#include <bits/stdc++.h>
// #include "grader.cpp"
using namespace std;
typedef pair<int, int> pii;
const int N = 2e5 + 10;
bool vis[N];
vector<int> g[N];
void dfs(int v){
vis[v] = 1;
for (int u : g[v])
if (!vis[u]) dfs(u);
}
void build(vector<int> u, vector<int> v, vector<int> a, vector<int> b);
int construct_roads(vector<int> x, vector<int> y){
int n = x.size();
vector<int> edge[2], bench[2];
vector<pii> vec;
for (int i = 0; i < n; i ++)
vec.push_back({x[i], y[i]});
sort(vec.begin(), vec.end());
map<pair<int, int>, int> ind;
map<pair<int, int>, bool> done;
for (int i=0; i<n; i++)
ind[{x[i], y[i]}] = i;
bool bad = 0;
for (int i=0; i<n; i++){
int px = vec[i].first;
int py = vec[i].second;
int cur = ind[{px, py}];
if (ind.find({px, py + 2}) != ind.end()){
edge[0].push_back(cur);
edge[1].push_back(ind[{px, py + 2}]);
g[cur].push_back(ind[{px, py + 2}]);
g[ind[{px, py + 2}]].push_back(cur);
if (!done[{px - 1, py + 1}]){
done[{px - 1, py + 1}] = 1;
bench[0].push_back(px - 1);
bench[1].push_back(py + 1);
}
else if (!done[{px + 1, py + 1}]){
done[{px + 1, py + 1}] = 1;
bench[0].push_back(px + 1);
bench[1].push_back(py + 1);
}
else
bad = 1;
}
if (ind.find({px + 2, py}) != ind.end()){
edge[0].push_back(cur);
edge[1].push_back(ind[{px + 2, py}]);
g[cur].push_back(ind[{px + 2, py}]);
g[ind[{px + 2, py}]].push_back(cur);
if (!done[{px + 1, py - 1}]){
done[{px + 1, py - 1}] = 1;
bench[0].push_back(px + 1);
bench[1].push_back(py - 1);
}
else if (!done[{px + 1, py + 1}]){
done[{px + 1, py + 1}] = 1;
bench[0].push_back(px + 1);
bench[1].push_back(py + 1);
}
else
bad = 1;
}
}
dfs(0);
for (int v = 0; v < n; v ++)
if (!vis[v]) bad = 1;
if (bad)
return 0;
build(edge[0], edge[1], bench[0], bench[1]);
return 1;
}
