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:
line = raw_input()

tokens = line.split(' ')

a,b,c = int(tokens[0]), int(tokens[1]), int(tokens[2])

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]

cache = (a * b * c + 1)* [0]

div_sum = 0

def compute_div_count(num):
    ans = 1
    for prime in primes:
        count = 1
        while num % prime == 0:
            count += 1
            num /= prime
        ans *= count
    return ans

for i in xrange(1, a + 1):
    for j in xrange(1, b + 1):
        for k in xrange(1, c + 1):
            num = i * j * k
            if cache[num] == 0:
                cache[num] = compute_div_count(num)
            div_sum = (div_sum + cache[num]) % 1073741824
print div_sum