This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
#define int long long
const int MAXN = 1e5+4;
vector<int> h;
vector<int> lc,rc,a;
int pr[MAXN];
int inited = 0;
vector<int> usef;
map<int,int> nxt;
map<int,int> prv;
int sum (int l, int r) {
	if (l > r) return 0;
	if (r==0) return pr[r];
	return pr[r] - pr[l-1];
}
int dfs(int i, int d){
	if (i==-1) return 0;
	if (lc[i]==-1 && rc[i]==-1) return -a[i];
	int lans = dfs(lc[i],d);
	int rans = dfs(rc[i],d);
	if (lans < 0 && a[i] - d >= -lans) lans = 1;
	if (rans < 0 && a[i] - d >= -rans) rans = 1;
	if (lans < 0) {
		lc[lc[i]] = -2; rc[lc[i]] = -2;
		lc[i] = -1;
	}
	if (rans < 0) {
		lc[rc[i]] = -2; rc[rc[i]] = -2;
		rc[i] = -1;
	}
	if (!lans) return rans; if (!rans) return lans;
	if (lans < 0 && rans < 0) return max(lans,rans);
	if (lans < 0) return rans;
	if (rans < 0) return lans;
	return lans + rans;
}
signed helper(signed l, signed r, int d){
	int sz = r-l+1;
	a.assign(sz,0); for (int i=l; i<=r; i++) a[i-l] = h[i];
	a.push_back(3e9);
	stack<int> st; st.push(sz);
	lc.assign(sz+1,-1); rc.assign(sz+1,-1);
	for (int i=0; i<sz; i++){
		int last = -1;
		while (a[i] > a[st.top()]) {
			last=st.top();
			st.pop();
		}
		lc[i] = last;
		rc[st.top()]=i;
		st.push(i);
	}
	return dfs(sz,d);
}
void init(signed N, std::vector<signed> H){
	h.resize(N); for (int i = 0; i < N; i++) h[i] = H[i];
}
void init0(int d) {
	helper(0, h.size()-1, d);
	pr[0] = (lc[0]==-1 && rc[0]==-1);
	for (int i=1; i<h.size(); i++) pr[i] = pr[i-1] + (lc[i]==-1 && rc[i]==-1);
	for (int i=0; i<h.size(); i++) if (lc[i]!=-2) usef.push_back(h[i]);
	for (int i=0; i<usef.size()-1; i++) nxt[usef[i]] = usef[i+1];
	for (int i=1; i<usef.size(); i++) prv[usef[i]] = usef[i-1];
}
signed max_towers(signed l, signed r, signed d) {
	if (!inited) init0(d), inited = 1;
	if (r-l <= 1) return 1;
	int s = sum(l+1,r-1);
	s += nxt.count(h[l]) && h[l] < nxt[h[l]]; s += prv.count(h[r]) && h[r] < prv[h[r]];
	return s;
}
Compilation message (stderr)
towers.cpp: In function 'long long int dfs(long long int, long long int)':
towers.cpp:36:2: warning: this 'if' clause does not guard... [-Wmisleading-indentation]
   36 |  if (!lans) return rans; if (!rans) return lans;
      |  ^~
towers.cpp:36:26: note: ...this statement, but the latter is misleadingly indented as if it were guarded by the 'if'
   36 |  if (!lans) return rans; if (!rans) return lans;
      |                          ^~
towers.cpp: In function 'void init0(long long int)':
towers.cpp:72:17: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   72 |  for (int i=1; i<h.size(); i++) pr[i] = pr[i-1] + (lc[i]==-1 && rc[i]==-1);
      |                ~^~~~~~~~~
towers.cpp:73:17: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   73 |  for (int i=0; i<h.size(); i++) if (lc[i]!=-2) usef.push_back(h[i]);
      |                ~^~~~~~~~~
towers.cpp:74:17: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   74 |  for (int i=0; i<usef.size()-1; i++) nxt[usef[i]] = usef[i+1];
      |                ~^~~~~~~~~~~~~~
towers.cpp:75:17: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   75 |  for (int i=1; i<usef.size(); i++) prv[usef[i]] = usef[i-1];
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