Background

There is a competition, and you are asked to compute the number of people who advance to the final.

Problem Description

The number of people who advance to the final satisfies the following rules:

You are given $n$ integers $A_1, A_2, \cdots, A_n$.

You need to find a positive integer $x$. Suppose there are $m$ ($m \geq 2$) values among $A_i$ that are multiples of $x$, then the number of finalists is $s$, whose value is $m \cdot x$.

Note that for a positive integer $x$, if the corresponding value of $m$ is $1$, then this choice is invalid.

Please find an $x$ that makes $s$ as large as possible, and output $s$.

Input Format

The first line contains a positive integer $n$.

The second line contains $n$ integers $A_i$ separated by spaces.

Output Format

Output an integer $s$.

3
1 2 4

4

2
1 5

2

5
4 6 3 8 9

9

Hint

Explanation for Sample 1

Let $x = 2$. Then $A_{2,3}$ satisfy the condition, and the answer is $2 \times 2 = 4$.

Constraints

• For $30\%$ of the testdata, $n < 1000$.
• For $100\%$ of the testdata, $2 \le n \le 2 \times 10^5$, $1 \le A_i \le 2 \times 10^6$.

Notes

This problem is translated from COCI2013-2014 CONTEST #1 T5 ORGANIZATOR.

Translated by ChatGPT 5