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;
import java.util.StringTokenizer;


public class C {
	
	static class Scanner{
		BufferedReader br=null;
		StringTokenizer tk=null;
		public Scanner(){
			br=new BufferedReader(new InputStreamReader(System.in));
		}
		public String next() throws IOException{
			while(tk==null || !tk.hasMoreTokens())
				tk=new StringTokenizer(br.readLine());
			return tk.nextToken();
		}
		public int nextInt() throws NumberFormatException, IOException{
			return Integer.valueOf(next());
		}
		public long nextLong() throws NumberFormatException, IOException{
			return Long.valueOf(next());
		}
		public double nextDouble() throws NumberFormatException, IOException{
			return Double.valueOf(next());
		}
	}
	
	static boolean well_formed(char a, char b) {
		String t1 = a + "" + b;
		if (t1.equals("()") || t1.equals("{}") || t1.equals("<>") || t1.equals("[]"))
			return true;
		return false;
	}
	
	static boolean closing(char a, char b) {
		char[] first = {'(', '{', '<', '['};
		boolean f = false;
		for(int i = 0; i < first.length; i++)
			if (first[i] == a) {
				f = true;
				break;
			}
		if (!f)
			return false;
		char[] second = {')', '}', '>', ']'};
		boolean s = false;
		for(int i = 0; i < second.length; i++)
			if (second[i] == b) {
				s = true;
				break;
			}
		return s;
	}
	
	public static void main(String args[]) throws IOException {
		Scanner sc = new Scanner();
		char[] text = sc.next().toCharArray();
		Stack<Character> st = new Stack<Character>();
		int count = 0;
		for(int i = 0; i < text.length; i++) {
			if (st.isEmpty() || !closing(st.peek(), text[i]))
				st.push(text[i]);
			else {
				//closing
				if(!well_formed(st.peek(), text[i]))
					count++;
				st.pop();
			}
		}
		if (st.isEmpty())
			System.out.println(count);
		else
			System.out.println("Impossible");
	}

}