#include "railroad.h"
#ifndef EVAL
#include "grader.cpp"
#endif
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pii pair<int,int>
const int MAXN = 4e5+5;
ll inf = 1e18;
int n;
vector<int> s, t;
vector<int> edges[MAXN], rev[MAXN];
vector<pii> Eedges[MAXN], Erev[MAXN];
vector<pii> all;
int used[MAXN];
struct segtree{
int sz;
vector<int> t;
void init(int n){
sz = n;
t.assign(n*2,0);
}
void update(int l, int r, int val){
assert(l <= r);
for(l+=sz,r+=sz; l<=r; l>>=1,r>>=1){
if(l%2==1)t[l++] += val;
if(r%2==0)t[r--] += val;
}return;
}
int get(int pos){
int res = 0;
for(pos += sz; pos > 0; pos >>= 1)res += t[pos];
return res;
}
}seg[2];
int pos[MAXN];
ll plan_roller_coaster(vector<int> sk, vector<int> tk) {
s = sk, t = tk;
n = s.size();
seg[0].init(n*2);
seg[1].init(n*2);
for(int i=0;i<n;i++){
all.push_back({s[i], i});
all.push_back({t[i], i+n});
edges[i].push_back(i+n);
rev[i+n].push_back(i);
}
sort(all.begin(), all.end());
for(int i=0;i<(int)all.size();i++){
auto [x, y] = all[i];
pos[y] = i;
}
auto [no_need_1, fff] = all[0];
auto [no_need_2, sss] = all.back();
edges[sss].push_back(fff);
rev[fff].push_back(sss);
for(int i=0;i<(int)all.size();i++){
auto [u, p] = all[i];
for(auto to : edges[p]){
if(pos[to] > i){
seg[0].update(i, pos[to]-1, 1);
}else {
seg[1].update(pos[to], i-1, 1);
}
}
}
{ /// Making A = B
for(int i=0;i<(int)all.size()-1;i++){
int ind1 = all[i].second;
int ind2 = all[i+1].second;
int A = seg[0].get(i);
int B = seg[1].get(i);
//~ if(i >= 15000)cout << i << ": ";
//~ if(i >= 15000)cout << A << '-' << B << '\n';
//~ if(A > B)return 1000000000;
if(A < B){
Eedges[ind1].push_back({ind2,B-A});
Erev[ind2].push_back({ind1,B-A});
//~ seg[0].update(i,i,B-A);
A = B;
}
}
}
/// check for connectivity
queue<int> q;
q.push(0);
used[0] = true;
while(!q.empty()){
int u = q.front();q.pop();
for(auto v : edges[u]){
if(!used[v]){
q.push(v);used[v] = true;
}
}for(auto [v,c] : Eedges[u]){
if(!used[v]){
q.push(v);used[v] = true;
}
}
}
for(int i=0;i<n;i++){
if(!used[i])return 987654321;
}
memset(used, 0, sizeof used);
q.push(0);
used[0] = true;
while(!q.empty()){
int u = q.front();q.pop();
for(auto v : rev[u]){
if(!used[v]){
q.push(v);used[v] = true;
}
}for(auto [v,c] : Erev[u]){
if(!used[v]){
q.push(v);used[v] = true;
}
}
}
for(int i=0;i<n*2;i++){
if(!used[i])return 123456789;
}
/// check for eulerian circuit
for(int i=0;i<n*2;i++){
ll s1 = edges[i].size(), s2 = rev[i].size();
for(auto [u, c] : Eedges[i])s1 += c;
for(auto [u, c] : Erev[i])s2 += c;
if(s1 != s2)return 999999999;
}
return 0;
}
