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:
def dic(n):
    i=2
    f=1
    t=0
    while i*i<=n:
        
        while n%i==0:
            t+=1
            n//=i
        
        f=f*(t+1)
        t=0
        if i==2:
            i=3
        else:
            i+=2
    if n>1:
        f*=2
    
    return f
        
        
a,b,c=map(int,input().split())
d=dict()
a+=1
b+=1
c+=1
g=0
for i in range(1,a):
    for j in range(1,b):
        for z in range(1,c):
            ans=dic(i*j*z)
       
            g+=ans

print(g)