Your are given a sequence of integers a₁, …, a_n. Find an arithmetic progression b₁, …, b_n for which the value ∑(a_i − b_i)² is minimal. The elements of the progression can be non-integral.

The first line contains the number n of elements in the sequence (2 ≤ n ≤ 10⁴). In the second line you are given the integers a₁, …, a_n; their absolute values do not exceed 10⁴.

Output two numbers separated with a space: the first term of the required arithmetic progression and its difference, with an absolute or relative error of at most 10⁻⁶. It is guaranteed that the answer is unique for all input data.