#include <bits/stdc++.h>
#include "supertrees.h"
using namespace std;
#define ll long long
#define pii pair<int,int>
#define ff first
#define ss second
#define sz(a) (int)a.size()
#define pb push_back
const int maxn=1e3+5;
// head
int n;
int d[maxn];
int b[maxn];
vector<vector<int>> p;
vector<vector<int>> ans;
int ata(int x){
if(x==d[x]) return x;
return d[x]=ata(d[x]);
}
int ata2(int x){
if(x==b[x]) return x;
return b[x]=ata2(b[x]);
}
int f(vector<int>v){
if(sz(v)==0) return 1;
for(int i = 0;i < sz(v);i++) b[v[i]]=v[i];
for(int i = 0;i < sz(v);i++){
for(int j = 0;j < i;j++){
if(p[v[i]][v[j]]==1){
int x=ata2(v[i]),y=ata2(v[j]);
if(x != y) b[y]=x;
}
}
}
vector<int> br[n+1];
set<int> s;
for(int i = 0;i < sz(v);i++){
ata2(v[i]);
br[b[v[i]]].pb(v[i]);
s.insert(b[v[i]]);
}
for(int i = 0;i < n;i++){
for(int j = 0;j < sz(br[i]);j++){
for(int k = 0;k < j;k++){
if(p[br[i][j]][br[i][k]]==2) return 0;
}
if(j > 0) ans[br[i][j]][br[i][j-1]]=1,ans[br[i][j-1]][br[i][j]]=1;
}
}
if(sz(s)==2) return 0;
if(sz(s)==1) return 1;
int fi=-1,ls=-1;
for(auto i : s){
if(fi==-1) fi=i;
if(ls != -1) ans[i][ls]=1,ans[ls][i]=1;
ls=i;
}
ans[ls][fi]=1,ans[fi][ls]=1;
return 1;
}
int construct(vector<vector<int>> _p) {
p = _p;
n = p.size();
ans.resize(n);
for(int i = 0;i < n;i++){
d[i]=i;
ans[i].resize(n);
}
for(int i = 0;i < n;i++)
for(int j = 0;j < n;j++) if(p[i][j]==3) return 0;
for(int i = 0;i < n;i++){
for(int j = 0;j < i;j++){
if(p[i][j]>0){
int x=ata(i),y=ata(j);
if(x != y) d[y]=x;
}
}
}
vector<int>v[n+1];
for(int i = 0;i < n;i++){
ata(i);
v[d[i]].pb(i);
}
for(int i = 0;i < n;i++){
for(int j = 0;j < sz(v[i]);j++){
for(int k = 0;k < j;k++){
if(p[v[i][j]][v[i][k]] == 0) return 0;
}
}
}
for(int i = 0;i < n;i++){
int jog = f(v[i]);
if(jog==0) return 0;
}
build(ans);
return 1;
}
