More efficient algorithm to find OR of two sets

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Given a matrix of n rows and m columns of 1's and 0's, it is required to find out the number of pairs of rows that can be selected so that their OR is 11111....m times.

Example:

1 0 1 0 1
0 1 0 0 1
1 1 1 1 0

Answer:

2 ---> OR of row number [1,3] and [2,3]

Given n and m can be an order upto <= 3000, how efficiently can this problem be solved?

PS: I already tried with a naive O(n*n*m) method. I was thinking of a better solution.

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