Max n value for $\frac{1}{x^x}=y^y+n$?

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I was looking at the graph of $$\frac{1}{x^x}=y^y+n$$ and found that it disappears at n greater than about $0.752$. What is the exact constant definition for n and why does the graph disappear (perhaps it becomes undefined or imaginary) at n greater than that?