Minimum Possible Value of Function

Given a sequence X, find an integer k that minimizes Σ|X[i]−(k+i+1)|, and output the minimum value.

The standard input/output format and any supplementary ranges on this site are as stated in this problem.

输入格式

n (1≤n≤200000), and the next line has n integers X[i] (1≤X[i]≤10^9).

输出格式

Output the minimum value of the function as an integer.

样例 1

输入：

5
2 2 3 5 5

输出：

2

样例 2

输入：

1
1

输出：

0

样例 3

输入：

3
10 1 10

输出：

10