#include #include #include using namespace std; const int kBitCount = 22; class PersistentTrie { vector roots, last, last_rec; vector> nodes; inline int get_root(int ind) { return ind == -1 ? 0 : roots[ind]; } vector get_bits(int val) { vector bits(kBitCount, 0); for (int i = 0; i < kBitCount; i++) { if (val & (1 << i)) { bits[kBitCount - i - 1] = 1; } } return bits; } public: void reset(int n) { last.assign(1, -1); last_rec.assign(1, -1); nodes.assign(2, vector(1, -1)); roots.clear(); roots.reserve(n + 1); last.reserve((n + 1) * (kBitCount + 1)); last_rec.reserve((n + 1) * (kBitCount + 1)); nodes[0].reserve((n + 1) * (kBitCount + 1)); nodes[1].reserve((n + 1) * (kBitCount + 1)); } void add(int val, int ind) { vector bits = get_bits(val); int r = roots.size(), node_id = nodes[0].size(); roots.push_back(node_id); int root_id = get_root(r - 1); nodes[0].push_back(nodes[0][root_id]); nodes[1].push_back(nodes[1][root_id]); last.push_back(ind); vector visited_nodes(1, node_id); visited_nodes.reserve(kBitCount + 1); for (int i = 0; i < kBitCount; ++i) { int next_node_id = nodes[bits[i]][node_id]; if (next_node_id == -1) { nodes[0].push_back(-1); nodes[1].push_back(-1); } else { nodes[0].push_back(nodes[0][next_node_id]); nodes[1].push_back(nodes[1][next_node_id]); } last.push_back(ind); next_node_id = (int)nodes[0].size() - 1; nodes[bits[i]][node_id] = next_node_id; node_id = next_node_id; visited_nodes.push_back(node_id); } last_rec.resize(last.size()); last_rec[visited_nodes.back()] = last[visited_nodes.back()]; for (int i = (int)visited_nodes.size() - 2; i >= 0; i--) { const int node_id = visited_nodes[i]; last_rec[node_id] = last[node_id]; for (int j = 0; j < 2; ++j) { const int child_node_id = nodes[j][node_id]; if (child_node_id == -1) { last_rec[node_id] = -1; } else { last_rec[node_id] = min(last_rec[node_id], last_rec[child_node_id]); } } } } int get_mex(int l, int r, int val) { if (!r) { return val ? 0 : 1; } int res = 0; vector bits = get_bits(val); int node_id = get_root(r); for (int i = 0; i < kBitCount; ++i) { if (node_id == -1) { break; } for (int j = 0; j < 2; ++j) { const int bit_val = bits[i] ^ j; const int child_node_id = nodes[bit_val][node_id]; if (child_node_id == -1) { node_id = child_node_id; res |= (j << (kBitCount - i - 1)); break; } if (last_rec[child_node_id] < l) { node_id = child_node_id; res |= (j << (kBitCount - i - 1)); break; } } } return res; } }; PersistentTrie trie; long long solve() { int N, x1, y1, z1, x2, y2, z2, x3, y3, z3; cin >> N >> x1 >> y1 >> z1 >> x2 >> y2 >> z2 >> x3 >> y3 >> z3; vector A(N), B(N), C(N); long long pa = 0LL, pb = 0LL, pc = 0LL; for (int i = 0; i < N; i++) { pa = (pa * x1 + y1) % z1; pb = (pb * x2 + y2) % z2; pc = (pc * x3 + y3) % z3; A[i] = min(i + 1, (int)(1 + pa)); B[i] = max(A[i], (int)(i + 1 - pb)); C[i] = min(i, (int)pc); } A.insert(A.begin(), 0); B.insert(B.begin(), 0); C.insert(C.begin(), 0); trie.reset(N); trie.add(0, 0); vector f(N + 1, 0); for (int i = 1; i <= N; ++i) { f[i] = trie.get_mex(i - B[i], i - A[i], f[C[i]]); trie.add(f[i], i); } vector lnk(1 << kBitCount, -1); long long ans = 0LL; for (int i = 1; i <= N; i++) { if (lnk[f[i]] == -1) { lnk[f[i]] = i; } ans += lnk[f[i]]; } return ans; } int main() { int T; cin >> T; for (int t = 1; t <= T; t++) { cout << "Case #" << t << ": " << solve() << endl; } return 0; }