The Little Elephant loves the LCM (least common multiple) operation of a non-empty set of positive integers. The result of the LCM operation of k positive integers x₁, x₂, ..., x_k is the minimum positive integer that is divisible by each of numbers x_i.

Let's assume that there is a sequence of integers b₁, b₂, ..., b_n. Let's denote their LCMs as lcm(b₁, b₂, ..., b_n) and the maximum of them as max(b₁, b₂, ..., b_n). The Little Elephant considers a sequence b good, if lcm(b₁, b₂, ..., b_n) = max(b₁, b₂, ..., b_n).

The Little Elephant has a sequence of integers a₁, a₂, ..., a_n. Help him find the number of good sequences of integers b₁, b₂, ..., b_n, such that for all i (1 ≤ i ≤ n) the following condition fulfills: 1 ≤ b_i ≤ a_i. As the answer can be rather large, print the remainder from dividing it by 1000000007 (10⁹ + 7).

Input

The first line contains a single positive integer n (1 ≤ n ≤ 10⁵) — the number of integers in the sequence a. The second line contains n space-separated integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁵) — sequence a.

Output

In the single line print a single integer — the answer to the problem modulo 1000000007 (10⁹ + 7).

Little Elephant and LCM

Examples