#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse4,popcnt,abm,mmx,tune=native")
#include <bits/stdc++.h>
//using namespace std;
#define INT_INF 0x3f3f3f3f
#define mp std::make_pair
#define MAXN 2001
typedef long long ll;
typedef std::pair<int,int> pii;
int num_rows,num_cols,arr[MAXN][MAXN],bit[MAXN],cnt[MAXN][MAXN],ans,l,r,lst[MAXN],pp;
std::vector<pii> row_dp[MAXN][MAXN],col_dp[MAXN][MAXN];
std::vector<std::pair<pii,int>> dep[MAXN];
pii dq[MAXN];
inline void update(int i, int val, int curr){
for(; i<=num_cols; i+=i&-i){
if(lst[i] != curr) bit[i] = val, lst[i] = curr;
else bit[i]+=val;
}
}
inline int query(int i, int curr){
int res = 0;
for(; i>0; i-=i&-i)
if(lst[i] == curr)
res+=bit[i];
return res;
}
inline void init_rows(){
// memset(cnt,0,sizeof cnt);
for(int i=2; i<num_rows; i++){
l = 1, r = 0;
for(int k=1; k<=num_cols; k++){
while(r-l+1 > 0 && dq[r].first < arr[i][k]) r--;
int lft = (r-l+1>0?dq[r].second:INT_INF);
if(lft < k-1 && (row_dp[lft+1][k-1].empty() || row_dp[lft+1][k-1].back().first != i))
row_dp[lft+1][k-1].emplace_back(i,i), cnt[lft+1][k-1]++; //rows[i].pb(mp(lft+1,k-1));
while(r-l+1 > 0 && dq[r].first == arr[i][k]) r--;
dq[++r] = mp(arr[i][k],k);
}
l = 1, r = 0;
for(int k=num_cols; k>=1; k--){
while(r-l+1 > 0 && dq[r].first < arr[i][k]) r--;
int rgt = (r-l+1>0?dq[r].second:-INT_INF);
if(rgt > k+1 && (row_dp[k+1][rgt-1].empty() || row_dp[k+1][rgt-1].back().first != i))
row_dp[k+1][rgt-1].emplace_back(i,i), cnt[k+1][rgt-1]++; //rows[i].pb(mp(k+1,rgt-1));
while(r-l+1 > 0 && dq[r].first == arr[i][k]) r--;
dq[++r] = mp(arr[i][k],k);
}
}
}
inline void init_cols(){
memset(cnt,0,sizeof cnt);
for(int i=2; i<num_cols; i++){
l = 1, r = 0;
for(int k=1; k<=num_rows; k++){
while(r-l+1 > 0 && dq[r].first < arr[k][i]) r--;
int lft = (r-l+1>0?dq[r].second:INT_INF);
if(lft < k-1 && (col_dp[lft+1][k-1].empty() || col_dp[lft+1][k-1].back().first != i))
col_dp[lft+1][k-1].emplace_back(i,i), cnt[lft+1][k-1]++; //cols[i].pb(mp(lft+1,k-1));
while(r-l+1 > 0 && dq[r].first == arr[k][i]) r--;
dq[++r] = mp(arr[k][i],k);
}
l = 1, r = 0;
for(int k=num_rows; k>=1; k--){
while(r-l+1 > 0 && dq[r].first < arr[k][i]) r--;
int rgt = (r-l+1>0?dq[r].second:-INT_INF);
if(rgt > k+1 && (col_dp[k+1][rgt-1].empty() || col_dp[k+1][rgt-1].back().first != i))
col_dp[k+1][rgt-1].emplace_back(i,i), cnt[k+1][rgt-1]++; //cols[i].pb(mp(k+1,rgt-1));
while(r-l+1 > 0 && dq[r].first == arr[k][i]) r--;
dq[++r] = mp(arr[k][i],k);
}
}
}
inline void calc_hor_dp(){
// for(int i=2; i<num_rows; i++){
// sort(all(rows[i])); complete_unique(rows[i]);
// for(pii check:rows[i]){
// h_segs[check.first][check.second].pb(i);
//// r_range[i][check.first].pb(check.second);
// }
// rows[i].clear();
// }
for(int l=2; l<=num_cols-1; l++){
for(int r=l; r<=num_cols-1; r++){
