#include "towers.h"
#include <bits/stdc++.h>
using namespace std;
#define forn(i,n) for(int i=0;i<n;++i)
struct minsgt {
vector<int> t;
int n, sz;
int merge(int x, int y) {
return min(x,y);
}
void build(int v, int l, int r) {
if (r-l==1) return;
int m=(l+r)>>1;
build(2*v+1,l,m);
build(2*v+2,m,r);
t[v]=merge(t[2*v+1],t[2*v+2]);
}
minsgt(vector<int>&a) {
n=a.size();
sz=1;
while (sz<n) sz<<=1;
t.assign(2*sz-1,1e9+7);
forn(i,n) t[sz-1+i]=a[i];
build(0,0,sz);
}
int query(int v, int l, int r, int lx, int rx) {
if (r<=lx || l>=rx) return 1e9+7;
if (lx<=l && r<=rx) return t[v];
int m=(l+r)>>1;
int L=query(2*v+1,l,m,lx,rx);
int R=query(2*v+2,m,r,lx,rx);
return merge(L,R);
}
int query(int l, int r) {
return query(0,0,sz,l,r);
}
};
struct maxsgt {
vector<int> t;
int n, sz;
int merge(int x, int y) {
return max(x,y);
}
void build(int v, int l, int r) {
if (r-l==1) return;
int m=(l+r)>>1;
build(2*v+1,l,m);
build(2*v+2,m,r);
t[v]=merge(t[2*v+1],t[2*v+2]);
}
maxsgt(vector<int>&a) {
n=a.size();
sz=1;
while (sz<n) sz<<=1;
t.assign(2*sz-1,0);
forn(i,n) t[sz-1+i]=a[i];
build(0,0,sz);
}
int query(int v, int l, int r, int lx, int rx) {
if (r<=lx || l>=rx) return 0;
if (lx<=l && r<=rx) return t[v];
int m=(l+r)>>1;
int L=query(2*v+1,l,m,lx,rx);
int R=query(2*v+2,m,r,lx,rx);
return merge(L,R);
}
int query(int l, int r) {
return query(0,0,sz,l,r);
}
};
int n;
vector<int> h;
int paiu=1;
int pos=0,mx;
int D=-1;
int Q=0;
vector<int> pr(1e5+3,0);
void init(int N, vector<int> H) {
n=N, h=H;
forn(i,n) {
if (h[i]>h[pos]) {
pos=i;
}
}
mx=h[pos];
for(int i=pos-1; i+1; --i) paiu&=h[i+1]>h[i];
for(int i=pos+1; i<n; ++i) paiu&=h[i-1]>h[i];
pr[1]=h[0]<h[1];
for (int i=1; i<n-1; ++i) {
pr[i+1]=pr[i]+((h[i]<h[i-1])&&(h[i]<h[i+1]));
}
pr[n]=pr[n-1]+(h[n-1]<h[n-2]);
}
minsgt minst(pr);
maxsgt maxst(pr);
vector<int> nxt(1e5+3,0);
vector<int> jump(1e5+3,0);
int sq;
void build() {
minst = minsgt(h);
maxst = maxsgt(h);
vector<int> less(n+1,n);
forn(i,n) {
int l=i, r=n;
while (l<r) {
int m=(l+r)>>1;
int x=minst.query(i,m+1);
if (h[i]-x>=D) r=m;
else l=m+1;
}
less[i]=r;
}
for (int i=n-2; i+1; --i) less[i]=min(less[i],less[i+1]);
vector<int> greater(n+1,n);
forn(i,n) {
int l=i, r=n;
while (l<r) {
int m=(l+r)>>1;
int x=maxst.query(i,m+1);
if (x-h[i]>=D) r=m;
else l=m+1;
}
greater[i]=r;
}
for (int i=n-2; i+1; --i) {
greater[i]=min(greater[i],greater[i+1]);
}
for (int i=n-1; i+1; --i) {
nxt[i]=less[greater[i]];
}
sq = sqrt(n);
for (int i=0; i<n; ++i) {
int p=i;
for (int cnt=0; cnt<sq; ++cnt) {
if (p>=n) {
break;
}
p=nxt[p];
}
jump[i]=p;
}
nxt[n]=jump[n]=n;
}
int max_towers(int l, int r, int d) {
if (n==1) return 1;
if (paiu) {
if (r<=pos || l>=pos) return 1;
int L=h[l], R=h[r];
return 1+(max(L,R) <= mx-d);
}
++Q;
if (Q>=2) {
if (D==-1) {
D=d;
build();
}
//forn(i,n+1) cout<<nxt[i]<<' '; cout<<'\n';
//forn(i,n+1) cout<<jump[i]<<' '; cout<<'\n';
int ans=0;
int i=l;
while (jump[i+1]<=r) {
//cout<<"j"<<i<<' ';
i=jump[i];
ans+=sq;
}
while (i<=r) {
//cout<<"ok"<<i<<' ';
i=nxt[i];
ans++;
}
//cout<<"~"<<i<<' ';
return max(ans,1);
}
vector<int> ans = {h[l]};
for (int i=l+1; i<=r; ++i) {
if (ans.size()&1) {
if (h[i]<ans.back()) {
ans[ans.size()-1]=h[i];
} else if (h[i]-d>=ans.back()) ans.push_back(h[i]);
} else {
if (h[i]>ans.back()) {
ans[ans.size()-1]=h[i];
} else if (h[i]+d<=ans.back()) ans.push_back(h[i]);
}
}
return (ans.size()+1)>>1;
}
int old(int l, int r, int d) {
vector<int> ans = {h[l]};
for (int i=l+1; i<=r; ++i) {
if (ans.size()&1) {
if (h[i]<ans.back()) {
ans[ans.size()-1]=h[i];
} else if (h[i]-d>=ans.back()) ans.push_back(h[i]);
} else {
if (h[i]>ans.back()) {
ans[ans.size()-1]=h[i];
} else if (h[i]+d<=ans.back()) ans.push_back(h[i]);
}
}
return (ans.size()+1)>>1;
}
