#include "elephants.h"
#include <bits/stdc++.h>
#define pb push_back
#define All(x) x.begin(), x.end()
#define pii pair<int,int>
#define ff first
#define ss second
using namespace std;
#define debug(args...) kout("[ " + string(#args) + " ]", args)
void kout() { cerr << endl; }
template <class T, class ...U> void kout(T a, U ...b) { cerr << a << ' ',kout(b...); }
template <class T> void pary(T L, T R) { while (L != R) cerr << *L << " \n"[++L==R]; }
const int MAXN = 150000;
const int K = 380;
int n, m, seg;
vector <pii> a;
vector <vector<pii>> B;
vector <pii> rng;
vector <int> pos;
vector <pii> info;
void build_block(int id) {
int len = B[id].size();
sort(All(B[id]));
for (int i = len-1; i >= 0; i--) {
pos[B[id][i].ss] = id;
auto it = upper_bound(All(B[id]), pii(B[id][i].ff + seg, n));
if (it == B[id].end()) {
info[B[id][i].ss] = pii(1, B[id][i].ff + seg);
} else {
info[B[id][i].ss] = pii(info[it->ss].ff + 1, info[it->ss].ss);
}
}
if (len) {
rng[id] = pii(B[id][0].ff, B[id][len-1].ff);
} else {
rng[id] = pii(-1, -1);
}
}
void build() {
sort(All(a));
for (int i = 0; i < m; i++)
B[i].clear();
for (int i = 0; i < n; i++)
B[i/K].pb(a[i]);
for (int i = 0; i < m; i++)
build_block(i);
sort(All(a), [](const pii x, const pii y) {
return x.ss < y.ss;
});
}
int solve() {
int ans = 0, now = -1;
for (int i = 0; i < m; i++) {
// debug(i);
// for (int j = 0; j < B[i].size(); j++) debug(B[i][j].ff, B[i][j].ss);
auto tmp = upper_bound(All(B[i]), pii(now, n+1));
if (tmp == B[i].end()) continue;
ans += info[tmp->ss].ff;
now = info[tmp->ss].ss;
}
// kout();
return ans;
}
void init(int N, int L, int X[]) {
n = N, m = (n-1)/K+1, seg = L;
a.clear(), a.resize(n);
pos.clear(), pos.resize(n);
info.clear(), info.resize(n);
B.clear(), B.resize(m);
rng.clear(), rng.resize(m);
for (int i = 0; i < n; i++)
a[i].ff = X[i], a[i].ss = i;
build();
solve();
}
int update(int i, int y) {
int id = pos[i];
for (int j = 0; j < (int)B[id].size(); j++)
if (B[id][j].ss == i) B[id].erase(B[id].begin()+j);
build_block(id);
a[i].ff = y;
pos[i] = -1;
for (int j = 0; j < m; j++) {
if ((!j || rng[j-1].ss <= y) && (j==m-1 || rng[j+1].ff >= y)) {
B[j].pb(a[i]);
pos[i] = j;
build_block(j);
break;
}
}
// assert(pos[i] != -1);
return solve();
}
