  The notion of shuffle-compatible permutation statistics was implicit in
Stanley's work on P-partitions and was first explicitly studied by Gessel and
Zhuang. The aim of this paper is to prove that the triple ${\rm (udr, pk,
des)}$ is shuffle-compatible as conjectured by Gessel and Zhuang, where ${\rm
udr}$ denotes the number of up-down runs, ${\rm pk}$ denotes the peak number,
and ${\rm des}$ denotes the descent number. This is accomplished by
establishing an ${\rm (udr, pk, des)}$-preserving bijection in the spirit of
Baker-Jarvis and Sagan's bijective proofs of shuffle-compatibility property of
permutation statistics. As an application, our bijection also enables us to
prove that the pair $({\rm cpk}, {\rm cdes})$ is cyclic shuffle-compatible,
where ${\rm cpk}$ denotes the cyclic peak number and ${\rm cdes}$ denotes the
cyclic descent number.
