Problem: 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:

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Find the sum modulo 1073741824 (230).

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 (230).

Examples

Input

2 2 2


Output

20


Input

4 4 4


Output

328


Input

10 10 10


Output

11536

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.

Solution (in PYTHON):

Solution:
l=lambda:map(int,raw_input().split())
p = [2]
p+=[i for i in range(3,100,2) if all(i%m for m in p)]
d={1:1,2:2,3:2}
def f(x):
    if x not in d:         
        t=x
        s=1
        for m in p:
            if m>t: break
            q=1
            while t%m==0:
                q+=1
                t/=m
            s*=q
        d[x]=s
    return d[x]
a,b,c=l()
print sum(f(i*j*k) for i in range(1,a+1) for j in range(1,b+1) for k in range(1,c+1))