#include "rect.h"
#include<bits/stdc++.h>
#pragma GCC optimize ("Ofast")
using namespace std;
//#define int long long
#define maxn 2505
#define f first
#define s second
#define db(x) cerr << #x << ": " << (x) << '\n';
#define ll long long
#define ii pair<int,int>
int vx[202][202][202], vy[202][202][202];
map<pair<ii,ii>,bool> mp;
ll ans;
int valid[maxn][maxn], valend[maxn][maxn], mnx, mny, mxx, mxy, cnt;
bool valbgn[maxn][maxn], mk[maxn][maxn];
int n, m, A[maxn][maxn];
void dfs(int i,int j){
mnx = min( mnx , i );
mxx = max( mxx , i );
mny = min( mny , j );
mxy = max( mxy , j );
cnt++;
mk[i][j] = 1;
if( i + 1 <= n - 1 && A[i+1][j] == 0 && !mk[i+1][j] ) dfs(i+1,j);
if( i - 1 >= 0 && A[i-1][j] == 0 && !mk[i-1][j] ) dfs(i-1,j);
if( j + 1 <= m - 1 && A[i][j+1] == 0 && !mk[i][j+1] ) dfs(i,j+1);
if( j - 1 >= 0 && A[i][j-1] == 0 && !mk[i][j-1] ) dfs(i,j-1);
}
ll f(int x){
for(int i=0; i<n; i++)
for(int j=0; j<m; j++)
valid[i][j] = valend[i][j] = valbgn[i][j] = 0;
for(int i=1; i<n-1; i++){
int mx = A[i][x];
valend[i][x-1] = 1 + i;
valbgn[i][x-1] = 1;
for(int j=x; j<m-1; j++){
if( A[i][j] > mx ) mx = A[i][j];
valid[i][j] = ( mx < A[i][x-1] && mx < A[i][j+1] );
valend[i][j] = ( ( ( valend[i][j-1] - valend[i-1][j-1] ) != 0 ) && A[i][j] < A[i-1][j] );
valbgn[i][j] = ( valbgn[i][j-1] && A[i][j] < A[i+1][j] );
if( valid[i][j] ) valid[i][j] += valid[i-1][j];
valend[i][j] += valend[i-1][j];
}
}
ll res = 0;
for(int j=x; j<m-1; j++){
for(int i=1; i<n-1; i++){
if( valbgn[i][j] ){
int k = i - valid[i][j];
res += valend[i][j] - valend[k][j];
//if( valend[i][j] - valend[k][j] ){
// db(x)db(j)
// db(i)db(k)
// db(valend[i][j] - valend[k][j])
//}
}
}
}
return res;
}
long long count_rectangles(std::vector<std::vector<int> > a) {
n = a.size();
m = a[0].size();
int maximum = 0;
for(int i=0; i<n; i++)
for(int j=0; j<m; j++){
A[i][j] = a[i][j];
maximum = max( maximum , A[i][j] );
}
if( maximum <= 1 ){
for(int i=1; i<n-1; i++)
for(int j=1; j<m-1; j++)
if( !mk[i][j] && A[i][j] == 0 ){
mnx = i;
mxx = i;
mny = j;
mxy = j;
cnt = 0;
dfs(i,j);
if( ( mxx - mnx + 1 ) * ( mxy - mny + 1 ) == cnt ){
if( mnx >= 1 && mxx <= n - 2 && mny >= 1 && mxy <= m - 2 ){
ans ++;
}
}
}
}
else{
if( n <= 200 && m <= 200 ){
for(int i=1; i<n-1; i++){
for(int j=1; j<m-1; j++){
int mx = A[i][j];
for(int k=j; k<m-1; k++){
if( A[i][k] > mx ) mx = A[i][k];
vx[i][j][k] = ( mx < A[i][j-1] && mx < A[i][k+1] );
if( vx[i][j][k] ){ vx[i][j][k] = vx[i][j][k] + vx[i-1][j][k]; }
}
}
}
for(int i=1; i<m-1; i++){
for(int j=1; j<n-1; j++){
int mx = A[j][i];
for(int k=j; k<n-1; k++){
if( A[k][i] > mx ) mx = A[k][i];
vy[i][j][k] = ( mx < A[j-1][i] && mx < A[k+1][i] );
if( vy[i][j][k] )
vy[i][j][k] += vy[i-1][j][k];
}
}
}
for(int i=1; i<n-1; i++){
for(int j=i; j<n-1; j++){
for(int k=1; k<m-1; k++){
for(int l=k; l<m-1; l++){
if( j - vx[j][k][l] < i && l - vy[l][i][j] < k ){
ans ++;
}
}
}
}
}
}
else{
for(int i=1; i<m-1; i++)
ans += f(i);
}
}
return ans;
}
