#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
using LL = long long;
#define UP 0
#define LEFT 1
#define DOWN 2
#define RIGHT 3
vector<int> next_geq_val(vector<int> v) {
int n = v.size();
stack<pair<int, int>> st;
st.push({1e9, n});
vector<int> ans(n);
for (int i = n-1; i >= 0; --i) {
while (st.top().first < v[i]) st.pop();
ans[i] = st.top().second;
st.push({v[i], i});
}
return ans;
}
vector<int> prev_geq_val(vector<int> v) {
int n = v.size();
reverse(v.begin(), v.end());
auto r = next_geq_val(v);
reverse(r.begin(), r.end());
for (int& i : r) {
i = n - 1 - i;
}
return r;
}
int n, m;
/**/
constexpr int INF = 1e9;
const vector<array<int, 2>> dd{{0,1},{0,-1},{1,0},{-1,0}};
struct comp {
int sz;
array<int, 4> ext;
comp() : sz(0), ext({INF, INF, -INF, -INF}) {}
comp(int i, int j) : sz(1), ext({i,j,i,j}) {}
bool good() {
if (ext[UP] == 0 || ext[DOWN] == n-1) return false;
if (ext[LEFT] == 0 || ext[RIGHT] == m-1) return false;
return sz == (ext[DOWN] - ext[UP] + 1) * (ext[RIGHT] - ext[LEFT] + 1);
}
};
comp join(const comp& a, const comp& b) {
comp ans;
ans.sz = a.sz + b.sz;
ans.ext[UP] = min(a.ext[UP], b.ext[UP]);
ans.ext[LEFT] = min(a.ext[LEFT], b.ext[LEFT]);
ans.ext[DOWN] = max(a.ext[DOWN], b.ext[DOWN]);
ans.ext[RIGHT] = max(a.ext[RIGHT], b.ext[RIGHT]);
return ans;
}
/**/
LL count_rectangles(vector<vector<int>> a) {
n = a.size();
m = a[0].size();
int mx = 0;
for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) {
mx = max(mx, a[i][j]);
}
if (mx <= 1) {
/**/
LL ans = 0;
vector<vector<bool>> vis(n, vector<bool>(m, false));
for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) {
if (vis[i][j] || a[i][j] == 1) continue;
comp cur(i, j);
queue<array<int, 2>> Q;
Q.push({i, j});
vis[i][j] = true;
while (!Q.empty()) {
auto [x, y] = Q.front();
Q.pop();
for (auto [dx, dy] : dd) {
int nx = x + dx;
int ny = y + dy;
if (nx < 0 || nx >= n || ny < 0 || ny >= m) continue;
if (vis[nx][ny] || a[nx][ny] == 1) continue;
vis[nx][ny] = true;
Q.push({nx, ny});
cur = join(cur, comp(nx, ny));
}
}
ans += cur.good();
}
return ans;
/**/
}
vector<vector<array<int, 4>>> ext(n, vector<array<int, 4>>(m));
// LEFT & RIGHT
for (int i = 0; i < n; ++i) {
auto v = a[i];
auto nxt = next_geq_val(v);
auto prv = prev_geq_val(v);
for (int j = 0; j < m; ++j) {
ext[i][j][LEFT] = prv[j];
ext[i][j][RIGHT] = nxt[j];
}
}
// UP & DOWN
for (int j = 0; j < m; ++j) {
vector<int> v(n);
for (int i = 0; i < n; ++i) v[i] = a[i][j];
auto nxt = next_geq_val(v);
auto prv = prev_geq_val(v);
for (int i = 0; i < n; ++i) {
ext[i][j][UP] = prv[i];
ext[i][j][DOWN] = nxt[i];
}
}
LL ans = 0;
for (int r = 0; r < n; ++r) for (int c = 0; c < m; ++c) {
int rwall = m-1;
for (int rr = r+2; rr < n; ++rr) {
rwall = min(rwall, ext[rr-1][c][RIGHT]);
int dwall = n-1;
for (int cc = c+2; cc <= rwall; ++cc) {
dwall = min(dwall, ext[r][cc-1][DOWN]);
if (rr > dwall) break;
bool works = true;
// orizzontali
for (int j = c+1; works && j < cc; ++j) {
// works &= (ext[r][j][DOWN] >= rr);
works &= (ext[rr][j][UP] <= r);
}
// verticali
for (int i = r+1; works && i < rr; ++i) {
// works &= (ext[i][c][RIGHT] >= cc);
works &= (ext[i][cc][LEFT] <= c);
}
ans += works;
}
}
}
return ans;
}
