Y by
It is known that
is a positive integer, and function
is defined as
Hence if the function
is defined as
Find the largest positive integer
, such that
, for all values of
.


![\[
f(x)=\frac{\pi^x}{\pi^x+\pi^{2a-x}}
\]](http://latex.artofproblemsolving.com/a/6/8/a681afafa08e945aaf115e333e502c0853a0bf7e.png)

![\[
g(a)=f(0)+f(\frac{a}{2025})+f(\frac{2a}{2025})+f(\frac{3a}{2025})+\dots +f(\frac{4049a}{2025})+f(2a)
\]](http://latex.artofproblemsolving.com/f/e/9/fe90cb9df8ef66c3b6642f244d90d055229cd887.png)



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