#include "rect.h"
#include<bits/stdc++.h>
using namespace std;
using ll = int;
using lll = long long;
const ll maxn = 2500;
const ll big = 1e18;
struct BIT{
ll n;
vector<ll> a;
BIT(ll N):n(N),a(N+1,0){}
void add(ll i, ll v){
for(;i<=n;i+=i&-i) a[i] += v;
}
ll get(ll i){
ll x = 0;
for(;i>0;i-=i&-i) x += a[i];
return x;
}
};
struct dsu{
vector<ll> p;
dsu(ll N):p(N,-1){}
ll g(ll i){
return p[i]<0?i:p[i] = g(p[i]);
}
bool m(ll a,ll b){
a = g(a),b = g(b);
if (a==b) return false;
if (p[a]>p[b]) swap(a,b);
p[a] += p[b];
p[b] = a;
return true;
}
};
struct node{
ll l,r,m,v;
node *L,*R;
node(ll a, ll b):l(a),r(b),m(a+b>>1),v(0),L(nullptr),R(nullptr){
if (l<r){
L = new node(l,m);
R = new node(m+1,r);
}
}
void add(ll i, ll x){
if(l<r){
if(i<=m) (L=new node(*L))->add(i,x);
else (R=new node(*R))->add(i,x);
}else v+=x;
}
ll qry(ll i){
if(l<r){
if(i<=m) return L->qry(i);
else return R->qry(i);
}else return v;
}
};
struct segtree{
vector<node*> rt;
segtree(ll l, ll r){
rt.push_back(new node(l,r));
}
void nw(){
rt.push_back(new node(*rt.back()));
}
void add(ll t, ll i, ll x){
rt[t]->add(i,x);
}
ll qry(ll t, ll i){
return rt[t]->qry(i);
}
};
struct mxt{
ll n;
vector<ll> a;
mxt(ll N):n(N),a(N<<2,0){}
void mod(ll i, ll l, ll r, ll x, ll v){
if (l==r) a[i] = v;
else{
ll m = l+r>>1;
if (x<=m) mod(i<<1,l,m,x,v);
else mod(i<<1|1,m+1,r,x,v);
a[i] = max(a[i<<1],a[i<<1|1]);
}
}
ll qry(ll i, ll l, ll r, ll ql, ll qr){
if (ql<=l&&r<=qr) return a[i];
else{
ll m = l+r>>1;
ll ret = -big;
if (ql<=m)ret = max(ret,qry(i<<1,l,m,ql,qr));
if(qr>m)ret = max(ret,qry(i<<1|1,m+1,r,ql,qr));
return ret;
}
}
};
long long count_rectangles(std::vector<std::vector<int> > a) {
ll n = a.size(), m = a[0].size();
if (n<3||m<3) return 0;
ll sub6 = 1;
for(auto &o : a) for(ll &i : o) if (i>1) sub6 = 0;
if (0&&sub6){
dsu d(n*m);
for(ll i = 1;i<n-1;i++){
for(ll j = 1;j<m-1;j++){
if(i>1&&!a[i][j]&&!a[i-1][j]){
d.m((i)*m+(j),(i-1)*m+(j));
}
if(j>1&&!a[i][j]&&!a[i][j-1]){
d.m((i)*m+(j),(i)*m+(j-1));
}
}
}
vector<ll> gs;
for(ll i = 1;i<n-1;i++){
for(ll j = 1;j<m-1;j++){
if(!a[i][j]){
gs.push_back(d.g((i)*m+(j)));
}
}
}
sort(gs.begin(),gs.end());
gs.erase(unique(gs.begin(),gs.end()),gs.end());
ll gc = gs.size();
vector<vector<pair<ll,ll>>> ps(gc);
for(ll i = 1;i<n-1;i++){
for(ll j = 1;j<m-1;j++){
if(!a[i][j]){
ll p = d.g((i)*m+(j));
ll idx = lower_bound(gs.begin(),gs.end(),p)-gs.begin();
ps[idx].push_back({i,j});
}
}
}
ll ans = 0;
for(auto &o : ps){
ll x1 = o[0].first, x2=o[0].first, y1=o[0].second, y2=o[0].second;
for(auto [x,y] : o){
x1 = min(x,x1);
x2 = max(x,x2);
y1 = min(y,y1);
y2 = max(y,y2);
}
ll req = (x2-x1+1)*(y2-y1+1);
if (req==o.size()) ans++;
}
return ans;
}
vector<vector<pair<ll,ll>>> row(n),col(m);
for(ll i = 0;i<n;i++){
vector<pair<ll,ll>> st;
for(ll j = 0;j<m;j++){
while(st.size()&&st.back().first<a[i][j]){
if(j>st.back().second+1)row[i].push_back({st.back().second,j});
st.pop_back();
}
if(st.size()){
