#include <cmath>
#include <cassert>
#include <iostream>
#include <set>
#include <climits>
#include <algorithm>
#include <vector>
#include <iomanip>
#include <type_traits>
#include <string>
#include <queue>
#include <map>
#include "supertrees.h"
#pragma GCC target ("avx2")
#pragma GCC optimization ("O3")
#pragma GCC optimization ("Ofast")
#pragma GCC optimization ("unroll-loops")
using namespace std;
class DisjointSetUnion {
protected:
vector<int> parent;
vector<int> compSize;
const int n;
int connectedComponents;
public:
int getConnectedComponents() const {
return connectedComponents;
}
public:
DisjointSetUnion(int sz) : n(sz), connectedComponents(sz) {
parent.resize(sz), compSize.resize(sz);
for (int i = 0; i < n; i++) {
parent[i] = i, compSize[i] = 1;
}
}
int find_head(int x) const {
int cur = x;
while (cur != parent[cur]) {
cur = parent[cur];
}
return cur;
}
void join(int x, int y) {
x = find_head(x);
y = find_head(y);
if (x == y) {
return;
}
if (compSize[x] > compSize[y]) {
swap(x, y);
//ensures that compSize[x1] <= compSize[y1]
}
parent[x] = y;
compSize[y] += compSize[x];
connectedComponents--;
}
bool comp(int x, int y) {
return (find_head(x) == find_head(y));
}
};
/*
void build (vector<vector<int>> grid) {
for (int i = 0; i < grid.size(); i++) {
for (int j: grid[i]) {
cout << j << ' ';
}
cout << '\n';
}
}
*/
int construct(vector<vector<int>> grid) {
vector<vector<int>> ans(grid.size());
for (int i = 0; i < grid.size(); i++) {
ans[i].assign(grid[0].size(), 0);
}
set<int> s;
map<int, int> cnt;
DisjointSetUnion disjointSetUnion(grid.size());
for (int i = 0; i < grid.size(); i++) {
for (int j = 0; j < grid.size(); j++) {
s.insert(grid[i][j]);
cnt[grid[i][j]]++;
if (grid[i][j] != 0) {
disjointSetUnion.join(i, j);
}
}
}
map<int, vector<int>> myMap;
for (int i = 0; i < grid.size(); i++) {
myMap[disjointSetUnion.find_head(i)].push_back(i);
}
for (auto &p: myMap) {
DisjointSetUnion dsu(grid.size());
map<int, vector<int>> m;
bool h3 = false;
bool h2 = false;
for (int x: p.second) {
for (int y: p.second) {
if (grid[x][y] == 3) {
h3 = true;
}
if (grid[x][y] == 2) {
h2 = true;
}
if (grid[x][y] == 1) {
dsu.join(x, y);
}
}
}
if (h2 && h3) {
return 0;
}
for (int i: p.second) {
m[dsu.find_head(i)].push_back(i);
}
vector<int> vec;
for (auto &q: m) {
vec.push_back(q.first);
}
if (vec.size() != 1) {
if (vec.size() == 2) {
return false;
}
if (vec.size() == 3 && h3) {
return false;
}
for (int i = 0; i < vec.size(); i++) {
if (ans[vec[i]][vec[(i + 1) % (int) vec.size()]]) return false;
ans[vec[i]][vec[(i + 1) % (int) vec.size()]] = ans[vec[(i + 1) % (int) vec.size()]][vec[i]] = 1;
}
if (h3) {
if (ans[vec[0]][vec[2]]) return false;
ans[vec[0]][vec[2]] = ans[vec[2]][vec[0]] = 1;
}
for (int x: vec) {
for (int y: vec) {
if (x == y) continue;
if (grid[x][y] == 0 || grid[x][y] == 1) {
return false;
}
}
}
}
for (auto &q: m) {
vector<int> v = q.second;
for (int i: v) {
for (int j: v) {
if (grid[i][j] == 0) {
return false;
}
}
}
for (int i = 1; i < (int) v.size(); i++) {
if (ans[v[0]][v[i]]) return false;
ans[v[i]][v[0]] = 1;
ans[v[0]][v[i]] = 1;
}
for (int x: v) {
for (int y: v) {
if (grid[x][y] != 1) {
return 0;
}
}
for (int y = 0; y < grid.size(); y++) {
if (grid[x][y] == 1 && x != y) return false;
}
}
}
}
build(ans);
return 1;
}
/*
int main () {
const int N = 7;
vector<vector<int>> grid = {{1, 3, 3, 3}, {3, 1, 3, 3}, {3, 3, 1, 3}, {3, 3, 3, 1}};
construct(grid);
}
*/
