# Is there a nice factorization?

$256+128\left(\sum_{1\leq i\leq 8} a_i\right) + 64\left(\sum_{1\le i<j\le 8} a_ia_j\right) + \\ + 32\left(\sum_{1\le i<j<k\le 8} a_ia_ja_k\right) + \ldots + a_1a_2\cdots a_7a_8 = 111546435$

There exist some positive integers $$a_{i}$$ for $$i=1,2,..8$$ such that they satisfy the above equation find the sum of all possible value of $$a_{3}$$

hint - 111546435 has quite interesting factors.

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