#include #include #include #include #include #include #include using namespace std; const int MOD = 1000000007; int N; struct Seg { // Directions: U / R / D / L int i = -1, r, c, p, d, t = 0; long long get_time_val() { return N * ((long long)t - r - c) + i; } bool operator<(const Seg& b) const { return make_pair(r, c) < make_pair(b.r, b.c); } }; struct BIT { int N; vector V; BIT() {} BIT(int _N): N(_N) { init(_N); } void init(int _N) { N = _N; V.resize(N + 1); } void clear() { fill(V.begin(), V.end(), 0); } void update(int i, int v) { for (i++; i <= N; i += (i & -i)) { V[i] += v; } } int query(int i) { int v = 0; i = min(i, N - 1); for (i++; i > 0; i -= (i & -i)) { v += V[i]; } return v; } }; struct SegTree { int N, sz; vector> keys; vector B; SegTree() {} SegTree(int _N) { init(_N); } void init(int _N) { N = _N; for (sz = 1; sz < N; sz <<= 1) ; keys.resize(sz << 1); B.resize(sz << 1); } void init_keys() { for (int i = sz; i < sz + N; i++) { auto &K = keys[i]; sort(K.begin(), K.end()); B[i].init(K.size()); } for (int i = sz - 1; i >= 1; i--) { auto &K = keys[i]; auto &c1 = keys[i << 1], &c2 = keys[(i << 1) + 1]; int a = 0, b = 0; while (a < c1.size() || b < c2.size()) { if (b == c2.size() || (a < c1.size() && c1[a] < c2[b])) { K.push_back(c1[a++]); } else { K.push_back(c2[b++]); } } B[i].init(K.size()); } } int query_larger(int a, int b, long long 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 0; } r2 = sz - 1; } if (a <= r1 && r2 <= b) { auto &K = keys[i]; v = lower_bound(K.begin(), K.end(), v) - K.begin(); return B[i].query(K.size() - 1) - B[i].query(v - 1); } int m = (r1 + r2) >> 1, c = i << 1; int res = 0; if (a <= m) { res += query_larger(a, b, v, c, r1, m); } if (b > m) { res += query_larger(a, b, v, c + 1, m + 1, r2); } return res; } void update_one(int i, long long v, int d) { i += sz; while (i >= 1) { auto &K = keys[i]; B[i].update(lower_bound(K.begin(), K.end(), v) - K.begin(), d); i >>= 1; } } }; vector SS; Seg trim_seg(Seg s, int a, int b, bool hor) { if (s.d == 1 || s.d == 2) { // Forward segment. int& sv1 = hor ? s.c : s.r; // First value. int sv2 = sv1 + s.p - 1; // Last value. int t1 = max(0, a - sv1); // Truncation at start. int t2 = max(0, sv2 - b); // Truncation at end. sv1 += t1, s.t += t1; s.p -= t1 + t2; } else { // Backward segment. int& sv2 = hor ? s.c : s.r; // Last value. int sv1 = sv2 - (s.p - 1); // First value. int t1 = max(0, a - sv1); // Truncation at start. int t2 = max(0, sv2 - b); // Truncation at end. sv2 -= t2, s.t += t2; s.p -= t1 + t2; } return s; } vector merge_opp_segs(Seg s1, Seg s2, bool hor) { int nc = (hor ? s2.c - s1.c : s2.r - s1.r) + 1; int t1 = s1.t; // Time for s1 to reach start. int t2 = s2.t + nc - 1 - (s2.i < s1.i ? 1 : 0); // Time for s2 to reach start. int m = (hor ? s1.c : s1.r) + (t2 - t1 + 2) / 2 - 1; // Last value painted over by s2. vector S; S.push_back(trim_seg(s2, -1e9 - 1, m, hor)); S.push_back(trim_seg(s1, m + 1, 2e9 + 1, hor)); return S; } void process_linear_segs(vector V, bool hor) { // Collect and sort forward / backward segments. int d1, d2; if (hor) { d1 = 1; d2 = 3; } else { d1 = 2; d2 = 0; } vector> P1, P2; for (auto s : V) { if (s.d == d1) { P1.emplace_back(s.r + s.c, -s.i, s); } else { P2.emplace_back(-(s.r + s.c), -s.i, s); } } sort(P1.begin(), P1.end()); sort(P2.begin(), P2.end()); // Reduce forward / backward segments independently. vector S1, S2; int last = -1e9 - 1; for (auto p : P1) { Seg s = trim_seg(get<2>(p), last + 1, 2e9 + 1, hor); // Trim to after last. if (s.p > 0) { // Include