#pragma GCC optimize("O3")
#include "bits/stdc++.h" /** keep-include */
using namespace std;
#define rep(i, b, e) for(int i = (b); i <= (e); i++)
#define per(i, b, e) for(int i = (e); i >= (b); i--)
#define FOR(i, b, e) rep(i, b, (e) - 1)
#define SZ(x) int(x.size())
#define all(x) x.begin(), x.end()
#define pb push_back
#define mp make_pair
#define st first
#define nd second
using ll = long long;
using vi = vector<int>;
using pii = pair<int, int>;
auto &operator<<(auto &o, pair<auto, auto> p) {
return o << "(" << p.st << ", " << p.nd << ")"; }
auto operator<<(auto &o, auto x)->decltype(end(x), o) {
o << "{"; int i=0; for(auto e: x) o << ", " + 2*!i++ << e;
return o << "}"; }
#ifdef LOCAL
#define deb(x...) cerr << "[" #x "]: ", [](auto...$) { \
((cerr << $ << "; "),...) << endl; }(x)
#else
#define deb(...)
#endif
#include "Alicelib.h"
void Alice( int n, int m, int A[], int B[] ){
vector<pii> edg;
for(int i=0; i<m; i++){
deb("Alice", A[i], B[i]);
edg.pb(mp(A[i], B[i]));
}
int full=n;
int bit_ptr=n+1;
int bits_beg=n+2;
int bits=10;
for(int i=0; i<n; i++){
edg.pb(mp(full, i));
for(int j=0; j<bits; j++){
if(i&(1<<j)){
edg.pb(mp(i, bits_beg+j));
}
}
}
edg.pb(mp(bits_beg, bits_beg+2));
edg.pb(mp(bits_beg, bits_beg+3));
for(int j=0; j<bits; j++){
if(j>1)edg.pb(mp(bits_beg+j-1, bits_beg+j));
edg.pb(mp(full, bits_beg+j));
edg.pb(mp(bit_ptr, bits_beg+j));
}
InitG( bits_beg+bits, edg.size() );
for(int i=0; i<SZ(edg); i++){
MakeG(i, edg[i].st, edg[i].nd );
}
}
#pragma GCC optimize("O3")
#include "bits/stdc++.h" /** keep-include */
using namespace std;
#define rep(i, b, e) for(int i = (b); i <= (e); i++)
#define per(i, b, e) for(int i = (e); i >= (b); i--)
#define FOR(i, b, e) rep(i, b, (e) - 1)
#define SZ(x) int(x.size())
#define all(x) x.begin(), x.end()
#define pb push_back
#define mp make_pair
#define st first
#define nd second
using ll = long long;
using vi = vector<int>;
using pii = pair<int, int>;
auto &operator<<(auto &o, pair<auto, auto> p) {
return o << "(" << p.st << ", " << p.nd << ")"; }
auto operator<<(auto &o, auto x)->decltype(end(x), o) {
o << "{"; int i=0; for(auto e: x) o << ", " + 2*!i++ << e;
return o << "}"; }
#ifdef LOCAL
#define deb(x...) cerr << "[" #x "]: ", [](auto...$) { \
((cerr << $ << "; "),...) << endl; }(x)
#else
#define deb(...)
#endif
#include "Boblib.h"
vector<int> get_bits(vector<vi> &E, vi V){
int k=V.size();
vector<vi> E2(k);
assert(k==10);
for(int i=0; i<k; i++){
for(int j=0; j<k; j++){
if(find(all(E[V[i]]), V[j])!=E[V[i]].end()){
E2[i].push_back(j);
}
}
}
vi deg3;
for(int i=0; i<k; i++){
if(E2[i].size()==3)deg3.pb(i);
}
assert(deg3.size()==2);
vi ans(k, -1);
for(int i=0; i<k; i++){
if(binary_search(all(E2[i]), deg3[0]) && binary_search(all(E2[i]), deg3[1])){
assert(ans[0]==-1);
ans[0]=i;
}
}
assert(ans[0]!=-1);
E2[deg3[0]].erase(find(all(E2[deg3[0]]), ans[0]));
E2[deg3[1]].erase(find(all(E2[deg3[1]]), ans[0]));
E2[deg3[0]].erase(find(all(E2[deg3[0]]), deg3[1]));
E2[deg3[1]].erase(find(all(E2[deg3[1]]), deg3[0]));
if(E2[E2[deg3[0]][0]].size()==2){
assert(E2[E2[deg3[1]][0]].size()==1);
swap(deg3[0], deg3[1]);
}
ans[1]=E2[deg3[0]][0];
ans[2]=deg3[0];
ans[3]=deg3[1];
for(int i=3; i<k-1; i++){
E2[E2[ans[i]][0]].erase(find(all(E2[E2[ans[i]][0]]), ans[i]));
assert(E2[ans[i]].size()==1);
ans[i+1]=E2[ans[i]][0];
}
for(int &i:ans){
i=V[i];
}
return ans;
}
void Bob( int n, int m, int A[], int B[] ){
vector<vector<int> > E(n);
for(int i=0; i<m; i++){
E[A[i]].pb(B[i]);
E[B[i]].pb(A[i]);
deb("Bob", A[i], B[i]);
}
int full=-1;
int bit_ptr=-1;
for(int i=0; i<n; i++){
if(SZ(E[i])==n-2){
sort(all(E[i]));
int cand=-1;
for(int j=0; j<n; j++){
if(j!=i && !binary_search(all(E[i]), j)){
assert(cand==-1);
cand=j;
}
}
if(SZ(E[cand])==10){
assert(full==-1);
full=i;
bit_ptr=cand;
}
}
}
deb(full, bit_ptr);
assert(full!=-1);
vector<int> bits=get_bits(E, E[bit_ptr]);
deb(bits);
vector<int> labels(n);
for(int i:bits)labels[i]=-1;
for(int i=0; i<m; i++){
if(labels[A[i]]==-1 && labels[B[i]]==-1){
deb(A[i], B[i]);
}
}
labels[full]=-1;
labels[bit_ptr]=-1;
for(int i=0; i<n; i++){
if(labels[i]!=-1){
sort(all(E[i]));
for(int j=0; j<SZ(bits); j++){
if(binary_search(all(E[i]), bits[j]))labels[i]+=(1<<j);
}
}
}
vector<pii> edg;
for(int i=0; i<n; i++){
if(labels[i]==-1)continue;
for(int j:E[i]){
if(labels[j]!=-1 && j<i){
edg.pb(mp(labels[i], labels[j]));
}
}
}
for(auto &[x, y]:edg){
deb(x, y);
}
InitMap( n-SZ(bits)-2, SZ(edg) );
for(auto &[x, y]:edg){
MakeMap( x, y );
}
}
