This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include "rect.h"
#include "bits/stdc++.h"
using namespace std;
#define FAST ios_base::sync_with_stdio(false); cin.tie(0);
#define pb push_back
#define eb emplace_back
#define ins insert
#define f first
#define s second
#define cbr cerr<<"hi\n"
#define mmst(x, v) memset((x), v, sizeof ((x)))
#define siz(x) ll(x.size())
#define all(x) (x).begin(), (x).end()
#define lbd(x,y) (lower_bound(all(x),y)-x.begin())
#define ubd(x,y) (upper_bound(all(x),y)-x.begin())
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); //can be used by calling rng() or shuffle(A, A+n, rng)
inline long long rand(long long x, long long y) { return rng() % (y+1-x) + x; } //inclusivesss
string inline to_string(char c) {string s(1,c);return s;} template<typename T> inline T gcd(T a,T b){ return a==0?llabs(b):gcd(b%a,a); }
using ll=long long;
using ld=long double;
#define FOR(i,s,e) for(ll i=s;i<=ll(e);++i)
#define DEC(i,s,e) for(ll i=s;i>=ll(e);--i)
using pi=pair<ll,ll>; using spi=pair<ll,pi>; using dpi=pair<pi,pi>;
#define LLINF ((long long)1e18)
#define INF int(1e9+1e6)
#define MAXN (2502)
ll n, m, ans;
vector<pair<int,int>> row[MAXN][MAXN], col[MAXN][MAXN];
vector<int> r[MAXN][MAXN], c[MAXN][MAXN];
vector<dpi> e;
long long count_rectangles(std::vector<std::vector<int>> A) {
n = siz(A), m=siz(A[0]);
FOR(i,0,n-1){
vector<int> v;
DEC(j,m-1,0){
reverse(all(v));
for(auto k:v) { if(abs(k-j)>1) e.pb({{i,j},{i,k}}); if(A[i][k]>=A[i][j]) break; }
reverse(all(v));
while(v.size()&&A[i][v.back()]<=A[i][j])v.pop_back();
v.eb(j);
}
}
FOR(j,0,m-1){
vector<int> v;
FOR(i,0,n-1){
reverse(all(v));
for(auto k:v) { if(abs(k-i)>1) e.pb({{k,j},{i,j}}); if(A[k][j]>=A[i][j]) break; }
reverse(all(v));
while(v.size()&&A[v.back()][j]<=A[i][j])v.pop_back();
v.eb(i);
}
}
vector<ll> len(siz(e), 0);
ll ind=0;
for(auto i:e)if(i.f.f==i.s.f){
col[i.f.s][i.s.s].eb(i.f.f, ind++);
}else{
assert(i.f.s==i.s.s);
row[i.f.f][i.s.f].eb(i.f.s, ind++);
}
FOR(i,0,siz(e)-1){
if(e[i].f.s==e[i].s.s) r[e[i].f.f][e[i].f.s].eb(i);
else c[e[i].f.f][e[i].f.s].eb(i);
}
FOR(i,0,n-1)FOR(j,0,n-1){
FOR(k,0,siz(row[i][j])-1){
if(k == 0 || row[i][j][k-1].f-1 != row[i][j][k].f) len[row[i][j][k].s]=1;
else len[row[i][j][k].s]=len[row[i][j][k-1].s]+1;
}
}
FOR(i,0,m-1)FOR(j,0,m-1){
FOR(k,0,siz(col[i][j])-1){
if(k == 0 || col[i][j][k-1].f-1 != col[i][j][k].f) len[col[i][j][k].s]=1;
else len[col[i][j][k].s]=len[col[i][j][k-1].s]+1;
}
}
FOR(i,0,n-2)FOR(j,1,m-2){
for(auto i1:r[i][j]){
for(auto i2:c[i+1][j-1]){
if(len[i2]>=e[i1].s.f-i-1&&len[i1]>=e[i2].s.s-(j-1)-1)++ ans;
}
}
}
return ans;
}
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