#include<bits/stdc++.h>
#define MAXN 707
using namespace std;
int n,m,pr[MAXN][MAXN],nxt[MAXN][MAXN];
int a[MAXN][MAXN],last,ans;
int maxs[MAXN];
short pref[MAXN][MAXN][MAXN];
bool eq[MAXN][MAXN];
long long count_rectangles(vector< vector<int> > A){
n=int(A.size()); m=int(A[0].size());
for(int i=1;i<=n;i++){
for(int f=1;f<=m;f++){
a[i][f]=A[i-1][f-1];
}
}
for(int i=1;i<=n;i++){
for(int f=1;f<=m;f++){
for(int k=f;k<=m;k++){
pref[i][f][k]=pref[i-1][f][k];
}
}
for(int f=2;f<=m-1;f++){
pr[i][f]=0; nxt[i][f]=m+1;
for(int k=f-1;k>=1;k--){
if(a[i][k]==a[i][f])eq[i][f]=true;
if(a[i][k]>a[i][f]){pr[i][f]=k;break;}
}
for(int k=f+1;k<=m;k++){
if(a[i][k]>a[i][f]){nxt[i][f]=k;break;}
}
pref[i][pr[i][f]][nxt[i][f]]=pref[i-1][pr[i][f]][nxt[i][f]]+1;
}
}
for(int i=2;i<=n-1;i++){
for(int f=1;f<=m;f++)maxs[f]=a[i][f];
for(int f=i;f<=n-1;f++){
last=2;
for(int k=2;k<=m-1;k++){
maxs[k]=max(maxs[k],a[f][k]);
if(maxs[k]<a[i-1][k] and maxs[k]<a[f+1][k])continue;
for(int p=last;p<=k-1;p++){
if(pr[f][p]+1<last or nxt[f][p]-1>k-1)continue;
if(!eq[f][p] and pref[f][pr[f][p]][nxt[f][p]] - pref[i-1][pr[f][p]][nxt[f][p]] == f-i+1)ans++;
}
last=k+1;
}
for(int p=last;p<=m-1;p++){
if(pr[f][p]+1<last or nxt[f][p]-1>m-1)continue;
if(!eq[f][p] and pref[f][pr[f][p]][nxt[f][p]] - pref[i-1][pr[f][p]][nxt[f][p]] == f-i+1)ans++;
}
}
}
return ans;
}
/*
int main(){
cout<<count_rectangles({{4, 8, 7, 5, 6},
{7, 4, 10, 3, 5},
{9, 7, 20, 14, 2},
{9, 14, 7, 3, 6},
{5, 7, 5, 2, 7},
{4, 5, 13, 5, 6}})<<"\n";
return 0;
}
*/
