#include "game.h"
#include <algorithm>
#include <iostream>
#include <iomanip>
#include <numeric>
#include <cassert>
#include <random>
#include <vector>
#include <cmath>
#include <queue>
#include <set>
#include <map>
#define syosu(x) fixed<<setprecision(x)
using namespace std;
typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<string> vs;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<pll> vpll;
typedef pair<P,int> pip;
typedef vector<pip> vip;
const int inf=1<<30;
const ll INF=1ll<<60;
const double pi=acos(-1);
const double eps=1e-8;
const ll mod=1e9+7;
const int dx[4]={-1,0,1,0},dy[4]={0,-1,0,1};
class Union_Find_Tree{
public:
vi p,r,s;
Union_Find_Tree(int n){
p=r=vi(n);
s=vi(n,1);
for(int i=0;i<n;i++) p[i]=i;
}
int Par(int x){
if(p[x]==x) return x;
return p[x]=Par(p[x]);
}
int Size(int x){return s[Par(x)];}
bool Unite(int x,int y){
x=Par(x);
y=Par(y);
if(x==y) return 0;
if(r[x]<r[y]){
p[x]=y;
s[y]+=s[x];
}
else{
p[y]=x;
s[x]+=s[y];
if(r[x]==r[y]) r[x]++;
}
return 1;
}
bool Same(int x,int y){return Par(x)==Par(y);}
};
vvi g,G;
vi b;
void initialize(int n){
Union_Find_Tree uft(n);
g=vvi(n,vi(n));
G=vvi(n,vi(n,1));
b=vi(n);
vp a;
for(int i=0;i<n;i++) for(int j=i+1;j<n;j++) a.push_back({i,j});
mt19937 rnd(1001);
shuffle(a.begin(),a.end(),rnd);
for(auto p:a){
int u=p.first,v=p.second;
if(uft.Unite(u,v)) g[u][v]=g[v][u]=1;
}
}
void dfs(int v,int t,vi &c){
b[v]=t;
c.push_back(v);
for(auto u:g[v]) if(b[u]!=t) dfs(u,t,c);
}
int hasEdge(int u,int v){
if(!g[u][v]) return G[u][v]=G[v][u]=0;
fill(b.begin(),b.end(),0);
g[u][v]=g[v][u]=0;
vi c,d;
dfs(u,1,c);
dfs(v,-1,d);
for(auto i:c) for(auto j:d) if(G[i][j])return g[i][j]=g[j][i]=1;
return G[u][v]=G[v][u]=0;
}
