#include "towers.h"
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define ii pair<int,int>
#define fi first
#define se second
#define puf push_front
#define pof pop_front
#define pub push_back
#define pob pop_back
#define lb lower_bound
#define ub upper_bound
#define rep(x,s,e) for (int x=(s)-((s)>(e));x!=(e)-((s)>(e));((s)<(e))?x++:x--)
#define all(x) (x).begin(),(x).end()
#define sz(x) (int) (x).size()
mt19937 rng(chrono::system_clock::now().time_since_epoch().count());
struct dat{
int mn,mx;
int a,b;
dat(){};
dat (int i){
mn=mx=i;
a=b=0;
}
};
dat merge(dat a,dat b){
dat res;
res.mn=min(a.mn,b.mn);
res.mx=max(a.mx,b.mx);
res.a=max({a.a,b.a,a.mx-b.mn});
res.b=max({a.b,b.b,b.mx-a.mn});
return res;
}
struct node{
int s,e,m;
dat val;
node *l,*r;
node (int _s,int _e){
s=_s,e=_e,m=s+e>>1;
if (s!=e){
l=new node(s,m);
r=new node(m+1,e);
}
}
void update(int i,int k){
if (s==e) val=dat(k);
else{
if (i<=m) l->update(i,k);
else r->update(i,k);
val=merge(l->val,r->val);
}
}
dat query(int i,int j){
if (s==i && e==j) return val;
else if (j<=m) return l->query(i,j);
else if (m<i) return r->query(i,j);
else return merge(l->query(i,m),r->query(m+1,j));
}
} *root=new node(0,100005);
int n;
int arr[100005];
void init(signed N, vector<signed> H) {
n=N;
rep(x,0,n) arr[x+1]=H[x];
rep(x,1,n+1) root->update(x,arr[x]);
}
bool proc=false;
ii tkd[200005][20]; //(nxt,score)
signed max_towers(signed l, signed r, signed d) {
if (l==r) return 1;
l++,r++; //0-based indexing is cringe
if (!proc){
memset(tkd,-1,sizeof(tkd));
int r=n+1;
rep(x,n+1,1){
while (x<r && root->query(x,r-1).a>=d) r--;
if (r!=n+1) tkd[x*2][0]={2*r+1,1};
}
r=n+1;
rep(x,n+1,1){
while (x<r && root->query(x,r-1).b>=d) r--;
if (r!=n+1) tkd[x*2+1][0]={2*r,0};
}
rep(layer,0,19){
rep(x,0,200005) if (tkd[x][layer].fi!=-1){
int nxt=tkd[x][layer].fi;
if (tkd[nxt][layer].fi==-1) continue;
tkd[x][layer+1]={tkd[nxt][layer].fi,tkd[x][layer].se+tkd[nxt][layer].se};
}
}
proc=true;
}
int curr=l*2+1;
int ans=1;
rep(x,20,0){
if (tkd[curr][x].fi!=-1 && tkd[curr][x].fi/2<=r){
ans+=tkd[curr][x].se;
curr=tkd[curr][x].fi;
}
}
return ans;
}
