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Given a boolean function $f : \{0, 1\}^n \rightarrow \{0, 1\}$ define the function $f \circ \mathsf{XOR}$ on $2n$ bits by $f \circ \mathsf{XOR} (x_1, \dots, x_n, y_1, \dots, y_n) = f(x_1 \oplus y_1, \dots, x_n \oplus y_n)$. Such a function is cal