CF337E.Divisor Tree
普及/提高-
通过率:0%
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题目描述
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,...,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.
输入格式
The first line contains a single integer n ( 1<=n<=8 ). The second line contains n distinct space-separated integers ai ( 2<=ai<=1012 ).
输出格式
Print a single integer — the minimum number of vertices in the divisor tree that contains each of the numbers ai .
输入输出样例
输入#1
2 6 10
输出#1
7
输入#2
4 6 72 8 4
输出#2
12
输入#3
1 7
输出#3
1
说明/提示
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.