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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