AWS provides scalable systems. A set of n servers are used for horizontally scaling an application. The goal is to have the computational power of the servers in non-decreasing order. To do so, you can increase the computational power of each server in any contiguous segment by x. Choose the values of x such that after the computational powers are in non-decreasing order, the sum of the x values is minimum.

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Function Description

Complete the findMinimumSum function.

findMinimumSum has the following parameter(s):

• int power[n]: an array of integers representing the initial computational power of the servers.

Returns

• int: the minimum possible sum of integers required to make the array non-decreasing. (Note: The code template expects a long / long_integer return type to prevent overflow).

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Constraints

• 1 <= n <= 10^5
• 1 <= power[i] <= 10^9

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Examples

Example 1

Input: power = [3, 4, 1, 6, 2]

Output: 7

Explanation: There are n = 5 servers and their computational power = [3, 4, 1, 6, 2].

• Add 3 units to the subarray (2, 4). The array becomes [3, 4, 4, 9, 5].
• Add 4 units to the subarray (4, 4). The array becomes [3, 4, 4, 9, 9].
• The final arrangement of the servers is in non-decreasing order. The answer is 3 + 4 = 7.

Sample Case 0

Input:

3
3
2
1

(power[] size n = 3, power = [3, 2, 1])

Output: 2

Explanation: Add 1 unit to subarray (1, 2) and 1 unit to subarray (2, 2). The final arrangement of servers is [3, 3, 3].

Sample Case 1

Input:

4
3
5
2
3

(power[] size n = 4, power = [3, 5, 2, 3])

Output: 3

Explanation: Add 3 units to subarray (2, 3). The final arrangement of servers is [3, 5, 5, 6].