Fix a positive integer $n$. For a partition $λ$ of $n$, let $e(λ)$ be the number of even parts in $λ$. Using bijections, we can show the statistic $e(λ)$ is equidistributed on the set of partitions of $n$ with the following statistics:
(1) The largest part in $λ$ that occurs more than once.
(2) $∑⌊a_i/2⌋$, where $a_i$ is the number of occurrences of $i$ in $λ$.
(3) The number of cells in the Young diagram of $λ$ whose leg is zero and arm is odd.
Question: are there any other statistics equidistributed with $e(λ)$ that admit bijective descriptions?