#include <bits/stdc++.h>
#define DEBUG false
#include "rail.h"
using namespace std;
const int MAX_N = 5e3 + 10;
const int INF = 1e9 + 7;
int min_dist, firstD, latestC, latestD;
int dist[MAX_N][MAX_N];
vector <pair <int, int>> L, R;
bool processed[MAX_N];
void findLocation(int N, int first, int location[], int stype[]) {
for(int i = 1; i < N; i++) {
dist[0][i] = dist[i][0] = getDistance(0, i);
}
processed[0] = true;
location[0] = first;
stype[0] = 1;
min_dist = INF;
for(int i = 1; i < N; i++) {
if(min_dist > dist[0][i]) {
min_dist = dist[0][i];
firstD = i;
}
}
processed[firstD] = true;
location[firstD] = first + min_dist;
stype[firstD] = 2;
for(int i = 1; i < N; i++) {
if(i != firstD) {
dist[firstD][i] = dist[i][firstD] = getDistance(firstD, i);
}
}
for(int i = 1; i < N; i++) {
if(i == firstD) {
continue;
}
if(dist[firstD][i] < dist[0][i]) { // it is on the left of the station 0
location[i] = location[firstD] - dist[firstD][i];
stype[i] = 1;
if(location[i] < first) {
L.emplace_back(location[i], i);
}
else {
processed[i] = true;
}
}
else { // it is on the right of the first station that is type D
location[i] = first + dist[0][i];
stype[i] = 2;
R.emplace_back(location[i], i);
}
}
sort(L.rbegin(), L.rend());
sort(R.begin(), R.end());
if(!L.empty()) {
latestC = L.front().second;
latestD = firstD;
location[latestC] = location[firstD] - dist[firstD][latestC];
stype[latestC] = 1;
processed[latestC] = true;
for(auto [distFromFirstD, idx] : L) {
if(idx == latestC) {
continue;
}
processed[idx] = true;
dist[idx][latestC] = dist[latestC][idx] = getDistance(latestC, idx);
if(dist[latestC][idx] < dist[latestD][idx]) {
location[idx] = location[latestC] + dist[latestC][idx];
stype[idx] = 2;
for(int i = 0; i < N; i++) {
if(processed[i] == true) {
continue;
}
dist[idx][i] = dist[i][idx] = dist[latestD][i] - (location[latestD] - location[idx]);
}
latestD = idx;
}
else {
location[idx] = location[latestD] - dist[latestD][idx];
stype[idx] = 1;
latestC = idx;
}
}
}
if(!R.empty()) {
latestC = 0;
latestD = R.front().second;
location[latestD] = first + dist[0][latestD];
stype[latestD] = 2;
processed[latestD] = true;
for(auto [distFrom0, idx] : R) {
if(idx == latestD) {
continue;
}
processed[idx] = true;
dist[idx][latestD] = dist[latestD][idx] = getDistance(latestD, idx);
if(DEBUG) {
cout << "pos : " << latestC << ' ' << latestD << endl;
cout << "dist: " << dist[latestC][idx] << ' ' << dist[latestD][idx] << endl;
}
if(dist[latestD][idx] < dist[latestC][idx]) {
location[idx] = location[latestD] - dist[latestD][idx];
stype[idx] = 1;
for(int i = 0; i < N; i++) {
if(processed[i] == true) {
continue;
}
dist[idx][i] = dist[i][idx] = dist[latestC][i] - (location[idx] - location[latestC]);
}
latestC = idx;
}
else {
location[idx] = location[latestC] + dist[latestC][idx];
stype[idx] = 2;
latestD = idx;
}
}
}
if(DEBUG) {
for(int i = 0; i < N; i++) {
cout << stype[i] << ' ' << location[i] << endl;
}
}
}
