An alternative bijective proof, given by Aigner and Ziegler and credited by them to André Joyal, involves a bijection between, on the one hand, "n"-node trees with two designated nodes (that may be the same as each other), and on the other hand, "n"-node directed pseudoforests. If there are "Tn" "n"-node trees, then there are "n"2"Tn" trees with two designated nodes. And a pseudoforest may be determined by specifying, for each of its nodes, the endpoint of the edge extending outwards from that node; there are "n" possible choices for the endpoint of a single edge (allowing self-loops) and therefore "nn" possible pseudoforests. By finding a bijection between trees with two labeled nodes and pseudoforests, Joyal's proof shows that "Tn" = "n""n" − 2.