#include "towers.h"

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")


struct Set {
  // max{ceil(log_64(n)), 1}
  int log64N, n;
  vector<unsigned long long> a[6];
  explicit Set(int n_ = 0) : n(n_) {
    assert(n >= 0);
    int m = n ? n : 1;
    for (int d = 0; ; ++d) {
      m = (m + 63) >> 6;
      a[d].assign(m, 0);
      if (m == 1) {
        log64N = d + 1;
        break;
      }
    }
  }
  bool empty() const {
    return !a[log64N - 1][0];
  }
  bool contains(int x) const {
    return (a[0][x >> 6] >> (x & 63)) & 1;
  }
  void insert(int x) {
    for (int d = 0; d < log64N; ++d) {
      const int q = x >> 6, r = x & 63;
      a[d][q] |= 1ULL << r;
      x = q;
    }
  }
  void erase(int x) {
    for (int d = 0; d < log64N; ++d) {
      const int q = x >> 6, r = x & 63;
      if ((a[d][q] &= ~(1ULL << r))) break;
      x = q;
    }
  }
  // max s.t. <= x (or -1)
  int prev(int x) const {
    if (x > n - 1) x = n - 1;
    for (int d = 0; d <= log64N; ++d) {
      if (x < 0) break;
      const int q = x >> 6, r = x & 63;
      const unsigned long long lower = a[d][q] << (63 - r);
      if (lower) {
        x -= __builtin_clzll(lower);
        for (int e = d; --e >= 0; ) x = x << 6 | (63 - __builtin_clzll(a[e][x]));
        return x;
      }
      x = q - 1;
    }
    return -1;
  }
  // min s.t. >= x (or n)
  int next(int x) const {
    if (x < 0) x = 0;
    for (int d = 0; d < log64N; ++d) {
      const int q = x >> 6, r = x & 63;
      if (static_cast<unsigned>(q) >= a[d].size()) break;
      const unsigned long long upper = a[d][q] >> r;
      if (upper) {
        x += __builtin_ctzll(upper);
        for (int e = d; --e >= 0; ) x = x << 6 | __builtin_ctzll(a[e][x]);
        return x;
      }
      x = q + 1;
    }
    return n;
  }
};

////////////////////////////////////////////////////////////////////////////////


constexpr int INF = 1001001001;

int N;
vector<pair<int, int>> anss;

void init(int N_, std::vector<int> H) {
  N = N_;
  vector<int> is;
  for (int i = 0, j, k; i < N - 1; i = k) {
    for (j = i; j < N - 1 && H[j] < H[j + 1]; ++j) {}
    for (k = j; k < N - 1 && H[k] > H[k + 1]; ++k) {}
    if (i < j && j < k) {
      if (is.size()) {
        assert(is.back() == i);
        is.pop_back();
      }
      is.push_back(i);
      is.push_back(j);
      is.push_back(k);
    }
  }
  int now = (int)is.size() / 2;
  Set on(N);
  using Entry = pair<int, pair<int, int>>;
  priority_queue<Entry, vector<Entry>, greater<Entry>> que;
  for (const int i : is) {
    on.insert(i);
  }
  for (int j = 0; j < 2 * now; ++j) {
    que.emplace(abs(H[is[j]] - H[is[j + 1]]), make_pair(is[j], is[j + 1]));
  }
  for (; que.size(); ) {
    const int d = que.top().first;
    const int i = que.top().second.first;
    const int j = que.top().second.second;
    que.pop();
    if (on.contains(i) && on.contains(j)) {
// cerr<<"d = "<<d<<", i = "<<i<<", j = "<<j<<"; on = ";for(int k=0;k<N;++k)if(on.contains(k))cerr<<make_pair(H[k],k)<<" ";cerr<<endl;
      anss.emplace_back(d, -now);
      now -= 2;
      on.erase(i);
      on.erase(j);
      const int l = on.prev(i);
      const int r = on.next(j);
      if (0 <= l && r < N) {
        que.emplace(abs(H[l] - H[r]), make_pair(l, r));
      }
    }
  }
  anss.emplace_back(INF, -1);
// cerr<<"anss = "<<anss<<endl;
}

int max_towers(int L, int R, int D) {
  ++R;
  assert(L == 0);
  assert(R == N);
  return -lower_bound(anss.begin(), anss.end(), make_pair(D, -INF))->second + 1;
}