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 ≤ 100).

Output

Print a single integer — the required sum modulo 1073741824 (230).

Examples

Input

2 2 2


Output

20


Input

5 6 7


Output

1520

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.
a, b, c = map(int, input().strip().split())
dp = {}
ut = {}
res = 0



def findFactors(n):
    if n in ut:
        pass
    else:
        factors = {}
        curr = 2
        while n % 2 == 0:
            factors[2] = factors.get(2, 0) + 1
            n = n//2
        i = 3
        while i < n:
            while n % i == 0:
                factors[i] = factors.get(i, 0) + 1
                n //= i
            i += 2
        if n > 1:
            factors[n] = 1
        ut[n] = 1
        for i in factors:
            ut[n] *= (factors[i] + 1)
    return ut[n]



for aa in range(1, a + 1):
    for bb in range(1, b + 1):
        for cc in range(1, c + 1):
            n = aa * bb * cc
            if n in dp:
                pass
            else:
                dp[n] = findFactors(n)
            res += dp[n]
print(res)