#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
vector<int> C;
struct sparse_table{
int LOG;
vector<vector<int>> B;
sparse_table(){
}
sparse_table(vector<int> A){
int N = A.size();
LOG = 32 - __builtin_clz(N);
B = vector<vector<int>>(LOG, vector<int>(N, 0));
for (int i = 0; i < N; i++){
B[0][i] = A[i];
}
for (int i = 0; i < LOG - 1; i++){
B[i + 1] = B[i];
for (int j = 0; j < N - (1 << i); j++){
B[i + 1][j] = max(B[i + 1][j], B[i][j + (1 << i)]);
}
}
}
int range_max(int L, int R){
int d = R - L;
return max(B[C[d]][L], B[C[d]][R - (1 << C[d])]);
}
};
long long count_rectangles(vector<vector<int>> a){
int n = a.size();
int m = a[0].size();
assert(n <= 700 && m <= 700);
C = vector<int>(1000);
for (int i = 1; i < 1000; i++){
C[i] = 32 - __builtin_clz(i) - 1;
}
vector<vector<int>> L(n, vector<int>(m));
vector<vector<int>> R(n, vector<int>(m));
for (int i = 0; i < n; i++){
map<int, vector<int>> mp;
for (int j = 0; j < m; j++){
mp[a[i][j]].push_back(j);
}
set<int> st = {-1, m};
for (auto itr = mp.rbegin(); itr != mp.rend(); itr++){
for (int x : (*itr).second){
L[i][x] = *prev(st.lower_bound(x)) + 1;
R[i][x] = *st.lower_bound(x);
}
for (int x : (*itr).second){
st.insert(x);
}
}
}
vector<vector<int>> U(n, vector<int>(m));
vector<vector<int>> D(n, vector<int>(m));
for (int i = 0; i < m; i++){
map<int, vector<int>> mp;
for (int j = 0; j < n; j++){
mp[a[j][i]].push_back(j);
}
set<int> st = {-1, n};
for (auto itr = mp.rbegin(); itr != mp.rend(); itr++){
for (int x : (*itr).second){
U[x][i] = *prev(st.lower_bound(x)) + 1;
D[x][i] = *st.lower_bound(x);
}
for (int x : (*itr).second){
st.insert(x);
}
}
}
vector<sparse_table> STh(n);
for (int i = 0; i < n; i++){
STh[i] = sparse_table(a[i]);
}
vector<sparse_table> STv(m);
for (int i = 0; i < m; i++){
vector<int> b(n);
for (int j = 0; j < n; j++){
b[j] = a[j][i];
}
STv[i] = sparse_table(b);
}
set<tuple<int, int, int, int>> st;
for (int i = 1; i < n - 1; i++){
for (int j = 1; j < m - 1; j++){
if (L[i][j] > 0 && R[i][j] < m && U[i][j] > 0 && D[i][j] < n){
if (st.count(make_tuple(L[i][j], R[i][j], U[i][j], D[i][j])) == 0){
bool ok = true;
for (int x = U[i][j]; x < D[i][j]; x++){
if (STh[x].range_max(L[i][j], R[i][j]) >= min(a[x][L[i][j] - 1], a[x][R[i][j]])){
ok = false;
break;
}
}
if (ok){
for (int y = L[i][j]; y < R[i][j]; y++){
if (STv[y].range_max(U[i][j], D[i][j]) >= min(a[U[i][j] - 1][y], a[D[i][j]][y])){
ok = false;
break;
}
}
}
if (ok){
st.insert(make_tuple(L[i][j], R[i][j], U[i][j], D[i][j]));
}
}
}
}
}
return st.size();
}
