#include "towers.h"
#include <bits/stdc++.h>
using namespace std;
int N, p;
vector<int> H;
void init(int n, vector<int> h) {
N = n, H = h, p = -1;
for (int i = 0; i < N; i++) {
if ((i == 0 || H[i] > H[i - 1]) && (i == N - 1 || H[i] > H[i + 1])) {
p = i;
}
}
for (int i = 0; i < p; i++) {
if (H[i] > H[i + 1]) {
p = -1;
return;
}
}
for (int i = p + 1; i < N; i++) {
if (H[i - 1] < H[i]) {
p = -1;
return;
}
}
}
int max_towers(int L, int R, int D) {
if (p != -1) {
int l = upper_bound(H.begin(), H.begin() + p, H[p] - D) - H.begin() - 1;
int r = lower_bound(H.begin() + p, H.end(), H[p] - D, [&](int x, int y) {return x > y;}) - H.begin();
return (L <= l && r <= R) ? 2 : 1;
}
vector<int> lg(N + 1);
for (int i = 2; i <= N; i++) {
lg[i] = lg[i / 2] + 1;
}
vector st(N, vector<int>(lg[N] + 1));
for (int i = 0; i < N; i++) {
st[i][0] = i;
}
auto f = [&](int i, int j) {
if (i == -1) {
return j;
}
if (j == -1) {
return i;
}
return H[i] > H[j] ? i : j;
};
for (int j = 0; j < lg[N]; j++) {
for (int i = 0; i + (2 << j) <= N; i++) {
st[i][j + 1] = f(st[i][j], st[i + (1 << j)][j]);
}
}
auto query = [&](int l, int r) {
if (l == r) {
return -1;
}
int k = lg[r - l];
return f(st[l][k], st[r - (1 << k)][k]);
};
if (D == 1) {
auto rec = [&](auto rec, int l, int r) -> int {
if (l + 1 <= r) {
return r - l;
}
int m = query(l, r);
return rec(rec, l, m) + rec(rec, m + 1, r);
};
return rec(rec, L, R + 1);
}
vector<int> l(N, -1), r(N, N);
for (int i = 0; i < N; i++) {
if (H[query(0, i)] >= H[i] + D) {
int lo = 0, hi = i - 1;
while (lo < hi) {
int mi = (lo + hi + 1) / 2;
if (H[query(mi, i)] >= H[i] + D) {
lo = mi;
} else {
hi = mi - 1;
}
}
l[i] = lo;
}
if (H[query(i + 1, N)] >= H[i] + D) {
int lo = i + 1, hi = N - 1;
while (lo < hi) {
int mi = (lo + hi) / 2;
if (H[query(i + 1, mi + 1)] >= H[i] + D) {
hi = mi;
} else {
lo = mi + 1;
}
}
r[i] = lo;
}
}
vector<int> dp(N + 1), t(N + 1);
for (int i = L; i <= R; i++) {
t[i + 1] = max(t[i + 1], t[i]);
dp[i + 1] = max(dp[i], t[l[i] + 1] + 1);
if (r[i] < N) {
t[r[i] + 1] = max(t[r[i] + 1], dp[i + 1]);
}
}
return dp[R + 1];
}
