#include using namespace std; struct Layout { int w = 0, h = 0; // total rectangle size including 1-cell border int innerW = 0, innerH = 0; // inner size int childrenH = 0; // packed children height inside inner area int sep = 0; // separator rows between children and gadgets (0/1) int gadgetW = 0, gadgetH = 0; int gadgetStartY = 0; // relative to top of rectangle vector order; // children order vector> pos; // child positions in inner coords (y,x), aligned with order }; static int pack_children_height(const vector& order, const vector& lay, int innerW) { if (order.empty()) return 0; int x = 0, y = 0, rowH = 0; for (int v : order) { int wv = lay[v].w; int hv = lay[v].h; if (x > 0 && x + wv > innerW) { y += rowH + 1; // 1-row gap between shelves x = 0; rowH = 0; } // place at (y, x) x += wv; if (x < innerW) x += 1; // 1-col gap to next rowH = max(rowH, hv); } return y + rowH; } static int pack_children_positions(const vector& order, const vector& lay, int innerW, vector>& outPos) { outPos.clear(); if (order.empty()) return 0; outPos.reserve(order.size()); int x = 0, y = 0, rowH = 0; for (int v : order) { int wv = lay[v].w; int hv = lay[v].h; if (x > 0 && x + wv > innerW) { y += rowH + 1; x = 0; rowH = 0; } outPos.push_back({y, x}); x += wv; if (x < innerW) x += 1; rowH = max(rowH, hv); } return y + rowH; } struct Builder { int N = 0, M = 0; vector A, B; vector> adj; bool isEdge[41][41]{}; bool isTree[41][41]{}; vector parent; vector> children; vector> gadgets; vector lay; int slotRows = 2; // gadget slots rows count => gadgetH = 2*slotRows-1 = 3 int gadgetHConst = 3; bool build_spanning_tree() { parent.assign(N + 1, -1); children.assign(N + 1, {}); queue q; parent[1] = 0; q.push(1); while (!q.empty()) { int u = q.front(); q.pop(); for (int v : adj[u]) { if (parent[v] == -1) { parent[v] = u; q.push(v); } } } for (int i = 2; i <= N; i++) { if (parent[i] == -1) return false; int p = parent[i]; isTree[min(i,p)][max(i,p)] = true; children[p].push_back(i); } return true; } void assign_gadgets() { gadgets.assign(N + 1, {}); vector load(N + 1, 0); for (int i = 0; i < M; i++) { int a = A[i], b = B[i]; int x = min(a,b), y = max(a,b); if (isTree[x][y]) continue; int u; if (load[a] < load[b]) u = a; else if (load[b] < load[a]) u = b; else u = min(a,b); int v = (u == a ? b : a); gadgets[u].push_back(v); load[u]++; } } void compute_gadget_dims(int u, int& gW, int& gH) { int g = (int)gadgets[u].size(); if (g == 0) { gW = 0; gH = 0; return; } int cols = (g + slotRows - 1) / slotRows; gW = 2 * cols - 1; gH = gadgetHConst; } bool dfs_size(int u, int Kmax) { for (int v : children[u]) { if (!dfs_size(v, Kmax)) return false; } Layout L; int gW, gH; compute_gadget_dims(u, gW, gH); L.gadgetW = gW; L.gadgetH = gH; // child order: sort by width desc, then height desc L.order = children[u]; sort(L.order.begin(), L.order.end(), [&](int a, int b) { if (lay[a].w != lay[b].w) return lay[a].w > lay[b].w; return lay[a].h > lay[b].h; }); int maxChildW = 0; for (int v : L.order) maxChildW = max(maxChildW, lay[v].w); int minInnerW = max(1, max(maxChildW, gW)); int bestInnerW = -1; int bestInnerH = -1; int bestChildrenH = -1; int bestSep = 0; long long bestMetric = (1LL << 60); for (int innerW = minInnerW; innerW <= Kmax - 2; innerW++) { int cH = pack_children_height(L.order, lay, innerW); int sep = (cH > 0 && gH > 0) ? 1 : 0; int innerH = cH + sep + gH; if (innerH < 1) innerH = 1; int W = innerW + 2; int H = innerH + 2; if (W > Kmax || H > Kmax) continue; long long metric = (long long)max(W, H) * 1000000LL + (long long)(W + H); if (metric < bestMetric) { bestMetric = metric; bestInnerW = innerW; bestInnerH = innerH; bestChildrenH = cH; bestSep = sep; } } if (bestInnerW == -1) return false; L.innerW = bestInnerW; L.innerH = bestInnerH; L.w = bestInnerW + 2; L.h = bestInnerH + 2; L.childrenH = bestChildrenH; L.sep = bestSep; L.gadgetStartY = 1 + bestChildrenH + bestSep; // store positions pack_children_positions(L.order, lay, bestInnerW, L.pos); lay[u] = std::move(L); return true; } void paint(int u, int top, int left, vector>& C) { const Layout& L = lay[u]; for (int i = 0; i < L.h; i++) { for (int j = 0; j < L.w; j++) { C[top + i][left + j] = u; } } // children for (size_t i = 0; i < L.order.size(); i++) { int v = L.order[i]; int y = L.pos[i].first; int x = L.pos[i].second; paint(v, top + 1 + y, left + 1 + x, C); } // gadgets (only overwrite in gadget area) int g = (int)gadgets[u].size(); if (g > 0) { int baseY = top + L.gadgetStartY; int baseX = left + 1; for (int idx = 0; idx < g; idx++) { int rr = (idx % slotRows) * 2; int cc = (idx / slotRows) * 2; C[baseY + rr][baseX + cc] = gadgets[u][idx]; } } } vector> create_map() { if (N == 1) return vector>(1, vector(1, 1)); adj.assign(N + 1, {}); memset(isEdge, 0, sizeof(isEdge)); memset(isTree, 0, sizeof(isTree)); for (int i = 0; i < M; i++) { int a = A[i], b = B[i]; isEdge[a][b] = isEdge[b][a] = true; adj[a].push_back(b); adj[b].push_back(a); } if (!build_spanning_tree()) { // Shouldn't happen due to guarantee; fallback to trivial (may be invalid) return vector>(1, vector(1, 1)); } assign_gadgets(); int Kfound = -1; int Kfinal = -1; int Kstart = max(3, N); lay.assign(N + 1, Layout()); for (int K = Kstart; K <= 240; K++) { lay.assign(N + 1, Layout()); if (!dfs_size(1, K)) continue; int rw = lay[1].w, rh = lay[1].h; if (rw <= K && rh <= K) { Kfound = K; Kfinal = max(rw, rh); break; } } if (Kfound == -1) { // Guaranteed to exist; last resort Kfinal = 240; lay.assign(N + 1, Layout()); dfs_size(1, 240); } vector> C(Kfinal, vector(Kfinal, 1)); paint(1, 0, 0, C); return C; } }; static vector> create_map(int N, int M, vector A, vector B) { Builder b; b.N = N; b.M = M; b.A = std::move(A); b.B = std::move(B); return b.create_map(); } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int T; if (!(cin >> T)) return 0; for (int tc = 0; tc < T; tc++) { int N, M; cin >> N >> M; vector A(M), B(M); for (int i = 0; i < M; i++) cin >> A[i] >> B[i]; auto C = create_map(N, M, A, B); int K = (int)C.size(); cout << K << "\n"; for (int i = 0; i < K; i++) { if (i) cout << ' '; cout << K; } cout << "\n\n"; for (int i = 0; i < K; i++) { for (int j = 0; j < K; j++) { if (j) cout << ' '; cout << C[i][j]; } cout << "\n"; } } return 0; }