#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#include <bits/stdc++.h>
#include "rect.h"
//#include "grader.cpp"
using namespace std;
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef pair<int, int> pi;
#define debug(x) cerr << #x << ": " << x << endl;
#define debug2(x, y) debug(x) debug(y);
#define repn(i, a, b) for(int i = (int)(a); i < (int)(b); i++)
#define rep(i, a) for(int i = 0; i < (int)(a); i++)
#define all(v) v.begin(), v.end()
#define mp make_pair
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define fi first
#define se second
#define sq(x) ((x) * (x))
template<class T> T gcd(T a, T b){ return ((b == 0) ? a : gcd(b, a % b)); }
bool ver[705][705][705];
bool hor[705][705][705];
ll count_rectangles(vector<vi> a){
int n = a.size();
int m = a[0].size();
memset(ver, 0, sizeof(ver));
memset(hor, 0, sizeof(hor));
repn(i, 1, n - 1){
int hor1[705][705];
memset(hor1, 0, sizeof(hor1));
repn(j, 1, m - 1) repn(k, j, m - 1){
if(j == k){
hor1[j][k] = a[i][j];
if(hor1[j][k] < a[i][j - 1] && hor1[j][k] < a[i][k + 1]) hor[i][j][k] = 1;
}
else{
hor1[j][k] = max(hor1[j][k - 1], a[i][k]);
if(hor1[j][k] < a[i][j - 1] && hor1[j][k] < a[i][k + 1]) hor[i][j][k] = 1;
}
}
}
repn(j, 1, m - 1){
int ver1[705][705];
memset(ver1, 0, sizeof(ver1));
repn(i, 1, n - 1) repn(k, i, n - 1){
if(i == k){
ver1[i][k] = a[i][j];
if(ver1[i][k] < a[i - 1][j] && ver1[i][k] < a[k + 1][j]) ver[j][i][k] = 1;
}
else{
ver1[i][k] = max(ver1[i][k - 1], a[k][j]);
if(ver1[i][k] < a[i - 1][j] && ver1[i][k] < a[k + 1][j]) ver[j][i][k] = 1;
}
}
}
ll ans = 0;
repn(i, 1, n - 1) repn(j, 1, m - 1) repn(k, i, n - 1) repn(l, j, m - 1){
int f = 1;
repn(x, i, k + 1){
if(!hor[x][j][l] || !hor[x][j][l]){
f = 0;
break;
}
}
if(!f) continue;
repn(x, j, l + 1){
if(!ver[x][i][k] || !ver[x][i][k]){
f = 0;
break;
}
}
if(!f) continue;
ans++;
}
return ans;
}
/*
Things to look out for:
- Integer overflows
- Array bounds
- Special cases
Be careful!
*/
