Let's denote $*d*(*n*)$ as the number of divisors of a positive integer $*n*$. You are given three integers $*a*$, $*b*$ and $*c*$. Your task is to calculate the following sum:

Find the sum modulo $1073741824$ $(2^{30})$.

Input

The first line contains three space-separated integers $*a*$, $*b*$ and $*c*$ ($1 ≤ *a*, *b*, *c* ≤ 2000$).

Output

Print a single integer — the required sum modulo $1073741824$ $(2^{30})$.

Note

For the first example.

• $*d*(1·1·1) = *d*(1) = 1$;
• $*d*(1·1·2) = *d*(2) = 2$;
• $*d*(1·2·1) = *d*(2) = 2$;
• $*d*(1·2·2) = *d*(4) = 3$;
• $*d*(2·1·1) = *d*(2) = 2$;
• $*d*(2·1·2) = *d*(4) = 3$;
• $*d*(2·2·1) = *d*(4) = 3$;
• $*d*(2·2·2) = *d*(8) = 4$.

So the result is $1 + 2 + 2 + 3 + 2 + 3 + 3 + 4 = 20$.