
				}
				else
					prevs.removeLast();
			}			
			
			if (ss==1)
				prevs.addLast(j);
		}
		
		if (v!=0){
			System.out.println("Impossible");
			return;
		}
						
		System.out.println(ch);
		
	}

	public static void main(String[] args) throws NumberFormatException, IOException {
		C a = new C();
		a.readInput();
		a.solve();
	}

}