Empire Strikes Back

题意翻译

给定k个数$a_1$,$a_2$...$a_k$，求一个数p=n!使得p能被$\prod_{i=1}^ka_i!$整除。

题目描述

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.

输入输出格式

输入格式

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}) $ .

输出格式

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.

输入输出样例

输入样例 #1

2
1000 1000

输出样例 #1

2000

输入样例 #2

1
2

输出样例 #2

2