#include "shortcut.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pii pair<int, int>
#define all(c) ((c).begin()), ((c).end())
#define sz(x) ((int)(x).size())
#ifdef LOCAL
#include <print.h>
#else
#define trace(...)
#define endl '\n'
#endif
const int N = 1 << 20;
const ll INF = 1e18;
ll A[N], B[N];
ll p[N];
int perm1[N], perm2[N];
long long find_shortcut(int n, std::vector<int> l, std::vector<int> d, int c){
for(int i = 1; i < n; i++) p[i] = p[i - 1] + l[i - 1];
iota(perm1, perm1 + n, 0);
iota(perm2, perm2 + n, 0);
sort(perm1, perm1 + n, [&](int i, int j){return d[i] - p[i] > d[j] - p[j];});
sort(perm2, perm2 + n, [&](int i, int j){return d[i] + p[i] < d[j] + p[j];});
int mx = 0, mx2 = 0, ind_mx = 0;
A[0] = -INF; B[0] = INF;
for(int i = 1; i <= n; i++){
int ind = perm1[i - 1];
A[i] = max(A[i - 1], p[ind] + d[ind]);
B[i] = min(B[i - 1], p[ind] - d[ind]);
if(d[ind] > mx){
mx2 = mx;
mx = d[ind];
ind_mx = ind;
} else if(d[ind] > mx2) mx2 = d[ind];
}
ll lo = mx + mx2, hi = p[n - 1] / 2 + 3e9;
lo = max(lo, (p[n - 1] - 1000000000) / 3);
while(lo < hi){
ll D = (lo + hi) / 2;
ll L1 = -INF, R1 = INF;
ll L2 = -INF, R2 = INF;
int cur = 0;
for(int ind = 0; ind < n; ind++){
int i = perm2[ind];
while(cur < n && d[perm1[cur]] + d[i] + p[i] - p[perm1[cur]] > D) cur++;
ll a = A[cur], b = B[cur];
if(D < 2 * mx && i == ind_mx){
a = -INF; b = INF;
for(int r = 0; r < cur; r++){
int _r = perm1[r];
if(_r == i) continue;
a = max(a, p[_r] + d[_r]);
b = min(b, p[_r] - d[_r]);
}
}
L1 = max(L1, a + d[i] + c - p[i] - D);
R1 = min(R1, b - d[i] - c - p[i] + D);
L2 = max(L2, a + p[i] - D + d[i] + c);
R2 = min(R2, b + p[i] + D - d[i] - c);
}
if(L1 > R1 || L2 > R2){
lo = D + 1;
continue;
}
bool ok = false;
int ptr1 = 0;
int ptr2 = n;
for(int v = 1; v < n; v++){
while(ptr1 < n && p[ptr1] - p[v] < L1) ptr1++;
while(ptr2 > 0 && p[ptr2 - 1] + p[v] >= L2) ptr2--;
int u = max(ptr1, ptr2);
if(u >= v) continue;
if(p[u] - p[v] > R1 || p[u] + p[v] > R2) continue;
ok = true;
break;
}
if(ok) hi = D;
else lo = D + 1;
}
return lo;
}
