#include "shortcut.h"
#include <bits/stdc++.h>
typedef long long ll;
using namespace std;
const ll INF = 1e12;
void update(vector<ll> &segtree, int pos, ll val, int node, int l, int r) {
if (l == r) segtree[node] = val;
else {
int mid = (l + r) / 2;
if (pos > mid) update(segtree, pos, val, node * 2 + 1, mid + 1, r);
else update(segtree, pos, val, node * 2, l, mid);
segtree[node] = max(segtree[node * 2], segtree[node * 2 + 1]);
}
}
ll query(vector<ll> &segtree, int a, int b, int node, int l, int r) {
if (a > b || l > b || r < a) return -INF;
if (l >= a && r <= b) return segtree[node];
int mid = (l + r) / 2;
return max(query(segtree, a, b, node * 2, l, mid), query(segtree, a, b, node * 2 + 1, mid + 1, r));
}
ll find_shortcut(int n, vector<int> l, vector<int> d, int c) {
vector<ll> p(n);
for (int i = 1; i < n; i++) p[i] = p[i - 1] + l[i - 1];
// Order the stations by their inequality stuff
vector<pair<ll, int>> iot(n);
vector<int> ord(n);
// Order by d[i] + p[i]
for (int i = 0; i < n; i++) iot[i] = {d[i] + p[i], i};
sort(iot.begin(), iot.end());
for (int i = 0; i < n; i++) ord[iot[i].second] = i;
// A segtree for each inequality
vector<ll> seg[2];
for (int i : {0, 1}) seg[i].resize(4 * n);
// Binary search for the answer
ll lo = 0, hi = INF;
while (lo != hi) {
ll mid = (lo + hi) / 2;
// Reset the segtrees
for (int i : {0, 1}) fill(seg[i].begin(), seg[i].end(), -INF);
vector<ll> half_plane(4, -4 * INF);
for (int i = n - 1; ~i; i--) {
// Get the index of the first non-ignored station
int threshold = upper_bound(iot.begin(), iot.end(), make_pair(mid - d[i] + p[i], n)) - iot.begin();
// Update the half planes
half_plane[0] = max(half_plane[0], c - mid + d[i] + p[i] + query(seg[0], threshold, n - 1, 1, 0, n - 1));
half_plane[1] = max(half_plane[1], c - mid + d[i] - p[i] + query(seg[0], threshold, n - 1, 1, 0, n - 1));
half_plane[2] = max(half_plane[2], c - mid + d[i] + p[i] + query(seg[1], threshold, n - 1, 1, 0, n - 1));
half_plane[3] = max(half_plane[3], c - mid + d[i] - p[i] + query(seg[1], threshold, n - 1, 1, 0, n - 1));
// Then add station i to the segtrees
update(seg[0], ord[i], d[i] + p[i], 1, 0, n - 1);
update(seg[1], ord[i], d[i] - p[i], 1, 0, n - 1);
}
// Check that the half-planes have a common intersection
if (half_plane[0] <= -half_plane[3] && half_plane[1] <= -half_plane[2]) hi = mid;
else lo = mid + 1;
}
return lo;
}
