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 OCaml (4.10.0) (judge verdict: Accepted)

Scanf.scanf "%d %d %d %d" (fun a b c d ->
    let l1 = if a <= 0 && 0 <= b then [| a; 0; b |] else [| a; a; b |] in
    let l2 = if c <= 0 && 0 <= d then [| c; 0; d |] else [| c; c; d |] in

    let rec loop_i i acc =
        let rec loop_j j acc =
            if j = 3 then loop_i (i + 1) acc else
                loop_j (j + 1) (max acc (l1.(i) * l2.(j)))
        in
        if i = 3 then acc else loop_j 0 acc
    in
    loop_i 0 min_int |> Printf.printf "%d\n"
)