#include "towers.h"
#include <vector>
#include<bits/stdc++.h>
using namespace std;
vector<int> h;
pair<int, int> st[500005][20];
int stt[500005][20];
vector<pair<int, int>> x;
vector<int> suff;
int solve(int l, int r, int d, int lim){
if(r < l){
return -1;
}
if(l == r){
x.push_back({lim - h[l], 1});
return lim - h[l];
}
int dist = log2(r - l + 1);
int mid = st[l][dist].second;
int mn = min(stt[l][dist], stt[r - (1 << dist) + 1][dist]);
if(st[r - (1 << dist) + 1][dist].first > st[l][dist].first){
mid = st[r - (1 << dist) + 1][dist].second;
}
//cout << l << " " << r << " " << mid << endl;
if(lim == 1000000001){
x.push_back({1000000001, 1});
}else
x.push_back({lim - mn, 1});
int ans = max(solve(l, mid-1, d, h[mid]), solve(mid+1, r, d, h[mid]));
x.push_back({ans, -1});
return max(lim - mn, ans);
}
void init(int N, std::vector<int> H) {
int mx = 0;
for(int i = 0; i < N; ++i){
st[i][0] = {H[i], i};
stt[i][0] = H[i];
h.push_back(H[i]);
}
for(int bit = 1; bit <= 18; ++bit){
//cout << bit << endl;s
for(int i = 0; i < N; ++i){
st[i][bit] = max(st[i][bit-1], st[i + (1 << (bit-1))][bit-1]);
stt[i][bit] = min(stt[i][bit-1], stt[i + (1 << (bit-1))][bit-1]);
}
}
solve(0, N-1, N, 1000000001);
sort(x.begin(), x.end());
for(int i = (int)x.size()-1; i >= 0; --i){
suff.push_back(x[i].second);
if((int)suff.size() > 1){
suff[(int)suff.size()-1] += suff[(int)suff.size()-2];
}
}
reverse(suff.begin(), suff.end());
}
int max_towers(int L, int R, int D) {
if(D <= x[0].first){
return suff[0];
}
int lo = 0;
int hi = (int)x.size();
while(hi - lo > 1){
int mid = lo + (hi - lo) / 2;
if(x[mid].first < D){
lo = mid;
}else{
hi = mid;
}
}
return suff[hi];
}
