#include<bits/stdc++.h>
#include "Alicelib.h"
using namespace std;
#define all(fl) fl.begin(),fl.end()
#define pb push_back
#define fi first
#define se second
#define for1(i,j,k) for(int i=j;i<=k;i++)
#define for2(i,j,k) for(int i=j;i>=k;i--)
#define for3(i,j,k,l) for(int i=j;i<=k;i+=l)
#define lb lower_bound
#define ub upper_bound
#define sz(a) (int)a.size()
#define pii pair<int,int>
#define pli pair<long long,int>
#define gcd __gcd
#define lcm(x,y) x*y/__gcd(x,y)
void Alice( int N, int M, int A[], int B[] ){
vector<pii>t;
for1(i,0,M-1)t.pb({A[i],B[i]});
for1(i,0,N+10){
if (i==N)continue;
t.pb({N,i});
}
for1(i,N+1,N+10)t.pb({N+11,i});
for1(i,N+2,N+10)t.pb({i,i-1});
for1(i,1,N)for1(j,0,9)if (i>>j&1)t.pb({i-1,j+1+N});
InitG(N+12,sz(t));
for1(i,0,sz(t)-1)MakeG(i,t[i].fi,t[i].se);
}
#include<bits/stdc++.h>
#include "Boblib.h"
using namespace std;
#define all(fl) fl.begin(),fl.end()
#define pb push_back
#define fi first
#define se second
#define for1(i,j,k) for(int i=j;i<=k;i++)
#define for2(i,j,k) for(int i=j;i>=k;i--)
#define for3(i,j,k,l) for(int i=j;i<=k;i+=l)
#define lb lower_bound
#define ub upper_bound
#define sz(a) (int)a.size()
#define pii pair<int,int>
#define pli pair<long long,int>
#define gcd __gcd
#define lcm(x,y) x*y/__gcd(x,y)
const int maxn=2e3+9;
int deg[maxn],encode[maxn];
vector<int>a[maxn];
bool b[maxn][maxn],isbit[maxn],vis[maxn];
vector<int>ord;
void dfs(int u){
vis[u]=1,ord.pb(u);
for (auto v:a[u])if (isbit[v]&&!vis[v])dfs(v);
}
void Bob( int V, int U, int C[], int D[] ){
for1(i,0,U-1){
deg[C[i]]++,deg[D[i]]++,a[C[i]].pb(D[i]),a[D[i]].pb(C[i]),b[C[i]][D[i]]=b[D[i]][C[i]]=1;
}
int nw=0;
for1(i,0,V-1)if (deg[i]>deg[nw])nw=i;
int sec=0;
for1(i,0,V-1){
if (i==nw)continue;
if (!b[nw][i])sec=i;
}
vector<int>bit;
for (auto v:a[sec])isbit[v]=1,bit.pb(v);
vector<int>bit09;
for (auto v:bit){
int cnt=0;
for (auto u:a[v])cnt+=isbit[u];
if (cnt==1)bit09.pb(v);
}
int u=bit09[0],v=bit09[1];
if (sz(a[u])>sz(a[v]))bit09.pop_back();
int bit0=bit09.back();
dfs(bit0);
for1(i,0,sz(ord)-1){
for (auto v:a[ord[i]]){
if (v==nw||v==sec)continue;
encode[v]+=(1<<i);
}
}
vector<pii>t;
for1(i,0,U-1){
if (C[i]==nw||C[i]==sec||isbit[C[i]]||D[i]==nw||D[i]==sec||isbit[D[i]])continue;
t.pb({encode[C[i]]-1,encode[D[i]]-1});
}
InitMap(V-12,sz(t));
for (auto v:t)MakeMap(v.fi,v.se);
}
