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:
a, b, c = map(int, input().split())

def count_div(x):
	count = 2

	for i in range(2, int(x**0.5)+1):
		if not x%i:
			if i*i != x:
				count += 2
			else:
				count += 1
	return count

k = 10**5
d = [0 for i in range(10**6+1)]
d[1] = 1; d[2] = 2; d[3] = 2

N = 2**30
ans = 0

for i in range(1, a+1):
	for j in range(1, b+1):
		for k in range(1, c+1):
			if not d[i*j*k]:
				d[i*j*k] = count_div(i*j*k)
			
			ans = (ans + d[i*j*k])%N
print(ans)