#include <bits/stdc++.h>
#include "walk.h"
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define pb push_back
#define FIO ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
using namespace std;
typedef long long ll;
typedef pair <ll, ll> pii;
typedef vector <int> vi;
const int N = 1e5 + 7;
const ll inf = 1e18;
ll dis[6*N];
map <int, int> ma[N];
map <int, set <int> > se;
vector <int> ad[N], re[N];
vector <pii> adj[6*N];
inline void Edge(int x, int y, int w) {
adj[x].pb({y, w});
adj[y].pb({x, w});
}
ll min_distance(vi x, vi h, vi l, vi r, vi y, int sta, int en) {
int n = x.size(), m = l.size();
vector <int> v, gl(n, -1), gr(n, -1);
stack <int> st;
for (int i = 0; i < n; i++) {
while (!st.empty() && h[st.top()] <= h[i]) st.pop();
if (!st.empty()) gl[i] = st.top();
st.push(i);
}
while (!st.empty()) st.pop();
for (int i = n-1; i >= 0; i--) {
while (!st.empty() && h[st.top()] <= h[i]) st.pop();
if (!st.empty()) gr[i] = st.top();
st.push(i);
}
auto Do = [&](int z) {
v.clear();
for (int i = 0; i < m; i++) if (l[i] < z && z < r[i] && y[i] <= h[z]) {
l.pb(z);
r.pb(r[i]);
y.pb(y[i]);
r[i] = z;
}
m = l.size();
for (int i = 0; i < m; i++) if (l[i] < z && z < r[i] && y[i] > h[z]) v.pb(i);
sort(all(v), [&](int a, int b) {return y[a] < y[b];});
int le = z, ri = z;
for (int i = 0; i < v.size(); i++) {
while (h[le] < y[v[i]]) le = gl[le];
while (h[ri] < y[v[i]]) ri = gr[ri];
if (le != l[v[i]]) {
l.pb(l[v[i]]);
r.pb(le);
y.pb(y[v[i]]);
}
if (ri != r[v[i]]) {
l.pb(ri);
r.pb(r[v[i]]);
y.pb(y[v[i]]);
}
l[v[i]] = le;
r[v[i]] = ri;
}
m = l.size();
};
Do(sta);
Do(en);
int cnt = 0;
ma[sta][0] = cnt++;
ma[en][0] = cnt++;
for (int i = 0; i < m; i++) {
if (ma[l[i]].find(y[i]) == ma[l[i]].end()) ma[l[i]][y[i]] = cnt++;
if (ma[r[i]].find(y[i]) == ma[r[i]].end()) ma[r[i]][y[i]] = cnt++;
ad[l[i]].pb(y[i]);
re[r[i]].pb(y[i]);
se[y[i]].insert(l[i]);
se[y[i]].insert(r[i]);
}
multiset <int> t;
t.insert(0);
for (int i = 0; i < n; i++) {
for (auto it : ad[i]) t.insert(it);
auto down = [&](int it) {
int z = *(--t.lower_bound(it));
if (ma[i].find(z) == ma[i].end()) ma[i][z] = cnt++;
Edge(ma[i][it], ma[i][z], it-z);
se[z].insert(i);
};
for (auto it : ad[i]) down(it);
for (auto it : re[i]) down(it);
for (auto it : re[i]) t.erase(t.find(it));
}
for (int i = 0; i < m; i++) {
auto p = se[y[i]].find(l[i]);
int la = l[i]; ++p;
while (p != se[y[i]].end() && *p <= r[i]) {
Edge(ma[la][y[i]], ma[*p][y[i]], x[*p]-x[la]);
la = *p;
++p;
}
}
for (int i = 1; i < cnt; i++) dis[i] = inf;
set <pii> s;
s.insert({0, 0});
while (!s.empty()) {
auto p = s.begin();
int xx = p->S;
s.erase(p);
for (auto yy : adj[xx]) {
if (dis[xx] + yy.S < dis[yy.F]) {
if (dis[yy.F] != inf) s.erase({dis[yy.F], yy.F});
dis[yy.F] = dis[xx] + yy.S;
s.insert({dis[yy.F], yy.F});
}
}
}
if (dis[1] == inf) return -1;
return dis[1];
}
