#include "walk.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
#define X first
#define Y second
#define lc id<<1
#define rc lc|1
#define mid ((l+r)>>1)
const int MXN = 1e5+5;
const ll inf = 1e18;
namespace sub4 {
int n, m, ord[MXN], pos[MXN];
ll dis[MXN];
vector<int> y, op[MXN], cl[MXN];
ll seg[MXN<<2][2];
void build(int l=0, int r=m, int id=1) {
seg[id][0] = seg[id][1] = inf*2;
if(r-l == 1) return;
build(l, mid, lc);
build(mid, r, rc);
}
void upd(int p, bool x, int l=0, int r=m, int id=1) {
if(r-l == 1) {
if(x) seg[id][0] = dis[ord[l]]+y[ord[l]], seg[id][1] = dis[ord[l]]-y[ord[l]];
else seg[id][0] = seg[id][1] = inf*2;
return;
}
p<mid ? upd(p, x, l, mid, lc) : upd(p, x, mid, r, rc);
seg[id][0] = min(seg[lc][0], seg[rc][0]);
seg[id][1] = min(seg[lc][1], seg[rc][1]);
}
ll get(int s, int e, bool x, int l=0, int r=m, int id=1) {
if(s>=r || l>=e) return inf*2;
if(s<=l && r<=e) return seg[id][x];
return min(get(s, e, x, l, mid, lc), get(s, e, x, mid, r, rc));
}
ll min_distance(vector<int> x, vector<int> h, vector<int> l, vector<int> r, vector<int> y, int s, int g) {
n = x.size(); m = y.size();
sub4::y = y;
iota(ord, ord+m, 0);
sort(ord, ord+m, [&](int i, int j) {
return y[i]<y[j];
});
for(int i=0; i<m; i++)
pos[ord[i]] = i;
build();
for(int i=0; i<m; i++) {
op[l[i]].push_back(i);
if(r[i]+1<n) cl[r[i]+1].push_back(i);
}
for(int i : op[0]) {
dis[i] = y[i];
upd(pos[i], 1);
}
for(int i=1; i<n; i++) {
for(int j : cl[i]) upd(pos[j], 0);
for(int j : op[i]) {
int lb=-1, rb=m, mb;
while(rb-lb>1) {
mb = (lb+rb)>>1;
(y[ord[mb]]>h[i] ? rb : lb) = mb;
}
dis[j] = min(get(pos[j], rb, 0)-y[j], get(0, pos[j]+1, 1)+y[j]);
upd(pos[j], 1);
}
}
int lb=-1, rb=m, mb;
while(rb-lb>1) {
mb = (lb+rb)>>1;
(y[ord[mb]]>h[n-1] ? rb : lb) = mb;
}
ll ans = get(0, rb, 0);
if(ans>=inf) return -1;
return ans + x[n-1] - x[0];
}
}
int ordn[MXN], ordm[MXN], N;
vector<pii> vec[MXN];
vector<pii> G[MXN*23];
ll dis[MXN*23];
inline void add(int u, int v, int w) {
G[u].push_back({v, w});
G[v].push_back({u, w});
}
ll min_distance(vector<int> x, vector<int> h, vector<int> l, vector<int> r, vector<int> y, int s, int g) {
if(s==0 && g==x.size()-1) return sub4::min_distance(x, h, l, r, y, s, g);
int n = x.size(), m = y.size();
iota(ordn, ordn+n, 0);
sort(ordn, ordn+n, [&](int i, int j) {
return h[i]>h[j];
});
iota(ordm, ordm+m, 0);
sort(ordm, ordm+m, [&](int i, int j) {
return y[i]>y[j];
});
int ptr=0;
set<int> st;
for(int i=0; i<m; i++) {
while(ptr<n && h[ordn[ptr]]>=y[ordm[i]])
st.insert(ordn[ptr++]);
int lst = -1, id = -1;
for(auto it = st.lower_bound(l[ordm[i]]); it!=st.end() && (*it)<=r[ordm[i]]; it++) {
if(lst != -1) add(id, N, x[*it]-x[lst]);
lst = *it;
id = N;
vec[*it].push_back({N++, y[ordm[i]]});
}
}
vec[s].push_back({N++, 0});
vec[g].push_back({N++, 0});
for(int i=0; i<n; i++)
for(int j=1; j<vec[i].size(); j++)
add(vec[i][j-1].X, vec[i][j].X, vec[i][j-1].Y-vec[i][j].Y);
fill(dis, dis+N, inf);
priority_queue<pll> pq;
pq.push({dis[N-2]=0, N-2});
while(!pq.empty()) {
ll d = -pq.top().X;
int v = pq.top().Y;
pq.pop();
if(d!=dis[v]) continue;
for(auto [u, w] : G[v])
if(dis[u]>d+w)
pq.push({-(dis[u]=d+w), u});
}
return dis[N-1] >= inf ? -1 : dis[N-1];
}
