#include <bits/stdc++.h>
using namespace std;
const int N = 1000001;
long long sum_s[N], diff_s[N], sum_d[N], diff_d[N];
long long prefix_sum[N], prefix_diff[N];
long long sum[N], diff[N], x[N];
int order[N], n;
long long find_shortcut(int n, vector<int> l, vector<int> d, int c) {
::n = n;
for (int i = 0; i < n - 1; ++i) {
x[i + 1] = x[i] + l[i];
}
for (int i = 0; i < n; ++i) {
sum[i] = x[i] + d[i];
diff[i] = x[i] - d[i];
}
sort(d.rbegin(), d.rend());
iota(order, order + n, 0);
sort(order, order + n, [&](int a, int b) {
return diff[a] < diff[b];
});
for (int i = 0; i < n; ++i) {
sum_d[i] = sum[order[i]];
diff_d[i] = diff[order[i]];
}
iota(order, order + n, 0);
sort(order, order + n, [&](int a, int b) {
return sum[a] < sum[b];
});
for (int i = 0; i < n; ++i) {
sum_s[i] = sum[order[i]];
diff_s[i] = diff[order[i]];
}
prefix_sum[0] = LLONG_MIN, prefix_diff[0] = LLONG_MAX;
for (int i = 0; i < n; ++i) {
prefix_sum[i + 1] = max(prefix_sum[i], sum_d[i]);
prefix_diff[i + 1] = min(prefix_diff[i], diff_d[i]);
}
long long low = d[0] + d[1], high = sum_s[n - 1] - diff_d[0];
while (low < high) {
long long mid = (low + high) / 2;
long long min_sum = LLONG_MIN, max_sum = LLONG_MAX;
long long min_diff = LLONG_MIN, max_diff = LLONG_MAX;
for (int i = 0, j = 0; j < n; ++j) {
while (i < n && sum_s[j] - diff_d[i] > mid) {
++i;
}
if (sum_s[j] - diff_s[j] > mid) {
int y = order[j];
for (int x = 0; x < y; ++x) {
if (sum[y] - diff[x] > mid) {
min_sum = max(min_sum, -mid + c + sum[y] + sum[x]);
max_sum = min(max_sum, mid - c + diff[y] + diff[x]);
min_diff = max(min_diff, -mid + c + sum[y] - diff[x]);
max_diff = min(max_diff, mid - c + diff[y] - sum[x]);
}
}
} else if (i > 0) {
min_sum = max(min_sum, -mid + c + sum_s[j] + prefix_sum[i]);
max_sum = min(max_sum, mid - c + diff_s[j] + prefix_diff[i]);
min_diff = max(min_diff, -mid + c + sum_s[j] - prefix_diff[i]);
max_diff = min(max_diff, mid - c + diff_s[j] - prefix_sum[i]);
}
}
bool ok = false;
int l1 = n - 1, l2 = 0, r1 = n - 1, r2 = 0;
for (int i = 0; i < n; ++i) {
while (l1 >= 0 && x[i] + x[l1] >= min_sum) {
--l1;
}
while (r1 >= 0 && x[i] + x[r1] > max_sum) {
--r1;
}
while (l2 < n && x[i] - x[l2] > max_diff) {
++l2;
}
while (r2 < n && x[i] - x[r2] >= min_diff) {
++r2;
}
ok |= max(l1 + 1, l2) < min(r1 + 1, r2);
}
if (ok) {
high = mid;
} else {
low = mid + 1;
}
}
return low;
}
