A9096 | Divisor Tree

A divisor tree is a rooted tree that meets the following conditions:

- Each vertex of the tree contains a positive integer number.
- The numbers written in the leaves of the tree are prime numbers.
- For any inner vertex, the number within it is equal to the product of the numbers written in its children.

Manao has $n$ distinct integers $a_{1},a_{2},...,a_{n}$ . He tries to build a divisor tree which contains each of these numbers. That is, for each $a_{i}$ , there should be at least one vertex in the tree which contains $a_{i}$ . Manao loves compact style, but his trees are too large. Help Manao determine the minimum possible number of vertices in the divisor tree sought.

The first line contains a single integer $n$ ( $1<=n<=8$ ). The second line contains $n$ distinct space-separated integers $a_{i}$ ( $2<=a_{i}<=10^{12}$ ).

Print a single integer — the minimum number of vertices in the divisor tree that contains each of the numbers $a_{i}$ .