#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
#define ff first
#define ss second
#define pb push_back
#define all(a) (a).begin(), (a).end()
#define replr(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define reprl(i, a, b) for (int i = int(a); i >= int(b); --i)
#define rep(i, n) for (int i = 0; i < int(n); ++i)
#define mkp(a, b) make_pair(a, b)
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> PII;
typedef vector<int> VI;
typedef vector<PII> VPI;
typedef vector<VI> VVI;
typedef vector<VVI> VVVI;
typedef vector<VPI> VVPI;
typedef pair<ll, ll> PLL;
typedef vector<ll> VL;
typedef vector<PLL> VPL;
typedef vector<VL> VVL;
typedef vector<VVL> VVVL;
typedef vector<VPL> VVPL;
template<class T> T setmax(T& a, T b) {if (a < b) return a = b; return a;}
template<class T> T setmin(T& a, T b) {if (a < b) return a; return a = b;}
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
template<class T>
using indset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#include "rect.h"
namespace TEST1 {
int lg[3001];
struct SPARSETABLE {
VVI table;
SPARSETABLE(){};
SPARSETABLE(VI a) {
int n = a.size();
table = VVI(n, VI(14));
reprl(i, n-1, 0) {
table[i][0] = a[i];
for (int j = 1; i+(1<<(j-1)) < n; j++) {
table[i][j] = max(table[i][j-1], table[i + (1<<(j-1))][j-1]);
}
}
}
int get(int l, int r) {
int s = lg[r - l + 1];
return max(table[l][s], table[r-(1<<s)+1][s]);
}
};
ll count_rectangles(VVI a) {
lg[1] = 0; replr(i, 2, 3000) lg[i] = lg[i/2]+1;
int n = a.size();
int m = a[0].size();
vector<SPARSETABLE> rows(n);
vector<SPARSETABLE> cols(m);
rep(i, n) {
rows[i] = SPARSETABLE(a[i]);
}
rep(j, m) {
VI b;
rep(i, n) b.pb(a[i][j]);
cols[j] = SPARSETABLE(b);
}
ll ans = 0;
replr(r1, 1, n-2) replr(r2, r1, n-2) {
replr(c1, 1, m-2) replr(c2, c1, m-2) {
bool good = true;
replr(i, r1, r2) {
if (rows[i].get(c1, c2) >= min(a[i][c1-1], a[i][c2+1])) {
good = false;
break;
}
}
if (!good) continue;
replr(j, c1, c2) {
if (cols[j].get(r1, r2) >= min(a[r1-1][j], a[r2+1][j])) {
good = false;
break;
}
}
if (!good) continue;
/*cout << r1 << " " << r2 << " " << c1 << " " << c2 << endl;*/
ans++;
}
}
return ans;
}
}
namespace TEST6 {
bool check(VVI a) {
for (VI& vec : a) for (int x : vec) if (x > 1) return false;
return true;
}
int n, m;
int r1, r2, c1, c2;
VPI harevan(int ux, int uy) {
return VPI{{ux-1, uy}, {ux+1, uy}, {ux, uy-1}, {ux, uy+1}};
}
void dfs(int ux, int uy, VVI& a) {
VPI harevan = {{ux-1, uy}, {ux+1, uy}, {ux, uy-1}, {ux, uy+1}};
a[ux][uy] = 2;
setmin(r1, ux);
setmax(r2, ux);
setmin(c1, uy);
setmax(c2, uy);
for (auto[vx, vy] : harevan) {
if (vx < 0 || vx >= n) continue;
if (vy < 0 || vy >= m) continue;
if (a[vx][vy]) continue;
dfs(vx, vy, a);
}
}
void bfs(int sx, int sy, VVI& a) {
queue<PII> q;
q.push({sx, sy});
a[sx][sy] = 2;
while (q.size()) {
auto[ux, uy] = q.front();
q.pop();
setmin(r1, ux);
setmax(r2, ux);
setmin(c1, uy);
setmax(c2, uy);
for (auto[vx, vy] : harevan(ux, uy)) {
if (vx < 0 || vx >= n) continue;
if (vy < 0 || vy >= m) continue;
if (a[vx][vy]) continue;
q.push({vx, vy});
a[vx][vy] = 2;
}
}
}
ll count_rectangles(VVI a) {
n = a.size();
m = a[0].size();
VVI pref(n+1, VI(m+1));
replr(i, 1, n) replr(j, 1, m) {
pref[i][j] = a[i-1][j-1] + pref[i-1][j] + pref[i][j-1] - pref[i-1][j-1];
