#include <bits/stdc++.h>
using namespace std;
#include "meetings.h"
const int N = 750000, L = __lg(N) + 1;
struct segtree {
segtree *left = nullptr, *right = nullptr;
long long lazy_m = -1, lazy_b = 0, first = 0, last = 0;
void apply(long long m, long long b, int l, int r) {
if (m == -1) {
first += b;
last += b;
lazy_b += b;
} else {
first = m * l + b;
last = m * r + b;
lazy_m = m;
lazy_b = b;
}
}
void push(int l, int r) {
if (!left) {
left = new segtree();
right = new segtree();
}
int m = (l + r) / 2;
left->apply(lazy_m, lazy_b, l, m);
right->apply(lazy_m, lazy_b, m + 1, r);
lazy_m = -1, lazy_b = 0;
}
void pull() {
first = left->first;
last = right->last;
}
long long query(int a, int l, int r) {
if (l == r) {
return first;
} else {
push(l, r);
int m = (l + r) / 2;
if (a <= m) {
return left->query(a, l, m);
} else {
return right->query(a, m + 1, r);
}
}
}
void update(int a, int b, long long x, long long y, long long z, int l, int r) {
if (b < l || r < a) {
return;
} else if (a <= l && r <= b) {
if (first + x <= y * l + z) {
apply(-1, x, l, r);
return;
} else if (last + x >= y * r + z) {
apply(y, z, l, r);
return;
}
}
push(l, r);
int m = (l + r) / 2;
left->update(a, b, x, y, z, l, m);
right->update(a, b, x, y, z, m + 1, r);
pull();
}
};
int adj[N][2], first[N], last[N], n;
vector<array<int, 3>> queries[N];
array<int, 2> sparse[L][N];
long long cost[N], ans[N];
vector<int> h;
segtree *mini;
void dfs(int u) {
for (auto c : adj[u]) {
if (c != -1) {
dfs(c);
}
}
long long maxi = h[u];
for (auto [l, r, i] : queries[u]) {
ans[i] = min(ans[i], (u - l + 1) * maxi +
(r == u ? 0 : mini->query(r, 0, n - 1)));
}
first[u] = adj[u][0] == -1 ? u : first[adj[u][0]];
last[u] = adj[u][1] == -1 ? u : last[adj[u][1]];
mini->update(u, last[u], (u - first[u] + 1) * maxi,
maxi, (adj[u][0] == -1 ? 0 : mini->query(u - 1, 0, n - 1)) - (u - 1) * maxi, 0, n - 1);
}
vector<long long> minimum_costs(vector<int> h, vector<int> l, vector<int> r) {
int q = l.size();
n = h.size();
fill(ans, ans + q, LLONG_MAX);
for (int z = 0; z < 2; ++z) {
::h = h;
fill(queries, queries + n, vector<array<int, 3>>());
for (int i = 0; i < n; ++i) {
for (int j = 0; j < 2; ++j) {
adj[i][j] = -1;
}
}
int root = -1;
vector<int> stk;
for (int i = 0; i < n; ++i) {
while (!stk.empty() && h[stk.back()] < h[i]) {
stk.pop_back();
}
if (!stk.empty()) {
int j = stk.back();
adj[i][0] = adj[j][1];
adj[j][1] = i;
} else {
adj[i][0] = root;
root = i;
}
stk.push_back(i);
}
for (int i = 0; i <= __lg(n); ++i) {
for (int j = 0; j + (1 << i) <= n; ++j) {
if (i == 0) {
sparse[i][j] = {h[j], -j};
} else {
sparse[i][j] = max(sparse[i - 1][j], sparse[i - 1][j + (1 << (i - 1))]);
}
}
}
for (int i = 0; i < q; ++i) {
int k = __lg(r[i] - l[i] + 1);
auto [y, j] = max(sparse[k][l[i]], sparse[k][r[i] - (1 << k) + 1]);
queries[-j].push_back({l[i], r[i], i});
}
mini = new segtree();
dfs(root);
reverse(h.begin(), h.end());
for (int i = 0; i < q; ++i) {
int temp = l[i];
l[i] = n - 1 - r[i];
r[i] = n - 1 - temp;
}
}
return vector<long long>(ans, ans + q);
}
