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())

uniquenums = {}
ret = 0


def dfunc(n):
    score = 0
    for i in range(1,int(n**(1/2))+1):
        if n%i == 0:
            score += 1
    score *= 2
    if n**(1/2) == int(n**(1/2)):
        score -=1
    return score

for i in range(1,a+1):
    for j in range(1,b+1):
        for k in range(1,c+1):
            mult = i * j * k
            
            if mult not in uniquenums:
                uniquenums[mult] = dfunc(mult)
            ret += uniquenums[mult]
#print(uniquenums)
print(ret%1073741824)