Source

This problem is adapted from Long Long OJ. All rights reserved.

Problem Description

Given $n$ sticks, select 3 of them to form a triangle, then select another 3 distinct sticks to form a second triangle. Find the maximum sum of the perimeters of these two triangles.

It is guaranteed that a calculation error within $10^{-4}$ will not lead to a wrong answer.

Note 1: Three sticks can only form a triangle if they are connected end to end in sequence. Note 2: For a valid triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Input Format

The first line contains an integer $n$, with the meaning as described in the problem statement. The second line contains $n$ floating-point numbers, where the $i$-th number $a_i$ represents the length of the $i$-th stick.

Output Format

Output a single floating-point number, representing the maximum sum of the perimeters of the two triangles. Your answer must have an absolute or relative error within $10^{-4}$.

If no valid solution exists, output $-1$.

Samples

6
1.123 2.234 3.345 4.456 5.567 6.678

23.403

1
123.456

-1

Data Range

$1 \le n \le 2^{20}$, $1 \le a_i \le 1.875\times10^{12}$.