What a cute rabbit ! BaiQian has white rabbits , and the rabbit has a cute value of . Now Sister Bai Qian will paint these rabbits . Some rabbits are painted green , and the rest are still white . (Please note that you can't painted all rabbits green)

Now , BaiQian uses the numbers on each white rabbit to find the remainder of the numbers on the green rabbits . Suppose that there are green rabbits and white rabbits (obviously: , then remainder results will be obtained . If these remainder results are all the same , it indicates that this is a good coloring scheme .

BaiQian wants to know that among all the good coloring schemes , there can be at most how many green rabbits . If there is no good painting scheme , output 0 .

The first line contains one integers  . As described in the statement . 

Then the second line contains  integers  .

Output an integer in a single line , indicates the answer .

5
4 10 14 4 4

3

In the first sample , paint the first, fourth and fifth rabbits green, so that each white rabbit can get a result of 2 from the green rabbit.

3
4 10 16

2