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 PYTHON3):

Solution:
def d(x):
    if x == 1:
        return 1
    
    k = 0
    i = 1
    
    while i * i <= x:
        if x % i == 0:
            k += 2
            if i * i == x:
                k -= 1
        i += 1

    return k

a, b, c = map(int, input().split())
n = 1073741824

ans = 0
s = [0 for i in range(1000001)]

for x in range(1, a + 1):
    for y in range(1, b + 1):
        for z in range(1, c + 1):
            p = x * y * z
            if s[p] == 0:
                s[p] = d(p)
            ans = (ans + s[p]) % n

print(ans)