$$x^x=y^y$$ part 2

Algebra Level 4

The graph of $$x^x =y^y$$ where $$x$$ and $$y$$ are in the interval $$(0,1)$$ consists of a curve and a straight line (which is $$y=x$$), as shown. Let the intersection point be $$(p,p)$$. Find the value of $$\lfloor 100000p \rfloor$$.


Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

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