#include "towers.h"
#include "bits/stdc++.h"
using namespace std;
#define rep(i,a,b) for(int i=(a);i<(b);++i)
#define all(x) begin(x), end(x)
#define sz(x) (int)x.size()
typedef long long ll;
typedef pair<int,int> pii;
typedef vector<int> vi;
#ifdef DEBUG
auto& operator<<(auto &os, const pair<auto,auto> &p) {
return os<<"("<<p.first<<", "<<p.second<<")";
}
auto& operator<<(auto &os, const auto &v) {
os<<"{";
for(auto it=begin(v);it!=end(v);++it) {
if(it != begin(v)) os<<", ";
os<<(*it);
}
return os<<"}";
}
void dbg_out(auto... x) {
((cerr<<' '<<x), ...) << endl;
}
#define dbg(x...) cerr<<"("<<#x<<"):", dbg_out(x);
#else
#define dbg(...)
#endif
const int inf = 1e9 + 7;
int n, root;
vi h;
vi L, R, siz;
int get_max(int l, int r) {
int maxi = l;
rep(i,l+1,r)
if(h[i] > h[maxi])
maxi = i;
return maxi;
}
int build_tree(int l, int r) {
if(l == r) return -1;
if(l+1 == r) {
siz[l] = 1;
return l;
}
int index = get_max(l, r);
L[index] = build_tree(l, index);
R[index] = build_tree(index+1, r);
siz[index] = (L[index] == -1 ? 0 : siz[L[index]])
+(R[index] == -1 ? 0 : siz[R[index]]);
return index;
}
void init(int N, vi H) {
n = N;
h = H;
L.resize(n);
R.resize(n);
siz.assign(n, 0);
root = build_tree(0, n);
dbg(root);
dbg(L);
dbg(R);
}
int solve(int v, int l, int r, int a, int b, int d, int maxi) {
if(l == r || r <= a || b <= l) return 0;
dbg(v, l, r, a, b, d, maxi);
if(l+1 == r) return h[v] <= maxi;
int res = 0;
if(L[v] == -1 || v < a)
res += solve(R[v], v+1, r, a, b, d, maxi);
else if(R[v] == -1 || v >= b)
res += solve(L[v], l, v, a, b, d, maxi);
else {
res += solve(L[v], l , v, a, b, d, min(maxi, h[v] - d));
res += solve(R[v], v+1, r, a, b, d, min(maxi, h[v] - d));
res = max(res, solve(R[v], v+1, r, a, b, d, maxi));
res = max(res, solve(L[v], l, v, a, b, d, maxi));
}
if(res == 0 && (a <= v && v < b && h[v] <= maxi))
return 1;
return res;
}
int max_towers(int L, int R, int D) {
int res = solve(root, 0, n, L, R+1, D, inf);
return res == 0 ? 1 : res;
}
