#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
#define ff first
#define ss second
#define pb push_back
#define all(a) (a).begin(), (a).end()
#define replr(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define reprl(i, a, b) for (int i = int(a); i >= int(b); --i)
#define rep(i, n) for (int i = 0; i < int(n); ++i)
#define mkp(a, b) make_pair(a, b)
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> PII;
typedef vector<int> VI;
typedef vector<PII> VPI;
typedef vector<VI> VVI;
typedef vector<VVI> VVVI;
typedef vector<VPI> VVPI;
typedef pair<ll, ll> PLL;
typedef vector<ll> VL;
typedef vector<PLL> VPL;
typedef vector<VL> VVL;
typedef vector<VVL> VVVL;
typedef vector<VPL> VVPL;
template<class T> T setmax(T& a, T b) {if (a < b) return a = b; return a;}
template<class T> T setmin(T& a, T b) {if (a < b) return a; return a = b;}
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
template<class T>
using indset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#include "rect.h"
int gu[3000][3000], gd[3000][3000], gl[3000][3000], gr[3000][3000];
int lu[3000][3000], ru[3000][3000], ul[3000][3000], dl[3000][3000];
VL rect;
void check(int x1, int x2, int y1, int y2) {
if (x2 < x1 || y2 < y1) return;
if ((gu[x2+1][y2] == x1-1 && ul[x2+1][y2] <= y1) || (gd[x1-1][y2] == x2+1 && dl[x1-1][y2] <= y1)); else return;
if ((gr[x2][y1-1] == y2+1 && ru[x2][y1-1] <= x1) || (gl[x2][y2+1] == y1-1 && lu[x2][y2+1] <= x1)); else return;
rect.pb(1ll*x1*3000*3000*3000 + 1ll*x2*3000*3000 + 1ll*y1*3000 + 1ll*y2);
}
ll count_rectangles(VVI a) {
int n = a.size();
int m = a[0].size();
rep(i, n) {
stack<int> st;
replr(j, 0, m-1) {
while (st.size() && a[i][st.top()] < a[i][j]) st.pop();
gl[i][j] = (st.size() ? st.top() : -1);
st.push(j);
}
st = stack<int>();
reprl(j, m-1, 0) {
while (st.size() && a[i][st.top()] < a[i][j]) st.pop();
gr[i][j] = (st.size() ? st.top() : -1);
st.push(j);
}
}
rep(j, m) {
stack<int> st;
replr(i, 0, n-1) {
while (st.size() && a[st.top()][j] < a[i][j]) st.pop();
gu[i][j] = (st.size() ? st.top() : -1);
st.push(i);
}
st = stack<int>();
reprl(i, n-1, 0) {
while (st.size() && a[st.top()][j] < a[i][j]) st.pop();
gd[i][j] = (st.size() ? st.top() : -1);
st.push(i);
}
}
rep(i, n) {
rep(j, m) {
if (~gl[i][j]) {
if (i && gl[i-1][j] == gl[i][j]) lu[i][j] = lu[i-1][j];
else if (i && gr[i-1][gl[i][j]] == j) lu[i][j] = ru[i-1][gl[i][j]];
else lu[i][j] = i;
}
if (~gr[i][j]) {
if (i && gr[i-1][j] == gr[i][j]) ru[i][j] = ru[i-1][j];
else if (i && gl[i-1][gr[i][j]] == j) ru[i][j] = lu[i-1][gr[i][j]];
else ru[i][j] = i;
}
}
}
rep(j, m) {
rep(i, n) {
if (~gu[i][j]) {
if (j && gu[i][j-1] == gu[i][j]) ul[i][j] = ul[i][j-1];
else if (j && gd[gu[i][j]][j-1] == i) ul[i][j] = dl[gu[i][j]][j-1];
else ul[i][j] = j;
}
if (~gd[i][j]) {
if (j && gd[i][j-1] == gd[i][j]) dl[i][j] = dl[i][j-1];
else if (j && gu[gd[i][j]][j-1] == i) dl[i][j] = ul[gd[i][j]][j-1];
else dl[i][j] = j;
} else dl[i][j] = -1;
}
}
rect.clear();
replr(i, 1, n-2) replr(j, 1, m-2) {
if (~gd[i-1][j] && ~gr[i][j-1]) check(i, gd[i-1][j]-1, j, gr[i][j-1]-1);
if (~gd[i-1][j] && ~gl[i][j+1]) check(i, gd[i-1][j]-1, gl[i][j+1]+1, j);
if (~gu[i+1][j] && ~gr[i][j-1]) check(gu[i+1][j]+1, i, j, gr[i][j-1]-1);
if (~gu[i+1][j] && ~gl[i][j+1]) check(gu[i+1][j]+1, i, gl[i][j+1]+1, j);
if (!~gr[i][j-1]) continue;
int nextj = gr[i][j-1]-1;
if (~gu[i+1][nextj]) check(gu[i+1][nextj]+1, i, j, nextj);
if (~gd[i-1][nextj]) check(i, gd[i-1][nextj]-1, j, nextj);
}
ll ans = 0;
if (rect.size()) {
sort(all(rect));
ans = 1;
rep(i, rect.size()-1) ans += (rect[i] != rect[i+1]);
}
return ans;
}
