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 = (1 << 30)
memo = dict()

def dp(x):
	if x in memo:
		return memo[x]
	res, q, t = 1, 2, 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
	memo[t] = res
	return res

a, b, c = sorted(map(int, input().split()))
res = 0
for i in range(1, a+1):
	for j in range(1, b+1):
		for k in range(1, c+1):
			res = (res + dp(i * j * k)) % mod
print(res)