#include "supertrees.h"
#include <bits/stdc++.h>
using namespace std;
#define sz(x) int((x).size())
#define bg(x) (x).begin()
#define en(x) (x).end()
#define all(x) bg((x)), en((x))
#define FOR(i, a, b) for (int i = a; i < b; i++)
#define pb push_back
using vi = vector<int>;
using vvi = vector<vi>;
struct DSU {
int n; vector<int> par, siz;
DSU(int N) {
n = N;
par.resize(n); iota(all(par), 0);
siz.assign(n, 1);
}
int find(int v) {
if (par[v] == v) return v;
return par[v] = find(par[v]);
}
void unite(int a, int b) {
a = find(a); b = find(b);
if (a != b) {
if (siz[a] < siz[b]) swap(a, b);
par[b] = a;
siz[a] += siz[b];
}
}
};
int construct(vvi p) {
int n = sz(p);
auto dsu = DSU(n);
vector<bool> all2(n, true);
FOR(i, 0, n) FOR(j, 0, n) all2[i] = all2[i] && (i == j || (p[i][j] == 0 || p[i][j] == 2));
for (int i = 0; i < n; i++) {
for (int j = i+1; j < n; j++) {
if (p[i][j] == 0) continue;
if (p[i][j] == 3) return 0;
if (all2[i] && all2[j]) dsu.unite(i, j);
else if (!all2[i] && !all2[j] && p[i][j] == 1) {
dsu.unite(i, j);
}
}
}
FOR(i, 0, n) {
FOR(j, i+1, n) {
if (p[i][j] == 0 && dsu.find(i) == dsu.find(j)) {
return 0;
}
if (p[i][j] == 2 && dsu.siz[dsu.find(i)] <= 2) {
return 0;
}
}
}
vvi cmps(n); FOR(i, 0, n) cmps[dsu.find(i)].pb(i);
vi tail(n, -1), head(n, -1);
vvi answer(n, vector<int>(n, 0));
FOR(cmpid, 0, n) {
if (dsu.find(cmpid) != cmpid) continue;
if (sz(cmps[cmpid]) == 0) continue;
if (sz(cmps[cmpid]) == 1) {
head[cmpid] = tail[cmpid] = cmpid;
continue;
}
int fst = cmps[cmpid][0], prev = cmps[cmpid][0];
FOR(i, 1, sz(cmps[cmpid])) {
int cur = cmps[cmpid][i];
answer[cur][prev] = answer[prev][cur] = 1;
prev = cur;
}
tail[cmpid] = fst;
head[cmpid] = prev;
}
// FOR(i, 0, n) {
// if (all2[i]) continue;
// FOR(j, 0, n) {
// if (dsu.find(i) == dsu.find(j) && p[i][j] != 1) return 0;
// }
// }
FOR(cmpid, 0, n) {
// if (sz(cmps[cmpid]) <= 1) continue;
if (sz(cmps[cmpid]) == 0) continue;
if (dsu.find(cmpid) != cmpid) continue;
if (!all2[cmpid]) continue;
vector<int> substituents;
for (int i = 0; i < n; i++) {
if (all2[i]) continue;
if (p[cmpid][i] < 1) continue;
substituents.push_back(dsu.find(i));
// cout << cmpid << " has substituent " << dsu.find(i) << "\n";
}
sort(all(substituents));
substituents.erase(unique(all(substituents)), en(substituents));
int h = head[cmpid], t = tail[cmpid];
if (sz(substituents) == 0) {
if (sz(cmps[cmpid]) > 2) {
answer[h][t] = answer[t][h] = 1;
}
} else {
int prev = substituents[0];
int fst = prev;
for (int i = 1; i < sz(substituents); i++) {
answer[prev][substituents[i]] = answer[substituents[i]][prev] = 1;
dsu.unite(prev, substituents[i]);
prev = substituents[i];
}
answer[h][prev] = answer[prev][h] = 1;
answer[t][fst] = answer[fst][t] = 1;
dsu.unite(h, prev); dsu.unite(fst, t);
}
}
cmps.assign(n, vector<int>());
FOR(i, 0, n) cmps[dsu.find(i)].pb(i);
vector<bool> vcmp(n, true); FOR(cmpid, 0, n) {for (auto &el : cmps[cmpid]) {vcmp[cmpid] = vcmp[cmpid] && !all2[el];}}
FOR(cmpid, 0, n) {
if (!vcmp[cmpid]) continue;
if (sz(cmps[cmpid]) <= 0) continue;
if (dsu.find(cmpid) != cmpid) continue;
vector<int> substituents;
for (int i = 0; i < n; i++) {
if (p[cmpid][i] != 2) continue;
if (dsu.find(i) == dsu.find(cmpid)) continue;
if (all2[i]) continue;
substituents.pb(dsu.find(i));
}
sort(all(substituents));
substituents.erase(unique(all(substituents)), en(substituents));
if (substituents.size() == 0) continue;
if (sz(substituents) == 1) return 0;
int prev = substituents[0];
int fst = prev;
FOR(i, 1, sz(substituents)) {
answer[prev][substituents[i]] = answer[substituents[i]][prev] = 1;
dsu.unite(prev, substituents[i]);
prev = substituents[i];
}
answer[prev][cmpid] = answer[cmpid][prev] = 1;
answer[fst][cmpid] = answer[cmpid][fst] = 1;
dsu.unite(prev, cmpid); dsu.unite(fst, cmpid);
}
build(answer);
return 1;
}
