#include "railroad.h"
#include <vector>
#include <set>
#include <map>
#include <algorithm>
#include <iostream>
using namespace std;
const int INF = 1'000'000'001;
int N;
set<int> pos;
map<int, int> norm;
vector<int> act;
int K;
struct ds
{
int Z;
vector<int> parent;
vector<int> subtree;
vector<int> mx;
vector<int> mn;
ds()
{
;
}
ds(int Z_)
{
Z = Z_;
parent = vector<int>(Z);
subtree = vector<int>(Z, 1);
mx = vector<int>(Z);
mn = vector<int>(Z);
for(int i = 0; i < Z; i++) parent[i] = mx[i] = mn[i] = i;
}
int root(int u)
{
if(parent[u] == u) return u;
parent[u] = root(parent[u]);
return parent[u];
}
bool connected(int u, int v)
{
return root(u) == root(v);
}
void join(int u, int v)
{
u = root(u);
v = root(v);
if(u == v) return;
if(subtree[u] < subtree[v]) swap(u, v);
parent[v] = u;
subtree[u] += subtree[v];
mx[u] = max(mx[u], mx[v]);
mn[u] = min(mn[u], mn[v]);
}
};
long long plan_roller_coaster(vector<int> s, vector<int> t)
{
s.push_back(INF);
t.push_back(1);
N = int(s.size());
for(int i = 0; i < N; i++)
{
pos.insert(s[i]);
pos.insert(t[i]);
}
int ct = -1;
for(int p: pos)
{
ct++;
norm[p] = ct;
act.push_back(p);
}
K = 1+ct;
ds DSU(K);
for(int i = 0; i < N; i++)
{
s[i] = norm[s[i]];
t[i] = norm[t[i]];
// DSU.join(s[i], t[i]);
}
// for(int i = 0; i < K; i++) cerr << i << ' ' << act[i] << '\n';
vector<int> indegree(K, 0), outdegree(K, 0);
for(int i = 0; i < N; i++)
{
outdegree[s[i]]++;
indegree[t[i]]++;
}
set<int> positive, negative;
for(int i = 0; i < K; i++)
{
if(outdegree[i] > indegree[i])
positive.insert(i);
else if(outdegree[i] < indegree[i])
negative.insert(i);
}
// cerr << "positive: ";
// for(int p: positive) cerr << p << ' ';
// cerr << '\n';
//
// cerr << "negative: ";
// for(int n: negative) cerr << n << ' ';
// cerr << '\n';
long long ans = 0;
while(!positive.empty())
{
int p = *positive.begin();
int n = *negative.begin();
// cerr << p << ' ' << n << '\n';
int a = min(p, n);
int b = max(p, n);
while(1)
{
a = DSU.root(a);
if(DSU.mx[a] >= b) break;
DSU.join(a, DSU.mx[a]+1);
}
// DSU.join(p, n);
if(n > p) ans += act[n] - act[p];
outdegree[n]++;
indegree[p]++;
// cerr << "extra edge " << n << ' ' << p << '\n';
// cerr << "ans = " << ans << '\n';
if(outdegree[n] - indegree[n] == 0) negative.erase(n);
if(indegree[p] - outdegree[p] == 0) positive.erase(p);
}
for(int i = 0; i < N; i++) DSU.join(s[i], t[i]);
// cerr << "DSU: ";
// for(int i = 0; i < K; i++) cerr << i << ' ' << DSU.root(i) << '\n';
vector< pair<int, int> > H;
for(int i = 0; i+1 < K; i++) H.push_back(make_pair(i, i+1));
sort(H.begin(), H.end(), [] (pair<int, int> g, pair<int, int> h)
{
return act[g.second] - act[g.first] < act[h.second] - act[h.first];
});
for(pair<int, int> h: H)
{
if(!DSU.connected(h.first, h.second))
{
ans += act[h.second] - act[h.first];
DSU.join(h.first, h.second);
}
}
// ans += INF;
return ans;
}
