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:
lst=list(map(int,input().split()))
# a=[0]*1000000
# def d(n):
# 	if a[n]!=0:
# 		return a[n]
# 	else:
# 		for i in range(1,n+1):
x=1073741824
sum=0
y=[0]*(lst[0]*lst[1]*lst[2]+1)
a,b,c=lst
for i in range(1,a*b*c+1):
	for j in range(i,a*b*c+1,i):
		y[j]+=1
for i in range(1,lst[0]+1):
	for j in range(1,lst[1]+1):
		for k in range(1,lst[2]+1):
			sum+=y[i*j*k]%x

print(sum%x)