Mochi

Let $F$ be the maximum frequency of any size. Each bundle needs two rice cakes of different sizes.

If some size appears more than $N/2$ times, each rice cake of that size must be paired with a rice cake of another size, so at most $N-F$ bundles are possible. If $F\leq N/2$, the most frequent size can be paired with the remaining cakes and $\lfloor N/2\rfloor$ bundles can be formed.

Hence the answer is $\min(\lfloor N/2\rfloor,N-F)$. Counting frequencies with a hash table takes expected $O(N)$ time. Solution written by GPT5.6