#define _CRT_SECURE_NO_WARNINGS
#include "supertrees.h"
#include <iostream>
#include <iomanip>
#include <array>
#include <string>
#include <algorithm>
#include <cmath>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <vector>
#include <stack>
#include <queue>
#include <deque>
#include <bitset>
#include <list>
#include <iterator>
#include <numeric>
#include <complex>
#include <utility>
#include <random>
#include <cassert>
#include <fstream>
using namespace std;
mt19937 rnd(7069);
/* -------------------- Typedefs -------------------- */
typedef int itn;
typedef long long ll;
typedef unsigned long long ull;
typedef double db;
typedef float fl;
typedef long double ld;
/* -------------------- Usings -------------------- */
using vi = vector<int>;
using vll = vector<ll>;
using mii = map<int, int>;
using mll = map<ll, ll>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
/* -------------------- Defines -------------------- */
#define ff first
#define ss second
#define pub push_back
#define pob pop_back
#define puf push_front
#define pof pop_front
#define mpr make_pair
#define yes cout<<"Yes\n"
#define no cout<<"No\n"
#define all(x) (x).begin(), (x).end()
#define USACO freopen("feast.in", "r", stdin); freopen("feast.out", "w", stdout);
/* -------------------- Constants -------------------- */
const int MAX = int(1e9 + 5);
const ll MAXL = ll(1e18) + 5ll;
const ll MOD = ll(998244353);
const ll MOD2 = ll(998244353);
/* -------------------- Functions -------------------- */
void fastio() {
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
}
void precision(int x) {
cout.setf(ios::fixed | ios::showpoint);
cout.precision(x);
}
ll gcd(ll a, ll b) {
if (a == 0 || b == 0) return(max(a, b));
while (b) {
a %= b;
swap(a, b);
}
return a;
}
ll lcm(ll a, ll b) {
return a / gcd(a, b) * b;
}
ll range_sum(ll a, ll b) {
if (a > b) return 0ll;
ll dif = a - 1, cnt = b - a + 1;
ll ans = ((b - a + 1) * (b - a + 2)) / 2;
ans += ((b - a + 1) * dif);
return ans;
}
string dec_to_bin(ll a) {
string s = "";
for (ll i = a; i > 0; ) {
ll k = i % 2;
i /= 2;
char c = k + 48;
s += c;
}
if (a == 0) {
s = "0";
}
reverse(all(s));
return s;
}
ll bin_to_dec(string s) {
ll num = 0;
for (int i = 0; i < s.size(); i++) {
num *= 2ll;
num += (s[i] - '0');
}
return num;
}
ll factorial_by_mod(ll n, ll mod) {
ll ans = 1;
ll num;
for (ll i = 1; i <= n; ++i) {
num = i % mod;
ans *= num;
ans %= mod;
}
return ans;
}
int isPrime(ll a) {
if (a == 1) return 0;
for (ll i = 2; i * i <= a; i++) {
if (a % i == 0) return 0;
}
return 1;
}
ll binpow(ll a, ll b) {
if (!a) return 0;
ll ans = 1;
while (b) {
if (b & 1) {
ans *= a;
}
b >>= 1;
a *= a;
}
return ans;
}
ll binpow_by_mod(ll a, ll b, ll mod) {
if (!a) return 0;
ll ans = 1;
while (b) {
if (b & 1) {
ans *= a;
ans %= mod;
}
b >>= 1;
a *= a;
a %= mod;
}
return ans;
}
/* -------------------- Solution -------------------- */
const int N = 1005;
int used[N], a[N][N], p[N];
vi comp[N], gr[N];
vector<vi> edge;
int n;
void make_set(int x) {
p[x] = x;
comp[x] = { x };
}
int find_set(int x) {
if (x == p[x]) return x;
return p[x] = find_set(p[x]);
}
void union_sets(int x, int y) {
x = find_set(x), y = find_set(y);
if (x == y) return;
if (comp[x].size() > comp[y].size()) swap(x, y);
p[x] = y;
for (auto elem : comp[x]) comp[y].pub(elem);
}
void connect(int x, int y) {
edge[x][y] = edge[y][x] = 1;
}
int construct(vector<vi> P) {
n = P[0].size();
edge.resize(n);
for (int i = 0; i < n; ++i) {
edge[i].resize(n);
make_set(i);
for (int j = 0; j < n; ++j) {
a[i][j] = P[i][j];
}
}
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
if (!a[i][j]) continue;
union_sets(i, j);
}
}
int sz = 0;
for (int i = 0; i < n; ++i) {
int ind = find_set(i);
if (used[ind]) continue;
used[ind] = 1;
gr[sz] = comp[ind];
++sz;
}
for (int i = 0; i < sz; ++i) {
for (auto elem : gr[i]) {
make_set(elem);
}
for (int i1 = 0; i1 < gr[i].size(); ++i1) {
for (int i2 = i1 + 1; i2 < gr[i].size(); ++i2) {
int d = a[gr[i][i1]][gr[i][i2]];
if (d == 0) {
return 0;
}
if (d == 1) union_sets(gr[i][i1], gr[i][i2]);
}
}
for (int i1 = 0; i1 < gr[i].size(); ++i1) {
for (int i2 = i1 + 1; i2 < gr[i].size(); ++i2) {
int d = a[gr[i][i1]][gr[i][i2]];
if (!d) return 0;
if (d == 1) union_sets(gr[i][i1], gr[i][i2]);
}
}
bool f = false;
for (int i1 = 0; i1 < gr[i].size(); ++i1) {
for (int i2 = i1 + 1; i2 < gr[i].size(); ++i2) {
int x = find_set(gr[i][i1]);
int y = find_set(gr[i][i2]);
int d = a[gr[i][i1]][gr[i][i2]];
if (d == 2) f = true;
if (x == y && d != 1) return 0;
if (x != y && d != 2) return 0;
}
}
set<int> st;
for (auto elem : gr[i]) {
int ind = find_set(elem);
st.insert(comp[ind][0]);
for (int j = 1; j < comp[ind].size(); ++j) {
connect(comp[ind][j - 1], comp[ind][j]);
}
}
if (!f) continue;
if (st.size() <= 2) return 0;
vi vec;
for (auto elem : st) vec.pub(elem);
for (int j = 1; j < vec.size(); ++j) {
connect(vec[j], vec[j - 1]);
}
connect(vec[0], vec.back());
}
build(edge);
return 1;
}
