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:

<image>

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())
p= [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
mod = 1073741824
def divisor(x):
    y=0
    ans=1
    for i in p:
        if x < i:
            break
        y=1
        while x%i==0 and x>= i:
            x/=i
            y+=1
        ans*=y
    return ans
sm = 0
dict = {}
for i in range(1,a+1):
    for j in range(1,b+1):
        for k in range(1,c + 1):
            if (i*j*k) not in dict.keys():
                dict[i*j*k] = divisor(i*j*k)
                
            
            sm = sm + dict[i*j*k]
            
print(sm % mod)