#include "meetings.h"
#include <iostream>
#include <vector>
#include <algorithm>
#include <cassert>
#include <set>
#define debug(x) #x << " = " << x << '\n'
using ll = long long;
const ll INF = 1e18;
struct RMQ {
int n;
std::vector<int> a;
std::vector<std::vector<int>> rmq;
int myMax(int x, int y) {
if (a[x] == a[y]) {
return x > y? x : y;
} else {
return a[x] > a[y]? x : y;
}
}
RMQ() {}
void build(const std::vector<int> &_a) {
a = _a;
n = (int) a.size();
int lg2 = std::__lg(n);
rmq = std::vector<std::vector<int>>(lg2 + 1, std::vector<int>(n, n));
for (int i = 0; i < n; i++) {
rmq[0][i] = i;
}
for (int j = 1; j <= lg2; j++) {
for (int i = 0; i + (1 << j) - 1 < n; i++) {
rmq[j][i] = myMax(rmq[j - 1][i], rmq[j - 1][i + (1 << (j - 1))]);
}
}
}
int query(int l, int r) {
int k = std::__lg(r - l + 1);
return myMax(rmq[k][l], rmq[k][r - (1 << k) + 1]);
}
};
struct Brut {
std::vector<ll> a;
Brut() {}
void init(int n) {
a = std::vector<ll>(n, 0);
}
void addConstant(int l, int r, ll c) {
for (int i = l; i <= r; i++) {
a[i] += c;
}
}
void minLine(int l, int r, int x, ll y) {
for (int i = l; i <= r; i++) {
a[i] = std::min(a[i], (ll) x * i + y);
}
}
void pointUpdate(int p, ll v) {
a[p] = v;
}
ll pointQuery(int p) {
return a[p];
}
};
struct LiChao {
struct Line {
ll a, b;
Line() {}
Line(ll x, ll y) : a(x), b(y) {}
Line operator + (const Line &other) const {
return Line(a + other.a, b + other.b);
}
ll eval(ll x) {
return (ll) a * x + b;
}
};
struct Node {
Line L;
Line lazy;
Node* l;
Node* r;
Node() {
L = {0, +INF};
lazy = {0, 0};
l = r = nullptr;
}
};
LiChao() {}
int n;
Node* root;
void init(int _n) {
n = _n;
root = new Node();
}
void pushLazy(Node* &node, int tl, int tr) {
if (tl != tr) {
if (node -> l == nullptr) {
node -> l = new Node();
}
if (node -> r == nullptr) {
node -> r = new Node();
}
node -> l -> lazy = node -> l -> lazy + node -> lazy;
node -> r -> lazy = node -> r -> lazy + node -> lazy;
}
node -> L = node -> L + node -> lazy;
node -> lazy = {0, 0};
}
void insertLine(Node* &node, int tl, int tr, Line L) {
if (node == nullptr) {
node = new Node();
}
pushLazy(node, tl, tr);
int mid = (tl + tr) / 2;
if (L.eval(tl) < node -> L.eval(tl)) {
std::swap(L, node -> L);
}
if (tl == tr) {
return;
}
if (node -> L.eval(mid) < L.eval(mid)) {
insertLine(node -> r, mid + 1, tr, L);
} else {
std::swap(node -> L, L);
insertLine(node -> l, tl, mid, L);
}
}
void pushLine(Node* &node, int tl, int tr) {
if (tl < tr) {
int mid = (tl + tr) / 2;
insertLine(node -> l, tl, mid, node -> L);
insertLine(node -> r, mid + 1, tr, node -> L);
}
node -> L = {0, +INF};
}
void addConstant(Node* &node, int tl, int tr, int l, int r, ll c) {
if (node == nullptr) {
node = new Node();
}
pushLazy(node, tl, tr);
if (l <= tl && tr <= r) {
node -> lazy.b += c;
} else {
pushLine(node, tl, tr);
int mid = (tl + tr) / 2;
if (l <= mid) {
addConstant(node -> l, tl, mid, l, r, c);
}
if (mid < r) {
addConstant(node -> r, mid + 1, tr, l, r, c);
}
}
}
void minLine(Node* &node, int tl, int tr, int l, int r, Line L) {
if (node == nullptr) {
node = new Node();
}
pushLazy(node, tl, tr);
if (l <= tl && tr <= r) {
insertLine(node, tl, tr, L);
} else {
int mid = (tl + tr) / 2;
if (l <= mid) {
minLine(node -> l, tl, mid, l, r, L);
}
if (mid < r) {
minLine(node -> r, mid + 1, tr, l, r, L);
}
}
}
ll pointQuery(Node* &node, int tl, int tr, int p) {
if (node == nullptr) {
return +INF;
}
pushLazy(node, tl, tr);
if (tl == tr) {
return node -> L.eval(p);
}
int mid = (tl + tr) / 2;
if (p <= mid) {
return std::min(node -> L.eval(p), pointQuery(node -> l, tl, mid, p));
