(6,2,2,6,2,5,10,9,9)

Build Tree by Prüfer Code $(6,2,2,6,2,5,10,9,9)$

I have the Prufer Code (6,2,2,6,2,5,10,9,9)(6,2,2,6,2,5,10,9,9).

I want to build the corresponding tree.

My algorithm:

1) Tree = {}{}, code = (6,2,2,6,2,5,10,9,9)(6,2,2,6,2,5,10,9,9), count = (1,2,3,4,5,6,7,8,9,10,11)(1,2,3,4,5,6,7,8,9,10,11)

2) Tree ={(2,6)}{(2,6)}, code = (2,2,6,2,5,10,9,9)(2,2,6,2,5,10,9,9), count = (1,3,4,5,6,7,8,9,10,11)(1,3,4,5,6,7,8,9,10,11)

3) Tree ={(2,6),(2,3)}{(2,6),(2,3)}, code = (2,6,2,5,10,9,9)(2,6,2,5,10,9,9), count = (1,4,5,6,7,8,9,10,11)(1,4,5,6,7,8,9,10,11)

4) Tree ={(2,6),(2,3),(2,4)}{(2,6),(2,3),(2,4)}, code = (6,2,5,10,9,9)(6,2,5,10,9,9), count = (1,5,6,7,8,9,10,11)(1,5,6,7,8,9,10,11)

5) Tree ={(2,6),(2,3),(2,4),(5,6)}{(2,6),(2,3),(2,4),(5,6)}, code = (2,5,10,9,9)(2,5,10,9,9), count = (1,6,7,8,9,10,11)(1,6,7,8,9,10,11)

6) Tree ={(2,6),(2,3),(2,4),(5,6),(2,6)}{(2,6),(2,3),(2,4),(5,6),(2,6)}, code = (5,10,9,9)(5,10,9,9), count = (1,7,8,9,10,11)(1,7,8,9,10,11)

7) Tree ={(2,6),(2,3),(2,4),(5,6),(2,6),(5,7)}{(2,6),(2,3),(2,4),(5,6),(2,6),(5,7)}, code = (10,9,9)(10,9,9), count = (1,8,9,10,11)(1,8,9,10,11)

8) Tree ={(2,6),(2,3),(2,4),(5,6),(2,6),(5,7),(8,10)}{(2,6),(2,3),(2,4),(5,6),(2,6),(5,7),(8,10)}, code = (9,9)(9,9), count = (1,9,10,11)(1,9,10,11)

9) Tree ={(2,6),(2,3),(2,4),(5,6),(2,6),(5,7),(8,10),(9,10)}{(2,6),(2,3),(2,4),(5,6),(2,6),(5,7),(8,10),(9,10)}, code = (9)(9), count = (1,9,11)(1,9,11)

10) Tree ={(2,6),(2,3),(2,4),(5,6),(2,6),(5,7),(8,10),(9,10),(9,11)}{(2,6),(2,3),(2,4),(5,6),(2,6),(5,7),(8,10),(9,10),(9,11)}, code = ()(), count = (1,9)(1,9)

11) Tree = {(2,6),(2,3),(2,4),(5,6),(2,6),(5,7),(8,10),(9,10),(9,11),(1,9)}{(2,6),(2,3),(2,4),(5,6),(2,6),(5,7),(8,10),(9,10),(9,11),(1,9)}

Is my solution correct?