GAIC Math 2024 Problem 72

Set $X=\{1,2,\cdots,10\}$, mapping $f:X\rightarrow X$ satisfy:\ (1) $f\circ f = I_x$, where, $f\circ f$ is a composite mapping, $I_x$ is an identity mapping on X.\ (2) $|f(i)-i|=2$, for any $i\in X$.\ Then the number of mapping $f$ is _____.