MSE08H - GCD Determinant

We say that a set S = {x1, x2, …, xn} is factor closed if for any xi ∈ S and any divisor d of xi we have d ∈ S. Let’s build a GCD matrix (S) = (sij), where sij = GCD(xi, xj) – the greatest common divisor of xi and xj. Given the factor closed set S, find the value of the determinant:

Input

The input file contains several test cases. Each test case starts with an integer n (0 < n < 1000), that stands for the cardinality of S. The next line contains the numbers of S: x1, x2, …, xn. It is known that each xi is an integer, 0 < xi < 2*10^9. The input data set is correct and ends with an end of file.

Output

For each test case find and print the value Dn mod 1000000007.

Sample

Input :
2 
1 2 
3 
1 3 9 
4 
1 2 3 6 

Ouput: 
1 
12 
4 


Added by:psetter
Date:2009-04-10
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:Southeastern European 2008

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2022-11-08 09:39:26
Oh my God
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