#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
#include <rail.h>
#include <cstdio>
using namespace std;
#ifndef ONLINE_JUDGE
#define dbg(x) cerr << #x <<" "; print(x); cerr << endl;
#else
#define dbg(x)
#endif
#define sz(x) (int((x).size()))
#define len(x) (int)x.length()
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define clr(x) (x).clear()
#define uniq(x) x.resize(unique(all(x)) - x.begin());
#define pb push_back
#define popf pop_front
#define popb pop_back
#define ld long double
#define ll long long
void print(long long t) {cerr << t;}
void print(int t) {cerr << t;}
void print(string t) {cerr << t;}
void print(char t) {cerr << t;}
void print(double t) {cerr << t;}
void print(unsigned long long t) {cerr << t;}
void print(long double t) {cerr << t;}
template <class T, class V> void print(pair <T, V> p);
template <class T> void print(vector <T> v);
template <class T> void print(set <T> v);
template <class T, class V> void print(map <T, V> v);
template <class T> void print(multiset <T> v);
template <class T> void print(T v[],T n) {cerr << "["; for(int i = 0; i < n; i++) {cerr << v[i] << " ";} cerr << "]";}
template <class T, class V> void print(pair <T, V> p) {cerr << "{"; print(p.first); cerr << ","; print(p.second); cerr << "}";}
template <class T> void print(vector <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(deque <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(set <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(multiset <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T, class V> void print(map <T, V> v) {cerr << "[ "; for (auto i : v) {print(i); cerr << " ";} cerr << "]";}
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
#define nl '\n'
// for random generations
mt19937 myrand(chrono::steady_clock::now().time_since_epoch().count());
// mt19937 myrand(131);
// for grid problems
int dx[8] = {-1,0,1,0,1,-1,1,-1};
int dy[8] = {0,1,0,-1,1,1,-1,-1};
long long ka() {
long long x = 0;
bool z = false;
while (1)
{
char y = getchar();
if (y == '-')
z = true;
else if ('0' <= y && y <= '9')
x = x * 10 + y - '0';
else
{
if (z)
x *= -1;
return x;
}
}
}
// lowest / (1 << 17) >= 1e5 / (1 << 18) >= 2e5 / (1 << 21) >= 1e6
void fastIO() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr); cout.tie(nullptr);
}
// file in/out
void setIO(string str = "") {
fastIO();
if (str != "") {
freopen((str + ".in").c_str(), "r", stdin);
freopen((str + ".out").c_str(), "w", stdout);
} else {
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
}
}
// Indexed Set
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
const int N = 5015;
int getDistance(int i, int j);
long long dd[N][N];
void findLocation(int n, int first, int location[], int stype[]) {
location[0] = first;
stype[0] = 1;
if(n == 1) {
return;
}
vector<pair<int, int>> dist;
for(int i = 0; i < n; i++) {
for(int j = i + 1; j < n; j++) {
dd[i][j] = getDistance(i, j);
dd[j][i] = dd[i][j];
}
}
for(int i = 1; i < n; i++) {
dist.emplace_back(dd[0][i], i);
}
sort(all(dist));
long long start = 0;
long long motik = dist[0].second;
stype[motik] = 2;
location[motik] = first + dist[0].first;
dist.clear();
for(int i = 0; i < n; i++) {
if(i == motik) continue;
dist.emplace_back(dd[motik][i], i);
}
sort(all(dist));
start = dist[0].second;
location[dist[0].second] = location[motik] - dist[0].first;
stype[dist[0].second] = 1;
dist.clear();
for(int i = 0; i < n; i++) {
if(i == start) {
continue;
}
dist.emplace_back(dd[motik][i], i);
}
sort(all(dist));
vector<long long> rig_up, lef_dw;
int mt = -1;
for(int i = 1; i < sz(dist); i++) {
int cur = dist[i].second;
if(dd[start][cur] < dd[motik][cur]) {
if(rig_up.empty()) {
stype[cur] = 2;
location[cur] = location[start] + dd[start][cur];
rig_up.push_back(cur);
} else {
vector<pair<long long, long long>> dists;
int ok = 0;
for(auto j: rig_up) {
if(dd[start][j] + dd[j][cur] == dd[start][cur]) {
stype[cur] = 1;
location[cur] = location[j] - dd[j][cur];
ok = 1;
break;
}
}
if(!ok) {
stype[cur] = 2;
location[cur] = location[start] + dd[start][cur];
rig_up.push_back(cur);
}
}
} else {
if(lef_dw.empty()) {
stype[cur] = 1;
location[cur] = location[motik] - dd[motik][cur];
lef_dw.push_back(cur);
} else {
int ok = 0;
for(auto j: lef_dw) {
if((dd[motik][j] + dd[j][cur]) == dd[motik][cur]) {
stype[cur] = 2;
location[cur] = location[j] + dd[j][cur];
ok = 1;
break;
}
}
if(!ok) {
stype[cur] = 1;
location[cur] = location[motik] - dd[motik][cur];
lef_dw.push_back(cur);
}
}
}
}
}
