#include using namespace std; #define rep(i, n) for (int i = 0; i < n; i++) #define rep2(i, x, n) for (int i = x; i <= n; i++) #define rep3(i, x, n) for (int i = x; i >= n; i--) #define each(e, v) for (auto &e : v) #define pb push_back #define eb emplace_back #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define sz(x) (int)x.size() using ll = long long; using pii = pair; using pil = pair; using pli = pair; using pll = pair; template bool chmax(T &x, const T &y) { return (x < y) ? (x = y, true) : false; } template bool chmin(T &x, const T &y) { return (x > y) ? (x = y, true) : false; } template int flg(T x, int i) { return (x >> i) & 1; } template void print(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' '); if (v.empty()) cout << '\n'; } template void printn(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << '\n'; } template int lb(const vector &v, T x) { return lower_bound(begin(v), end(v), x) - begin(v); } template int ub(const vector &v, T x) { return upper_bound(begin(v), end(v), x) - begin(v); } template void rearrange(vector &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } template vector id_sort(const vector &v, bool greater = false) { int n = v.size(); vector ret(n); iota(begin(ret), end(ret), 0); sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; }); return ret; } template pair operator+(const pair &p, const pair &q) { return make_pair(p.first + q.first, p.second + q.second); } template pair operator-(const pair &p, const pair &q) { return make_pair(p.first - q.first, p.second - q.second); } template istream &operator>>(istream &is, pair &p) { S a; T b; is >> a >> b; p = make_pair(a, b); return is; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } struct io_setup { io_setup() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); } } io_setup; const int inf = (1 << 30) - 1; const ll INF = (1LL << 60) - 1; const int MOD = 1000000007; // const int MOD = 998244353; template struct Segment_Tree { using F = function; int n; vector seg; const F f; const Monoid e1; // f(f(a,b),c) = f(a,f(b,c)), f(e1,a) = f(a,e1) = a Segment_Tree(const vector &v, const F &f, const Monoid &e1) : f(f), e1(e1) { int m = v.size(); n = 1; while (n < m) n <<= 1; seg.assign(2 * n, e1); copy(begin(v), end(v), seg.begin() + n); for (int i = n - 1; i > 0; i--) seg[i] = f(seg[2 * i], seg[2 * i + 1]); } Segment_Tree(int m, const Monoid &x, const F &f, const Monoid &e1) : f(f), e1(e1) { n = 1; while (n < m) n <<= 1; seg.assign(2 * n, e1); vector v(m, x); copy(begin(v), end(v), begin(seg) + n); for (int i = n - 1; i > 0; i--) seg[i] = f(seg[2 * i], seg[2 * i + 1]); } void change(int i, const Monoid &x, bool update = true) { if (update) { seg[i + n] = x; } else { seg[i + n] = f(seg[i + n], x); } i += n; while (i >>= 1) seg[i] = f(seg[2 * i], seg[2 * i + 1]); } Monoid query(int l, int r) const { Monoid L = e1, R = e1; l += n, r += n; while (l < r) { if (l & 1) L = f(L, seg[l++]); if (r & 1) R = f(seg[--r], R); l >>= 1, r >>= 1; } return f(L, R); } Monoid operator[](int i) const { return seg[n + i]; } template int find_subtree(int i, const C &check, const Monoid &x, Monoid &M, int type) const { while (i < n) { Monoid nxt = type ? f(seg[2 * i + type], M) : f(M, seg[2 * i + type]); if (check(nxt, x)) { i = 2 * i + type; } else { M = nxt; i = 2 * i + (type ^ 1); } } return i - n; } template int find_first(int l, const C &check, const Monoid &x) const { // check((区間 [l,r] での演算結果), x) を満たす最小の r Monoid L = e1; int a = l + n, b = n + n; while (a < b) { if (a & 1) { Monoid nxt = f(L, seg[a]); if (check(nxt, x)) return find_subtree(a, check, x, L, 0); L = nxt, a++; } a >>= 1, b >>= 1; } return n; } template int find_last(int r, const C &check, const Monoid &x) const { // check((区間 [l,r) での演算結果), x) を満たす最大の l Monoid R = e1; int a = n, b = r + n; while (a < b) { if ((b & 1) || a == 1) { Monoid nxt = f(seg[--b], R); if (check(nxt, x)) return find_subtree(b, check, x, R, 1); R = nxt; } a >>= 1, b >>= 1; } return -1; } }; template