Problem Description

Given $n$ positive integers $a_i$, please choose three numbers $i, j, k$ ($i \ne j$, $i \ne k$, $j \ne k$) such that the value of $(a_i + a_j) \bmod a_k$ is maximized.

Input Format

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

Output Format

Output one line with one integer, indicating the answer.

6
4 7 7 5 2 2

6

见附件中的 mod/mod2.in。

见附件中的 mod/mod2.ans。

Hint

For $30\%$ of the testdata, $n \le 100$.
For $60\%$ of the testdata, $n \le 3000$.
For $100\%$ of the testdata, $3 \le n \le 2 \times {10}^5$, $1 \le a_i \le {10}^8$.

Translated by ChatGPT 5