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)

//#define NDEBUG
#define _CRT_SECURE_NO_WARNINGS
#include <array>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <limits>
#include <memory>
#include <string>
#include <type_traits>

class rep {
	const ::std::size_t f, l;

public:
	using value_type = ::std::size_t;
	using reference = value_type;
	class repitr {
		friend rep;
		value_type i;
		repitr(value_type x) noexcept : i(x) {}

	public:
		void operator++() noexcept { ++i; }
		reference operator*() const noexcept { return i; }
		bool operator!=(const repitr x) const noexcept { return i != x.i; }
	};
	explicit rep(value_type first, value_type last) noexcept
		: f(first), l(last) {}
	repitr begin() const noexcept { return repitr(f); }
	repitr end() const noexcept { return repitr(l); }
};
class Rrep {
	const ::std::size_t f, l;

public:
	using value_type = ::std::size_t;
	using reference = value_type;
	class Rrepitr {
		friend Rrep;
		value_type i;
		Rrepitr(value_type x) noexcept : i(x) {}

	public:
		void operator++() noexcept { --i; }
		reference operator*() const noexcept { return i - 1; }
		bool operator!=(const Rrepitr x) const noexcept { return i != x.i; }
	};
	explicit Rrep(value_type first, value_type last) noexcept
		: f(first), l(last) {}
	Rrepitr begin() const noexcept { return Rrepitr(l); }
	Rrepitr end() const noexcept { return Rrepitr(f); }
};
template <class T> bool maxi(T &a, const T &b) {
	if (b < a)
		return 0;
	a = b;
	return 1;
}
template <class T> bool mini(T &a, const T &b) {
	if (a < b)
		return 0;
	a = b;
	return 1;
}
template <class T> bool smaxi(T &a, const T &b) {
	if (a < b) {
		a = b;
		return 1;
	}
	return 0;
}
template <class T> bool smini(T &a, const T &b) {
	if (b < a) {
		a = b;
		return 1;
	}
	return 0;
}
class customIO {
	int c;
	bool f;
	::std::array<int, 30> buf;
	void get_c() { c = fgetc(stdin); }
	void put_c(int x) { fputc(x, stdout); }
	bool vacant() { return c == ' ' || c == '\n'; }

	// in

	void cueing() {
		while (get_c(), vacant())
			;
	}

public:
	template <class T>
	auto operator>>(T &d) ->
		typename ::std::enable_if<::std::is_signed<T>::value, customIO &>::type {
		d = 0;
		f = 0;
		cueing();
		if (c == '-')
			f = 1, get_c();
		do
			d = d * 10 + c - '0';
		while (get_c(), !vacant());
		if (f)
			d = -d;
		return *this;
	}
	template <class T>
	auto operator>>(T &d) ->
		typename ::std::enable_if<!::std::is_signed<T>::value, customIO &>::type {
		d = 0;
		cueing();
		do
			d = d * 10 + c - '0';
		while (get_c(), !vacant());
		return *this;
	}
	customIO &operator>>(char &d) {
		cueing();
		d = c;
		return *this;
	}
	customIO &operator>>(double &d) {
		scanf("%lf", &d);
		return *this;
	}
	customIO &operator>>(::std::string &d) {
		d.clear();
		cueing();
		do
			d.push_back(c);
		while (get_c(), !vacant());
		return *this;
	}

	// out

	template <class T>
	auto operator<<(T d) ->
		typename ::std::enable_if<::std::is_signed<T>::value, customIO &>::type {
		c = 0;
		f = 0;
		if (d < static_cast<T>(0))
			f = 1, d = -d;
		while (d)
			buf[c++] = d % 10 + '0', d /= 10;
		if (!c)
			buf[c++] = '0';
		if (f)
			put_c('-');
		while (c--)
			put_c(buf[c]);
		return *this;
	}
	template <class T>
	auto operator<<(T d) ->
		typename ::std::enable_if<!::std::is_signed<T>::value, customIO &>::type {
		c = 0;
		while (d)
			buf[c++] = d % 10 + '0', d /= 10;
		if (!c)
			buf[c++] = '0';
		while (c--)
			put_c(buf[c]);
		return *this;
	}
	customIO &operator<<(char d) {
		put_c(d);
		return *this;
	}
	customIO &operator<<(const ::std::string &d) {
		for (const auto e : d)
			put_c(e);
		return *this;
	}
	customIO &operator<<(const char *d) {
		while (*d != '\0')
			put_c(*(d++));
		return *this;
	}
	customIO &operator<<(double d) {
		/*
		printf("%1.9f",d);
		/*/
		printf("%f", d);
		//*/
		return *this;
	}
	void endl() { put_c('\n'); }
	void space() { put_c(' '); }
	operator int() { return 0; }
} IO;
template <class T = ::std::size_t> T scan() {
	T ret;
	IO >> ret;
	return ret;
}

using int32 = ::std::int_fast32_t;
using int64 = ::std::int_fast64_t;
using uint32 = ::std::uint_fast32_t;
using uint64 = ::std::uint_fast64_t;
using intl32 = ::std::int_least32_t;
using intl64 = ::std::int_least64_t;
using uintl32 = ::std::uint_least32_t;
using uintl64 = ::std::uint_least64_t;

#include <algorithm>
#include <utility>
#include <vector>

int main() {
	const auto n = scan();
	::std::vector<int64> a(n);
	for (auto &e : a)
		IO >> e;
	for (const auto i : rep(0, n))
		a[i] -= i + 1;
	::std::sort(a.begin(), a.end());
	int64 b = a[n / 2];
	int64 ans = 0;
	for (const auto e : a)
		ans += ::std::abs(e- b);
	IO << ans << '\n';
	return 0;
}