#include <bits/stdc++.h>
using namespace std;
const int INF = 88888888;
typedef vector<vector<int> > vvi;
typedef vector<int> vi;
#define all(x) (x).begin(), (x).end()
long long count_rectangles(vector<vector<int> > a)
{
int n = a.size(), m = a[0].size();
vvi le(n, vi(m)), ri(n, vi(m)), up(n, vi(m)), down(n, vi(m));
for (int i = 0; i < n; i++)
{
vector<pair<int, int> > st;
st.push_back({-1, INF});
for (int j = 0; j < m; j++)
{
while (st.back().second < a[i][j]) st.pop_back();
le[i][j] = st.back().first;
st.push_back({j, a[i][j]});
}
}
for (int i = 0; i < n; i++)
{
vector<pair<int, int> > st;
st.push_back({m, INF});
for (int j = m - 1; j >= 0; j--)
{
while (st.back().second < a[i][j]) st.pop_back();
ri[i][j] = st.back().first;
st.push_back({j, a[i][j]});
}
}
for (int j = 0; j < m; j++)
{
vector<pair<int, int> > st;
st.push_back({-1, INF});
for (int i = 0; i < n; i++)
{
while (st.back().second < a[i][j]) st.pop_back();
up[i][j] = st.back().first;
st.push_back({i, a[i][j]});
}
}
for (int j = 0; j < m; j++)
{
vector<pair<int, int> > st;
st.push_back({n, INF});
for (int i = n - 1; i >= 0; i--)
{
while (st.back().second < a[i][j]) st.pop_back();
down[i][j] = st.back().first;
st.push_back({i, a[i][j]});
}
}
vector<vector<vector<pair<int, int> > > > rooted(n, vector<vector<pair<int, int> > >(m));
for (int i = 1; i + 1 < n; i++)
{
for (int j = 1; j + 1 < m; j++)
{
{
int r = ri[i][j - 1] - 1;
int u0 = up[i + 1][j] + 1;
int u1 = up[i + 1][r] + 1;
int d0 = down[i - 1][j] - 1;
int d1 = down[i - 1][r] - 1;
rooted[u0][j].push_back({i, r});
rooted[u1][j].push_back({i, r});
rooted[i][j].push_back({d0, r});
rooted[i][j].push_back({d1, r});
}
{
int l = le[i][j + 1] + 1;
int u0 = up[i + 1][l] + 1;
int u1 = up[i + 1][j] + 1;
int d0 = down[i - 1][l] - 1;
int d1 = down[i - 1][j] - 1;
rooted[u0][l].push_back({i, j});
rooted[u1][l].push_back({i, j});
rooted[i][l].push_back({d0, j});
rooted[i][l].push_back({d1, j});
}
}
}
int ans = 0;
for (int i = 1; i < n; i++)
{
for (int j = 1; j < m; j++)
{
sort(all(rooted[i][j]));
rooted[i][j].resize(unique(all(rooted[i][j])) - rooted[i][j].begin());
for (auto p : rooted[i][j])
{
int i2 = p.first, j2 = p.second;
if (i <= i2 && j <= j2 && i2 < n - 1 && j2 < m - 1)
{
int t = 1;
for (int y = j; y <= j2; y++)
if (down[i - 1][y] <= i2) t = 0;
for (int y = j; y <= j2; y++)
if (up[i2 + 1][y] >= i) t = 0;
for (int x = i; x <= i2; x++)
if (ri[x][j - 1] <= j2) t = 0;
for (int x = i; x <= i2; x++)
if (le[x][j2 + 1] >= j) t = 0;
ans += t;
}
}
}
}
return ans;
}
