# Not so equal subsets

The set of numbers $$\{x_1,x_2,...,x_n\}$$ consists of integers from $$1$$ to $$45$$ inclusive, such that all their finite subsets have distinct sums (for example, $$x_1+x_3\neq x_2+x_5+x_6$$). What is the largest possible value of $$n$$?

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