#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
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;
}
/**/
void print(comp a) {
cerr << "sz: " << a.sz << " ; ";
cerr << "ext: ";
for (int i = 0; i < 4; ++i) cerr << a.ext[i] << " ";
cerr << "\n";
}
vector<int> p;
vector<comp> cc;
int findset(int v) {
return (v == -1 || p[v] == v) ? v : p[v] = findset(p[v]);
}
bool unionset(int a, int b) {
a = findset(a);
b = findset(b);
if (a == b || a == -1 || b == -1) return false;
if (cc[a].sz < cc[b].sz) swap(a, b);
p[b] = a;
// cerr << "union (" << a/m << "," << a%m << "), (" << b/m << "," << b%m << ")\n";
cc[a] = join(cc[a], cc[b]);
return true;
}
LL count_rectangles(vector<vector<int>> a) {
n = a.size();
m = a[0].size();
p.assign(n*m, -1);
cc.resize(n*m);
int mx = 0;
for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) {
mx = max(mx, a[i][j]);
}
vector<vector<array<int, 2>>> v(mx + 1);
for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) {
v[a[i][j]].push_back({i, j});
}
vector<int> last_time(n*m, -1);
auto add_tile = [&](int i, int j) -> void {
int id = m*i + j;
p[id] = id;
cc[id] = comp(i, j);
for (auto [dx, dy] : dd) {
int nx = i + dx;
int ny = j + dy;
if (0 > nx || nx >= n || 0 > ny || ny >= m) continue;
unionset(m*i+j, m*nx+ny);
}
};
LL ans = 0;
for (int i = 0; i <= mx; ++i) {
for (auto [x, y] : v[i]) {
add_tile(x, y);
}
for (auto [x, y] : v[i]) {
int id = findset(m*x + y);
if (last_time[id] != i) {
last_time[id] = i;
ans += cc[id].good();
if (cc[id].good()) {
print(cc[id]);
}
}
}
}
return ans;
#if 0
if (mx <= 1) {
/**/
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;
#endif
}
