#include "rail.h"
#include<bits/stdc++.h>
using namespace std;
const int maxn = 5050;
const int inf = 1e9+10;
#define pb push_back
#define mp make_pair
#define fr first
#define sc second
#define all(x) x.begin(),x.end()
int n;
int d[maxn][maxn];
int p[maxn], tp[maxn];
int CNT =0;
int dist(int a, int b) {
if(a == b) return d[a][b] = 0;
if(d[a][b] != -1) return d[a][b];
CNT++;
assert(CNT <= 3*n-2);
return d[a][b] = getDistance(a,b);
}
void findLocation(int N, int first, int location[], int stype[]) {
n = N;
for(int i = 0; i < n; i++){
p[i] = -1;
for(int j = 0; j < n; j++) {
d[i][j] = -1;
}
}
p[0] = first;
tp[0] = 0;
// find the closest to 0
int b = -1;
for(int i = 1; i < n; i++) {
if(b == -1 || dist(0,i) < dist(0,b)) b = i;
}
p[b] = p[0]+dist(0,b);
tp[b] = 1;
// find the closest to b
// int a = -1;
// for(int i = 0; i < n; i++) {
// if(i == b) continue;
// if(a == -1 || dist(b,i) < dist(b,a)) a = i;
// }
// p[a] = p[b]-dist(b,a);
// tp[a] = 0;
int a = 0;
int a1 = -1;
for(int i = 0; i < n; i++) {
if(i == b) continue;
if(a1 == -1 || dist(b,i) < dist(b,a1)) a1 = i;
}
p[a1] = p[b]-dist(b,a1);
tp[a1] = 0;
// location[a] = p[a]; stype[a] = tp[a]+1;
// location[b] = p[b]; stype[b] = tp[b]+1;
// for(int i = 0; i < n; i++) {
// if(i == a || i == b) continue;
// if(dist(a,i) <= dist(b,i)) {
// location[i] = p[a]+dist(a,i);
// stype[i] = 2;
// }
// else {
// location[i] = p[b]-dist(b,i);
// stype[i] = 1;
// }
// }
vector<pair<int,int>> lft,rgt;
for(int i = 0; i < n; i++) {
if(i == a || i == b) continue;
if(dist(a,i)-(p[a1]-p[a]) < dist(b,i)) {
rgt.pb(mp(dist(a,i),i));
}
else {
lft.pb(mp(dist(b,i),i));
}
}
sort(all(rgt));
sort(all(lft));
int lastdw = a;
int lastup = b;
a = 0;
assert(CNT <= 2*n-2);
for(int i = 0; i < rgt.size(); i++) {
int u = rgt[i].sc;
int pup = p[a]+dist(a,u);
int pdw = p[lastup]-dist(u,lastup);
int v = lastup;
for(int j = 0; j < i; j++) {
int v1 = rgt[j].sc;
if(tp[v1] == 1 && p[v1] > pdw) {
v = v1;
break;
}
}
if(dist(a,u) == dist(a,v)+p[v]-pdw) {
p[u] = pdw;
tp[u] = 0;
}
else {
p[u] = pup;
tp[u] = 1;
lastup = u;
}
}
for(int i = 0; i < n; i++) {
if(dist(b,i) < dist(a,i)) {
if(dist(b,i) < dist(b,a) && p[i] == -1) {
p[i] = p[b]-dist(b,i);
tp[i] = 0;
}
}
}
for(int i = 0; i < lft.size(); i++) {
int u = lft[i].sc;
if(p[u] != -1) continue;
int pdw = p[b]-dist(b,u);
int pup = p[lastdw]+dist(u,lastdw);
int v = lastdw;
for(int j = 0; j < i; j++) {
int v1 = lft[j].sc;
if(tp[v1] == 0 && p[v1] < pup) {
v = v1;
break;
}
}
if(dist(b,u) == dist(b,v) + pup-p[v]) {
p[u] = pup;
tp[u] = 1;
}
else {
p[u] = pdw;
tp[u] = 0;
lastdw = u;
}
// p[u] = inf;
// for(int j = 0; j < i; j++) {
// int v = lft[j].sc;
// if(tp[v] == 0 && 2*p[v]+dist(b,u)-p[b] > p[v] && dist(b,u) == dist(b,v)+dist(v,u)) {
// p[u] = min(p[u],2*p[v]+dist(b,u)-p[b]);
// }
// }
// if(p[u] == inf) {
// tp[u] = 0;
// p[u] = p[b]-dist(b,u);
// }
// else {
// tp[u] = 1;
// }
}
for(int i = 0; i < n; i++) {
location[i] = p[i];
stype[i] = tp[i]+1;
// cout << i << " - " << p[i] << " " << tp[i]+1 << endl;
}
}
