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 PYTHON):

Solution:
I=lambda:map(int, raw_input().split())
dp = {}
MOD = 1073741824
def d(x):
    if x in dp:
        return dp[x]
    res = 1
    q = 2
    xx = x
    while q * q <= x:
        r = 1
        while x % q == 0:
            x /= q
            r += 1
        res = (res * r) % MOD
        q += 1
    if x > 1:
        res = (res * 2) % MOD
    dp[xx] = res
    return res
a, b, c = I()

res = 0
for i in xrange(1, a + 1):
    for j in xrange(1, b + 1):
        for k in xrange(1, c + 1):
            res = (res + d(i * j * k)) % MOD
print res