You are given a sequence a consisting of n integers. Find the maximum possible value of $$a_i \bmod a_j$$ (integer remainder of ai divided by aj), where 1 ≤ i, j ≤ n and ai ≥ aj.

Input

The first line contains integer n — the length of the sequence (1 ≤ n ≤ 2·105).

The second line contains n space-separated integers ai (1 ≤ ai ≤ 106).

Output

Print the answer to the problem.

见题面 Input 部分

见题面 Output 部分