#include "shortcut.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 3000;
const ll INF = 1e18;
ll L[N],R[N],mxL[N],mxR[N],pre[N];
vector<int> d,l;
char vis[N][N],vsId=1;
ll dp[N][N];
int n;
ll c;
bool check(ll mid){
vsId++;
for(int len = 1; len <= n ; ++len){
for(int i = n-len ; i>=0 ; --i){
int j = i + len - 1;
if(len==1){
dp[i][j]= INF;
continue;
}
if(pre[j]-pre[i] +d[i]+d[j] > mid)
dp[i][j]=(pre[j]-pre[i]) - d[i] - d[j];
else
dp[i][j]=INF;
dp[i][j] = min(dp[i][j],min(dp[i+1][j],dp[i][j-1]));
}
}
for(int i = 0 ; i < n ; ++i){
if(mxL[i] > mid)
continue;
ll fage3 = -INF;
ll csum = 0;
for (int j = i+1; j < n; ++j){
csum += l[j-1];
if(L[j]+d[j] > mid)
fage3 = max(fage3,L[i]+c+d[j]);
if(fage3 > mid)
break;
if(min(csum,c)+L[i]+R[j]<=mid && mxR[j]<=mid && (dp[i][j] ==INF || csum+c-dp[i][j]<=mid)){
vis[i][j] = vsId;
}
if(j != n-1)
fage3 += l[j];
}
}
for(int i = n-1 ; i >= 0 ;--i){
if(mxR[i] > mid)
continue;
ll fage3 = -INF;
for (int j = i-1; j>= 0 ;j--){
if(R[j]+d[j] > mid)
fage3 = max(fage3,R[i]+c+d[j]);
if(fage3 > mid)
break;
if(mxL[j]<=mid && vis[j][i] == vsId){
return true;
}
if(j != 0)
fage3 += l[j-1];
}
}
return false;
}
ll find_shortcut(int n, vector<int> l, vector<int> d, int c){
if(n>3000)
return -1;
::n=n;
::d=d;
::c=c;
::l=l;
for (int i = 0; i < n; ++i){
L[i] = d[i];
if(i)
pre[i] = l[i-1] + pre[i-1];
if(i)
L[i] = max(L[i-1]+l[i-1],L[i]);
mxL[i] = max(i?mxL[i-1]:0,d[i]+ (i?L[i-1]+l[i-1]:0));
}
for(int i = n - 1 ; i >= 0 ; i--){
R[i] = d[i];
if(i != n-1)
R[i] = max(R[i],R[i+1]+l[i]);
mxR[i] = max(i!=n-1?mxR[i+1]:0,d[i] + (i!=n-1?R[i+1]+l[i]:0));
}
ll lo = *max_element(d.begin(),d.end()) , hi = 1e9*(N+3),best = -1;
while(lo <= hi){
ll mid = (lo + hi)/2;
if(check(mid)){
best = mid;
hi = mid -1;
}else{
lo = mid + 1;
}
}
assert(best!=-1);
return best;
}
