Product Max

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.

Examples

Input

1 2 1 1

Output

2

Input

3 5 -4 -2

Output

-6

Input

-1000000000 0 -1000000000 0

Output

1000000000000000000

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

a b c d

outputFormat

Output

Print the answer.

Examples

Input

1 2 1 1

Output

2

Input

3 5 -4 -2

Output

-6

Input

-1000000000 0 -1000000000 0

Output

1000000000000000000

样例

-1000000000 0 -1000000000 0

1000000000000000000