if not obsolete. S1.push_back(s); } last = max(last, (hor ? s.c : s.r) + (s.p - 1)); } last = 2e9 + 1; for (auto p : P2) { Seg s = trim_seg(get<2>(p), -1e9 - 1, last - 1, hor); // Trim to before last. if (s.p > 0) { // Include if not obsolete. S2.push_back(s); } last = min(last, (hor ? s.c : s.r) - (s.p - 1)); } // Merge forward / backward segments. vector> E; for (int i = 0; i < S1.size(); i++) { Seg s = S1[i]; int sv = hor ? s.c : s.r; E.emplace_back(sv, 1, i); E.emplace_back(sv + s.p, 0, i); } for (int i = 0; i < S2.size(); i++) { Seg s = S2[i]; int sv = hor ? s.c : s.r; E.emplace_back(sv - (s.p - 1), 3, i); E.emplace_back(sv + 1, 2, i); } sort(E.begin(), E.end()); vector inds{-1, -1}; for (int i = 0; i < E.size(); i++) { int v = get<0>(E[i]), e = get<1>(E[i]); // Update set of ongoing segments. int j = e / 2; if (e % 2) { inds[j] = get<2>(E[i]); } else { inds[j] = -1; } // Process ongoing segments? if (i + 1 < E.size() && v < get<0>(E[i + 1])) { vector S; if (inds[0] >= 0 && inds[1] >= 0) { S = merge_opp_segs(S1[inds[0]], S2[inds[1]], hor); } else if (inds[0] >= 0) { S.push_back(S1[inds[0]]); } else if (inds[1] >= 0) { S.push_back(S2[inds[1]]); } for (auto s : S) { Seg s2 = trim_seg(s, v, get<0>(E[i + 1]) - 1, hor); if (s2.p > 0) { SS.push_back(s2); } } } } } int solve() { SS.clear(); map> rowS, colS; // Input. cin >> N; for (int i = 0; i < N; i++) { Seg s; s.i = i + 1; char d; cin >> s.r >> s.c >> s.p >> d; s.d = d == 'N' ? 0 : d == 'E' ? 1 : d == 'S' ? 2 : 3; if (s.d % 2) { rowS[s.r].push_back(s); } else { colS[s.c].push_back(s); } } // Reduce each relevant row / column to disjoint segments for (auto p : rowS) { process_linear_segs(p.second, true); } for (auto p : colS) { process_linear_segs(p.second, false); } // Compute base answer. int ans = 0; for (auto s : SS) { ans = (ans + (long long)s.i * s.p) % MOD; } // Consider 4 different rotations of the grid. for (int r = 0; r < 4; r++) { // Rotate everything 90 degrees clockwise. for (int i = 0; i < SS.size(); i++) { Seg &s = SS[i]; int r = s.r, c = s.c, d = s.d; s.r = c; s.c = -r; s.d = (d + 1) % 4; } // Consider 2 different vertical flips of the grid. for (int _ : {0, 1}) { // Flip everything vertically. for (int i = 0; i < SS.size(); i++) { Seg &s = SS[i]; s.r = -s.r; if (s.d % 2 == 0) { s.d = 2 - s.d; } } // Assemble list of line sweep events and distinct D segment columns. vector> E; vector cc; for (auto s : SS) { if (s.d == 1) { // R E.emplace_back(s.r, 1, s); } else if (s.d == 2) { // D E.emplace_back(s.r, 0, s); E.emplace_back(s.r + s.p - 1, 2, s); cc.push_back(s.c); } } sort(E.begin(), E.end()); sort(cc.begin(), cc.end()); cc.resize(unique(cc.begin(), cc.end()) - cc.begin()); // Initialize 2D segment tree. SegTree ST(cc.size()); for (auto s : SS) { if (s.d == 2) { // D ST.keys[ST.sz + (lower_bound(cc.begin(), cc.end(), s.c) - cc.begin())] .push_back(s.get_time_val()); } } ST.init_keys(); // Line sweep to subtract R segments covered by D ones. for (auto p : E) { int e = get<1>(p); Seg s = get<2>(p); if (e == 1) { int a = lower_bound(cc.begin(), cc.end(), s.c) - cc.begin(); int b = lower_bound(cc.begin(), cc.end(), s.c + s.p) - cc.begin() - 1; long long v = s.get_time_val(); ans = (ans + MOD - (long long)s.i * ST.query_larger(a, b, v) % MOD) % MOD; } else { ST.update_one( lower_bound(cc.begin(), cc.end(), s.c) - cc.begin(), s.get_time_val(), e == 0 ? 1 : -1 ); } } } } return ans; } int main() { int T; cin >> T; for (int t = 1; t <= T; t++) { cout << "Case #" << t << ": " << solve() << endl; } return 0; }