#include "shortcut.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> P;
typedef vector<ll> vi;
typedef vector<vi> vvi;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<bool> vb;
#define rep(i,n) for(ll i=0;i<(ll)(n);i++)
#define REP(i,k,n) for(ll i=(ll)(k);i<(ll)(n);i++)
#define all(a) a.begin(),a.end()
#define fi first
#define se second
#define lb(v,k) (lower_bound(all(v),k)-v.begin())
#define dupli(a) {sort(all(a));a.erase(unique(all(a)),a.end());}
#define pb emplace_back
template<class T> bool chmin(T&a,T b){if(a>b){a=b;return true;}return false;}
template<class T> bool chmax(T&a,T b){if(a<b){a=b;return true;}return false;}
template<class T> void out(T a){cout<<a<<endl;}
template<class T> void outv(T v){rep(i,v.size()){if(i)cout<<' ';cout<<v[i];}cout<<endl;}
template<class T> void outvv(T v){for(auto x:v)outv(x);}
const ll inf=1001001001001001001;
const ll INF=1001001001;
long long find_shortcut1(int n, std::vector<int> l_, std::vector<int> d_, int c){
vi d(n),v(n);
rep(i,n-1)d[i+1]=d[i]+l_[i];
rep(i,n)v[i]=d_[i];
vi memol(n),memor(n);
rep(l,n)REP(r,l+1,n){
chmax(memol[r],v[l]+v[r]+d[r]-d[l]);
chmax(memor[l],v[l]+v[r]+d[r]-d[l]);
}
rep(i,n-1)chmax(memol[i+1],memol[i]);
for(int i=n-1;i>0;i--)chmax(memor[i-1],memor[i]);
auto calc1=[&](ll l,ll r){
ll vl=v[l];
rep(i,l)chmax(v[l],d[l]-d[i]+v[i]);
ll cycle_len=c+d[r]-d[l];
deque<P> deq;
ll ma=-inf,t=l,res=memol[l];
REP(i,l,r+1){
while(t<i&&(d[i]-d[t])*2>cycle_len){
chmax(ma,d[t]+v[t]+cycle_len);
if(deq.size()&&deq.front().fi==t)deq.pop_front();
t++;
}
if(deq.size())chmax(res,d[i]+v[i]+deq.front().se);
chmax(res,-d[i]+v[i]+ma);
while(deq.size()&&deq.back().se<=v[i]-d[i])deq.pop_back();
deq.pb(i,v[i]-d[i]);
}
v[l]=vl;
return res;
};
auto calc2=[&](ll l,ll r){
ll vr=-inf,res=memor[r];
REP(i,r+1,n)chmax(vr,d[i]-d[r]+v[i]);
rep(i,r)chmax(res,min(d[r]-d[i]+v[i],c+abs(d[l]-d[i])+v[i])+vr);
return res;
};
rep(i,n)REP(j,i+1,n)cout<<i<<' '<<j<<' '<<calc1(i,j)<<' '<<calc2(i,j)<<endl;
ll ans=inf;
rep(i,n)REP(j,i+1,n)chmin(ans,max(calc1(i,j),calc2(i,j)));
return ans;
}
long long find_shortcut2(int n, std::vector<int> l_, std::vector<int> d_, int c){
vi d(n),v(n);
rep(i,n-1)d[i+1]=d[i]+l_[i];
rep(i,n)v[i]=d_[i];
vi memol(n),memor(n);
rep(l,n)REP(r,l+1,n){
chmax(memol[r],v[l]+v[r]+d[r]-d[l]);
chmax(memor[l],v[l]+v[r]+d[r]-d[l]);
}
rep(i,n-1)chmax(memol[i+1],memol[i]);
for(int i=n-1;i>0;i--)chmax(memor[i-1],memor[i]);
