#include <bits/stdc++.h>
#define pb push_back
using namespace std;
void build(vector<int> u, vector<int> v, vector<int> a, vector<int> b);
int construct_roads(vector<int> x, vector<int> y);
#ifdef __DEBUG__
void build(vector<int> u, vector<int> v, vector<int> a, vector<int> b){}
#endif
constexpr static int SIZE = 200001;
vector<array<int, 3>> m;
vector<array<int, 2>> pos;
set<array<int, 2>> fountains;
bitset<SIZE> visited;
vector<int> uu, vv, aa, bb;
int get_node(int x, int y)
{
array<int, 3> a = {x, y, 0};
auto it = lower_bound(m.begin(), m.end(), a);
if (it != m.end() && (*it)[0] == x && (*it)[1] == y)
return (*it)[2];
return -1;
}
void dfs(int node, int last, int fx, int fy);
bool try_insert(int u, int v, int fx, int fy)
{
if (v != -1 && !visited[v] && fountains.find({fx, fy}) == fountains.end())
{
uu.pb(u), vv.pb(v), aa.pb(fx), bb.pb(fy);
fountains.insert({fx, fy});
dfs(v, u, fx, fy);
return true;
}
return false;
}
// direction: 1 vertical, 0 horizontal
// orientation: 1 ccw, 0 cw
void dfs(int node, int last, int fx, int fy)
{
visited[node] = true;
auto [node_x, node_y] = pos[node];
auto [last_x, last_y] = pos[last];
int left_x = 2 * fx - last_x, left_y = 2 * fy - last_y;
int top_x = 2 * node_x - last_x, top_y = 2 * node_y - last_y;
int right_x = 2 * node_x - left_x, right_y = 2 * node_y - left_y;
int left_fx = node_x + left_x - fx, left_fy = node_y + left_y - fy;
int left = get_node(left_x, left_y), top = get_node(top_x, top_y), right = get_node(right_x, right_y);
if (try_insert(node, left, left_fx, left_fy))
{
int top_fx = top_x + node_x - left_fx, top_fy = top_y + node_y - left_fy;
int right_fx, right_fy;
if (try_insert(node, top, top_fx, top_fy))
right_fx = node_x + right_x - top_fx, right_fy = node_y + right_y - top_fy;
else
right_fx = top_fx, right_fy, top_fy;
try_insert(node, right, right_fx, right_fy);
}
else
{
int right_fx = node_x * 2 - fx, right_fy = node_y * 2 - fy;
try_insert(node, right, right_fx, right_fy);
int top_fx = left_fx, top_fy = left_fy;
try_insert(node, top, top_fx, top_fy);
}
}
int construct_roads(vector<int> x, vector<int> y)
{
for (int i = 0; i < x.size(); i++)
{
m.pb({x[i], y[i], i});
pos.pb({x[i], y[i]});
}
sort(m.begin(), m.end());
int a = m[0][2];
visited[a] = true;
int b = get_node(m[0][0], m[0][1] + 2);
if (b != -1)
{
uu.pb(a), vv.pb(b), aa.pb(m[0][0] -1), bb.pb(m[0][1] + 1);
fountains.insert({m[0][0] - 1, m[0][1] + 1});
dfs(b, a, m[0][0] - 1, m[0][1] + 1);
}
int c = get_node(m[0][0] + 2, m[0][1]);
if (c != -1 && !visited[c])
{
uu.pb(a), vv.pb(c), aa.pb(m[0][0] + 1), bb.pb(m[0][1] - 1);
fountains.insert({m[0][0] + 1, m[0][1] - 1});
dfs(c, a, m[0][0] + 1, m[0][1] - 1);
}
if (visited.count() == x.size())
{
build(uu, vv, aa, bb);
return 1;
}
return 0;
}
#ifdef __DEBUG__
int main()
{
int n;
cin >> n;
vector<int> x(n), y(n);
for (int i = 0; i < n; i++)
cin >> x[i] >> y[i];
if (construct_roads(x, y))
{
cout << "YES\n";
for (int i = 0; i < uu.size(); i++)
cout << uu[i] << "-" << vv[i] << ": (" << aa[i] << ", " << bb[i] <<")\n";
}
else
{
cout << "NO\n";
}
}
#endif
