#include "rail.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;
int dist[5001];
void findLocation(int n, int first, int location[], int stype[])
{
rep2(i,1,n-1)
{
dist[i] = getDistance(0,i);
}
int min_left = first;
location[0] = first;
stype[0] = 1;
int max_right = 1e9;
rep2(i,1,n-1) max_right = min(max_right,dist[i]);
int query = 0;
rep2(i,1,n-1) if(dist[i] == max_right) query = i;
location[query] = first + max_right;
max_right = location[query];
stype[query] = 2;
vector<pii> verts;
rep2(i,1,n-1) verts.pb({dist[i],i});
sort(all(verts));
rep2(i,1,siz(verts)-1)
{
int v = verts[i].ss;
int dist2 = getDistance(v,query);
if(dist[query] + dist2 == dist[v])
{
location[v] = first + dist[query] - dist2;
if(dist2 < min_left)
{
stype[v] = 1;
}
else
{
if(location[v] < min_left)
{
stype[v] = 1;
}
else
{
stype[v] = 2;
}
}
}
else
{
location[v] = first + dist[v];
if(location[v] < max_right)
{
stype[v] = 1;
}
else
{
stype[v] = 2;
}
}
max_right = max(max_right,location[v]);
min_left = min(min_left,location[v]);
}
}
