#include "rail.h"
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vii;
typedef vector<ll> vll;
typedef vector<pii> vpii;
typedef vector<pll> vpll;
typedef vector<vii> vvii;
typedef vector<vll> vvll;
typedef vector<vpii> vvpii;
typedef vector<vpll> vvpll;
#define ffor(i, a, b) for (ll i = (a); i < (ll)(b); i++)
#define fford(i, a, b) for (ll i = (a); i > (ll)(b); i--)
#define rep(i, n) ffor(i, 0, n)
#define forin(x, a) for (auto &x: a)
#define all(a) a.begin(), a.end()
map<pii, int> memo;
int dist(int i, int j) {
if (i > j) {
swap(i, j);
}
if (!memo[{i, j}]) {
memo[{i, j}] = getDistance(i, j);
}
return memo[{i, j}];
}
void findLocation(int N, int first, int location[], int stype[]) {
set<pii> cs, ds;
location[0] = first;
stype[0] = 1;
int closest = 1, mindist = dist(0, 1);
ffor(i, 2, N) {
if (dist(0, i) < mindist) {
mindist = dist(0, i);
closest = i;
}
}
location[closest] = first + dist(0, closest);
stype[closest] = 2;
vii left, right;
ffor(i, 1, N) {
if (i != closest) {
if (dist(0, i) == dist(0, closest) + dist(closest, i)) {
left.emplace_back(i);
} else {
right.emplace_back(i);
}
}
}
function<void(vii&, int, bool)> search;
search = [&](vii &curr, int bound, bool lbound) {
if (curr.empty()) {
return;
}
int closest2 = curr[0], mindist2 = dist(curr[0], bound);
forin(i, curr) {
if (dist(i, bound) < mindist2) {
mindist2 = dist(i, bound);
closest2 = i;
}
}
if (lbound) {
location[closest2] = location[bound] + dist(closest2, bound);
stype[closest2] = 2;
vii right2;
int nbound = bound;
forin(i, curr) {
if (i != closest2) {
if (dist(bound, i) == dist(bound, closest2) + dist(closest2, i)) {
location[i] = location[closest2] - dist(closest2, i);
stype[i] = 1;
if (location[i] > location[nbound]) {
nbound = i;
}
} else {
right2.emplace_back(i);
}
}
}
search(right2, nbound, true);
} else {
location[closest2] = location[bound] - dist(closest2, bound);
stype[closest2] = 1;
vii left2;
int nbound = bound;
forin(i, curr) {
if (i != closest2) {
if (dist(bound, i) == dist(bound, closest2) + dist(closest2, i)) {
location[i] = location[closest2] + dist(closest2, i);
stype[i] = 2;
if (location[i] < location[nbound]) {
nbound = i;
}
} else {
left2.emplace_back(i);
}
}
}
search(left2, nbound, false);
}
};
search(left, closest, false);
search(right, 0, true);
}
