E - Flatten

Score : $500$ points

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 ($10^9 +7$).

Constraints

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

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 ($10^9 +7$).

3
2 3 4

13

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

5
12 12 12 12 12

5

We can let all $B_i$ be $1$.

3
1000000 999999 999998

996989508

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