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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define lli long long
lli a[200005];
lli p[200005];
lli s[200005];

int main() {
	int n;
	cin>>n;
	
	
	for(int i=1;i<=n;i++){
	    cin>>a[i];
	    a[i]=a[i]-i;
	}
	
	p[0]=0;
	for(int i=1;i<=n;i++) p[i]=p[i-1]+a[i];
	
	s[n+1]=0;
	
	for(int i=n;i>=1;i--) s[i]=s[i+1]+a[i];
	lli ans=(lli)(1e17+100);
	
	for(int i=1;i<=n;i++){
	    if(i==1){
	        lli sum = abs(s[i+1] - 1LL*(n-i)*a[i]);
	        ans=min(ans,sum);
	    }
	    else if(i==n){
	        lli sum = abs(p[i-1] - 1LL*(i-1)*a[i]);
	        ans=min(ans,sum);
	    }
	    else{
	        lli sum = abs(p[i-1] - 1LL*(i-1)*a[i]) + abs(s[i+1] - 1LL*(n-i)*(a[i]));
	        ans=min(ans,sum);
	    }
	}
	
	cout<<ans<<endl;
	return 0;
}