#include "shortcut.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define all(x) (x).begin(), (x).end()
const int mxn = 1e6 + 100;
vector<int> l, d;
ll n, c, prf[mxn], prfR[mxn], suf[mxn];
ll get(int l, int r, bool side) {
l = max(l, 0);
r--;
if (l > r) return 0;
if (side) return prf[r] - (l == 0 ? 0 : prf[l - 1]);
return prfR[r] - (l == 0 ? 0 : prfR[l - 1]);
}
ll minCost(int x, int y, bool side) {
ll res = 0, mx[n];
memset(mx, 0, sizeof(mx));
mx[0] = d[0];
for (int i = 1; i <= x; i++) {
ll dist = mx[i - 1] + l[i - 1];
mx[i] = max(dist, (ll) d[i]);
res = max(res, dist + d[i]);
}
int split = x;
for (int i = x; i <= y; i++) {
ll goF = get(x, i, side);
ll goA = c + get(i, y - 1, side);
if (goF <= goA) split = i;
else break;
}
for (int i = x + 1; i <= split; i++) {
ll dist = mx[i - 1] + l[i - 1];
mx[i] = max(dist, (ll) d[i]);
res = max(res, dist + d[i]);
}
mx[y] = mx[x] + c;
res = max(res, mx[y] + d[y]);
for (int i = y - 1; i > split; i--) {
ll dist = mx[i + 1] + l[i];
mx[i] = max(dist, (ll) d[i]);
res = max(res, dist + d[i]);
}
for (int i = y + 1; i < n; i++) {
ll dist = mx[i - 1] + l[i - 1];
mx[i] = max(dist, (ll) d[i]);
res = max(res, dist + d[i]);
}
return res;
}
struct SGT {
vector<ll> sgt;
SGT(int sz) {
sgt.resize(4 * sz);
}
void update(int k, int l, int r, int i, ll val) {
if (l > i || r < i) return;
if (l == r) {
sgt[k] = val;
return;
}
int mid = (l + r) / 2;
update(k * 2, l, mid, i, val);
update(k * 2 + 1, mid + 1, r, i, val);
sgt[k] = max(sgt[k * 2], sgt[k * 2 + 1]);
}
ll get(int k, int l, int r, int i, int j) {
if (l > j || r < i) return 0;
if (i <= l && r <= j) return sgt[k];
int mid = (l + r) / 2;
return max(get(k * 2, l, mid, i, j), get(k * 2 + 1, mid + 1, r, i, j));
}
} sgt(mxn), sgtR(mxn);
ll only(int x, int y) {
int r = x;
ll ans = 0;
for (int i = x; i < y; i++) {
while (r < y && get(i, r + 1, 1) <= get(x, i, 1) + c + get(r + 1, y - 1, 1)) r++;
ans = max({ans, d[i] + sgt.get(1, 0, n - 1, i + 1, r) - (i == 0 ? 0 : prf[i - 1]) - (r < l.size() ? l[r] : 0), d[i] + get(x, i, 1) + c + sgtR.get(1, 0, n - 1, r + 1, y) - suf[y]});
// cout << x << " " << y << " : " << i << " " << r << " " << d[i] + sgt.get(1, 0, n - 1, i + 1, r) - (i == 0 ? 0 : prf[i - 1]) - (r < l.size() ? l[r] : 0) << endl;
}
return ans;
}
ll find_shortcut(int _n, vector<int> _l, vector<int> _d, int _c) {
n = _n, l = _l, d = _d, c = _c;
prf[0] = l[0];
for (int i = 1; i < n - 1; i++) prf[i] = prf[i - 1] + l[i];
for (int i = 0; i < n; i++) sgt.update(1, 0, n - 1, i, prf[i] + d[i]);
reverse(all(l));
prfR[0] = l[0];
for (int i = 1; i < n - 1; i++) prfR[i] = prfR[i - 1] + l[i];
reverse(all(l));
sgtR.update(1, 0, n - 1, n - 1, d[n - 1]);
for (int i = n - 2; i >= 0; i--) {
suf[i] = suf[i + 1] + l[i];
sgtR.update(1, 0, n - 1, i, suf[i] + d[i]);
}
c = 0;
ll minAns = minCost(0, 0, 1);
c = _c;
for (int i = 0; i < n; i++) {
for (int j = i + 1; j < n; j++) {
ll dist = get(i, j, 1);
if (c < dist) {
ll mx = max(minCost(i, j, 1), only(i, j));
reverse(all(l));
reverse(all(d));
mx = max(mx, minCost(n - j - 1, n - i - 1, 0));
minAns = min(minAns, mx);
reverse(all(l));
reverse(all(d));
}
}
}
return minAns;
}
