#pragma region preprocessor #ifdef LOCAL //* #define _GLIBCXX_DEBUG // gcc /*/ #define _LIBCPP_DEBUG 0 // clang //*/ // #define __buffer_check__ #else #pragma GCC optimize("Ofast") // #define NDEBUG #endif #define __precision__ 15 #define __iostream_untie__ true #include #include #ifdef LOCAL #include "dump.hpp" #define mesg(str) std::cerr << "[ " << __LINE__ << " : " << __FUNCTION__ << " ] " << str << "\n" #else #define dump(...) ((void)0) #define mesg(str) ((void)0) #endif #pragma endregion #pragma region std-overload namespace std { // hash template size_t hash_combine(size_t seed, T const &key) { return seed ^ (hash()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2)); } template struct hash> { size_t operator()(pair const &pr) const { return hash_combine(hash_combine(0, pr.first), pr.second); } }; template ::value - 1> struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(tuple_hash_calc::apply(seed, t), get(t)); } }; template struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(seed, get<0>(t)); } }; template struct hash> { size_t operator()(tuple const &t) const { return tuple_hash_calc>::apply(0, t); } }; // iostream template istream &operator>>(istream &is, pair &p) { return is >> p.first >> p.second; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } template struct tupleis { static istream &apply(istream &is, tuple_t &t) { tupleis::apply(is, t); return is >> get(t); } }; template struct tupleis { static istream &apply(istream &is, tuple_t &t) { return is; } }; template istream &operator>>(istream &is, tuple &t) { return tupleis, tuple_size>::value - 1>::apply(is, t); } template <> istream &operator>>(istream &is, tuple<> &t) { return is; } template struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { tupleos::apply(os, t); return os << ' ' << get(t); } }; template struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } }; template ostream &operator<<(ostream &os, const tuple &t) { return tupleos, tuple_size>::value - 1>::apply(os, t); } template <> ostream &operator<<(ostream &os, const tuple<> &t) { return os; } template , string>::value, nullptr_t> = nullptr> istream& operator>>(istream& is, Container &cont) { for(auto&& e : cont) is >> e; return is; } template , string>::value, nullptr_t> = nullptr> ostream& operator<<(ostream& os, const Container &cont) { bool flag = 1; for(auto&& e : cont) flag ? flag = 0 : (os << ' ', 0), os << e; return os; } } // namespace std #pragma endregion #pragma region config namespace config { const auto start_time{std::chrono::system_clock::now()}; int64_t elapsed() { using namespace std::chrono; const auto end_time{std::chrono::system_clock::now()}; return duration_cast(end_time - start_time).count(); } __attribute__((constructor)) void setup() { using namespace std; if(__iostream_untie__) ios::sync_with_stdio(false), cin.tie(nullptr); cout << fixed << setprecision(__precision__); #ifdef DEBUG freopen("debug.out","w",stdout); freopen("debug.err","w",stderr); if(!freopen("debug.in","r",stdin)) { cerr << "error: \"./debug.in\" not found.\n"; exit(EXIT_FAILURE); } #endif #ifdef stderr_path freopen(stderr_path, "a", stderr); #endif #ifdef LOCAL cerr << fixed << setprecision(__precision__) << boolalpha << "\n----- stderr at LOCAL -----\n\n"; atexit([]{ cerr << "\n----- Exec time : " << elapsed() << " ms -----\n\n"; }); #endif #ifdef __buffer_check__ atexit([]{ ofstream cnsl("CON"); char bufc; if(cin >> bufc) cnsl << "\n\033[1;35mwarning\033[0m: buffer not empty.\n\n"; }); #endif } } // namespace config #pragma endregion #pragma region utility // lambda wrapper for recursive method. template class fixed_point { lambda_type func; public: fixed_point(lambda_type &&f) : func(std::move(f)) {} template auto operator()(Args &&... args) const { return func(*this, std::forward(args)...); } }; // read with std::cin. template struct read { typename std::remove_const::type value; template read(types... args) : value(args...) { std::cin >> value; } operator T() const { return value; } }; template <> struct read { template operator T() const { T value; std::cin >> value; return value; } }; // substitute y for x if x > y. template inline bool chmin(T &x, const T &y) { return