Maximizing Rational Expression

We are given N different natural numbers. When we pick four diffrent ones from them and let them be $A$, $B$, $C$, $D$ , we want to find the maximum value of the following expression:

$\frac{A + B}{C - D}$

Your program must find the maximum value of the maximum value of the expression above when N diffrent natural numbers are given.

Input

Input is given in following format.

N
a1 a2 ... aN

First line is the number of given natural numbers: N (4 ≤ N ≤ 1000). Second line provides the value of each natural numbers: a_i (1 ≤ a_i ≤ 10⁸) . Same natural numbers are NOT given in one case. (when i ≠ j, a_i ≠ a_j)。

Output

According to N natural numbers given, output the maximum value of the expression above in real number. The acceptable error range is +/- 10^-5 .

Sample Input 1

10
1 2 3 4 5 6 7 8 9 10

Sample Output 1

19.00000

In this case, letting $A=9$, $B=10$, $C=2$, $D=1$ miximizes the value.

Sample Input 2

5
22 100 42 3 86

Sample Output 2

9.78947

In this case, letting $A=100$, $B=86$, $C=22$, $D=3$ miximizes the value.

Sample Input 3

6
15 21 36 10 34 5

Sample Output 3

18.00000

In this case, letting $A=21$, $B=15$, $C=36$, $D=34$ maximizes the value.

Sample Input 4

4
100000 99999 8 1

Sample Output 4

28571.285714

---