Planetary Alignment

Planetary alignment is when planets appear to lie in a straight line. After 18 years, a planetary alignment could be observed from Earth again.

Junseo lives on Earth in a parallel world, where $N$ planets can be observed. Junseo wants to know how long he must wait to see the moment when all $N$ planets are lined up in a row.

After watching the sky closely, Junseo found the following facts.

• There is a moment when the $N$ planets are lined up in a row.
• The period of planetary alignment is at most $10^9$ seconds.
• Planets 1, 2, and 3 line up every $T_1$ seconds.
• Planets 2, 3, and 4 line up every $T_2$ seconds.
• ...
• Planets $N-2$, $N-1$, and $N$ line up every $T_{N-2}$ seconds.

Find the period of planetary alignment for Junseo.

The first line contains the number of planets $N$ that should be aligned. ($3 \leq N \leq 100\,000$)

The second line contains integers $T_1, T_2, \cdots, T_{N-2}$, separated by spaces, that give the period at which the planets line up. ($1 \leq T_i \leq 100\,000$)

Print the period of planetary alignment. The period of planetary alignment is at most $10^9$ seconds.