#include "walk.h"
#include <bits/stdc++.h>
using namespace std;
#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define trav(a, x) for(auto& a : x)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
#define eb emplace_back
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
const ll INF =1e18;
#ifdef LOCAL
#include "../../../../MixedFunc/pretty_debug.h"
#else
#define debug(...) //ignore
#endif
struct Graph {
int n,m;
vi x,y,h;
unordered_map<ll, int> V; // verts, indexed by 2e9*x+h
vector<vector<pair<int,ll>>> E; // adj-list
vector<map<ll,int> > perBuild, perWalk;
Graph(vi x, vi y, vi h)
: n(sz(x)), m(sz(y)), x(x), y(y), h(h), perBuild(n), perWalk(m) {}
int at(ll x, ll h) { // return vertex handle of (x,h)
auto p = x*(ll(2e9))+ h;
if (!V.count(p)) { V[p] = sz(E); E.eb(); }
return V[p];
}
void add(int build, int walk) { // pt (x[build], y[walk]) is important
ll X = x[build], Y = y[walk];
assert(h[build] >= Y);
int q = at(X, Y);
perBuild[build][Y] = q;
perWalk[walk][X] = q;
}
void edge(int a, int b, ll c){ // create edge
E[a].eb(b,c);
E[b].eb(a,c);
}
void edges(map<ll,int>& vert) { // create edges on line
vector<pair<ll,int> > vv(all(vert));
rep(i,1,sz(vv))
edge(vv[i-1].second, vv[i].second, vv[i].first-vv[i-1].first);
}
void addUpDown(vi l, vi r) { // add things directely above/below points added.
vector<vi> start(n), end(n);
rep(i,0,m) start[l[i]].eb(i), end[r[i]].eb(i);
map<ll,int> active;
rep(i,0,n) {
trav(w,end[i]) active.erase(y[w]);
trav(w,start[i]) active[y[w]] = w;
vi toAdd;
for(auto [hh, _] : perBuild[i]) {
auto it = active.upper_bound(hh);
auto maybeAdd = [&](int w) { if (y[w] <= h[i]) toAdd.eb(w); };
if(it != active.end()) maybeAdd(it->second);
it = active.lower_bound(hh);
if(it != active.begin()) maybeAdd((--it)->second);
}
trav(w, toAdd) add(i,w);
}
}
void build(){
trav(v, perBuild) edges(v);
trav(v, perWalk) edges(v);
}
};
template<class T>
auto dijkstra(int source, vector<vector<pair<int, T>>> &g) {
int n = sz(g);
vector<T> dist(n, numeric_limits<T>::max());
//vector<pair<int,T> > dad(n, {-1, 0});
priority_queue<pair<T,int> > pq;
dist[source] = 0;
pq.emplace(0,source);
while(!pq.empty()) {
T d; int x;
tie(d,x) = pq.top();
d = -d;
pq.pop();
if(d > dist[x]) continue;
for(auto [y,w] : g[x]) {
if(dist[y] > d + w) {
dist[y] = d + w;
//dad[y] = {x, w};
pq.emplace(-dist[y], y);
}
}
}
return dist;
}
ll min_distance(vi x, vi h, vi l, vi r, vi y, int s, int g) {
int n = sz(x), m = sz(l);
debug(n,m);
auto stALL= [&](){
vector<map<ll,int>> Q;
auto pcomp = [&] (vi idx) {
Q.eb();
int hh = 0;
for(int i : idx) if(h[i] > hh) {
hh = h[i];
Q.back()[hh] = i;
}
};
{ vi ind; rep(i,s,n) ind.eb(i); pcomp(ind); }
{ vi ind; for(int i = s; i >= 0; --i) ind.eb(i); pcomp(ind); }
{ vi ind; rep(i,g,n) ind.eb(i); pcomp(ind); }
{ vi ind; for(int i = g; i >= 0; --i) ind.eb(i); pcomp(ind); }
//debug(Q);
Graph G(x,y,h);
int S = G.perBuild[s][0] = G.at(x[s], 0);
int T = G.perBuild[g][0] = G.at(x[g], 0);
debug("added", s, g);
rep(i,0,m) {
// add endpoints
G.add(l[i],i);
G.add(r[i],i);
// add closest to s and g in each direction.
// for(auto &q: Q) {
// auto it = q.lower_bound(y[i]);
// if(it == q.end()) continue;
// int j = it->second;
// if(l[i] <= j && j <= r[i]) G.add(j, i);
// }
}
debug("added pts 1");
debug(sz(G.E));
G.addUpDown(l,r);
debug("added pts 2");
debug(sz(G.E));
G.build();
debug("added edges");
auto dist = dijkstra(S, G.E);
//auto[dist, dad] = dijkstra(at(x[s],0),E);
//for(int q = at(x[g],0); dad[q].first != -1; q = dad[q].first) {
// debug(iV[q]);
//}
ll ans = dist[T];
if (ans >= INF) ans = -1;
return ans;
};
return stALL();
}
