#include "supertrees.h"
/*
ID: awesome35
LANG: C++14
TASK: vans
*/
#define _CRT_SECURE_NO_WARNINGS
#include<bits/stdc++.h>
#include<unordered_set>
#include<unordered_map>
#include<chrono>
using namespace std;
typedef pair<int, int> pii;
typedef long long ll;
typedef pair<ll, ll> pll;
typedef long double ld;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<pair<int, int>> vpi;
typedef vector<pair<ll, ll>> vpll;
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)
#define pb push_back
#define mp make_pair
#define rsz resize
#define sz(x) int(x.size())
#define all(x) x.begin(),x.end()
#define f first
#define s second
#define cont continue
#define endl '\n'
#define ednl '\n'
#define test int testc;cin>>testc;while(testc--)
#define pr(a, b) trav(x,a)cerr << x << b; cerr << endl;
#define message cout << "Hello World" << endl;
//const int dx[4] = { 1,0,-1,0 }, dy[4] = { 0,1,0,-1 }; // for every grid problem!!
const ll linf = 4000000000000000000LL;
const ll inf = 1000000007;//998244353
const ld pi = 3.1415926535;
void pv(vi a) { trav(x, a)cout << x << " "; cout << endl; }void pv(vll a) { trav(x, a)cout << x << " "; cout << endl; }void pv(vector<vi>a) {
F0R(i, sz(a)) { cout << i << endl; pv(a[i]); cout << endl; }
}void pv(vector<vll>a) { F0R(i, sz(a)) { cout << i << endl; pv(a[i]); }cout << endl; }void pv(vector<string>a) { trav(x, a)cout << x << endl; cout << endl; }
void setIO(string s) {
ios_base::sync_with_stdio(0); cin.tie(0);
if (sz(s))
{
freopen((s + ".in").c_str(), "r", stdin);
if (s != "ioi")
freopen((s + ".out").c_str(), "w", stdout);
}
}
int n;
vector<vi>a, ans;
int val = 0;
bool sub1()
{
F0R(i, n)F0R(j, n)if (a[i][j] != 1)return 0;
val = 1;
F0R(i, n - 1)ans[i][i + 1] = 1, ans[i + 1][i] = 1;
build(ans);
return 1;
}
vi link, sizes;
int find(int i)
{
return link[i] == i ? i : link[i] = find(link[i]);
}
void unite(int i, int j)
{
i = find(i), j = find(j);
if (i != j)
{
if (sizes[i] > sizes[j])swap(i, j);
link[i] = j;
sizes[j] += sizes[i];
}
}
bool sub2()
{
F0R(i, n)F0R(j, n)if (a[i][j] > 1)return 0;
link.rsz(n);
iota(all(link), 0);
sizes.rsz(n, 1);
F0R(i, n)F0R(j, n)if (a[i][j])unite(i, j);
vector<vi>t(n);
F0R(i, n)t[find(i)].pb(i);
val = 1;
F0R(i, n)
{
F0R(j, sz(t[i]))FOR(k, j + 1, sz(t[i]))
{
if (!a[t[i][j]][t[i][k]])
{
val = 0;
return 1;
}
}
}
F0R(i, n)
{
F0R(j, sz(t[i]) - 1)
{
ans[t[i][j]][t[i][j + 1]] = 1;
ans[t[i][j + 1]][t[i][j]] = 1;
}
}
build(ans);
return 1;
}
bool sub3()
{
F0R(i, n)FOR(j, i + 1, n)if (a[i][j] == 1 || a[i][j] == 3)return 0;
link.rsz(n);
iota(all(link), 0);
sizes.rsz(n, 1);
F0R(i, n)F0R(j, n)if (a[i][j])unite(i, j);
vector<vi>t(n);
F0R(i, n)t[find(i)].pb(i);
val = 1;
F0R(i, n)
{
if (sz(t[i]) == 2)
{
val = 0;
return 1;
}
F0R(j, sz(t[i]))FOR(k, j + 1, sz(t[i]))
{
if (!a[t[i][j]][t[i][k]])
{
val = 0;
return 1;
}
}
}
F0R(i, n)
{
if (sz(t[i]) == 1)continue;
F0R(j, sz(t[i]))
{
ans[t[i][j]][t[i][(j + 1) % sz(t[i])]] = 1;
ans[t[i][(j + 1) % sz(t[i])]][t[i][j]] = 1;
}
}
build(ans);
return 1;
}
struct uf
{
vi link, sizes;
void init(int n)
{
link.rsz(n);
iota(all(link), 0);
sizes.rsz(n, 1);
}
int find(int i)
{
return link[i] == i ? i : link[i] = find(link[i]);
}
void unite(int i, int j)
{
i = find(i), j = find(j);
if (i != j)
{
if (sizes[i] > sizes[j])swap(i, j);
link[i] = j;
sizes[j] += sizes[i];
}
}
};
bool sub45()
{
F0R(i, n)FOR(j, i + 1, n)if (a[i][j] == 3)return 0;
uf bridge;// the arms of the graph.
bridge.init(n);
F0R(i, n)FOR(j, i + 1, n)if (a[i][j] == 1)bridge.unite(i, j);
uf comp;// components of the graph.
comp.init(n);
F0R(i, n)FOR(j, i + 1, n)if (a[i][j])comp.unite(bridge.find(i), bridge.find(j));
vector<vi>t(n), t1(n);
vi index1(n), index(n, -1);
F0R(i, n)
{
t1[bridge.find(i)].pb(i);
index1[i] = bridge.find(i);
t[comp.find(i)].pb(i);
index[i] = comp.find(i);
}
// check if possible
F0R(i, n)
{
FOR(j, i + 1, n)
{
if (a[i][j] == 0)
{
if (index[i] == index[j])
{
val = 0;
return 1;
}
}
else if (a[i][j] == 1)
{
if (index1[i] != index1[j])
{
val = 0;
return 1;
}
}
else
{
if (index1[i] == index1[j])
{
// bug
val = 0;
return 1;
}
}
}
}
// else
val = 1;
F0R(i, n)
{
F0R(j, sz(t1[i]) - 1)
{
ans[t1[i][j]][t1[i][j + 1]] = 1;
ans[t1[i][j + 1]][t1[i][j]] = 1;
}
}
F0R(i, n)
{
if (sz(t[i]) == 1)continue;
F0R(j, sz(t[i]))
{
ans[t[i][j]][t[i][(j + 1) % sz(t[i])]] = 1;
ans[t[i][(j + 1) % sz(t[i])]][t[i][j]] = 1;
}
}
build(ans);
return 1;
}
int construct(vector<vi>t)
{
n = sz(t);
a = t;
ans.rsz(n, vi(n));
if (sub1())return val;
if (sub2())return val;
if (sub3())return val;
if (sub45())return val;
assert(0);
return 0;
}
