Source

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

Attention

The memory limit for this problem is 8 MB.

Problem Description

Given an integer sequence $a_1\sim a_n$ of length $n$, find the pair $(x,y)$ that minimizes the value of $\sum\limits_{i=1}^{n}(x+iy-a_i)^2$.

Input Format

The first line contains an integer $n$, and the second line contains the sequence $a_1\sim a_n$.

Output Format

Output a single line with two floating-point numbers $x$ and $y$, with a relative or absolute error within $10^{-3}$.

Samples

20
-1711 5271 1865 -7326 7975 -4709 5564 5578 -121 -8285 -10084 902 3610 -4082 -8018 6737 6038 -621 5880 -958

-121.971429 31.286466

Data Range

The first test case is the sample.

For $100\%$ of the data, $1 \le n \le 10^6$ and $|a_i|\le 10^9$.