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using namespace std;
struct Layout {
int w = 0, h = 0;
int innerW = 0, innerH = 0;
int childrenH = 0;
int sep = 0;
int gadgetW = 0, gadgetH = 0;
int gadgetStartY = 0;
vector<int> order;
vector<pair<int,int>> pos;
};
static int pack_children_height(const vector<int>& order, const vector<Layout>& 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;
x = 0;
rowH = 0;
}
x += wv;
if (x < innerW) x += 1;
rowH = max(rowH, hv);
}
return y + rowH;
}
static int pack_children_positions(const vector<int>& order, const vector<Layout>& lay, int innerW, vector<pair<int,int>>& 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<int> A, B;
vector<vector<int>> adj;
bool isEdge[41][41]{};
bool isTree[41][41]{};
vector<int> parent;
vector<vector<int>> children;
vector<vector<int>> gadgets;
vector<Layout> lay;
int slotRows = 2;
int gadgetHConst = 3;
int root = 1;
// mode: 0=BFS, 1=DFS
bool build_spanning_tree_from(int r, int mode = 0) {
root = r;
parent.assign(N + 1, -1);
children.assign(N + 1, {});
memset(isTree, 0, sizeof(isTree));
parent[r] = 0;
if (mode == 0) {
// BFS
queue<int> q;
q.push(r);
while (!q.empty()) {
int u = q.front(); q.pop();
for (int v : adj[u]) {
if (parent[v] == -1) {
parent[v] = u;
q.push(v);
}
}
}
} else {
// DFS
stack<int> st;
st.push(r);
while (!st.empty()) {
int u = st.top(); st.pop();
for (int v : adj[u]) {
if (parent[v] == -1) {
parent[v] = u;
st.push(v);
}
}
}
}
// Handle disconnected: connect isolated nodes to root
for (int i = 1; i <= N; i++) {
if (parent[i] == -1) {
parent[i] = r;
}
}
for (int i = 1; i <= N; i++) {
if (i == r) continue;
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<int> 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; }
// Try different arrangements and pick most compact
int bestGW = INT_MAX, bestGH = INT_MAX;
long long bestArea = (long long)INT_MAX * INT_MAX;
for (int rows = 1; rows <= g; rows++) {
int cols = (g + rows - 1) / rows;
int gw = 2 * cols - 1;
int gh = 2 * rows - 1;
long long area = (long long)gw * gh;
int maxDim = max(gw, gh);
int bestMaxDim = max(bestGW, bestGH);
if (maxDim < bestMaxDim || (maxDim == bestMaxDim && area < bestArea)) {
bestGW = gw;
bestGH = gh;
bestArea = area;
}
}
gW = bestGW;
gH = bestGH;
}
int gadgetRows(int u) {
int g = (int)gadgets[u].size();
if (g == 0) return 0;
int gW, gH;
compute_gadget_dims(u, gW, gH);
return (gH + 1) / 2;
}
int gadgetCols(int u) {
int g = (int)gadgets[u].size();
if (g == 0) return 0;
int gW, gH;
compute_gadget_dims(u, gW, gH);
return (gW + 1) / 2;
}
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;
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;
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<vector<int>>& 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;
}
}
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);
}
int g = (int)gadgets[u].size();
if (g > 0) {
int baseY = top + L.gadgetStartY;
int baseX = left + 1;
int gW, gH;
compute_gadget_dims(u, gW, gH);
int gCols = (gW + 1) / 2;
for (int idx = 0; idx < g; idx++) {
int rr = (idx / gCols) * 2;
int cc = (idx % gCols) * 2;
C[baseY + rr][baseX + cc] = gadgets[u][idx];
}
}
}
int try_build(int r, int mode) {
build_spanning_tree_from(r, mode);
assign_gadgets();
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(r, K)) continue;
int rw = lay[r].w, rh = lay[r].h;
if (rw <= K && rh <= K) {
return max(rw, rh);
}
}
return 241; // failed
}
vector<vector<int>> create_map() {
if (N == 1) return vector<vector<int>>(1, vector<int>(1, 1));
adj.assign(N + 1, {});
memset(isEdge, 0, sizeof(isEdge));
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);
}
// Try all roots with both BFS and DFS, pick best
int bestK = 241;
int bestRoot = 1;
int bestMode = 0;
for (int mode = 0; mode <= 1; mode++) {
for (int r = 1; r <= N; r++) {
int K = try_build(r, mode);
if (K < bestK) {
bestK = K;
bestRoot = r;
bestMode = mode;
}
}
}
// Rebuild with best root and mode
build_spanning_tree_from(bestRoot, bestMode);
assign_gadgets();
lay.assign(N + 1, Layout());
dfs_size(bestRoot, bestK);
int Kfinal = bestK;
if (Kfinal > 240) Kfinal = 240;
vector<vector<int>> C(Kfinal, vector<int>(Kfinal, bestRoot));
paint(bestRoot, 0, 0, C);
return C;
}
};
static vector<vector<int>> create_map(int N, int M, vector<int> A, vector<int> 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<int> 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;
}
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