문제

Bessie has woken up on a strange planet. In this planet, there are $N$ ($1\le N\le 10^4$) months, with $a_1, \ldots, a_N$ days, respectively ($1\leq a_i \leq 4 \cdot 10^9$, all $a_i$ are integers). In addition, on the planet, there are also weeks, where each week is $L$ days, with $L$ being a positive integer. Interestingly, Bessie knows the following: For the correct $L$, each month is at least $4$ weeks long. For the correct $L$, there are at most $3$ distinct values of $a_i\bmod L$.

Unfortunately, Bessie has forgotten what $L$ is! Help her by printing the sum of all possible values of $L$.

Note that the large size of integers involved in this problem may require the use of 64-bit integer data types (e.g., a "long long" in C/C++).

입력

The first line contains a single integer $N$. The second line contains $N$ space-separated integers, $a_1, \ldots, a_N$.

출력

A single integer, the sum of all possible values of $L$.

예제 입력 1

12
31 28 31 30 31 30 31 31 30 31 30 31

예제 출력 1

28

예제 입력 2

4
31 35 28 29

예제 출력 2

23

점수

Inputs 3-4: $1 \leq a_i \leq 10^6$Inputs 5-14: No additional constraints