You are given a 0-indexed integer array nums. In one operation, you can:

• Choose an index i in the range 0 <= i < nums.length
• Set nums[i] to nums[i] + 1 or nums[i] - 1

Return the minimum number of operations to make nums non-decreasing or non-increasing.

 

Example 1:

Input: nums = [3,2,4,5,0]
Output: 4
Explanation:
One possible way to turn nums into non-increasing order is to:
- Add 1 to nums[1] once so that it becomes 3.
- Subtract 1 from nums[2] once so it becomes 3.
- Subtract 1 from nums[3] twice so it becomes 3.
After doing the 4 operations, nums becomes [3,3,3,3,0] which is in non-increasing order.
Note that it is also possible to turn nums into [4,4,4,4,0] in 4 operations.
It can be proven that 4 is the minimum number of operations needed.

Example 2:

Input: nums = [2,2,3,4]
Output: 0
Explanation: nums is already in non-decreasing order, so no operations are needed and we return 0.

Example 3:

Input: nums = [0]
Output: 0
Explanation: nums is already in non-decreasing order, so no operations are needed and we return 0.

 

Constraints:

• 1 <= nums.length <= 1000
• 0 <= nums[i] <= 1000

 

Follow up: Can you solve it in O(n*log(n)) time complexity?