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.*;    //PrintWriter
import java.math.*;  //BigInteger, BigDecimal
import java.util.*;  //StringTokenizer, ArrayList


public class R337_Ed4_C
{	
	FastReader in;
	PrintWriter out;
	
	public static void main(String[] args)  {
		new R337_Ed4_C().run();
	}
	
	void run()
	{		
		in = new FastReader(System.in);
		out = new PrintWriter(System.out);
		solve();
		out.close();
	}
	
	void solve()
	{
		String s = in.next();
		ArrayList<Character> al = new ArrayList<Character>();
		int cnt = 0;
		boolean impossible = false;
		for (char c : s.toCharArray())
		{
			if ("[({<".contains(c+""))
				al.add(c);
			else
			{
				int ind = al.size() - 1;
				if (ind < 0)
				{
					impossible = true;
					break;
				}
				char ch = al.get(ind);
				if (c == ']' && ch != '[') cnt++;
				if (c == ')' && ch != '(') cnt++;
				if (c == '}' && ch != '{') cnt++;
				if (c == '>' && ch != '<') cnt++;
				al.remove(al.size() - 1);
			}
		}
		if (impossible || al.size() > 0)
			out.println("Impossible");
		else
			out.println(cnt);

	}

	//-----------------------------------------------------
	void runWithFiles() {
		in = new FastReader(new File("input.txt"));
		try {
			out = new PrintWriter(new File("output.txt"));
		} 
		catch (FileNotFoundException e) {
			e.printStackTrace();
		}
		solve();
		out.close();
	}
	
	class FastReader
	{
	    BufferedReader br;
	    StringTokenizer tokenizer;
	    
	    public FastReader(InputStream stream)
	    {
	        br = new BufferedReader(new InputStreamReader(stream));
	        tokenizer = null;
	    }
		public FastReader(File f) {
			try {
				br = new BufferedReader(new FileReader(f));
				tokenizer = null;
			}
			catch (FileNotFoundException e) {
				e.printStackTrace();
			}
		}
	    
	    private String next() {
	        while (tokenizer == null || !tokenizer.hasMoreTokens())
	            try {
	            	tokenizer = new StringTokenizer(br.readLine());
	            }
	            catch (IOException e) {
	                throw new RuntimeException(e);
	            }
	        return tokenizer.nextToken();
	    }
		public String nextLine() {
			try	{
				return br.readLine();
			}
			catch(Exception e) {
				throw(new RuntimeException());
			}
		}

	    int nextInt() {
	        return Integer.parseInt(next());
	    }
	    long nextLong() {
	        return Long.parseLong(next());
	    }
	    double nextDouble() {
	        return Double.parseDouble(next());
	    }	    
	    BigInteger nextBigInteger() {
	        return new BigInteger(next());
	    }
	    BigDecimal nextBigDecimal() {
	        return new BigDecimal(next());
	    }
	}
}