#include "bits/extc++.h"
using namespace std;
template <typename T>
void dbgh(const T& t) {
cerr << t << endl;
}
template <typename T, typename... U>
void dbgh(const T& t, const U&... u) {
cerr << t << " | ";
dbgh(u...);
}
#ifdef DEBUG
#define dbg(...) \
cerr << "L" << __LINE__ << " [" << #__VA_ARGS__ << "]: "; \
dbgh(__VA_ARGS__);
#else
#define dbg(...)
#define cerr \
if (false) \
cerr
#endif
#define endl "\n"
#define long int64_t
#define sz(x) int((x).size())
void build(std::vector<std::vector<int>> b);
int construct(vector<vector<int>> arr) {
for (auto& a : arr) {
for (auto& b : a) {
if (b == 3) {
return 0;
}
}
}
int n = sz(arr);
bool vis[n] {};
vector<vector<int>> trees;
for (int i = 0; i < n; i++) {
if (vis[i]) {
continue;
}
vis[i] = true;
trees.push_back({i});
for (int j = 0; j < n; j++) {
if (!vis[j] && arr[i][j] == 1) {
trees.back().push_back(j);
vis[j] = true;
}
}
}
vector<vector<int>> cycles;
memset(vis, 0, sizeof(vis));
for (int i = 0; i < sz(trees); i++) {
if (vis[i]) {
continue;
}
vis[i] = true;
cycles.push_back({i});
for (int j = 0; j < sz(trees); j++) {
if (!vis[j] && arr[trees[i][0]][trees[j][0]] == 2) {
cycles.back().push_back(j);
vis[j] = true;
}
}
if (sz(cycles.back()) == 2) {
return 0;
}
}
int rtree[n], rcycle1[n], rcycle[n];
for (int i = 0; i < sz(trees); i++) {
for (auto& a : trees[i]) {
rtree[a] = i;
}
}
for (int i = 0; i < sz(cycles); i++) {
for (auto& a : cycles[i]) {
rcycle1[a] = i;
}
}
for (int i = 0; i < n; i++) {
rcycle[i] = rcycle1[rtree[i]];
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
int x;
if (rtree[i] == rtree[j]) {
x = 1;
} else if (rcycle[i] == rcycle[j]) {
x = 2;
} else {
x = 0;
}
if (arr[i][j] != x) {
return 0;
}
}
}
vector<vector<int>> graph(n, vector<int>(n));
auto add_edge = [&](int u, int v) -> void {
graph[u][v] = graph[v][u] = true;
};
for (auto& a : trees) {
for (int i = 1; i < sz(a); i++) {
add_edge(a[0], a[i]);
}
}
for (auto& a : cycles) {
if (sz(a) == 1) {
continue;
}
for (int i = 0; i < sz(a); i++) {
add_edge(trees[a[i]][0], trees[a[(i + 1) % sz(a)]][0]);
}
}
build(graph);
return 1;
}
