#include <bits/stdc++.h>
#include "supertrees.h"
using namespace std;
#ifdef LOCAL
#define deb(...) logger(#__VA_ARGS__, __VA_ARGS__)
template<typename ...Args>
void logger(string vars, Args&&... values) {
cerr<<vars<<" = ";
string delim="";
(...,(cerr<<delim<<values,delim=", "));
cerr<<"\n";
}
#else
#define deb(...) logger(#__VA_ARGS__, __VA_ARGS__)
template<typename ...Args>
void logger(string vars, Args&&... values) {}
#endif
#define pb push_back
#define sz(x) (int)(x.size())
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
template<typename T> inline void maxa(T& a,T b){a=max(a,b);}
template<typename T> inline void mina(T& a,T b){a=min(a,b);}
// void build(vector<vector<int>> b){
// int n=sz(b);
// for(int i=0;i<n;i++){
// for(int j=0;j<n;j++){
// cout<<b[i][j]<<" ";
// }
// cout<<"\n";
// }
// }
const int mxN=1e3+5;
int uf[mxN],seen[mxN],is_triple[mxN];
vector<int> component[mxN];
vector<vector<int>> g;
int find(int x){return uf[x]<0?x:uf[x]=find(uf[x]);}
bool same(int x,int y){return find(x)==find(y);}
void unite(int x,int y){
x=find(x); y=find(y);
if(x==y)
return;
if(uf[x]>uf[y])
swap(x,y);
uf[x]+=uf[y]; uf[y]=x;
}
int construct(vector<vector<int>> p){
g=p;
memset(uf,-1,sizeof(uf));
int n=sz(p);
vector<vector<int>> b;
b.resize(n);
for(auto &u:b)
u.resize(n);
for(int i=0;i<n;i++){
for(int j=0;j<n;j++){
if(g[i][j]){
unite(i,j);
}
}
}
for(int i=0;i<n;i++){
component[find(i)].pb(i);
for(int j=0;j<n;j++){
if(!g[i][j] && same(i,j))
return 0;
}
}
for(int i=0;i<n;i++){
if(sz(component[i])<=1)
continue;
vector<vector<int>> line; vector<int> ring; vector<int> triple; vector<int> single;
int twocnt=0; int cnt=0;
for(int &j:component[i]){
if(seen[j]){
single.pb(j);
continue;
}
int three=1; int has=0;
vector<int> one={j};
for(int k=0;k<n;k++){
if(g[j][k]==1 && j!=k){
one.pb(k);
seen[k]=1;
}
twocnt+=(g[j][k]==2);
if((g[j][k]==1 || g[j][k]==2) && j!=k){
three=0;
}
if(g[j][k]==3)
has=1;
}
if(sz(one)==1)
ring.pb(j);
else
line.pb(one);
if(three)
triple.pb(j);
else
single.pb(j);
cnt+=has;
}
if(cnt && twocnt)
return 0;
if(cnt && sz(triple)<4)
return 0;
if(cnt){
for(int j=0;j<sz(single);j++){
for(int k=j+1;k<sz(single);k++){
if(g[single[k]][single[j]]!=1){
return 0;
}
}
for(int k=0;k<sz(triple);k++){
if(g[single[j]][triple[k]]!=3)
return 0;
}
}
for(int j=0;j<sz(single)-1;j++){
b[single[j]][single[j+1]]=b[single[j+1]][single[j]]=1;
}
for(int j=0;j<sz(triple)-1;j++){
b[triple[j]][triple[j+1]]=b[triple[j+1]][triple[j]]=1;
}
b[triple[0]][triple.back()]=b[triple.back()][triple[0]]=1;
b[triple[0]][triple[sz(triple)-2]]=b[triple[sz(triple)-2]][triple[0]]=1;
if(sz(single)){
b[single[0]][triple.back()]=b[triple.back()][single[0]]=1;
}
continue;
}
if(sz(line)==0){
if(sz(ring)==2)
return 0;
for(int j=0;j<sz(ring);j++){
b[ring[j]][ring[(j+1)%sz(ring)]]=b[ring[(j+1)%sz(ring)]][ring[j]]=1;
}
} else{
for(int j=0;j<sz(ring)-1;j++){
b[ring[j]][ring[j+1]]=b[ring[j+1]][ring[j]]=1;
}
for(auto u:line){
for(int j=0;j<sz(u)-1;j++){
b[u[j]][u[j+1]]=b[u[j+1]][u[j]]=1;
}
}
for(int j=0;j<sz(line)-1;j++){
b[line[j][0]][line[j+1][0]]=b[line[j+1][0]][line[j][0]]=1;
}
if(sz(ring)){
b[line.back()[0]][ring.back()]=b[ring.back()][line.back()[0]]=1;
b[line[0][0]][ring[0]]=b[ring[0]][line[0][0]]=1;
} else if(sz(line)>1){
b[line.back()[0]][line[0][0]]=b[line[0][0]][line.back()[0]]=1;
}
}
}
build(b);
return 1;
}
