# AkshajDice

Level pending

A group of friends named $$A_1, A_2, \cdots, A_{2013}$$ decide to each play the single-player game AkshajDice. The rules to AkshajDice are as follows

-For $$1 \le k \le 2013$$, person $$A_k$$ has to roll $$k$$ $$2013$$-sided dice numbered $$d_1, d_2, \cdots, d_k$$

-He wins if for all possible pairs of his dice $$d_i$$ and $$d_j$$, dice $$d_j$$ rolls a larger number than dice $$d_i$$ if and only if $$j > i$$.

Let the expected value of the number of friends who win be $$n$$. If $$n$$ can be expressed as $$\dfrac{a}{b}$$ for relatively prime positive integers $$a,b$$, find the sum of the greatest prime factors of $$a$$ and $$b$$.

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