Problem Statement

Rian, who loves arithmetic progressions, found a sequence with $N$ elements by the roadside.

Because Rian loves arithmetic progressions so much, he decided to ask the Sequence Old Man, who can change the value of each element of a sequence, to turn the sequence he found into an arithmetic progression.

However, the Sequence Old Man charges a cost of $(a_i - b_i)^2$ to change the $i$-th element $a_i$ of the sequence to $b_i$. (Also, he will change the value of each element at most once.)

For example, the cost of changing the sequence {3, 3, 4} to {5, 5, 5} is 4 + 4 + 1 = 9, and the cost of changing it to {3, 3.5, 4} is 0 + 0.25 + 0 = 0.25.

Rian wants to obtain an arithmetic progression at as low a cost as possible, so find the first term $b_1$ and the common difference $d$ that minimize the cost, as well as the cost $c$ incurred in that case.

Input

$N$
$a_1 \ a_2 \ \ldots \ a_N$

The first line contains the number of elements $N$ of the sequence.

The second line contains the values $a_i \ (1 \le i \le N)$ of the elements of the sequence, separated by spaces.

All inputs are integers and satisfy the following constraints.

• $2 \le N \le 1000$
• $0 \le a_i \le 10^5$

Output

On the first line, output the first term $b_1$ and the common difference $d$ of the resulting arithmetic progression that minimizes the cost, separated by a space.

On the second line, output the cost $c$ incurred in that case.

For each value, an error of at most $10^{-6}$ is allowed.

Print a newline at the end.

Sample

3
3 3 4

2.83333333333333 0.5
0.166666666666667

5
0 0 0 0 10000

-2000 2000
40000000

7
6 5 4 3 2 1 0

6 -1
0