Problem Statement

Given are N positive integers A_1,...,A_N.
Consider positive integers B_1, ..., B_N that satisfy the following condition.
Condition: For any i, j such that $1 \leq i < j \leq N, A_i B_i = A_j B_j$ holds.
Find the minimum possible value of B_1 + ... + B_N for such B_1,...,B_N.
Since the answer can be enormous, print the sum modulo (10^9 +7).

Input

Input is given from Standard Input in the following format:
N
A_1 ... A_N

Output

Print the minimum possible value of B_1 + ... + B_N for B_1,...,B_N that satisfy the condition, modulo (10^9 +7).

Constraints

• $1 \leq N \leq 10^4$
• $1 \leq A_i \leq 10^6$
• All values in input are integers.

Sample Input 1

3
2 3 4

Sample Output 1

13

Let B_1=6, B_2=4, and B_3=3, and the condition will be satisfied.

Sample Input 2

5
12 12 12 12 12

Sample Output 2

5

We can let all B_i be 1.

Sample Input 3

3
1000000 999999 999998

Sample Output 3

996989508

Print the sum modulo (10^9+7).

见题面 Input 部分

见题面 Output 部分