#include "supertrees.h"
#include "bits/stdc++.h"
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#define ld double
#define ll long long
#define ull unsigned long long
#define llinf 100000000000000000LL // 10^17
#define iinf 2000000000 // 2*10^9
#define pb push_back
#define popb pop_back
#define fi first
#define sc second
#define endl '\n'
#define pii pair<int,int>
#define pll pair<ll,ll>
#define pld pair<ld,ld>
#define sz(a) ((ll)(a.size()))
#define all(a) a.begin(),a.end()
#define rall(a) a.begin(),a.end(),greater<int>()
#define getunique(v) {sort(all(v)); v.erase(unique(all(v)), v.end());}
#define pi 3.14159265358979323846
#define here cerr<<"=============================================================================\n"
#define ceri(a,l,r) {for(ll i_ = l;i_<=r;i_++) cerr<<a[i_]<< " ";cerr<<endl;}
#define ceri2(a,l,r,n,m) {for(ll i = l;i<=r;i++){for(ll j = n;j<=m;j++) cerr<<a[i][j]<< " ";cerr<<endl;}}
#define yes cout<<"YES"<<endl
#define no cout<<"NO"<<endl
#define daj_mi_malo_vremena ios_base::sync_with_stdio(false);cerr.tie(0);cout.tie(0);cin.tie(0);
using namespace std;
#define maxn 1005
ll dsu[maxn];
ll root(ll x){
while(x!=dsu[x]){
dsu[x] = dsu[dsu[x]];
x = dsu[x];
}
return x;
}
void upd(ll x,ll y){dsu[root(x)] = root(y);}
bool get(ll x,ll y){return root(x)==root(y);}
vector<ll> v[maxn];
vector<std::vector<int>> answer;
bool cyc[maxn];
void upd2(ll x,ll y){
answer[x][y] = 1;
answer[y][x] = 1;
cyc[y] = 1;
cyc[x] = 1;
}
bool bio[maxn];
bool vis[maxn];
vector<ll> g[maxn];
ll d[maxn][maxn];
void dfs(ll poc,ll u,ll dis,bool c){
vis[u] = 1;
for(ll s : g[u]){
if(vis[s]) continue;
if(cyc[u]==0&&cyc[s]==1) d[poc][s] =1 ;
else if(c||dis==0) d[poc][s] = 2;
else d[poc][s] = 1;
dfs(poc,s,dis+1,c|cyc[s]);
}
}
int construct(std::vector<std::vector<int>> p) {
int n = p.size();
for(ll i = 0;i<n;i++){
vector<int> w(n);
answer.pb(w);
}
iota(dsu,dsu+n,0);
for(ll i = 0;i<n;i++){
for(ll j = 0;j<n;j++){
if(p[i][j]==3) return 0;
}
for(ll j = 0;j<n;j++){
if(p[i][j]==1) upd(i,j);
}
}
vector<vector<ll> >w;
for(ll i = 0;i<n;i++) v[root(i)].pb(i);
for(ll i = 0;i<n;i++) if(sz(v[i])) w.pb(v[i]);
for(ll i = 0;i<sz(w);i++){
for(ll j = 0;j<sz(w[i])-1;j++){
answer[w[i][j]][w[i][j+1]] = 1;
answer[w[i][j+1]][w[i][j]] = 1;
}
}
/*here;
for(vector<ll> v : w){
for(ll x : v) cerr<<x<< " ";
cerr<<endl;
}
here;
for(vector<int> v : answer){
for(ll x : v) cerr<<x<< " ";
cerr<<endl;
}
here;*/
for(ll i = 0;i<sz(w);i++){
ll last = i;
for(ll j = i+1;j<sz(w);j++){
if(bio[j]) continue;
if(p[root(w[last].back())][root(w[j].back())]>0){
upd2(w[last].back(),w[j].back());
last = j;
bio[j] = 1;
}
}
if(last!=i) upd2(w[last].back(),w[i].back());
}
for(ll i = 0;i<n;i++){
for(ll j = i+1;j<n;j++){
if(answer[i][j]){
//cerr<<i<< " "<<j<<endl;
g[i].pb(j);
g[j].pb(i);
}
}
}
fill(vis,vis+n,0);
for(ll i = 0;i<n;i++){
d[i][i] = 1;
fill(vis,vis+n+1,0);
dfs(i,i,0,cyc[i]);
}
for(ll i = 0;i<n;i++){
for(ll j = 0;j<n;j++){
d[i][j] = min(d[i][j],d[j][i]);
//cerr<<d[i][j]<< " ";
}
//cerr<<endl;
}
for(ll i = 0;i<n;i++){
for(ll j = 0;j<n;j++){
if(d[i][j]!=p[i][j]) return 0;
}
}
build(answer);
return 1;
}
/*
4
1 1 2 2
1 1 2 2
2 2 1 2
2 2 2 1
*/
