#line 2 "/home/user/competitive_programming/library_for_cpp/Algebra/modint.hpp" #line 2 "/home/user/competitive_programming/library_for_cpp/template/template.hpp" using namespace std; // intrinstic #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include // utility #line 2 "/home/user/competitive_programming/library_for_cpp/template/utility.hpp" using ll = long long; // a ← max(a, b) を実行する. a が更新されたら, 返り値が true. template inline bool chmax(T &a, const U b){ return (a < b ? a = b, 1: 0); } // a ← min(a, b) を実行する. a が更新されたら, 返り値が true. template inline bool chmin(T &a, const U b){ return (a > b ? a = b, 1: 0); } #line 59 "/home/user/competitive_programming/library_for_cpp/template/template.hpp" // math #line 2 "/home/user/competitive_programming/library_for_cpp/template/math.hpp" // 除算に関する関数 // floor(x / y) を求める. template T div_floor(T x, U y){ return (x > 0 ? x / y: (x - y + 1) / y); } // ceil(x / y) を求める. template T div_ceil(T x, U y){ return (x > 0 ? (x + y - 1) / y: x / y) ;} // x を y で割った余りを求める. template T safe_mod(T x, U y){ T q = div_floor(x, y); return x - q * y ; } // x を y で割った商と余りを求める. template pair divmod(T x, U y){ T q = div_floor(x, y); return {q, x - q * y}; } // 四捨五入を求める. template T round(T x, U y){ T q, r; tie (q, r) = divmod(x, y); return (r >= div_ceil(y, 2)) ? q + 1 : q; } // 指数に関する関数 // x の y 乗を求める. ll intpow(ll x, ll y){ ll a = 1; while (y){ if (y & 1) { a *= x; } x *= x; y >>= 1; } return a; } // x の y 乗を z で割った余りを求める. ll modpow(ll x, ll y, ll z){ ll a = 1; while (y){ if (y & 1) { (a *= x) %= z; } (x *= x) %= z; y >>= 1; } return a; } // x の y 乗を z で割った余りを求める. template T modpow(T x, U y, T z) { T a = 1; while (y) { if (y & 1) { (a *= x) %= z; } (x *= x) %= z; y >>= 1; } return a; } // vector の要素の総和を求める. ll sum(vector &X){ ll y = 0; for (auto &&x: X) { y+=x; } return y; } // vector の要素の総和を求める. template T sum(vector &X){ T y = T(0); for (auto &&x: X) { y += x; } return y; } // a x + b y = gcd(a, b) を満たす整数の組 (a, b) に対して, (x, y, gcd(a, b)) を求める. tuple Extended_Euclid(ll a, ll b) { ll s = 1, t = 0, u = 0, v = 1; while (b) { ll q; tie(q, a, b) = make_tuple(div_floor(a, b), b, safe_mod(a, b)); tie(s, t) = make_pair(t, s - q * t); tie(u, v) = make_pair(v, u - q * v); } return make_tuple(s, u, a); } // floor(sqrt(N)) を求める (N < 0 のときは, 0 とする). ll isqrt(const ll &N) { if (N <= 0) { return 0; } ll x = sqrt(N); while ((x + 1) * (x + 1) <= N) { x++; } while (x * x > N) { x--; } return x; } // floor(sqrt(N)) を求める (N < 0 のときは, 0 とする). ll floor_sqrt(const ll &N) { return isqrt(N); } // ceil(sqrt(N)) を求める (N < 0 のときは, 0 とする). ll ceil_sqrt(const ll &N) { ll x = isqrt(N); return x * x == N ? x : x + 1; } #line 62 "/home/user/competitive_programming/library_for_cpp/template/template.hpp" // inout #line 1 "/home/user/competitive_programming/library_for_cpp/template/inout.hpp" // 入出力 template void input(T&... a){ (cin >> ... >> a); } void print(){ cout << "\n"; } template void print(const T& a, const Ts&... b){ cout << a; (cout << ... << (cout << " ", b)); cout << "\n"; } template istream &operator>>(istream &is, pair &P){ is >> P.first >> P.second; return is; } template ostream &operator<<(ostream &os, const pair &P){ os << P.first << " " << P.second; return os; } template vector vector_input(int N, int index){ vector X(N+index); for (int i=index; i> X[i]; return X; } template istream &operator>>(istream &is, vector &X){ for (auto &x: X) { is >> x; } return is; } template ostream &operator<<(ostream &os, const vector &X){ int