#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef pair<int,int> pii;
#define F first
#define S second
const int MN = 2505, MM = 15e6;
int N, M, C, i, j, x, y, h[MM], hp[MM], cnt, pre[MN], ds[MN], nxt[MN]; ll ans;
pii bnd[MM]; vi vec[MN], adj[MM], hid[MN];
vector<pii> evt[MN];
pii hist[MN][MN];
stack<pii> stk;
vector<pii> st[MN];
inline void process(vi vec,int x,bool col){
C = (int)vec.size();
for(int i=0;i<=C;i++) st[i].clear();
while(stk.size()) stk.pop();
for(int i=0;i<C;i++){
while(stk.size()){
if(stk.top().S+1<i){
if(col) evt[i-1].push_back({x,stk.top().S+1});
else{
bnd[++cnt] = {stk.top().S+1,i-1};
h[cnt] = x;
st[stk.top().S+1].push_back({i-1,cnt});
}
}
if(stk.top().F<=vec[i]) stk.pop();
else break;
}
stk.push({vec[i],i});
}
while(stk.size()) stk.pop();
for(int i=0;i<=C;i++){
for(auto v : st[i]){
while(stk.size()){
if(stk.top().F<v.F) stk.pop();
else break;
}
if(stk.size()){
adj[stk.top().S].push_back(v.S);
hp[v.S] = 1;
}
stk.push(v);
}
}
}
vi res;
inline void mrg(int x,int y){
if(x^y){
res.clear();
if(vec[x].empty()||vec[y].empty()){
vec[x].clear(); vec[y].clear();
return;
}
if(vec[x].size()>vec[y].size()) swap(x,y);
for(int i=0,j=0;i<(int)vec[x].size();i++){
while(j+1<(int)vec[y].size()&&vec[y][j]<vec[x][i]) j++;
if(j<vec[y].size()&&vec[x][i]==vec[y][j]) res.push_back(vec[x][i]);
}
vec[min(x,y)].clear();
vec[max(x,y)]=res;
}
}
int fnd(int x){return ds[x]=ds[x]==x?x:fnd(ds[x]);}
void dfs(int n){
for(auto v : adj[n]) dfs(v);
for(auto v : adj[n]) mrg(bnd[v].S, bnd[n].S);
int it = fnd(bnd[n].F);
while(it<M&&it<=bnd[n].S){
mrg(it,bnd[n].S);
ds[fnd(it)]=fnd(it+1);
it = fnd(it);
}
int p = upper_bound(vec[bnd[n].S].begin(),vec[bnd[n].S].end(),h[n])-vec[bnd[n].S].begin();
ans += vec[bnd[n].S].size()-p;
}
long long count_rectangles(vector<vector<int>> a){
vi col;
N = a.size(), M = a[0].size();
memset(hist,-1,sizeof(hist));
for(i=0;i<M;i++){
col.clear();
for(j=0;j<N;j++) col.push_back(a[j][i]);
process(col,i,1);
}
memset(hist,-1,sizeof(hist));
for(i=0;i<N;i++)
process(a[i],i,0);
for(i=1;i<=cnt;i++){
hid[h[i]].push_back(i);
}
memset(hist,-1,sizeof(hist));
for(i=0;i<N;i++){
for(j=0;j<M;j++) vec[j].clear(), ds[j]=j;
for(auto v : evt[i]) vec[v.F].push_back(v.S);
for(j=0;j<M;j++) sort(vec[j].begin(),vec[j].end());
for(auto v : hid[i]){
if(hist[bnd[v].F][bnd[v].S].F==i) h[v] = hist[bnd[v].F][bnd[v].S].S+1;
else h[v] = 1;
hist[bnd[v].F][bnd[v].S]={i+1,h[v]};
h[v] = i-h[v];
}
for(auto v : hid[i]){
if(hp[v]) continue;
dfs(v);
}
}
return ans;
}
