#include "towers.h"
#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define all(x) x.begin(),x.end()
#define ll long long int
#define en cout << '\n'
#define pii pair<int,int>
#define vi vector<int>
#define ff first
#define ss second
struct Node{
Node *L, *R;
int sum;
Node(){
L=R=nullptr;
sum=0;
}
Node(Node*l, Node*r): L(l), R(r){
sum = 0;
if(l != nullptr) sum += l->sum;
if(r != nullptr) sum += r->sum;
}
Node(int s): sum(s){
L=R=nullptr;
}
};
vector<bool> is_peak(300005);
Node *build(int l, int r){
if(l == r){
return new Node(is_peak[l]);
}
int m = l+r>>1;
return new Node(build(l, m), build(m+1, r));
}
Node *upd(Node *v, int l, int r, int p, int val){
if(l == r){
return new Node(val);
}
int m = l+r>>1;
if(p <= m) return new Node(upd(v->L, l, m, p, val), v->R);
return new Node(v->L, upd(v->R, m+1, r, p, val));
}
int get(Node *vl, Node *vr, int l, int r, int ql, int qr){
if(ql > r || l > qr) return 0;
if(ql <= l && r <= qr) return vr->sum - vl->sum;
int m = l+r>>1;
return get(vl->L, vr->L, l, m, ql, qr) + get(vl->R, vr->R, m+1, r, ql, qr);
}
void op(vector<int> &a, vector<int> &A, vector<int> &B){
if(a.size() <= 1){
A = a;
B.pb(0);
return;
}
A.pb(a[0]);
A.pb(a[1]);
B.pb(0);
B.pb(1);
for(int i = 2; i < a.size(); ++i){
if(a[i] > A.back() && A.back() > A[int(A.size()) - 2]){
A.pop_back();
B.pop_back();
A.pb(a[i]);
B.pb(i);
}else if(a[i] < A.back() && A.back() < A[int(A.size()) - 2]){
A.pop_back();
B.pop_back();
A.pb(a[i]);
B.pb(i);
}else{
A.pb(a[i]);
B.pb(i);
}
}
}
int n;
vector<int> A, B, a;
vector<pair<int, int>> ans;
void init(int nn, std::vector<int> aa) { n=nn;a=aa;
if(n == 1) return;
op(a, A, B);
if(A[0] > A[1]) A.erase(A.begin()), B.erase(B.begin());
if(A.size()==1) return;
if(A.back() > A[A.size() - 2]) A.pop_back(), B.pop_back();
if(A.size()==1) return;
set<pair<int,int>> S;
priority_queue<array<int, 3>> Q;
int m = A.size();
for(int i = 0; i < m; ++i){
S.insert({i, A[i]});
if(i%2) is_peak[B[i]] = 1;
if(i + 1 < m && A[i + 1] > A[i]) Q.push({-(A[i + 1] - A[i]), i, i + 1});
if(i > 0 && A[i - 1] > A[i]) Q.push({-(A[i - 1] - A[i]), i, i - 1});
}
vector<pair<int, Node*>> roots;
// roots.pb({1, });
ans.pb({0, A.size() / 2 + 1});
vector<bool> rem(A.size());
while(!Q.empty()){
auto V = Q.top();
int v = V[1], u = V[2];
int val = V[0];
Q.pop();
if(rem[u] || rem[v]) continue;
S.erase({v, A[v]});
S.erase({u, A[u]});
rem[u] = rem[v] = 1;
int mx = max(u, v);
auto it = S.lower_bound(pair<int,int>{mx, -1});
if(it != S.begin() && it != S.end()){
auto it2 = prev(it);
auto x = *it;
auto y = *it2;
Q.push({-abs(x.ss - y.ss), x.ff, y.ff});
}
// assert(S.size()%2);
if(ans.back().ff == -val){
ans.back().ss = S.size() / 2 + 1;
}else ans.pb({-val, S.size() / 2 + 1});
}
}
int max_towers(int L, int R, int D) { ++L, ++R;
if(n == 1 || L == R || A.size() == 1) return 1;
int pos = upper_bound(all(ans), pii{D, -1}) - ans.begin() - 1;
// if(D==1) return ans[0].ss;
return max(pos == ans.size() ? 1 : ans[pos].ss, 1);
}
