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 ≤ 100).

Output

Print a single integer — the required sum modulo 1073741824 (230).

Examples

Input

2 2 2


Output

20


Input

5 6 7


Output

1520

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.
a,b,c=map(int,input().split())
primes=[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]
dict1={}
for prime in primes:
    dict1[prime]=2
def countfact(num):
    if num in dict1:
        return dict1[num]
    xnum=num
    count=1
    for prime in primes:
        if num%prime==0:
            c=0
            while num%prime==0:
                c+=1
                num//=prime
            count*=c+1
    dict1[xnum]=count
    return count




summ=0
for i in range(1,a+1):
    for j in range(1,b+1):
        for k in range(1,c+1):
            summ+=countfact(i*j*k)
print(summ%1073741824)
