#include "supertrees.h"
#include <vector>
#include <bits/stdc++.h>
using namespace std;
struct DisjointSetUnion {
int n;
vector<int> par;
vector<int> sz;
DisjointSetUnion(int n) {
par.resize(n);
sz.assign(n, 1);
iota(par.begin(), par.end(), 0);
}
int find(int x) {
return par[x] = (x == par[x] ? x : find(par[x]));
}
void unite(int u, int v) {
u = find(u);
v = find(v);
if (u == v) return;
if (sz[u] < sz[v]) swap(u, v);
par[v] = u;
sz[u] += sz[v];
}
bool same(int u, int v) {
return (find(u) == find(v));
}
};
int construct(vector<vector<int>> p) {
int n = p.size();
bool bad = false;
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
bad |= (p[i][j] == 3);
}
}
if (bad) return 0;
vector<vector<int>> b(n, vector<int> (n, 0));
DisjointSetUnion dsu(n);
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (p[i][j] == 1) {
dsu.unite(i, j);
}
}
}
vector<int> roots;
for (int i = 0; i < n; i++) {
if (dsu.par[i] == i) {
vector<int> nodes;
for (int j = 0; j < n; j++) {
if (dsu.par[j] == i) {
nodes.push_back(j);
}
}
for (int u : nodes) {
for (int v : nodes) {
bad |= (p[u][v] != 1);
}
}
roots.push_back(i);
for (int j = 1; j < (int) nodes.size(); j++) b[nodes[j]][nodes[j - 1]] = b[nodes[j - 1]][nodes[j]] = 1;
}
}
if (bad) return 0;
DisjointSetUnion rot(n);
for (int u : roots) {
for (int v : roots) {
if (p[u][v] == 2) {
rot.unite(u, v);
}
}
}
for (int u : roots) {
if (u == rot.par[u] && rot.sz[u] > 1) {
vector<int> nodes;
for (int v : roots) {
if (u == rot.par[v]) {
nodes.push_back(v);
}
}
for (int i : nodes) {
for (int j : nodes) {
if (i != j && p[i][j] != 2) bad = true;
}
}
int sz = nodes.size();
for (int i = 0; i < sz; i++) {
b[nodes[i]][nodes[(i + 1) % sz]] = b[nodes[(i + 1) % sz]][nodes[i]] = 1;
}
}
}
if (bad) return 0;
build(b);
return 1;
}
