#include <bits/stdc++.h>
#include "meetings.h"
using namespace std;
const int MAX_N = 75e4 + 5;
const long long INF = 1e18 + 7;
int N, Q;
long long H[MAX_N];
pair <int, int> table[MAX_N][20];
vector <int> graph[MAX_N];
struct A {
int ans, pre, suf, mx;
A() {}
A(int a, int p, int s, int m) : ans(a), pre(p), suf(s), mx(m) {}
A operator+(const A &o) const {
int ans_, pre_, suf_, max_;
ans_ = max({ans, o.ans, suf + o.pre});
pre_ = max(pre, (mx == 1) * (pre + o.pre));
suf_ = max(o.suf, (o.mx == 1) * (o.suf + suf));
max_ = max(mx, o.mx);
return {ans_, pre_, suf_, max_};
}
}tree[4 * MAX_N];
void build(int idx, int l, int r) {
if(l == r) {
return void(tree[idx] = {H[l] == 1, H[l] == 1, H[l] == 1, H[l]});
}
int mid = (l + r) / 2;
build(idx * 2, l, mid);
build(idx * 2 + 1, mid + 1, r);
tree[idx] = tree[idx * 2] + tree[idx * 2 + 1];
}
A query(int idx, int l, int r, int ql, int qr) {
if(r < ql or qr < l) {
return {0, 0, 0, 0};
}
if(ql <= l and r <= qr) {
return tree[idx];
}
int mid = (l + r) / 2;
return query(idx * 2, l, mid, ql, qr) + query(idx * 2 + 1, mid + 1, r, ql, qr);
}
pair <int, int> getMax(int l, int r) {
int j = log2(r - l + 1);
return max(table[l][j], table[r - (1<<j) + 1][j]);
}
int build_tree(int l, int r) {
if(l > r) {
return -1;
}
int u = getMax(l, r).second;
int L = build_tree(l, u - 1);
int R = build_tree(u + 1, r);
if(L != -1) {
graph[u].push_back(L);
}
if(R != -1) {
graph[u].push_back(R);
}
return u;
}
long long dfs(int u, int l, int r, long long total = 0) {
long long now = total + H[u] * (r - l + 1);
for(auto v : graph[u]) {
if(v < u) {
now = min(now, dfs(v, l, u - 1, total + H[u] * (r - u + 1)));
}
else {
now = min(now, dfs(v, u + 1, r, total + H[u] * (u - l + 1)));
}
}
return now;
}
vector <long long> minimum_costs(vector <int> h, vector <int> L, vector <int> R) {
N = h.size(), Q = L.size();
vector <long long> C;
for(int i = 1; i <= N; i++) {
H[i] = h[i - 1];
}
for(int i = 0; i < Q; i++) {
L[i]++, R[i]++;
}
if(N <= 5000 and Q <= 5000) {
for(int i = 1; i <= N; i++) {
table[i][0] = make_pair(H[i], i);
}
for(int j = 1; j < 20; j++) {
for(int i = 1; i + (1<<j) - 1 <= N; i++) {
table[i][j] = max(table[i][j - 1], table[i + (1<<(j - 1))][j - 1]);
}
}
for(int i = 0; i < Q; i++) {
for(int i = 1; i <= N; i++) {
graph[i].clear();
}
C.push_back(dfs(build_tree(L[i], R[i]), L[i], R[i]));
}
}
else {
build(1, 1, N);
for(int i = 0; i < Q; i++) {
int maxseq1 = query(1, 1, N, L[i], R[i]).ans;
C.push_back(2 * (R[i] - L[i] + 1 - maxseq1) + maxseq1);
}
}
return C;
}
