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).

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.

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