You are given a histogram consisting of columns of heights , respectively. The histogram needs to be transformed into a roof using a series of operations. A roof is a histogram that has the following properties:
- A single column is called the top of the roof. Let it be the column at position .
- The height of the column at position is .
- All heights are positive integers.
An operation can be increasing or decreasing the heights of a column of the histogram by . It is your task to determine the minimal number of operations needed in order to transform the given histogram into a roof.
The first line of input contains the number , the number of columns in the histogram. The following line contains numbers , the initial column heights.
You must output the minimal number of operations from the task.
In test cases worth 60% of total points, it will hold .
Sample Input 1
4 1 1 2 3
Sample Output 1
Explanation for Sample Output 1
By increasing the height of the second, third, and fourth column, we created a roof where the fourth column is the top of the roof.
Sample Input 2
5 4 5 7 2 2
Sample Output 2
Explanation for Sample Output 2
By decreasing the height of the third column three times, and increasing the height of the fourth column, we transformed the histogram into a roof. The example is illustrated below.
Sample Input 3
6 4 5 6 5 4 3
Sample Output 3