x > y ? x = y, true : false; } // substitute y for x if x < y. template inline bool chmax(T &x, const T &y) { return x < y ? x = y, true : false; } // binary search on discrete range. template iter_type binary(iter_type __ok, iter_type __ng, pred_type pred) { assert(__ok != __ng); std::ptrdiff_t dist(__ng - __ok); while(std::abs(dist) > 1) { iter_type mid(__ok + dist / 2); if(pred(mid)) __ok = mid, dist -= dist / 2; else __ng = mid, dist /= 2; } return __ok; } // binary search on real numbers. template long double binary(long double __ok, long double __ng, const long double eps, pred_type pred) { assert(__ok != __ng); while(std::abs(__ok - __ng) > eps) { long double mid{(__ok + __ng) / 2}; (pred(mid) ? __ok : __ng) = mid; } return __ok; } // trinary search on discrete range. template iter_type trinary(iter_type __first, iter_type __last, comp_type comp) { assert(__first < __last); std::ptrdiff_t dist(__last - __first); while(dist > 2) { iter_type __left(__first + dist / 3), __right(__first + dist * 2 / 3); if(comp(__left, __right)) __last = __right, dist = dist * 2 / 3; else __first = __left, dist -= dist / 3; } if(dist > 1 && comp(next(__first), __first)) ++__first; return __first; } // trinary search on real numbers. template long double trinary(long double __first, long double __last, const long double eps, comp_type comp) { assert(__first < __last); while(__last - __first > eps) { long double __left{(__first * 2 + __last) / 3}, __right{(__first + __last * 2) / 3}; if(comp(__left, __right)) __last = __right; else __first = __left; } return __first; } // size of array. template size_t size(A (&array)[N]) { return N; } // be careful that val is type-sensitive. template void init(A (&array)[N], const T &val) { std::fill((T*)array, (T*)(array + N), val); } #pragma endregion #pragma region alias using namespace std; using i32 = int_least32_t; using i64 = int_least64_t; using u32 = uint_least32_t; using u64 = uint_least64_t; using p32 = pair; using p64 = pair; template > using heap = priority_queue, Comp>; template using hashset = unordered_set; template using hashmap = unordered_map; using namespace __gnu_cxx; #pragma endregion #pragma region library #ifndef modint_hpp #define modint_hpp #include #include template class modint { int val; public: static constexpr modint identity() noexcept { return 1; } constexpr modint() noexcept : val(0) {} template ::value, std::nullptr_t> = nullptr> constexpr modint(int_type _val) noexcept : val((_val %= mod) < 0 ? mod + _val : _val) {} constexpr long long value() const noexcept { return val; } constexpr modint operator++(int) noexcept { modint t = *this; return ++val, t; } constexpr modint operator--(int) noexcept { modint t = *this; return --val, t; } constexpr modint &operator++() noexcept { return ++val, *this; } constexpr modint &operator--() noexcept { return --val, *this; } constexpr modint operator-() const noexcept { return modint(-val); } constexpr modint &operator+=(const modint &rhs) noexcept { return (val += rhs.val) < mod ? 0 : val -= mod, *this; } constexpr modint &operator-=(const modint &rhs) noexcept { return (val += mod - rhs.val) < mod ? 0 : val -= mod, *this; } constexpr modint &operator*=(const modint &rhs) noexcept { return val = (long long)val * rhs.val % mod, *this; } constexpr modint &operator/=(const modint &rhs) noexcept { return *this *= inverse(rhs); } constexpr modint operator+(const modint &rhs) const noexcept { return modint(*this) += rhs; } constexpr modint operator-(const modint &rhs) const noexcept { return modint(*this) -= rhs; } constexpr modint operator*(const modint &rhs) const noexcept { return modint(*this) *= rhs; } constexpr modint operator/(const modint &rhs) const noexcept { return modint(*this) /= rhs; } constexpr bool operator==(const modint &rhs) const noexcept { return val == rhs.val; } constexpr bool operator!=(const modint &rhs) const noexcept { return val != rhs.val; } constexpr bool operator!