#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned int ul;
typedef unsigned long long ull;
#define MASK(i) (1ULL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
#define ALL(v) (v).begin(), (v).end()
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll gcd(ll a, ll b){return __gcd(abs(a), abs(b));}
ll lcm(ll a, ll b){return abs(a) / gcd(a, b) * abs(b);}
ll LASTBIT(ll mask){return (mask) & (-mask);}
int pop_cnt(ull mask){return __builtin_popcountll(mask);}
int ctz(ull mask){return __builtin_ctzll(mask);}
int logOf(ull mask){return 63 - __builtin_clzll(mask);}
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
ll rngesus(ll l, ll r){return l + (ull) rng() % (r - l + 1);}
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b) {a = b; return true;}
return false;
}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b) {a = b; return true;}
return false;
}
template <class T>
void printArr(T container, string separator = " ", string finish = "\n", ostream &out = cout){
for(auto item: container) out << item << separator;
out << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
#include "towers.h"
const int INF = 1e9 + 69;
struct SegmentTree{
int n;
vector<pair<int,int>> a;
SegmentTree(int _n = 0){
n = _n;
a.resize(n * 2 + 2, {-INF, -INF});
}
void update(int i, int v){
i += n; a[i] = make_pair(v, i - n);
while(i > 1){
i >>= 1;
a[i] = max(a[i * 2], a[i * 2 + 1]);
}
}
pair<int, int> get(int l, int r){
l += n; r += n + 1;
pair<int, int> ans = make_pair(-INF, -INF);
while(l < r){
if (l & 1) maximize(ans, a[l++]);
if (r & 1) maximize(ans, a[--r]);
l >>= 1; r >>= 1;
}
return ans;
}
};
const int N = MASK(17);
struct Persistent{
struct Node{
int child[2];
int sum;
Node(){
memset(child, 0, sizeof child);
sum = 0;
}
};
static const int L = 1, R = N;
vector<Node> a;
vector<int> root_stack;
void add_node(int &x){
x = a.size();
a.emplace_back();
}
Persistent(){
a.emplace_back();
a.emplace_back();
root_stack.push_back(1);
}
int get_cur_version(){
return root_stack.size() - 1;
}
void update(int i, int v, int l, int r, int prev_id, int id){
a[id] = a[prev_id];
a[id].sum += v;
if (l == r) return;
int mid = (l + r) >> 1;
if (i <= mid){
add_node(a[id].child[0]);
update(i, v, l, mid, a[prev_id].child[0], a[id].child[0]);
}
else{
add_node(a[id].child[1]);
update(i, v, mid + 1, r, a[prev_id].child[1], a[id].child[1]);
}
}
void update(int i, int v){
int prev_id = root_stack.back();
int id; add_node(id);
root_stack.push_back(id);
update(i, v, L, R, prev_id, id);
}
int get(int u, int v, int l, int r, int id){
if (u <= l && r <= v) return a[id].sum;
int mid = (l + r) >> 1;
int ans = 0;
if (u <= mid) ans += get(u, v, l, mid, a[id].child[0]);
if (v > mid) ans += get(u, v, mid+1, r, a[id].child[1]);
return ans;
}
int get(int l, int r, int version){
return get(l, r, L, R, root_stack[version]);
}
int walk_left(int i, int l, int r, int id){
if (r < i) return -1;
if (a[id].sum == 0) return -1;
if (l == r) return l;
int mid = (l + r) >> 1;
int left = walk_left(i, l, mid, a[id].child[0]);
if (left != -1) return left;
return walk_left(i, mid+1, r, a[id].child[1]);
}
int walk_left(int i, int version){
return walk_left(i, L, R, root_stack[version]);
}
int walk_right(int i, int l, int r, int id){
if (l > i) return -1;
if (a[id].sum == 0) return -1;
if (l == r) return l;
int mid = (l + r) >> 1;
int right = walk_right(i, mid+1, r, a[id].child[1]);
if (right != -1) return right;
return walk_right(i, l, mid, a[id].child[0]);
}
int walk_right(int i, int version){
return walk_right(i, L, R, root_stack[version]);
}
};
int n;
vector<int> a;
SegmentTree st1, st2;
vector<pair<int, int>> subtract_op, plus_op;
vector<int> X;
vector<pair<int,int>> packets[N * 4];
Persistent pst;
int version_at[N * 4];
void dnc(int l, int r){
if (l > r) return;
int mid = st1.get(l, r).second;
dnc(l, mid-1);
dnc(mid+1, r);
int cur_ma = st1.get(l, r).first;
if (mid > l){
int left_ma = st1.get(l, mid-1).first;
int left_mi = -st2.get(l, mid-1).first;
int left_pos = st2.get(l, mid-1).second;
plus_op.push_back(make_pair(left_ma - left_mi + 1, left_pos));
subtract_op.push_back(make_pair(cur_ma - left_mi + 1, left_pos));
}
if (mid < r){
int right_ma = st1.get(mid+1, r).first;
int right_mi = -st2.get(mid+1, r).first;
int right_pos = st2.get(mid+1, r).second;
plus_op.push_back(make_pair(right_ma - right_mi + 1, right_pos));
subtract_op.push_back(make_pair(cur_ma - right_mi + 1, right_pos));
}
}
void init(int N, vector<int> H) {
H.insert(H.begin(), 0);
n = N; a = H;
st1 = SegmentTree(n), st2 = SegmentTree(n);
for(int i = 1; i <= n; ++i){
st1.update(i, a[i]);
st2.update(i, -a[i]);
}
dnc(1, n);
for(pair<int, int> i: subtract_op) X.push_back(i.first);
for(pair<int, int> i: plus_op) X.push_back(i.first);
X.push_back(0);
remove_dup(X);
for(pair<int, int> i: subtract_op){
i.first = lower_bound(ALL(X), i.first) - X.begin();
packets[i.first].push_back(make_pair(i.second, -1));
}
for(pair<int, int> i: plus_op){
i.first = lower_bound(ALL(X), i.first) - X.begin();
packets[i.first].push_back(make_pair(i.second, 1));
}
pst.a.reserve(1e7);
for(int i = 0; i < (int) X.size(); ++i){
for(pair<int, int> j: packets[i]){
pst.update(j.first, j.second);
}
version_at[i] = pst.get_cur_version();
}
}
int max_towers(int l, int r, int d) {
l++; r++;
int idx = upper_bound(ALL(X), d) - X.begin() - 1;
int ans = pst.get(l, r, version_at[idx]);
if (ans == 0){
pair<int, int> cur = st1.get(l, r);
int mid = cur.second;
if (mid > l){
int bruh = -st2.get(l, mid-1).first;
if (cur.first - bruh >= d) ans++;
}
if (mid < r){
int bruh = -st2.get(mid+1, r).first;
if (cur.first - bruh >= d) ans++;
}
maximize(ans, 1);
}
else{
int le = pst.walk_left(l, version_at[idx]);
int ri = pst.walk_right(r, version_at[idx]);
if (l < le){
pair<int, int> cur = st1.get(l, le - 1);
if (cur.second > l){
int bruh = -st2.get(l, cur.second - 1).first;
if (cur.first - max(bruh, a[le]) >= d) ans++;
}
}
if (ri < r){
pair<int, int> cur = st1.get(ri+1, r);
if (cur.second < r){
int bruh = -st2.get(cur.second+1, r).first;
if (cur.first - max(bruh, a[ri]) >= d) ans++;
}
}
}
return ans;
}
