Minimum range boosts to make server power non-decreasing

You manage a row of n machines. Machine i has an integer capacity power[i]. You want the capacities to be non-decreasing from left to right (power[i] <= power[i+1] for every i).

You may apply the following operation any number of times:

• Pick a contiguous range [l, r] and a positive integer x, then add x to every machine in that range.

The cost of a plan is the sum of the x values across all operations. The number of operations does not matter. Return the minimum possible cost.

Implement:

def min_increase_sum(power: list[int]) -> int: ...

Constraints

• 0 <= n <= 10^5
• 1 <= power[i] <= 10^9
• The answer may exceed 32 bits.

Example 1

power = [3, 1, 2]
output: 2

Add 2 to the range [1, 2], giving [3, 3, 4]. Raising each element to the running maximum would cost 3. A single range operation does better.

Example 2

power = [5, 2, 4, 1, 6]
output: 6

Add 3 to [1, 4] to get [5, 5, 7, 4, 9]. Then add 3 to [3, 4] to get [5, 5, 7, 7, 12].

Be ready to explain why no cheaper plan exists, and to return the operations themselves.