// correct/rect-mruxim-n2lg.java 🤣🤣🤣
import java.util.Arrays;
class rect {
final int maxn = 3000 + 10;
int n, m;
int[][] H;
short[][] L, R, U, D;
short[][] UL, DL, LU, RU;
long[] v;
int vs;
private void precalc() {
L = new short[maxn][maxn];
R = new short[maxn][maxn];
U = new short[maxn][maxn];
D = new short[maxn][maxn];
UL = new short[maxn][maxn];
DL = new short[maxn][maxn];
LU = new short[maxn][maxn];
RU = new short[maxn][maxn];
short[] st = new short[maxn];
for(int i = 0; i < n; i++) {
int t = 0;
for(int j = 0; j < m; j++) {
while(t > 0 && H[i][j] > H[i][st[t-1]]) t--;
L[i][j] = (t > 0 ? st[t-1] : -1);
st[t++] = (short)j;
}
}
for(int i = 0; i < n; i++) {
int t = 0;
for(int j = m; j-- > 0; ) {
while(t > 0 && H[i][j] > H[i][st[t-1]]) t--;
R[i][j] = (t > 0 ? st[t-1] : -1);
st[t++] = (short)j;
}
}
for(int j = 0; j < m; j++) {
int t = 0;
for(int i = 0; i < n; i++) {
while(t > 0 && H[i][j] > H[st[t-1]][j]) t--;
U[i][j] = (t > 0 ? st[t-1] : -1);
st[t++] = (short)i;
}
}
for(int j = 0; j < m; j++) {
int t = 0;
for(int i = n; i-- > 0; ) {
while(t > 0 && H[i][j] > H[st[t-1]][j]) t--;
D[i][j] = (t > 0 ? st[t-1] : -1);
st[t++] = (short)i;
}
}
for(int j = 0; j < m; j++) for(int i = 0; i < n; i++) {
if(U[i][j] != -1) {
if(j > 0 && U[i][j] == U[i][j-1]) UL[i][j] = UL[i][j-1];
else if(j > 0 && i == D[U[i][j]][j-1]) UL[i][j] = DL[U[i][j]][j-1];
else UL[i][j] = (short)j;
}
if(D[i][j] != -1) {
if(j > 0 && D[i][j] == D[i][j-1]) DL[i][j] = DL[i][j-1];
else if(j > 0 && i == U[D[i][j]][j-1]) DL[i][j] = UL[D[i][j]][j-1];
else DL[i][j] = (short)j;
}
}
for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) {
if(L[i][j] != -1) {
if(i > 0 && L[i][j] == L[i-1][j]) LU[i][j] = LU[i-1][j];
else if(i > 0 && j == R[i-1][L[i][j]]) LU[i][j] = RU[i-1][L[i][j]];
else LU[i][j] = (short)i;
}
if(R[i][j] != -1) {
if(i > 0 && R[i][j] == R[i-1][j]) RU[i][j] = RU[i-1][j];
else if(i > 0 && j == L[i-1][R[i][j]]) RU[i][j] = LU[i-1][R[i][j]];
else RU[i][j] = (short)i;
}
}
}
private void check(int i1, int i2, int j1, int j2) {
if(i2 < i1 || j2 < j1) return;
if(!((R[i2][j1-1]-1 == j2 && RU[i2][j1-1] <= i1) || (L[i2][j2+1]+1 == j1 && LU[i2][j2+1] <= i1))) return;
if(!((D[i1-1][j2]-1 == i2 && DL[i1-1][j2] <= j1) || (U[i2+1][j2]+1 == i1 && UL[i2+1][j2] <= j1))) return;
v[vs++] = (((long)i1 * maxn + i2) * maxn + j1) * maxn + j2;
}
public long count_rectangles(int[][] _H) {
H = _H;
n = H.length;
m = H[0].length;
precalc();
v = new long[maxn * maxn * 4];
vs = 0;
for(int i = 1; i < n-1; i++) for(int j = 1; j < m-1; j++) {
if(U[i+1][j] != -1 && L[i][j+1] != -1) check(U[i+1][j]+1, i, L[i][j+1]+1, j);
if(U[i+1][j] != -1 && R[i][j-1] != -1) check(U[i+1][j]+1, i, j, R[i][j-1]-1);
if(D[i-1][j] != -1 && L[i][j+1] != -1) check(i, D[i-1][j]-1, L[i][j+1]+1, j);
if(D[i-1][j] != -1 && R[i][j-1] != -1) check(i, D[i-1][j]-1, j, R[i][j-1]-1);
if(D[i-1][j] != -1 && R[D[i-1][j]-1][j-1] != -1) check(i, D[i-1][j]-1, j, R[D[i-1][j]-1][j-1]-1);
if(D[i-1][j] != -1 && L[D[i-1][j]-1][j+1] != -1) check(i, D[i-1][j]-1, L[D[i-1][j]-1][j+1]+1, j);
}
Arrays.sort(v, 0, vs);
int ans = 0;
for(int i = 0; i < vs; i++)
if(i == 0 || v[i] != v[i-1])
ans++;
return ans;
}
}
