#include "elephants.h"
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#define ALL(x) x.begin(), x.end()
using namespace std;
const int MX_N = 150000, B = 300, IB = 500;
int n, l, x[MX_N];
vector<pair<int, int>> bckt[IB];
int b_idx[MX_N];
pair<int, int> dp[MX_N];
int to_reset;
pair<int, int> by_x[MX_N];
inline void reset() {
for (int i = 0; i < n; i++) by_x[i] = {x[i], i};
sort(by_x, by_x + n);
for (int i = 0; i < IB; i++) bckt[i].clear();
for (int i = 0; i < n; i++) {
bckt[i / B].push_back(by_x[i]);
b_idx[by_x[i].second] = i / B;
}
for (int i = 0; i < IB; i++) {
for (int j = bckt[i].size() - 1; ~j; j--) {
int ub = upper_bound(ALL(bckt[i]), make_pair(bckt[i][j].first + l, INT_MAX)) - bckt[i].begin();
if (ub == int(bckt[i].size())) dp[bckt[i][j].second] = {1, bckt[i][j].first + l};
else {
dp[bckt[i][j].second] = dp[bckt[i][ub].second];
dp[bckt[i][j].second].first++;
}
}
}
to_reset = B;
}
void init(int N, int L, int X[]) {
n = N, l = L;
for (int i = 0; i < n; i++) x[i] = X[i];
reset();
}
int update(int i, int y) {
// Erase elephant i and update bucket
bckt[b_idx[i]].erase(find(ALL(bckt[b_idx[i]]), make_pair(x[i], i)));
for (int j = bckt[b_idx[i]].size() - 1; ~j; j--) {
int ub = upper_bound(ALL(bckt[b_idx[i]]), make_pair(bckt[b_idx[i]][j].first + l, INT_MAX)) - bckt[b_idx[i]].begin();
if (ub == int(bckt[b_idx[i]].size())) dp[bckt[b_idx[i]][j].second] = {1, bckt[b_idx[i]][j].first + l};
else {
dp[bckt[b_idx[i]][j].second] = dp[bckt[b_idx[i]][ub].second];
dp[bckt[b_idx[i]][j].second].first++;
}
}
// Insert elephant i and update bucket
x[i] = y;
for (int new_b = 0; new_b < IB; new_b++) {
if ((bckt[new_b].size() && bckt[new_b].back().first >= x[i]) || new_b == IB - 1) {
bckt[new_b].insert(upper_bound(ALL(bckt[new_b]), make_pair(x[i], i)), make_pair(x[i], i));
for (int j = bckt[new_b].size() - 1; ~j; j--) {
int ub = upper_bound(ALL(bckt[new_b]), make_pair(bckt[new_b][j].first + l, INT_MAX)) - bckt[new_b].begin();
if (ub == int(bckt[new_b].size())) dp[bckt[new_b][j].second] = {1, bckt[new_b][j].first + l};
else {
dp[bckt[new_b][j].second] = dp[bckt[new_b][ub].second];
dp[bckt[new_b][j].second].first++;
}
}
b_idx[i] = new_b;
break;
}
}
// Reset buckets after B queries
if (!--to_reset) reset();
// Get the answer
int ans = 0;
for (int j = 0, curr_x = -1; j < IB; j++) if (bckt[j].size() && curr_x < bckt[j].back().first) {
int ub = upper_bound(ALL(bckt[j]), make_pair(curr_x, INT_MAX))->second;
ans += dp[ub].first;
curr_x = dp[ub].second;
}
return ans;
}
