Let $a$, $b$, $c$, $d$ be real numbers and all zeroes **$\beta_1, \beta_2, \beta_3,$** and **$\beta_4$** of the polynomial **$P(x)=x^4+ax^3+bx^2+cx+d$** are real. Find the smallest value the product **$(\beta_1^2+1)(\beta_2^2+1)(\beta_3^2+1)(\beta_4^2+1)$** can take.

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