#include "supertrees.h"
#include <vector>
#include <bits/stdc++.h>
using namespace std;
vector<int> m_link, sz;
int m_find(int x) {
if (m_link[x] != x) m_link[x] = m_find(m_link[x]);
return m_link[x];
}
bool same(int a, int b) {
return m_find(a) == m_find(b);
}
void unite(int a, int b) {
if (a > b) swap(a, b);
int x = m_find(b), y = m_find(a);
if (same(x, y)) return;
sz[y] += sz[x];
m_link[x] = y;
}
int construct(vector<vector<int>> p) {
int n = p.size();
vector<vector<int>> answer(n, vector<int>(n));
m_link = vector<int>(n);
sz = vector<int>(n, 1);
iota(m_link.begin(), m_link.end(), 0);
bool res = true;
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (i == j) res &= p[i][j] == 1;
else if (p[i][j] == 1) unite(i, j);
else if (p[i][j] == 3) res = false;
}
}
for (int i = 0; i < n; i++) {
int par = m_find(i);
if (par != i) {
answer[par][i] = 1;
answer[i][par] = 1;
for (int j = 0; j < n; j++) {
res &= p[i][j] == p[par][j];
}
}
}
vector<set<int>> newNodes(n);
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (i == j) continue;
if (p[i][j] == 2) {
int p1 = m_find(i), p2 = m_find(j);
unite(p1, p2);
newNodes[m_find(p1)].insert(p1);
newNodes[m_find(p2)].insert(p2);
}
}
}
for (int i = 0; i < n; i++) {
if (newNodes[i].size() == 0) continue;
res &= newNodes[i].size() > 2;
for (auto it = newNodes[i].begin(); it != newNodes[i].end(); it++) {
auto nxt = it;
nxt++;
if (nxt == newNodes[i].end()) {
nxt = newNodes[i].begin();
}
answer[*it][*nxt] = 1;
answer[*nxt][*it] = 1;
}
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (i == j) continue;
res &= ((p[i][j] > 0) == same(i, j));
}
}
if (res) {
build(answer);
return 1;
} else return 0;
}