if(j>st.back().second+1)row[i].push_back({st.back().second,j});
}
if (st.size()&&st.back().first==a[i][j]) st.pop_back();
st.push_back({a[i][j],j});
}
}
for(ll j = 0;j<m;j++){
vector<pair<ll,ll>> st;
for(ll i = 0;i<n;i++){
while(st.size()&&st.back().first<a[i][j]){
if(i>st.back().second+1)col[j].push_back({st.back().second,i});
st.pop_back();
}
if(st.size()){
if(i>st.back().second+1)col[j].push_back({st.back().second,i});
}
if (st.size()&&st.back().first==a[i][j]) st.pop_back();
st.push_back({a[i][j],i});
}
}
for(auto &o : row) sort(o.begin(),o.end());
for(auto &o : col) sort(o.begin(),o.end());
vector<vector<ll>> down(n,vector<ll>(m,0)),up(n,vector<ll>(m,n));
for(ll i = 0;i<m;i++){
for(auto [l,r] : col[i]){
down[l][i] = r;
up[l][i] = min(up[l][i],r);
}
}
segtree tree(0,m*m);
for(ll i = 0;i<n;i++){
tree.nw();
for(auto [l,r] : row[i]){
ll idx = l*m+r;
tree.add(i+1,idx,1);
}
}
lll ans = 0;
for(ll r1 = 1;r1<n-1;r1++){
vector<pair<ll,ll>> cur;
vector<pair<ll,ll>> nw;
BIT t(m);
vector<vector<pair<ll,ll>>> ops(n);
BIT t0(m);
vector<vector<pair<ll,ll>>> ops0(n);
BIT t1(m);
vector<vector<pair<ll,ll>>> ops1(n);
vector<vector<pair<ll,ll>>> nws(n);
mxt mt(m);
if (1||sub6) for(ll i = 0;i<m;i++) {
mt.mod(1,0,m-1,i,max(up[r1-1][i]-1,r1));
ops[max(up[r1-1][i]-1,r1)].push_back({i+1,1});
ops[down[r1-1][i]].push_back({i+1,-1});
ops1[r1].push_back({i+1,1});
ops1[down[r1-1][i]].push_back({i+1,-1});
auto itl = lower_bound(col[i].begin(),col[i].end(),make_pair(r1-1,r1+1));
auto itr = lower_bound(col[i].begin(),col[i].end(),make_pair(r1,0));
for(auto it = itl;it!=itr;it++){
ll r = (*it).second;
ops0[r-1].push_back({i+1,1});
ops0[r].push_back({i+1,-1});
}
}
for(auto &o : row[r1]){
ll g = mt.qry(1,0,m-1,o.first+1,o.second-1);
nws[g].push_back(o);
//cerr << r1 << " " << g << " " << o.first << " " << o.second << "\n";
}
for(ll r2 = r1;r2<n-1;r2++){
if (1||sub6) for(auto [i,v] : ops[r2]){
t.add(i,v);
}
if (1||sub6) for(auto [i,v] : ops0[r2]){
t0.add(i,v);
}
if (1||sub6) for(auto [i,v] : ops1[r2]){
t1.add(i,v);
}
//cerr << "r2=" << r2 << " has " << nws[r2].size() <<"\n";
if (1||sub6) for(auto o: nws[r2]){
ll idx = o.first*m+o.second;
ll cnt = tree.qry(r2,idx)-tree.qry(r1,idx);
if(cnt>=r2-r1)cur.push_back(o);
//cerr << "add " << o.first << " " << o.second << "\n";
}
if(r2>r1){
for(auto &o : cur){
if (t1.get(o.second)-t1.get(o.first+1)==(o.second-o.first-1)&&binary_search(row[r2].begin(),row[r2].end(),o)){
nw.push_back(o);
}
}
nw.swap(cur);
nw.clear();
}
if (1||sub6){
for(auto &o : cur){
if (t.get(o.second)-t.get(o.first+1)==(o.second-o.first-1)&&
t0.get(o.second)-t0.get(o.first+1)==(o.second-o.first-1)) ans++;
}
}else{
pair<ll,ll> t = {r1-1,r2+1};
vector<ll> ok(m,0);
for(ll i = 0;i<m;i++) ok[i] = down[r1-1][i]>r2&&up[r1-1][i]-1<=r2&&binary_search(col[i].begin(),col[i].end(),t);
vector<ll> p(m+1,0);
for(ll i = 0;i<m;i++) p[i+1] = p[i]+ok[i];
for(auto &o : cur){
if (p[o.second]-p[o.first+1]==(o.second-o.first-1)) ans++;
}
}
}
}
return ans;
}
