#include <bits/stdc++.h>
using namespace std;
#define popcount(n) (__builtin_popcountll((n)))
#define clz(n) (__builtin_clzll((n)))
#define ctz(n) (__builtin_ctzll((n)))
#define lg(n) (63 - __builtin_clzll((n)))
#define BIT(n, i) (((n) >> (i)) & 1ll)
#define MASK(i) (1ll << (i))
#define FLIP(n, i) ((n) ^ (1ll << (i)))
#define ON(n, i) ((n) | MASK(i))
#define OFF(n, i) ((n) & ~MASK(i))
#define Int __int128
#define fi first
#define se second
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
typedef pair<long long, int> pli;
typedef pair<int, long long> pil;
typedef vector<pair<int, int>> vii;
typedef vector<pair<long long, long long>> vll;
typedef vector<pair<long long, int>> vli;
typedef vector<pair<int, long long>> vil;
template <class T1, class T2>
bool maximize(T1 &x, T2 y) {
if (x < y) {
x = y;
return true;
}
return false;
}
template <class T1, class T2>
bool minimize(T1 &x, T2 y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <class T>
void remove_duplicate(vector<T> &ve) {
sort (ve.begin(), ve.end());
ve.resize(unique(ve.begin(), ve.end()) - ve.begin());
}
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
template <class T> T random(T l, T r) {
return uniform_int_distribution<T>(l, r)(rng);
}
template <class T> T random(T r) {
return rng() % r;
}
const int N = 1e5 + 5;
const int MOD = 1e9 + 7;
const int inf = 1e9;
const ll INF = 1e18;
int n, q, D;
ll ans;
ll pref[N];
vii edges, que;
struct Artifact {
int w, one, two;
Artifact(int _w = 0, int _one = 0, int _two = 0) {
w = _w, one = _one, two = _two;
}
bool operator< (const Artifact &other) {
return w < other.w;
}
} a[N];
struct DSU {
struct Component {
int lab, L, R;
int best_odd, best_even;
int odd, even;
Component() {
lab = -1, L = R = 0;
best_odd = best_even = odd = even = -1;
}
void show() {
cerr << "mk " << lab << ' ' << L << ' ' << R << ' ' << best_odd << ' ' << best_even << ' ' << odd << ' ' << even << ' ' << eval() << '\n';
}
ll eval() {
assert(-lab == R - L + 1);
ll ret = pref[R] - pref[L - 1];
// if (L == 2 && R == 5) {
// cerr << "ret = " << ret << '\n';
// }
if ((-lab) & 1) {
// cerr << L << ' ' << R << '\n';
int mi = inf;
if (best_odd != -1) minimize(mi, a[best_odd].one - a[best_odd].two);
if (even != -1) minimize(mi, a[even].one - a[even].two);
// for (int i = L; i <= R; i += 2) minimize(real_mi, a[i].one - a[i].two);
// for (int i = L + 1; i < R; i += 2) if (a[i + 1].w - a[i - 1].w <= D) {
// minimize(real_mi, a[i].one - a[i].two);
// }
assert(mi < inf);
ret += mi;
// real_ret += real_mi;
}
// assert(real_ret == ret);
return ret;
}
};
vector<Component> comp;
void resize(int n) {
comp.assign(n + 1, Component());
for (int i = 1; i <= n; ++i) {
// comp[i].lab = -1;
comp[i].L = comp[i].R = i;
comp[i].best_odd = i;
ans += a[i].one;
}
}
int find_set(int p) {
return comp[p].lab < 0 ? p : comp[p].lab = find_set(comp[p].lab);
}
bool compare(int p, int q) {
if (q == -1) return true;
if (p == -1) return false;
return a[p].one - a[p].two < a[q].one - a[q].two;
}
void update(int &x, int y) {
if (compare(y, x)) x = y;
}
Component merge(Component A, Component B) {
// cerr << A.L << ' ' << A.R << ' ' << B.L << ' ' << B.R << '\n';
if (A.L > B.R) swap(A, B);
// if (make_pair(A.L, A.R) == make_pair(2, 2)) {
// A.show(), B.show();
// }
if ((-A.lab) & 1) {
update(A.best_odd, B.best_even);
update(A.best_even, B.best_odd);
update(A.odd, B.even);
update(A.even, B.odd);
}
else {
update(A.best_odd, B.best_odd);
update(A.best_even, B.best_even);
update(A.odd, B.odd);
update(A.even, B.even);
}
A.R = B.R, A.lab += B.lab;
return A;
}
bool join(int u, int v) {
u = find_set(u), v = find_set(v);
if (u != v) {
if (comp[u].lab > comp[v].lab) swap(u, v);
ans -= comp[u].eval() + comp[v].eval();
comp[u] = merge(comp[u], comp[v]);
comp[v].lab = u;
// if (comp[u].L == 2 && comp[u].R == 4) {
// comp[u].show(), comp[v].show();
// }
ans += comp[u].eval();
return true;
}
return false;
}
} dsu;
vector<long long> calculate_costs(vector<int> W, vector<int> A, vector<int> B, vector<int> E) {
n = W.size(), q = E.size();
for (int i = 1; i <= n; ++i) {
a[i] = Artifact(W[i - 1], A[i - 1], B[i - 1]);
}
sort (a + 1, a + 1 + n);
for (int i = 1; i <= n; ++i) {
pref[i] = pref[i - 1] + a[i].two;
if (i < n) edges.emplace_back(a[i + 1].w - a[i].w, -i);
if (i + 1 < n) edges.emplace_back(a[i + 2].w - a[i].w, i + 1);
}
sort (edges.begin(), edges.end());
for (int i = 0; i < q; ++i) {
int d = E[i];
que.emplace_back(d, i);
}
sort (que.begin(), que.end());
int p = -1; dsu.resize(n); vector<ll> res(q);
for (auto &[d, id] : que) {
D = d;
while (p + 1 < edges.size() && edges[p + 1].fi <= d) {
int i = edges[++p].se;
if (i < 0) dsu.join(-i, -i + 1);
else {
// i = -i;
int s = dsu.find_set(i);
// assert(dsu.find_set(i - 1) == s && s == dsu.find_set(i + 1));
if (i % 2 == dsu.comp[s].L % 2) {
dsu.update(dsu.comp[s].odd, i);
}
else {
ans -= dsu.comp[s].eval();
dsu.update(dsu.comp[s].even, i);
ans += dsu.comp[s].eval();
}
}
}
// if (id == 1) {
// for (int i = 1; i <= n; ++i) if (dsu.find_set(i) == i) {
// dsu.comp[i].show();
// }
// }
res[id] = ans;
}
return res;
}
#ifdef hwe
signed main() {
ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
#ifdef hwe
freopen("input.inp", "r", stdin);
freopen("output.out", "w", stdout);
#else
#define taskname ""
if (fopen(taskname".inp", "r")) {
freopen(taskname".inp", "r", stdin);
freopen(taskname".out", "w", stdout);
}
#endif
cerr << '\n'; return 0;
}
#endif
