Triple Summation of Divisor Counts

Time flies, and once again the provincial selection season has arrived. Little Q is participating in the team selection for the second time. This year, having learned from his past mistakes, he decided not to take any risks by peeking at the problems. Instead, he prepared rigorously by practicing old contest problems. However, the sheer volume of these problems left him exhausted and confused, unable to see the light at the end of the tunnel.

One day, after overworking himself and falling asleep, Little Q dreamed that he was sitting in an exam hall facing a problem that seemed very familiar — a problem he was sure he had solved before, but couldn’t recall how. Still shaken upon waking, he approached you for assistance.

Your task is to help him solve the following problem:

$$ \left( \sum_{i=1}^{A} \sum_{j=1}^{B} \sum_{k=1}^{C} d(i\times j\times k) \right) \bmod (10^9+7) $$

Here, \( d(n) \) denotes the number of positive divisors of \( n \). Compute the above expression modulo \(10^9+7\).

inputFormat

The input consists of a single line with three positive integers \( A \), \( B \), and \( C \) separated by spaces.

outputFormat

Output a single integer, which is the value of the expression given above.

sample

2 2 2

20