Problem:
Score : 300 points

Problem Statement

Snuke has an integer sequence A of length N.

He will freely choose an integer b.
Here, he will get sad if A_i and b+i are far from each other.
More specifically, the sadness of Snuke is calculated as follows:

abs(A_1 - (b+1)) + abs(A_2 - (b+2)) + ... + abs(A_N - (b+N))

Here, abs(x) is a function that returns the absolute value of x.

Find the minimum possible sadness of Snuke.

Constraints

1 \leq N \leq 2 \times 10^5

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the minimum possible sadness of Snuke.

Sample Input 1

5
2 2 3 5 5

Sample Output 1

2

If we choose b=0, the sadness of Snuke would be abs(2-(0+1))+abs(2-(0+2))+abs(3-(0+3))+abs(5-(0+4))+abs(5-(0+5))=2.
Any choice of b does not make the sadness of Snuke less than 2, so the answer is 2.

Sample Input 2

9
1 2 3 4 5 6 7 8 9

Sample Output 2

0

Sample Input 3

6
6 5 4 3 2 1

Sample Output 3

18

Sample Input 4

7
1 1 1 1 2 3 4

Sample Output 4

6

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>

typedef long long ll;

int N;
int A[200010];

ll f(const ll b){
  ll res = 0;
  for (int i = 0; i < N; ++i) {
    res += abs(A[i] - (b + i + 1));
  }
  // printf("f: %lld\n", res);
  return res;
}

int main(void){
  scanf("%d", &N);
  for (int i = 0; i < N; ++i)
    scanf("%d", &A[i]);

  ll l = -2e9;
  ll r = 2e9;
  for (int i = 0; i < 100; ++i) {
    ll l2 = (l * 2 + r) / 3;
    ll r2 = (l + r * 2) / 3;
    ll fl2 = f(l2);
    ll fr2 = f(r2);
    if (fl2 < fr2)
      r = r2;
    else
      l = l2;
    // printf("l: %d, r: %d\n", l, r);
  }
  // printf("c: %d, ans:%lld\n", (l + r) / 2, f((l + r) / 2));
  printf("%lld\n", f((l + r) / 2));
}