#include #include #include #include #include #include using namespace std; const int LIM = 300003; using pii = pair; #define x first #define y second struct Compressor { int N; vector V; Compressor() {} Compressor(vector _V) { V = _V; comp(); } void insert(pii v) { V.push_back(v); } void comp() { sort(V.begin(), V.end()); N = unique(V.begin(), V.end()) - V.begin(); V.resize(N); } int get(pii v) { return lower_bound(V.begin(), V.end(), v) - V.begin(); } }; const int TLIM = 2100000; const int ZERO_VAL = 0; const int ZERO_LAZY = 0; struct MaxRangeSegTree { static void update_value(int &a, int v, int r1, int r2) { a += v; } static void update_lazy(int &a, int v, int r1, int r2) { a += v; } static int join_values(int v1, int v2) { return max(v1, v2); } int N, sz; int tree[TLIM]; int lazy[TLIM]; MaxRangeSegTree() {} MaxRangeSegTree(int _N) { init(_N); } void init(int _N) { N = _N; for (sz = 1; sz < N; sz <<= 1) ; clear(); } void clear() { for (int i = 0; i < (sz << 1); i++) { tree[i] = ZERO_VAL; lazy[i] = ZERO_LAZY; } } void propagate(int i, int r1, int r2) { int v = lazy[i]; lazy[i] = ZERO_LAZY; update_value(tree[i], v, r1, r2); if (i < sz) { int m = (r1 + r2) >> 1, c1 = i << 1, c2 = c1 + 1; update_lazy(lazy[c1], v, r1, m); update_lazy(lazy[c2], v, m + 1, r2); } } void comp(int i) { int c1 = i << 1, c2 = c1 + 1; tree[i] = join_values(tree[c1], tree[c2]); } int query(int a, int b, int i = 1, int r1 = 0, int r2 = -1) { if (r2 < 0) { a = max(a, 0); b = min(b, sz - 1); if (a > b) { return ZERO_VAL; } r2 = sz - 1; } propagate(i, r1, r2); if (a <= r1 && r2 <= b) { return tree[i]; } int m = (r1 + r2) >> 1, c = i << 1; int res = ZERO_VAL; if (a <= m) { res = join_values(res, query(a, b, c, r1, m)); } if (b > m) { res = join_values(res, query(a, b, c + 1, m + 1, r2)); } return res; } void update(int a, int b, int v, int i = 1, int r1 = 0, int r2 = -1) { if (r2 < 0) { a = max(a, 0); b = min(b, sz - 1); if (a > b) { return; } r2 = sz - 1; } if (r2 < 0) { r2 = sz - 1; } propagate(i, r1, r2); if (a <= r1 && r2 <= b) { update_lazy(lazy[i], v, r1, r2); propagate(i, r1, r2); return; } int m = (r1 + r2) >> 1, c = i << 1; if (a <= m) { update(a, b, v, c, r1, m); } if (b > m) { update(a, b, v, c + 1, m + 1, r2); } propagate(c, r1, m); propagate(c + 1, m + 1, r2); comp(i); } }; const pii NONE{-1, -1}; struct MaxElemSegTree { pii join_values(pii v1, pii v2) { return max(v1, v2); } int N, sz; vector tree; MaxElemSegTree() {} MaxElemSegTree(int _N) { init(_N); } void init(int _N) { N = _N; for (sz = 1; sz < N; sz <<= 1) ; clear(); } void clear() { tree.clear(); tree.resize(sz << 1, NONE); } void comp(int i) { int c1 = i << 1, c2 = c1 + 1; tree[i] = join_values(tree[c1], tree[c2]); } pii query(int a, int b, int i = 1, int r1 = 0, int r2 = -1) { if (r2 < 0) { a = max(a, 0); b = min(b, sz - 1); if (a > b) { return NONE; } r2 = sz - 1; } if (a <= r1 && r2 <= b) { return tree[i]; } int m = (r1 + r2) >> 1, c = i << 1; pii res = NONE; if (a <= m) { res = join_values(res, query(a, b, c, r1, m)); } if (b > m) { res = join_values(res, query(a, b, c + 1, m + 1, r2)); } return res; } void update_one(int i, pii p) { i += sz; tree[i] = p; while (i > 1) { i >>= 1; comp(i); } } }; struct NestedSegTree { int N, sz; bool has_init_keys; vector keys[TLIM]; MaxElemSegTree T[TLIM]; NestedSegTree() {} NestedSegTree(int _N) { init(_N); } void init(int _N) { N = _N; for (sz = 1; sz < N; sz <<= 1) ; has_init_keys = false; } void init_keys() { for (int i = sz; i < sz + N; i++) { auto &k = keys[i]; sort(k.begin(), k.end()); k.resize(unique(k.begin(), k.end()) - k.begin()); T[i].init(k.size()); } for (int i = sz - 1; i >= 1; i--) { auto &k = keys[i], &c1 = keys[i << 1], &c2 = keys[(i << 1) + 1]; int a = 0, b = 0; while (a < c1.size() || b < c2.size()) { if (a < c1.size() && b < c2.size() && c1[a] == c2[b]) { k.push_back(c1[a++]); b++; } else if (b == c2.size() || (a < c1.size() && c1[a] < c2[b])) { k.push_back(c1[a++]); } else { k.push_back(c2[b++]); } } T[i].init(k.size()); } has_init_keys = true; } pii query_max_up_to_k(int a, int b, int k, int i = 1, int r1 = 0, int r2 = -1) { if (r2 < 0) { a = max(a, 0); b = min(b, sz - 1); if (a > b) { return NONE; } r2 = sz - 1; } if (a <= r1 && r2 <= b) { k = lower_bound(keys[i].begin(), keys[i].end(), k + 1) - keys[i].begin() - 1; return T[i].query(0, k); } int m = (r1 + r2) >> 1, c = i << 1; pii res = NONE; if (a <= m) { res = max(res, query_max_up_to_k(a, b, k, c, r1, m)); } if (b > m) { res = max(res, query_max_up_to_k(a, b, k, c + 1, m + 1, r2)); } return res; } void update_one(int i, int k, pii p) { i += sz; if (!has_init_keys) { keys[i].push_back(k); return; } while (i >= 1) { T[i].update_one( lower_bound(keys[i].begin(), keys[i].end(), k) - keys[i].begin(), p ); i >>= 1; } } }; int N; pair A[LIM], B[LIM]; int Axx[LIM], Axy[LIM]; int lowerX[3 * LIM], lowerY[3 * LIM]; bool visit[LIM]; NestedSegTree STX, STY; void update_A_rect(int i, bool ins) { STX.update_one(A[i].x.x, Axy[i], ins ? make_pair(A[i].y.y, i) : NONE); STX.update_one(A[i].y.x, Axy[i], ins ? make_pair(A[i].y.y, i) : NONE); STY.update_one(A[i].x.y, Axx[i], ins ? make_pair(A[i].y.x, i) : NONE); STY.update_one(A[i].y.y, Axx[i], ins ? make_pair(A[i].y.x, i) : NONE); } int get_A_rect_for_B_rect(int i) { pii p = STX.query_max_up_to_k(B[i].x.x, B[i].y.x, B[i].y.y); if (p.x >= B[i].x.y) { return p.y; } p = STY.query_max_up_to_k(B[i].x.y, B[i].y.y, B[i].y.x); if (p.x >= B[i].x.x) { return p.y; } return -1; } bool rec(int i) { visit[i] = true; for (;;) { int j = get_A_rect_for_B_rect(i); if (j < 0) { break; } if (visit[j]) { return true; } if (rec(j)) { return true; } } update_A_rect(i, 0); return false; } bool solve() { Compressor cx, cy; // Input, and compute flipped rectangles. cin >> N; for (int i = 0; i < N; i++) { char c; cin >> A[i].x.x >> A[i].x.y >> A[i].y.x >> A[i].y.y >> c; B[i] = A[i]; switch (c) { case 'U': B[i].x.y += A[i].y.y; break; case 'D': B[i].x.y -= A[i].y.y; break; case 'L': B[i].x.x -= A[i].y.x; break; case 'R': B[i].x.x += A[i].y.x; break; } A[i].y.x += A[i].x.x; A[i].y.y += A[i].x.y; B[i].y.x += B[i].x.x; B[i].y.y += B[i].x.y; cx.insert({A[i].x.x, i}); cx.insert({A[i].y.x, i}), cx.insert({B[i].x.x, i}); cx.insert({B[i].y.x, i}); cy.insert({A[i].x.y, i}); cy.insert({A[i].y.y, i}); cy.insert({B[i].x.y, i}); cy.insert({B[i].y.y, i}); } // Compress coordinates. cx.comp(), cy.comp(); auto V = cx.V; for (int i = 0; i < V.size(); i++) { lowerX[i] = (i == 0 || V[i - 1].x != V[i].x) ? i : lowerX[i - 1]; } V = cy.V; for (int i = 0; i < V.size(); i++) { lowerY[i] = (i == 0 || V[i - 1].x != V[i].x) ? i : lowerY[i - 1]; } for (int i = 0; i < N; i++) { A[i].x.x = cx.get({A[i].x.x, i}); A[i].x.y = cy.get({A[i].x.y, i}), A[i].y.x = cx.get({A[i].y.x, i}); A[i].y.y = cy.get({A[i].y.y, i}); B[i].x.x = cx.get({B[i].x.x, i}); B[i].x.y = cy.get({B[i].x.y, i}), B[i].y.x = cx.get({B[i].y.x, i}); B[i].y.y = cy.get({B[i].y.y, i}); // Remember exact (unique) lower coordinates. Axx[i] = A[i].x.x, Axy[i] = A[i].x.y; // Round coordinates up to value boundaries (with exclusive upper // coordinates). A[i].x.x = lowerX[A[i].x.x]; B[i].x.x = lowerX[B[i].x.x]; A[i].x.y = lowerY[A[i].x.y]; B[i].x.y = lowerY[B[i].x.y]; A[i].y.x = lowerX[A[i].y.x] - 1; B[i].y.x = lowerX[B[i].y.x] - 1; A[i].y.y = lowerY[A[i].y.y] - 1; B[i].y.y = lowerY[B[i].y.y] - 1; } // Check for any overlap between final tables via line sweep. vector> E; for (int i = 0; i < N; i++) { E.emplace_back(B[i].x.y, 1, B[i].x.x, B[i].y.x); E.emplace_back(B[i].y.y + 1, -1, B[i].x.x, B[i].y.x); } sort(E.begin(), E.end()); MaxRangeSegTree ST(cx.V.size()); for (auto e : E) { ST.update(get<2>(e), get<3>(e), get<1>(e)); if (ST.query(0, cx.V.size() - 1) > 1) { return false; } } // Initialize segment trees of initial tables, over x and y coordinates. STX = NestedSegTree(cx.V.size()); STY = NestedSegTree(cy.V.size()); for (int j : {0, 1}) { if (j) { // Initialize keys second time around. STX.init_keys(); STY.init_keys(); } for (int i = 0; i < N; i++) { // Set up keys first time around, then perform actual updates. update_A_rect(i, 1); } } // Search for cycles via DFS. memset(visit, 0, sizeof visit); for (int i = 0; i < N; i++) { if (!visit[i]) { if (rec(i)) { return false; // Cycle found. } } } return true; } int main() { int T; cin >> T; for (int t = 1; t <= T; t++) { cout << "Case #" << t << ": " << (solve() ? "YES" : "NO") << endl; } return 0; }