#include <bits/stdc++.h>
#include "worldmap.h"
using namespace std;
using ll = long long;
#define MOD 998244353
#define MOD2 1000000007
#define vt vector
template <class T> using vvt = vt<vt<T>>;
template <class T> using vvvt = vt<vvt<T>>;
template <class T> using vvvvt = vt<vvvt<T>>;
typedef vt<int> vi;
typedef vvt<int> vvi;
typedef vvvt<int> vvvi;
typedef vvvvt<int> vvvvi;
typedef vt<ll> vl;
typedef vvt<ll> vvl;
typedef vvvt<ll> vvvl;
typedef vvvvt<ll> vvvvl;
#define endl '\n'
#define pb push_back
#define pf push_front
#define all(x) x.begin(),x.end()
#define sz(x) (int)((x).size())
#define mset multiset
#define fi first
#define se second
#define rep(i,a,b) for(int i=a;i<b;i++)
#define repl(i,a,b) for(ll i=a;i<b;i++)
#define rrep(i,a,b) for(int i=a;i>=b;i--)
#define rrepl(i,a,b) for(ll i=a;i>=b;i--)
#define each(i,a) for(auto &i:a)
#define yesno(x) cout<<(x?"YES":"NO")<<endl
struct pii {
int x, y;
bool operator<(const pii &a) const { return x == a.x ? y < a.y : x < a.x; }
bool operator>(const pii &a) const { return x == a.x ? y > a.y : x > a.x; }
bool operator==(const pii &a) const { return x == a.x && y == a.y; }
bool operator!=(const pii &a) const { return x != a.x || y != a.y; }
pii operator+(const pii &a) const { return {x+a.x, y+a.y}; }
pii operator-(const pii &a) const { return {x-a.x, y-a.y}; }
pii operator*(const int &a) const { return {x*a, y*a}; }
pii operator/(const int &a) const { return {x/a, y/a}; }
void operator+=(const pii &a) { x += a.x; y += a.y; }
void operator-=(const pii &a) { x -= a.x; y -= a.y; }
void operator*=(const int &a) { x *= a; y *= a; }
void operator/=(const int &a) { x /= a; y /= a; }
friend ostream& operator<<(ostream &os, const pii &p) {return os << "(" << p.x << ", " << p.y << ")";}
friend istream& operator>>(istream &is, pii &p) {return is >> p.x >> p.y;}
};
struct pll {
ll x, y;
bool operator<(const pll &a) const { return x == a.x ? y < a.y : x < a.x; }
bool operator>(const pll &a) const { return x == a.x ? y > a.y : x > a.x; }
bool operator==(const pll &a) const { return x == a.x && y == a.y; }
bool operator!=(const pll &a) const { return x != a.x || y != a.y; }
pll operator+(const pll &a) const { return {x+a.x, y+a.y}; }
pll operator-(const pll &a) const { return {x-a.x, y-a.y}; }
pll operator*(const ll &a) const { return {x*a, y*a}; }
pll operator/(const ll &a) const { return {x/a, y/a}; }
void operator+=(const pll &a) { x += a.x; y += a.y; }
void operator-=(const pll &a) { x -= a.x; y -= a.y; }
void operator*=(const ll &a) { x *= a; y *= a; }
void operator/=(const ll &a) { x /= a; y /= a; }
friend ostream& operator<<(ostream &os, const pll &p) {return os << "(" << p.x << ", " << p.y << ")";}
friend istream& operator>>(istream &is, pll &p) {return is >> p.x >> p.y;}
};
static uint64_t splitmix64(uint64_t x) {
x += 0x9e3779b97f4a7c15;
x = (x^(x>>30))*0xbf58476d1ce4e5b9;
x = (x^(x>>27))*0x94d049bb133111eb;
return x^(x>>31);
}
struct custom_hash {
static const uint64_t FIXED_RANDOM;
size_t operator()(uint64_t x) const {return splitmix64(x + FIXED_RANDOM);}
template<typename T> size_t operator()(const T& t) const {return splitmix64(uint64_t(std::hash<T>{}(t)) + FIXED_RANDOM);}
};
const uint64_t custom_hash::FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
mt19937 rng(custom_hash::FIXED_RANDOM);
template<typename K, typename V> using umap = unordered_map<K, V, custom_hash>;
template<typename K> using uset = unordered_set<K, custom_hash>;
template<typename T> using umset = unordered_multiset<T, custom_hash>;
template<class T> bool ckmin(T& a, const T& b) {
return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) {
return a < b ? a = b, 1 : 0; }
void dfs(vvi &adj, int u, int p, vi &ans, vvi &up, vi &ids, vi &dep, int d) {
dep[u] = d;
ans.pb(u);
ids[u] = sz(ans);
ans.pb(u);
ans.pb(u);
each(v,adj[u]) {
if (v == p) continue;
if (dep[v] != -1 && dep[v] < dep[u]) {
up[u].pb(v);
} else if (dep[v] == -1) {
dfs(adj, v, u, ans, up, ids, dep, d+1);
ans.pb(u);
}
}
}
vvi create_map(int N, int M, vi A, vi B) {
vvi adj(N+1);
rep(i,0,M) {
adj[A[i]].pb(B[i]);
adj[B[i]].pb(A[i]);
}
vi ans;
vvi up(N+1);
vi ids(N+1, -1);
vi dep(N+1, -1);
dfs(adj, 1, -1, ans, up, ids, dep, 0);
int n = (sz(ans)+1)/2;
// cerr << "n: " << n << endl;
vvi res(n, vi(n,0));
rep(i,0,n){
rep(j,0,n) {
res[i][j] = ans[i+j];
}
}
rep(i,1,N+1) {
int id = ids[i];
rep(j,0,sz(up[i])) {
int v = up[i][j];
int k = max(id-(n-1), 0);
// cerr << "id: " << id << ", v: " << v << ", j: " << j << ", k: " << k << endl;
// cerr << "x: " << id-j-k << ", y: " << j+k << endl;
res[id-j-k][j+k] = v;
}
}
return res;
}
