#include "towers.h"
#include <iostream>
#include <vector>
#include <cmath>
#include <set>
#include <algorithm>
using namespace std;
int ind = -1;
bool ch = true;
vector <int> h;
const int N = 100100, M = 20;
int mx[N][M], Left[N], Right[N], pref[N], LS[N], RS[N];
int mxleft[N][M], mnright[N][M];
vector <int> esim;
vector <int> indexes;
bool check = true;
int findmaxinrange(int L, int R) {
if (L > R) return 0;
int u = log2(R - L + 1);
return max(mx[L][u], mx[R - (1 << u) + 1][u]);
}
int findmininrange(int L, int R, int w) {
if (L > R) return 2e9 + 1;
int u = log2(R - L + 1);
if (w == 1) return max(mxleft[L][u], mxleft[R - (1 << u) + 1][u]);
return min(mnright[L][u], mnright[R - (1 << u) + 1][u]);
}
void init(int n, vector<int> a) {
ch = true;
ind = -1;
h = a;
pref[0] = 0;
for (int i = 0; i < n - 1; ++i)
{
if (a[i] > a[i + 1]) {
if (ind == -1) ind = i;
}
else {
if (ind != -1) ch = false;
}
}
LS[0] = -1;
RS[n - 1] = -1;
for (int i = 1; i < n; i++) {
int v = i - 1;
while (v != -1 && a[i] < a[v]) {
v = LS[v];
}
LS[i] = v;
}
for (int i = n - 2; i >= 0; i--) {
int v = i + 1;
while (v != -1 && a[i] < a[v]) {
v = RS[v];
}
RS[i] = v;
}
for (int i = 1; i < n - 1; i++) {
pref[i] = pref[i - 1];
if (a[i] < a[i + 1] && a[i] < a[i - 1]) pref[i]++;
}
for (int i = 0; i < n; i++) {
mx[i][0] = a[i];
}
for (int j = 1; j < 20; j++) {
for (int i = n - 1; i >= 0; i--) {
mx[i][j] = max(mx[i][j - 1], mx[min(n - 1, i + (1 << (j - 1)))][j - 1]);
}
}
for (int i = 0; i < n; i++) {
int hmn = 2e9;
if (LS[i] != -1) {
hmn = min(hmn, findmaxinrange(LS[i] + 1, i - 1));
}
if (RS[i] != -1) {
hmn = min(hmn, findmaxinrange(i + 1, RS[i] - 1));
}
int u = hmn - a[i];
esim.push_back(u);
}
sort(esim.begin(), esim.end());
}
int querynumber = 0;
int max_towers(int L, int R, int D) {
int n = (int)h.size();
++querynumber;
if (ch) {
if (R < ind || L > ind) return 1;
if (h[ind] >= (max(h[L], h[R]) + D)) return 2;
return 1;
}
if (querynumber == 1) {
vector <pair<int, int>> v;
set <int> ms;
for (int i = 0; i < n; i++) {
int l = 0, r = i - 1;
Left[i] = -1;
while (l <= r) {
int mid = (l + r) / 2;
if (findmaxinrange(mid, i - 1) >= h[i] + D) {
Left[i] = mid;
l = mid + 1;
}
else r = mid - 1;
}
Right[i] = n;
l = i + 1, r = n - 1;
while (l <= r) {
int mid = (l + r) / 2;
if (findmaxinrange(i + 1, mid) >= h[i] + D) {
Right[i] = mid;
r = mid - 1;
}
else l = mid + 1;
}
v.push_back({ h[i], i });
}
int ans = 0;
sort(v.begin(), v.end());
for (auto q : v) {
int ind = q.second;
if (ind > R || ind < L) continue;
auto it = ms.lower_bound(ind);
if (it != ms.begin()) {
it--;
if (*it > Left[ind]) continue;
}
it = ms.lower_bound(ind);
if (it != ms.end() && *it < Right[ind]) {
continue;
}
ms.insert(ind);
++ans;
}
return ans;
}
if (D == 1) {
if (L == R) {
return 1;
}
int cnt = pref[R - 1] - pref[L];
if (h[L] < h[L + 1]) ++cnt;
if (h[R] < h[R - 1]) ++cnt;
return cnt;
}
if (L == 0 && R == n - 1) {
int u = lower_bound(esim.begin(), esim.end(), D) - esim.begin();
return n - u;
}
if (check) {
check = false;
vector <pair<int, int>> v;
set <int> ms;
for (int i = 0; i < n; i++) {
int l = 0, r = i - 1;
Left[i] = -1;
while (l <= r) {
int mid = (l + r) / 2;
if (findmaxinrange(mid, i - 1) >= h[i] + D) {
Left[i] = mid;
l = mid + 1;
}
else r = mid - 1;
}
Right[i] = n;
l = i + 1, r = n - 1;
while (l <= r) {
int mid = (l + r) / 2;
if (findmaxinrange(i + 1, mid) >= h[i] + D) {
Right[i] = mid;
r = mid - 1;
}
else l = mid + 1;
}
}
for (int i = 0; i < n; i++) {
int hmn = 2e9;
if (LS[i] != -1) {
hmn = min(hmn, findmaxinrange(LS[i] + 1, i - 1));
}
if (RS[i] != -1) {
hmn = min(hmn, findmaxinrange(i + 1, RS[i] - 1));
}
int u = hmn - h[i];
if (u >= D) {
indexes.push_back(i);
}
}
for (int i = 0; i < n; i++) {
mxleft[i][0] = Left[i];
mnright[i][0] = Right[i];
}
for (int j = 1; j < 20; j++) {
for (int i = n - 1; i >= 0; i--) {
mxleft[i][j] = max(mxleft[i][j - 1], mxleft[min(n - 1, i + (1 << (j - 1)))][j - 1]);
mnright[i][j] = min(mnright[i][j - 1], mnright[min(n - 1, i + (1 << (j - 1)))][j - 1]);
}
}
}
auto it = lower_bound(indexes.begin(), indexes.end(), L);
int ans = upper_bound(indexes.begin(), indexes.end(), R) - lower_bound(indexes.begin(), indexes.end(), L);
if (it != indexes.end()) {
int q = Left[*it];
if (L < q) {
if (findmininrange(L, q - 1, 2) < *it) {
++ans;
}
}
}
it = upper_bound(indexes.begin(), indexes.end(), R);
if (it != indexes.begin()) {
--it;
int q = Right[*it];
if (q < R) {
if (findmininrange(q + 1, R, 1) > *it) {
++ans;
}
}
}
return ans;
}
