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<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N=2e5+5;
ll read(){
	ll x=0,w=1;
	char ch=0;
	while (ch<'0' || ch>'9'){
		  if (ch=='-') w=-1;
		  ch=getchar();
	}
	while (ch<='9' && ch>='0'){
		  x=(x<<1)+(x<<3)+ch-'0';
		  ch=getchar();
	}
	return x*w;
}
ll a[N];
ll n,ans;
int main(){
	n=read();
	for (int i=1;i<=n;++i)
		a[i]=read()-i;
	sort(a+1,a+n+1);
	for (int i=1;i<=n;++i)
		ans+=max(a[i]-a[(n+1)>>1],a[(n+1)>>1]-a[i]);
	printf("%lld\n",ans);
	return 0;
}