Let $f : \mathbb{Z}^+ \longrightarrow \mathbb{Z}^*$ the function that assigns to each positive integer $n$ the number of rational numbers $\frac{p}{q}$ such that $\left\lbrace \begin{array}{ccc} p+q = n \\ 0<\frac{p}{q}<1 \\ \gcd(p,q)=1. \end{array}\right.$ For example, when $n=8,$ we have $2$ such rational numbers: $\frac{1}{7}$ and $\frac{3}{5}$. Hence $f(8)=2$.

What is the first positive integer $m$ such that there is no solution to $f(n)=m?$

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