#include <bits/stdc++.h>
using namespace std;
const int INF = 88888888;
const int N = 2502;
typedef vector<vector<int> > vvi;
typedef vector<int> vi;
#define all(x) (x).begin(), (x).end()
int le[N][N], ri[N][N], up[N][N], down[N][N];
int go_le[2][N][N], go_ri[2][N][N], go_up[2][N][N], go_down[2][N][N];
long long count_rectangles(vector<vector<int> > a)
{
int n = a.size(), m = a[0].size();
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]});
}
}
for (int i = 1; i < n; i++)
{
vector<pair<int, int> > st;
st.push_back({-1, INF});
vector<int> pack;
pack.push_back(n);
for (int j = 0; j < m; j++)
{
int unpack = n;
while (st.back().second < a[i][j])
{
unpack = min(unpack, down[i - 1][st.back().first]);
st.pop_back();
unpack = min(unpack, pack.back());
pack.pop_back();
}
st.push_back({j, a[i][j]});
pack.push_back(unpack);
go_down[0][i][j] = unpack;
}
}
for (int i = 1; i < n; i++)
{
vector<pair<int, int> > st;
st.push_back({m, INF});
vector<int> pack;
pack.push_back(m);
for (int j = m - 1; j >= 0; j--)
{
int unpack = n;
while (st.back().second < a[i][j])
{
unpack = min(unpack, down[i - 1][st.back().first]);
st.pop_back();
unpack = min(unpack, pack.back());
pack.pop_back();
}
st.push_back({j, a[i][j]});
pack.push_back(unpack);
go_down[1][i][j] = unpack;
}
}
for (int i = 0; i + 1 < n; i++)
{
vector<pair<int, int> > st;
st.push_back({-1, INF});
vector<int> pack;
pack.push_back(-1);
for (int j = 0; j < m; j++)
{
int unpack = -1;
while (st.back().second < a[i][j])
{
unpack = max(unpack, up[i + 1][st.back().first]);
st.pop_back();
unpack = max(unpack, pack.back());
pack.pop_back();
}
st.push_back({j, a[i][j]});
pack.push_back(unpack);
go_up[0][i][j] = unpack;
}
}
for (int i = 0; i + 1 < n; i++)
{
vector<pair<int, int> > st;
st.push_back({-1, INF});
vector<int> pack;
pack.push_back(-1);
for (int j = m - 1; j >= 0; j--)
{
int unpack = -1;
while (st.back().second < a[i][j])
{
unpack = max(unpack, up[i + 1][st.back().first]);
st.pop_back();
unpack = max(unpack, pack.back());
pack.pop_back();
}
st.push_back({j, a[i][j]});
pack.push_back(unpack);
go_up[1][i][j] = unpack;
}
}
int ans = 0;
for (int x1 = 1; x1 <= n - 2; x1++)
{
for (int x2 = x1; x2 <= n - 2; x2++)
{
for (int y1 = 1; y1 <= m - 2; y1++)
{
for (int y2 = y1; y2 <= m - 2; y2++)
{
int t = 1;
for (int r = x1; r <= x2; r++) if (ri[r][y1 - 1] <= y2) t = 0;
for (int r = x1; r <= x2; r++) if (le[r][y2 + 1] >= y1) t = 0;
int D = 0;
if (a[x1][y1 - 1] <= a[x1][y2 + 1])
{
D = go_down[1][x1][y1 - 1];
}
else
{
D = go_down[0][x1][y2 + 1];
}
int U = 0;
if (a[x2][y1 - 1] <= a[x2][y2 + 1])
{
U = go_up[1][x2][y1 - 1];
}
else
{
U = go_up[0][x2][y2 + 1];
}
if (D <= x2 || x1 <= U) t = 0;
ans += t;
}
}
}
}
return ans;
}
