#include "towers.h"
#include <bits/stdc++.h>
using namespace std;
#define sz(v) int(v.size())
#define ar array
typedef long long ll;
const int N = 1e5+10, MOD = 1e9+7;
const ll INF = 1e18+10;
const int L = 20;
int n, a[N], st[N][L];
vector<pair<int, int>> store;
vector<int> base;
vector<int> ord;
void build_rmq() {
for (int i = 0; i < n; i++) st[i][0] = a[i];
for (int k = 2, l = 1; k <= n; k *= 2, l++) {
for (int i = 0; i + k <= n; i++) {
st[i][l] = max(st[i][l-1], st[i + k / 2][l-1]);
}
}
}
int qry_max(int l, int r) {
int len = r - l + 1;
int use = 31 - __builtin_clz(len);
return max(st[l][use], st[r - (1 << use) + 1][use]);
}
void init(int _n, vector<int> H) {
n = _n;
for (int i = 0; i < n; i++) {
a[i] = H[i];
}
build_rmq();
set<int> s;
for (int i = 0; i < n; i++) {
bool use = 1;
if (i && a[i-1] < a[i]) use = 0;
if (i < n-1 && a[i+1] < a[i]) use = 0;
if (use) s.insert(i);
}
base = vector<int>(s.begin(), s.end());
auto f = [&](int i) {
auto it = s.lower_bound(i); assert(*it == i);
--it;
return qry_max(*it, i) - max(a[*it], a[i]);
};
set<pair<int, int>> q;
auto get_v = [&](int x) {
return pair<int, int>{f(x), x};
};
for (auto it = next(s.begin()); it != s.end(); it++) {
q.insert(get_v(*it));
}
vector<pair<int, int>> v;
v.emplace_back(0, sz(s)); // d > 0, ans = sz(s)
while (sz(q)) {
auto [d, i] = *q.begin(); q.erase(q.begin());
v.emplace_back(d, -1); // need to update v.back().second
auto it = s.lower_bound(i); assert(*it == i);
int one = i;
int two = *prev(it);
if (next(it) != s.end()) {
q.erase(get_v(*next(it)));
}
if (prev(it) != s.begin()) {
q.erase(get_v(two));
}
if (a[one] > a[two]) {
s.erase(one);
ord.push_back(one);
it = s.lower_bound(two);
if (next(it) != s.end()) {
q.insert(get_v(*next(it)));
}
if (it != s.begin()) {
q.insert(get_v(*it));
}
} else {
s.erase(two);
ord.push_back(two);
it = s.lower_bound(one);
if (next(it) != s.end()) {
q.insert(get_v(*next(it)));
}
if (it != s.begin()) {
q.insert(get_v(*it));
}
}
v.back().second = sz(s);
}
store.push_back(v[0]);
for (int i = 1; i < sz(v); i++) {
if (v[i].first <= store.back().first) {
store.back().second = v[i].second;
} else {
store.push_back(v[i]);
}
}
}
bool has[N];
int max_towers(int l, int r, int d) {
// find the last thing < d
int idx = lower_bound(store.begin(), store.end(), pair<int, int>{d, -1}) - store.begin() - 1;
int gone = sz(base) - store[idx].second;
memset(has, 0, sizeof(has));
for (int x : base) has[x] = 1;
// cerr << "> " << gone << endl;
for (int i = 0; i < gone; i++) has[ord[i]] = 0;
int ans = 0;
int first = n, last = -1;
for (int i = l; i <= r; i++) {
ans += has[i];
if (has[i]) {
first = min(first, i);
last = max(last, i);
// cerr << i << ' ';
}
}
// cerr << endl;
if (ans == 0) {
int mx = qry_max(l, r);
return max(1, (mx - d >= a[l]) + (mx - d >= a[r]));
}
bool one = 0, two = 0;
for (int i = l; i < first; i++) {
int x = qry_max(i, first);
if (a[i] <= x - d && x - d >= a[first]) {
one = 1;
break;
}
}
for (int i = last+1; i <= r; i++) {
int x = qry_max(last, i);
if (a[i] <= x - d && x - d >= a[last]) {
two = 1;
break;
}
}
ans += one;
ans += two;
return ans;
}
