#pragma GCC target("avx2")
#pragma GCC optimization("O3")
#pragma GCC optimization("unroll-loops")
#include<bits/stdc++.h>
//#include "meetings.h"
#define rc(x) return cout<<x<<endl,0
#define pb push_back
#define mkp make_pair
#define in insert
#define er erase
#define fd find
#define fr first
#define sc second
typedef long long ll;
typedef long double ld;
const ll INF=0x3f3f3f3f3f3f3f3f;
const ll llinf=(1LL<<62);
const int inf=(1<<30);
const ll nmax=1e5+50;
const int mod=1e9+7;
using namespace std;
int n,q,i,j,x,y,lst,t,st[4*nmax];
ll h[nmax],p[5050][5050],s[5050][5050],mx;
vector<pair<int,int> >a[nmax],b[nmax];
vector<ll>rs;
void upd(int nod,int l,int r,int p,int v)
{
if(l==r)
{
st[nod]=max(v,st[nod]);
return;
}
int mid=(l+r)/2;
if(p<=mid)upd(2*nod,l,mid,p,v);
else upd(2*nod+1,mid+1,r,p,v);
st[nod]=max(st[2*nod],st[2*nod+1]);
}
int qry(int nod,int l,int r,int tl,int tr)
{
if(tr<l || tl>r)return 0;
if(tl<=l && r<=tr)return st[nod];
int mid=(l+r)/2;
int v=0;
if(tl<=mid)v=qry(2*nod,l,mid,tl,tr);
if(tr>mid)v=max(v,qry(2*nod+1,mid+1,r,tl,tr));
return v;
}
vector<ll> minimum_costs(vector<int>H,vector<int>L,vector<int>R)
{
n=H.size(),q=L.size();
for(i=1;i<=n;i++)h[i]=H[i-1];
h[n+1]=h[0]=2;
for(i=0;i<q;i++)
{
x=L[i],y=R[i];
x++,y++;
if(x>y)swap(x,y);
a[y].pb(mkp(x,i));
b[x].pb(mkp(y,i));
}
rs.resize(q);
if(n<=5000 && q<=5000)
{
for(i=0;i<q;i++)rs[i]=llinf;
for(i=1;i<=n;i++)
{
mx=0;
for(j=i;j<=n;j++)
{
mx=max(mx,h[j]);
p[i][j]=p[i][j-1]+mx;
}
mx=0;
for(j=i-1;j>=1;j--)
{
mx=max(mx,h[j]);
s[i][j]=s[i][j+1]+mx;
}
}
for(i=1;i<=n;i++)
{
for(j=0;j<a[i].size();j++)
{
x=a[i][j].fr,y=i;
for(t=x;t<=y;t++)
{
rs[a[i][j].sc]=min(rs[a[i][j].sc],p[t][y]+s[t][x]);
}
}
}
return rs;
}
for(i=1;i<=n;i++)
{
if(h[i]==2)lst=i;
if(lst!=i && h[i+1]==2)upd(1,1,n,lst+1,i-lst);
for(j=0;j<a[i].size();j++)rs[a[i][j].sc]=qry(1,1,n,a[i][j].fr,i);
}
lst=0;
for(i=1;i<=n;i++)
{
if(h[i]==2)lst=i;
for(j=0;j<a[i].size();j++)rs[a[i][j].sc]=max(rs[a[i][j].sc],1LL*i-1LL*max(lst,a[i][j].fr-1));
}
lst=n+1;
for(i=n;i>=1;i--)
{
if(h[i]==2)lst=i;
for(j=0;j<b[i].size();j++)rs[b[i][j].sc]=max(rs[b[i][j].sc],1LL*min(lst,b[i][j].fr+1)-1LL*i);
}
for(i=1;i<=n;i++)
{
for(j=0;j<a[i].size();j++)
{
rs[a[i][j].sc]=rs[a[i][j].sc]+(i-a[i][j].fr+1-rs[a[i][j].sc])*2;
}
}
return rs;
}
