Two rules generate a sequence; what do the first 100 terms add to?

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The function \(f(n)\) is defined for positive integers \(n\) according to the rules \[f(1)=1,\qquad f(2n)=f(n),\qquad f(2n+1)=(f(n))^2-2.\] The value of \(f(1)+f(2)+f(3)+\cdots+f(100)\) is

1. \(-86\),

2. \(-31\),

3. \(23\),

4. \(58\).