#include "shortcut.h"
#include <bits/stdc++.h>
using namespace std;
const int MAX = 1000005;
const long long inf = (long long) 1e18;
int n, c, d[MAX], order[2][MAX];
long long x[MAX], val[MAX][2];
bool Check(long long diam) {
long long xl = -inf, xr = inf;
long long yl = -inf, yr = inf;
vector<pair<int, int>> mn(2, {-1, -1});
vector<pair<int, int>> mx(2, {-1, -1});
auto Update = [&](int i) {
if (mn[0].first == -1 || val[i][0] < val[mn[0].first][0]) {
swap(mn[0].first, mn[0].second);
mn[0].first = i;
} else if (mn[0].second == -1 || val[i][0] < val[mn[0].second][0]) {
mn[0].second = i;
}
if (mn[1].first == -1 || val[i][1] < val[mn[1].first][1]) {
swap(mn[1].first, mn[1].second);
mn[1].first = i;
} else if (mn[1].second == -1 || val[i][1] < val[mn[1].second][1]) {
mn[1].second = i;
}
if (mx[0].first == -1 || val[i][0] > val[mx[0].first][0]) {
swap(mx[0].first, mx[0].second);
mx[0].first = i;
} else if (mx[0].second == -1 || val[i][0] > val[mx[0].second][0]) {
mx[0].second = i;
}
if (mx[1].first == -1 || val[i][1] > val[mx[1].first][1]) {
swap(mx[1].first, mx[1].second);
mx[1].first = i;
} else if (mx[1].second == -1 || val[i][1] > val[mx[1].second][1]) {
mx[1].second = i;
}
};
int ptr = 0;
for (int _i = 0; _i < n; _i++) {
int i = order[0][_i];
while (ptr < n && val[i][0] - val[order[1][ptr]][1] > diam) {
Update(order[1][ptr]);
ptr += 1;
}
if (mx[0].first != i && mx[0].first != -1) {
xl = max(xl, val[i][0] - diam + c + val[mx[0].first][0]);
} else if (mx[0].second != -1) {
xl = max(xl, val[i][0] - diam + c + val[mx[0].second][0]);
}
if (mn[1].first != i && mn[1].first != -1) {
xr = min(xr, val[i][1] + diam - c + val[mn[1].first][1]);
} else if (mn[1].second != -1) {
xr = min(xr, val[i][1] + diam - c + val[mn[1].second][1]);
}
if (mn[1].first != i && mn[1].first != -1) {
yl = max(yl, val[i][0] - diam + c - val[mn[1].first][1]);
} else if (mn[1].second != -1) {
yl = max(yl, val[i][0] - diam + c - val[mn[1].second][1]);
}
if (mx[0].first != i && mx[0].first != -1) {
yr = min(yr, val[i][1] + diam - c - val[mx[0].first][0]);
} else if (mx[0].second != -1) {
yr = min(yr, val[i][1] + diam - c - val[mx[0].second][0]);
}
}
int plx = n, prx = n - 1, ply = 0, pry = -1;
for (int i = 0; i < n; i++) {
while (plx > 0 && x[i] + x[plx - 1] >= xl) {
plx--;
}
while (prx >= 0 && x[i] + x[prx] > xr) {
prx--;
}
while (ply < n && x[ply] - x[i] < yl) {
ply++;
}
while (pry + 1 < n && x[pry + 1] - x[i] <= yr) {
pry++;
}
int L = max({i + 1, plx, ply}), R = min(prx, pry);
if (L <= R) {
return true;
}
}
return false;
}
long long find_shortcut(int n, vector<int> l, vector<int> d, int c) {
::n = n; ::c = c;
for (int i = 1; i < n; i++) {
x[i] = x[i - 1] + l[i - 1];
}
for (int i = 0; i < n; i++) {
::d[i] = d[i];
}
for (int i = 0; i < n; i++) {
val[i][0] = x[i] + d[i];
val[i][1] = x[i] - d[i];
}
for (int t = 0; t < 2; t++) {
for (int i = 0; i < n; i++) {
order[t][i] = i;
}
sort(order[t], order[t] + n, [&](int i, int j) {
return (t == 0 ? val[i][0] < val[j][0] : val[i][1] < val[j][1]);
});
}
long long low = 0, high = inf / 50, ans = 0;
while (low <= high) {
long long mid = (low + high) >> 1;
if (Check(mid)) {
ans = mid;
high = mid - 1;
} else {
low = mid + 1;
}
}
return ans;
}
