#include <bits/stdc++.h>
using namespace std;
#define int long long
#define INF (int)1e18
mt19937_64 RNG(chrono::steady_clock::now().time_since_epoch().count());
vector<vector<int32_t>> create_map(int32_t n, int32_t m, vector <int32_t> a, vector <int32_t> b){
vector <int> c(4 * n - 1);
vector <int> dfs_ord;
vector<vector<int>> adj(n + 1);
for (int i = 0; i < m; i++){
adj[a[i]].push_back(b[i]);
adj[b[i]].push_back(a[i]);
}
vector <bool> vis(n + 1, false);
vector <int> dep(n + 1, 0);
vector <int> p(n + 1, -1);
vector<vector<int>> ch(n + 1);
vector <int> tin(n + 1), tout(n + 1);
int timer = 0;
auto calc_dfs = [&](auto self, int u, int par) -> void{
vis[u] = true;
p[u] = par;
tin[u] = ++timer;
for (int v : adj[u]){
if (!vis[v]){
ch[u].push_back(v);
dep[v] = dep[u] + 1;
self(self, v, u);
}
}
tout[u] = timer;
};
calc_dfs(calc_dfs, 1, -1);
int id = 1;
for (int i = 2; i <= n; i++){
if (dep[i] > dep[id]){
id = i;
}
}
vector <bool> bad(n + 1, false);
while (id != 1){
bad[id] = true;
id = p[id];
}
auto dfs = [&](auto self, int u, int par) -> void{
dfs_ord.push_back(u);
for (int v : ch[u]){
if (!bad[v]){
self(self, v, u);
dfs_ord.push_back(u);
}
}
for (int v : ch[u]){
if (bad[v]){
self(self, v, u);
dfs_ord.push_back(u);
}
}
};
dfs(dfs, 1, -1);
assert(dfs_ord.size() == 2 * n - 1);
vector<vector<int>> need(n + 1);
for (int i = 0; i < m; i++){
int u = a[i], v = b[i];
if (u == p[v] || v == p[u]) continue;
if (tin[v] <= tin[u] && tout[v] >= tout[u]){
swap(u, v);
}
need[v].push_back(u);
}
vector <bool> seen(n + 1, false);
assert(need[1].size() == 0);
vector<vector<int>> rows;
for (auto x : dfs_ord){
rows.push_back({x});
if (!seen[x] && need[x].size() > 0){
rows.push_back(need[x]);
rows.push_back({x});
seen[x] = true;
}
}
assert(rows.size() <= 4 * n - 1);
while (rows.size() < 4 * n - 1){
rows.push_back(rows.back());
}
vector<vector<int>> ans(2 * n, vector<int>(2 * n));
for (int i = 0; i < 4 * n - 1; i++){
int sz = min(i + 1, 4 * n - i - 1);
assert(sz >= rows[i].size());
assert(rows[i].size() > 0);
while (rows[i].size() < sz){
rows[i].push_back(rows[i].back());
}
// diag is x + y = i - 1
int p = 0;
for (int x = 0; x < 2 * n; x++){
int y = i - x;
if (0 <= y && y < 2 * n){
assert(p < rows[i].size());
ans[x][y] = rows[i][p];
p++;
}
}
}
return ans;
}
void validate(vector<vector<int>> c, int n, int m, vector <int> a, vector <int> b){
vector<vector<bool>> allow(n + 1, vector<bool>(n + 1, false));
vector<vector<int>> done(n + 1, vector<int>(n + 1, 0));
for (int i = 1; i <= n; i++){
allow[i][i] = true;
}
for (int i = 0; i < m; i++){
allow[a[i]][b[i]] = true;
allow[b[i]][a[i]] = true;
}
assert(c.size() == 2 * n);
for (int i = 0; i < 2 * n; i++) assert(c[i].size() == 2 * n);
for (int i = 0; i < 2 * n; i++){
for (int j = 0; j < 2 * n; j++){
assert(1 <= c[i][j] && c[i][j] <= n);
}
}
auto add = [&](int x, int y){
assert(allow[x][y] == true);
done[x][y]++;
done[y][x]++;
};
for (int i = 0; i < 2 * n; i++){
for (int j = 0; j < 2 * n; j++){
if (i + 1 < 2 * n){
add(c[i][j], c[i + 1][j]);
}
if (j + 1 < 2 * n){
add(c[i][j], c[i][j + 1]);
}
}
}
for (int i = 0; i < m; i++){
assert(done[a[i]][b[i]] >= 1);
}
}
