Find the largest possible integer value of $$N$$ such that $$\gcd(N, 2033) = 1$$ and $$\frac{N}{2033}$$ cannot be written as the sum of two positive rational numbers, each with denominators strictly less than 2033.

Details and assumptions

As an explicit example, since $$\frac{ 170} { 2033} = \frac{1}{214} + \frac{ 3 }{38 }$$, hence the answer is not 170.

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