Subsequences of Subsequences

Define $f(A)$ for an array $A$ of length $N$ as the number of elements $X$ such that there exists an array $C$, also of length $N$, satisfying : - $0 \le C_i \le 1$ - $\bigoplus_{i = 1}^{N} (A_i \cdot C_i) = X$, where $\oplus$ represents the bitwise XOR operator. This is equivalent to choosing some (possibly-empty) subsequence of $A$ (the elements with $C_i = 1$), and then their XOR should