#include "towers.h"
#pragma GCC target ("avx2")
#pragma GCC optimize ("O3")
#pragma GCC optimize ("unroll-loops")
#include<bits/stdc++.h>
#include<math.h>
using namespace std;
typedef long long int ll;
typedef long double ld;
typedef pair<ll, ll> pl;
typedef vector<ll> vl;
#define FD(i, r, l) for(ll i = r; i > (l); --i)
#define K first
#define V second
#define G(x) ll x; cin >> x;
#define GD(x) ld x; cin >> x;
#define GS(s) string s; cin >> s;
#define EX(x) { cout << x << '\n'; exit(0); }
#define A(a) (a).begin(), (a).end()
#define F(i, l, r) for (ll i = l; i < (r); ++i)
#define NN 100010
#define M 1000000007 // 998244353
ll h[NN];
ll n;
namespace seg {
typedef pl T;
T id={-1, -1};
T f(T a, T b) {return pair(max(a.K, b.K), max(a.V, b.V)) ;}
T t[2 * NN];
ll n=NN; // array size
void init(ll p, ll value) { // set value at position p
for (p+=n, t[p].K = value; p /= 2;) t[p] = f(t[2*p], t[2*p+1]);
}
void modify(ll p, ll value) { // set value at position p
for (p+=n, t[p].V = max(t[p].V, value); p /= 2;) t[p] = f(t[2*p], t[2*p+1]);
}
T query(ll l, ll r) { // fold f on interval [l, r)
T resl=id, resr=id;
for (l += n, r += n; l < r; l /= 2, r /= 2) {
if (l&1) resl = f(resl, t[l++]);
if (r&1) resr = f(t[--r], resr);
}
return f(resl, resr);
}
}
int brute_force(int L, int R, int D) {
// vl dp(n+1, -1);/
F(i, 0, 2*NN) seg::t[i].V = -1;
ll res = 0;
// ll res2 = 0;
F(i, L, R+1) {
ll ans = 1;
// ll ans2 = 1;
{
// for (ll cur = i-1; cur >= L; cur--) if (h[cur] >= D + h[i]) ans2 = max(ans2, dp[cur] + 1);
ll l = L - 1, r = i + 1;
while (l+1<r) {
ll m = (l+r)/2;
if (seg::query(m, i).K >= D + h[i]) l = m;
else r = m;
}
// if (i == 5) {
// cout << L << " " << l+1 << " " << seg::query(L, l+1).V << " " << endl;
// cout << seg::query(l, l+1).V << endl;
// }
ans = max(ans, seg::query(L, l+1).V + 1);
}
{
// for (ll cur = i+1; cur <= R; cur++) if (h[cur] >= D + h[i]) dp[cur] = max(dp[cur], ans2);
ll l = i, r = R+1;
while (l+1<r) {
ll m = (l+r)/2;
if (seg::query(i, m+1).K >= D + h[i]) r = m;
else l = m;
}
seg::modify(r, ans);
// if (ans2 == 3) cout << "TURNEd 3 AT " << i << endl;
}
res = max(res, ans);
// res2 = max(ans, ans2);
// cout << "ARRAYS FOR " << i << endl;
// F(i, L, R+1) cout << dp[i] << " "; cout << endl;
// F(i, L, R+1) cout << seg::query(i, i+1).V << " "; cout << endl;
}
// assert(res == res2);
return res;
}
namespace segval {
typedef ll T;
T id=0;
T f(T a, T b) {return a+b;}
T t[2 * NN];
ll n=NN; // array size
void modify(ll p, T value) { // set value at position p
for (p+=n, t[p] = value; p /= 2;) t[p] = f(t[2*p], t[2*p+1]);
}
T query(ll l, ll r) { // fold f on interval [l, r)
T resl=id, resr=id;
for (l += n, r += n; l < r; l /= 2, r /= 2) {
if (l&1) resl = f(resl, t[l++]);
if (r&1) resr = f(t[--r], resr);
}
return f(resl, resr);
}
}
vl valleys;
void init(int N, std::vector<int> H) {
n = N;
F(i, 0, n) h[i] = H[i];
F(i, 0, n) seg::init(i, H[i]);
valleys.resize(n);
F(i, 0, n) {
valleys[i] = 1;
if (i + 1 < n) valleys[i] &= h[i] < h[i+1];
if (i > 0) valleys[i] &= h[i-1] > h[i];
segval::modify(i, valleys[i]);
}
}
void gen_graph(int L, int R, int D) {
cout << "Query: " << L << " " << R << " " << D << endl;
F(i, L, R+1) cout << h[i] << " "; cout << endl;
vector<ll> peak(n), valley(n);
F(i, L, R+1) {
peak[i] = 1, valley[i] = 1;
if (i > 0) {
peak[i] &= h[i-1] < h[i];
valley[i] &= h[i-1] > h[i];
}
if (i + 1 < n) {
peak[i] &= h[i+1] < h[i];
valley[i] &= h[i+1] > h[i];
}
// cout << h[i] << ": " << peak[i] << " " << valley[i] << endl;
}
F(i, L, R+1) {
if (valley[i]) {
for (ll j = i + 1; j <= R; ++j) if (peak[j] and h[j] - h[i] >= D) {
cout << "V" << i << " P" << j << endl; break;
}
} else if (peak[i]) {
for (ll j = i + 1; j <= R; ++j) if (valley[j] and h[i] - h[j] >= D) {
cout << "P" << i << " V" << j << endl; break;
}
}
}
}
// if (valley[i]) {
// for (ll l = i-1; l >= L; --l) if (peak[l] and h[l] - h[i] >= D) {
// cout << l << " " << i << endl; break;
// }
// }
// for (ll r = i+1; r <= R; ++r) if (valley[r] and h[r] - h[i] >= D) {
// cout << i << " " << r << endl; break;
// }
int max_towers(int L, int R, int D) {
if (L == R) return 1;
if (D == 1) {
if (!valleys[L] and h[L] < h[L+1]) segval::modify(L, 1);
if (!valleys[R] and h[R] < h[R-1]) segval::modify(R, 1);
int ans = segval::query(L, R+1);
if (!valleys[R] and h[R] < h[R-1]) segval::modify(R, 0);
if (!valleys[L] and h[L] < h[L+1]) segval::modify(L, 0);
// ll temp = brute_force(L, R, D);
// if (temp != ans) cout << L << " " << R << " " << D << ", " << temp << " " << ans << endl;
// assert(temp == ans);
return ans;
}
// gen_graph(L, R, D);
// cout << "Actual: " << brute_force(L, R, D) << endl;
return brute_force(L, R, D);
}
