#include <bits/stdc++.h>
#include "meetings.h"
using namespace std;
using lint = long long;
using pi = pair<int, int>;
const int MAXN = 750005;
const int MAXT = 2100000;
const int inf = 1e9 + 10;
struct seg{
int lim;
pi tree[MAXT];
void init(vector<int> &v){
for(lim = 1; lim <= v.size(); lim <<= 1);
fill(tree, tree + MAXT, pi(-1e9, 0));
for(int i=0; i<v.size(); i++) tree[i + lim] = pi(v[i], i);
for(int i=lim-1; i; i--) tree[i] = max(tree[2*i], tree[2*i+1]);
}
pi query(int s, int e){
s += lim;
e += lim;
pi ret(-1e9, 0);
while(s < e){
if(s%2 == 1) ret = max(ret, tree[s++]);
if(e%2 == 0) ret = max(ret, tree[e--]);
s >>= 1;
e >>= 1;
}
if(s == e) ret = max(ret, tree[s]);
return ret;
}
}seg;
struct node{
int s, e, rep; // node range
int lp, rp; // pointers
int h; // height
}tr[MAXN];
int ptr, loc[MAXN], parL[MAXN], parR[MAXN];
lint dp[MAXN], lgo[MAXN], rgo[MAXN];
lint L_intercept[MAXN], R_intercept[MAXN];
void make_tree(int s, int e, int v){
int h, m;
tie(h, m) = seg.query(s, e);
loc[m] = v;
tr[v] = {s, e, m, -1, -1, h};
if(s <= m - 1){
ptr++;
tr[v].lp = ptr;
make_tree(s, m-1, tr[v].lp);
}
if(m + 1 <= e){
ptr++;
tr[v].rp = ptr;
make_tree(m+1, e, tr[v].rp);
}
}
struct tree_cht{
struct queries{
int s, e, x;
};
int par[MAXN];
int a[MAXN]; lint b[MAXN];
vector<queries> query;
void build(int n, int *p, node *t, lint *intercept){
for(int i=1; i<=n; i++){
par[i] = p[i-1] + 1;
a[i] = t[i-1].h;
b[i] = intercept[i-1];
}
}
void add_query(int s, int e, int x){
query.push_back({s + 1, e + 1, x});
}
vector<lint> batch(){
vector<lint> ret;
for(auto &i : query){
lint val = 1e18;
int s = i.s, e = i.e;
while(s != e){
val = min(val, 1ll * a[s] * i.x + b[s]);
s = par[s];
}
ret.push_back(val);
}
return ret;
}
}t1, t2;
vector<lint> minimum_costs(vector<int> H, vector<int> L, vector<int> R){
int n = H.size();
int q = L.size();
seg.init(H);
make_tree(0, n-1, 0);
for(int i=ptr; i>=0; i--){
dp[i] = 1ll * H[tr[i].rep] * (tr[i].e - tr[i].s + 1);
if(~tr[i].lp){
dp[i] = min(dp[i], dp[tr[i].lp] + 1ll * H[tr[i].rep] * (tr[i].e - tr[i].rep + 1));
}
if(~tr[i].rp){
dp[i] = min(dp[i], dp[tr[i].rp] + 1ll * H[tr[i].rep] * (tr[i].rep - tr[i].s + 1));
}
}
for(int i=0; i<=ptr; i++){
if(tr[i].s - 1 >= 0) parR[i] = loc[tr[i].s - 1];
else parR[i] = -1;
if(tr[i].e + 1 < n) parL[i] = loc[tr[i].e + 1];
else parL[i] = -1;
if(~tr[i].lp){
lgo[tr[i].lp] = lgo[i] + 1ll * H[tr[i].rep] * (tr[i].e - tr[i].rep + 1);
rgo[tr[i].lp] = rgo[i];
}
if(~tr[i].rp){
lgo[tr[i].rp] = lgo[i];
rgo[tr[i].rp] = rgo[i] + 1ll * H[tr[i].rep] * (tr[i].rep - tr[i].s + 1);
}
L_intercept[i] = lgo[i] + 1ll * tr[i].h * (tr[i].e + 1);
if(~tr[i].rp){
L_intercept[i] = min(L_intercept[i], lgo[i] + 1ll * tr[i].h * (tr[i].rep + 1) + dp[tr[i].rp]);
}
R_intercept[i] = rgo[i] + 1ll * tr[i].h * (1 - tr[i].s);
if(~tr[i].lp){
R_intercept[i] = min(R_intercept[i], rgo[i] + 1ll * tr[i].h * (1 - tr[i].rep) + dp[tr[i].lp]);
}
}
t1.build(ptr + 1, parL, tr, L_intercept);
t2.build(ptr + 1, parR, tr, R_intercept);
vector<pi> lca(q);
for(int i=0; i<q; i++){
lca[i] = seg.query(L[i], R[i]);
t1.add_query(loc[L[i]], loc[lca[i].second], -L[i]);
t2.add_query(loc[R[i]], loc[lca[i].second], R[i]);
}
auto sol1 = t1.batch();
auto sol2 = t2.batch();
vector<lint> ret(q);
for(int i=0; i<q; i++){
pi p = lca[i];
int root_num = loc[p.second];
ret[i] = 1ll * (R[i] - L[i] + 1) * p.first;
if(L[i] < p.second){
ret[i] = min(ret[i], sol1[i] + 1ll * (R[i] - p.second + 1) * p.first - lgo[tr[root_num].lp]);
}
if(p.second < R[i]){
ret[i] = min(ret[i], sol2[i] + 1ll * (p.second - L[i] + 1) * p.first - rgo[tr[root_num].rp]);
}
}
return ret;
}
