How to create a row that displays the counts of column entries in a matrix using python/sage?

edit

so here is my matrix:

A = matrix([[1,1,2,2,2], 
            [3,1,4,3,3], 
            [0,4,2,4,0], 
            [0,0,2,0,0], 
            [0,0,2,0,0]])

I would like to insert a 0 row that displays the amount of row entries in each column.

This was my original code:

A = matrix([[1,1,2,2,2],
            [3,1,4,3,3],
            [0,4,2,4,0],
            [0,0,2,0,0],
            [0,0,2,0,0]])

puzzle = A.insert_row(0, sum(A)) Whats wrong with this code is that it gives me the sum of each column, when I just need the count of each column.

What I have

[ 4  6 12  9  5]
[ 1  1  2  2  2]
[ 3  1  4  3  3]
[ 0  4  2  4  0]
[ 0  0  2  0  0]
[ 0  0  2  0  0]

Desired

[ 2  3  5  3  2]
[ 1  1  2  2  2]
[ 3  1  4  3  3]
[ 0  4  2  4  0]
[ 0  0  2  0  0]
[ 0  0  2  0  0]