Time Limit: 0.5 seconds
Memory Limit: 256 megabytes
A divisor tree is a rooted tree that meets the following conditions:
Manao has n distinct integers a1, a2, ..., an. He tries to build a divisor tree which contains each of these numbers. That is, for each ai, there should be at least one vertex in the tree which contains ai. 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 ai (2 ≤ ai ≤ 1012).
Print a single integer — the minimum number of vertices in the divisor tree that contains each of the numbers ai.
Sample 1. The smallest divisor tree looks this way:
Sample 2. In this case you can build the following divisor tree:
Sample 3. Note that the tree can consist of a single vertex.