You are given a histogram consisting of N columns of heights X₁, X₂, … 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:</p>

• 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 ≤ j ≤ 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.

입력 형식

The first line of input contains the number N (1 ≤ N ≤ 10⁵), the number of columns in the histogram.</p>

The following line contains N numbers X_i (1 ≤ X_i ≤ 10⁹), the initial column heights.

출력 형식

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

예제 입력 1

4
1 1 2 3

예제 출력 1

3

예제 입력 2

5
4 5 7 2 2

예제 출력 2

4

예제 입력 3

6
4 5 6 5 4 3

예제 출력 3

0

힌트

Clarification of the first test case: ​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.</p>

Clarification of the second test case: ​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.