#include <bits/stdc++.h>
#include "rect.h"
#define fi first
#define se second
#define pll pair<ll, ll>
#define pii pair<int, int>
using namespace std;
typedef long long ll;
typedef long double ld;
const ll MAXN = 1123456;
const ll N = 2510, M = 90;
int prv[N][N], nxt[N][N];
int prv1[N][N], nxt1[N][N];
int pos[N][N];
int p[N * N], kol[N * N], mxy[N * N], mnx[N * N], mxx[N * N], mny[N * N], id, zp[N * N], zapros;
int get(int x){
if(p[x] != x)p[x] = get(p[x]);
return p[x];
}
void unite(int a, int b){
a = get(a), b = get(b);
if(a == b)return;
kol[a] += kol[b];
mxx[a] = max(mxx[a], mxx[b]);
mxy[a] = max(mxy[a], mxy[b]);
mnx[a] = min(mnx[a], mnx[b]);
mny[a] = min(mny[a], mny[b]);
p[b] = a;
return;
}
long long count_rectangles(vector<vector<int> > a) {
ll n = a.size(), m = a[0].size();
if(n < 3)return 0;
if(n == 3){
int ans = 0, mx = 0;
for(int i = 1; i < m - 1; i++){
mx = 0;
for(int j = i; j < m - 1; j++){
mx = max(mx, a[1][j]);
if(a[0][j] <= a[1][j] || a[2][j] <= a[1][j])break;
if(a[1][i - 1] > mx && mx < a[1][j + 1])ans++;
}
}
return ans;
}
if(n <= 80 && m <= 80){
for(int i = 0; i < n; i++){
vector <pii> st;
st.push_back({1e8, -1});
for(int j = 0; j < m; j++){
while(!st.empty() && st.back().fi < a[i][j])st.pop_back();
prv[i][j] = st.back().se;
st.push_back({a[i][j], j});
}
st.clear();
st.push_back({1e8, m});
for(int j = m - 1; j >= 0; j--){
while(!st.empty() && st.back().fi < a[i][j])st.pop_back();
nxt[i][j] = st.back().se;
st.push_back({a[i][j], j});
}
st.clear();
}
for(int j = 0; j < m; j++){
vector <pii> st;
st.push_back({1e8, -1});
for(int i = 0; i < n; i++){
while(!st.empty() && st.back().fi < a[i][j])st.pop_back();
prv1[i][j] = st.back().se;
st.push_back({a[i][j], i});
}
st.clear();
st.push_back({1e8, n});
for(int i = n - 1; i >= 0; i--){
while(!st.empty() && st.back().fi < a[i][j])st.pop_back();
nxt1[i][j] = st.back().se;
st.push_back({a[i][j], i});
}
st.clear();
}
int ans = 0;
for(int r1 = 1; r1 < n - 1; r1++)
for(int c1 = 1; c1 < m - 1; c1++)
for(int r2 = r1; r2 < n - 1; r2++)
for(int c2 = c1; c2 < m - 1; c2++){
bool ok = 1;
for(int i = c1; i <= c2; i++){
if(nxt1[r1 - 1][i] <= r2)ok = 0;
}
for(int i = c1; i <= c2; i++){
if(prv1[r2 + 1][i] >= r1)ok = 0;
}
for(int i = r1; i <= r2; i++){
if(nxt[i][c1 - 1] <= c2)ok = 0;
}
for(int i = r1; i <= r2; i++){
if(prv[i][c2 + 1] >= c1)ok = 0;
}
//if(ok)cout << r1 << " " << c1 << " " << r2 << " " << c2 << "\n";
ans += ok;
}
return ans;
}
map < int, vector<pii> > v;
for(int i = 0; i < n; i++)
for(int j = 0; j < m; j++)v[a[i][j]].push_back({i, j});
ll res = 0;
for(auto kek : v){
for(auto j : kek.se){
pos[j.fi][j.se] = ++id;
//cout << j.fi << " " << j.se << "\n";
p[id] = id;
kol[id] = 1;
mxx[id] = mnx[id] = j.fi;
mxy[id] = mny[id] = j.se;
if(j.fi > 0 && pos[j.fi - 1][j.se])unite(get(pos[j.fi][j.se]), get(pos[j.fi - 1][j.se]));
if(j.fi < n - 1 && pos[j.fi + 1][j.se])unite(get(pos[j.fi][j.se]), get(pos[j.fi + 1][j.se]));
if(j.se > 0 && pos[j.fi][j.se - 1])unite(get(pos[j.fi][j.se]), get(pos[j.fi][j.se - 1]));
if(j.se < m - 1 && pos[j.fi][j.se + 1])unite(get(pos[j.fi][j.se]), get(pos[j.fi][j.se + 1]));
}
zapros++;
for(auto j : kek.se)if(zp[get(pos[j.fi][j.se])] != zapros){
zp[get(pos[j.fi][j.se])] = zapros;
int cmp = get(pos[j.fi][j.se]);
if((mxx[cmp] != n - 1 && mnx[cmp] && mny[cmp] && mxy[cmp] != m - 1) && (kol[cmp] == (mxx[cmp] - mnx[cmp] + 1) * (mxy[cmp] - mny[cmp] + 1))){
res++;
//cout << j.fi << " " << j.se << "\n";
}
}
//cout << res << "\n";
}
return res;
}
