E. Madoka and The Best Universitytime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputMadoka wants to enter to "Novosibirsk State University", but in the entrance exam she came across a very difficult task:Given an integer n, it is required to calculate \sum{\operatorname{lcm}(c, \gcd(a, b))}, for all triples of positive integers (a, b, c), where a + b + c = n.In this problem \gcd(x, y) denotes the greatest common divisor of x and y, and \operatorname{lcm}(x, y) denotes the least common multiple of x and y.Solve this problem for Madoka and help her to enter to the best university!InputThe first and the only line contains a single integer n (3 \le n \le 10^5).OutputPrint exactly one interger — \sum{\operatorname{lcm}(c, \gcd(a, b))}. Since the answer can be very large, then output it modulo 10^9 + 7.ExamplesInput
3
Output
1
Input
5
Output
11
Input
69228
Output
778304278
NoteIn the first example, there is only one suitable triple (1, 1, 1). So the answer is \operatorname{lcm}(1, \gcd(1, 1)) = \operatorname{lcm}(1, 1) = 1.In the second example, \operatorname{lcm}(1, \gcd(3, 1)) + \operatorname{lcm}(1, \gcd(2, 2)) + \operatorname{lcm}(1, \gcd(1, 3)) + \operatorname{lcm}(2, \gcd(2, 1)) + \operatorname{lcm}(2, \gcd(1, 2)) + \operatorname{lcm}(3, \gcd(1, 1)) = \operatorname{lcm}(1, 1) + \operatorname{lcm}(1, 2) + \operatorname{lcm}(1, 1) + \operatorname{lcm}(2, 1) + \operatorname{lcm}(2, 1) + \operatorname{lcm}(3, 1) = 1 + 2 + 1 + 2 + 2 + 3 = 11
3

1 
['math', 'number theory', '*2200']