#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
struct Dsu {
ll cnt;
vector<ll> parent, rank, size;
Dsu(ll N) {
cnt = 2 * N;
parent.resize(N);
rank.resize(N);
size.resize(N, 1);
for (ll i = 0; i < N; i++) {
parent[i] = i;
}
}
bool isSameSet(ll i, ll j) {
return findSet(i) == findSet(j);
}
ll findSet(ll i) {
if (parent[i] == i) {
return i;
} else {
return parent[i] = findSet(parent[i]);
}
}
void unionSet(ll i, ll j) {
ll x = findSet(i);
ll y = findSet(j);
if (x != y) {
if((size[x]%2)==(size[y]%2)&&size[y]%2==1){
cnt -= 2;
}
if (rank[x] > rank[y]) {
parent[y] = x;
size[x] += size[y];
} else if (rank[x] < rank[y]) {
parent[x] = y;
size[y] += size[x];
} else {
parent[x] = y;
size[y] += size[x];
rank[y]++;
}
}
}
ll res() {
return cnt;
}
};
vector<ll> calculate_costs(vector<int> W, vector<int> A, vector<int> B, vector<int> E) {
if(E.size()>10){
vector<pair<ll, int>> sorted_W;
ll n = W.size();
for (int i = 0; i < n; i++) {
sorted_W.push_back({W[i], i});
}
sort(sorted_W.begin(), sorted_W.end());
vector<int> new_A(n), new_B(n);
for (int i = 0; i < n; i++) {
new_A[i] = A[sorted_W[i].second];
new_B[i] = B[sorted_W[i].second];
}
A = new_A;
B = new_B;
Dsu dsu(n);
vector<vector<ll>> edges;
for (ll i = 0; i < n - 1; i++) {
edges.push_back({abs(sorted_W[i + 1].first - sorted_W[i].first), i, i + 1});
}
edges.push_back({INT_MAX, -1, -1});
sort(edges.begin(), edges.end());
vector<pair<ll, ll>> q;
for (ll i = 0; i < E.size(); i++) {
q.push_back({E[i], i});
}
sort(q.begin(), q.end());
vector<ll> queries(E.size());
ll puntero = 0;
for (auto [d, pos] : q) {
while (edges[puntero][0] <= d && puntero < edges.size()) {
ll u = edges[puntero][1], v = edges[puntero][2];
if (u != -1 && v != -1 && !dsu.isSameSet(u, v)) {
dsu.unionSet(u, v);
}
puntero++;
}
queries[pos] = dsu.res();
}
return queries;
}
else{
int Q = (int)E.size();
int N=(int)W.size();
vector<ll>ans;
vector<tuple<int,int,int>>ordenar;
for(int i=0;i<N;i++){
ordenar.push_back({W[i],B[i],A[i]});
}
sort(ordenar.begin(),ordenar.end());
W.clear();
A.clear();
B.clear();
for(auto[w,b,a]:ordenar){
A.push_back(a);
B.push_back(b);
W.push_back(w);
}
for(int e=0;e<Q;e++){
int d=E[e];
vector<ll>dp(N,LLONG_MAX);
for(int i=0;i<N;i++){
if(i==0){
dp[i]=A[i];
}
if(i==1){
if((W[i]-W[i-1])<=d){
dp[i]=(B[i]+B[i-1]);
}
else{
dp[i]=(dp[i-1]+A[i]);
}
}
if(i>=2){
dp[i]=((ll)A[i]+dp[i-1]);
if((W[i]-W[i-1])<=d){
dp[i]=min(dp[i],(ll)((ll)B[i]+(ll)B[i-1]+dp[i-2]));
}
if((W[i]-W[i-2])<=d){
if(i>=3){
dp[i]=min(dp[i],(ll)((ll)B[i]+(ll)B[i-2]+(ll)A[i-1]+dp[i-3]));
}
else{
dp[i]=min(dp[i],(ll)((ll)B[i]+(ll)B[i-2]+(ll)A[i-1]));
}
}
}
}
ans.push_back(dp[N-1]);
}
return ans;
}
}