if(cnt[l][r] == 0) continue;
#define nums row_dp[l][r]
// std::vector<pii> &nums = row_dp[l][r];
// sort(all(nums)); complete_unique(nums);
// std::vector<pii> t;
int lst = 0;
for(int i=1; i<cnt[l][r]; i++){
if(nums[i].first == nums[i-1].first+1) continue;
for(int k=nums[lst].first; k<=nums[i-1].first; k++)
dep[nums[i-1].first-k+1].emplace_back(mp(k,l),r);
// row_dp[k][l].pb(mp(nums[i-1].first-k+1,r));
lst = i;
}
for(int k=nums[lst].first; k<=nums[cnt[l][r]-1].first; k++)
dep[nums[cnt[l][r]-1].first-k+1].emplace_back(mp(k,l),r);
// row_dp[k][l].pb(mp(nums[cnt[l][r]-1].first-k+1,r));
nums.clear();
}
}
for(int i=1; i<=num_rows; i++){
for(auto &check:dep[i])
row_dp[check.first.first][check.first.second].emplace_back(i,check.second);
}
// for(int l=2; l<=num_cols-1; l++){
// for(int r=l; r<=num_cols-1; r++){
// reverse(all(row_dp[l][r]));
// while(cnt[l][r]--) row_dp[l][r].pop_back();
// reverse(all(row_dp[l][r]));
// }
// }
}
inline void calc_col_dp(){
// for(int i=2; i<num_cols; i++){
// sort(all(cols[i])); complete_unique(cols[i]);
// for(pii check:cols[i]){
// v_segs[check.first][check.second].pb(i);
//// v_range[check.first][i].pb(check.second);
// }
// cols[i].clear();
// }
for(int l=2; l<=num_rows-1; l++){
for(int r=l; r<=num_rows-1; r++){
if(cnt[l][r] == 0) continue;
#define nums col_dp[l][r]
// std::vector<pii> &nums = col_dp[l][r];
// sort(all(nums)); complete_unique(nums);
int lst = 0;
for(int i=1; i<cnt[l][r]; i++){
if(nums[i].first == nums[i-1].first+1) continue;
for(int k=nums[lst].first; k<=nums[i-1].first; k++)
col_dp[l][k].emplace_back(r,nums[i-1].first);
lst = i;
}
for(int k=nums[lst].first; k<=nums[cnt[l][r]-1].first; k++)
col_dp[l][k].emplace_back(r,nums[cnt[l][r]-1].first);
}
}
// for(int l=2; l<=num_cols-1; l++){
// for(int r=l; r<=num_cols-1; r++){
// reverse(all(col_dp[l][r]));
// while(cnt[l][r]--) col_dp[l][r].pop_back();
// reverse(all(col_dp[l][r]));
// }
// }
}
ll count_rectangles(std::vector<std::vector<int>> a){
ans = 0, num_rows = (int)a.size(), num_cols = (int)a[0].size();
for(int i=0; i<a.size(); i++)
for(int k=0; k<a[i].size(); k++)
arr[i+1][k+1] = a[i][k];
init_rows(); calc_hor_dp();
init_cols(); calc_col_dp();
for(int i=num_rows-1; i>=2; i--){
for(int k=num_cols-1; k>=2; k--){
// sort(all(row_dp[i][k]));
// sort(all(col_dp[i][k]));
int ptr = cnt[i][k], res = 0, cc = 0; ++pp;
for(int v=0; v<row_dp[i][k].size(); v++){
// pii curr = row_dp[i][k][v];
while(ptr < col_dp[i][k].size() && col_dp[i][k][ptr].first-i+1 <= row_dp[i][k][v].first){
// assert(col_dp[i][k][ptr].second>=k);
update(col_dp[i][k][ptr].second-k+1,1,pp);
ptr++, cc++;
}
res+=cc-query(row_dp[i][k][v].second-k,pp);
}
// while(--ptr >= cnt[i][k]) update(col_dp[i][k][ptr].second-k+1,-1);
ans+=res;
}
}
return ans;
}
