#include "rect.h"
#include <stdio.h>
#include <vector>
#include <queue>
#include <algorithm>
#include <iostream>
#include <string>
#include <bitset>
#include <map>
#include <set>
#include <tuple>
#include <string.h>
#include <math.h>
#include <random>
#include <functional>
#include <assert.h>
#include <math.h>
#include <stack>
#define all(x) (x).begin(), (x).end()
#define xx first
#define yy second
using namespace std;
using i64 = long long int;
using ii = pair<int, int>;
using ii64 = pair<i64, i64>;
int up[2505][2505];
int down[2505][2505];
bool visited[2505][2505];
int dx[] = { -1, 0, 1, 0 };
int dy[] = { 0, -1, 0, 1 };
i64 sub6(vector<vector<int>> a)
{
int n = a.size();
int m = a[0].size();
i64 ans = 0;
for (int x = 1; x < n - 1; x++)
{
for (int y = 1; y < m - 1; y++)
{
if (visited[x][y] || a[x][y] == 1)
continue;
int lx = x, ly = y, rx = x, ry = y;
int c = 0;
queue<ii> q;
q.emplace(x, y);
visited[x][y] = true;
while (!q.empty())
{
auto now = q.front();
q.pop();
lx = min(now.xx, lx);
ly = min(now.yy, ly);
rx = max(now.xx, rx);
ry = max(now.yy, ry);
c++;
for (int i = 0; i < 4; i++)
{
int nx = now.xx + dx[i];
int ny = now.yy + dy[i];
if (nx == 0 || nx == n - 1 || ny == 0 || ny == m - 1 || visited[nx][ny] || a[nx][ny] == 1)
continue;
visited[nx][ny] = true;
q.emplace(nx, ny);
}
}
bool ok = true;
if (c != (rx - lx + 1) * (ry - ly + 1))
ok = false;
for (int i = ly; i <= ry; i++)
if (a[lx - 1][i] != 1 || a[rx + 1][i] != 1)
ok = false;
for (int i = lx; i <= rx; i++)
if (a[i][ly - 1] != 1 || a[i][ry + 1] != 1)
ok = false;
if (ok)
ans++;
}
}
return ans;
}
i64 count_rectangles(vector<vector<int>> a)
{
int n = a.size();
int m = a[0].size();
i64 ans = 0;
int amax = 0;
for (int x = 0; x < n; x++)
{
for (int y = 0; y < m; y++)
{
amax = max(amax, a[x][y]);
int yu = y - 1;
int yd = y + 1;
while (yd < m && a[x][yd] < a[x][y])
yd++;
while (yu >= 0 && a[x][yu] < a[x][y])
yu--;
down[x][y] = yd - y - 1;
up[x][y] = y - yu - 1;
}
}
if (amax == 1)
return sub6(a);
for (int l = 0; l < n - 2; l++)
{
vector<int> dnow(m, 987654321);
vector<int> unow(m, 987654321);
vector<int> maxv(m, 0); // 좌우에서 y별 최댓값값
for (int r = l + 2; r < n; r++)
{
vector<int> newup(m + 1, 0);
vector<int> newdown(m + 1, 0);
vector<int> delup(m + 1, 0);
vector<int> deldown(m + 1, 0);
vector<int> lrup(m + 1, 0);
vector<int> lrdown(m + 1, 0);
vector<bool> lr(m, 0); // l - r은 가능한지
vector<int> depth(m + 1, 0);
for (int y = 0; y < m; y++)
{
dnow[y] = min(dnow[y], down[r - 1][y]);
unow[y] = min(unow[y], up[r - 1][y]);
maxv[y] = max(maxv[y], a[r - 1][y]);
lr[y] = maxv[y] < a[l][y] && maxv[y] < a[r][y];
}
int lru = 0, lrd = 0;
vector<int> dval(m + 1, 0);
vector<int> uval(m + 1, 0);
for (int y = 0; y < m; y++)
{
uval[y] = min(unow[y], lru);
if (lr[y])
lru++;
else
lru = 0;
}
for (int y = m - 1; y >= 0; y--)
{
dval[y] = min(dnow[y], lrd);
if (lr[y])
lrd++;
else
lrd = 0;
}
for (int y = 0; y < m; y++)
{
if (uval[y] >= 1)
{
newup[y - uval[y]]++;
delup[y - 1]++;
}
if (dval[y] >= 1)
{
newdown[y + 1]++;
deldown[y + dval[y]]++;
}
}
int d = 0;
for (int y = 0; y < m; y++)
{
d += newup[y];
d -= delup[y];
depth[y] = d;
}
// (ypos, minvalue)
stack<ii> s;
for (int y = 1; y < m; y++)
{
for (int j = 0; j < newdown[y]; j++)
s.emplace(y, 987654321);
if (!s.empty())
{
s.top().yy = min(s.top().yy, depth[y]);
}
for (int j = 0; j < deldown[y]; j++)
{
ii top = s.top();
int f = depth[top.xx - 1] + newup[top.xx];
ans += f - top.yy;
s.pop();
if (!s.empty())
s.top().yy = min(s.top().yy, top.yy);
}
}
}
}
return ans;
}
