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:
from operator import mul
from functools import reduce
from collections import Counter

a, b, c = map(int, input().split())
mod = 2 ** 30

prime = [None] * 100

for i in range(2, 101):
    if prime[i - 1] is None:
        for j in range(i, 101, i):
            prime[j - 1] = i


d = {}
result = 0
for ai in range(1, a + 1):
    for bi in range(1, b + 1):
        for ci in range(1, c + 1):
            n = ai * bi * ci
            res = d.get(n)

            if res is None:
                cd = Counter()

                n_ai = ai
                while prime[n_ai - 1] is not None:
                    cd[prime[n_ai - 1]] += 1
                    n_ai //= prime[n_ai - 1]
                
                n_bi = bi
                while prime[n_bi - 1] is not None:
                    cd[prime[n_bi - 1]] += 1
                    n_bi //= prime[n_bi - 1]
                
                n_ci = ci
                while prime[n_ci - 1] is not None:
                    cd[prime[n_ci - 1]] += 1
                    n_ci //= prime[n_ci - 1]
                
                res = reduce(mul, map(lambda x: x + 1, cd.values()), 1)
                d[n] = res
            
            result += res

print(result % mod)