#include "worldmap.h"
#include <bits/stdc++.h>
using namespace std;
/*
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
*/
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
template <class T> using PQMax = priority_queue<T>;
template <class T> using PQMin = priority_queue<T, vector<T>, greater<T>>;
template <class T1, class T2>
void maximize(T1 &a, T2 b){
if (b > a) a = b;
}
template <class T1, class T2>
void minimize(T1 &a, T2 b){
if (b < a) a = b;
}
template <class T>
void read(T &number)
{
bool negative = false;
register int c;
number = 0;
c = getchar();
while (c != '-' && !isalnum(c)) c = getchar();
if (c=='-'){
negative = true;
c = getchar();
}
for (; (c>47 && c<58); c=getchar())
number = number *10 + c - 48;
if (negative)
number *= -1;
}
template <class T, class ...Ts>
void read(T &a, Ts& ... args){
read(a);
read(args...);
}
/*
struct Node
{
int node, len;
Node() {node = len = 0;}
Node(int node, int len) {this -> node = node, this -> len = len;}
};
typedef vector<Node> vg;
*/
#define fi first
#define se second
#define FOR(type, i, a, b) for(type i = (a); i <= (b); i++)
#define REV(type, i, b, a) for(type i = (b); i >= (a); i--)
#define testBit(n, bit) (((n) >> (bit)) & 1)
#define flipBit(n, bit) ((n) ^ (1ll << (bit)))
#define cntBit(n) __builtin_popcount(n)
#define cntBitll(n) __builtin_popcountll(n)
#define log2(n) (31 - __builtin_clz(n))
#define log2ll(n) (63 - __builtin_clzll(n))
#define CURRENT_TIMESTAMP chrono::steady_clock::now().time_since_epoch().count()
#define randomize mt19937_64 mt(CURRENT_TIMESTAMP)
#define MAX 50
#define MOD 1000000007
randomize;
struct Rand {
ll next(ll n) {
return mt() % n;
}
ll next(ll l, ll r) {
return l + next(r-l+1);
}
} rnd;
int n, m;
vector<int> graph[MAX];
namespace Subtask12 {
vector<int> euler;
void dfs(int u, int p) {
// cerr << u << ' ' << p << '\n';
euler.push_back(u);
bool oke = false;
for (int v: graph[u]) if (v != p)
dfs(v, u), euler.push_back(u);
}
vector<vector<int>> solve() {
dfs(1, 0);
int sz = euler.size();
return vector<vector<int>>(sz, euler);
}
}
namespace Subtask3 {
vector<vector<int>> answer;
vector<vector<int>> solve() {
vector<int> allnum;
for (int i = 1; i <= n; i++) for (int j = i + 1; j <= n; j++)
allnum.push_back(i), allnum.push_back(j);
answer = vector<vector<int>>(40, vector<int>(40, 1));
int ptr = 0;
for (int row = 0; row < 40; row++) {
if (ptr > 0) ptr--;
int from = (row % 2 == 0) ? 0 : 39;
int to = 39 - from;
int add = (row % 2 == 0) ? 1 : -1;
for (int col = from; col >= 0 and col <= 39; col += add) {
if (ptr == (int)allnum.size()) break;
answer[row][col] = allnum[ptr++];
}
if (ptr == (int)allnum.size()) break;
}
return answer;
}
}
namespace Subtask4 {
vector<vector<int>> answer;
vector<vector<int>> solve() {
answer = vector<vector<int>>(100, vector<int>(100, 1));
for (int i = 2, row = 0; i <= n; i++, row += 2) {
int ptr = 0;
answer[row][ptr++] = i;
for (int j: graph[i]) {
answer[row][ptr++] = j;
answer[row][ptr++] = i;
}
}
return answer;
}
}
namespace Subtask56 {
void clear();
vector<vector<int>> answer;
vector<bool> visited;
vector<int> buildArray(int u) {
vector<int> ans;
for (int v: graph[u]) if (not visited[v]) {
ans.push_back(u);
ans.push_back(v);
}
return ans;
}
void dfs(int u, int p) {
visited[u] = true;
vector<int> tmp = buildArray(u);
if (not tmp.empty()) {
answer.push_back(tmp);
answer.push_back(vector<int>{u});
}
for (int v: graph[u]) {
if (visited[v]) continue;
answer.push_back(vector<int>{v});
dfs(v, u);
answer.push_back(vector<int>{u});
}
// answer.pop_back();
}
vector<vector<int>> trying() {
clear();
if (n == 1) return vector<vector<int>>(1, {1});
visited.resize(n+1, false);
int root = rnd.next(1, n);
dfs(root, 0);
while ((int) answer.rbegin() -> size() == 1) answer.pop_back();
// cerr << "oke" << ' ' << answer.size() << endl;;
int maxWidth = answer.size();
for (vector<int> &v: answer)
maximize(maxWidth, (int)v.size());
// cerr << maxWidth << endl;
answer.resize(maxWidth, vector<int> {(*answer.rbegin())[0]});
for (vector<int> &v: answer)
v.resize(maxWidth, v[0]);
// cerr << maxWidth << endl;
return answer;
}
vector<vector<int>> solve() {
vector<vector<int>> answer = trying();
FOR(int, i, 1, 15) {
vector<vector<int>> tmp = trying();
if (tmp.size() < answer.size()) answer = tmp;
}
return answer;
}
void clear() {
answer.clear();
visited.clear();
}
}
void clear();
std::vector<std::vector<int>> create_map(int _N, int _M, std::vector<int> _A, std::vector<int> _B) {
clear();
n = _N, m = _M;
for (int i = 0; i < m; i++) {
int u = _A[i], v = _B[i];
graph[u].push_back(v);
graph[v].push_back(u);
}
return Subtask56::solve();
// return ans;
}
void clear(){
Subtask12::euler.clear();
Subtask3::answer.clear();
Subtask4::answer.clear();
Subtask56::clear();
FOR(int, i, 1, n) graph[i].clear();
n = m =0;
}
