# Maximum Sum Value

Number Theory Level 3

Given 10 non-negative reals such that $$a_i \leq i$$ and $$(1-a_1)(2-a_2)\ldots(9-a_9)(10-a_{10}) \geq 1$$. What is the maximum value of $$a_1 + a_2 + \ldots + a_9 + a_{10}$$?

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