Largest Matrix Subsequences

Define an 'increasing sequence' as a matrix of numbers which grows when read from left to right and from top to bottom along every row and every column. An example:

1 2 3 6
3 5 7 9

Find the largest increasing sequence sub-matrix (or sub-matrices) in a matrix of integers (whose range is [0..32,000]). The largest sub-matrix is that sub-matrix with the largest product of nrows*ncolumns. If more than one largest sub-matrix exists, print each of them, with the list in 'numerical order'.

In the example above, row 1 is "1 2 3 6" and column 1 is "1 3".

• Line 1: Two space separated integers: R, C (1 ≤ R,C ≤ 150). These are the number of rows and columns, respectively.
• Line 2..end: R*C space-separated integers that represent the matrix. These integers are presented 20 per line, except possibly the last line. The first integer belongs in row 1 column 1; the second integer belongs in row 1 column 2; and so on for a total of R*C integers.

A series of one or more lines, each with four space-separated integers. The first two integers are the row and column of the upper left element; the second two integers are the extent of the submatrix (number of rows, number of columns).