시간 제한메모리 제한제출정답맞힌 사람정답 비율
3 초 (추가 시간 없음) 256 MB222100.000%

문제

You are given an array $a_1, a_2, \ldots, a_n$. Let $x_1 = a_1$, and $x_i = x_{i - 1} \bmod a_i$ for each $i$ from $2$ to $n$.

Suppose that we can rearrange $a_1, \ldots, a_n$ in any way. What is the largest possible value of $x_n$ we can obtain?

입력

The first line contains an integer $n$ --- the size of the array ($2\leq n\leq 10^5$).

The second line containing $n$ integers $a_1, \ldots, a_n$ ($1\leq a_i\leq 10^5$).

출력

Print one integer --- the largest possible value of $x_n$.

예제 입력 1

5
5 5 10 17 23

예제 출력 1

3