#include <bits/stdc++.h>
using namespace std;
long long min_distance(vector<int> x, vector<int> h, vector<int> l, vector<int> r, vector<int> y, int s, int g){
int n = x.size();
int m = y.size();
vector<tuple<int, int, int>> T;
for (int i = 0; i < n; i++){
T.push_back(make_tuple(h[i], 1, i));
}
for (int i = 0; i < m; i++){
T.push_back(make_tuple(y[i], 0, i));
}
sort(T.begin(), T.end(), greater<tuple<int, int, int>>());
vector<vector<int>> id(m);
set<int> st;
for (int i = 0; i < n + m; i++){
int t = get<1>(T[i]);
int p = get<2>(T[i]);
if (t == 0){
auto itr = st.lower_bound(l[p]);
while (true){
id[p].push_back(*itr);
if (*itr == r[p]){
break;
}
itr++;
}
}
if (t == 1){
st.insert(p);
}
}
vector<vector<int>> h2(n);
for (int i = 0; i < n; i++){
h2[i].push_back(0);
}
for (int i = 0; i < m; i++){
for (int j : id[i]){
h2[j].push_back(y[i]);
}
}
for (int i = 0; i < n; i++){
sort(h2[i].begin(), h2[i].end());
h2[i].erase(unique(h2[i].begin(), h2[i].end()), h2[i].end());
}
int V = 0;
vector<vector<int>> id2(n);
for (int i = 0; i < n; i++){
int cnt = h2[i].size();
id2[i] = vector<int>(cnt);
for (int j = 0; j < cnt; j++){
id2[i][j] = V;
V++;
}
}
vector<vector<pair<int, int>>> E(V);
for (int i = 0; i < n; i++){
int cnt = h2[i].size();
for (int j = 0; j < cnt - 1; j++){
int v = id2[i][j];
int w = id2[i][j + 1];
int d = h2[i][j + 1] - h2[i][j];
E[v].push_back(make_pair(d, w));
E[w].push_back(make_pair(d, v));
}
}
for (int i = 0; i < m; i++){
int cnt = id[i].size();
vector<int> t(cnt);
for (int j = 0; j < cnt; j++){
int p = lower_bound(h2[id[i][j]].begin(), h2[id[i][j]].end(), y[i]) - h2[id[i][j]].begin();
t[j] = id2[id[i][j]][p];
}
for (int j = 0; j < cnt - 1; j++){
int v = t[j];
int w = t[j + 1];
int d = x[id[i][j + 1]] - x[id[i][j]];
E[v].push_back(make_pair(d, w));
E[w].push_back(make_pair(d, v));
}
}
int s2 = id2[s][0];
int g2 = id2[g][0];
vector<long long> d(V, -1);
priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> pq;
pq.push(make_pair(0, s2));
while (!pq.empty()){
long long dd = pq.top().first;
int v = pq.top().second;
pq.pop();
if (d[v] == -1){
d[v] = dd;
for (auto P : E[v]){
int w = P.second;
if (d[w] == -1){
pq.push(make_pair(dd + P.first, w));
}
}
}
}
return d[g2];
}
