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;
typedef long long ll;
const int N=2e5+10;
const ll inf=2e16;
int n,num;
ll ans,res,t[N],rv[N],a[N];

int main(){
     int i,j,pos;
	 scanf("%d",&n);
     for(i=1;i<=n;++i){
     	scanf("%I64d",&a[i]);
     	a[i]-=i;
     }t[0]=0;rv[n+1]=0;
     if(n==1) {printf("0\n");return 0;}
     sort(a+1,a+n+1);t[1]=-a[1];rv[n]=a[n];
     for(i=2;i<=n;++i) t[i]=t[i-1]-a[i];
     for(i=n-1;i>=1;--i) rv[i]=rv[i+1]+a[i];
     if(n&1){pos=(n+1)>>1;
	 ans=t[pos-1]+rv[pos+1];}
     else{pos=n>>1;ans=t[pos]+rv[pos+1];}
     printf("%I64d\n",ans);
}