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: Accepted)

#include <cstdio>  
#include <cmath>  
#include <string>  
#include<vector>
#include <cstring>  
#include<algorithm>
#include <cstdlib>  
#include<queue>
#include <iostream>  
#include<set>
#define pb push_back 
#define lb lower_bound 
#define lowbit(x) (x)&(-x)   
#define forup(i,a,b) for(int i=(a);i<=(b);i++)  
#define fordown(i,a,b) for(int i=(a);i>=(b);i--)  
#define maxn 1000005
#define INF 107000000 

#define mod 997
using namespace std;  
typedef long long ll;  
typedef unsigned long long ull;  
   #define int ll 
template<class T> inline  void read(T& num){   num = 0; bool f = true;char ch = getchar();   while(ch < '0' || ch > '9') { if(ch == '-') f = false;ch = getchar();}   while(ch >= '0' && ch <= '9') {num = num * 10 + ch - '0';ch = getchar();}   num = f ? num: -num;  } 
int out[100]; 
template<class T> inline
void write(T x,char ch){  if (x==0) {putchar('0'); putchar(ch); return;}  if (x<0) {putchar('-'); x=-x;} int num=0; while (x){ out[num++]=(x%10); x=x/10;} fordown(i,num-1,0) putchar(out[i]+'0'); putchar(ch); } 
/*========================================================*/
int n;
int a[maxn];
int mid;
signed main()
{  cin>>n; 
   forup(i,1,n)
    {read(a[i]); a[i]-=i;}
  sort(a+1,a+n+1);
  mid=a[n/2];
  ll sum=0; 
  forup(i,1,n) sum+=abs(mid-a[i]);	
  ll sum2=0;
  if(n/2-1>0) forup(i,1,n) sum2+=abs(a[i]-a[n/2-1]);
  ll sum3=0;
  if(n/2+1>0) forup(i,1,n) sum3+=abs(a[i]-a[n/2+1]);
  ll ans=min(sum,sum2); ans=min(ans,sum3);
  cout<<ans<<endl; 
return 0;	
 }