#include "rect.h"
#include <bits/stdc++.h>
#define all(x) (x).begin(), (x).end()
#define ff first
#define ss second
#define pb push_back
#define mp make_pair
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<ll, ll> pll;
typedef pair<ull, ull> pull;
typedef pair<int, int> pii;
typedef pair<ld, ld> pld;
int bit[2509][2509];
int bitsz;
void upd(int x, int y, int val){
for(int i1 = x+1; i1 > 0; i1 -= i1&(-i1))
for(int i2 = y+1; i2 <= bitsz; i2 += i2&(-i2))
bit[i1][i2] += val;
}
int get(int x, int y){
int ret = 0;
for(int i1 = x+1; i1 <= bitsz; i1 += i1&(-i1))
for(int i2 = y+1; i2 > 0; i2 -= i2&(-i2))
ret += bit[i1][i2];
return ret;
}
ll pickdouble(int n){
return ll(n)*(n+1)/2;
}
long long count_rectangles(std::vector<std::vector<int> > a) {
int n = a.size(), m = a[0].size();
bitsz = max(n, m);
for(int i = 1; i <= bitsz; ++i)
for(int j = 1; j <= bitsz; ++j)
bit[i][j] = 0;
vector<vector<pair<pii, int>>> pos(n);
for(int i = 0; i < n; ++i){
vector<int> cur;
for(int j = m-1; j >= 0; --j){
while(cur.size() && a[i][cur.back()] < a[i][j]){
pos[i].pb({{j, cur.back()}, 0});
cur.pop_back();
}
if(cur.size())
pos[i].pb({{j, cur.back()}, 0});
while(cur.size() && a[i][cur.back()] <= a[i][j])
cur.pop_back();
cur.pb(j);
}
sort(all(pos[i]));
}
vector<vector<pair<pii, int>>> maxval(m);
for(int i = 0; i < n; ++i)
for(auto u : pos[i]){
if(u.ss) continue;
int j;
for(j = i+1; j < n; ++j){
auto it = lower_bound(all(pos[j]), u);
if(it == pos[j].end() || *it != u)
break;
it->ss = 1;
}
--j;
if(u.ff.ss-u.ff.ff > 1)
maxval[u.ff.ff].pb({{i, j}, u.ff.ss});
//cout << u.ff << ' ' << u.ss << ' ' << i << ' ' << j << '\n';
}
pos = vector<vector<pair<pii, int>>>(m);
for(int i = 0; i < m; ++i){
vector<int> cur;
for(int j = n-1; j >= 0; --j){
while(cur.size() && a[cur.back()][i] < a[j][i]){
pos[i].pb({{j, cur.back()}, 0});
cur.pop_back();
}
if(cur.size())
pos[i].pb({{j, cur.back()}, 0});
while(cur.size() && a[cur.back()][i] <= a[j][i])
cur.pop_back();
cur.pb(j);
}
sort(all(pos[i]));
}
vector<vector<pair<pii, int>>> fin(m);
for(int i = 0; i < m; ++i)
for(auto u : pos[i]){
if(u.ss) continue;
int j;
for(j = i+1; j < m; ++j){
auto it = lower_bound(all(pos[j]), u);
if(it == pos[j].end() || *it != u)
break;
it->ss = 1;
}
--j;
if(u.ff.ss-u.ff.ff > 1)
for(int k = i; k <= j; ++k)
fin[k].pb({{u.ff.ff, u.ff.ss}, j});
}
ll ans = 0;
for(int i = 1; i < m; ++i){
sort(all(fin[i]));
int curidx = 0;
for(auto u : fin[i]){
while(curidx < (int)maxval[i-1].size() && maxval[i-1][curidx].ff.ff <= u.ff.ff+1){
upd(maxval[i-1][curidx].ff.ss, maxval[i-1][curidx].ss, 1);
++curidx;
}
int val = get(u.ff.ss-1, u.ss+1);
//cout << i << ' ' << u.ss << ' ' << u.ff.ff << ' ' << u.ff.ss << ' ' << val << '\n';
ans += val;
}
for(int j = 0; j < curidx; ++j)
upd(maxval[i-1][j].ff.ss, maxval[i-1][j].ss, -1);
}
return ans;
}
