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.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Stack;
import java.util.StringTokenizer;

public class C
{
	public static void main(String[] args) throws IOException
	{
		Scanner sc = new Scanner(System.in);
		String s = sc.next();
		Stack<Character> stack = new Stack<>();
		int cnt = 0;
		for (int i = 0; i < s.length(); i++)
		{
			char c = s.charAt(i);
			if (open(c))
				stack.push(c);
			else
			{
				if (stack.isEmpty())
				{
					System.out.println("Impossible");
					return;
				} else
				{
					char c2 = stack.pop();
					if (!(c == '>' && c2 == '<' || c == '}' && c2 == '{' || c == ']' && c2 == '['
							|| c == ')' && c2 == '('))
						cnt++;
				}
			}
		}
		if (!stack.isEmpty())
			System.out.println("Impossible");
		else
			System.out.println(cnt);

	}

	static boolean open(char c)
	{
		return c == '(' || c == '{' || c == '[' || c == '<';
	}

	static class Scanner
	{
		StringTokenizer st;
		BufferedReader br;

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

		public Scanner(String s) throws FileNotFoundException
		{
			br = new BufferedReader(new FileReader(new File(s)));
		}

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

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

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

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

		public double nextDouble() throws IOException
		{
			return Double.parseDouble(next());
		}

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