/*************************************
* author: marvinthang *
* created: 04.07.2023 09:31:20 *
*************************************/
#include "towers.h"
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define left ___left
#define right ___right
#define TIME (1.0 * clock() / CLOCKS_PER_SEC)
#define MASK(i) (1LL << (i))
#define BIT(x, i) ((x) >> (i) & 1)
#define __builtin_popcount __builtin_popcountll
#define ALL(v) (v).begin(), (v).end()
#define REP(i, n) for (int i = 0, _n = (n); i < _n; ++i)
#define REPD(i, n) for (int i = (n); i--; )
#define FOR(i, a, b) for (int i = (a), _b = (b); i < _b; ++i)
#define FORD(i, b, a) for (int i = (b), _a = (a); --i >= _a; )
#define FORE(i, a, b) for (int i = (a), _b = (b); i <= _b; ++i)
#define FORDE(i, b, a) for (int i = (b), _a = (a); i >= _a; --i)
#define scan_op(...) istream & operator >> (istream &in, __VA_ARGS__ &u)
#define print_op(...) ostream & operator << (ostream &out, const __VA_ARGS__ &u)
#ifdef LOCAL
#include "debug.h"
#else
#define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
#define DB(...) 23
#define db(...) 23
#define debug(...) 23
#endif
template <class U, class V> scan_op(pair <U, V>) { return in >> u.first >> u.second; }
template <class T> scan_op(vector <T>) { for (size_t i = 0; i < u.size(); ++i) in >> u[i]; return in; }
template <class U, class V> print_op(pair <U, V>) { return out << '(' << u.first << ", " << u.second << ')'; }
template <size_t i, class T> ostream & print_tuple_utils(ostream &out, const T &tup) { if constexpr(i == tuple_size<T>::value) return out << ")"; else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); }
template <class ...U> print_op(tuple<U...>) { return print_tuple_utils<0, tuple<U...>>(out, u); }
template <class Con, class = decltype(begin(declval<Con>()))> typename enable_if <!is_same<Con, string>::value, ostream&>::type operator << (ostream &out, const Con &con) { out << '{'; for (__typeof(con.begin()) it = con.begin(); it != con.end(); ++it) out << (it == con.begin() ? "" : ", ") << *it; return out << '}'; }
const int INF = 1e9;
struct Node {
int ma, s_p, p_s;
pair <int, int> mi;
Node(): ma(-INF), mi(INF, INF), s_p(-INF), p_s(-INF) {}
Node(int h, int i): ma(h), mi(h, i), s_p(-INF), p_s(-INF) {}
Node operator + (const Node &other) const {
Node res;
res.ma = max(ma, other.ma);
res.mi = min(mi, other.mi);
res.s_p = max({s_p, other.s_p, other.ma - mi.fi});
res.p_s = max({p_s, other.p_s, ma - other.mi.fi});
return res;
}
};
struct PNode {
int mi, ma, cnt, left_child, right_child;
PNode(): ma(-INF), mi(INF), cnt(0), left_child(-1), right_child(-1) {}
PNode(int v): ma(v), mi(v), cnt(1), left_child(-1), right_child(-1) {}
PNode operator + (const PNode &other) const {
PNode res;
res.mi = min(mi, other.mi);
res.ma = max(ma, other.ma);
res.cnt = cnt + other.cnt;
return res;
}
};
// end of template
int N;
vector <int> H, val, versions;
vector <Node> st;
void build(int i, int l, int r) {
if (r - l == 1) {
st[i] = Node(H[l], l);
return;
}
int m = l + r >> 1;
build(i << 1, l, m);
build(i << 1 | 1, m, r);
st[i] = st[i << 1] + st[i << 1 | 1];
}
Node get(int i, int l, int r, int u, int v) {
if (l >= v || r <= u || u >= v) return Node();
if (u <= l && r <= v) return st[i];
int m = l + r >> 1;
return get(i << 1, l, m, u, v) + get(i << 1 | 1, m, r, u, v);
}
vector <PNode> pnodes;
int createNode(int l, int r) {
int i = pnodes.size();
pnodes.push_back(pnodes[l] + pnodes[r]);
pnodes[i].left_child = l;
pnodes[i].right_child = r;
return i;
}
int createNode(int v = -1) {
int i = pnodes.size();
if (v == -1) pnodes.push_back(PNode());
else pnodes.push_back(PNode(v));
return i;
}
int pbuild(int i, int l, int r) {
if (r - l == 1) return createNode(-1);
int m = l + r >> 1;
return createNode(pbuild(i << 1, l, m), pbuild(i << 1 | 1, m, r));
}
int pupdate(int id, int l, int r, int p) {
if (r - l == 1) return createNode(p);
int m = l + r >> 1;
if (p < m) return createNode(pupdate(pnodes[id].left_child, l, m, p), pnodes[id].right_child);
return createNode(pnodes[id].left_child, pupdate(pnodes[id].right_child, m, r, p));
}
PNode pget(int id, int l, int r, int u, int v) {
if (l >= v || r <= u || u >= v) return PNode();
if (u <= l && r <= v) return pnodes[id];
int m = l + r >> 1;
return pget(pnodes[id].left_child, l, m, u, v) + pget(pnodes[id].right_child, m, r, u, v);
}
void init(int n, vector<int> h) {
N = n;
H = h;
st.resize(N * 4 + 23);
build(1, 0, N);
stack <int> st;
vector <int> v(N);
REP(i, N) {
while (!st.empty() && H[st.top()] >= H[i]) st.pop();
v[i] = st.empty() ? INF : get(1, 0, N, st.top() + 1, i).ma - H[i];
st.push(i);
}
while (!st.empty()) st.pop();
REPD(i, N) {
while (!st.empty() && H[st.top()] >= H[i]) st.pop();
v[i] = min(v[i], st.empty() ? INF : get(1, 0, N, i + 1, st.top()).ma - H[i]);
st.push(i);
val.push_back(v[i]);
}
sort(ALL(val));
val.erase(unique(ALL(val)), val.end());
vector <vector <int>> add(val.size());
REP(i, N) add[lower_bound(ALL(val), v[i]) - val.begin()].push_back(i);
versions.resize(val.size() + 1);
versions[val.size()] = pbuild(1, 0, N);
REPD(i, val.size()) {
versions[i] = versions[i + 1];
for (int x: add[i]) versions[i] = pupdate(versions[i], 0, N, x);
}
}
int max_towers(int l, int r, int d) {
int p = lower_bound(ALL(val), d) - val.begin();
PNode pn = pget(versions[p], 0, N, l, r + 1);
int res = pn.cnt;
int x = pn.mi;
int y = pn.ma;
if (!res) {
x = y = get(1, 0, N, l, r + 1).mi.se;
++res;
}
res += get(1, 0, N, l, x).s_p >= d;
res += get(1, 0, N, y + 1, r + 1).p_s >= d;
return res;
}
