#pragma GCC optimize "Ofast"
#pragma GCC optimize "unroll-loops"
#pragma GCC target "sse,sse2,sse3,sse4,abm,avx,mmx,popcnt,tune=native"
#include <bits/stdc++.h>
using namespace std;
typedef pair<int, int> pi;
typedef long long ll;
#define f first
#define s second
const int MM = 2505;
int N, M, a[MM][MM], st[MM], top, l[MM], r[MM], u[MM], d[MM], toclear[MM], cnt; ll bit[MM], ans;
vector<pi> h[MM][MM], v[MM][MM];
bool cmp(pi x, pi y){ return x.s < y.s; }
void upd(int x, int val){
for(int i=x; i<MM; i+=i&-i) bit[i] += val;
}
ll qry(int x){
ll sum = 0;
for(int i=x; i; i-=i&-i) sum += bit[i];
return sum;
}
long long count_rectangles(std::vector<std::vector<int>> x){
N = x.size(); M = x[0].size();
for(int i=1; i<=N; i++){
top = 0;
for(int j=1; j<=M; j++){
a[i][j] = x[i-1][j-1];
while(top > 0 && a[i][st[top]] < a[i][j]) top--;
l[j] = st[top]; st[++top] = j;
}
top = 0;
for(int j=M; j>=1; j--){
while(top > 0 && a[i][st[top]] <= a[i][j]) top--;
r[j] = st[top]; st[++top] = j;
if(l[j] && r[j] && a[i][l[j]] > a[i][j]) h[i][l[j]+1].push_back({r[j]-l[j]-1, 1});
}
}
for(int j=1; j<=M; j++){
top = 0;
for(int i=1; i<=N; i++){
while(top > 0 && a[st[top]][j] < a[i][j]) top--;
u[i] = st[top]; st[++top] = i;
}
top = 0 ;
for(int i=N; i>=1; i--){
while(top > 0 && a[st[top]][j] <= a[i][j]) top--;
d[i] = st[top]; st[++top] = i;
if(u[i] && d[i] && a[u[i]][j] > a[i][j]) v[u[i]+1][j].push_back({d[i]-u[i]-1, 1});
}
}
for(int i=N; i>=1; i--){
for(int j=M; j>=1; j--){
if(!h[i][j].empty()){
sort(h[i][j].begin(), h[i][j].end());
for(int p=0, q=0; p<h[i][j].size(); p++){
while(q < h[i+1][j].size() && h[i+1][j][q].f < h[i][j][p].f) q++;
if(q < h[i+1][j].size() && h[i+1][j][q].f == h[i][j][p].f) h[i][j][p].s = h[i+1][j][q].s+1;
}
}
if(!v[i][j].empty()){
sort(v[i][j].begin(), v[i][j].end());
for(int p=0, q=0; p<v[i][j].size(); p++){
while(q<v[i][j+1].size() && v[i][j+1][q].f < v[i][j][p].f) q++;
if(q<v[i][j+1].size() && v[i][j+1][q].f == v[i][j][p].f) v[i][j][p].s = v[i][j+1][q].s+1;
}
}
}
}
for(int i=1; i<=N; i++){
for(int j=1; j<=M; j++){
if(h[i][j].empty() || v[i][j].empty()) continue;
cnt = 0;
sort(v[i][j].begin(), v[i][j].end(), cmp);
for(int p=(int)h[i][j].size()-1, q=(int)v[i][j].size()-1; p>=0; p--){
for( ;q>=0 && v[i][j][q].s >= h[i][j][p].f; q--) {
upd(v[i][j][q].f, 1); toclear[cnt++] = v[i][j][q].f;
}
ans += qry(h[i][j][p].s);
}
for(int p=0; p<cnt; p++) upd(toclear[p], -1);
}
}
return ans;
}
