#include "shortcut.h"
#include <bits/stdc++.h>
using namespace std;
const int maxn = 3e3 + 20;
const long long inf = 1e18L;
long long len[maxn];
long long max3[maxn][maxn];
long long max5[maxn][maxn];
long long max6[maxn][maxn];
int depth[maxn];
int n, c;
long long calc(long long lim) {
for (int j = 1; j <= n; j++) {
for (int i = 1; i < j; i++) {
max3[i][j] = (i > 1 ? max3[i - 1][j] : -inf);
long long d1 = - len[i] - len[j] + c + depth[i] + depth[j];
long long d2 = len[j] - len[i] + depth[i] + depth[j];
if (d2 > lim) {
max3[i][j] = max(max3[i][j], d1);
}
}
}
for (int i = 1; i <= n; i++) {
for (int j = i + 2; j <= n; j++) {
max3[i][j] = max(max3[i][j], max3[i][j - 1]);
}
}
for (int j = 1; j <= n; j++) {
for (int i = j - 1; i >= 1; i--) {
max5[i][j] = (i + 1 < j ? max(max5[i + 1][j], max5[i][j - 1]) : -inf);
long long d1 = len[i] - len[j] + c + depth[i] + depth[j];
long long d2 = len[j] - len[i] + depth[i] + depth[j];
if (d2 > lim) {
max5[i][j] = max(max5[i][j], d1);
}
}
}
for (int j = n; j >= 1; j--) {
for (int i = 1; i <= n; i++) {
max6[i][j] = max((i > 1 ? max6[i - 1][j] : -inf), (j < n ? max6[i][j + 1] : -inf));
long long d1 = len[j] - len[i] + c + depth[i] + depth[j];
long long d2 = len[j] - len[i] + depth[i] + depth[j];
if (d2 > lim) {
max6[i][j] = max(max6[i][j], d1);
}
}
}
long long res = inf;
for (int x = 1; x <= n; x++) {
for (int y = x + 1; y <= n; y++) {
long long mx = 0;
for (int i = 1; i <= n; i++) {
for (int j = i + 1; j <= x; j++) {
if (len[j] - len[i] + depth[i] + depth[j] > lim) {
mx = max(mx, inf);
}
}
}
for (int i = y; i <= n; i++) {
for (int j = i + 1; j <= n; j++) {
if (len[j] - len[i] + depth[i] + depth[j] > lim) {
mx = max(mx, inf);
}
}
}
mx = max(mx, max3[x][y] + (len[x] + len[y]));
for (int i = x; i <= y - 1; i++) {
for (int j = y; j <= n; j++) {
long long d1 = len[i] + len[j] + c + depth[i] + depth[j] - (len[x] + len[y]);
long long d2 = len[j] - len[i] + depth[i] + depth[j];
if (d2 > lim) {
mx = max(mx, d1);
}
}
}
mx = max(mx, max5[x][y] + (len[y] - len[x]));
mx = max(mx, max6[x][y] - (len[y] - len[x]));
res = min(res, mx);
}
}
return res;
}
long long dist[maxn * maxn];
long long find_shortcut(int _n, vector<int> _len, vector<int> _depth, int _c) {
n = _n;
c = _c;
len[1] = 0;
for (int i = 2; i <= n; i++) {
len[i] = len[i - 1] + _len[i - 2];
}
for (int i = 1; i <= n; i++) {
depth[i] = _depth[i - 1];
}
int cnt = 0;
for (int i = 1; i <= n; i++) {
for (int j = i + 1; j <= n; j++) {
dist[cnt++] = len[j] - len[i] + depth[i] + depth[j];
}
}
sort(dist, dist + cnt, greater<>());
long long res = dist[0];
int lt = 0;
int rt = cnt - 1;
while (lt <= rt) {
int mt = (lt + rt) / 2;
long long mx = calc(dist[mt] - 1);
if (mx < dist[mt]) {
res = max(mx, dist[mt + 1]);
lt = mt + 1;
}
else {
rt = mt - 1;
}
}
return res;
}
