#include <bits/stdc++.h>
using namespace std;
const int INF = 88888888;
const int N = 2512;
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];
vector<pair<int, int> > rooted[N][N];
struct query{
int l, r;
int x, tm;
};
bool incr(query a, query b)
{
return a.x < b.x;
}
bool decr(query a, query b)
{
return a.x > b.x;
}
int fenw[N];
void reset()
{
for (int i = 0; i < N; i++) fenw[i] = 0;
}
int get(int pos)
{
int res = 0;
while (pos >= 0)
{
res += fenw[pos];
pos = (pos & (pos + 1)) - 1;
}
return res;
}
void add(int pos)
{
while (pos < N)
{
fenw[pos]++;
pos |= (pos + 1);
}
}
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 + 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});
}
}
}
vector<int> res;
vector<vector<query> > qd(n);
vector<vector<query> > qu(n);
vector<vector<query> > qr(m);
vector<vector<query> > ql(m);
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)
{
qd[i - 1].push_back({j, j2, i2, res.size()});
qu[i2 + 1].push_back({j, j2, i, res.size()});
qr[j - 1].push_back({i, i2, j2, res.size()});
ql[j2 + 1].push_back({i, i2, j, res.size()});
res.push_back(1);
}
}
rooted[i][j].clear();
}
}
for (int i = 0; i < n; i++)
{
sort(all(qd[i]), incr);
vector<pair<int, int> > p;
for (int j = 0; j < m; j++) p.push_back({down[i][j], j});
sort(all(p));
p.push_back({INF, 0});
int j = 0;
for (auto e : p)
{
while (j < qd[i].size() && qd[i][j].x < e.first)
{
if (get(qd[i][j].r) - get(qd[i][j].l - 1) != 0) res[qd[i][j].tm] = 0;
j++;
}
add(e.second);
}
reset();
}
for (int i = 0; i < n; i++)
{
sort(all(qu[i]), decr);
vector<pair<int, int> > p;
for (int j = 0; j < m; j++) p.push_back({up[i][j], j});
sort(all(p));
reverse(all(p));
p.push_back({-INF, 0});
int j = 0;
for (auto e : p)
{
while (j < qu[i].size() && qu[i][j].x > e.first)
{
if (get(qu[i][j].r) - get(qu[i][j].l - 1) != 0) res[qu[i][j].tm] = 0;
j++;
}
add(e.second);
}
reset();
}
for (int i = 0; i < m; i++)
{
sort(all(qr[i]), incr);
vector<pair<int, int> > p;
for (int j = 0; j < n; j++) p.push_back({ri[j][i], j});
sort(all(p));
p.push_back({INF, 0});
int j = 0;
for (auto e : p)
{
while (j < qr[i].size() && qr[i][j].x < e.first)
{
if (get(qr[i][j].r) - get(qr[i][j].l - 1) != 0) res[qr[i][j].tm] = 0;
j++;
}
add(e.second);
}
reset();
}
for (int i = 0; i < m; i++)
{
sort(all(ql[i]), decr);
vector<pair<int, int> > p;
for (int j = 0; j < n; j++) p.push_back({le[j][i], j});
sort(all(p));
reverse(all(p));
p.push_back({-INF, 0});
int j = 0;
for (auto e : p)
{
while (j < ql[i].size() && ql[i][j].x > e.first)
{
if (get(ql[i][j].r) - get(ql[i][j].l - 1) != 0) res[ql[i][j].tm] = 0;
j++;
}
add(e.second);
}
reset();
}
return accumulate(all(res), 0);
}
