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:
from collections import Counter


def factors(n):
    fact = Counter()

    i = 2
    while i * i <= n:
        while n % i == 0:
            fact[i] += 1
            n //= i
        i += 1

    if n != 1:
        fact[n] += 1

    fact[1] = 1

    return fact


def solve(a, b, c):
    fact = {i: factors(i) for i in range(1, max(a, b, c) + 1)}

    ans = 0
    cache = {}
    for i in range(1, a+1):
        for j in range(1, b+1):
            for k in range(1, c+1):
                p = i * j * k
                if p not in cache:
                    f = fact[i] + fact[j] + fact[k]
                    f[1] = 1
                    res = 1
                    for k, v in f.items():
                        res *= v + 1
                    
                    cache[p] = res // 2

                ans += cache[p]

    return ans % 1073741824


def main():
    a, b, c = map(int, input().split())
    ans = solve(a, b, c)
    print(ans)


if __name__ == "__main__":
    main()