#include "supertrees.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define eb emplace_back
#define pb push_back
#define ft first
#define sd second
#define pi pair<int, int>
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define dbg(...) dbg_out(__VA_ARGS__)
using ll = long long;
using ld = long double;
using namespace std;
using namespace __gnu_pbds;
//Constants
const ll INF = 5 * 1e18;
const int IINF = 2 * 1e9;
const ll MOD = 1e9 + 7;
// const ll MOD = 998244353;
const ll dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const ld PI = 3.14159265359;
//Templates
template<typename A, typename B> ostream& operator<<(ostream &os, const pair<A, B> &p) {return os << '(' << p.first << ", " << p.second << ')';}
template<typename T_container, typename T = typename enable_if<!is_same<T_container, string>::value, typename T_container::value_type>::type> ostream& operator<<(ostream &os, const T_container &v) {os << '['; string sep; for (const T &x : v) os << sep << x, sep = ", "; return os << ']';}
void dbg_out() {cerr << endl;}
template<typename Head, typename... Tail> void dbg_out(Head H, Tail... T) { cerr << H << ' '; dbg_out(T...); }
template<typename T> void mins(T& x, T y) {x = min(x, y);}
template<typename T> void maxs(T& x, T y) {x = max(x, y);}
template<typename T> using oset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T> using omset = tree<T, null_type, less_equal<T>, rb_tree_tag, tree_order_statistics_node_update>;
//order_of_key(k): number of elements strictly less than k
//find_by_order(k): k-th element in the set
void setPrec() {cout << fixed << setprecision(15);}
void unsyncIO() {cin.tie(0)->sync_with_stdio(0);}
void setIn(string s) {freopen(s.c_str(), "r", stdin);}
void setOut(string s) {freopen(s.c_str(), "w", stdout);}
void setIO(string s = "") {
unsyncIO(); setPrec();
if(s.size()) setIn(s + ".in"), setOut(s + ".out");
}
int construct(vector<vector<int>> p) {
int n = p.size();
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (p[i][j] == 3) return 0;
}
}
// build cycles
vector<vector<int>> ans(n, vector<int> (n, 0));
vector<int> comp(n, -1);
int comp_num = 0;
{
vector<bool> vis(n, false);
vector<int> path;
function<void(int)> dfs = [&](int f) {
vis[f] = true;
path.pb(f);
for (int to = 0; to < n; to++) {
if (!vis[to] && p[f][to] == 2) {
dfs(to);
}
}
};
for (int i = 0; i < n; i++) {
if (!vis[i]) {
path.clear();
dfs(i);
if ((int) path.size() == 2) {
return 0;
}
if ((int) path.size() > 2) {
int sz = path.size();
for (int j = 0; j < sz; j++) {
comp[path[j]] = comp_num;
ans[path[j]][path[(j + 1) % sz]] = ans[path[(j + 1) % sz]][path[j]] = 1;
}
comp_num++;
}
}
}
}
// build bamboos
{
vector<bool> vis(n, false);
vector<int> path; set<int> comps_vis;
function<void(int)> dfs = [&](int f) {
vis[f] = true;
path.pb(f);
for (int to = 0; to < n; to++) {
if (!vis[to]) {
if (p[f][to] == 1)
dfs(to);
else if (p[f][to] == 2)
comps_vis.insert(comp[to]);
}
}
};
for (int i = 0; i < n; i++) {
if (!vis[i]) {
comps_vis.clear();
path.clear();
dfs(i);
if ((int) comps_vis.size() > 1) {
return 0;
}
int sz = path.size();
for (int j = 0; j < sz - 1; j++) {
ans[path[j]][path[j + 1]] = ans[path[j + 1]][path[j]] = 1;
}
}
}
}
build(ans);
return 1;
}
