結果
| 問題 |
No.1144 Triangles
|
| コンテスト | |
| ユーザー |
 anqooqie
|
| 提出日時 | 2021-07-23 18:51:32 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 200 ms / 3,000 ms |
| コード長 | 27,219 bytes |
| コンパイル時間 | 1,268 ms |
| コンパイル使用メモリ | 121,888 KB |
| 最終ジャッジ日時 | 2025-01-23 07:41:25 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 25 |
ソースコード
#line 1 "main.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1144"
#include <cstdint>
#include <iostream>
#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp"
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_math.hpp"
#include <utility>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m < 2^31`
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
} // namespace atcoder
#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_type_traits.hpp"
#line 7 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_type_traits.hpp"
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
#line 14 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp"
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
#line 1 "/home/anqooqie/.proconlib/tools/vector2.hpp"
#include <cmath>
#line 6 "/home/anqooqie/.proconlib/tools/vector2.hpp"
#include <cstddef>
#include <array>
#include <string>
#include <functional>
#include <limits>
#line 1 "/home/anqooqie/.proconlib/tools/pair_hash.hpp"
#line 6 "/home/anqooqie/.proconlib/tools/pair_hash.hpp"
#include <random>
#line 9 "/home/anqooqie/.proconlib/tools/pair_hash.hpp"
namespace tools {
template <class T1, class T2>
struct pair_hash {
using result_type = ::std::size_t;
using argument_type = ::std::pair<T1, T2>;
::std::size_t operator()(const ::std::pair<T1, T2>& key) const {
static const ::std::size_t salt = ::std::random_device()();
static const ::std::hash<T1> hasher1 = ::std::hash<T1>();
static const ::std::hash<T2> hasher2 = ::std::hash<T2>();
static const ::std::hash<::std::size_t> hasher3 = ::std::hash<::std::size_t>();
::std::size_t result = 0;
result ^= hasher1(key.first) + static_cast<::std::size_t>(0x9e3779b9) + (result << static_cast<::std::size_t>(6)) + (result >> static_cast<::std::size_t>(2));
result ^= hasher2(key.second) + static_cast<::std::size_t>(0x9e3779b9) + (result << static_cast<::std::size_t>(6)) + (result >> static_cast<::std::size_t>(2));
result ^= hasher3(salt) + static_cast<::std::size_t>(0x9e3779b9) + (result << static_cast<::std::size_t>(6)) + (result >> static_cast<::std::size_t>(2));
return result;
}
};
template <>
struct pair_hash<::std::uint64_t, ::std::uint64_t> {
using result_type = ::std::size_t;
using argument_type = ::std::pair<::std::uint64_t, ::std::uint64_t>;
::std::size_t operator()(const ::std::pair<::std::uint64_t, ::std::uint64_t>& key) const {
static const ::std::hash<::std::uint64_t> hasher = ::std::hash<::std::uint64_t>();
return hasher(((key.first << static_cast<::std::uint64_t>(32)) | (key.first >> static_cast<::std::uint64_t>(32))) ^ key.second);
}
};
template <>
struct pair_hash<::std::int64_t, ::std::int64_t> {
using result_type = ::std::size_t;
using argument_type = ::std::pair<::std::int64_t, ::std::int64_t>;
::std::size_t operator()(const ::std::pair<::std::int64_t, ::std::int64_t>& key) const {
static const ::tools::pair_hash<::std::uint64_t, ::std::uint64_t> hasher = ::tools::pair_hash<::std::uint64_t, ::std::uint64_t>();
return hasher(::std::make_pair<::std::uint64_t, ::std::uint64_t>(key.first, key.second));
}
};
template <>
struct pair_hash<::std::uint32_t, ::std::uint32_t> {
using result_type = ::std::size_t;
using argument_type = ::std::pair<::std::uint32_t, ::std::uint32_t>;
::std::size_t operator()(const ::std::pair<::std::uint32_t, ::std::uint32_t>& key) const {
static const ::std::hash<::std::uint64_t> hasher = ::std::hash<::std::uint64_t>();
return hasher((static_cast<::std::uint64_t>(key.first) << static_cast<::std::uint64_t>(32)) | static_cast<::std::uint64_t>(key.second));
}
};
