#include<bits/stdc++.h>
using namespace std;
#include "rail.h"
#define F first
#define S second
typedef int ll;
int const M = 5e3 + 20;
int Dis[M][M] , mn[M] , closer[M] , cur , n;
bool vis[M];
set<ll>TypeC , TypeD;
bool cmp(int a , int b) {
return (Dis[0][a] < Dis[0][b]);
}
inline ll dis(int a , int b) {
if(a == b) return 0;
if(a > b) swap(a , b);
return Dis[a][b];
}
inline ll Getbehind(int node) {
int Mn = 1e9;
for(int next = 0 ; next < n ; ++next) {
if(dis(node , next) == mn[node] + dis(closer[node] , next) && dis(closer[node] , next) > mn[node]) {
Mn = min(Mn , dis(node , next));
}
}
int res = 0;
for(int next = 0 ; next < n ; ++next) {
if(dis(node , next) == mn[node] + dis(closer[node] , next) && dis(closer[node] , next) > mn[node]) {
if(dis(node , next) == Mn) res = next;
}
}
return res;
}
void findLocation(int x , int first , int location[], int stype[]) {
n = x;
for(int i = 0 ; i < n ; ++i) {
mn[i] = 1e9;
for(int j = i + 1 ; j < n ; ++j)
Dis[i][j] = getDistance(i , j);
for(int j = 0 ; j < n ; ++j) {
if(i == j) continue;
if(dis(i , j) < mn[i]) closer[i] = j;
mn[i] = min(mn[i] , dis(i , j));
}
}
stype[0] = 1;
location[0] = first;
set<ll>st;
st.insert(0);
while(st.size()) {
int node = *st.begin();
st.erase(st.begin());
if(vis[node]) continue;
vis[node] = 1;
if(stype[node] == 1) {
int Left = Getbehind(node);
if(Left) {
location[Left] = location[node] + mn[node] - dis(closer[node] , Left);
stype[Left] = 1;
st.insert(Left);
}
location[closer[node]] = location[node] + mn[node];
stype[closer[node]] = 2;
st.insert(closer[node]);
}
else {
int Right = Getbehind(node);
if(Right) {
location[Right] = location[node] - mn[node] + dis(closer[node] , Right);
stype[Right] = 2;
st.insert(Right);
}
location[closer[node]] = location[node] - mn[node];
stype[closer[node]] = 1;
st.insert(closer[node]);
}
}
for(int i = 0 ; i < n ; ++i) for(int j = 0 ; j < n ; ++j) Dis[i][j] = dis(i , j);
int a = 0 , b , MinDis = 1e9;
location[a] = first;
stype[a] = 1;
TypeC.insert(location[a]);
for(int station = 1 ; station < n ; ++station) {
//Dis[a][station] = getDistance(a , station);
if(Dis[a][station] < MinDis) {
b = station;
MinDis = Dis[a][b];
}
}
location[b] = location[a] + Dis[a][b];
stype[b] = 2;
TypeD.insert(location[b]);
vector<ll>rem;
for(int station = 1 ; station < n ; ++station) {
if(station == b) continue;
//Dis[b][station] = getDistance(b , station);
rem.push_back(station);
}
sort(rem.begin() , rem.end() , cmp);
int LeftMost = a , RightMost = b;
for(auto station : rem) {
if(Dis[a][station] < Dis[b][station]) {
//int CurDis = getDistance(RightMost , station);
int CurDis = dis(RightMost , station);
int Expect = location[RightMost] - CurDis;
auto it = TypeD.lower_bound(Expect);
if(*it - location[a] + *it - Expect == Dis[a][station] && Expect > location[b]) {
assert(stype[station] == 1);
location[station] = Expect;
stype[station] = 1;
TypeC.insert(location[station]);
} else {
//assert(stype[station] == 2);
RightMost = station;
location[RightMost] = location[a] + Dis[a][RightMost];
stype[RightMost] = 2;
TypeD.insert(location[RightMost]);
}
}
else {
//int CurDis = getDistance(LeftMost , station);
int CurDis = dis(LeftMost , station);
int Expect = location[LeftMost] + CurDis;
auto it = TypeC.upper_bound(Expect); --it;
if(location[b] - *it + Expect - *it == Dis[b][station] && Expect < location[a]) {
assert(stype[station] == 2);
location[station] = Expect;
stype[station] = 2;
TypeD.insert(location[station]);
} else {
//assert(stype[station] == 1);
LeftMost = station;
location[LeftMost] = location[b] - Dis[b][LeftMost];
stype[LeftMost] = 1;
TypeC.insert(location[LeftMost]);
}
}
}
return;
}
