#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 ,d ;
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; vector <int> az;
int lf[maxn] ,ri[maxn] , vj[maxn] , pr[maxn] ,pr2[maxn] ,ok[maxn] , rpar[maxn] , lpar[maxn];
void bui(int l , int r){
int m = mx.que(l , r).S ;
az.pb(m);
vj[m] = 1;
ok[m] =1 ;
if(m!=l){
if(h[m]-mn.que(l,m-1).F >= d){
int x = mx.que(l , m-1).S ;
rpar[x] = m ;
lpar[x] = lpar[m] ;
bui(l , m-1) ;
ok[m] =0 ;
lf[m] =1 ;
}
}
if(m!=r){
if(h[m]-mn.que(m+1,r).F >= d){
int x = mx.que(m+1, r).S ;
lpar[x] = m ;
rpar[x] = rpar[m] ;
bui(m+1,r) ;
ok[m] =0 ;
ri[m] =1 ;
}
}
}
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();
}
bool ook =0 ;
void solve(int D){
d = D ;
bui(1 , n);
sort(all(az)) ;
rep(i ,1, n){
pr[i] = pr[i-1] + vj[i] ;
pr2[i] = pr2[i-1] + ok[i] ;
}
}
int max_towers(int l, int r, int D) {
if(ook == 0){
solve(D);
ook =1 ;
}
l++;
r++;
if(pr[r] - pr[l-1] <= 2)return 1;
int x =lower_bound(all(az) , l) - az.begin() ;
int y = lower_bound(all(az) , r+1) - az.begin() - 1 ;
int ans = pr2[r]-pr2[l-1];
x = az[x];
y = az[y];
if(ok[x] == 0 && ri[x] == 0 && h[rpar[x]]-h[x] >= d)ans++;
if(ok[y]==0 && lf[y] ==0 && h[lpar[y]]-h[y] >= d)ans++;
return ans;
}
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