} else {
return std::min(node -> L.eval(p), pointQuery(node -> r, mid + 1, tr, p));
}
}
void addConstant(int l, int r, ll c) {
if (l > r) {
return;
}
assert(0 <= l && l <= r && r <= n - 1);
addConstant(root, 0, n - 1, l, r, c);
}
void minLine(int l, int r, ll x, ll y) {
if (l > r) {
return;
}
assert(0 <= l && l <= r && r <= n - 1);
minLine(root, 0, n - 1, l, r, Line(x, y));
}
ll pointQuery(int p) {
return pointQuery(root, 0, n - 1, p);
}
void pointUpdate(int p, ll v) {
addConstant(p, p, v - pointQuery(p));
}
void deb(Node* node, int tl, int tr) {
if (node == nullptr) {
return;
}
// pushLazy(node, tl, tr);
std::cout << " ? " << tl << ' ' << tr << '\n';
std::cout << node -> L.a << ' ' << node -> L.b << ' ' << node -> lazy.a << ' ' << node -> lazy.b << '\n';
int mid = (tl + tr) / 2;
deb(node -> l, tl, mid);
deb(node -> r, mid + 1, tr);
}
void deb() {
deb(root, 0, n - 1);
}
};
std::vector<ll> minimum_costs(std::vector<int> a, std::vector<int> L, std::vector<int> R) {
int n = (int) a.size();
int q = (int) L.size();
std::vector<ll> answer(q, +INF);
LiChao DS;
RMQ rmq;
std::vector<std::set<std::pair<int, int>>> lHere(n);
std::vector<std::set<std::pair<int, int>>> rHere(n);
auto solve = [&](auto &self, int l, int r) -> void {
if (l > r) {
return;
}
int p = rmq.query(l, r);
self(self, l, p - 1);
self(self, p + 1, r);
// raspund la query uri
if (p - l < r - p) {
for (int st = l; st <= p; st++) {
// iau mereu l cel mai mare
while (!lHere[st].empty() && (*lHere[st].rbegin()).first >= p) {
auto [dr, index] = *lHere[st].lower_bound({p, 0});
if (dr <= r) {
answer[index] = std::min(answer[index], DS.pointQuery(dr) + (ll) a[p] * (p - st + 1));
lHere[st].erase({dr, index});
rHere[dr].erase({st, index});
} else {
break;
}
}
}
} else {
for (int dr = p; dr <= r; dr++) {
while (!rHere[dr].empty() && (*rHere[dr].rbegin()).first >= l) {
// vreau l minim
auto [st, index] = *rHere[dr].lower_bound({l, 0});
if (st <= p) {
answer[index] = std::min(answer[index], DS.pointQuery(dr) + (ll) a[p] * (p - st + 1));
lHere[st].erase({dr, index});
rHere[dr].erase({st, index});
} else {
break;
}
}
}
}
// acum trebuie sa recalculez pref[l..r]
// pref[l..p-1] ramane la fel
// pref[p]
ll c = p == l? 0 : DS.pointQuery(p - 1);
// if (l == 2 && r == 2) {
// std::cout << debug(DS.pointQuery(2));
// std::cout << debug(c);
// DS.pointUpdate(p, c);
// std::cout << debug(DS.pointQuery(2));
// }
DS.pointUpdate(p, c + a[p]);
// // pref[p+1..r]
DS.addConstant(p + 1, r, (ll) a[p] * (p - l + 1));
DS.minLine(p + 1, r, a[p], c + (ll) a[p] * (-p + 1));
};
auto addQueries = [&]() {
for (int i = 0; i < n; i++) {
lHere[i].clear();
rHere[i].clear();
}
for (int i = 0; i < q; i++) {
lHere[L[i]].insert({R[i], i});
rHere[R[i]].insert({L[i], i});
}
};
auto prepare = [&]() {
DS.init(n);
for (int i = 0; i < n; i++) {
DS.pointUpdate(i, 0);
}
rmq.build(a);
addQueries();
};
// DS.init(n);
// DS.deb();
// std::cout << "\n\n";
// DS.pointUpdate(0, 0);
// std::cout << debug(DS.pointQuery(0));
// DS.deb();
// // DS.pointUpdate(1, 0);
// // DS.pointUpdate(2, 0);
// DS.pointUpdate(0, 1);
// DS.deb();
// std::cout << debug(DS.pointQuery(0));
// // std::cout << DS.pointQuery(0) << '\n';
// // DS.addConstant(0, 0, 1);
// // std::cout << DS.pointQuery(0) << '\n';
// answer[0] = -1;
// return answer;
prepare();
solve(solve, 0, n - 1);
std::reverse(a.begin(), a.end());
for (int i = 0; i < q; i++) {
L[i] = n - 1 - L[i];
R[i] = n - 1 - R[i];
std::swap(L[i], R[i]);
}
prepare();
solve(solve, 0, n - 1);
return answer;
}
