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:
def gen_primes(n):
    ret = [2]
    if n < 3:
        return ret
    n += 1
    buf = [0] * n
    buf[2] = 1
    for i in xrange(3, n, 2):
        if buf[i] == 0:
            ret.extend([i])
            for j in xrange(2 * i, n, i):
                buf[j] = 1
    return ret
def count_divisor(n, primes):
    ret = 1
    for p in primes:
        if n < p:
            break
        cnt = 1
        while n % p == 0:
            cnt += 1
            n /= p
        ret *= cnt
    return ret
def main():
    p = gen_primes(1000000)
    a, b, c = map(int, raw_input().split())
    a, b, c, ans = a + 1, b + 1, c + 1, 0
    buf = [1] * (a * b * c)
    for ai in xrange(1, a):
        for bi in xrange(1, b):
            for ci in xrange(1, c):
                i = ai * bi * ci
                if buf[i] == 1 and i > 1:
                    buf[i] = count_divisor(i, p)
                ans += buf[i]
    print ans
if __name__ == '__main__':
    main()