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.
def fact(n):
    ans = []
    x = 2
    while x * x <= n:
        if n % x == 0:
            ans.append(x)
            n //= x
        else:
            x += 1
    if n > 1:
        ans.append(n)
    return ans

a, b, c = map(int, input().split())
facts = []
ans = []
all = 0
for i in range(1, 101):
    facts.append(fact(i))
#print(facts)
for i in range(1, a + 1):
    for j in range(1, b + 1):
        for h in range(1, c + 1):
            ans = []
            #print(i, j, h)
            for l in range(len(facts[i - 1])):
                ans.append(facts[i - 1][l])
            #print(ans, end = ' ')
            for l in range(len(facts[j - 1])):
                ans.append(facts[j - 1][l])
            #print(ans, end = ' ')
            for l in range(len(facts[h - 1])):
                ans.append(facts[h - 1][l])
            #print(ans)
            k = []
            for q in range(100):
                k.append(0)
            for q in range(len(ans)):
                k[ans[q] - 1] += 1
            anss = 1
            for q in k:
                anss *= q + 1
            all += anss
print(all)