Empire Strikes Back（素数的理解）

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.

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 С++. It is preferred to use the cin, cout streams or the %I64dspecificator.

题意就是：　给定k个数字，求最小的正整数n，使得“n的阶乘”是“这k个数字的阶乘的积”的倍数。

这个题明显是可以二分的，然后就是素数ｐ在ｎ的阶乘中出现的次数，就是：　ｎ／ｐ＋ｎ／ｐ＾２．．．．．．，。　现在我们遇到的问题就是如何求符合情况的ｎ

然后二分答案就行了。我们现在知道的就是阶乘相乘，就相当于他们的指数相加，就是这个东西，然后我们用一个查分的数组弄一下。