#include "meetings.h"
#include<bits/stdc++.h>
using namespace std;
const long long maxn=750000+10,lg=20,kaf=(1<<lg),maxr=1e9+5;
long long ezaf=0,all[maxn],n,dpl[maxn],dpr[maxn],tr[maxn],tl[maxn],psl[maxn],psr[maxn],inf=1e16;
vector<pair<long long,long long>>allql[maxn],allqr[maxn];
long long q,res[maxn];
struct func{
long long x0,y0,sh,ta,w,tb,wb;
func(){
x0=0;
y0=inf;
sh=0;
ta=inf;
tb=-inf;
wb=-inf;
w=inf;
}
long long get(long long x){
// if(x>=ta){
// return w;
// }
// if(x<=tb){
// return wb;
// }
// cout<<"wtf: "<<(x-x0)*sh+y0<<" "<<x0<<" "<<y0<<" "<<sh<<" "<<x<<endl;
return (x-x0)*sh+y0;
}
}fakefunc;
struct lichao{
struct node{
func f;
long long cl,cr;
node(){
cl=cr=-1;
}
}fakenode;
vector<node>alln;
long long te=1;
vector<vector<pair<int,func>>>bar;
lichao(){
te=1;
bar.push_back({});
alln.resize(1);
}
void back(){
// cout<<"wtf: "<<(int)bar.size()<<endl;
bar.pop_back();
for(auto x:bar.back()){
alln[x.first].f=x.second;
}
bar.pop_back();
bar.push_back({});
// cout<<"khor: "<<(int)bar.size()<<endl;
}
long long getl(long long i){
if(alln[i].cl==-1){
alln.push_back(fakenode);
alln[i].cl=te;
te++;
}
return alln[i].cl;
}
long long getr(long long i){
if(alln[i].cr==-1){
alln.push_back(fakenode);
alln[i].cr=te;
te++;
}
return alln[i].cr;
}
long long pors(long long i,long long l,long long r,long long x){
if(i==-1){
return inf;
}
// cout<<"pors: "<<i<<" "<<l<<" "<<r<<" "<<alln[i].f.get(x)<<" "<<alln[i].f.sh<<"\n";
long long ret=alln[i].f.get(x);
long long mid=(l+r)>>1;
if(r==l+1){
return ret;
}
if(x<mid){
ret=min(ret,pors(alln[i].cl,l,mid,x));
}else{
ret=min(ret,pors(alln[i].cr,mid,r,x));
}
return ret;
}
void ins(long long i,long long l,long long r,func fa){
bar.back().push_back(make_pair(i,alln[i].f));
//if(fa.sh!=0||alln[i].f.sh!=0)
//cout<<i<<" "<<l<<" "<<r<<" "<<fa.x0<<" "<<fa.sh<<" "<<alln[i].f.get(l)<<" "<<fa.get(l)<<"\n";
if(alln[i].f.get(l)>fa.get(l)){
swap(alln[i].f,fa);
}
//if(fa.sh!=0||alln[i].f.sh!=0)
// cout<<alln[i].f.sh<<endl;
if(r==l+1){
bar.push_back({});
return ;
}
long long mid=(l+r)>>1;
if(alln[i].f.get(mid)<=fa.get(mid)){
return ins(getr(i),mid,r,fa);
}else{
swap(alln[i].f,fa);
return ins(getl(i),l,mid,fa);
}
}
}lch;
struct segment{
lichao seg[(1<<(lg+1))];
void erase(int i){
i+=kaf;
while(i>0){
//seg[i].back();
i>>=1;
}
}
void ins(long long i,func f){
i+=kaf;
while(i>0){
seg[i].ins(0,0,maxr,f);
i>>=1;
}
}
long long pors(long long i,long long l,long long r,long long tl,long long tr,long long x){
if(l>r||l>tr||r<tl||tl>tr){
return inf;
}
if(l>=tl&&r<=tr){
// cout<<l<<" "<<r<<" "<<seg[i].pors(1,0,maxr,x)<<endl;
