#include <bits/stdc++.h>
#include "supertrees.h"
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
#define N 1005
#define PB push_back
#define sz(x) int(x.size())
#define P 31
#define F first
#define M ll(1e9 + 7)
#define S second
#define all(x) x.begin(), x.end()
#define endl '\n'
//#pragma GCC optimize("unroll-loops")
//#pragma GCC optimize("-O3")
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("fast-math")
//#pragma GCC optimize("no-stack-protector")
using namespace std;
//using namespace __gnu_pbds;
typedef long long ll;
//typedef tree<int, null_type, less_equal <int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
ll mlt(ll a, ll b) {return (a * b) % M;}
ll sm(ll a, ll b) {return (a + b) % M;}
int rk[N], pr[N], cnt[N][N], n, glob;
vector <vector <int> > g;
void make(int x) {pr[x] = x; rk[x] = 1;}
int fnd(int x) {if (pr[x] != x) pr[x] = fnd(pr[x]); return pr[x];}
void link(int a, int b)
{
if (rk[b] > rk[a]) swap(a, b);
rk[a] += rk[b];
pr[b] = a;
}
//void build(vector <vector <int> > pr)
//{
// for (int i = 0; i < sz(pr); i++)
// {
// cout << i << ": ";
//
// for (auto itr : pr[i]) cout << itr << " "; cout << endl;
// }
//}
void dfs(int v, int p)
{
cnt[glob][v]++;
for (int i = 0; i < n; i++)
if (i != p && g[v][i] == 1) dfs(i, v);
}
int construct(vector<vector<int> > p)
{
n = sz(p);
vector<vector<int> > answer; answer.clear();
bool f = 1, fr = 1, ft = 1;
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
if (i != j) {if (p[i][j] == 2 || p[i][j] == 3) fr = 0; if (p[i][j] != 1) f = 0; if (p[i][j] == 1 || p[i][j] == 3) ft = 0;}
if (f)
{
answer.resize(n);
for (int i = 0; i < n; i++)
answer[i].resize(n, 0);
for (int i = 1; i < n; i++) answer[0][i] = 1;
for (int i = 1; i < n; i++) answer[i][0] = 1;
build(answer);
return 1;
}
if (fr)
{
bool good = 1;
answer.resize(n);
for (int i = 0; i < n; i++)
answer[i].resize(n, 0);
for (int i = 0; i < n; i++) make(i);
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
if (p[i][j] == 1)
{
int a = fnd(i), b = fnd(j);
if (a != b) {answer[i][j] = answer[j][i] = 1; link(a, b);}
}
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
if ((p[i][j] == 1 && fnd(i) != fnd(j)) || (p[i][j] == 0 && fnd(i) == fnd(j))) good = 0;
if (good) build(answer);
return good;
}
if (ft)
{
bool good = 1;
answer.resize(n);
for (int i = 0; i < n; i++)
answer[i].resize(n, 0);
for (int i = 0; i < n; i++) make(i);
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
if (p[i][j] == 2)
{
int a = fnd(i), b = fnd(j);
if (a != b) link(a, b);
}
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
if (i != j && ((p[i][j] == 2 && fnd(i) != fnd(j)) || (p[i][j] == 0 && fnd(i) == fnd(j)))) good = 0;
if (!good) return 0;
set <int> se; se.clear();
for (int i = 0; i < n; i++)
{
int id = fnd(i);
if (se.find(id) != se.end()) continue;
se.insert(id);
vector <int> pr; pr.clear();
for (int j = 0; j < n; j++)
if (fnd(j) == id)
pr.PB(j);
if (sz(pr) == 1) continue;
