Given $n$ positive integers $a_i$, choose three indices $i, j, k$ ($i \neq j$, $i \neq k$, $j \neq k$) such that the value of $(a_i + a_j) \pmod{a_k}$ is maximized.

Input

The first line contains an integer $n$, representing the number of integers. The second line contains $n$ integers representing $a_i$.

Output

Output a single integer representing the answer.

Examples

Input 1

6
4 7 7 5 2 2

Output 1

6

Input 2

(See mod/mod2.in)

Output 2

(See mod/mod2.ans)

Constraints

For 30% of the data: $n \leq 100$. For 60% of the data: $n \leq 3000$. For 100% of the data: $2 \leq n \leq 2 \times 10^5$, $1 \leq a_i \leq 10^8$.