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 SORT(a) sort(a.begin(), a.end())
#define RSORT(a) sort(a.rbegin(), a.rend())
#define REP(i, n) for (int i = 0; i < n; i++)
#define RREP(i, n) for (int i = n - 1; 0 <= i; i--)
#define FOR(i, start, end) for (int i = start; i < end; i++)
#define RFOR(i, start, end) for (int i = start - 1; 0 <= i; i--)
#define ALL(a) a.begin(), a.end()
using ll = long long;
using namespace std;
constexpr int INF32       = 1'050'000'000;
constexpr long long INF64 = 4'000'000'000'000'000'000;
constexpr int MOD7        = 1'000'000'007;
constexpr int MOD9        = 1'000'000'009;
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;
}
void print() { std::cout << '\n'; }
template <class H, class... T> void print(H &&head, T &&... args) {
    std::cout << head;
    sizeof...(args) == 0 ? std::cout << "" : std::cout << ' ';
    print(std::forward<T>(args)...);
}
template <class T> void print(std::vector<T> &v) {
    for (int i = 0; i < v.size(); i++) {
        std::cout << v[i];
        i == v.size() - 1 ? std::cout << '\n' : std::cout << ' ';
    }
}
template <class T> void print(std::vector<std::vector<T>> &v) {
    for (int i = 0; i < v.size(); i++) {
        for (int j = 0; j < v[i].size(); j++) {
            std::cout << v[i][j];
            j == v[i].size() - 1 ? std::cout << '\n' : std::cout << ' ';
        }
    }
}
void scan() {}
template <class H, class... T> void scan(H &&head, T &&... args) {
    std::cin >> head;
    scan(std::forward<T>(args)...);
}
template <class T> void scan(std::vector<T> &v) {
    for (auto &&i : v) {
        scan(i);
    }
}
template <class T> T up(T a, T div) { return (a + div - 1) / div; }
int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    int N;
    scan(N);
    vector<ll> v(N);
    scan(v);

    REP(i, N) { v[i] -= i + 1; }
    SORT(v);
    int b   = v[N / 2 - 1];
    ll ans1 = 0;
    REP(i, N) { ans1 += abs(v[i] - b); }
    b       = v[N / 2];
    ll ans2 = 0;
    REP(i, N) { ans2 += abs(v[i] - b); }

    print(min(ans1, ans2));

    return 0;
}