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.Stack;

public class ReplaceToMakeRegularBracketSequence {


	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));

		String st = in.readLine();

		int t = 0;
		long res = 0;
		Stack<Character> s = new Stack<>();
//		int c = 0;
//		int s = 0;
//		int p = 0;
//		int g = 0;

		for (int i = 0; i < st.length(); i++) {
//			if(st.charAt(i) == '{'){
//				c++;
//				t++;
//			}
//			else if(st.charAt(i) == '<'){
//				g++;
//				t++;
//			}
//			else if(st.charAt(i) == '['){
//				s++;
//				t++;
//			}
//			else if(st.charAt(i) == '('){
//				p++;
//				t++;
//			}
//			if(st.charAt(i) == '}'){
//				c--;
//				t--;
//			}
//			else if(st.charAt(i) == '>'){
//				g--;
//				t--;
//			}
//			else if(st.charAt(i) == ']'){
//				s--;
//				t--;
//			}
//			else if(st.charAt(i) == ')'){
//				p--;
//				t--;
//			}
			
			if(opening(st.charAt(i)))
				t++;
			else
				t--;
			
			if(t < 0){
				System.out.println("Impossible");
				return;
			}
			
			if(opening(st.charAt(i)))
				s.push(st.charAt(i));
			else if(!isSameType(s.pop(), st.charAt(i)))
				res++;
		}

		if(t == 0){
//			long res = 0;
//
//			if(c >= 0)
//				res += c;
//			if(s >= 0)
//				res += s;
//			if(p >= 0)
//				res += p;
//			if(g >= 0)
//				res += g;

			System.out.println(res);
		}
		else
			System.out.println("Impossible");
	}
	
	public static boolean isSameType(char a, char b){
		return ((a == '[' && b == ']') || (a == '{' && b == '}') || (a == '(' && b == ')') || (a == '<' && b == '>'));
	}
	
	public static boolean closing(char c){
		return (c == ')' || c == '}' || c == '>' || c == ']');
	}
	
	public static boolean opening(char c){
		return (c == '(' || c == '{' || c == '<' || c == '[');
	}
}


//test this case [[><]]