Let M denote the set of all real matrices of order 3 × 3 and let S=-3,-2,-1,1,2. Let … If n ( ~S_1 ∪_2 US_3 )=125 α, then α equals

Let M denote the set of all real matrices of order $3 \times 3$3×3 and let $\mathrm{S}=\{-3,-2,-1,1,2\}$S={−3,−2,−1,1,2}. Let $$\begin{aligned} & \mathrm{S}_1=\left\{\mathrm{A}=\left[a_{\mathrm{ij}}\right] \in \mathrm{M}: \mathrm{A}=\mathrm{A}^{\mathrm{T}} \text { and } a_{\mathrm{ij}} \in \mathrm{~S}, \forall \mathrm{i}, \mathrm{j}\right\}, \\ & \mathrm{S}_2=\left\{\mathrm{A}=\left[a_{\mathrm{ij}}\right] \in \mathrm{M}: \mathrm{A}=-\mathrm{A}^{\mathrm{T}} \text { and } a_{\mathrm{ij}} \in \mathrm{~S}, \forall \mathrm{i}, \mathrm{j}\right\}, \\ & \mathrm{S}_3=\left\{\mathrm{A}=\left[a_{\mathrm{ij}}\right] \in \mathrm{M}: a_{11}+a_{22}+a_{33}=0 \text { and } a_{\mathrm{ij}} \in \mathrm{~S}, \forall \mathrm{i}, \mathrm{j}\right\} . \end{aligned}$$​S1​={A=[aij​]∈M:A=AT and aij​∈ S,∀i,j},S2​={A=[aij​]∈M:A=−AT and aij​∈ S,∀i,j},S3​={A=[aij​]∈M:a11​+a22​+a33​=0 and aij​∈ S,∀i,j}.​ If $n\left(\mathrm{~S}_1 \cup_2 \mathrm{US}_3\right)=125 \alpha$n( S1​∪2​US3​)=125α, then $\alpha$α equals _______