#include "meetings.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> line;
typedef pair<int,int> ii;
#define fi first
#define se second
#define lc 2*i+1
#define rc 2*i+2
#define pb push_back
#define LINF 1023456789123456789
#define pf printf
#define maxn 750005
int n,q;
vector<int> h;
vector<ll> ans;
struct query{
int l,r,i;
};
vector<query> qrys[maxn];
ll eval(line l,ll x){
return l.fi*x+l.se;
}
struct seg{
ii v[maxn*4];
void init(int i,int s,int e){
if(s==e){v[i]={h[s],s};return;}
int m=(s+e)>>1;
init(lc,s,m);
init(rc,m+1,e);
v[i]=max(v[lc],v[rc]);
}
void init(){
init(0,0,n-1);
}
ii qry(int i,int s,int e,int x,int y){
if(s==x&&e==y)return v[i];
int m=(s+e)>>1;
if(y<=m)return qry(lc,s,m,x,y);
if(x>m)return qry(rc,m+1,e,x,y);
return max(qry(lc,s,m,x,m),qry(rc,m+1,e,m+1,y));
}
int qry(int x,int y){
return qry(0,0,n-1,x,y).se;
}
}maxseg;
struct lichao{
int s,e,m;
lichao *l,*r;
line val={0,LINF};
ll lz=0;
lichao(int _s,int _e){
s=_s;e=_e;m=(s+e)>>1;
if(s!=e){
l=new lichao(s,m);
r=new lichao(m+1,e);
}
}
void ppo(){
val.se+=lz;
if(s!=e)l->lz+=lz,r->lz+=lz;
lz=0;
}
void insert(int x,int y,line v){
if(x>y)return;
ppo();
if(s==x&&e==y){
if(eval(v,m)<eval(val,m))swap(v,val);
if(s==e)return;
if(eval(v,s)>=eval(val,s)&&eval(v,e)>=eval(val,e))return;
if(eval(v,s)<eval(val,s))l->insert(x,m,v);
else r->insert(m+1,y,v);
}
if(y<=m)l->insert(x,y,v);
else if(x>m)r->insert(x,y,v);
else l->insert(x,m,v),r->insert(m+1,y,v);
}
void add(int x,int y,ll v){
if(x>y)return;
if(s==x&&e==y){lz+=v;return;}
if(y<=m)l->add(x,y,v);
else if(x>m)r->add(x,y,v);
else l->add(x,m,v),r->add(m+1,y,v);
}
ll qry(int x){
ppo();
if(s==x&&e==x)return eval(val,x);
if(x<=m)return min(eval(val,x),l->qry(x));
else return min(eval(val,x),r->qry(x));
}
}*llct,*rlct;
void solve(int l,int r){
if(l>r)return;
int m=maxseg.qry(l,r);
solve(l,m-1);
solve(m+1,r);
llct->insert(m,m,{0,0});
rlct->insert(m,m,{0,0});
for(query &q:qrys[m]){
ans[q.i]=min(llct->qry(q.l)+(ll)(q.r-m+1)*h[m],
rlct->qry(q.r)+(ll)(m-q.l+1)*h[m]);
}
llct->add(l,m,(ll)(r-m+1)*h[m]);
llct->insert(l,m,{-h[m],(ll)(m+1)*h[m]+(m==r?0:llct->qry(m+1))});
rlct->add(m,r,(ll)(m-l+1)*h[m]);
rlct->insert(m,r,{h[m],(ll)(1-m)*h[m]+(l==m?0:rlct->qry(m-1))});
}
vector<ll> minimum_costs(vector<int> _h,vector<int> l,vector<int> r){
n=_h.size();
q=l.size();
h=_h;
maxseg.init();
ans.resize(q);
for(int i=0;i<q;++i){
int m=maxseg.qry(l[i],r[i]);
qrys[m].pb({l[i],r[i],i});
}
llct=new lichao(0,n-1);
rlct=new lichao(0,n-1);
solve(0,n-1);
return ans;
}
