#include <bits/stdc++.h>
using namespace std;
typedef long long int lli;
typedef pair<int,int> pii;
typedef pair<lli,lli> pll;
void sc(){}
template<typename T,typename... Args>
void sc(T& a, Args&... args) {cin>>a,sc(args...);}
template<typename T>
void pr(T a){cout<<a;}
template<typename T,typename... Args>
void pr(T a, Args... args) {cout<<a<<" ",pr(args...);}
template<typename T>
void prl(T a){cout<<a<<"\n";}
template<typename T,typename... Args>
void prl(T a, Args... args) {cout<<a<<" ",prl(args...);}
#define rep(i, begin, end) for (__typeof(end) i = (begin) - ((begin) > (end)); i != (end) - ((begin) > (end)); i += 1 - 2 * ((begin) > (end)))
int bit[2505];
int n,m;
void update(int loc, int val){
for(;loc<=n;loc+=loc&-loc)bit[loc]+=val;
}
int sum(int loc){
int ans=0;
for(;loc>0;loc-=loc&-loc)ans+=bit[loc];
return ans;
}
long long count_rectangles(std::vector<std::vector<int>> a){
n=a.size();
m=a[0].size();
vector<pii> rowranges[n][m];
vector<pii> colranges[n][m];
rep(i,0,n){
int preloc[m];
int sufloc[m];
pii deq[m];
int l=0,r=-1;
rep(j,0,m){
while(r>=l&&deq[r].second<=a[i][j])r--;
if(r>=l)preloc[j]=deq[r].first;
else preloc[j]=-1;
deq[++r]={j,a[i][j]};
}
l=0,r=-1;
rep(j,m,0){
while(r>=l&&deq[r].second<=a[i][j])r--;
if(r>=l)sufloc[j]=deq[r].first;
else sufloc[j]=-1;
deq[++r]={j,a[i][j]};
}
rep(j,0,m){
if(preloc[j]!=-1&&sufloc[j]!=-1){
while(rowranges[i][preloc[j]+1].size()&&rowranges[i][preloc[j]+1].back().first==sufloc[j]-1)rowranges[i][preloc[j]+1].pop_back();
rowranges[i][preloc[j]+1].push_back({sufloc[j]-1,1});
}
}
}
rep(i,0,m){
int preloc[n];
int sufloc[n];
pii deq[n];
int l=0,r=-1;
rep(j,0,n){
while(r>=l&&deq[r].second<=a[j][i])r--;
if(r>=l)preloc[j]=deq[r].first;
else preloc[j]=-1;
deq[++r]={j,a[j][i]};
}
l=0,r=-1;
rep(j,n,0){
while(r>=l&&deq[r].second<=a[j][i])r--;
if(r>=l)sufloc[j]=deq[r].first;
else sufloc[j]=-1;
deq[++r]={j,a[j][i]};
}
rep(j,0,n){
if(preloc[j]!=-1&&sufloc[j]!=-1){
while(colranges[preloc[j]+1][i].size()&&colranges[preloc[j]+1][i].back().first==sufloc[j]-1)colranges[preloc[j]+1][i].pop_back();
colranges[preloc[j]+1][i].push_back({sufloc[j]-1,1});
}
}
}
rep(i,0,m){
rep(j,n-1,0){
int l=0,r=0;
while(l<rowranges[j][i].size()&&r<rowranges[j+1][i].size()){
if(rowranges[j][i][l].first==rowranges[j+1][i][r].first){
rowranges[j][i][l].second+=rowranges[j+1][i][r].second;
l++;
}
else if(rowranges[j][i][l].first>rowranges[j+1][i][r].first){
r++;
}
else l++;
}
}
}
rep(i,0,n){
rep(j,m-1,0){
int l=0,r=0;
while(l<colranges[i][j].size()&&r<colranges[i][j+1].size()){
if(colranges[i][j][l].first==colranges[i][j+1][r].first){
colranges[i][j][l].second+=colranges[i][j+1][r].second;
l++;
}
else if(colranges[i][j][l].first>colranges[i][j+1][r].first){
r++;
}
else l++;
}
}
}
int cnt=0;
rep(i,0,n)rep(j,0,m){
sort(colranges[i][j].begin(),colranges[i][j].end(),[&] (const pii &a, const pii &b) {
return a.second < b.second;
});
int r=colranges[i][j].size();
rep(k,rowranges[i][j].size(),0){
while(r>0&&colranges[i][j][r-1].second+j-1>=rowranges[i][j][k].first){
r-=1;
update(colranges[i][j][r].first+1,1);
}
cnt+=sum(rowranges[i][j][k].second+i);
}
rep(k,r,colranges[i][j].size())update(colranges[i][j][k].first+1,-1);
}
return cnt;
}
//int main(){
// cin.tie(NULL);
// ios_base::sync_with_stdio(false);
// prl(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}}));
// return 0;
//}
