#include "towers.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
void debug_out(){cerr << endl;}
template<typename Head, typename... Tail>
void debug_out(Head H, Tail... T){
cerr << H << ' ';
debug_out(T...);
}
#define debug(...) cerr << "(" << #__VA_ARGS__ << "): ", debug_out(__VA_ARGS__)
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define MP(x, y) make_pair(x, y)
const int maxn = 1e5 + 10;
const int lg = 20;
int n, h[maxn], mx[lg][maxn], l[maxn], r[maxn], f[2][maxn];
void add(int *f, int idx, int x){
for (; idx <= n; idx += idx & -idx) f[idx] += x;
}
void add(int *f, int l, int r, int x){
add(f, l, x);
add(f, r+1, -x);
}
int get(int *f, int idx){
int res = 0;
for (; idx; idx -= idx & -idx) res += f[idx];
return res;
}
int get(int *f, int l, int r){
if (r < l) return 0;
return get(f, r) - get(f, l-1);
}
int getmax(int l, int r){
r++;
int x = 31 - __builtin_clz(r-l);
return max(mx[x][l], mx[x][r-(1 << x)]);
}
void init(int N, std::vector<int> H) {
n = N;
for (int i = 0; i < n; i++){
h[i] = H[i];
mx[0][i] = h[i];
}
for (int i = 1; i < lg; i++){
for (int j = 0; j + (1 << i) <= n; j++){
mx[i][j] = max(mx[i-1][j], mx[i-1][j+(1<<(i-1))]);
}
}
}
int max_towers(int L, int R, int D) {
memset(l, 0, sizeof l);
memset(r, 0, sizeof r);
memset(f, 0, sizeof f);
for (int i = L; i <= R; i++){
int lo = L, hi = i;
while(lo + 1 < hi){
int mid = (lo + hi) >> 1;
if (getmax(mid, i-1) - D >= h[i]) lo = mid;
else hi = mid;
}
l[i] = lo;
}
vector<pii> val;
for (int i = L; i <= R; i++){
int lo = i, hi = R;
while(lo + 1 < hi){
int mid = (lo + hi) >> 1;
if (getmax(i+1, mid) - D >= h[i]) hi = mid;
else lo = mid;
}
r[i] = hi;
val.push_back({h[i], i});
}
//debug(1);
sort(all(val));
int ans = 0;
for (auto [x, y]: val){
if (get(f[0], y+1)) continue;
if (get(f[1], l[y]+1, r[y]+1)) continue;
ans++;
add(f[0], l[y]+1, r[y]+1, 1);
add(f[1], y+1, 1);
}
return ans;
}
