#include "towers.h"
#include<bits/stdc++.h>
#define pb push_back
#define mp make_pair
#define int long long
#define vi vector<int>
#define vvi vector<vector<int>>
#define pii pair<int, int>
#define vpii vector<pair<int, int>>
#define vc vector<char>
#define vb vector<bool>
#define mii map<int,int>
#define f0r(i,n) for(int i=0;i<n;i++)
#define FOR(i,k,n) for(int i=k;i<n;i++)
#define all(v) (v).begin(),(v).end()
#define rall(v) (v).rbegin(),(v).rend()
#define in(a) int a; cin>>a
#define in2(a,b) int a,b; cin>>a>>b
#define in3(a,b,c) int a,b,c; cin>>a>>b>>c
#define in4(a,b,c,d) int a,b,c,d; cin>>a>>b>>c>>d
#define vin(v,n); vi v(n); f0r(i,n){cin>>v[i];}
#define out(a) cout<<a<<'\n'
#define out2(a,b) cout<<a<<' '<<b<<'\n'
#define out3(a,b,c) cout<<a<<' '<<b<<' '<<c<<'\n'
#define out4(a,b,c,d) cout<<a<<' '<<b<<' '<<c<<' '<<d<<'\n'
#define vout(v) for(auto u : v){cout<<u<<' ';} cout<<'\n'
#define dout(a) cout<<a<<' '<<#a<<'\n'
#define dout2(a,b) cout<<a<<' '<<#a<<' '<<b<<' '<<#b<<'\n'
#define yn(x); if(x){cout<<"YES"<<'\n';}else{cout<<"NO"<<'\n';}
const int leg = 1e9 + 7;
const int mod = 998244353;
using namespace std;
vi V;
struct segtree{
int n; vi mn, mx;
segtree(vi v){
n = v.size();
mn.resize(4 * n + 5);
mx.resize(4 * n + 5);
build(1, 0, n-1, v);
}
void pull(int v){
mn[v] = min(mn[v*2], mn[v*2+1]);
mx[v] = max(mx[v*2], mx[v*2+1]);
}
void build(int v, int l, int r, vi &a){
if(l == r){
mn[v] = a[l];
mx[v] = a[l];
return;
}
int mid = (l + r) / 2;
build(v*2, l, mid, a);
build(v*2+1, mid+1, r, a);
pull(v);
}
int firstlarger(int v, int tl, int tr, int l, int r, int d){
if(tl > r || tr < l)return -1;
if(mx[v] <= d)return -1;
if(tl == tr)return tl;
int tm = (tl + tr) / 2;
int left = firstlarger(v*2, tl, tm, l, r, d);
if(left != -1)return left;
return firstlarger(v*2+1, tm+1, tr, l, r, d);
}
int leftlarger(int v, int tl, int tr, int l, int r, int d){
if(tl > r || tr < l)return -1;
if(mx[v] <= d)return -1;
if(tl == tr)return tl;
int tm = (tl + tr) / 2;
int right = leftlarger(v*2+1, tm+1, tr, l, r, d);
if(right != -1)return right;
return leftlarger(v*2, tl, tm, l, r, d);
}
int firstsmaller(int v, int tl, int tr, int l, int r, int d){
if(tl > r || tr < l)return -1;
if(mn[v] >= d)return -1;
if(tl == tr)return tl;
int tm = (tl + tr) / 2;
int left = firstsmaller(v*2, tl, tm, l, r, d);
if(left != -1)return left;
return firstsmaller(v*2+1, tm+1, tr, l, r, d);
}
int leftsmaller(int v, int tl, int tr, int l, int r, int d){
if(tl > r || tr < l)return -1;
if(mn[v] >= d)return -1;
if(tl == tr)return tl;
int tm = (tl + tr) / 2;
int right = leftsmaller(v*2+1, tm+1, tr, l, r, d);
if(right != -1)return right;
return leftsmaller(v*2, tl, tm, l, r, d);
}
void update(int v, int tl, int tr, int d, int x){
if(tl == tr){
mn[v] = x; mx[v] = x; return;
}
int tm = (tl + tr) / 2;
if(tm >= d){
update(v*2, tl, tm, d, x);
}
else{
update(v*2+1, tm+1, tr, d, x);
}
pull(v);
}
int maxquer(int v, int tl, int tr, int l, int r){
if(l > r)return -4e18;
if(tl == l && tr == r){
return mx[v];
}
int tm = (tl + tr) / 2;
return max(maxquer(v*2, tl, tm, l, min(r, tm)), maxquer(v*2+1, tm+1, tr, max(l, tm+1), r));
}
int minquer(int v, int tl, int tr, int l, int r){
if(l > r)return 4e18;
if(tl == l && tr == r){
return mn[v];
}
int tm = (tl + tr) / 2;
return min(minquer(v*2, tl, tm, l, min(r, tm)), minquer(v*2+1, tm+1, tr, max(l, tm+1), r));
}
};
vi l,r,ls,rs;
vpii w; int n;
void init(signed N, std::vector<signed> H) {
V.resize(N); ::n = N;
f0r(i, N){
V[i] = H[i];
}
vi v;
for(int i = 0; i<=N-1; i++){
v.pb(V[i]);
}
int n = v.size();
segtree s = segtree(v);
vpii pts;
f0r(i,n){
pts.pb(mp(v[i], i));
}
sort(all(pts));
l.resize(n); r.resize(n); ls.resize(n); rs.resize(n);
f0r(i,n){
// l[i] = s.leftlarger(1, 0, n-1, 0, i-1, v[i] + D - 1);
// if(l[i] == -1)l[i] = 0;
// r[i] = s.firstlarger(1, 0, n-1, i + 1, n-1, v[i] + D - 1);
// if(r[i] == -1)r[i] = n-1;
ls[i] = s.leftsmaller(1, 0, n-1, 0, i-1, v[i]);
rs[i] = s.firstsmaller(1,0,n-1,i+1,n-1,v[i]);
}
// vout(ls);
// vout(rs);
vi mxd(n);
f0r(i,n){
int lm,rm;
if(ls[i] == -1)lm = 4e18;
else lm = s.maxquer(1, 0, n-1, ls[i], i);
if(rs[i] == -1)rm = 4e18;
else rm = s.maxquer(1, 0, n-1, i, rs[i]);
// dout2(lm,rm);
mxd[i] = min(lm, rm) - v[i];
}
f0r(i,n){
w.pb(mp(mxd[i], i));
}
sort(rall(w));
// f0r(i,n)cout<<w[i].first<<' ';
// cout<<'\n';
}
signed max_towers(signed L, signed R, signed D) {
// vout(l);
// vout(r);
int lo = 0; int hi = n;
while(lo < hi){
int mid = lo + (hi - lo) / 2;
if(w[mid].first < D){
hi = mid;
}
else lo = mid + 1;
}
return lo;
return 0;
}
