#include <bits/stdc++.h>
#include "walk.h"
using ll = long long;
template <class T> using Vec = std::vector<T>;
template <class T> using Heap = std::priority_queue<T, Vec<T>, std::greater<T>>;
constexpr ll INF = std::numeric_limits<ll>::max() / 2;
struct RMQ {
int size;
Vec<ll> min;
RMQ(const int n): size(n), min(2 * n, INF) {}
void assign(int i, const ll x) {
i += size;
min[i] = x;
while (i > 1) {
i >>= 1;
min[i] = std::min(min[2 * i], min[2 * i + 1]);
}
}
ll fold(int l, int r) const {
l += size;
r += size;
ll x = INF;
while (l < r) {
if (l & 1) x = std::min(x, min[l++]);
if (r & 1) x = std::min(x, min[--r]);
l >>= 1;
r >>= 1;
}
return x;
}
};
ll min_distance(Vec<int> x, Vec<int> h, Vec<int> l, Vec<int> r, Vec<int> y, int s, int g) {
const int n = (int) x.size();
const int m = (int) y.size();
if (s == 0 and g == n - 1) {
Vec<Vec<int>> start(n), end(n);
for (int i = 0; i < m; ++i) {
start[l[i]].push_back(i);
end[r[i]].push_back(i);
}
Vec<int> cmp = y;
std::sort(cmp.begin(), cmp.end());
cmp.erase(std::unique(cmp.begin(), cmp.end()), cmp.end());
Vec<int> idx(m);
for (int i = 0; i < m; ++i) {
idx[i] = std::lower_bound(cmp.begin(), cmp.end(), y[i]) - cmp.begin();
}
const int sz = (int) cmp.size();
RMQ down(sz), up(sz);
Vec<int> alive(sz);
for (const int j: start[0]) {
down.assign(idx[j], y[j] - y[j]);
up.assign(idx[j], y[j] + y[j]);
alive[idx[j]] += 1;
}
for (int i = 1; i < n; ++i) {
const int height = std::upper_bound(cmp.begin(), cmp.end(), h[i]) - cmp.begin();
for (const auto j: start[i]) {
const ll a = down.fold(0, idx[j] + 1);
const ll b = up.fold(idx[j], sz);
ll d = INF;
if (a != INF) {
d = std::min(d, a + y[j]);
}
if (b != INF) {
d = std::min(d, b - y[j]);
}
if (d != INF) {
down.assign(idx[j], d - y[j]);
up.assign(idx[j], d + y[j]);
} else {
down.assign(idx[j], INF);
down.assign(idx[j], INF);
}
alive[idx[j]] += 1;
}
if (i != n - 1) {
for (const auto j: end[i]) {
alive[idx[j]] -= 1;
if (alive[idx[j]] == 0) {
down.assign(idx[j], INF);
up.assign(idx[j], INF);
}
}
}
}
ll ret = up.fold(0, sz);
return ret == INF ? -1 : (ret + x[n - 1] - x[0]);
}
Vec<std::tuple<int, int, int>> query;
query.reserve(n + m);
for (int i = 0; i < n; ++i) {
query.emplace_back(h[i], n, i);
}
for (int i = 0; i < m; ++i) {
query.emplace_back(y[i], l[i], r[i]);
}
Vec<Vec<ll>> height(n);
Vec<Vec<Vec<std::pair<int, int>>>> graph(n);
std::sort(query.rbegin(), query.rend());
std::map<int, int> alive;
for (const auto [t, u, v]: query) {
if (u == n) {
alive.emplace(x[v], v);
} else {
const auto end = alive.upper_bound(x[v]);
int li = -1, lj = -1;
for (auto itr = alive.lower_bound(x[u]); itr != end; ++itr) {
const auto i = itr -> second;
if (height[i].empty() or height[i].back() != t) {
height[i].push_back(t);
graph[i].emplace_back();
}
const auto j = (int) height[i].size() - 1;
if (li != -1) {
graph[i][j].emplace_back(li, lj);
graph[li][lj].emplace_back(i, j);
}
li = i, lj = j;
}
}
}
Vec<Vec<ll>> dist(n);
for (int i = 0; i < n; ++i) {
height[i].push_back(0);
graph[i].emplace_back();
dist[i].assign(height[i].size(), INF);
}
Heap<std::tuple<ll, int, int>> heap;
const auto push = [&](const int i, const int j, const ll d) {
if (dist[i][j] > d) {
dist[i][j] = d;
heap.emplace(d, i, j);
}
};
push(s, (int) height[s].size() - 1, 0);
while (!heap.empty()) {
const auto [d, i, j] = heap.top();
heap.pop();
if (dist[i][j] < d) {
continue;
}
for (const auto [ni, nj]: graph[i][j]) {
push(ni, nj, d + std::abs(x[i] - x[ni]));
}
if (j > 0) {
push(i, j - 1, d + std::abs(height[i][j] - height[i][j - 1]));
}
if (j + 1 < (int) height[i].size()) {
push(i, j + 1, d + std::abs(height[i][j + 1] - height[i][j]));
}
}
const auto ret = dist[g][height[g].size() - 1];
return ret == INF ? -1 : ret;
}
