//나는 가상 소녀들에게 큰 호감이 있습니다.
#include <iostream>
#include <cmath>
#include <algorithm>
#include <stdio.h>
#include <cstring>
#include <string>
#include <cstdlib>
#include <vector>
#include <bitset>
#include <map>
#include <chrono>
#include <functional>
#include <unordered_set>
#include <unordered_map>
#include <numeric>
#include <queue>
#include <ctime>
#include <stack>
#include <set>
#include <list>
#include <deque>
#include <iomanip>
#include <sstream>
#include <fstream>
#include <stdarg.h>
#include <utility>
using namespace std;
#define pb push_back
#define mp make_pair
#define ll long long
#define ull unisgned long long
#define ld long double
#define all(a) a.begin(), a.end()
#define SORT(a) sort(all(a))
#define pii pair<int, int>
#define tii triple<int, int, int>
#define e 1e-7
#define PI acos(-1)
#define sz(a) (int)(a.size())
#define inf 1e17
#define vi vector<int>
#define F first
#define S second
#define rng(x) for(int _ = 0; _ < (x); _++)
#define rngi(i, x) for(int i = 0; i < (x); i++)
#define rngsi(s, i, x) for(int i = (s); i <(x); i++)
#define problem "a"
template<typename A, typename B, typename C>
struct triple {
A X;
B Y;
C Z;
triple(A a = 0, B b = 0, C c = 0) :X(a), Y(b), Z(c) {}
};
template<typename A, typename B, typename C>
triple<A, B, C> make_triple(A a = 0, B b = 0, C c = 0) {
return triple<A, B, C>(a, b, c);
}
template<typename A, typename B, typename C>
bool operator<(const triple<A, B, C>& a, const triple<A, B, C>& b) {
if (a.X != b.X)
return a.X < b.X;
if (a.Y != b.Y)
return a.Y < b.Y;
return a.Z < b.Z;
}
template<typename T, typename SS>
ostream& operator<<(ostream& ofs, const pair<T, SS>& p) {
ofs << "( " << p.F << " , " << p.S << " )";
return ofs;
}
template<typename T>
void print(T a) {
for (auto i : a)
cout << i << ' ';
cout << '\n';
}
template<typename T>
T max(T a, T b, T c) {
return max(a, max(b, c));
}
template<typename T>
T min(T a, T b, T c) {
return min(a, min(b, c));
}
template<typename T, typename D>
D min(T a) {
return *min_element(all(a));
}
template<typename T, typename D>
D max(T a) {
return *max_element(all(a));
}
struct custom_hash {
static uint64_t splitmix64(uint64_t x) {
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
#include "rect.h"
long long count_rectangles(std::vector<std::vector<int> > a) {
int n = sz(a), m = sz(a[0]);
bool s6 = 1;
rngi(i, n) rngi(j, m) if (a[i][j] > 1)s6 = 0;
ll ans = 0;
if (s6) {
vector<vi> posr(n), posc(m);
auto b(a);
rngi(i, n) partial_sum(all(b[i]), b[i].begin());
rngi(i, n - 1) rngi(j, m) b[i + 1][j] += b[i][j];
auto s = [&](int x1, int y1, int x2, int y2) {
return b[x2][y2] - (y1?b[x2][y1 - 1]:0) - (x1?b[x1 - 1][y2]:0) + (x1 && y1 ? b[x1 - 1][y1 - 1] : 0);
};
auto ok = [&](int x1, int y1, int x2, int y2) {
if (x1 > x2 || y1 > y2)return 0;
if (s(x1, y1, x2, y2))return 0;
if (s(x1, y1 - 1, x2, y1 - 1) != x2 - x1 + 1)return 0;
if (s(x1, y2 + 1, x2, y2 + 1) != x2 - x1 + 1)return 0;
if (s(x1 - 1, y1, x1 - 1, y2) != y2 - y1 + 1)return 0;
if (s(x2 + 1, y1, x2 + 1, y2) != y2 - y1 + 1)return 0;
return 1;
};
rngi(i, n) rngi(j, m) if (a[i][j] == 1) posr[i].push_back(j), posc[j].push_back(i);
for(int i = 1; i + 1 < n; i++)
for (int j = 1; j + 1 < m; j++) if(!a[i][j]){
if (a[i - 1][j] != 1 || a[i][j - 1] != 1)continue;
int x = upper_bound(all(posc[j]), i) - posc[j].begin();
if (x >= sz(posc[j])) continue;
x = posc[j][x];
int y = upper_bound(all(posr[i]), j) - posr[i].begin();
if (y >= sz(posr[i])) continue;
y = posr[i][y];
if (ok(i, j, x - 1, y - 1)) ans++;
}
}
else if (n <= 3) {
if (n <= 2)return 0;
auto b(a);
for (int i = 1; i + 1 < m; i++)
if (a[0][i] <= a[1][i] || a[2][i] <= a[1][i]) a[1][i] = inf;
rngi(i, m - 2) {
int j = i + 1; int mn = a[1][j];
while (j < m - 1 && b[1][i] > mn) {
if(mn < b[1][j + 1]) ans++;
j++;
mn = max(mn, a[1][j]);
}
}
}
else {
for(int x1 = 1; x1 < n - 1; x1++)
for(int y1 = 1; y1 < m - 1; y1++)
for(int x2 = x1; x2 < n - 1; x2++)
for (int y2 = y1; y2 < m - 1; y2++) {
bool ok = 1;
for (int i = x1; ok && i <= x2; i++) {
if (!ok)break;
for (int j = y1; ok && j <= y2; j++) {
if (a[i][y1 - 1] <= a[i][j] || a[i][y2 + 1] <= a[i][j] || a[x1 - 1][j] <= a[i][j] || a[x2 + 1][j] <= a[i][j]) {
ok = 0; break;
}
}
}
ans += ok;
}
}
return ans;
}
