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Language: GCD Determinant
Description 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 Sample Output 1 12 4 Source |

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