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.io.PrintWriter;
import java.util.Stack;
import java.util.StringTokenizer;


public class C {
	
	public static boolean isOpening(char ch){
		return "<{[(".indexOf(ch)>=0;
	}
	
	public static int getType(char ch){
		return "<{[(>}])".indexOf(ch);
	}
			
	public static void main(String[] args) {
		
		MyScanner in = new MyScanner();
		String s = in.next();
		int n = s.length();
		int count = 0;
		for(int i=0;i<n;++i){
			if(isOpening(s.charAt(i))){
				count++;
			}else{
				count--;
				if(count<0){
					System.out.println("Impossible");
					return;
				}
			}
		}
		if(count!=0){
			System.out.println("Impossible");
			return;
		}
		int result = 0;
		Stack<Integer> stack = new Stack<Integer>();
		for(int i=0;i<n;++i){
			char ch = s.charAt(i);
			if(isOpening(ch)){
				stack.push(getType(ch));
			}else{
				if(stack.peek()+4!=getType(ch)){
					result++;
				}
				stack.pop();
			}
		}
		System.out.println(result);
	}
		 	

	//-----------PrintWriter for faster output---------------------------------
	   public static PrintWriter out = new PrintWriter(System.out);
	      
	   //-----------MyScanner class for faster input----------
	   public static class MyScanner {
	      BufferedReader br;
	      StringTokenizer st;
	 
	      public MyScanner() {
	         br = new BufferedReader(new InputStreamReader(System.in));
	      }
	 
	      String next() {
	          while (st == null || !st.hasMoreElements()) {
	              try {
	                  st = new StringTokenizer(br.readLine());
	              } catch (IOException e) {
	                  e.printStackTrace();
	              }
	          }
	          return st.nextToken();
	      }
	 
	      int nextInt() {
	          return Integer.parseInt(next());
	      }
	 
	      long nextLong() {
	          return Long.parseLong(next());
	      }
	 
	      double nextDouble() {
	          return Double.parseDouble(next());
	      }
	 
	      String nextLine(){
	          String str = "";
		  try {
		     str = br.readLine();
		  } catch (IOException e) {
		     e.printStackTrace();
		  }
		  return str;
	      }

	   }
	   //--------------------------------------------------------
	

}