auto calc1=[&](ll l,ll r){
ll vl=v[l];
rep(i,l)chmax(v[l],d[l]-d[i]+v[i]);
ll cycle_len=c+d[r]-d[l];
deque<P> deq;
ll ma=-inf,t=l,res=memol[l];
REP(i,l,r+1){
while(t<i&&(d[i]-d[t])*2>cycle_len){
chmax(ma,d[t]+v[t]+cycle_len);
if(deq.size()&&deq.front().fi==t)deq.pop_front();
t++;
}
if(deq.size())chmax(res,d[i]+v[i]+deq.front().se);
chmax(res,-d[i]+v[i]+ma);
while(deq.size()&&deq.back().se<=v[i]-d[i])deq.pop_back();
deq.pb(i,v[i]-d[i]);
}
v[l]=vl;
return res;
};
auto calc2=[&](ll l,ll r){
ll vr=-inf,res=memor[r];
REP(i,r+1,n)chmax(vr,d[i]-d[r]+v[i]);
rep(i,r)chmax(res,min(d[r]-d[i]+v[i],c+abs(d[l]-d[i])+v[i])+vr);
return res;
};
ll ans=inf;
ll r=0;
rep(l,n-1){
r=max(r-1,l+1);
while(true){
ll a=calc1(l,r),b=calc2(l,r);
chmin(ans,max(a,b));
if(a>=b)break;
r++;
}
}
return ans;
}
long long find_shortcut(int n, std::vector<int> l_, std::vector<int> d_, int c){
vi d(n),v(n);
rep(i,n-1)d[i+1]=d[i]+l_[i];
rep(i,n)v[i]=d_[i];
vi memol(n),memor(n);
rep(l,n)REP(r,l+1,n){
chmax(memol[r],v[l]+v[r]+d[r]-d[l]);
chmax(memor[l],v[l]+v[r]+d[r]-d[l]);
}
rep(i,n-1)chmax(memol[i+1],memol[i]);
for(int i=n-1;i>0;i--)chmax(memor[i-1],memor[i]);
auto calc1=[&](ll l,ll r){
ll vl=v[l];
rep(i,l)chmax(v[l],d[l]-d[i]+v[i]);
ll cycle_len=c+d[r]-d[l];
deque<P> deq;
ll ma=-inf,t=l,res=memol[l];
REP(i,l,r+1){
while(t<i&&(d[i]-d[t])*2>cycle_len){
chmax(ma,d[t]+v[t]+cycle_len);
if(deq.size()&&deq.front().fi==t)deq.pop_front();
t++;
}
if(deq.size())chmax(res,d[i]+v[i]+deq.front().se);
chmax(res,-d[i]+v[i]+ma);
while(deq.size()&&deq.back().se<=v[i]-d[i])deq.pop_back();
deq.pb(i,v[i]-d[i]);
}
v[l]=vl;
return res;
};
auto calc2=[&](ll l,ll r){
ll vr=-inf,res=memor[r];
REP(i,r+1,n)chmax(vr,d[i]-d[r]+v[i]);
rep(i,r)chmax(res,min(d[r]-d[i]+v[i],c+abs(d[l]-d[i])+v[i])+vr);
return res;
};
ll ans=inf;
rep(l,n-1){
ll ok=l,ng=n-1;
while(ng-ok>1){
ll md=(ok+ng)/2;
if(calc1(l,md)>=calc2(l,md))ng=md;
else ok=md;
}
if(l!=ok)chmin(ans,max(calc1(l,ok),calc2(l,ok)));
chmin(ans,max(calc1(l,ng),calc2(l,ng)));
}
return ans;
}
/*
int main(){
int n=7,c=1;
vector<int> l={4,8,5,10,1,8},d={8,3,6,4,3,9,3};
ll a=find_shortcut1(n,l,d,c);
ll b=find_shortcut(n,l,d,c);
out(a);out(b);
/*
rep(tt,10000){
int n=rand()%7+2,c=rand()%10;
vector<int> l(n-1),d(n);
rep(i,n-1)l[i]=rand()%10+1;
rep(i,n)d[i]=rand()%10;
ll a=find_shortcut1(n,l,d,c);
ll b=find_shortcut(n,l,d,c);
if(a!=b){
out(n);
out(c);
outv(l);outv(d);
out(a);out(b);
break;
}
}
*/
// }
