#include "towers.h"
#include <bits/stdc++.h>
using namespace std;
const int maxN = 1e5 + 20;
bool sub1;
vector<int> events[maxN];
int firstL[maxN];
int firstR[maxN];
int dp[maxN];
int bit[maxN];
int cnt_min[maxN];
int H[maxN];
int N;
int max_id;
void init(int _N, vector<int> _H) {
N = _N;
for (int i = 0; i < N; i++) {
H[i] = _H[i];
}
max_id = 0;
for (int i = 0; i < N; i++) {
if (H[i] > H[max_id]) {
max_id = i;
}
}
sub1 = true;
for (int i = 0; i < max_id; i++) {
sub1 &= H[i] < H[i + 1];
}
for (int i = max_id; i + 1 < N; i++) {
sub1 &= H[i] > H[i + 1];
}
for (int i = 1; i < N - 1; i++) {
cnt_min[i] = cnt_min[i - 1] + (H[i] < H[i - 1] && H[i] < H[i + 1]);
}
}
void update(int pos, int val) {
for (int i = pos; i <= N; i += i & (-i)) {
bit[i] = max(bit[i], val);
}
}
int get(int pos) {
int res = 0;
for (int i = pos; i > 0; i -= i & (-i)) {
res = max(res, bit[i]);
}
return res;
}
int max_towers(int L, int R, int D) {
if (L == R) {
return 1;
}
if (sub1) {
if (R <= max_id) {
return 1;
}
else if (L >= max_id) {
return 1;
}
else {
return 1 + (H[max_id] >= max(H[L], H[R]) + D);
}
}
if (D == 1) {
return cnt_min[R - 1] - cnt_min[L] + (H[L] < H[L + 1]) + (H[R] < H[R - 1]);
}
for (int i = L; i <= R; i++) {
firstL[i] = L - 1;
firstR[i] = R + 1;
for (int j = i; j <= R; j++) {
if (H[j] >= H[i] + D) {
firstR[i] = j;
break;
}
}
for (int j = i; j >= L; j--) {
if (H[j] >= H[i] + D) {
firstL[i] = j;
break;
}
}
if (firstR[i] < R) {
events[firstR[i] + 1].push_back(i);
}
}
int res = 0;
for (int i = L; i <= R; i++) {
for (auto id: events[i]) {
update(id + 1, dp[id]);
}
dp[i] = 1 + (firstL[i] > L ? get(firstL[i]) : 0);
res = max(res, dp[i]);
}
return res;
}
