#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx,popcnt,sse4,abm")
#include <bits/stdc++.h>
using namespace std;
#ifndef WAIMAI
#include "towers.h"
#else
#include "stub.cpp"
#endif
#ifdef WAIMAI
#define debug(HEHE...) cout << "[" << #HEHE << "] : ", dout(HEHE)
void dout() {cout << '\n';}
template<typename T, typename...U>
void dout(T t, U...u) {cout << t << (sizeof...(u) ? ", " : ""), dout(u...);}
#else
#define debug(...) 7122
#endif
#define ll long long
#define Waimai ios::sync_with_stdio(false), cin.tie(0)
#define FOR(x,a,b) for (int x = a, I = b; x <= I; x++)
#define pb emplace_back
#define F first
#define S second
#define lpos pos*2
#define rpos pos*2+1
const int INF = 2e9 + 1;
const int SIZE = 1e5 + 5;
int n;
int a[SIZE], ty[SIZE];
struct Segtree {
struct T {
int mx, mn, ld, rd;
T operator + (const T &o) const {
T re;
re.mx = max(mx, o.mx);
re.mn = min(mn, o.mn);
re.ld = max({ld, o.ld, o.mx - mn});
re.rd = max({rd, o.rd, mx - o.mn});
return re;
}
} node[SIZE << 2];
void build(int pos, int l, int r) {
if (l == r) {
node[pos].mx = node[pos].mn = a[l];
return;
}
int mid = (l + r) / 2;
build(lpos, l, mid);
build(rpos, mid + 1, r);
node[pos] = node[lpos] + node[rpos];
}
int schl(int pos, int l, int r, int L, int R, int x) {
if (l == L && r == R) {
if (node[pos].mx < x) return 0;
if (l == r) return l;
int mid = (L + R) / 2, re = schl(lpos, l, mid, L, mid, x);
return re == 0 ? schl(rpos, mid + 1, r, mid + 1, R, x) : re;
}
int mid = (L + R) / 2, re;
if (r <= mid) return schl(lpos, l, r, L, mid, x);
if (l > mid) return schl(rpos, l, r, mid + 1, R, x);
re = schl(lpos, l, mid, L, mid, x);
return re == 0 ? schl(rpos, mid + 1, r, mid + 1, R, x) : re;
}
int schr(int pos, int l, int r, int L, int R, int x) {
if (l == L && r == R) {
if (node[pos].mx < x) return 0;
if (l == r) return l;
int mid = (L + R) / 2, re = schr(rpos, mid + 1, r, mid + 1, R, x);
return re == 0 ? schr(lpos, l, mid, L, mid, x) : re;
}
int mid = (L + R) / 2, re;
if (r <= mid) return schr(lpos, l, r, L, mid, x);
if (l > mid) return schr(rpos, l, r, mid + 1, R, x);
re = schr(rpos, mid + 1, r, mid + 1, R, x);
return re == 0 ? schr(lpos, l, mid, L, mid, x) : re;
}
T que(int pos, int l, int r, int L, int R) {
if (l == L && r == R) return node[pos];
int mid = (L + R) / 2;
if (r <= mid) return que(lpos, l, r, L, mid);
if (l > mid) return que(rpos, l, r, mid + 1, R);
return que(lpos, l, mid, L, mid) + que(rpos, mid + 1, r, mid + 1, R);
}
} tree;
struct Node {
int cnt, pcnt, ls, rs;
} node[2 * SIZE * (__lg(SIZE) + 3)];
int sz, root;
vector<pair<int, int>> vroot;
void upd(int &pos, int l, int r, int p, int t, int x) {
node[++sz] = node[pos];
pos = sz;
(t == 1 ? node[pos].cnt : node[pos].pcnt) += x;
if (l == r) return;
int mid = (l + r) / 2;
if (p <= mid) upd(node[pos].ls, l, mid, p, t, x);
else upd(node[pos].rs, mid + 1, r, p, t, x);
}
int que(int pos, int l, int r, int L, int R, int t) {
if (l == L && r == R) return t == 1 ? node[pos].cnt : node[pos].pcnt;
int mid = (L + R) / 2;
if (r <= mid) return que(node[pos].ls, l, r, L, mid, t);
if (l > mid) return que(node[pos].rs, l, r, mid + 1, R, t);
