#include "towers.h"
#include <bits/stdc++.h>
using namespace std;
#define OPTM ios_base::sync_with_stdio(0); cin.tie(0);
#define INF int(1e9+7)
#define ln '\n'
#define ll long long
#define ull unsigned long long
#define ui unsigned int
#define us unsigned short
#define FOR(i,s,n) for (int i = s; i < n; i++)
#define FORR(i,n,s) for (int i = n; i > s; i--)
#define FORX(u, arr) for (auto u : arr)
#define PB push_back
#define in(v,x) (v.find(x) != v.end())
#define F first
#define S second
#define PII pair<int, int>
#define PLL pair<ll, ll>
#define UM unordered_map
#define US unordered_set
#define PQ priority_queue
#define ALL(v) v.begin(), v.end()
const ll LLINF = 1e18+1;
const int MAXN = 1e5+5;
int n,l,r,d;
int h[MAXN], le[MAXN], ri[MAXN], p[MAXN];
bool done;
bool z[MAXN];
void precalc() {
PQ<PII> pq;
FOR(i,0,n) {
while (!pq.empty() && -pq.top().F <= h[i]-d) {
ri[pq.top().S] = i;
pq.pop();
}
pq.push({-h[i],i});
}
while (!pq.empty()) {
ri[pq.top().S] = n;
pq.pop();
}
FORR(i,n-1,-1) {
while (!pq.empty() && -pq.top().F <= h[i]-d) {
le[pq.top().S] = i;
pq.pop();
}
pq.push({-h[i],i});
}
while (!pq.empty()) {
le[pq.top().S] = -1;
pq.pop();
}
vector<PII> v;
FOR(i,0,n) v.PB({h[i],i});
int vn = v.size();
sort(ALL(v));
set<int> s;
s.insert(-INF);
s.insert(INF);
FOR(i,0,vn) {
int idx = v[i].S;
auto it = s.lower_bound(idx);
auto it1 = it;
it1--;
if (le[idx] > (*it1) && ri[idx] < (*it)) s.insert(idx);
}
s.erase(-INF);
s.erase(INF);
FORX(u,s) {
p[u+1]++;
z[u] = 1;
}
FOR(i,1,n+1) p[i] += p[i-1];
// FOR(i,0,n) cout << z[i] << " ";
// cout << ln;
}
void init(int N, std::vector<int> H) {
n = N;
FOR(i,0,n) h[i] = H[i];
}
int max_towers(int L, int R, int D) {
l = L, r = R, d = D;
if (!done) {
precalc();
done = 1;
}
if (l == r) return 1;
int res = p[r+1]-p[l];
if (!z[l] && (l+1 >= n || h[l+1] > h[l])) res++;
if (!z[r] && (r-1 < 0 || h[r-1] > h[r])) res++;
// FOR(i,0,n) cout << le[i] << " ";
// cout << ln;
// FOR(i,0,n) cout << ri[i] << " ";
// cout << ln;
return res;
}