return seg[i].pors(0,0,maxr,x);
}
long long m=(l+r)>>1;
return min(pors((i<<1),l,m,tl,tr,x),pors((i<<1)^1,m+1,r,tl,tr,x));
}
}seg;
void caltltr(){
vector<long long>v;
all[0]=inf;
all[n+1]=inf;
v.push_back(0);
for(long long i=1;i<=n;i++){
while(all[v.back()]<all[i]){
v.pop_back();
}
tl[i]=v.back();
v.push_back(i);
}
v.clear();
v.push_back(n+1);
for(long long i=n;i>=1;i--){
while(all[v.back()]<all[i]){
v.pop_back();
}
tr[i]=v.back();
v.push_back(i);
}
}
void solvel(){
vector<long long>v;
v.push_back(0);
for(long long i=1;i<=n;i++){
// cout<<i<<endl;
dpl[i]=inf;
while(all[v.back()]<all[i]){
dpl[i]=min(dpl[i],dpl[v.back()]+(i-v.back()-1)*all[v.back()]);
seg.erase(v.size()-1);
v.pop_back();
}
v.push_back(i);
if(tl[i]==i-1){
dpl[i]=psl[i]=psl[tl[i]]+all[i];
}else{
dpl[i]+=all[i];
}
psl[i]=psl[tl[i]]+(i-tl[i])*all[i];
func fa;
fa.x0=i;
fa.y0=dpl[i];
fa.sh=all[i];
fa.ta=tr[i];
fa.w=inf+ezaf;
fa.tb=i-1;
fa.wb=-inf-ezaf;
ezaf++;
//cout<<"av "<<fa.x0<<" "<<fa.y0<<" "<<fa.sh<<" "<<fa.ta<<" "<<fa.w<<" "<<(int)v.size()-1<<endl;
seg.ins(v.size()-1,fa);
// cout<<"dov"<<endl;
for(auto x:allqr[i]){
long long p=lower_bound(v.begin(),v.end(),x.first)-v.begin();
long long now=i;
now=v[p];
long long manf=psl[tl[now]]+(x.first-1-tl[now])*all[now];
//now=i;
//while(tl[now]>=x.first){
// res[x.second]=min(res[x.second],dpl[now]+(i-now)*all[now]-manf);
// now=tl[now];
// }
// cout<<"wtf: "<<seg.pors(1,0,kaf-1,0,100,i)<<" "<<p<<" "<<v.size()<<endl;
res[x.second]=min(res[x.second],seg.pors(1,0,kaf-1,p+1,(long long)v.size()-1,i)-manf);
}
}
}
void solver(){
vector<long long>v;
v.push_back(n+1);
for(long long i=n;i>=1;i--){
dpr[i]=inf;
while(all[v.back()]<all[i]){
dpr[i]=min(dpr[i],dpr[v.back()]+(v.back()-i-1)*all[v.back()]);
v.pop_back();
}
v.push_back(i);
if(tr[i]==i+1){
dpr[i]=psr[i]=psr[tr[i]]+all[i];
}else{
dpr[i]+=all[i];
}
psr[i]=psr[tr[i]]+(tr[i]-i)*all[i];
for(auto x:allql[i]){
long long now=i;
while(tr[now]<=x.first){
now=tr[now];
}
long long manf=psr[tr[now]]+(tr[now]-x.first-1)*all[now];
now=i;
while(tr[now]<=x.first){
res[x.second]=min(res[x.second],dpr[now]+(now-i)*all[now]-manf);
now=tr[now];
}
}
}
}
std::vector<long long> minimum_costs(std::vector<int> H, std::vector<int> L,
std::vector<int> R) {
n=H.size();
for(long long i=1;i<=n;i++){
all[i]=H[i-1];
}
q=(long long)L.size();
for(long long i=0;i<q;i++){
L[i]++;
R[i]++;
res[i]=inf;
allql[L[i]].push_back(make_pair(R[i],i));
allqr[R[i]].push_back(make_pair(L[i],i));
}
caltltr();
solvel();
solver();
vector<long long>ret;
for(long long i=0;i<q;i++){
if(L[i]==R[i]){
res[i]=all[L[i]];
}
ret.push_back(res[i]);
}
return ret;
}
