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>
using namespace std;

//#define int long long
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define rep(i,n) for(int i=0;i<n;++i)
#define rep1(i,n) for(int i=1;i<n;++i)
#define exrep(i, a, b) for(ll i = a; i < b; i++)
#define out(x) cout << x << endl
#define EPS (1e-7)
#define gearup ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
typedef long double ld;
typedef long long int ll;
typedef unsigned long long int ull;
typedef vector<int> vi;
typedef vector<char> vc;
typedef vector<bool> vb;
typedef vector<double> vd;
typedef vector<string> vs;
typedef vector<pair<int,int> > vpii;
typedef vector<vector<int> > vvi;
typedef vector<vector<char> > vvc;
typedef vector<vector<bool> > vvb;
typedef vector<vector<double> > vvd;
typedef vector<vector<string> > vvs;
typedef vector<ll> vl;
typedef vector<vector<ll> > vvl;
typedef vector<vector<vector<ll> > > vvvl;
//ll MOD = 1000000007;
ll MOD = 998244353;
const long long L_INF = 1LL << 60;
const int INF = 2147483647; // 2^31-1
const double PI = acos(-1);
//cout<<fixed<<setprecision(10);

template<class T> inline bool chmin(T& a, T b) {if (a > b) {a = b;return true;}return false;}
template<class T> inline bool chmax(T& a, T b) {if (a < b) {a = b;return true;}return false;}
template<class T> void debug(T v){rep(i,v.size()) cout<<v[i]<<" ";cout<<endl;}
const ll dx[8] = {1, 1, 0, -1, -1, -1, 0, 1};
const ll dy[8] = {0, 1, 1, 1, 0, -1, -1, -1};

signed main()
{   
  gearup;
  int n; cin >> n;
  vl a(n);
  rep(i,n) cin>>a[i];
  vl c;
  rep(i,n)c.push_back(a[i]-(i+1));
  sort(all(c));
  ll b = c[n/2];
  ll res = 0;
  rep(i,n)res+=abs(c[i]-b);
  out(res);
}