You are given a histogram consisting of ~N~ columns of heights ~X_1, X_2, \dots, X_N~, 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 ~i~.
• The height of the column at position ~j~ ~(1 \le j \le N)~ is ~h_j = h_i - |i - j|~.
• All heights ~h_j~ are positive integers.

An operation can be increasing or decreasing the heights of a column of the histogram by ~1~. It is your task to determine the minimal number of operations needed in order to transform the given histogram into a roof.

Input Specification

The first line of input contains the number ~N~ ~(1 \le N \le 10^5)~, the number of columns in the histogram. The following line contains ~N~ numbers ~X_i~ ~(1 \le X_i \le 10^9)~, the initial column heights.

Output Specification

You must output the minimal number of operations from the task.

Scoring

In test cases worth 60% of total points, it will hold ~N \le 5\,000~.

Sample Input 1

4
1 1 2 3

Sample Output 1

3

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

4

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

0