Least common multiple P96564

Write a program such that, given $n$ strictly positive natural numbers $x_1 \dots x_n$, prints their least common multiple greater than zero.

Input

Input consists of several cases. Each case begins with a number $n \ge 1$, followed by $x_1 \dots x_n$. 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 $x_1 \dots x_n$. For the given cases, this number will always be between 1 and $10^9$.