template <>
struct pair_hash<::std::int32_t, ::std::int32_t> {
using result_type = ::std::size_t;
using argument_type = ::std::pair<::std::int32_t, ::std::int32_t>;
::std::size_t operator()(const ::std::pair<::std::int32_t, ::std::int32_t>& key) const {
static const ::tools::pair_hash<::std::uint32_t, ::std::uint32_t> hasher = ::tools::pair_hash<::std::uint32_t, ::std::uint32_t>();
return hasher(::std::make_pair<::std::uint32_t, ::std::uint32_t>(key.first, key.second));
}
};
}
#line 13 "/home/anqooqie/.proconlib/tools/vector2.hpp"
namespace tools {
template <typename T>
class vector2 {
public:
T x;
T y;
vector2() :
vector2(T(), T()) {
}
vector2(const T& x, const T& y) :
x(x),
y(y) {
}
double norm() const {
return ::std::sqrt(static_cast<double>(this->squared_norm()));
}
T squared_norm() const {
return this->inner_product(*this);
}
template <typename SFINAE_T = T, typename ::std::enable_if<::std::is_same<SFINAE_T, double>::value, ::std::nullptr_t>::type = nullptr>
::tools::vector2<double> normalized() const {
return *this / this->norm();
}
::tools::vector2<T> operator+() const {
return *this;
}
::tools::vector2<T> operator-() const {
return ::tools::vector2<T>(-this->x, -this->y);
}
friend ::tools::vector2<T> operator+(const ::tools::vector2<T>& lhs, const ::tools::vector2<T>& rhs) {
return ::tools::vector2<T>(lhs.x + rhs.x, lhs.y + rhs.y);
}
friend ::tools::vector2<T> operator-(const ::tools::vector2<T>& lhs, const ::tools::vector2<T>& rhs) {
return ::tools::vector2<T>(lhs.x - rhs.x, lhs.y - rhs.y);
}
template <typename OTHER, typename ::std::enable_if<!::std::is_same<OTHER, ::tools::vector2<T>>::value, ::std::nullptr_t>::type = nullptr>
friend ::tools::vector2<T> operator*(const ::tools::vector2<T>& lhs, const OTHER& rhs) {
return ::tools::vector2<T>(lhs.x * rhs, lhs.y * rhs);
}
template <typename OTHER, typename ::std::enable_if<!::std::is_same<OTHER, ::tools::vector2<T>>::value, ::std::nullptr_t>::type = nullptr>
friend ::tools::vector2<T> operator*(const OTHER& lhs, const ::tools::vector2<T>& rhs) {
return ::tools::vector2<T>(lhs * rhs.x, lhs * rhs.y);
}
template <typename OTHER, typename ::std::enable_if<!::std::is_same<OTHER, ::tools::vector2<T>>::value, ::std::nullptr_t>::type = nullptr>
friend ::tools::vector2<T> operator/(const ::tools::vector2<T>& lhs, const OTHER& rhs) {
return ::tools::vector2<T>(lhs.x / rhs, lhs.y / rhs);
}
T inner_product(const ::tools::vector2<T>& other) const {
return this->x * other.x + this->y * other.y;
}
T outer_product(const ::tools::vector2<T>& other) const {
return this->x * other.y - this->y * other.x;
}
::tools::vector2<T>& operator+=(const ::tools::vector2<T>& other) {
return *this = *this + other;
}
::tools::vector2<T>& operator-=(const ::tools::vector2<T>& other) {
return *this = *this - other;
}
template <typename OTHER, typename ::std::enable_if<!::std::is_same<OTHER, ::tools::vector2<T>>::value, ::std::nullptr_t>::type = nullptr>
::tools::vector2<T>& operator*=(const OTHER& other) {
return *this = *this * other;
}
template <typename OTHER, typename ::std::enable_if<!::std::is_same<OTHER, ::tools::vector2<T>>::value, ::std::nullptr_t>::type = nullptr>
::tools::vector2<T>& operator/=(const OTHER& other) {
return *this = *this / other;
}
friend bool operator==(const ::tools::vector2<T>& lhs, const ::tools::vector2<T>& rhs) {
return lhs.x == rhs.x && lhs.y == rhs.y;
}
friend bool operator!=(const ::tools::vector2<T>& lhs, const ::tools::vector2<T>& rhs) {
return lhs.x != rhs.x || lhs.y != rhs.y;
}
static ::std::array<::tools::vector2<T>, 4> four_directions() {
return ::std::array<::tools::vector2<T>, 4>({
::tools::vector2<T>(static_cast<T>(-1), static_cast<T>(0)),
::tools::vector2<T>(static_cast<T>(1), static_cast<T>(0)),
::tools::vector2<T>(static_cast<T>(0), static_cast<T>(-1)),
::tools::vector2<T>(static_cast<T>(0), static_cast<T>(1))
});
}
