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:
def sol(x):
    if d[x] != 0:
        return d[x]
    z = 1
    res, p, q = 0, 1, x
    while p * p <= x:
        if x % z == 0:
            res += 1
            if z * z != x:
                res += 1
        p += 1
        z += 1

    d[x] = res
    return res


a, b, c = map(int, input().split())
d = [0] * 10000001
ans = 0
MOD = 1073741824
for i in range(1, a + 1):
    for j in range(1, b + 1):
        for k in range(1, c + 1):
            ans += sol(i * j * k)

print(ans % MOD)