Question 99
Given a positive integer $n$, determine all functions $f$ from the first $n$ positive integers to the positive integers, satisfying the following two conditions:
$$
(1) \sum_{k=1}^{n} f(k) = 2n;
$$
$$
(2) \sum_{k \in K} f(k) = n \text{ for no subset } K \text{ of the first } n \text{ positive integers.}
$$
$$
(1) \sum_{k=1}^{n} f(k) = 2n;
$$
$$
(2) \sum_{k \in K} f(k) = n \text{ for no subset } K \text{ of the first } n \text{ positive integers.}
$$