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 PYTHON3):

Solution:
MOD = 1073741824
(a, b, c) = map(int, input().split(' '))

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

for i in range(2, maxProd + 1):
    d[i] = 2

for i in range(2, maxProd//2 + 1):
    for j in range(2 * i, maxProd + 1, i):
        d[j] += 1

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

print(ret)