#include "shortcut.h"
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define ar array
#define all(x) x.begin(), x.end()
using i64 = long long;
const i64 inf = 1e15;
struct square{
i64 x1, x2, y1, y2;
square(i64 x1 = 0, i64 x2 = 0, i64 y1 = 0, i64 y2 = 0) : x1(x1), x2(x2), y1(y1), y2(y2) {}
square f(square q){
return square(max(x1, q.x1), min(x2, q.x2), max(y1, q.y1), min(y2, q.y2));
}
bool check(i64 x, i64 y){
return x1 <= x && x2 >= x && y1 <= y && y2 >= y;
}
};
struct SegTree{
vector <ar<i64,2>> T;
int n;
bool isMax;
SegTree(int n, bool isMax = false) : n(n), isMax(isMax) {
T.resize(n * 4 + 5, {inf, -1});
}
void upd(int v, int l, int r, int p, i64 x, int j){
if ( l == r ){
if ( T[v][0] > x ){
T[v] = {x, j};
}
return;
}
int m = (l + r) / 2;
if ( p <= m ) upd(v * 2, l, m, p, x, j);
else upd(v * 2 + 1, m + 1, r, p, x, j);
T[v] = min(T[v * 2], T[v * 2 + 1]);
}
void upd(int p, i64 x, int j){
if ( isMax ) x = -x;
upd(1, 0, n, p, x, j);
}
ar <i64,2> get(int v, int l, int r, int tl, int tr){
ar <i64,2> ret = {inf, -1};
if ( l > tr or r < tl ) return ret;
if ( tl <= l && tr >= r ){
return T[v];
}
int m = (l + r) / 2;
return min(get(v * 2, l, m, tl, tr), get(v * 2 + 1, m + 1, r, tl, tr));
}
int get(int l, int r){
return get(1, 0, n, l, r)[1];
}
};
long long find_shortcut(int n, std::vector<int> L, std::vector<int> d, int C){
vector <i64> x(n), A(n), B(n);
for ( int i = 1; i < n; i++ ){
x[i] = x[i - 1] + L[i - 1];
}
for ( int i = 0; i < n; i++ ){
A[i] = x[i] + d[i];
B[i] = x[i] - d[i];
}
auto P = B;
P.pb(-inf), P.pb(inf);
sort(all(P));
P.resize(unique(all(P)) - P.begin());
int m = P.size();
auto get = [&](i64 x){
return lower_bound(all(P), x) - P.begin();
};
auto ok = [&](i64 k){
i64 kk = k - C;
vector <ar<i64,3>> pt;
auto add = [&](int i, int j){
if ( i == -1 ) return;
pt.pb({x[i] + x[j], x[i] - x[j], kk - (d[i] + d[j])});
};
vector <SegTree> seg(4, SegTree(m));
seg[1] = seg[3] = SegTree(m, 1);
for ( int i = 0; i < n; i++ ){
int u = get(A[i] - k) - 1, v = get(B[i]);
vector <i64> q = {A[i], A[i], B[i], B[i]};
for ( int j = 0; j < 4; j++ ){
add(seg[j].get(0, u), i);
seg[j].upd(v, q[j], i);
}
}
if ( pt.empty() ) return true;
auto [X, Y, d] = pt[0];
square t = square(X - d, X + d, Y - d, Y + d);
for ( int i = 1; i < (int)pt.size(); i++ ){
auto [x, y, d] = pt[i];
t = t.f(square(x - d, x + d, y - d, y + d));
}
if ( t.x1 > t.x2 || t.y1 > t.y2 ){ // area 0
return false;
}
bool flag = false;
int l = n, r = n - 1;
set <i64> st;
for ( int i = 0; i < n; i++ ){
while ( l > 0 && t.x1 - x[i] <= x[l - 1] ){
st.insert(x[--l]);
}
while ( r >= 0 && t.x2 - x[i] < x[r] ){
st.erase(x[r--]);
}
i64 p = -t.y2 + x[i], q = -t.y1 + x[i];
if ( l <= i && r >= i ) st.erase(x[i]);
if ( st.lower_bound(p) != st.upper_bound(q) ){
flag = true;
}
if ( l <= i && r >= i ) st.insert(x[i]);
}
//~ for ( int i = 0; i < n; i++ ){
//~ for ( int j = i + 1; j < n; j++ ){
//~ flag |= t.check(x[i] + x[j], x[i] - x[j]);
//~ }
//~ }
return flag;
};
i64 l = 0, r = 1e15;
while ( l < r ){
i64 m = (l + r) / 2;
if ( ok(m) ){
r = m;
} else l = m + 1;
}
return l;
}