() const noexcept { return !val; } friend constexpr modint operator+(long long lhs, modint rhs) noexcept { return modint(lhs) + rhs; } friend constexpr modint operator-(long long lhs, modint rhs) noexcept { return modint(lhs) - rhs; } friend constexpr modint operator*(long long lhs, modint rhs) noexcept { return modint(lhs) * rhs; } friend constexpr modint operator/(long long lhs, modint rhs) noexcept { return modint(lhs) / rhs; } static constexpr modint inverse(const modint &rhs) noexcept { assert(rhs != 0); int a{mod}, b{rhs.val}, u{}, v{1}, t{}; while(b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v; return {u}; } static constexpr modint pow(modint rhs, long long e) noexcept { if(e < 0) e = e % (mod - 1) + mod - 1; modint res{1}; while(e) { if(e & 1) res *= rhs; rhs *= rhs, e >>= 1; } return res; } friend std::ostream &operator<<(std::ostream &os, const modint &rhs) noexcept { return os << rhs.val; } friend std::istream &operator>>(std::istream &is, modint &rhs) noexcept { long long val; rhs = {(is >> val, val)}; return is; } }; // class modint template <> class modint<2> { bool val; public: static constexpr modint identity() noexcept { return 1; } constexpr modint() noexcept : val(false) {} template ::value, std::nullptr_t> = nullptr> constexpr modint(int_type _val) noexcept : val(_val & 1) {} constexpr operator bool() const noexcept { return val; } constexpr bool value() const noexcept { return val; } constexpr modint &operator+=(const modint &rhs) noexcept { return val ^= rhs.val, *this; } constexpr modint &operator-=(const modint &rhs) noexcept { return val ^= rhs.val, *this; } constexpr modint &operator*=(const modint &rhs) noexcept { return val &= rhs.val, *this; } constexpr modint &operator/=(const modint &rhs) noexcept { assert(rhs.val); return *this; } constexpr modint operator!() const noexcept { return !val; } constexpr modint operator-() const noexcept { return *this; } constexpr modint operator+(const modint &rhs) const noexcept { return val != rhs.val; } constexpr modint operator-(const modint &rhs) const noexcept { return val != rhs.val; } constexpr modint operator*(const modint &rhs) const noexcept { return val && rhs.val; } constexpr modint operator/(const modint &rhs) const noexcept { assert(rhs.val); return *this; } constexpr bool operator==(const modint &rhs) const noexcept { return val == rhs.val; } constexpr bool operator!=(const modint &rhs) const noexcept { return val != rhs.val; } friend constexpr modint operator+(long long lhs, modint rhs) noexcept { return lhs & 1 ? !rhs : rhs; } friend constexpr modint operator-(long long lhs, modint rhs) noexcept { return lhs & 1 ? !rhs : rhs; } friend constexpr modint operator*(long long lhs, modint rhs) noexcept { return lhs & 1 ? rhs : modint<2>{0}; } friend constexpr modint operator/(long long lhs, modint rhs) noexcept { assert(rhs.val); return lhs & 1 ? rhs : modint<2>{0}; } friend std::ostream &operator<<(std::ostream &os, const modint &rhs) noexcept { return os << rhs.val; } friend std::istream &operator>>(std::istream &is, modint &rhs) noexcept { long long val; rhs.val = (is >> val, val & 1); return is; } }; // class modint specialization #endif // modint_hpp #pragma endregion struct solver; template void main_(); int main() { main_(); } template void main_() { unsigned t = 1; #ifdef LOCAL t = 1; #endif // t = -1; // infinite loop // cin >> t; // case number given while(t--) solver(); } struct solver { struct point { int x,y; bool operator!=(const point &rhs) const { return x!=rhs.x or y!=rhs.y; } }; i64 cprod(point p1, point p2) { return p1.x*p2.y-p2.x*p1.y; } struct comp { int cx, cy; comp(int x,int y) : cx(x),cy(y) {} comp(point p) : cx(p.x),cy(p.y) {} bool operator()(point p1, point p2) const { auto [x1,y1]=p1; auto [x2,y2]=p2; x1-=cx,x2-=cx; y1-=cy,y2-=cy; if(y1*y2<0) { return y1>0; } if(y1==0 and y2==0) { return x1>0; } return x1*y2-x2*y1>0; } int ccw(point p1, point p2) const { auto [x1,y1]=p1; auto [x2,y2]=p2; x1-=cx,x2-=cx; y1-=cy,y2-=cy; return x1*y2-x2*y1>0; } bool prll(point p1, point p2) const { auto [x1,y1]=p1; auto [x2,y2]=p2; x1-=cx,x2-=cx; y1-=cy,y2-=cy; if(x1*y2==x2*y1) { if(x1!=0) return x1*x2>0; assert(y1!=0 and y2!=0); return y1*y2>0; } return false; } }; using mint=modint<1000000007>; solver() { const int n=read(); vector points(n); for(auto &[x,y]: points) cin>>x>>y; mint ans=0; for(int i=0; i doub; for(int j=0; j0) jjj++; int cnt=jjj-jj; mint tmp; for(int k=j; k