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:

<image>

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 main():
    from itertools import product
    a, b, c = sorted(map(int, input().split()))
    primes = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97)
    l = [None]
    for x in range(1, (c + 1)):
        tmp = [0] * 25
        for i, p in enumerate(primes):
            while not x % p:
                x //= p
                tmp[i] += 1
        l.append(tuple(tmp))
    res = 0
    cache = {}
    for x, y, z in product(range(1, a + 1), range(1, b + 1), range(1, c + 1)):
        xyz = x * y * z
        if xyz in cache:
            res += cache[xyz]
        else:
            u = 1
            for t in map(sum, zip(l[x], l[y], l[z])):
                if t:
                    u *= t + 1
            u &= 1073741823
            cache[xyz] = u
            res += u
    print(res & 1073741823)


if __name__ == '__main__':
    main()