#include "shortcut.h"
#include <bits/stdc++.h>
using namespace std;
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define eb emplace_back
using ll = long long;
ll find_shortcut(int n, vector<int> l, vector<int> d, int c) {
vector<ll> x(n, 0);
for (int i = 0; i + 1 < n; i++) {
x[i + 1] = x[i] + (ll)l[i];
}
ll min_x = -(ll)1e18, max_x = (ll)1e18, min_y = -(ll)1e18, max_y = (ll)1e18;
vector<tuple<ll, ll, int> > case_1_inserts(n), case_2_inserts(n);
vector<tuple<ll, ll, ll*, int> > case_1_queries(2 * n), case_2_queries(2 * n);
for (int i = 0; i < n; i++) {
case_1_inserts[i] = mt(d[i] - x[i], x[i] + d[i], i);
case_1_queries[2 * i] = mt(- d[i] - x[i], c + d[i] - x[i], &min_x, i);
case_1_queries[2 * i + 1] = mt(- d[i] - x[i], c + d[i] + x[i], &min_y, i);
case_2_inserts[i] = mt(d[i] - x[i], -(x[i] - d[i]), i);
case_2_queries[2 * i] = mt(- d[i] - x[i], - c - d[i] - x[i], &max_x, i);
case_2_queries[2 * i + 1] = mt(- d[i] - x[i], - c - d[i] + x[i], &max_y, i);
}
sort(case_1_inserts.begin(), case_1_inserts.end());
sort(case_1_queries.begin(), case_1_queries.end());
sort(case_2_inserts.begin(), case_2_inserts.end());
sort(case_2_queries.begin(), case_2_queries.end());
reverse(case_1_inserts.begin(), case_1_inserts.end());
reverse(case_1_queries.begin(), case_1_queries.end());
reverse(case_2_inserts.begin(), case_2_inserts.end());
reverse(case_2_queries.begin(), case_2_queries.end());
auto good = [&](ll k) {
min_x = -(ll)1e18, max_x = (ll)1e18, min_y = -(ll)1e18, max_y = (ll)1e18;
{
pair<ll, int> case_1_first_best = mp(-(ll)1e18, -1), case_1_second_best = mp(-(ll)1e18, -1);
int ptr = 0;
for (auto &[val, offset, addr, idx] : case_1_queries) {
while (ptr < n && get<0>(case_1_inserts[ptr]) > val + k) {
auto &[__, val_insert, idx_insert] = case_1_inserts[ptr];
case_1_second_best = max(case_1_second_best, mp(val_insert, idx_insert));
if (case_1_second_best > case_1_first_best) {
swap(case_1_first_best, case_1_second_best);
}
ptr++;
}
*addr = max(*addr, case_1_first_best.first + (idx == case_1_first_best.second) * (case_1_second_best.first - case_1_first_best.first) + offset - k);
}
}
{
pair<ll, int> case_2_first_best = mp(-(ll)1e18, -1), case_2_second_best = mp(-(ll)1e18, -1);
int ptr = 0;
for (auto &[val, offset, addr, idx] : case_2_queries) {
while (ptr < n && get<0>(case_2_inserts[ptr]) > val + k) {
auto &[__, val_insert, idx_insert] = case_2_inserts[ptr];
case_2_second_best = max(case_2_second_best, mp(val_insert, idx_insert));
if (case_2_second_best > case_2_first_best) {
swap(case_2_first_best, case_2_second_best);
}
ptr++;
}
*addr = min(*addr, -(case_2_first_best.first + (idx == case_2_first_best.second) * (case_2_second_best.first - case_2_first_best.first)) + offset + k);
}
}
if (min_x <= max_x && min_y <= max_y) {
vector<pair<ll, ll> > vec_1, vec_2;
for (int j = 0; j < n; j++) {
ll rb = min(max_x + x[j], max_y - x[j]);
if (min_x + x[j] <= min_y - x[j]) {
vec_1.eb(min_y - x[j], rb);
} else {
vec_2.eb(min_x + x[j], rb);
}
}
int ptr_1 = (int)vec_1.size() - 1, ptr_2 = 0;
for (int i = 0; i < n; i++) {
while (ptr_1 >= 0 && vec_1[ptr_1].first <= x[i]) {
if (x[i] <= vec_1[ptr_1].second) {
return true;
}
ptr_1--;
}
while (ptr_2 < (int)vec_2.size() && vec_2[ptr_2].first <= x[i]) {
if (x[i] <= vec_2[ptr_2].second) {
return true;
}
ptr_2++;
}
}
return false;
} else {
return false;
}
};
ll lo = 0, hi = (ll)1e15, ans = -1;
while (lo <= hi) {
ll mid = (lo + hi) / 2;
if (good(mid)) {
ans = mid;
hi = mid - 1;
} else {
lo = mid + 1;
}
}
return ans;
}
