Inequality with condition $x^2+y^2+z^2=1$.

let $x,y,z>0$ such that $x^2+y^2+z^2=1$. Find the minimum of $$\frac{1}{x}+\frac{1}{y}+\frac{1}{z}.$$

Is the answer $3\sqrt{3}$ by any chance?

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