Get distance matrix based on node tree

Hi, I need some help getting a phylogenetic distance matrix.

Here are two examples:

Example one:

tree=ete3.Tree('(((A,B),C),D);')
 print(tree)

         /-A
      /-|
   /-|   -B
  |  |
--|   -C
  |
   -D

The matrix should then be :

    A   B   C   D
A   0   1   2   3
B   1   0   2   3
C   2   2   0   3
D   3   3   3   0

As you can see A and B are the closest leaves, then C is closer to A and B than it is to D and finally the furthest leaf is D.

Here is another more complex example 2:

tree=ete3.Tree('((((((A,B),C),D),(E,F)),G),(H,I));')
print(tree)

                  /-A
               /-|
            /-|   -B
           |  |
         /-|   -C
        |  |
      /-|   -D
     |  |
     |  |   /-E
   /-|   -|
  |  |      -F
  |  |
--|   -G
  |
  |   /-H
   -|
      -I

and here I should get the followgin matrix:

    A   B   C   D   E   F   G   H   I
A   0   1   2   3   4   4   5   6   6
B   1   0   2   3   4   4   5   6   6
C   2   2   0   3   4   4   5   6   6
D   3   3   3   0   4   4   5   6   6
E   4   4   4   4   0   1   5   6   6
F   4   4   4   4   1   0   5   6   6
G   5   5   5   5   5   5   0   6   6
H   6   6   6   6   6   6   6   0   1
I   6   6   6   6   6   6   6   1   0

I tried get_distance functions on ete3 but it does not give matrix based on node distance...