Problem:
Score : 200 points

Problem Statement

Given are integers a,b,c and d.
If x and y are integers and a \leq x \leq b and c\leq y \leq d hold, what is the maximum possible value of x \times y?

Constraints

-10^9 \leq a \leq b \leq 10^9

-10^9 \leq c \leq d \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

a b c d

Output

Print the answer.

Sample Input 1

1 2 1 1

Sample Output 1

2

If x = 1 and y = 1 then x \times y = 1.
If x = 2 and y = 1 then x \times y = 2.
Therefore, the answer is 2.

Sample Input 2

3 5 -4 -2

Sample Output 2

-6

The answer can be negative.

Sample Input 3

-1000000000 0 -1000000000 0

Sample Output 3

1000000000000000000

Solution in Common Lisp (SBCL 2.0.3) (judge verdict: Wrong Answer)

(defun straddlep (a b)
  (and (< a 0)
       (>= b 0)))

(defun hoge (a b c d)
  (cond
    ((and (>= a 0) (>= c 0)) (* b d))
    ((and (< b 0) (< d 0)) (* a c))
    ((and (straddlep a b) (>= c 0)) (* c b))
    ((and (straddlep a b) (< d 0)) (* a c))
    ((and (>= a 0) (straddlep c d)) (* a c))
    ((and (< b 0) (straddlep c d)) (* a c))
    (t (let ((ac (* a c))
             (bd (* b d)))
         (if (> ac bd) ac bd)))))

(let ((a (read))
      (b (read))
      (c (read))
      (d (read)))
  (format t "~a" (hoge a b c d)))