#include "rect.h"
#include <vector>
#include <iostream>
#include <map>
#include <set>
#include <cmath>
using namespace std;
#define ll long long
#define pii pair<int,int>
int const N=2510,LG=12;
struct spmx //sparse table for max
{
int sp[N][LG]={};
spmx(vector<int>vals)
{
int n=vals.size();
for (int i=0;i<n;i++)
sp[i][0]=vals[i];
for (int j=1;(1<<j)<=n;j++)
for (int i=0;i+(1<<j)-1<n;i++)
sp[i][j]=max(sp[i][j-1],sp[i+(1<<(j-1))][j-1]);
}
int get(int l,int r)
{
if (l>r)
return 1e9;
int lg=log2(r-l+1);
return max(sp[l][lg],sp[r+1-(1<<lg)][lg]);
}
};
struct spmn //sparse table for min
{
int sp[N][LG]={};
spmn(vector<int>vals)
{
int n=vals.size();
for (int i=0;i<n;i++)
sp[i][0]=vals[i];
for (int j=1;(1<<j)<=n;j++)
for (int i=0;i+(1<<j)-1<n;i++)
sp[i][j]=min(sp[i][j-1],sp[i+(1<<(j-1))][j-1]);
}
int get(int l,int r)
{
if (l>r)
return 0;
int lg=log2(r-l+1);
return min(sp[l][lg],sp[r+1-(1<<lg)][lg]);
}
};
int l[N][N],r[N][N],u[N][N],d[N][N]={};
int n,m;int x[4];
vector<spmn>ml,md;
vector<spmx>mr,mu;
bool check(int u,int d,int l,int r)
{
if (u==0||d==n-1||l==0||r==m-1)
return 0;
if (md[u-1].get(l,r)<d)
return 0;
if (mu[d+1].get(l,r)>u)
return 0;
if (ml[r+1].get(u,d)>l)
return 0;
if (mr[l-1].get(u,d)<r)
return 0;
return 1;
}
long long count_rectangles(vector<vector<int>>a)
{
n=a.size(),m=a[0].size();
x[0]=m,x[1]=-m,x[2]=-1,x[3]=1;
map<int,vector<int>>ind;
set<int>s;
vector<spmx>rw,cl;
for (int i=0;i<n;i++)
{
vector<int>x;
for (int j=0;j<m;j++)
x.push_back(a[i][j]);
rw.push_back(spmx(x));
}
for (int i=0;i<m;i++)
{
vector<int>x;
for (int j=0;j<n;j++)
x.push_back(a[j][i]);
cl.push_back(spmx(x));
}
set<pair<pii,pii>>ans;
for (int i=0;i<n;i++)
{
for (int j=0;j<m;j++)
{
{// right
int st=j,en=m;
while (st+1<en)
{
int mid=(st+en)/2;
if (rw[i].get(j+1,mid)>=a[i][j])
en=mid;
else
st=mid;
}
r[i][j]=st;
}
{// left
int st=-1,en=j;
while (st+1<en)
{
int mid=(st+en)/2;
if (rw[i].get(mid,j-1)>=a[i][j])
st=mid;
else
en=mid;
}
l[i][j]=en;
}
{// up
int st=-1,en=i;
while (st+1<en)
{
int mid=(st+en)/2;
if (cl[j].get(mid,i-1)>=a[i][j])
st=mid;
else
en=mid;
}
u[i][j]=en;
}
{// down
int st=i,en=n;
while (st+1<en)
{
int mid=(st+en)/2;
if (cl[j].get(i+1,mid)>=a[i][j])
en=mid;
else
st=mid;
}
d[i][j]=st;
}
// cout<<u[i][j]<<' '<<d[i][j]<<' '<<l[i][j]<<' '<<r[i][j]<<endl;
}
}
for (int i=0;i<n;i++)
{
vector<int>u1,d1;
for (int j=0;j<m;j++)
{
u1.push_back(u[i][j]);
d1.push_back(d[i][j]);
}
mu.push_back(spmx(u1));
md.push_back(spmn(d1));
}
for (int i=0;i<m;i++)
{
vector<int>l1,r1;
for (int j=0;j<n;j++)
{
l1.push_back(l[j][i]);
r1.push_back(r[j][i]);
}
ml.push_back(spmn(l1));
mr.push_back(spmx(r1));
}
for (int i=0;i<n;i++)
{
for (int j=0;j<m;j++)
{
{// right
int st=j,en=m;
while (st+1<en)
{
int mid=(st+en)/2;
if (rw[i].get(j,mid)>a[i][j])
en=mid;
else
st=mid;
}
r[i][j]=st;
}
{// left
int st=-1,en=j;
while (st+1<en)
{
int mid=(st+en)/2;
if (rw[i].get(mid,j)>a[i][j])
st=mid;
else
en=mid;
}
l[i][j]=en;
}
{// up
int st=-1,en=i;
while (st+1<en)
{
int mid=(st+en)/2;
if (cl[j].get(mid,i)>a[i][j])
st=mid;
else
en=mid;
}
u[i][j]=en;
}
{// down
int st=i,en=n;
while (st+1<en)
{
int mid=(st+en)/2;
if (cl[j].get(i,mid)>a[i][j])
en=mid;
else
st=mid;
}
d[i][j]=st;
}
}
}
for (int i=1;i<n-1;i++)
{
for (int j=1;j<m-1;j++)
{
// cout<<i<<' '<<j<<endl;
// cout<<u[i][j]<<' '<<d[i][j]<<' '<<l[i][j]<<' '<<r[i][j]<<endl;
if (check(u[i][j],d[i][j],l[i][j],r[i][j]))
{
ans.insert({{u[i][j],d[i][j]},{l[i][j],r[i][j]}});
}
}
}
return ans.size();
}
