#include "towers.h"
#include<iostream>
#include <vector>
#include<algorithm>
using namespace std;
using pii = pair<int, int>;
#define forn(i, n) for(int i=0; i<(int)n; ++i)
#define dforn(i, n) for(int i=(int)n-1; i>=0; --i)
#define PB push_back
#define F first
#define S second
#define MP make_pair
const int MAXN = 100010, INF = 1000000010;
struct node{
vector<pii> vec;
vector<int> mn, mx;
node(){};
node(int value, int pos){
vec.PB({value, pos});
mn.PB(pos);
mx.PB(pos);
}
node(node& a, node& b){
vec.resize(a.vec.size() + b.vec.size());
mn.resize(vec.size());
mx.resize(vec.size());
merge(a.vec.begin(), a.vec.end(), b.vec.begin(), b.vec.end(), vec.begin());
int mi=MAXN, ma=-1;
dforn(i, vec.size()){
mi=min(mi, vec[i].S);
ma=max(ma, vec[i].S);
mn[i]=mi, mx[i]=ma;
}
}
};
int n, arr[MAXN], ml[MAXN], mr[MAXN], res[MAXN], sp[19][MAXN];
node tr[2*MAXN];
int spmin(int l, int r){
if(r<=l) return INF;
int sz = 8*sizeof(int) - __builtin_clz(r-l) - 1;
return min(sp[sz][l], sp[sz][r-(1<<sz)]);
}
pair<int, pii> query(int l, int r, int x){
int ret=0, mn=INF, mx=-1;
for(l+=n, r+=n; l<r; l>>=1, r>>=1){
if(l&1){
auto itr = lower_bound(tr[l].vec.begin(), tr[l].vec.end(), MP(x, -1));
int pos = (int)(itr - tr[l].vec.begin());
ret += (int)(tr[l].vec.end() - itr);
if(itr!=tr[l].vec.end()) mn=min(mn, tr[l].mn[pos]), mx=max(mx, tr[l].mx[pos]);
++l;
}
if(r&1){
--r;
auto itr = lower_bound(tr[r].vec.begin(), tr[r].vec.end(), MP(x, -1));
int pos = (int)(itr - tr[r].vec.begin());
ret += (int)(tr[r].vec.end() - itr);
if(itr!=tr[r].vec.end()) mn=min(mn, tr[r].mn[pos]), mx=max(mx, tr[r].mx[pos]);
}
}
return {ret, {mn, mx}};
}
void init(int N, vector<int> H) {
n=N;
forn(i, n) arr[i]=H[i];
forn(i, n) sp[0][i]=H[i];
forn(i, 18) forn(j, n-(1<<i)) sp[i+1][j]=min(sp[i][j], sp[i][j+(1<<i)]);
forn(i, n){
int x;
for(x=i-1; x!=-1 && H[x]<H[i]; x=ml[x]);
ml[i]=x;
}
dforn(i, n){
int x;
for(x=i+1; x!=n && H[x]<H[i]; x=mr[x]);
mr[i]=x;
}
forn(i, n){
int l = ml[i], r = mr[i];
int a = H[i] - spmin(l+1, i);
int b = H[i] - spmin(i+1, r);
res[i] = min(a, b);
}
forn(i, n) tr[n+i]=node(res[i], i);
dforn(i, n) tr[i]=node(tr[i<<1], tr[i<<1|1]);
}
int max_towers(int L, int R, int D) {
pair<int, pii> ans = query(L, R+1, D);
if(ans.F == 0) return 1;
int sa = (spmin(L, ans.S.F) > arr[ans.S.F] - D);
int sb = (spmin(ans.S.S+1, R+1) > arr[ans.S.S] - D);
return max(0, ans.F - sa - sb) + 1;
}
