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:
p = [2]
any(p.append(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:
    s, n = 1, x
    for m in p:
      if m>n: break
      q = 1
      while n%m==0:
        q += 1
        n /= m
      s *= q
    d[x] = s
  return d[x]
def go(v):
  a,b,c = [range(1, int(x)+1) for x in v]
  return sum(f(i*j*k) for i in a for j in b for k in c)
print go(raw_input().split())