Let $ f: \mathbb{P}^n \rightarrow (\mathbb{P}^1)^n , [x_0:\dots :x_n] \mapsto ([x_0,x_1],[x_0,x_2], \dots ,[x_0,x_n])$.

In particular, if $X$ is the blow-up of $\mathbb{P}^n$ at $r+n-1$ points and $X'$ is the blow-up of $(\mathbb{P}^1)^n$ at $r$ points. Consider $\phi : X \dashrightarrow X'$ the birational map that makes the diagram with the blow-up's and $f$ commute, is $\phi$ a Crepant birational map?