You are given a sequence $*a*$ consisting of $*n*$ integers. Find the maximum possible value of (integer remainder of $*a*_{*i*}$ divided by $*a*_{*j*}$), where $1 ≤ *i*, *j* ≤ *n*$ and $*a*_{*i*} ≥ *a*_{*j*}$.

Input

The first line contains integer $*n*$ — the length of the sequence ($1 ≤ *n* ≤ 2·10^{5}$).

The second line contains $*n*$ space-separated integers $*a*_{*i*}$ ($1 ≤ *a*_{*i*} ≤ 10^{6}$).

Output

Print the answer to the problem.