#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
#define int long long
const int MX = 7e6 + 5;
struct BIT
{
int n;
vector<int> ft;
void init(int N)
{
n = N + 5;
ft.assign(n + 5, 0);
}
void add(int pos, int val)
{
for (pos = pos + 1; pos <= n; pos += pos & -pos) ft[pos] += val;
}
int get(int pos, int res = 0)
{
for (pos = pos + 1; pos > 0; pos -= pos & -pos) res += ft[pos];
return res;
}
};
vector<array<int, 2>> ind[MX];
long long count_rectangles(vector<vector<int32_t>> a)
{
int n = a.size(), m = a[0].size();
set<int> r[n], c[m];
vector<int> v;
for (int i = 0; i < n; i++)
{
for (int j = 0; j < m; j++)
{
ind[a[i][j]].push_back({i, j});
}
}
for (int i = 0; i < n; i++) r[i].insert(-1), r[i].insert(m);
for (int i = 0; i < m; i++) c[i].insert(-1), c[i].insert(n);
set<array<int, 3>> r1, c1;
for (int i = MX - 1; i >= 0; i--)
{
for (array<int, 2> &x : ind[i])
{
int L = *prev(r[x[0]].lower_bound(x[1])), R = *r[x[0]].lower_bound(x[1]);
if (!(L < 0 || R >= m)) r1.insert({x[0], L + 1, R - 1});
L = *prev(c[x[1]].lower_bound(x[0])), R = *c[x[1]].lower_bound(x[0]);
if (!(L < 0 || R >= n)) c1.insert({x[1], L + 1, R - 1});
}
for (array<int, 2> &x : ind[i])
{
r[x[0]].insert(x[1]);
c[x[1]].insert(x[0]);
}
}
BIT ft;
ft.init(max(n, m));
vector<int> addR[n][m], addC[n][m];
for (array<int, 3> i : r1) addR[i[0]][i[2]].push_back(i[1]);
for (array<int, 3> i : c1) addC[i[2]][i[0]].push_back(i[1]);
int res = 0;
map<array<int, 2>, int> mpC, nwC, mpR, nwR;
vector<array<int, 2>> v1, v2;
for (int j = 0; j < m; j++)
{
nwC.clear();
for (int i = 0; i < n; i++)
{
nwR.clear(), v1.clear(), v2.clear();
for (int &x : addR[i][j])
{
int x1 = j - x + 1, y1 = (mpR.find({x, j}) != mpR.end() ? mpR[{x, j}] : 0) + 1;
v1.push_back({x1, y1});
}
for (int &y : addC[i][j])
{
int x2 = i - y + 1, y2 = (mpC.find({y, i}) != mpC.end() ? mpC[{y, i}] : 0) + 1;
v2.push_back({x2, y2});
}
sort(v1.begin(), v1.end(), [&](const array<int, 2> &x, const array<int, 2> &y)
{
return x[1] < y[1];
});
sort(v2.begin(), v2.end(), [&](const array<int, 2> &x, const array<int, 2> &y)
{
return x[0] < y[0];
});
int y = 0;
for (int x = 0; x < v1.size(); x++)
{
while (y < v2.size() && v1[x][1] >= v2[y][0])
{
ft.add(v2[y][1], 1);
y++;
}
res += ft.get(max(n, m)) - ft.get(v1[x][0] - 1);
}
for (int x = 0; x < y; x++) ft.add(v2[x][1], -1);
for (int &x : addR[i][j]) nwR[{x, j}] = mpR[{x, j}] + 1;
for (int &y : addC[i][j]) nwC[{y, i}] = mpC[{y, i}] + 1;
mpR = nwR;
}
mpC = nwC;
}
return res;
}
