#include "rect.h"
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
using namespace std;
typedef long long ll;
const int N = 2500 + 3;
vector<vector<int>> a;
int n, m;
short u[N][N], d[N][N], l[N][N], r[N][N];
struct n_Min_Segment_Tree{
static constexpr short DEFAULT_VALUE = SHRT_MAX;
short t[4 * N];
int merge(short l, short r){
return (l < r) ? l : r;
}
void init(short arr[], int i = 0, int l = 0, int r = n - 1){
if(l == r){
t[i] = arr[l];
return;
}
int mid = (l + r) >> 1;
init(arr, 2 * i + 1, l, mid);
init(arr, 2 * i + 2, mid + 1, r);
t[i] = merge(t[2 * i + 1], t[2 * i + 2]);
}
int query(int sl, int sr, int i = 0, int l = 0, int r = n - 1){
if(sr < l || r < sl) return DEFAULT_VALUE;
if(sl <= l && r <= sr) return t[i];
int mid = (l + r) >> 1;
return merge(query(sl, sr, 2 * i + 1, l, mid), query(sl, sr, 2 * i + 2, mid + 1, r));
}
};
struct m_Min_Segment_Tree{
static constexpr short DEFAULT_VALUE = SHRT_MAX;
short t[4 * N];
int merge(short l, short r){
return (l < r) ? l : r;
}
void init(short arr[], int i = 0, int l = 0, int r = m - 1){
if(l == r){
t[i] = arr[l];
return;
}
int mid = (l + r) >> 1;
init(arr, 2 * i + 1, l, mid);
init(arr, 2 * i + 2, mid + 1, r);
t[i] = merge(t[2 * i + 1], t[2 * i + 2]);
}
int query(int sl, int sr, int i = 0, int l = 0, int r = m - 1){
if(sr < l || r < sl) return DEFAULT_VALUE;
if(sl <= l && r <= sr) return t[i];
int mid = (l + r) >> 1;
return merge(query(sl, sr, 2 * i + 1, l, mid), query(sl, sr, 2 * i + 2, mid + 1, r));
}
};
struct m_Max_Segment_Tree{
static constexpr short DEFAULT_VALUE = SHRT_MIN;
short t[4 * N];
int merge(short l, short r){
return (l > r) ? l : r;
}
void init(short arr[], int i = 0, int l = 0, int r = m - 1){
if(l == r){
t[i] = arr[l];
return;
}
int mid = (l + r) >> 1;
init(arr, 2 * i + 1, l, mid);
init(arr, 2 * i + 2, mid + 1, r);
t[i] = merge(t[2 * i + 1], t[2 * i + 2]);
}
int query(int sl, int sr, int i = 0, int l = 0, int r = m - 1){
if(sr < l || r < sl) return DEFAULT_VALUE;
if(sl <= l && r <= sr) return t[i];
int mid = (l + r) >> 1;
return merge(query(sl, sr, 2 * i + 1, l, mid), query(sl, sr, 2 * i + 2, mid + 1, r));
}
};
struct n_Max_Segment_Tree{
static constexpr short DEFAULT_VALUE = SHRT_MIN;
short t[4 * N];
int merge(short l, short r){
return (l > r) ? l : r;
}
void init(short arr[], int i = 0, int l = 0, int r = m - 1){
if(l == r){
t[i] = arr[l];
return;
}
int mid = (l + r) >> 1;
init(arr, 2 * i + 1, l, mid);
init(arr, 2 * i + 2, mid + 1, r);
t[i] = merge(t[2 * i + 1], t[2 * i + 2]);
}
int query(int sl, int sr, int i = 0, int l = 0, int r = m - 1){
if(sr < l || r < sl) return DEFAULT_VALUE;
if(sl <= l && r <= sr) return t[i];
int mid = (l + r) >> 1;
return merge(query(sl, sr, 2 * i + 1, l, mid), query(sl, sr, 2 * i + 2, mid + 1, r));
}
};
m_Min_Segment_Tree u_st[N];
n_Min_Segment_Tree l_st[N];
m_Max_Segment_Tree d_st[N];
n_Max_Segment_Tree r_st[N];
void init(){
stack<int> st;
for(int j = 0; j < m; ++j){
for(int i = 0; i < n; ++i){
while(!st.empty() && a[i][j] > a[st.top()][j]){
d[st.top()][j] = i;
st.pop();
}
st.push(i);
}
while(!st.empty()){
d[st.top()][j] = n;
st.pop();
}
for(int i = n - 1; i >= 0; --i){
while(!st.empty() && a[i][j] > a[st.top()][j]){
u[st.top()][j] = i;
st.pop();
}
st.push(i);
}
while(!st.empty()){
u[st.top()][j] = -1;
st.pop();
}
}
for(int i = 0; i < n; ++i){
for(int j = 0; j < m; ++j){
while(!st.empty() && a[i][j] > a[i][st.top()]){
r[i][st.top()] = j;
st.pop();
}
st.push(j);
}
while(!st.empty()){
r[i][st.top()] = m;
st.pop();
}
for(int j = m - 1; j >= 0; --j){
while(!st.empty() && a[i][j] > a[i][st.top()]){
l[i][st.top()] = j;
st.pop();
}
st.push(j);
}
while(!st.empty()){
l[i][st.top()] = -1;
st.pop();
}
}
}
bool check(int x1, int y1, int x2, int y2){
return u_st[x2 + 1].query(y1, y2) <= x1 - 1 && d_st[x1 - 1].query(y1, y2) >= x2 + 1 && l_st[y2 + 1].query(x1, x2) <= y1 - 1 && r_st[y1 - 1].query(x1, x2) >= y2 + 1;
}
long long count_rectangles(vector<vector<int>> _a) {
swap(a, _a);
n = a.size(), m = a[0].size();
init();
for(int i = 0; i < n; ++i){
u_st[i].init(u[i]);
d_st[i].init(d[i]);
}
static short tmp[N];
for(int j = 0; j < m; ++j){
for(int i = 0; i < n; ++i)
tmp[i] = r[i][j];
r_st[j].init(tmp);
for(int i = 0; i < n; ++i)
tmp[i] = l[i][j];
l_st[j].init(tmp);
}
ll ans = 0;
vector<array<int, 4>> v;
for(int x = 1; x < n - 1; ++x)
for(int y = 1; y < m - 1; ++y)
v.push_back({u[x][y] + 1, l[x][y] + 1, d[x][y] - 1, r[x][y] - 1});
sort(v.begin(), v.end());
v.resize(unique(v.begin(), v.end()) - v.begin());
for(auto [x1, y1, x2, y2]: v){
if(x1 <= 0 || y1 <= 0 || x2 >= n - 1 || y2 >= m - 1) continue;
//cout << x1 << " " << y1 << " " << x2 << " " << y2 << endl;
ans += check(x1, y1, x2, y2);
}
return ans;
}
