Question 240, Set $S$ satisfies the following conditions: (1) The elements in $S$ are all positive integers not exceeding 100; (2) For any $a, b \in S, a \neq b$, there exists a $c \in S$ different from $a, b$, such that $(a+b, c)=1$; (3) For any $a, b \in S, a \neq b$, there exists a $c \in S$ different from $a, b$, such that $(a+b, c)>1$. Try to find the maximum value of $|S|$.

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Note: The notation $(a, b)$ represents the greatest common divisor (gcd) of $a$ and $b$.