#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;
stype[query] = 2;
vector<pii> verts;
rep2(i,1,n-1) verts.pb({dist[i],i});
sort(all(verts));
min_left = 0;
max_right = query;
set<int> C = {first};
set<int> D = {location[query]};
rep2(i,1,siz(verts)-1)
{
int v = verts[i].ss;
int dist2 = getDistance(v,query);
if(dist[query] + dist2 == dist[v])
{
int dist_end = getDistance(v,min_left);
if(dist_end >= (location[0]-location[min_left]))
{
if(dist[query] < dist[query])
{
location[v] = first - dist[v] + 2 * dist[query];
stype[v] = 1;
}
else
{
location[v] = location[query] - dist2;
stype[v] = 1;
}
}
else
{
auto it = C.upper_bound(location[min_left] + dist_end);
it--;
if(dist[min_left] + dist_end - 2 * ((*it) - location[min_left]) == dist[v])
{
location[v] = location[min_left] + dist_end;
stype[v] = 2;
}
else
{
location[v] = first - dist[v] + 2 * dist[query];
stype[v] = 1;
}
}
}
else
{
int dist_end = getDistance(v,max_right);
if(dist_end >= dist[max_right])
{
location[v] = first + dist[v];
stype[v] = 2;
}
else
{
auto it = D.lower_bound(location[max_right] - dist_end);
if(dist[max_right] + dist_end - 2 * (location[max_right] - (*it)) == dist[v])
{
location[v] = location[max_right] - dist_end;
stype[v] = 1;
}
else
{
location[v] = first + dist[v];
stype[v] = 2;
}
}
}
if(location[v] > location[max_right]) max_right = v;
if(location[v] < location[min_left]) min_left = v;
if(stype[v] == 1) C.insert(location[v]);
else D.insert(location[v]);
}
}
