#include "rect.h"
#include <bits/stdc++.h>
#define ll long long
#define ld long double
#define vi vector<int>
#define vl vector<long long>
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace std;
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;
const int tree_siz = 1024*8-1;
int sum[tree_siz+1];
int get_sum(int akt, int p1, int p2, int s1, int s2)
{
if(p2 < s1 || p1 > s2) return 0;
if(p1 >= s1 && p2 <= s2) return sum[akt];
return get_sum(akt*2,p1,(p1+p2)/2,s1,s2)+get_sum(akt*2+1,(p1+p2)/2+1,p2,s1,s2);
}
void upd(int v)
{
sum[v] = sum[v*2]+sum[v*2+1];
if(v != 1) upd(v/2);
}
void change(int ind, int x)
{
sum[tree_siz/2+ind+1] += x;
upd((tree_siz/2+1+ind)/2);
}
map<pii,int> X[2501];
map<pii,int> Y[2501];
vector<pii> X_segs[2501][2501];
vector<pii> Y_segs[2501][2501];
vector<pii> count_regions(vi x)
{
vector<pii> ans;
stack<int> st;
rep(i,siz(x))
{
while(!st.empty() && x[st.top()] < x[i]) st.pop();
if(i != 0 && siz(st) != 0)
{
int end_ = st.top()+1;
if(end_ <= i-1)
{
ans.pb({end_,i-1});
}
}
st.push(i);
}
while(!st.empty()) st.pop();
for(int i = siz(x)-1; i >= 0; i--)
{
while(!st.empty() && x[st.top()] < x[i]) st.pop();
if(i != siz(x)-1 && siz(st) != 0)
{
int end_ = st.top()-1;
if(end_ >= i+1)
{
ans.pb({i+1,end_});
}
}
st.push(i);
}
sort(all(ans));
vector<pii> ans2;
pii pop = {-1,-1};
forall(it,ans)
{
if(it.ff == pop.ff && it.ss == pop.ss) continue;
ans2.pb(it);
pop = it;
}
return ans2;
}
ll count_rectangles(vector<vi> arr)
{
int n = siz(arr);
int m = siz(arr[0]);
rep2(i,1,n-2)
{
vector<pii> segs = count_regions(arr[i]);
forall(it,segs)
{
Y[i][it] = i;
}
}
for(int i = n-2; i >= 0; i--)
{
forall(it,Y[i])
{
if(Y[i+1].find(it.ff) != Y[i+1].end()) Y[i][it.ff] = Y[i+1][it.ff];
Y_segs[i][it.ff.ff].pb({Y[i][it.ff],it.ff.ss});
}
}
rep2(j,1,m-2)
{
vi arr2;
rep(i,n) arr2.pb(arr[i][j]);
vector<pii> segs = count_regions(arr2);
forall(it,segs)
{
X[j][it] = j;
}
}
for(int j = m-2; j >= 0; j--)
{
forall(it,X[j])
{
if(X[j+1].find(it.ff) != X[j+1].end()) X[j][it.ff] = X[j+1][it.ff];
X_segs[it.ff.ff][j].pb({it.ff.ss,X[j][it.ff]});
}
}
ll ans = 0;
rep2(i,1,n-2)
{
rep2(j,1,m-2)
{
sort(all(X_segs[i][j]));
sort(all(Y_segs[i][j]));
int cur_Y = siz(Y_segs[i][j])-1;
forall(it,Y_segs[i][j])
{
change(it.ss,1);
}
forall(it,X_segs[i][j])
{
while(cur_Y >= 0 && Y_segs[i][j][cur_Y].ff < it.ff)
{
change(Y_segs[i][j][cur_Y].ss,-1);
cur_Y--;
}
ans += get_sum(1,0,tree_siz/2,0,it.ss);
}
rep(k,cur_Y+1)
{
change(Y_segs[i][j][k].ss,-1);
}
}
}
return ans;
}
