#include "rect.h"
#include<bits/stdc++.h>
using namespace std;
#define sz(x) (int)x.size()
#define REP(i,n) for(int i=0;i<n;i++)
#define REP1(i,n) for(int i=1;i<=n;i++)
#define pb push_back
#define lowb(x) (x&(-x))
#define ALL(_x) _x.begin(),_x.end()
#define pii pair<int,int>
#define f first
#define s second
#define SORT_UNIQUE(x) sort(ALL(x)),x.erase(unique(ALL(x)),x.end())
const int maxn=3e3+5;
#define ll long long
pii rng[maxn];
int par[maxn];
bool ded[maxn];
int find(int u){
if(par[u]==u) return u;
return par[u]=find(par[u]);
}
void merge(int a,int b){
a=find(a),b=find(b);
if(a==b) return;
rng[b]={min(rng[a].f,rng[b].f),max(rng[a].s,rng[b].s)};
par[a]=b;
}
int pf[maxn];
vector<int> mp[maxn][maxn],m2[maxn][maxn];
int lok[maxn][maxn],rok[maxn][maxn];
vector<pii> get(vector<int> &val){
int n=sz(val);
vector<pii> v;
REP(i,n) rng[i]={i,i},par[i]=i;
REP(j,n){
v.pb({val[j],j});
}
sort(ALL(v));
vector<pii> vv;
for(int j=0;j<sz(v);){
int p=j;
vector<int> ps;
while(j<sz(v) and v[p].f==v[j].f){
int z=v[j].s;
if(z and val[z-1]<=val[z]) merge(z-1,z);
if(z+1<n and val[z+1]<=val[z]) merge(z,z+1);
ps.pb(z);
++j;
}
for(int x:ps){
auto z=rng[find(x)];
if(z.f and z.s!=n-1) {
vv.pb(z);
}
}
}
SORT_UNIQUE(vv);
return vv;
}
int ans=0;
vector<vector<int>> a;
void calc(int l,int r,int u,int d){
vector<int> vv;
for(int i=u-1;i<=d+1;i++){
vv.pb(a[i][r]);
}
auto zz=get(vv);
for(auto x:zz){
if(lok[x.f+u-1][x.s+u-1]<=l){
++ans;
}
}
}
long long count_rectangles(std::vector<std::vector<int> > b) {
a=b;
int n=sz(a),m=sz(a[0]);
REP1(i,n-2){
vector<int> val;
REP(j,m) val.pb(a[i][j]);
auto vv=get(val);
for(auto x:vv){
mp[x.f][x.s].pb(i);
}
}
REP(i,n) REP(j,n) lok[i][j]=rok[i][j]=-1;
REP1(i,m-2){
vector<int> val;
REP(j,n){
val.pb(a[j][i]);
}
auto vv=get(val);
for(auto x:vv){
if(rok[x.f][x.s]<i-1){
lok[x.f][x.s]=i;
}
rok[x.f][x.s]=i;
}
REP1(j,i){
if(!sz(mp[j][i])) continue;
int pv=mp[j][i][0];
REP1(z,sz(mp[j][i])-1){
int x=mp[j][i][z];
if(x>mp[j][i][z-1]+1){
calc(j,i,pv,mp[j][i][z-1]);
pv=x;
}
}
calc(j,i,pv,mp[j][i].back());
}
}
return ans;
}
