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 ($10^9 +7$).