#include "towers.h"
#include <bits/stdc++.h>
using namespace std;
const int MAX = 1e5 + 5;
int N, lg[MAX], peaks[MAX], maxH[MAX][20];
bool isMountain = true;
vector<int> H;
struct FenwickTree {
int n;
vector<int> tree;
FenwickTree(int _n) {
n = _n;
tree.resize(n + 5);
}
void update(int idx, int val) {
idx++;
for (int i = idx; i <= n; i += i & -i)
tree[i] = max(tree[i], val);
}
int get(int idx) {
idx++;
int rs = 0;
for (int i = idx; i > 0; i -= i & -i)
rs = max(rs, tree[i]);
return rs;
}
};
int get(int l, int r) {
int k = lg[r - l + 1];
return max(maxH[l][k], maxH[r - (1 << k) + 1][k]);
}
void init(int _N, vector<int> _H) {
N = _N, H = _H;
for (int i = 1; i <= N; i++)
lg[i] = log2(i);
for (int i = 0; i < N; i++)
maxH[i][0] = H[i];
for (int i = 1; i < N - 1; i++)
peaks[i] = peaks[i - 1] + (H[i] > max(H[i - 1], H[i + 1]));
peaks[N - 1] = peaks[N - 2];
for (int t = 1; t <= 18; t++)
for (int i = 0; i + (1 << t) - 1 < N; i++)
maxH[i][t] = max(maxH[i][t - 1], maxH[i + (1 << (t - 1))][t - 1]);
int id = max_element(H.begin(), H.end()) - H.begin();
for (int i = id; i > 0 && isMountain; i--)
isMountain &= (H[i] > H[i - 1]);
for (int i = id; i < N - 1 && isMountain; i++)
isMountain &= (H[i] > H[i + 1]);
}
int max_towers(int L, int R, int D) {
if (isMountain)
return get(L, R) - D >= max(H[L], H[R]) ? 2 : 1;
if (D == 1)
return peaks[R - 1] - peaks[L] + 1;
vector<int> bl(R - L + 1, -1), br(R - L + 1, R - L + 1);
for (int i = L; i <= R; i++) {
int l = L, r = i - 1;
while (l <= r) {
int mid = (l + r) / 2;
if (get(mid, i - 1) - D >= H[i]) {
bl[i - L] = mid - L;
l = mid + 1;
} else
r = mid - 1;
}
l = i + 1, r = R;
while (l <= r) {
int mid = (l + r) / 2;
if (get(i + 1, mid) - D >= H[i]) {
br[i - L] = mid - L;
r = mid - 1;
} else
l = mid + 1;
}
}
vector<int> f(R - L + 1, 1);
FenwickTree tree(R - L + 1);
for (int i = 0; i < R - L + 1; i++) {
if (bl[i] != -1)
f[i] = tree.get(bl[i]) + 1;
tree.update(br[i], f[i]);
}
return *max_element(f.begin(), f.end());
}
//int main() {
// freopen("../_input", "r", stdin);
// int N, Q;
// assert(2 == scanf("%d %d", &N, &Q));
// std::vector<int> H(N);
// for (int i = 0; i < N; ++i) {
// assert(1 == scanf("%d", &H[i]));
// }
// init(N, H);
//
// for (int i = 0; i < Q; ++i) {
// int L, R, D;
// assert(3 == scanf("%d %d %d", &L, &R, &D));
// printf("%d\n", max_towers(L, R, D));
// }
// return 0;
//}