s = (int)X.size(); for (int i = 0; i < s; i++) { os << (i ? " " : "") << X[i]; } return os; } template ostream &operator<<(ostream &os, const unordered_set &S){ int i = 0; for (T a: S) {os << (i ? " ": "") << a; i++;} return os; } template ostream &operator<<(ostream &os, const set &S){ int i = 0; for (T a: S) { os << (i ? " ": "") << a; i++; } return os; } template ostream &operator<<(ostream &os, const unordered_multiset &S){ int i = 0; for (T a: S) { os << (i ? " ": "") << a; i++; } return os; } template ostream &operator<<(ostream &os, const multiset &S){ int i = 0; for (T a: S) { os << (i ? " ": "") << a; i++; } return os; } #line 65 "/home/user/competitive_programming/library_for_cpp/template/template.hpp" // macro #line 2 "/home/user/competitive_programming/library_for_cpp/template/macro.hpp" // マクロの定義 #define all(x) x.begin(), x.end() #define len(x) ll(x.size()) #define elif else if #define unless(cond) if (!(cond)) #define until(cond) while (!(cond)) #define loop while (true) // オーバーロードマクロ #define overload2(_1, _2, name, ...) name #define overload3(_1, _2, _3, name, ...) name #define overload4(_1, _2, _3, _4, name, ...) name #define overload5(_1, _2, _3, _4, _5, name, ...) name // 繰り返し系 #define rep1(n) for (ll i = 0; i < n; i++) #define rep2(i, n) for (ll i = 0; i < n; i++) #define rep3(i, a, b) for (ll i = a; i < b; i++) #define rep4(i, a, b, c) for (ll i = a; i < b; i += c) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define foreach1(x, a) for (auto &&x: a) #define foreach2(x, y, a) for (auto &&[x, y]: a) #define foreach3(x, y, z, a) for (auto &&[x, y, z]: a) #define foreach4(x, y, z, w, a) for (auto &&[x, y, z, w]: a) #define foreach(...) overload5(__VA_ARGS__, foreach4, foreach3, foreach2, foreach1)(__VA_ARGS__) #line 68 "/home/user/competitive_programming/library_for_cpp/template/template.hpp" // bitop #line 2 "/home/user/competitive_programming/library_for_cpp/template/bitop.hpp" // 非負整数 x の bit legnth を求める. ll bit_length(ll x) { if (x == 0) { return 0; } return (sizeof(long) * CHAR_BIT) - __builtin_clzll(x); } // 非負整数 x の popcount を求める. ll popcount(ll x) { return __builtin_popcountll(x); } // 正の整数 x に対して, floor(log2(x)) を求める. ll floor_log2(ll x) { return bit_length(x) - 1; } // 正の整数 x に対して, ceil(log2(x)) を求める. ll ceil_log2(ll x) { return bit_length(x - 1); } // x の第 k ビットを取得する int get_bit(ll x, int k) { return (x >> k) & 1; } // x のビット列を取得する. // k はビット列の長さとする. vector get_bits(ll x, int k) { vector bits(k); rep(i, k) { bits[i] = x & 1; x >>= 1; } return bits; } // x のビット列を取得する. vector get_bits(ll x) { return get_bits(x, bit_length(x)); } #line 4 "/home/user/competitive_programming/library_for_cpp/Algebra/modint.hpp" template class modint { public: static constexpr int _mod = M; uint64_t x; public: static int mod() { return _mod; } static modint raw(int v) { modint a; a.x = v; return a; } // 初期化 constexpr modint(): x(0) {} constexpr modint(int64_t a) { int64_t w = (int64_t)(a) % mod(); if (w < 0) { w += mod(); } x = w; } // マイナス元 modint operator-() const { return modint(-x); } // 加法 modint& operator+=(const modint &b){ if ((x += b.x) >= mod()) x -= mod(); return *this; } friend modint operator+(const modint &x, const modint &y) { return modint(x) += y; } // 減法 modint& operator-=(const modint &b){ if ((x += mod() - b.x) >= mod()) x -= mod(); return *this; } friend modint operator-(const modint &x, const modint &y) { return modint(x) -= y; } // 乗法 modint& operator*=(const modint &b){ (x *= b.x) %= mod(); return *this; } friend modint operator*(const modint &x, const modint &y) { return modint(x) *= y; } friend modint operator*(const int &x, const modint &y) { return modint(x) *= y; } friend modint operator*(const ll &x, const modint &y) { return modint(x) *= y; } // 除法 modint& operator/=(const modint &b){ return (*this) *= b.inverse(); } friend modint operator/(const modint &x, const modint &y) { return modint(x) /= y; } modint inverse() const { int64_t s = 1, t = 0; int64_t a = x, b = mod(); while (b > 0) { int64_t q = a / b; a -= q * b; swap(a, b); s -= q * t; swap(s, t); } assert (a == 1); return modint(s); } // 比較 friend bool operator==(const modint &a, const modint &b) { return (a.x == b.x); } friend bool operator==(const modint &a, const int &b) { return a.x == safe_mod(b, mod()); } friend bool operator!=(const modint &a, const modint &b) { return (a.x != b.x); } // 入力 friend istream &operator>>(istream &is, modint &a) { is >> a.x; a.x = (a.x % mod() + mod()) % mod(); return is; } // 出力 friend ostream &operator<<(ostream &os, const modint &a) { return os << a.x; } bool is_zero() const { return x == 0; } bool is_member(ll a) const { return x == (a % mod() + mod()) % mod(); } }; template modint pow(modint x, long long n) { if (n < 0) { return pow(x, -n).inverse(); } auto res = modint(1); for (; n; n >>= 1) { if (n & 1) { res *= x; } x *= x; } return res; } #line 2 "program.cpp" template struct Point_2D { R x, y; Point_2D() = default; Point_2D(R _x, R _y): x(_x), y(_y) {}; inline Point_2D& operator-=(const Point_2D &P) { x -= P.x; y -= P.y; return *this; } inline Point_2D operator-(const Point_2D &P) { return Point_2D(*this) -= P; } friend Point_2D operator-(const Point_2D &P, const Point_2D &Q) { return Point_2D(P) -= Q; } }; template struct Point_3D { R x, y, z; Point_3D() = default; Point_3D(R _x, R _y, R _z): x(_x), y(_y), z(_z) {}; inline Point_3D& operator-=(const Point_3D &P) { x -= P.x; y -= P.y; z -= P.z; return *this; } friend istream& operator>>(istream &is, Point_3D &point) { R a, b, c; is >> a >> b >> c; point = Point_3D(a, b, c); return is; } inline Point_3D operator-(const Point_3D &P) { return Point_3D(*this) -= P; } friend Point_3D operator-(const Point_3D &P, const Point_3D &Q) { return Point_3D(P) -= Q; } }; using mint = modint<998244353>; template Point_2D calculate_shadow(const Point_3D &L, const Point_3D &P) { auto Q = P - Point_3D(L.x, L.y, 0); mint rx = mint(L.z * Q.x) / mint(L.z - Q.z), ry = mint(L.z * Q.y) / mint(L.z - Q.z); return { rx + L.x, ry + L.y }; } template R triagnel_area(const Point_2D &A, const Point_2D &B, const Point_2D &C) { Point_2D u = B - A, v = C - A; return (u.x * v.y - u.y * v.x) / 2; } template R det_3D(const Point_3D &O, const Point_3D &A, const Point_3D &B, const Point_3D &C) { Point_3D a = A - O, b = B - O, c = C - O; R plus = a.x * b.y * c.z + a.y * b.z * c.x + a.z * b.x * c.y; R minus = a.x * b.z * c.y + a.z * b.y * c.x + a.y * b.x * c.z; return plus - minus; } Point_3D point_input() { ll x, y, z; scanf("%lld%lld%lld", &x, &y, &z); return Point_3D(x, y, z); } mint solve() { Point_3D P1 = point_input(); Point_3D P2 = point_input(); Point_3D P3 = point_input(); Point_3D L = point_input(); if (det_3D(L, P1, P2, P3) >= 0) { swap(P2, P3); } Point_2D Q1 = calculate_shadow(L, P1); Point_2D Q2 = calculate_shadow(L, P2); Point_2D Q3 = calculate_shadow(L, P3); return triagnel_area(Q1, Q2, Q3); } int main() { int T; cin >> T; for (int t = 1; t <= T; t++) { cout << solve() << endl; } }