return que(node[pos].ls, l, mid, L, mid, t) + que(node[pos].rs, mid + 1, r, mid + 1, R, t);
}
int sch(int pos, int l, int r, int t, int k) {
int tot = (t == 1 ? node[pos].cnt : node[pos].pcnt);
if (k > tot) return 0;
if (l == r) return l;
int mid = (l + r) / 2, ltot = (t == 1 ? node[node[pos].ls].cnt : node[node[pos].ls].pcnt);
return k <= ltot ? sch(node[pos].ls, l, mid, t, k) : sch(node[pos].rs, mid + 1, r, t, k - ltot);
}
void init(int N, vector<int> H) {
n = N;
if (n == 1) return;
FOR (i, 1, n) a[i] = H[i - 1];
FOR (i, 1, n) {
if ((i == 1 || a[i] < a[i - 1]) && (i == n || a[i] < a[i + 1])) ty[i] = 1;
if ((i == 1 || a[i] > a[i - 1]) && (i == n || a[i] > a[i + 1])) ty[i] = 2;
}
set<int> s;
multiset<pair<int, int>> ms;
for (int i = 1, x = 1; i <= n; i++) if (ty[i] == x) {
s.insert(i);
x ^= 3;
}
if (ty[*s.rbegin()] == 2) s.erase(*s.rbegin());
a[0] = a[n + 1] = INF;
s.insert(0), s.insert(n + 1);
bool f = 0;
for (auto it = s.begin(); it != s.end(); it++) {
f ^= 1;
if (f == 0) continue;
int i = *it;
if (it != s.begin()) {
int l = *prev(it);
ms.emplace(a[i] - a[l], i);
}
if (next(it) != s.end()) {
int r = *next(it);
ms.emplace(a[i] - a[r], i);
}
}
for (int i : s) if (ty[i]) upd(root, 1, n, i, ty[i], 1);
vroot.pb(0, root);
while (s.size() > 3) {
int d = ms.begin()->F;
while (ms.size() && ms.begin()->F == d) {
auto [_, i] = *ms.begin();
auto it = s.lower_bound(i), lit = prev(it), rit = next(it);
int l = *lit, r = *rit;
int il = *prev(lit), ir = *next(rit);
if (a[l] > a[r]) {
ms.erase(ms.find({a[i] - a[l], i}));
ms.erase(ms.find({a[il] - a[l], il}));
if (a[i] < a[il]) {
ms.erase({a[i] - a[r], i});
ms.emplace(a[il] - a[r], il);
s.erase(i), upd(root, 1, n, i, 2, -1);
} else {
int j = *prev(s.find(il));
ms.erase(ms.find({a[il] - a[j], il}));
ms.emplace(a[i] - a[j], i);
s.erase(il), upd(root, 1, n, il, 2, -1);
}
s.erase(l), upd(root, 1, n, l, 1, -1);
} else {
ms.erase(ms.find({a[i] - a[r], i}));
ms.erase(ms.find({a[ir] - a[r], ir}));
if (a[i] < a[ir]) {
ms.erase({a[i] - a[l], i});
ms.emplace(a[ir] - a[l], ir);
s.erase(i), upd(root, 1, n, i, 2, -1);
} else {
int j = *next(s.find(ir));
ms.erase(ms.find({a[ir] - a[j], ir}));
ms.emplace(a[i] - a[j], i);
s.erase(ir), upd(root, 1, n, ir, 2, -1);
}
s.erase(r), upd(root, 1, n, r, 1, -1);
}
}
vroot.pb(d + 1, root);
}
tree.build(1, 1, n);
}
int max_towers(int L, int R, int D) {
L++, R++;
if (L == R) return 1;
root = (lower_bound(vroot.begin(), vroot.end(), make_pair(D + 1, 0)) - 1)->S;
int ans = que(root, L, R, 1, n, 1);
if (ans == 0) {
int pcnt = que(root, L, R, 1, n, 2);
if (pcnt == 0) return 1;
int i = sch(root, 1, n, 2, L == 1 ? 1 : que(root, 1, L - 1, 1, n, 2) + 1);
return 1 + (tree.que(1, L, i, 1, n).mn + D <= a[i] && tree.que(1, i, R, 1, n).mn + D <= a[i]);
}
{
int i = sch(root, 1, n, 1, L == 1 ? 1 : que(root, 1, L - 1, 1, n, 1) + 1);
int j = tree.schr(1, L, i, 1, n, a[i] + D);
if (j) ans += (tree.que(1, L, j, 1, n).ld >= D);
}
{
int i = sch(root, 1, n, 1, que(root, 1, R, 1, n, 1));
int j = tree.schl(1, i, R, 1, n, a[i] + D);
if (j) ans += (tree.que(1, j, R, 1, n).rd >= D);
}
return ans;
}
/*
in1
7 3
10 20 60 40 50 30 70
1 5 10
2 2 100
0 6 17
out1
3
1
2
*/
