Empire Strikes Back - Problem

In a far away galaxy there is war again. The treacherous Republic made k precision strikes of power a_i on the Empire possessions. To cope with the republican threat, the Supreme Council decided to deal a decisive blow to the enemy forces.

To successfully complete the conflict, the confrontation balance after the blow should be a positive integer. The balance of confrontation is a number that looks like $\text{[math]}$ , where p=n! (n is the power of the Imperial strike), $\text{[math]}$ . After many years of war the Empire's resources are low. So to reduce the costs, n should be a minimum positive integer that is approved by the commanders.

Help the Empire, find the minimum positive integer n, where the described fraction is a positive integer.

Input

The first line contains integer k (1≤k≤10⁶). The second line contains k integers a₁,a₂,...,a_k (1≤a_i≤10⁷).

Output

Print the minimum positive integer n, needed for the Empire to win.

Please, do not use the %lld to read or write 64-but integers in C++. It is preferred to use the cin, cout streams or the %I64d specificator.

Examples

Input

2
1000 1000

Output

Input

1
2

Output

3462: Empire Strikes Back

Description

Source/Category