import java.util.Arrays;
class rect {
boolean[][] visited;
public long count_rectangles(int[][] a) {
int n = a.length;
int m = a[0].length;
int[][] dpUp = new int[n][m];
int[][] dpDown = new int[n][m];
int[][] dpLeft = new int[n][m];
int[][] dpRight = new int[n][m];
for (int i = 1; i < n - 1; i++) {
for (int j = m - 2; j > 0; j--) {
if (a[i - 1][j] > a[i][j]) dpUp[i][j] = dpUp[i][j + 1] + 1;
if (a[i + 1][j] > a[i][j]) dpDown[i][j] = dpDown[i][j + 1] + 1;
}
}
for (int i = n - 2; i > 0; i--) {
for (int j = 1; j < m - 1; j++) {
if (a[i][j + 1] > a[i][j]) dpRight[i][j] = dpRight[i + 1][j] + 1;
if (a[i][j - 1] > a[i][j]) dpLeft[i][j] = dpLeft[i + 1][j] + 1;
}
}
if (n <= 2 || m <= 2) return 0;
boolean allZeroAndOne = true;
for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) if (a[i][j] != 0 && a[i][j] != 1) allZeroAndOne = false;
if (n <= 3) {
int currLength = 0;
int goodStarts = 0;
long res = 0;
for (int i = 1; i < m - 1; i++) {
int h = a[1][i];
if (a[0][i] <= h || a[2][i] <= h) {
goodStarts = 0;
} else {
if (a[1][i - 1] > h) goodStarts++;
if (a[1][i + 1] > h) res += goodStarts;
}
}
return res;
/*} else if (allZeroAndOne) {
visited = new boolean[n][m];
Arrays.fill(visited[0], true);
Arrays.fill(visited[n - 1], true);
for (int i = 0; i < n; i++) {
visited[i][0] = true;
visited[i][m - 1] = true;
}
for (int i = 1; i < n - 1; i++) {
for (int j = 1; j < m - 1; j++) {
}
} */
} else {
int[][][] maxRight = new int[n][m][m];
for (int i = 1; i < n - 1; i++) {
for (int j = 1; j < m - 1; j++) {
for (int k = j; k < m - 1; k++) {
if (j == k) {
maxRight[i][j][k] = a[i][j];
} else {
maxRight[i][j][k] = Math.max(a[i][k], maxRight[i][j][k - 1]);
}
}
}
}
int[][][] maxDown = new int[m][n][n];
for (int j = 1; j < m - 1; j++) {
for (int i = 1; i < n - 1; i++) {
for (int k = i; k < n - 1; k++) {
if (i == k) {
maxDown[j][i][k] = a[i][j];
} else {
maxDown[j][i][k] = Math.max(a[k][j], maxDown[j][i][k - 1]);
}
}
}
}
boolean[][][][] okJ = new boolean[n][n][m][m];
for (int i = 1; i < n - 1; i++) {
for (int k = i; k < n - 1; k++) {
for (int j = 1; j < m - 1; j++) {
for (int l = j; l < m - 1; l++) {
okJ[i][k][j][l] = maxRight[k][j][l] < a[k][l + 1] && maxRight[k][j][l] < a[k][j - 1];
if (k != i) {
okJ[i][k][j][l] = okJ[i][k][j][l] && okJ[i][k - 1][j][l];
}
}
}
}
}
boolean[][][][] okI = new boolean[n][n][m][m];
for (int i = 1; i < n - 1; i++) {
for (int k = i; k < n - 1; k++) {
for (int j = 1; j < m - 1; j++) {
for (int l = j; l < m - 1; l++) {
okI[i][k][j][l] = maxDown[l][i][k] < a[i - 1][l] && maxDown[l][i][k] < a[k + 1][l];
if (j != l) {
okI[i][k][j][l] = okI[i][k][j][l] && okI[i][k][j][l - 1];
}
}
}
}
}
long rect = 0;
for (int i = 1; i < n - 1; i++) {
for (int j = 1; j < m - 1; j++) {
for (int k = i; k < n - 1; k++) {
if (a[k][j - 1] <= a[k][j]) break;
for (int l = j; l < m - 1; l++) {
if (maxDown[l][i][k] >= a[k + 1][l]) break;
if (maxDown[l][i][k] >= a[i - 1][l]) break;
if (okI[i][k][j][l] && okJ[i][k][j][l]) {
rect++;
//System.out.println(i + " " + j + " " + k + " " + l);
}
}
}
}
}
//System.out.println(Arrays.deepToString(maxDown));
//System.out.println(Arrays.deepToString(rightOk));
//System.out.println(maxDown[1][1][1]);
return rect;
}
}
private boolean checkIfGood(int[][] ar, int a, int b, int c, int d) {
for (int i = a; i <= c; i++) {
int max = 0;
for (int j = b; j <= d; j++) {
max = Math.max(max, ar[i][j]);
}
if (ar[i][d + 1] <= max) return false;
if (ar[i][b - 1] <= max) return false;
}
for (int j = b; j <= d; j++) {
int max = 0;
for (int i = a; i <= c; i++) {
max = Math.max(max, ar[i][j]);
}
if (ar[c + 1][j] <= max) return false;
if (ar[a - 1][j] <= max) return false;
}
return true;
}
}
