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.*;
import java.util.*;

public class Question {

	public static boolean sameCharchter(char openChar, char closeChar) {
		if (closeChar == ']' && openChar == '[') {
			return true;
		}
		if (closeChar == '}' && openChar == '{') {
			return true;
		}
		if (closeChar == ')' && openChar == '(') {
			return true;
		}
		if (closeChar == '>' && openChar == '<') {
			return true;
		}
		return false;
	}

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		String str = sc.nextLine();
		int score = 0;

		ArrayList<Character> open = new ArrayList<>();
		open.add('[');
		open.add('(');
		open.add('{');
		open.add('<');

		Stack<Character> s = new Stack<>();
		for (int i = 0; i < str.length(); i++) {
			if (open.contains(str.charAt(i))) {
				s.push(str.charAt(i));
			} else {
				if (s.isEmpty()) {
					System.out.println("Impossible");
					return;
				} else {
					char theChar = s.pop();
					if (sameCharchter(theChar, str.charAt(i))) {
						continue;
					} else {
						score++;
					}

				}
			}
		}
		if (s.isEmpty()) {
			System.out.println(score);
		}
		else{
			System.out.println("Impossible");
		}

	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		Scanner(FileReader f) {
			br = new BufferedReader(f);
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		String nextLine() throws IOException {
			return br.readLine();
		}

		int nextInt() throws NumberFormatException, IOException {
			return Integer.parseInt(next());
		}

		long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}
	}

}

class Pair implements Comparable<Pair> {
	int a;
	int b;

	public Pair(int a, int b) {
		this.a = a;
		this.b = b;
	}

	@Override
	public int compareTo(Pair o) {
		// TODO Auto-generated method stub
		return this.a - o.a;
	}
}