#include "shortcut.h"
#include<bits/stdc++.h>
using namespace std;
#define int long long
const int INF = 1e18;
const int MAXN = 3005;
int n,c;
int a[MAXN];//pozitii
int d[MAXN];
int worst_pref[MAXN],worst_suff[MAXN];
int only_pref[MAXN],only_suff[MAXN];
int inainte[MAXN][MAXN];
bool aux[MAXN][MAXN];
int prec[MAXN][MAXN];
bool verif(int lim)
{
if(only_pref[n] <= lim)
return 1;
for(int i=0;i<=n+1;i++)
for(int j=0;j<=n+1;j++)
prec[i][j] = -INF;
for(int u=n;u>0;u--)
{
for(int v=n;v>u;v--)
{
prec[u][v] = -INF;
if(a[v] + d[v] - a[u] + d[u] > lim)
{
prec[u][v] = a[u] - a[v] + d[u] + d[v];
}
if(u<n) prec[u][v] = max(prec[u][v], prec[u+1][v]);
aux[u][v]=1;
}
}
for(int i=1;i<=n;i++)
{
int mxm=-INF;
for(int j=i+2;j<=n;j++)
{
if(d[j-1] + a[j-1] > lim - worst_pref[i])
mxm = max(mxm, d[j-1] - a[j-1]);
if(mxm > lim - worst_pref[i] - a[i] - a[j] - c)
aux[i][j]=0;
prec[i][j] = max(prec[i][j],prec[i][j-1]);
}
}
for(int j=1;j<=n;j++)
{
int mxm=-INF;
for(int i=j-2;i>0;i--)
{
if(d[i+1] - a[i+1] > lim - worst_suff[j])
mxm = max(mxm, d[i+1] + a[i+1]);
if(mxm > lim - worst_suff[j] + a[i] + a[j] - c)
aux[i][j]=0;
}
}
for(int i=1;i<=n;i++)
{
for(int j=i+1;j<=n;j++)
{
if(c >= a[j]-a[i])
continue;
bool bun=1;
if(i+1<j-1 && prec[i+1][j-1] > lim - (a[j]+c-a[i]))
bun=0;
if(inainte[i][j] > lim)
bun=0;
if(aux[i][j]==0)
bun=0;
if(bun)
return 1;
}
}
return 0;
}
long long find_shortcut(int32_t cit_n, std::vector<int32_t> l, std::vector<int32_t> citd, int32_t cit_c)
{
n = cit_n;
c = cit_c;
for(int i=2;i<=n;i++)
a[i] = a[i-1] + l[i-2];
for(int i=1;i<=n;i++)
{
d[i] = citd[i-1];
}
worst_pref[0] = -INF;
for(int i=1;i<=n;i++)
worst_pref[i] = max(worst_pref[i-1], -a[i] + d[i]);
worst_suff[n+1] = -INF;
for(int i=n;i>0;i--)
worst_suff[i] = max(worst_suff[i+1], a[i] + d[i]);
only_pref[0] = -INF;
for(int i=1;i<=n;i++)
only_pref[i] = max({only_pref[i-1], a[i] + d[i] + worst_pref[i-1], d[i]});
only_suff[n+1] = -INF;
for(int i=n;i>0;i--)
only_suff[i] = max({only_suff[i+1], -a[i] + d[i] + worst_suff[i+1], d[i]});
int cv=0;
for(int i=1;i<=n;i++)
cv = max(cv, d[i]);
int minim=INF;
for(int i=1;i<=n;i++)
{
for(int j=i+1;j<=n;j++)
{
if(c >= a[j]-a[i])
continue;
int mxm=0;
mxm = max(mxm, a[i] + worst_pref[i] + c + worst_suff[j] - a[j]);
mxm = max(mxm, only_pref[i]);
mxm = max(mxm, only_suff[j]);
mxm = max(mxm, c);
mxm = max(mxm, cv);
inainte[i][j] = mxm;
minim = min(minim, inainte[i][j]);
}
}
int st=minim,dr=only_pref[n]-1,ans=only_pref[n];
while(st<=dr)
{
int mij=(st+dr)/2;
if(verif(mij))
{
ans = mij;
dr = mij-1;
}
else
st = mij+1;
}
return ans;
}
/*
4 10
10 20 20
0 40 0 30
output: 80
9 30
10 10 10 10 10 10 10 10
20 0 30 0 0 40 0 40 0
output: 110
*/
