#include "towers.h"
#include <vector>
#include <bits/stdc++.h>
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2")
#define pb push_back
#define F first
#define pii pair<int,int>
#define all(a) a.begin(),a.end()
#define S second
#define sz(a) (int)a.size()
#define rep(i , a , b) for(int i = (a) ; i <= (b) ; i++)
#define per(i , a , b) for(int i = (a) ; i >= (b) ; i--)
#define ld double
#define ll long long
using namespace std ;
const int maxn = 1e6 + 10 , inf = 1e9+ 10 , mod = 998244353;
int n ;
vector <int> h ;
struct segtree{
int mn[4*maxn] , id[4*maxn] ;
vector <int> a ;
void bui(int p = 1, int l = 0 , int r= n){
int mid = (l+r)/2 ,pl =p <<1,pr=p<<1|1;
if(l==r){
mn[p] = a[l] ;
id[p] = l ;
return;
}
bui(pl,l,mid);
bui(pr,mid+1,r) ;
mn[p] = min(mn[pl] , mn[pr]) ;
id[p] = id[pl] ;
if(mn[p] == mn[pr])id[p] = id[pr] ;
}
pii que(int le ,int ri , int p =1 , int l = 0 , int r= n){
int mid = (l+r)/2 ,pl =p <<1,pr=p<<1|1;
if(le > r || l > ri)return {inf , 0 };
if(le <= l && r <= ri)return {mn[p] , id[p]} ;
pii a= que(le,ri,pl,l,mid) ;
pii b = que(le,ri,pr,mid+1,r);
pii c ;
c.F = min(a.F ,b.F);
c.S = a.S ;
if(c.F == b.F)c.S = b.S ;
return c;
}
};
segtree mn , mx ;
vector <pii> ans ;
vector <pair<int,pii> > ed;
int bui(int l , int r){
int m = mx.que(l , r).S ;
if(m!=l){
ed.pb({h[m]-mn.que(l,m-1).F , {m , bui(l ,m-1)}}) ;
}
if(m!=r){
ed.pb({h[m]-mn.que(m+1,r).F , {m , bui(m+1,r)}}) ;
}
return m ;
}
int mark[maxn] ;
void init(int N, std::vector<int> H) {
n = N ;
h.pb(0);
rep(i , 0 , n-1)h.pb(H[i]) ;
mn.a = h;
vector <int> h2 ;
rep(i , 0 ,n){
h2.pb(-h[i]) ;
}
mx.a = h2 ;
mn.bui();
mx.bui() ;
int r = bui(1 , n);
mark[r] =1 ;
sort(all(ed)) ;
reverse(all(ed)) ;
int cnt = 1 ;
rep(i , 0 ,sz(ed)-1){
int v = ed[i].S.F , u= ed[i].S.S ;
if(mark[v] == 0)cnt++;
mark[u] =1 ;
mark[v] = 0 ;
ans.pb({ed[i].F , -cnt}) ;
}
ans.pb({inf , -1}) ;
sort(all(ans)) ;
}
int max_towers(int L, int R, int D) {
L++;
R++;
int x =lower_bound(all(ans) , (pii){D,0}) -ans.begin() ;
return -ans[x].S ;
}
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