Divisor Tree

0ms

262144K

Description:

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 a₁, a₂, ..., 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.

Input:

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 ≤ 10¹²).

Output:

Print a single integer — the minimum number of vertices in the divisor tree that contains each of the numbers a_i.

Sample Input:

2
6 10

Sample Output:

Sample Input:

4
6 72 8 4

Sample Output:

Sample Input:

1
7

Sample Output:

Note:

Sample 1. The smallest divisor tree looks this way: $\text{[math]}$

Sample 2. In this case you can build the following divisor tree: $\text{[math]}$

Sample 3. Note that the tree can consist of a single vertex.

Informação

Provedor Codeforces

Código CF337E