#include "jumps.h"
#include <bits/stdc++.h>
using namespace std;
int n;
vector<array<int,20> > pg,ng,hh,mxhh; //prev greater,next greater,highest height,max index reached while taking highest height jumps
//note: mxhh is -1 is jump is invalid, and answer otherwise
vector<int> Hq;
int pgq(int st,int x)
{
while(x>0 && st>-1)
{
st=pg[st][__builtin_ctz(x)];
x^=x&(-x);
}
return st;
}
int ngq(int st,int x)
{
while(x>0 && st>-1)
{
st=ng[st][__builtin_ctz(x)];
x^=x&(-x);
}
return st;
}
int hhq(int st,int x)
{
while(x>0 && st>-1)
{
st=hh[st][__builtin_ctz(x)];
x^=x&(-x);
}
return st;
}
int mxhhq(int st,int x)
{
if(hhq(st,x)==-1) return -1;
int res=st;
while(x>0)
{
res=max(res,mxhh[st][__builtin_ctz(x)]);
st=hh[st][__builtin_ctz(x)];
x^=x&(-x);
}
return res;
}
void init(int N, std::vector<int> H) {
n=N;
Hq=H;
pg.resize(N),ng.resize(N),hh.resize(N),mxhh.resize(N);
stack<int> st;
pg[0][0]=-1;
st.push(0);
for(int i=1;i<N;i++)
{
while(!st.empty() && H[st.top()]<H[i]) st.pop();
if(st.empty()) pg[i][0]=-1;
else pg[i][0]=st.top();
st.push(i);
}
while(!st.empty()) st.pop();
ng[N-1][0]=-1;
st.push(N-1);
for(int i=N-2;i>=0;i--)
{
while(!st.empty() && H[st.top()]<H[i]) st.pop();
if(st.empty()) ng[i][0]=-1;
else ng[i][0]=st.top();
st.push(i);
}
for(int i=0;i<N;i++)
{
int mx=-1,posmx=-1;
if(pg[i][0]>-1 && H[pg[i][0]]>mx) mx=H[pg[i][0]],posmx=pg[i][0];
if(ng[i][0]>-1 && H[ng[i][0]]>mx) mx=H[ng[i][0]],posmx=ng[i][0];
hh[i][0]=mxhh[i][0]=posmx;
if(posmx>-1) mxhh[i][0]=max(i,posmx);
}
for(int j=1;j<20;j++)
{
for(int i=0;i<N;i++)
{
pg[i][j]=ng[i][j]=hh[i][j]=mxhh[i][j]=-1;
if(pg[i][j-1]>-1) pg[i][j]=pg[pg[i][j-1]][j-1];
if(ng[i][j-1]>-1) ng[i][j]=ng[ng[i][j-1]][j-1];
if(hh[i][j-1]>-1) hh[i][j]=hh[hh[i][j-1]][j-1];
if(hh[i][j]>-1) mxhh[i][j]=max(mxhh[i][j-1],mxhh[mxhh[i][j-1]][j-1]);
}
}
//for(int i=0;i<N;i++) cout<<pg[i][0]<<" ";
//cout<<endl;
//for(int i=0;i<N;i++) cout<<ng[i][0]<<" ";
//cout<<endl;
}
int minimum_jumps(int A, int B, int C, int D) {
int l,r,mid,ans; //remember to reset this before each binary search
//find max in [C,D]
l=0,r=n-1,ans=-1;
while(l<=r)
{
mid=l+(r-l)/2;
int pos=ngq(C,mid);
if(pos==-1 || pos>D) r=mid-1;
else
{
ans=mid;
l=mid+1;
}
}
int mxCD=Hq[ngq(C,ans)];
//cout<<mxCD<<" ";
//find max in [A,B]<=max in [C,D] and not shadowed
l=0,r=n-1,ans=-1;
while(l<=r)
{
mid=l+(r-l)/2;
int pos=pgq(B,mid);
if(pos==-1 || pos<A || Hq[pos]>mxCD) r=mid-1;
else
{
ans=mid;
l=mid+1;
}
}
if(ans==-1) return ans;
int posAB=pgq(B,ans);
//cout<<posAB<<" ";
//^from here, first keep taking highest height jumps until you can't anymore, then keep jumping right until you reach something in [C,D]
int cnt=0,curpos=posAB;
while(curpos<C)
{
int nxtpos=hh[curpos][0];
if(nxtpos==-1) return -1;
if(Hq[nxtpos]>mxCD) nxtpos=ng[curpos][0];
if(nxtpos==-1) return -1;
if(nxtpos>D) return -1;
curpos=nxtpos;
cnt++;
}
return cnt;
}
