#include "shortcut.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn = 3010;
const ll inf = 1e18;
int n;
ll cp[maxn], cs[maxn], pref[maxn], bef[maxn], aft[maxn];
ll l[maxn], d[maxn], c;
ll dist[maxn];
struct edge
{
int to;
ll w;
edge(int _to = 0, ll _w = 0)
{
to = _to;
w = _w;
}
bool operator < (const edge &e) const
{
return w > e.w;
}
};
int used[maxn];
ll get_dist(int l, int r)
{
if (l > r)
swap(l, r);
return pref[r - 1] - pref[l - 1];
}
const int maxlog = 21;
struct sparse_table
{
ll dp[maxlog][maxn];
int lg[maxn];
void build(vector < ll > values)
{
int len = values.size();
for (int i = 1; i <= len; i ++)
{
lg[i] = lg[i / 2] + 1;
dp[0][i] = values[i - 1];
}
for (int j = 1; j < lg[len]; j ++)
{
for (int i = 1; i <= len - (1 << j) + 1; i ++)
{
dp[j][i] = dp[j - 1][i + (1 << (j - 1))];
if (dp[j - 1][i] > dp[j][i])
dp[j][i] = dp[j - 1][i];
}
}
}
ll query(int l, int r)
{
if (l > r)
return 0;
int mlog = lg[r - l + 1] - 1;
ll ans = dp[mlog][r - (1 << mlog) + 1];
if (dp[mlog][l] > ans)
ans = dp[mlog][l];
return ans;
}
};
struct point
{
ll x, y;
point(ll _x = 0, ll _y = 0)
{
x = _x;
y = _y;
}
};
struct rectangle
{
point centre;
ll diagonal;
rectangle(point _centre = point(), ll _diagonal = 0)
{
centre = _centre;
diagonal = _diagonal;
}
};
ll p[maxn];
struct event
{
int type;
};
ll up_bound[2][maxn];
ll dw_bound[2][maxn];
bool check(ll x)
{
vector < rectangle > con;
for (int i = 1; i <= n; i ++)
{
con.push_back(rectangle(point(p[i], 0), inf));
for (int j = i + 1; j <= n; j ++)
{
ll path = get_dist(i, j) + d[i] + d[j];
if (path <= x)
continue;
//cout << "condition " << i << " " << j << endl;
//cout << p[i] << " " << p[j] << " " << x - d[i] - d[j] << endl;
/// |x[i] - x[l]| + |x[j] - x[r]| + d[i] + d[j] + c<= k
/// |x[l] - x[i]| + |x[r] - x[j]| <= k - d[i] - d[j] - c
con.push_back(rectangle(point(p[i], p[j]), x - d[i] - d[j] - c));
}
}
if (con.empty())
return true;
///pair < ll, ll > ans;
dw_bound[0][0] = -inf;
up_bound[0][0] = inf;
for (int i = 0; i < con.size(); i ++)
{
up_bound[0][i + 1] = up_bound[0][i];
up_bound[0][i + 1] = min(up_bound[0][i + 1], con[i].centre.y + con[i].diagonal + con[i].centre.x);
}
for (int i = 0; i < con.size(); i ++)
{
ll top = inf;
ll bot = -inf;
top = min(top, -con[i].centre.x + up_bound[0][i + 1]);
for (int j = 0; j <= i; j ++)
{
///top = min(top, con[j].centre.y + con[j].diagonal - (con[i].centre.x - con[j].centre.x));
bot = max(bot, con[j].centre.y - con[j].diagonal + (con[i].centre.x - con[j].centre.x));
}
for (int j = i + 1; j < con.size(); j ++)
{
top = min(top, con[j].centre.y + con[j].diagonal - (con[j].centre.x - con[i].centre.x));
bot = max(bot, con[j].centre.y - con[j].diagonal + (con[j].centre.x - con[i].centre.x));
}
for (int f = 1; f <= n; f ++)
{
if (p[f] >= bot && p[f] <= top)
{
return true;
}
}
}
return false;
pair < ll, ll > ans = {-1, -1};
for (int l = 1; l <= n; l ++)
for (int r = l; r <= n; r ++)
{
bool tf = true;
for (rectangle rec : con)
{
ll val = abs(p[l] - rec.centre.x) + abs(p[r] - rec.centre.y);
if (val > rec.diagonal)
{
//cout << "fuck " << l << " " << r << endl;
//cout << "rectangle " << rec.centre.x << " " << rec.centre.y << " " << rec.diagonal << endl;
tf = false;
break;
}
}
if (tf)
{
ans = {p[l], p[r]};
}
}
if (ans.first == -1)
return false;
}
ll find_shortcut(int N, vector<int> L, vector<int> D, int C)
{
n = N;
c = C;
for (int i = 0; i < n - 1; i ++)
l[i + 1] = L[i];
for (int i = 0; i < n; i ++)
d[i + 1] = D[i];
p[1] = 0;
for (int i = 2; i <= n; i ++)
{
p[i] = p[i - 1] + l[i - 1];
}
for (int i = 1; i <= n; i ++)
{
pref[i] = pref[i - 1] + l[i];
}
for (int i = 1; i <= n; i ++)
{
cp[i] = cp[i - 1] + l[i - 1];
cp[i] = max(cp[i], d[i]);
bef[i] = bef[i - 1];
for (int j = 1; j < i; j ++)
{
bef[i] = max(bef[i], get_dist(i, j) + d[i] + d[j]);
}
}
for (int i = n; i > 0; i --)
{
cs[i] = cs[i + 1] + l[i];
cs[i] = max(cs[i], d[i]);
aft[i] = aft[i + 1];
for (int j = i + 1; j <= n; j ++)
{
aft[i] = max(aft[i], get_dist(i, j) + d[i] + d[j]);
}
}
ll lf = 0, rf = inf;
while(lf <= rf)
{
ll mf = (lf + rf) / 2;
if (check(mf))
rf = mf - 1;
else
lf = mf + 1;
}
return lf;
}