}
int ans = 0;
rep(i, n) rep(j, m) if (a[i][j] == 0) {
r1 = +2e9;
r2 = -2e9;
c1 = +2e9;
c2 = -2e9;
bfs(i, j, a);
if (r1 == 0 || r2 == n-1 || c1 == 0 || c2 == m-1) continue;
if (pref[r2+1][c2+1] - pref[r1][c2+1] - pref[r2+1][c1] + pref[r1][c1] == 0) {
ans++;
}
}
return ans;
}
}
int gu[3000][3000], gd[3000][3000], gl[3000][3000], gr[3000][3000];
int lu[3000][3000], ru[3000][3000], ul[3000][3000], dl[3000][3000];
bool check(int x1, int x2, int y1, int y2) {
/*cout << endl;*/
/*cout << "STATEMENTS:\n";*/
/*cout << (gu[x2+1][y2] == x1-1 && ul[x2+1][y2] <= y1) << " " << (gd[x1-1][y2] == x2+1 && dl[x1-1][y2] <= y1) << endl;*/
/*cout << (gr[x2][y1-1] == y2+1 && ru[x2][y1-1] <= x1) << " " << (gl[x2][y2+1] == y1-1 && lu[x2][y2+1] <= x1) << endl;*/
/*cout << endl;*/
if ((gu[x2+1][y2] == x1-1 && ul[x2+1][y2] <= y1) || (gd[x1-1][y2] == x2+1 && dl[x1-1][y2] <= y1)); else return false;
if ((gr[x2][y1-1] == y2+1 && ru[x2][y1-1] <= x1) || (gl[x2][y2+1] == y1-1 && lu[x2][y2+1] <= x1)); else return false;
return true;
}
ll count_rectangles(VVI a) {
int n = a.size();
int m = a[0].size();
rep(i, n) {
stack<int> st;
replr(j, 0, m-1) {
while (st.size() && a[i][st.top()] < a[i][j]) st.pop();
gl[i][j] = (st.size() ? st.top() : -1);
st.push(j);
}
st = stack<int>();
reprl(j, m-1, 0) {
while (st.size() && a[i][st.top()] < a[i][j]) st.pop();
gr[i][j] = (st.size() ? st.top() : -1);
st.push(j);
}
}
rep(j, m) {
stack<int> st;
replr(i, 0, n-1) {
while (st.size() && a[st.top()][j] < a[i][j]) st.pop();
gu[i][j] = (st.size() ? st.top() : -1);
st.push(i);
}
st = stack<int>();
reprl(i, n-1, 0) {
while (st.size() && a[st.top()][j] < a[i][j]) st.pop();
gd[i][j] = (st.size() ? st.top() : -1);
st.push(i);
}
}
rep(i, n) {
rep(j, m) {
if (~gl[i][j]) {
if (i && gl[i-1][j] == gl[i][j]) lu[i][j] = lu[i-1][j];
else if (i && gr[i-1][gl[i][j]] == j) lu[i][j] = ru[i-1][gl[i][j]];
else lu[i][j] = i;
}
if (~gr[i][j]) {
if (i && gr[i-1][j] == gr[i][j]) ru[i][j] = ru[i-1][j];
else if (i && gl[i-1][gr[i][j]] == j) ru[i][j] = lu[i-1][gr[i][j]];
else ru[i][j] = i;
}
}
}
rep(j, m) {
rep(i, n) {
if (~gu[i][j]) {
if (j && gu[i][j-1] == gu[i][j]) ul[i][j] = ul[i][j-1];
else if (j && gd[gu[i][j]][j-1] == i) ul[i][j] = dl[gu[i][j]][j-1];
else ul[i][j] = j;
}
if (~gd[i][j]) {
if (j && gd[i][j-1] == gd[i][j]) dl[i][j] = dl[i][j-1];
else if (j && gu[gd[i][j]][j-1] == i) dl[i][j] = ul[gd[i][j]][j-1];
else dl[i][j] = j;
} else dl[i][j] = -1;
}
}
/*auto print = [&](int a[3000][3000]) {*/
/* rep(i, n) {*/
/* rep(j, m) cout << a[i][j] << "\t";*/
/* cout << endl;*/
/* }*/
/*};*/
/*cout << "\na:\n";*/
/*rep(i, n) {*/
/* rep(j, m) cout << a[i][j] << "\t";*/
/* cout << endl;*/
/*}*/
/*cout << "\ngd:\n";*/
/*print(gd);*/
/*cout << "\ngu:\n";*/
/*print(gu);*/
/*cout << "\ndl:\n";*/
/*print(dl);*/
/*cout << "(1, 2, 1, 1)" << endl;*/
/*cout << check(1, 2, 1, 1) << endl;*/
/*return 0;*/
ll ans = 0;
replr(x1, 1, n-2) replr(x2, x1, n-2) {
replr(y1, 1, m-2) replr(y2, y1, m-2) {
if (check(x1, x2, y1, y2)) {
/*cout << "(" << x1 << ", " << x2 << ", " << y1 << ", " << y2 << ")" << endl;*/
ans++;
}
}
}
return ans;
if (TEST6::check(a)) return TEST6::count_rectangles(a);
return TEST1::count_rectangles(a);
}
