#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 n, m;
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];
inline int check_rect(int x1, int y1, int x2, int y2, vector<vector<int> > &a)
{
if (x1 <= 0 || x2 >= n - 1 || y1 <= 0 || y2 >= m - 1) return 0;
if (x1 > x2 || y1 > y2) return 0;
if (!(down[x1 - 1][y1] == x2 + 1 || up[x2 + 1][y1] == x1 - 1)) return 0;
if (!(down[x1 - 1][y2] == x2 + 1 || up[x2 + 1][y2] == x1 - 1)) return 0;
if (!(ri[x1][y1 - 1] == y2 + 1 || le[x1][y2 + 1] == y1 - 1)) return 0;
if (!(ri[x2][y1 - 1] == y2 + 1 || le[x2][y2 + 1] == y1 - 1)) return 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];
}
int R = 0;
if (a[x1 - 1][y1] <= a[x2 + 1][y1])
{
R = go_ri[1][x1 - 1][y1];
}
else
{
R = go_ri[0][x2 + 1][y1];
}
int L = 0;
if (a[x1 - 1][y2] <= a[x2 + 1][y2])
{
L = go_le[1][x1 - 1][y2];
}
else
{
L = go_le[0][x2 + 1][y2];
}
int t = (x2 < D && U < x1 && y2 < R && L < y1);
if (!t) return 0;
if ((down[x1 - 1][y1] == x2 + 1 || down[x1 - 1][y2] == x2 + 1) &&
(up[x2 + 1][y1] == x1 - 1 || up[x2 + 1][y2] == x1 - 1)) return 1;
return 2;
}
pair<int, int> st[N];
int stsz;
int pack[N];
int packsz;
long long count_rectangles(vector<vector<int> > a)
{
n = a.size(), m = a[0].size();
for (int i = 0; i < n; i++)
{
stsz = 0;
st[stsz++] = {-1, INF};
for (int j = 0; j < m; j++)
{
while (st[stsz - 1].second < a[i][j]) stsz--;
le[i][j] = st[stsz - 1].first;
st[stsz++] = {j, a[i][j]};
}
}
for (int i = 0; i < n; i++)
{
stsz = 0;
st[stsz++] = {m, INF};
for (int j = m - 1; j >= 0; j--)
{
while (st[stsz - 1].second < a[i][j]) stsz--;
ri[i][j] = st[stsz - 1].first;
st[stsz++] = {j, a[i][j]};
}
}
for (int j = 0; j < m; j++)
{
stsz = 0;
st[stsz++] = {-1, INF};
for (int i = 0; i < n; i++)
{
while (st[stsz - 1].second < a[i][j]) stsz--;
up[i][j] = st[stsz - 1].first;
st[stsz++] = {i, a[i][j]};
}
}
for (int j = 0; j < m; j++)
{
stsz = 0;
st[stsz++] = {n, INF};
for (int i = n - 1; i >= 0; i--)
{
while (st[stsz - 1].second < a[i][j]) stsz--;
down[i][j] = st[stsz - 1].first;
st[stsz++] = {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(n);
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({m, 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;
}
}
for (int j = 1; j < m; j++)
{
vector<pair<int, int> > st;
st.push_back({-1, INF});
vector<int> pack;
pack.push_back(m);
for (int i = 0; i < n; i++)
{
int unpack = m;
while (st.back().second < a[i][j])
{
unpack = min(unpack, ri[st.back().first][j - 1]);
st.pop_back();
unpack = min(unpack, pack.back());
pack.pop_back();
}
st.push_back({i, a[i][j]});
pack.push_back(unpack);
go_ri[0][i][j] = unpack;
}
}
for (int j = 1; j < m; j++)
{
vector<pair<int, int> > st;
st.push_back({n, INF});
vector<int> pack;
pack.push_back(m);
for (int i = n - 1; i >= 0; i--)
{
int unpack = m;
while (st.back().second < a[i][j])
{
unpack = min(unpack, ri[st.back().first][j - 1]);
st.pop_back();
unpack = min(unpack, pack.back());
pack.pop_back();
}
st.push_back({i, a[i][j]});
pack.push_back(unpack);
go_ri[1][i][j] = unpack;
}
}
for (int j = 0; j + 1 < m; j++)
{
vector<pair<int, int> > st;
st.push_back({-1, INF});
vector<int> pack;
pack.push_back(-1);
for (int i = 0; i < n; i++)
{
int unpack = -1;
while (st.back().second < a[i][j])
{
unpack = max(unpack, le[st.back().first][j + 1]);
st.pop_back();
unpack = max(unpack, pack.back());
pack.pop_back();
}
st.push_back({i, a[i][j]});
pack.push_back(unpack);
go_le[0][i][j] = unpack;
}
}
for (int j = 0; j + 1 < m; j++)
{
vector<pair<int, int> > st;
st.push_back({n, INF});
vector<int> pack;
pack.push_back(-1);
for (int i = n - 1; i >= 0; i--)
{
int unpack = -1;
while (st.back().second < a[i][j])
{
unpack = max(unpack, le[st.back().first][j + 1]);
st.pop_back();
unpack = max(unpack, pack.back());
pack.pop_back();
}
st.push_back({i, a[i][j]});
pack.push_back(unpack);
go_le[1][i][j] = unpack;
}
}
vector<vector<int> > rect;
int ans = 0;
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;
ans += check_rect(u0, j, i, r, a);
if (u0 != u1) ans += check_rect(u1, j, i, r, a);
ans += check_rect(i, j, d0, r, a);
if (d0 != d1) ans += check_rect(i, j, d1, r, a);
}
{
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;
if (a[i][j + 1] != a[i][l - 1]) ans += check_rect(u0, l, i, j, a);
if (a[i][j + 1] != a[i][l - 1] && u0 != u1) ans += check_rect(u1, l, i, j, a);
if (a[i][j + 1] != a[i][l - 1]) ans += check_rect(i, l, d0, j, a);
if (a[i][j + 1] != a[i][l - 1] && d0 != d1) ans += check_rect(i, l, d1, j, a);
}
}
}
return ans / 2;
}
