Time Limit: 1000 mSec Memory Limit : 32768 KB

Huahua and Mingming are two students in a grade school, they are both good at calculating. To prove their strength on calculating, they decide to hold a calculating contest. The problem they will do is simple.

Let [a1,a2,...,an] (n>=1) denotes the lease common multiple(LCM) of positive integers: a1,a2,...,an, and [a]=a, denotes the greatest integer which is no more than X/2.

The task is, given a series of positive integers a1,a2,...,an, they should calculate the product of the following two numbers as quickly as possible. Those who use much less time in calculation wins the competition.

This may not be a hard problem for Huahua and Mingming, but it is really not easy for their judger. So, their judger asks you, a smart student, to write a program to help him.

For example, given the positive integers 4,8 and 12, we can calcuate as follows:

So the result is:

Let [a1,a2,...,an] (n>=1) denotes the lease common multiple(LCM) of positive integers: a1,a2,...,an, and [a]=a, denotes the greatest integer which is no more than X/2.

The task is, given a series of positive integers a1,a2,...,an, they should calculate the product of the following two numbers as quickly as possible. Those who use much less time in calculation wins the competition.

For example, given the positive integers 4,8 and 12, we can calcuate as follows:

The input may contain multiple test cases. Each test case begins with a line containing a positive integer N (1<=N<=50), specify the number of integers in the sequence, the second line contains N positive integers ai (1<=ai<=10000, i=1,2,...,N), separated by a space.

N=0 terminates the input.

N=0 terminates the input.

For each test case, output two lines, the first line is the test case number, as shown in the sample output, the second line is the product.

3
4 8 12
1
15
0

Test Data 1:
4
Test Data 2:
15