Let S be the set of all passwords which are six to eight characters long, where each character is either an alphabet from { A, B, C, D, E } or a…

Let $\displaystyle S$ be the set of all passwords which are six to eight characters long, where each character is either an alphabet from $\displaystyle \{\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}\}$ or a number from $\displaystyle \{1,2,3,4,5\}$ with the repetition of characters allowed. If the number of passwords in S whose at least one character is a number from $\displaystyle \{1,2,3,4,5\}$ is $\displaystyle \alpha \times 5^6$, then $\displaystyle \alpha$ is equal to \_\_\_\_.