#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
//#include "temp.cpp"
#include <cstdio>
using namespace std;
#ifndef ONLINE_JUDGE
#define dbg(x) cerr << #x <<" "; print(x); cerr << endl;
#else
#define dbg(x)
#endif
#define sz(x) (int)x.size()
#define len(x) (int)x.length()
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define clr(x) (x).clear()
#define uniq(x) x.resize(unique(all(x)) - x.begin());
#define blt __builtin_popcount
#define pb push_back
#define popf pop_front
#define popb pop_back
#define ld long double
#define ll long long
void print(long long t) {cerr << t;}
void print(int t) {cerr << t;}
void print(string t) {cerr << t;}
void print(char t) {cerr << t;}
void print(double t) {cerr << t;}
void print(long double t) {cerr << t;}
void print(unsigned long long t) {cerr << t;}
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
#define nl '\n'
// Indexed Set
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template <class T, class V> void print(pair <T, V> p);
template <class T> void print(vector <T> v);
template <class T> void print(set <T> v);
template <class T, class V> void print(map <T, V> v);
template <class T> void print(multiset <T> v);
template <class T, class V> void print(T v[],V n) {cerr << "["; for(int i = 0; i < n; i++) {print(v[i]); cerr << " "; } cerr << "]";}
template <class T, class V> void print(pair <T, V> p) {cerr << "{"; print(p.first); cerr << ","; print(p.second); cerr << "}";}
template <class T> void print(vector <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
// template <class T> void print(vector <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(set <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(multiset <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(Tree <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T, class V> void print(map <T, V> v) {cerr << "[ "; for (auto i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(deque <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
// for random generations
mt19937 myrand(chrono::steady_clock::now().time_since_epoch().count());
// mt19937 myrand(131);
// for grid problems
int dx[8] = {-1,0,1,0,1,-1,1,-1};
int dy[8] = {0,1,0,-1,1,1,-1,-1};
// lowest / (1 << 17) >= 1e5 / (1 << 18) >= 2e5 / (1 << 21) >= 1e6
void fastIO() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr); cout.tie(nullptr);
}
// file in/out
// void setIO(string str = "") {
// fastIO();
// if(str == "input") {
// freopen("input.txt", "r", stdin);
// freopen("output.txt", "w", stdout);
// } else if(str != "") {
// freopen((str + ".in").c_str(), "r", stdin);
// freopen((str + ".out").c_str(), "w", stdout);
// }
// }
const int N = 2e5 + 10;
int a[N], mid = -1;
int f1 = 1, n;
vector<int> b;
int pi[N];
struct segTreeMax {
vector<long long> mTree;
int size;
void init(long long n) {
size = 1;
while(size < n) {
size *= 2;
}
mTree.assign(2 * size - 1, 0);
}
void upd(int u, long long v, int x, int lx, int rx) { // set value at pos u
if(rx - lx == 1) {
mTree[x] = v;
return;
}
int m = (lx + rx) / 2;
if(u < m) {
upd(u, v, 2 * x + 1, lx, m);
}else {
upd(u, v, 2 * x + 2, m, rx);
}
mTree[x] = max(mTree[2 * x + 1], mTree[2 * x + 2]);
}
void upd(int u, long long v) {
upd(u, v, 0, 0, size);
}
long long qry (int l, int r, int x, int lx, int rx) { // range queries
if(l >= rx || lx >= r) {
return 0;
}
if(lx >= l && r >= rx) {
return mTree[x];
}
int m = (rx + lx) / 2;
long long s1 = qry(l, r, 2 * x + 1, lx, m);
long long s2 = qry(l, r, 2 * x + 2, m, rx);
return max(s1, s2);
}
long long qry(int l, int r) {
if(l >= r) {
return -1;
}
return qry(l, r, 0, 0, size);
}
};
segTreeMax seg_max, seg_all;
vector<long long> ai;
void init(int maxN, std::vector<int> H) {
n = maxN;
pair<int, int> mx = {0, 0};
seg_all.init(n + 1);
for(int i = 0; i < n; i++) {
a[i] = H[i];
seg_all.upd(i, a[i]);
mx = max(mx, make_pair(a[i], i));
}
vector<int> lowRig(n + 1, n), lowLef(n + 1, -1);
stack<pair<int, int>> st;
for(int i = 0; i < n; i++) {
while(!st.empty() && st.top().first > a[i]) {
st.pop();
}
if(!st.empty()) {
lowLef[i] = st.top().second;
}
st.push({a[i], i});
}
while(!st.empty()) st.pop();
for(int i = n - 1; i >= 0; i--) {
while(!st.empty() && st.top().first > a[i]) {
st.pop();
}
if(!st.empty()) {
lowRig[i] = st.top().second;
}
st.push({a[i], i});
}
for(int i = 0; i < n; i++) {
long long curl = seg_all.qry(lowLef[i] + 1, i);
if(lowLef[i] == -1) curl = 1e10 + 10;
long long curr = seg_all.qry(i + 1, lowRig[i]);
if(lowRig[i] == n) curr = 1e10 + 10;
ai.push_back(min(curl, curr) - a[i]);
}
sort(all(ai));
mid = mx.second;
for(int i = 0; i < mid; i++) {
if(a[i + 1] <= a[i]) {
f1 = 0;
}
}
for(int i = mid + 1; i < n; i++) {
if(a[i] >= a[i - 1]) {
f1 = 0;
}
}
for(int i = 1; i < n - 1; i++) {
pi[i] = pi[i - 1] + (a[i] > a[i - 1] && a[i] > a[i + 1]);
}
pi[n - 1] = pi[n - 2];
}
int max_towers(int L, int R, int D) {
if(L == 0 && R == n - 1) {
auto it = lower_bound(all(ai), (long long )D);
int answ = 1;
if(it != ai.end()) {
int ind = it - ai.begin();
answ = max(answ, n - ind);
}
return answ;
}
if(f1) {
if(R <= mid || L >= mid) {
return 1;
}
if(R - L + 1 == 1) {
return 1;
}
if(a[mid] - D >= max(a[L], a[R])) {
return 2;
} else {
return 1;
}
} else if(D == 1) {
int cur = pi[R - 1] - pi[L] + 1;
return max(1, cur);
} else {
vector<long long> dp(n + 1);
long long answ = 0;
set<pair<long long, long long>> ft;
deque<pair<int, int>> vec;
seg_max.init(n + 5);
for(int i = L; i <= R; i++) {
dp[i] = 1;
auto it = lower_bound(all(vec), make_pair(a[i] + D, -1));
if(it != vec.end()) {
int ind = it - vec.begin();
if(vec[ind].second >= 1) {
dp[i] = max(dp[i], seg_max.qry(0, vec[ind].second) + 1);
}
}
while (!vec.empty() && a[i] > vec.front().first) {
vec.pop_front();
}
vec.push_front({a[i], i});
while(!ft.empty() && ft.begin()->first <= a[i] - D) {
seg_max.upd(ft.begin()->second, dp[ft.begin()->second]);
ft.erase(ft.begin());
}
ft.insert({a[i], i});
answ = max(answ, dp[i]);
}
return answ;
}
}
