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.

def main():
    MOD = 2 ** 30

    a, b, c = [int(i) for i in input().split()]

    n = a * b * c
    dp = [0 for i in range(n + 1)]

    for i in range(1, n + 1):
        for j in range(i, n + 1, i):
            dp[j] += 1

    sm = 0
    for i in range(1, a + 1):
        for j in range(1, b + 1):
            for k in range(1, c + 1):
                num = i * j * k
                sm = ((sm % MOD) + (dp[num] % MOD) ) % MOD

    print(sm)



if __name__ == '__main__':
    main()


