Given an array A of n integers. Calculate:
LCM(A_1, A_2,...,A_n) \mod 10^9+7
### Input
- The first line contains an integer n.
- The second line contains n integers A_i.
### Output
- Print the LCM of all elements in A modulo 10^9+7.
### Constraints
- 1 \le n \le 10^5.
- 1 \le A_i \le 10^5.
### Example
Input:
4
1 3 4 5
Output:
60