Cowlendar

문제

Bessie has woken up on a strange planet. In this planet, there are $NN$ ($1\le N\le {10}^{4}1\backslash le\; N\backslash le\; 10^4$) months, with $a_1,\dots ,a_{N}a\_1,\; \backslash ldots,\; a\_N$ days, respectively ($1\le a_i\le 4\cdot {10}^{9}1\backslash leq\; a\_i\; \backslash leq\; 4\; \backslash cdot\; 10^9$, all $a_{i}a\_i$ are integers). In addition, on the planet, there are also weeks, where each week is $LL$ days, with $LL$ being a positive integer. Interestingly, Bessie knows the following:

• For the correct $LL$, each month is at least $44$ weeks long.
• For the correct $LL$, there are at most $33$ distinct values of $a_{i}La\_i\backslash bmod\; L$.

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

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 $NN$. The second line contains $NN$ space-separated integers, $a_1,\dots ,a_{N}a\_1,\; \backslash ldots,\; a\_N$.

출력

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