Alternative parities

$\left({\color{#3D99F6} 1!} - {\color{#D61F06}2!} + {\color{#20A900} 3!} -{\color{#E81990}4!} + \cdots + {\color{#EC7300}75!}\right)^{{\color{#3D99F6} 1!} - {\color{#D61F06}2!} + {\color{#20A900} 3!} -{\color{#E81990}4!} + \cdots + {\color{#EC7300}75!}}$ If the last three digits of the expression above can be written as $xyz^{xyz}$ where $x,y$ and $z$ are all positive integers.

Find the last three digits of $xyz^{xyz}$ .

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Notation: $!$ denotes the factorial notation. For example, $8! = 1\times2\times3\times\cdots\times8$ .