#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define mt make_tuple
#define pb push_back
const int N=2505;
const int M=2*N;
const int inf=1e9+7;
int a[N][N],n,m,U1[N][N],D1[N][N],L1[N][N],R1[N][N],U2[N][N],D2[N][N],L2[N][N],R2[N][N],S[N],c,tmp[N];
struct SegmentTreeMax
{
int mx[M];
SegmentTreeMax(){ for(int i=0;i<M;i++) mx[i]=-inf;}
void Build(int a[])
{
for(int i=0;i<N;i++) mx[i+N]=a[i];
for(int i=N-1;i;i--) mx[i]=max(mx[i<<1],mx[i<<1|1]);
}
void Set(int i, int f){ for(i+=N;i;i>>=1) mx[i]=max(mx[i],f);}
int Get(int l, int r)
{
int ans=-inf;
for(l+=N,r+=N;l<=r;l>>=1,r>>=1)
{
if(l%2==1) ans=max(ans,mx[l++]);
if(r%2==0) ans=max(ans,mx[r--]);
}
return ans;
}
} RMX[N],CMX[N];
struct SegmentTreeMin
{
int mn[M];
SegmentTreeMin(){ for(int i=0;i<M;i++) mn[i]=inf;}
void Build(int a[])
{
for(int i=0;i<N;i++) mn[i+N]=a[i];
for(int i=N-1;i;i--) mn[i]=min(mn[i<<1],mn[i<<1|1]);
}
void Set(int i, int f){ for(i+=N;i;i>>=1) mn[i]=min(mn[i],f);}
int Get(int l, int r)
{
int ans=inf;
for(l+=N,r+=N;l<=r;l>>=1,r>>=1)
{
if(l%2==1) ans=min(ans,mn[l++]);
if(r%2==0) ans=min(ans,mn[r--]);
}
return ans;
}
} RMN[N],CMN[N];
void Build()
{
for(int i=1;i<=n;i++)
{
S[c=0]=0;
for(int j=1;j<=m;j++)
{
while(c && a[i][S[c]]<=a[i][j]) c--;
L1[i][j]=S[c];S[++c]=j;
}
S[c=0]=m+1;
for(int j=m;j>=1;j--)
{
while(c && a[i][S[c]]<=a[i][j]) c--;
R1[i][j]=S[c];S[++c]=j;
}
S[c=0]=0;
for(int j=1;j<=m;j++)
{
while(c && a[i][S[c]]<a[i][j]) c--;
L2[i][j]=S[c];S[++c]=j;
}
S[c=0]=m+1;
for(int j=m;j>=1;j--)
{
while(c && a[i][S[c]]<a[i][j]) c--;
R2[i][j]=S[c];S[++c]=j;
}
}
for(int j=1;j<=m;j++)
{
S[c=0]=0;
for(int i=1;i<=n;i++)
{
while(c && a[S[c]][j]<=a[i][j]) c--;
U1[i][j]=S[c];S[++c]=i;
}
S[c=0]=n+1;
for(int i=n;i>=1;i--)
{
while(c && a[S[c]][j]<=a[i][j]) c--;
D1[i][j]=S[c];S[++c]=i;
}
S[c=0]=0;
for(int i=1;i<=n;i++)
{
while(c && a[S[c]][j]<a[i][j]) c--;
U2[i][j]=S[c];S[++c]=i;
}
S[c=0]=n+1;
for(int i=n;i>=1;i--)
{
while(c && a[S[c]][j]<a[i][j]) c--;
D2[i][j]=S[c];S[++c]=i;
}
}
for(int i=1;i<=n;i++)
{
for(int j=1;j<=m;j++) tmp[j]=U2[i][j];
RMX[i].Build(tmp);
for(int j=1;j<=m;j++) tmp[j]=D2[i][j];
RMN[i].Build(tmp);
}
for(int j=1;j<=m;j++)
{
for(int i=1;i<=n;i++) tmp[i]=L2[i][j];
CMX[j].Build(tmp);
for(int i=1;i<=n;i++) tmp[i]=R2[i][j];
CMN[j].Build(tmp);
}
}
/*struct Rectangle
{
int x1,y1,x2,y2;
Rectangle(){}
Rectangle(int a, int b, int c, int d):x1(a),y1(b),x2(c),y2(d){}
bool operator == (Rectangle b){ return mt(x1,y1,x2,y2)==mt(b.x1,b.y1,b.x2,b.y2);}
bool operator < (Rectangle b){ return mt(x1,y1,x2,y2)<mt(b.x1,b.y1,b.x2,b.y2);}
};*/
//vector<Rectangle> work;
vector<pair<int,int>> work[N][N];
void Try(int x, int y)
{
if(L1[x][y]!=0 && R1[x][y]!=m+1 && U1[x][y]!=0 && D1[x][y]!=n+1)
{
int x1=U1[x][y];
int y1=L1[x][y];
int x2=D1[x][y];
int y2=R1[x][y];
//work.pb(Rectangle(x1,y1,x2,y2));
work[x1][y1].pb({x2,y2});
}
}
bool was[N][N];
ll Solve()
{
Build();
for(int i=1;i<=n;i++) for(int j=1;j<=m;j++) Try(i,j);
//sort(work.begin(),work.end());
//work.resize(unique(work.begin(),work.end())-work.begin());
ll ans=0;
for(int x1=1;x1<=n;x1++)
{
for(int y1=1;y1<=m;y1++)
{
for(auto p:work[x1][y1])
{
int x2,y2;
tie(x2,y2)=p;
if(was[x2][y2]) continue;
was[x2][y2]=1;
int ok=0;
if(RMN[x1].Get(y1+1,y2-1)>=x2) ok++;
if(RMX[x2].Get(y1+1,y2-1)<=x1) ok++;
if(CMN[y1].Get(x1+1,x2-1)>=y2) ok++;
if(CMX[y2].Get(x1+1,x2-1)<=y1) ok++;
if(ok==4) ans++;
}
for(auto p:work[x1][y1])
{
int x2,y2;
tie(x2,y2)=p;
was[x2][y2]=0;
}
}
}
/*for(Rectangle r:work)
{
int x1,y1,x2,y2;
tie(x1,y1,x2,y2)=mt(r.x1,r.y1,r.x2,r.y2);
int ok=0;
if(RMN[x1].Get(y1+1,y2-1)>=x2) ok++;
if(RMX[x2].Get(y1+1,y2-1)<=x1) ok++;
if(CMN[y1].Get(x1+1,x2-1)>=y2) ok++;
if(CMX[y2].Get(x1+1,x2-1)<=y1) ok++;
if(ok==4) ans++;
}*/
return ans;
}
ll count_rectangles(vector<vector<int> > a)
{
n=a.size();m=a[0].size();
for(int i=1;i<=n;i++) for(int j=1;j<=m;j++) ::a[i][j]=a[i-1][j-1];
return Solve();
}
