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 <bits/stdc++.h>
#define REP(i,n) for(int i=0;i<int(n);i++)
#define FOR(i,n,m) for(int i=n;i<int(m);i++)
#define ALL(v) (v).begin(),(v).end()
#define pb push_back
using namespace std;

typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

int vx[]={0,0,-1,1};
int vy[]={1,-1,0,0};
int dx[]={1,0,-1,1,-1,1,0,-1};
int dy[]={1,1,1,0,0,-1,-1,-1};

int gcd(int a,int b){return b?gcd(b,a%b):a;}
int lcm(int a,int b){return a*b/gcd(a,b);}	

const ll mod=1e9+7;
const int INF=INT_MAX/2;
const int N_MAX=100010;

int main(){
	int n;
	cin>>n;
	vector<int> a(n);
	REP(i,n){
		cin>>a[i];
		a[i]-=i;
	}
	sort(ALL(a));
	ll ans=LONG_MAX;
	if(n%2==0){
		ll sum=0;
		REP(i,n)sum+=abs(a[i]-a[n/2-1]);
		ans=min(ans,sum);
		sum=0;
		REP(i,n)sum+=abs(a[i]-a[n/2]);
		ans=min(ans,sum);
	}else {
		ans=0;
		REP(i,n)ans+=abs(a[i]-a[n/2]);
	}
	cout<<ans<<endl;
	return 0;
}