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E. Empire Strikes Back

time limit per test

5 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputIn 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* ≤ 10^{6}). The second line contains *k* integers *a*_{1}, *a*_{2}, ..., *a*_{k} (1 ≤ *a*_{i} ≤ 10^{7}).

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 %I64d specificator.

Examples

Input

2

1000 1000

Output

2000

Input

1

2

Output

2

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