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C. Little Elephant and LCM

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe 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 *x*_{1}, *x*_{2}, ..., *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 *b*_{1}, *b*_{2}, ..., *b*_{n}. Let's denote their LCMs as *lcm*(*b*_{1}, *b*_{2}, ..., *b*_{n}) and the maximum of them as *max*(*b*_{1}, *b*_{2}, ..., *b*_{n}). The Little Elephant considers a sequence *b* good, if *lcm*(*b*_{1}, *b*_{2}, ..., *b*_{n}) = *max*(*b*_{1}, *b*_{2}, ..., *b*_{n}).

The Little Elephant has a sequence of integers *a*_{1}, *a*_{2}, ..., *a*_{n}. Help him find the number of good sequences of integers *b*_{1}, *b*_{2}, ..., *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 (10^{9} + 7).

Input

The first line contains a single positive integer *n* (1 ≤ *n* ≤ 10^{5}) — the number of integers in the sequence *a*. The second line contains *n* space-separated integers *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 10^{5}) — sequence *a*.

Output

In the single line print a single integer — the answer to the problem modulo 1000000007 (10^{9} + 7).

Examples

Input

4

1 4 3 2

Output

15

Input

2

6 3

Output

13

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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