Maximization of Rational Expression

N different natural numbers are given. If you select four different ones and set them as $A$, $B$, $C$, $D$, the following formula

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

I want to find the maximum value of.

Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.

Input

The input is given in the following format.

N a1 a2 ... aN

The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10 1 2 3 4 5 6 7 8 9 10

Output

19.00000

Input

5 22 100 42 3 86

Output

9.78947

Input

6 15 21 36 10 34 5

Output

18.00000

Input

4 100000 99999 8 1

Output

28571.285714

inputFormat

Input

The input is given in the following format.

N a1 a2 ... aN

The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

outputFormat

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10 1 2 3 4 5 6 7 8 9 10

Output

19.00000

Input

5 22 100 42 3 86

Output

9.78947

Input

6 15 21 36 10 34 5

Output

18.00000

Input

4 100000 99999 8 1

Output

28571.285714

样例

5
22 100 42 3 86

9.78947