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.util.ArrayDeque;
import java.util.Deque;
import java.util.Scanner;

public class C {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		char[] line;
		Deque<Character> stack = new ArrayDeque<Character>();
		line=sc.nextLine().toCharArray();
		int wrong=0;
		
		for (int i = 0; i < line.length; i++) {
			int type;
			type=checkSym(line[i]);
			if(type==1){
				stack.push(line[i]);
			}
			else{
				int t=0;
				if(stack.isEmpty()){
					System.out.println("Impossible");
					return;
				}
				switch (line[i]) {
				case '>':
					if(stack.peek()!='<'){
						t=checkSym(stack.peek());
						if(t==1){
							wrong++;
							stack.pop();
						}
						else{
							System.out.println("Impossible");
							return;
						}
					}
					else{
						stack.pop();
					}
					break;
				case '}':
					if(stack.peek()!='{'){
						t=checkSym(stack.peek());
						if(t==1){
							wrong++;
							stack.pop();
						}
						else{
							System.out.println("Impossible");
							return;
						}
					}
					else
						stack.pop();
					break;
				case ']':
					if(stack.peek()!='['){
						t=checkSym(stack.peek());
						if(t==1){
							wrong++;
							stack.pop();
						}
						else{
							System.out.println("Impossible");
							return;
						}
					}
					else
						stack.pop();
					break;
				case ')':
					if(stack.peek()!='('){
						t=checkSym(stack.peek());
						if(t==1){
							wrong++;
							stack.pop();
						}
						else{
							System.out.println("Impossible");
							return;
						}
					}
					else
						stack.pop();
					break;	
				default:
					break;
				}
			}
		}
		if(!stack.isEmpty()){
			System.out.println("Impossible");
			return;
		}
		System.out.println(wrong);
		sc.close();
	}
	public static int checkSym(char c){
		int res=0;
		switch (c) {
		case '<':
			res=1;
			break;
		case '{':
			res=1;
			break;
		case '[':
			res=1;
			break;
		case '(':
			res=1;
			break;

		default:
			res=0;
			break;
		}
		return res;
	}
}