if (sz(pr) == 2) {good = 0; break;}
for (int j = 0; j < sz(pr); j++)
{
int nxt = (j + 1) % sz(pr);
answer[pr[j]][pr[nxt]] = answer[pr[nxt]][pr[j]] = 1;
}
}
if (!good) return 0;
build(answer);
return 1;
}
bool good = 1;
answer.resize(n);
for (int i = 0; i < n; i++)
answer[i].resize(n, 0);
for (int i = 0; i < n; i++) make(i);
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
if (p[i][j] == 1 || p[i][j] == 2)
{
int a = fnd(i), b = fnd(j);
if (a != b) link(a, b);
}
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
if ((p[i][j] == 1 && fnd(i) != fnd(j)) || (p[i][j] == 0 && fnd(i) == fnd(j))) good = 0;
if (!good) return 0;
bool mk[n], mkr[n];
for (int i = 0; i < n; i++)
{
mk[i] = 1;
mkr[i] = 1;
for (int j = 0; j < n; j++)
if (i != j && p[i][j] == 1) mk[i] = 0;
for (int j = 0; j < n; j++)
if (i != j && p[i][j] == 2) mkr[i] = 0;
}
set <int> se, str; se.clear(); str.clear();
for (int i = 0; i < n; i++)
{
int id = fnd(i);
if (se.find(id) != se.end()) continue;
se.insert(id);
vector <int> c; c.clear();
vector <int> pr; pr.clear();
bool bd = 1;
for (int j = 0; j < n; j++)
{
if (fnd(j) != fnd(i)) continue;
if (mk[j]) c.PB(j);
else pr.PB(j);
if (!mkr[j]) bd = 0;
}
if (sz(c) == 0)
{
if (bd)
{
for (int j = 1; j < sz(pr); j++)
{
int nxt = pr[j - 1];
answer[pr[j]][nxt] = answer[nxt][pr[j]] = 1;
}
continue;
}
int l = -1, r = -1;
for (int j = 0; j < sz(pr); j++)
{
auto it = pr[j];
if (str.find(it) != str.end()) continue;
str.insert(it);
if (r != -1) answer[r][it] = answer[it][r] = 1;
else l = it;
r = it;
int lst = it;
for (int u = j + 1; u < sz(pr); u++)
if (p[pr[u]][it] == 1)
{
str.insert(pr[u]);
answer[pr[u]][lst] = answer[lst][pr[u]] = 1;
lst = pr[u];
}
}
answer[l][r] = answer[r][l] = 1;
continue;
}
for (int j = 1; j < sz(c); j++) answer[c[j]][c[j - 1]] = answer[c[j - 1]][c[j]] = 1;
int l = c[0], r = c.back();
for (int j = 0; j < sz(pr); j++)
{
auto it = pr[j];
if (str.find(it) != str.end()) continue;
str.insert(it);
answer[l][it] = answer[it][l] = 1;
l = it;
int lst = it;
for (int u = j + 1; u < sz(pr); u++)
if (p[pr[u]][it] == 1)
{
str.insert(pr[u]);
answer[pr[u]][lst] = answer[lst][pr[u]] = 1;
lst = pr[u];
}
}
answer[l][r] = answer[r][l] = 1;
}
for (int i = 0; i < n; i++) answer[i][i] = 0;
g = answer;
for (int i = 0; i < n; i++)
{
memset(cnt[i], 0, sizeof(cnt[i]));
glob = i;
dfs(i, -1);
for (int j = 0; j < n; j++)
if (cnt[i][j] != p[i][j]) return 0;
}
build(answer);
return 1;
}
//int main()
//{
//// freopen("help.in", "r", stdin); freopen("help.out", "w", stdout);
//
// ios_base::sync_with_stdio(0); istream::sync_with_stdio(0); cin.tie(0); cout.tie(0);
//
// vector <vector <int> > vr(6);
//
// for (int i = 0; i < 6; i++) {vr[i].resize(6, 0); vr[i][i] = 1;}
//
// vr[0][3] = vr[3][0] = vr[2][4] = vr[4][2] = vr[1][5] = vr[5][1] = 1;
//
// for (int i = 0; i < 6; i++)
// for (int j = 0; j < 6; j++)
// if (vr[i][j] != 1) vr[i][j] = 2;
//
// cout << construct(vr) << endl;
//}
