#include "supertrees.h"
#include <bits/stdc++.h>
struct DSU {
std::vector<int> e;
DSU(int n) : e(n, -1) {}
int find(int u) {
return e[u] < 0 ? u : e[u] = find(e[u]);
}
bool merge(int u, int v) {
u = find(u), v = find(v);
if (u == v) return false;
if (e[u] > e[v]) std::swap(u, v);
e[u] += e[v];
e[v] = u;
return true;
}
bool same(int u, int v) {
return find(u) == find(v);
}
int size(int u) {
return -e[find(u)];
}
};
int construct(std::vector<std::vector<int>> p) {
int n = p.size();
DSU dsu(n);
for (int i = 0; i < n; i++) {
for (int j = i + 1; j < n; j++) {
if (p[i][j] == 3) return false;
if (p[i][j] != 0) {
dsu.merge(i, j);
}
}
}
for (int i = 0; i < n; i++) {
for (int j = i + 1; j < n; j++) {
if (!p[i][j] && dsu.same(i, j)) return false;
}
}
// now we have all the tplt we need
// now what can we do ?
// each tplt has only one fucking cycle
std::vector<std::vector<int>> comps(n);
for (int i = 0; i < n; i++) {
comps[dsu.find(i)].push_back(i);
}
// they must have connected to each other
std::vector<std::vector<int>> b(n, std::vector<int>(n));
DSU lmao(n);
std::vector<std::pair<int, int>> edges;
auto add_edge = [&](int u, int v) -> void {
b[u][v] = b[v][u] = 1;
};
for (int c = 0; c < n; c++) {
if (comps[c].empty()) continue;
std::map<std::vector<int>, std::vector<int>> mp;
for (int u : comps[c]) {
std::vector<int> key;
for (int j = 0; j < n; j++) {
if (p[u][j] == 2) {
key.push_back(j);
}
}
mp[key].push_back(u);
}
std::vector<int> rep;
for (auto& [key, val] : mp) {
int total = key.size() + val.size();
if (total != (int) comps[c].size()) {
return false;
}
for (int i = 0; i + 1 < (int) val.size(); i++) {
add_edge(val[i], val[i + 1]);
}
rep.push_back(val[0]);
}
if (rep.size() == 2) {
// we cannot do a cycle with two
return false;
}
if (rep.size() > 2) {
for (int i = 0; i < (int)rep.size(); i++) {
add_edge(rep[i], rep[(i + 1) % rep.size()]);
}
}
}
build(b);
return 1;
}
#ifdef LOCAL
#include <vector>
#include <cassert>
#include <cstdio>
#include <cstdlib>
#include <string>
static int n;
static std::vector<std::vector<int>> p;
static std::vector<std::vector<int>> b;
static bool called = false;
static void check(bool cond, std::string message) {
if (!cond) {
printf("%s\n", message.c_str());
fclose(stdout);
exit(0);
}
}
void build(std::vector<std::vector<int>> _b) {
check(!called, "build is called more than once");
called = true;
check((int)_b.size() == n, "Invalid number of rows in b");
for (int i = 0; i < n; i++) {
check((int)_b[i].size() == n, "Invalid number of columns in b");
}
b = _b;
}
int main() {
assert(scanf("%d", &n) == 1);
p.resize(n);
for (int i = 0; i < n; i++) {
p[i].resize(n);
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
assert(scanf("%d", &p[i][j]) == 1);
}
}
fclose(stdin);
int possible = construct(p);
check(possible == 0 || possible == 1, "Invalid return value of construct");
if (possible == 1) {
check(called, "construct returned 1 without calling build");
} else {
check(!called, "construct called build but returned 0");
}
printf("%d\n", possible);
if (possible == 1) {
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (j) {
printf(" ");
}
printf("%d", b[i][j]);
}
printf("\n");
}
}
fclose(stdout);
}
#endif
