HMMT November 2016 U7

What is the minimum value of the product

$$\prod_{i=1}^{6} \frac{a_{i}-a_{i+1}}{a_{i+2}-a_{i+3}}$$

given that $\left(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6}\right)$ is a permutation of $(1,2,3,4,5,6)$ ? (note $\left.a_{7}=a_{1}, a_{8}=a_{2} \cdots\right)$