struct Matrix { vector> A; Matrix(int m, int n) : A(m, vector(n, 0)) {} int height() const { return A.size(); } int width() const { return A.front().size(); } inline const vector &operator[](int k) const { return A[k]; } inline vector &operator[](int k) { return A[k]; } static Matrix I(int l) { Matrix ret(l, l); for (int i = 0; i < l; i++) ret[i][i] = 1; return ret; } Matrix &operator*=(const Matrix &B) { int m = height(), n = width(), p = B.width(); assert(n == B.height()); Matrix ret(m, p); for (int i = 0; i < m; i++) { for (int k = 0; k < n; k++) { for (int j = 0; j < p; j++) ret[i][j] += A[i][k] * B[k][j]; } } swap(A, ret.A); return *this; } Matrix operator*(const Matrix &B) const { return Matrix(*this) *= B; } Matrix pow(long long k) const { int m = height(), n = width(); assert(m == n); Matrix now = *this, ret = I(n); for (; k > 0; k >>= 1, now *= now) { if (k & 1) ret *= now; } return ret; } bool eq(const T &a, const T &b) const { return a == b; // return abs(a-b) <= EPS; } pair row_reduction(vector &b) { // 行基本変形を用いて簡約化を行い、(rank, det) の組を返す int m = height(), n = width(), check = 0, rank = 0; T det = 1; assert(b.size() == m); for (int j = 0; j < n; j++) { int pivot = check; for (int i = check; i < m; i++) { if (A[i][j] != 0) pivot = i; // if(abs(A[i][j]) > abs(A[pivot][j])) pivot = i; // T が小数の場合はこちら } if (check != pivot) det *= T(-1); swap(A[check], A[pivot]), swap(b[check], b[pivot]); if (eq(A[check][j], T(0))) { det = T(0); continue; } rank++; det *= A[check][j]; T r = T(1) / A[check][j]; for (int k = j + 1; k < n; k++) A[check][k] *= r; b[check] *= r; A[check][j] = T(1); for (int i = 0; i < m; i++) { if (i == check) continue; if (!eq(A[i][j], 0)) { for (int k = j + 1; k < n; k++) A[i][k] -= A[i][j] * A[check][k]; b[i] -= A[i][j] * b[check]; } A[i][j] = T(0); } if (++check == m) break; } return make_pair(rank, det); } pair row_reduction() { vector b(height(), T(0)); return row_reduction(b); } Matrix inverse() { // 行基本変形によって正方行列の逆行列を求める if (height() != width()) return Matrix(0, 0); int n = height(); Matrix ret = I(n); for (int j = 0; j < n; j++) { int pivot = j; for (int i = j; i < n; i++) { if (A[i][j] != 0) pivot = i; // if(abs(A[i][j]) > abs(A[pivot][j])) pivot = i; // T が小数の場合はこちら } swap(A[j], A[pivot]), swap(ret[j], ret[pivot]); if (eq(A[j][j], T(0))) return Matrix(0, 0); T r = T(1) / A[j][j]; for (int k = j + 1; k < n; k++) A[j][k] *= r; for (int k = 0; k < n; k++) ret[j][k] *= r; A[j][j] = T(1); for (int i = 0; i < n; i++) { if (i == j) continue; if (!eq(A[i][j], T(0))) { for (int k = j + 1; k < n; k++) A[i][k] -= A[i][j] * A[j][k]; for (int k = 0; k < n; k++) ret[i][k] -= A[i][j] * ret[j][k]; } A[i][j] = T(0); } } return ret; } vector> Gausiann_elimination(vector b) { // Ax = b の解の 1 つと解空間の基底の組を返す int m = height(), n = width(); row_reduction(b); vector> ret; vector p(m, n); vector is_zero(n, true); for (int i = 0; i < m; i++) { for (int j = 0; j < n; j++) { if (!eq(A[i][j], T(0))) { p[i] = j; break; } } if (p[i] < n) is_zero[p[i]] = false; else if (!eq(b[i], T(0))) return {}; } vector x(n, T(0)); for (int i = 0; i < m; i++) { if (p[i] < n) x[p[i]] = b[i]; } ret.push_back(x); for (int j = 0; j < n; j++) { if (!is_zero[j]) continue; x[j] = T(1); for (int i = 0; i < m; i++) { if (p[i] < n) x[p[i]] = -A[i][j]; } ret.push_back(x), x[j] = T(0); } return ret; } }; using mat = Matrix; int main() { int N; cin >> N; auto f = [](mat A, mat B) { return B * A; }; mat I = mat::I(3); vector v; double pi = acos(-1.0); rep(i, N) { double p, q, r; cin >> p >> q >> r; r *= pi / 180.0; double co = cos(r), si = sin(r); mat A(3, 3); A[0][0] = co, A[0][1] = -si, A[0][2] = p - p * co + q * si; A[1][0] = si, A[1][1] = co, A[1][2] = q - p * si - q * co; A[2][2] = 1.0; v.eb(A); } Segment_Tree seg(v, f, I); int Q; cin >> Q; while (Q--) { int L, R; cin >> L >> R; L--; double a, b; cin >> a >> b; mat A = seg.query(L, R); mat x(3, 1); x[0][0] = a, x[1][0] = b, x[2][0] = 1.0; x = A * x; cout << x[0][0] << ' ' << x[1][0] << '\n'; } }