1675\. Minimize Deviation in Array

Hard

You are given an array `nums` of `n` positive integers.

You can perform two types of operations on any element of the array any number of times:

*   If the element is **even**, **divide** it by `2`.
    *   For example, if the array is `[1,2,3,4]`, then you can do this operation on the last element, and the array will be `[1,2,3,2].`
*   If the element is **odd**, **multiply** it by `2`.
    *   For example, if the array is `[1,2,3,4]`, then you can do this operation on the first element, and the array will be `[2,2,3,4].`

The **deviation** of the array is the **maximum difference** between any two elements in the array.

Return _the **minimum deviation** the array can have after performing some number of operations._

**Example 1:**

**Input:** nums = [1,2,3,4]

**Output:** 1

**Explanation:** You can transform the array to [1,2,3,2], then to [2,2,3,2], then the deviation will be 3 - 2 = 1.

**Example 2:**

**Input:** nums = [4,1,5,20,3]

**Output:** 3

**Explanation:** You can transform the array after two operations to [4,2,5,5,3], then the deviation will be 5 - 2 = 3.

**Example 3:**

**Input:** nums = [2,10,8]

**Output:** 3

**Constraints:**

*   `n == nums.length`
*   <code>2 <= n <= 10<sup>5</sup></code>
*   <code>1 <= nums[i] <= 10<sup>9</sup></code>