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: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
#include <math.h>
#include <limits.h>
#include <assert.h>
#define FOR(i,a,n) for(i=(a);i<(n);i++)
#define swap(type,a,b) do{type t=a;a=b;b=t;}while(0)
#define MAX(a,b) (((a)>(b))?(a):(b))
#define MIN(a,b) (((a)<(b))?(a):(b))
#define ll long long
#define INF 100000000
#define MOD 1000000007
#define SIZE 100005
#define LOCAL
#ifdef LOCAL
    #define DEBUG(...) printf(" "__VA_ARGS__)
#else
    #define DEBUG(...)
#endif /* LOCAL */
int comp(const void* a,const void* b){
	return *(int*)a-*(int*)b;
}

int a[200000];
int main(void)
{
	int n,b,res,i;
	scanf("%d",&n);
	FOR(i,0,n){
		scanf("%d",&a[i]);
		a[i]-=(i+1);
	}
	qsort(a,n,sizeof(int),comp);
	//FOR(i,0,n) printf("%d\n",a[i]);
	b=a[n/2];
	res=0;
	FOR(i,0,n){
		res+=abs(a[i]-b);
	}
	printf("%d\n",res);
	return 0;
}