#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
#define endl "\n"
#define ll long long
#define IOS ios_base::sync_with_stdio(false); cin.tie(nullptr);
const int N = 6e5 + 5;
const int INF = 2e9 + 5;
int x[N];
int id[N];
bool is_white(int i) {
return i < 2 || i % 2 == 1;
}
struct Node {
Node* l = nullptr;
Node* r = nullptr;
Node* p = nullptr;
int i;
int val;
int sum;
bool rev = false;
Node() {}
Node(int x) {
i = x;
}
void push() {
if (rev) {
rev = false;
swap(l, r);
if (l) {
l->rev ^= true;
}
if (r) {
r->rev ^= true;
}
}
}
void pull() {
sum = val + (l ? l->sum : 0) + (r ? r->sum : 0);
}
bool is_root() {
return p == 0 || (p->l != this && p->r != this);
}
};
struct LCT {
vector<Node> a;
LCT(int n) {
a.resize(n);
for (int i = 0; i < n; i++) {
a[i].i = i;
if (is_white(i)) {
a[i].val = 0;
} else {
a[i].val = 1;
}
a[i].sum = a[i].val;
}
}
void rot(Node* c) {
Node* p = c->p;
Node* g = p->p;
if (!p->is_root()) {
(g->r == p ? g->r : g->l) = c;
}
p->push();
c->push();
if (p->l == c) {
p->l = c->r;
c->r = p;
if (p->l) {
p->l->p = p;
}
} else {
p->r = c->l;
c->l = p;
if (p->r) {
p->r->p = p;
}
}
p->p = c;
c->p = g;
p->pull();
c->pull();
}
void splay(Node* c) {
while (!c->is_root()) {
Node* p = c->p;
Node* g = p->p;
if (!p->is_root()) {
rot((g->r == p) == (p->r == c) ? p : c);
}
rot(c);
}
c->push();
}
Node* access(int v) {
Node* last = nullptr;
Node* c = &a[v];
for (Node* p = c; p; p = p->p) {
splay(p);
p->r = last;
p->pull();
last = p;
}
splay(c);
return last;
}
void make_root(int v) {
access(v);
Node* c = &a[v];
if (c->l) {
c->l->rev ^= true;
c->l = nullptr;
}
}
void link(int u, int v) {
make_root(u);
Node* c = &a[u];
c->p = &a[v];
}
void cut(int u, int v) {
make_root(u);
access(v);
if (a[v].l) {
a[v].l->p = nullptr;
a[v].l = nullptr;
}
}
void upd(int u, int x) {
access(u);
a[u].val = x;
a[u].pull();
}
long long query(int u, int v) {
make_root(u);
access(v);
return a[v].sum;
}
};
struct comp {
bool operator() (pair<int, int> a, pair<int, int> b) const {
if (a.first != b.first) {
return a.first < b.first;
}
if (is_white(a.second)) {
return false;
}
if (is_white(b.second)) {
return true;
}
return a.second < b.second;
}
};
LCT lct(N);
set<pair<int, int>, comp> st;
void add(int i, int x, int l) {
lct.link(2 * i, 2 * i + 1);
st.insert(make_pair(x, 2 * i));
auto la = st.lower_bound(make_pair(x, 2 * i));
la--;
auto ra = st.upper_bound(make_pair(x, 2 * i));
if (is_white(la->second)) {
lct.cut(la->second, ra->second);
lct.link(la->second, 2 * i);
}
st.insert(make_pair(x + l, 2 * i + 1));
la = st.lower_bound(make_pair(x + l, 2 * i + 1));
la--;
ra = st.upper_bound(make_pair(x + l, 2 * i + 1));
if (is_white(la->second)) {
lct.cut(la->second, ra->second);
lct.link(la->second, 2 * i + 1);
}
lct.link(2 * i + 1, ra->second);
return;
}
void rem(int i, int x, int l) {
lct.cut(2 * i, 2 * i + 1);
st.erase(make_pair(x, 2 * i));
auto la = st.lower_bound(make_pair(x, 2 * i));
la--;
auto ra = st.lower_bound(make_pair(x, 2 * i));
if (is_white(la->second)) {
lct.cut(la->second, 2 * i);
lct.link(la->second, ra->second);
}
st.erase(make_pair(x + l, 2 * i + 1));
la = st.lower_bound(make_pair(x + l, 2 * i + 1));
la--;
ra = st.lower_bound(make_pair(x + l, 2 * i + 1));
lct.cut(2 * i + 1, ra->second);
if (is_white(la->second)) {
lct.cut(la->second, 2 * i + 1);
lct.link(la->second, ra->second);
}
return;
}
map<int, set<int>> mp;
map<int, int> active;
int n, l;
void init(int N, int L, int X[]) {
n = N, l = L;
assert(l != 0);
st.insert(make_pair(-INF, 0));
st.insert(make_pair(INF, 1));
lct.link(0, 1);
for (int i = 0; i < n; i++) {
id[i] = i + 1;
x[i] = X[i];
mp[x[i]].insert(id[i]);
if (mp[x[i]].size() == 1) {
active[x[i]] = id[i];
add(id[i], x[i], l);
}
}
}
int update(int i, int y) {
mp[x[i]].erase(id[i]);
if (active[x[i]] == id[i]) {
rem(id[i], x[i], l);
if (mp[x[i]].size() > 0) {
int j = *mp[x[i]].begin();
active[x[i]] = j;
add(j, x[i], l);
}
}
x[i] = y;
mp[x[i]].insert(id[i]);
if (mp[x[i]].size() == 1) {
active[x[i]] = id[i];
add(id[i], x[i], l);
}
return lct.query(0, 1);
}
int main() {
IOS;
return 0;
}
