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:
a, b, c = map(int, raw_input().split())
d, r = {}, 0
for x in [(i + 1) * (j + 1) * (k + 1) for i in range(a) for j in range(b) for k in range(c)]:
	d[x] = d.get(x, 0) + 1
for k, v in d.items():
	t, i = 1, 2
	while i * i <= k:
		if k % i == 0:
			k /= i
			c = 2
			while k % i == 0:
				k /= i
				c += 1
			t *= c
		i += 1
	if k > 1:
		t *= 2
	r = (r + t * v) & 1073741823
print r