In a multiple linear regression model $Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \epsilon$, if the variance of $X_1$ is $100$, the variance of $X_2$ is $100$, and the correlation between $X_1$ and $X_2$ is $r_{12} = 0.9$, what is the Variance Inflation Factor ($VIF$) for the coefficient $\beta_1$?