#include <bits/stdc++.h>
using namespace std;
vector<int> dx = {1, 0, -1, 0};
vector<int> dy = {0, 1, 0, -1};
struct segment_tree{
int N;
vector<int> ST;
segment_tree(){
}
segment_tree(vector<int> A){
int N2 = A.size();
N = 1;
while (N < N2){
N *= 2;
}
ST = vector<int>(N * 2 - 1, 0);
for (int i = 0; i < N2; i++){
ST[N - 1 + i] = A[i];
}
for (int i = N - 2; i >= 0; i--){
ST[i] = max(ST[i * 2 + 1], ST[i * 2 + 2]);
}
}
int range_max(int L, int R, int i, int l, int r){
if (r <= L || R <= l){
return 0;
} else if (L <= l && r <= R){
return ST[i];
} else {
int m = (l + r) / 2;
return max(range_max(L, R, i * 2 + 1, l, m), range_max(L, R, i * 2 + 2, m, r));
}
}
int range_max(int L, int R){
return range_max(L, R, 0, 0, N);
}
};
long long count_rectangles(vector<vector<int>> a){
int n = a.size();
int m = a[0].size();
if (n <= 200 && m <= 200){
vector<segment_tree> STh(n);
for (int i = 0; i < n; i++){
STh[i] = segment_tree(a[i]);
}
vector<segment_tree> 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] = segment_tree(b);
}
set<tuple<int, int, int, int>> st;
for (int i = 1; i < n - 1; i++){
for (int j = 1; j < m - 1; j++){
int l = j;
while (l > 0){
if (a[i][l - 1] > a[i][j]){
break;
}
l--;
}
int r = j + 1;
while (r < m){
if (a[i][r] > a[i][j]){
break;
}
r++;
}
int u = i;
while (u > 0){
if (a[u - 1][j] > a[i][j]){
break;
}
u--;
}
int d = i + 1;
while (d < n){
if (a[d][j] > a[i][j]){
break;
}
d++;
}
if (l > 0 && r < m && u > 0 && d < n){
if (st.count(make_tuple(l, r, u, d)) == 0){
bool ok = true;
for (int x = u; x < d; x++){
if (STh[x].range_max(l, r) >= min(a[x][l - 1], a[x][r])){
ok = false;
}
}
for (int y = l; y < r; y++){
if (STv[y].range_max(u, d) >= min(a[u - 1][y], a[d][y])){
ok = false;
}
}
if (ok){
st.insert(make_tuple(l, r, u, d));
}
}
}
}
}
return st.size();
} else if (n < 3){
return 0;
} else if (n == 3){
vector<bool> c(m);
for (int i = 0; i < m; i++){
c[i] = a[0][i] > a[1][i] && a[2][i] > a[1][i];
}
vector<int> S(m + 1);
S[0] = 0;
for (int i = 0; i < m; i++){
S[i + 1] = S[i];
if (!c[i]){
S[i + 1]++;
}
}
map<int, vector<int>> mp;
for (int j = 0; j < m; j++){
mp[a[1][j]].push_back(j);
}
set<int> st = {-1, m};
set<pair<int, int>> ans;
for (auto itr = mp.rbegin(); itr != mp.rend(); itr++){
vector<int> id = (*itr).second;
for (int i : id){
if (i > 0 && i < m - 1){
int L = *prev(st.lower_bound(i)) + 1;
int R = *st.lower_bound(i);
if (0 < L && R < m){
if (S[R] - S[L] == 0){
ans.insert(make_pair(L, R));
}
}
}
}
for (int i : id){
st.insert(i);
}
}
return ans.size();
} else {
for (int i = 0; i < n; i++){
for (int j = 0; j < m; j++){
assert(a[i][j] <= 1);
}
}
int ans = 0;
vector<vector<bool>> used(n, vector<bool>(m, false));
for (int i = 0; i < n; i++){
for (int j = 0; j < m; j++){
if (a[i][j] == 0 && !used[i][j]){
used[i][j] = true;
int u = i, d = i, l = j, r = j;
int cnt = 0;
queue<pair<int, int>> Q;
Q.push(make_pair(i, j));
bool ok = true;
while (!Q.empty()){
int x = Q.front().first;
int y = Q.front().second;
Q.pop();
u = min(u, x);
d = max(d, x);
l = min(l, y);
r = max(r, y);
cnt++;
for (int k = 0; k < 4; k++){
int x2 = x + dx[k];
int y2 = y + dy[k];
if (0 <= x2 && x2 < n && 0 <= y2 && y2 < m){
if (a[x2][y2] == 0 && !used[x2][y2]){
used[x2][y2] = true;
Q.push(make_pair(x2, y2));
}
} else {
ok = false;
}
}
}
if (ok){
if (cnt == (d - u + 1) * (r - l + 1)){
ans++;
}
}
}
}
}
return ans;
}
}
