A9044 | Empire Strikes Back

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 , where $p=n!$ ( $n$ is the power of the Imperial strike), . 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.

The first line contains integer $k$ $(1<=k<=10^{6})$ . The second line contains $k$ integers $a_{1},a_{2},...,a_{k}$ $(1<=a_{i}<=10^{7})$ .

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 С++. It is preferred to use the cin, cout streams or the %I64d specificator.