arrayCenter

Consider an array of integers a. Let min(a)be its minimal element, and let avg(a) be its mean (The arithmetic mean (also known as mean or average) of the list of values x1, x2, ..., xn, usually denoted by x̅, is the sum of these values divided by their number, i.e. x̅ = (x1 + x2 + ... + xn) / n.)

Define the center of the array a as array bsuch that:

• b is formed from a by erasing some of its elements.
• For each i, |b[i] - avg(a)| < min(a).
• b has the maximum number of elements among all the arrays satisfying the above requirements.

Given an array of integers, return its center.

Example

• For a = [8, 3, 4, 5, 2, 8], the output should be arrayCenter(a) = [4, 5].

  Here min(a) = 2, avg(a) = 5.

• For a = [1, 3, 2, 1], the output should be
  arrayCenter(a) = [1, 2, 1].

  Here min(a) = 1, avg(a) = 1.75.

Input/Output

• [execution time limit] 0.5 seconds 

• [input] array.integer a

  Unsorted non-empty array of integers.

  Guaranteed constraints:
  2 ≤ a.length ≤ 1000,
  0 ≤ a[i] ≤ 3500.

• [output] array.integer