Least common multiple P96564

Write a program such that, given n strictly positive natural numbers x₁ … x_n, prints their least common multiple greater than zero.

Input

Input consists of several cases. Each case begins with a number n ≥ 1, followed by x₁ … x_n. A special case with n = 0 marks the end of input.

Output

For every case, print in a line the least common multiple greater than zero of x₁ … x_n. For the given cases, this number will always be between 1 and 10⁹.