#include "walk.h"
#include <bits/stdc++.h>
using namespace std;
#define sz(v) int(v.size())
#define ar array
typedef long long ll;
const int N = 2e5+10;
const ll INF = 1e18+10;
template <class T>
using min_pq = priority_queue<T, vector<T>, greater<T>>;
struct Solver {
int n, m;
vector<pair<int, int>> adj[N];
ll dist[N];
void clear() {
for (int i = 0; i < N; i++) adj[i].clear();
}
void add_edge(int a, int b, int w) {
// cerr << "add_edge: " << a << ' ' << b << endl;
adj[a].emplace_back(b, w);
adj[b].emplace_back(a, w);
}
void dijkstra(int S) {
fill(dist, dist + N, INF);
min_pq<pair<ll, int>> pq;
pq.push({dist[S] = 0, S});
while (!pq.empty()) {
auto [d_c, c] = pq.top(); pq.pop();
if (dist[c] != d_c) continue;
for (auto [nxt, w] : adj[c]) {
if (dist[nxt] > dist[c] + w) {
dist[nxt] = dist[c] + w;
pq.push({dist[nxt], nxt});
}
}
}
}
template <class T>
vector<ll> solve(vector<int> h, vector<int> l, vector<int> r, vector<int> y, vector<T> base) {
n = sz(h), m = sz(l);
auto build = [&]() {
vector<vector<pair<int, int>>> ev(n);
for (int i = 0; i < m; i++) {
ev[l[i]].push_back({i, 0});
ev[r[i]].push_back({i, 1});
}
set<pair<int, int>> s;
for (int i = 0; i < n; i++) {
for (auto [x, b] : ev[i]) if (b == 0) {
auto me = s.insert({y[x], x}).first;
{
auto it = next(me);
if (it != s.end() && it->first <= h[i]) {
add_edge(x, it->second, it->first - y[x]);
}
}
{
if (me != s.begin()) {
auto it = prev(me);
add_edge(x, it->second, y[x] - it->first);
}
}
}
for (auto [x, b] : ev[i]) if (b == 1) {
auto me = s.find({y[x], x});
{
auto it = next(me);
if (it != s.end() && it->first <= h[i]) {
add_edge(x, it->second, it->first - y[x]);
}
}
{
if (me != s.begin()) {
auto it = prev(me);
add_edge(x, it->second, y[x] - it->first);
}
}
s.erase({y[x], x});
}
}
};
build();
int S = m;
for (int i = 0; i < m; i++) if (l[i] == 0 && base[i] < INF) {
add_edge(S, i, base[i]);
}
dijkstra(S);
vector<ll> ans(m);
for (int i = 0; i < m; i++) {
ans[i] = dist[i];
}
return ans;
}
};
Solver solver;
long long min_distance(vector<int> x, vector<int> h, vector<int> l, vector<int> r, vector<int> y, int s, int g) {
int n = sz(x), m = sz(l);
// assert(s == 0 && g == n-1);
vector<ll> dist_left(m, INF);
{
vector<int> nh;
for (int i = s; i >= 0; i--) {
nh.push_back(h[i]);
}
vector<int> nl, nr, ny, ids;
for (int i = 0; i < m; i++) if (l[i] <= s) {
int L = l[i], R = min(s, r[i]);
while (h[R] < y[i]) R--; // TODO optimize
dist_left[i] = 2 * (x[s] - x[R]);
nl.push_back(s - R); nr.push_back(s - L); ny.push_back(y[i]);
ids.push_back(i);
}
solver.clear();
auto calc = solver.solve(nh, nl, nr, ny, ny);
for (int i = 0; i < sz(ids); i++) {
dist_left[ids[i]] += calc[i];
}
}
vector<ll> dist_right(m, INF);
{
vector<int> nh;
for (int i = g; i < n; i++) {
nh.push_back(h[i]);
}
vector<int> nl, nr, ny, ids;
for (int i = 0; i < m; i++) if (g <= r[i]) {
int L = max(g, l[i]), R = r[i];
while (h[L] < y[i]) L++; // TODO optimize
dist_right[i] = 2 * (x[L] - x[g]);
// cerr << "> " << dist_right[i] << endl;
nl.push_back(L - g); nr.push_back(R - g); ny.push_back(y[i]);
ids.push_back(i);
}
solver.clear();
auto calc = solver.solve(nh, nl, nr, ny, ny);
for (int i = 0; i < sz(ids); i++) {
dist_right[ids[i]] += calc[i];
}
}
auto dist_mid = dist_left;
{
vector<int> nh;
for (int i = s; i <= g; i++) {
nh.push_back(h[i]);
}
vector<int> nl, nr, ny, ids;
vector<ll> base;
for (int i = 0; i < m; i++) if (r[i] >= s && l[i] <= g) {
int L = max(s, l[i]), R = min(g, r[i]);
while (L <= R && h[L] < y[i]) L++;
while (R >= L && h[R] < y[i]) R--;
if (L > R) continue;
nl.push_back(L - s); nr.push_back(R - s); ny.push_back(y[i]);
ids.push_back(i);
base.push_back(dist_left[i]);
// cerr << "> " << L << ' ' << R << ' ' << y[i] << ' ' << dist_left[i] << endl;
}
solver.clear();
auto calc = solver.solve(nh, nl, nr, ny, base);
for (int i = 0; i < sz(ids); i++) {
int c = ids[i];
// cerr << "> " << calc[i] << endl;
dist_mid[c] = min(dist_mid[c], calc[i]);
}
}
// cerr << "dists\n";
// for (ll x : dist_left) cerr << x << ' ';
// cerr << endl;
// for (ll x : dist_mid) cerr << x << ' ';
// cerr << endl;
// for (ll x : dist_right) cerr << x << ' ';
// cerr << endl;
// cerr << "end dists\n";
ll ans = INF;
for (int i = 0; i < m; i++) {
ans = min(ans, dist_mid[i] + dist_right[i]);
}
// cerr << x[n-1] - x[0] << ' ' << ans << endl;
if (ans >= INF) return -1;
return ans + x[g] - x[s];
}