static ::std::array<::tools::vector2<T>, 8> eight_directions() {
return ::std::array<::tools::vector2<T>, 8>({
::tools::vector2<T>(static_cast<T>(-1), static_cast<T>(-1)),
::tools::vector2<T>(static_cast<T>(-1), static_cast<T>(0)),
::tools::vector2<T>(static_cast<T>(-1), static_cast<T>(1)),
::tools::vector2<T>(static_cast<T>(0), static_cast<T>(-1)),
::tools::vector2<T>(static_cast<T>(0), static_cast<T>(1)),
::tools::vector2<T>(static_cast<T>(0), static_cast<T>(-1)),
::tools::vector2<T>(static_cast<T>(1), static_cast<T>(-1)),
::tools::vector2<T>(static_cast<T>(1), static_cast<T>(0)),
::tools::vector2<T>(static_cast<T>(1), static_cast<T>(1))
});
}
};
}
namespace std {
template <typename T>
::std::string to_string(const ::tools::vector2<T>& f) {
return '(' + ::std::to_string(f.x) + ", " + ::std::to_string(f.y) + ')';
}
template <typename T>
struct hash<::tools::vector2<T>> {
using result_type = ::std::size_t;
using argument_type = ::tools::vector2<T>;
::std::size_t operator()(const ::tools::vector2<T>& key) const {
static const ::tools::pair_hash<T, T> hasher = ::tools::pair_hash<T, T>();
return hasher(key.x, key.y);
}
};
template <typename T>
::std::ostream& operator<<(::std::ostream& os, const ::tools::vector2<T>& self) {
return os << ::std::to_string(self);
}
template <typename T>
::std::istream& operator>>(::std::istream& is, ::tools::vector2<T>& self) {
return is >> self.x >> self.y;
}
}
#line 1 "/home/anqooqie/.proconlib/tools/less_by_arg.hpp"
#line 1 "/home/anqooqie/.proconlib/tools/ccw.hpp"
#line 5 "/home/anqooqie/.proconlib/tools/ccw.hpp"
namespace tools {
template <typename T>
::std::int_fast64_t ccw(const ::tools::vector2<T>& a, ::tools::vector2<T> b, ::tools::vector2<T> c) {
b -= a;
c -= a;
if (b.outer_product(c) > 0) return +1;
if (b.outer_product(c) < 0) return -1;
if (b.inner_product(c) < 0) return +2;
if (b.squared_norm() < c.squared_norm()) return -2;
return 0;
}
}
#line 7 "/home/anqooqie/.proconlib/tools/less_by_arg.hpp"
namespace tools {
template <bool DEFAULT, typename T>
class less_by_arg {
private:
::tools::vector2<T> d;
template <typename U>
int where(const ::tools::vector2<U>& p) const {
if constexpr (DEFAULT) {
return p.y > 0 || (p.y == 0 && p.x >= 0) ? 0 : 1;
} else {
if (this->d == p) return 0;
const int ccw = ::tools::ccw(::tools::vector2<U>(0, 0), this->d, p);
if (ccw == -2) return 0;
if (ccw == +1) return 1;
if (ccw == +2) return 2;
if (ccw == -1) return 3;
return 4;
}
}
public:
less_by_arg() = default;
template <typename U>
explicit less_by_arg(const ::tools::vector2<U>& d) : d(d) {
}
template <typename U>
bool operator()(const ::tools::vector2<U>& a, const ::tools::vector2<U>& b) const {
const int wa = this->where(a);
const int wb = this->where(b);
return wa == wb ? a.outer_product(b) > 0 || (a.outer_product(b) == 0 && a.squared_norm() < b.squared_norm()) : wa < wb;
}
};
less_by_arg() -> less_by_arg<true, int>;
template <typename U>
less_by_arg(const ::tools::vector2<U>&) -> less_by_arg<false, U>;
}
#line 8 "main.cpp"
using mint = atcoder::modint1000000007;
using i64 = std::int_fast64_t;
int main() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
i64 n;
std::cin >> n;
std::vector<tools::vector2<i64>> orig_p(n);
for (auto& orig_p_i : orig_p) std::cin >> orig_p_i;
mint answer(0);
for (auto it = orig_p.begin(); it != orig_p.end(); ++it) {
std::vector<tools::vector2<i64>> p(std::next(it), orig_p.end());
for (auto& p_i : p) p_i -= *it;
std::sort(p.begin(), p.end(), tools::less_by_arg());
auto whole = std::accumulate(p.begin(), p.end(), tools::vector2<i64>(0, 0));
i64 r = 0;
tools::vector2<i64> sum(0, 0);
for (i64 l = 0; l < i64(p.size()); ++l) {
for (; r < i64(p.size()) && tools::less_by_arg(p[l])(p[r], -p[l]); ++r) {
sum += p[r];
}
answer += mint(p[l].outer_product(sum));
answer -= mint(p[l].outer_product(whole - sum));
if (l == r) {
++r;
} else {
sum -= p[l];
}
whole -= p[l];
}
}
std::cout << answer.val() << '\n';
}