Perl (or R, or SQL): Count how often string appears across columns

I have a text file that looks like this:

gene1   gene2   gene3
a       d       c
b       e       d
c       f       g
d       g       
        h
        i

(Each column is a human gene, and each contains a variable number of proteins (strings, shown as letters here) that can bind to those genes).

What I want to do is count how many columns each string is represented in, output that number and all the column headers, like this:

a   1   gene1
b   1   gene1
c   2   gene1 gene3
d   3   gene1 gene2 gene3
e   1   gene2
f   1   gene2
g   2   gene2 gene3
h   1   gene2
i   1   gene2

I have been trying to figure out how to do this in Perl and R, but without success so far. Thanks for any help.