#include "shortcut.h"
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
using namespace std;
long long find_shortcut(int n, std::vector<int> l, std::vector<int> d, int c)
{
vector<long long> pre(n);
for(int i = 1; i < n; ++i){
pre[i] = pre[i - 1] + l[i - 1];
}
long long low = 0, high = (long long)1e18, mid;
int d1 = 0, d2 = 0;
for(int i = 0; i < n; ++i){
if(d[i] > d1){
d2 = d1;
d1 = d[i];
}
else if(d[i] > d2){
d2 = d[i];
}
}
low = d1 + d2;
vector<pair<long long, int>> srtp(n), srtm(n);
for(int i = 0; i < n; ++i){
srtp[i] = {d[i] + pre[i], i};
srtm[i] = {pre[i] - d[i], i};
}
sort(srtp.begin(), srtp.end());
sort(srtm.begin(), srtm.end());
while(low < high){
mid = low + high >> 1;
long long xmx = (long long)1e18, ymx = (long long)1e18;
long long xmn = -(long long)1e18, ymn = -(long long)1e18;
pair<long long, int> ppd1, pmd1, ppd2, pmd2;
ppd1 = {-(long long)1e18, -1}, pmd1 = {(long long)1e18, 1};
ppd2 = {-(long long)1e18, -1}, pmd2 = {(long long)1e18, 1};
for(int i = n - 1, j = n; i >= 0; --i){
int nid = srtm[i].second;
while(j && srtp[j - 1].first > srtm[i].first + mid){
--j;
if(srtp[j] > ppd1) ppd2 = ppd1, ppd1 = srtp[j];
else if(srtp[j] > ppd2) ppd2 = srtp[j];
if(make_pair(pre[srtp[j].second] - d[srtp[j].second], srtp[j].second) < pmd1) pmd2 = pmd1, pmd1 = make_pair(pre[srtp[j].second] - d[srtp[j].second], srtp[j].second);
else if(make_pair(pre[srtp[j].second] - d[srtp[j].second], srtp[j].second) < pmd2) pmd2 = make_pair(pre[srtp[j].second] - d[srtp[j].second], srtp[j].second);
}
if(pmd1.second != nid) xmn = max(xmn, pre[nid] + d[nid] - pmd1.first - mid + c), ymx = min(ymx, pre[nid] - d[nid] + pmd1.first + mid - c);
else xmn = max(xmn, pre[nid] + d[nid] - pmd2.first - mid + c), ymx = min(ymx, pre[nid] - d[nid] + pmd2.first + mid - c);
if(ppd1.second != nid) xmx = min(xmx, pre[nid] - d[nid] - ppd1.first + mid - c), ymn = max(ymn, pre[nid] + d[nid] + ppd1.first - mid + c);
else xmx = min(xmx, pre[nid] - d[nid] - ppd2.first + mid - c), ymn = max(ymn, pre[nid] + d[nid] + ppd2.first - mid + c);
}
// cout << low << ' ' << high << ' ' << mid << endl;
// cout << xmn << ' ' << xmx << ' ' << ymn << ' ' << ymx << endl;
int f = 0;
for(int i = 0, j1 = 1, j2 = n - 1; i < n; ++i){
while(j1 < n && (pre[i] - pre[j1] > xmx || i == j1)) ++j1;
while(j2 && (pre[i] + pre[j2 - 1] >= ymn)) --j2;
int j = max(j1, j2);
if(j < n && pre[i] - pre[j] >= xmn && pre[i] + pre[j] <= ymx){
f = 1;
break;
}
}
if(f){
high = mid;
}
else{
low = mid + 1;
}
}
return low;
}
