#include "supertrees.h"
#include <bits/stdc++.h>
using namespace std;
#define ar array
#define sz(v) int(v.size())
int n;
struct DSU {
vector<int> p, sz;
void init(int n){ sz.assign(n, 1); p.resize(n); iota(p.begin(), p.end(), 0); }
int find_set(int v){ return v==p[v]?v:p[v]=find_set(p[v]); }
bool union_sets(int a, int b){
if ((a=find_set(a))==(b=find_set(b))) return 0;
if (sz[a] < sz[b]) swap(a, b);
p[b]=a, sz[a]+=sz[b], sz[b]=0;
return 1;
}
} d;
int construct(vector<vector<int>> g) {
n = sz(g);
vector<vector<int>> ans(n, vector<int>(n));
bool done=0, bad=0;
[&](){ //handle case with a 3
if (done || bad) return;
for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) if (g[i][j] == 3) {
bad=1; return;
}
}();
[&](){ //only 1's (tree)
if (done || bad) return;
for (int i = 0; i < n; i++) for (int j = i+1; j < n; j++) if (g[i][j] != 1) return;
for (int i = 1; i < n; i++) ans[i][0] = ans[0][i] = 1;
build(ans), done=1;
}();
[&](){ //0, 1's (just deal with separate comps)
if (done || bad) return;
for (int i = 0; i < n; i++) for (int j = i+1; j < n; j++) if (g[i][j] != 0 && g[i][j] != 1) return;
d.init(n);
for (int i = 0; i < n; i++) for (int j = i+1; j < n; j++) if (g[i][j])
if (d.union_sets(i, j)) ans[i][j] = ans[j][i] = 1;
for (int i = 0; i < n; i++) for (int j = i+1; j < n; j++)
if ((d.find_set(i) == d.find_set(j))^bool(g[i][j])) return;
build(ans), done=1;
}();
[&](){ //0, 2's (just deal with separate comps, put everything into cycles instead of trees)
if (done || bad) return;
for (int i = 0; i < n; i++) for (int j = i+1; j < n; j++) if (g[i][j] != 0 && g[i][j] != 2) return;
d.init(n);
for (int i = 0; i < n; i++) for (int j = i+1; j < n; j++) if (g[i][j])
d.union_sets(i, j);
for (int i = 0; i < n; i++) for (int j = i+1; j < n; j++)
if ((d.find_set(i) == d.find_set(j))^bool(g[i][j])) return;
vector<vector<int>> comp(n);
for (int i = 0; i < n; i++) comp[d.find_set(i)].push_back(i);
for (int i = 0; i < n; i++) if (sz(comp[i]) > 1){
if (sz(comp[i]) == 2) return;
for (int j = 0; j < sz(comp[i]); j++){
int nxt=(j+1)%sz(comp[i]);
ans[comp[i][j]][comp[i][nxt]] = ans[comp[i][nxt]][comp[i][j]] = 1;
}
}
build(ans), done=1;
}();
return !bad && done;
}
