#include <bits/stdc++.h>
#include "walk.h"
using namespace std;
#define sz(x) (long long)x.size()
#define all(x) x.begin() , x.end()
const long long N = 1e9 + 7;
const long long inf = 1e18 + 7;
struct Segt{// range add update , range min query , polong long set update
struct Node{
long long left , right;
long long val , lzt;
Node():left(-1) , right(-1) , val(inf) , lzt(0ll){}
} dummy;
vector < Node > tree;
long long create_node(){
tree.push_back(dummy);
return sz(tree) - 1;
}
Segt(){
tree.resize(1);
}
void push(long long ind , long long l , long long r){
if(tree[ind].lzt){
if(tree[ind].val != inf)tree[ind].val += tree[ind].lzt;
if(tree[ind].left == -1)tree[ind].left = create_node();
tree[tree[ind].left].lzt += tree[ind].lzt;
if(tree[ind].right == -1)tree[ind].right = create_node();
tree[tree[ind].right].lzt += tree[ind].lzt;
tree[ind].lzt = 0;
}
}
void set(long long ind , long long l , long long r , long long p , long long v){
push(ind,l,r);
if(l == r){
tree[ind].val = v;
return;
}
long long mid = (l + r) / 2;
if(tree[ind].left == -1)tree[ind].left = create_node();
if(tree[ind].right == -1)tree[ind].right = create_node();
if(mid >= p){
set(tree[ind].left , l , mid , p , v);
}
else{
set(tree[ind].right , mid+1 , r , p , v);
}
push(tree[ind].left , l , mid);
push(tree[ind].right , mid+1 , r);
tree[ind].val = min(tree[tree[ind].left].val , tree[tree[ind].right].val);
}
void set(long long p , long long v){
set(0 , 0 , N , p , v);
}
void add(long long ind , long long l , long long r , long long ql , long long qr , long long qv){
push(ind,l,r);
if(l >= ql and r <= qr){
tree[ind].lzt += qv;
push(ind,l,r);
return;
}
else if(l > qr or r < ql){
return;
}
long long mid = (l + r) / 2;
if(tree[ind].left == -1)tree[ind].left = create_node();
if(tree[ind].right == -1)tree[ind].right = create_node();
add(tree[ind].left , l , mid , ql , qr , qv);
add(tree[ind].right , mid+1 , r , ql , qr , qv);
tree[ind].val = min(tree[tree[ind].left].val , tree[tree[ind].right].val);
}
void add(long long l , long long r , long long v){
add(0 , 0 , N , l , r , v);
}
long long query(long long ind , long long l , long long r , long long ql , long long qr){
if(ind == -1)return inf;
push(ind,l,r);
if(l >= ql and r <= qr){
return tree[ind].val;
}
else if(l > qr or r < ql)return inf;
else{
long long mid = (l + r) / 2;
return min(query(tree[ind].left , l , mid , ql , qr) , query(tree[ind].right , mid+1 , r , ql , qr));
}
}
long long query(long long l , long long r){
return query(0 , 0 , N , l , r);
}
};
long long min_distance(vector<int> X, vector<int> H, vector<int> L, vector<int> R, vector<int> Y, int S, int G) {
const int tar = 2036;
int bruh0 = 0 , bruh1 = 0;
for(int i = 0;i<sz(X);i++){
if(X[i] == tar){
bruh0 = H[i];
// cout << X[i] << " - height : " << H[i] << endl;
}
}
vector < long long > range_start[sz(X)] , range_end[sz(X)];
for(long long i = 0;i<sz(L);i++){
range_start[L[i]].push_back(i);
range_end[R[i]].push_back(i);
}
Segt segt_top , segt_down;
segt_top.set(0 , 0);
segt_down.set(0 , 0);
map < int , int > fuck2;
auto merge = [&](vector < long long > &a , vector < long long > &b){
if(sz(a) > sz(b))swap(a,b);
for(auto itr : a)b.push_back(itr);
a.clear();
};
for(long long i = 0;i<sz(X);i++){
bool is_reached = (segt_top.query(0 , H[i]) != inf) or (segt_down.query(0 , H[i]) != inf);
// bool is_reached = 1;
if(is_reached){
vector < pair < int , long long > > make_updates;
// cout << "X : " << X[i] << " " << H[i] << endl;
for(auto itr : range_start[i]){
if(R[itr] < i)continue;
fuck2[Y[itr]]++;
long long segres1 = segt_top.query(Y[itr] , H[i]) , segres2 = segt_down.query(0 , Y[itr]);
if(segres1 != inf or segres2 != inf){
long long min_distance = min(segt_top.query(Y[itr] , H[i]) - Y[itr], segt_down.query(0 , Y[itr]) + Y[itr]);
// cout << "new edge : " << X[i] << " : " << L[itr] << " " << R[itr] << " " << Y[itr] << " : " << min_distance << endl;
// cout << "res : " << segt_top.query(Y[itr] , H[i]) << " , " << segt_down.query(0 , Y[itr]) << endl;
make_updates.push_back({itr , min_distance});
}
// else cout << "failed : " << L[itr] << " " << R[itr] << " " << Y[itr] << endl;
}
for(long long j = 0;j<sz(make_updates);j++){
segt_top.set(Y[make_updates[j].first] , make_updates[j].second + Y[make_updates[j].first]);
segt_down.set(Y[make_updates[j].first] , make_updates[j].second - Y[make_updates[j].first]);
}
if(i != (sz(X)-1)){
for(auto itr : range_end[i]){
fuck2[Y[itr]]--;
if(fuck2[Y[itr]] == 0){
segt_top.set(Y[itr] , inf);
segt_down.set(Y[itr] , inf);
// cout << "SETTED " << Y[itr] << " to inf" << endl;
}
}
}
if(i == 0){
segt_top.set(0 , inf);
segt_down.set(0 , inf);
}
if(i != (sz(X)-1)){
segt_top.add(0 , N , X[i+1] - X[i]);
segt_down.add(0 , N , X[i+1] - X[i]);
}
// cout << "starts : ";for(auto itr : range_start[i])cout << R[itr] << "," << Y[itr] << "," << fuck2[Y[itr]] << " ";cout << endl;
// cout << "ends : ";for(auto itr : range_end[i])cout << L[itr] << "," << Y[itr] << "," << fuck2[Y[itr]] << " ";cout << endl;
// cout << "minimum : " << segt_top.query(0 , H[i]) << " , " << segt_down.query(0 , H[i]) << endl;
// if(segt_top.query(0 , N) >= inf and sz(range_start[i]) > 0 and X[i] != 2043 and X[i] != 2044 and X[i] != 2045 and X[i] != 2046 and X[i] != 2047 and X[i] != 2048 and X[i] != 2049 and X[i] != 2050 and X[i] != 2051 and X[i] != 2052){
// cout << "stop : " << X[i] << endl;
// return 0ll;
// }
// else cout << "continue : " << X[i] << " , " << (segt_top.query(0 , N) < inf) << endl;
}
else{
if(i != (sz(X)-1))merge(range_start[i] , range_start[i+1]);
}
}
long long ret = segt_top.query(0 , H[sz(H) - 1]);
if(ret < inf)return ret;
else return -1;
}
