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.
from math import sqrt, ceil
a, b, c = map(int, input().split())
cache = {}

def s(n):
    if n in cache:
        return cache[n]

    if n == 1:
        return 1

    sn = sqrt(n)
    r = 0
    for i in range(1, int(sn)+1):
        # print(i)
        if n%i == 0:
            # print(i)
            r += 1
            if i*i < n:
                # print(n//i)
                r += 1
    cache[n] = r
    return r

su = 0
# print(s(int(input())))

for i in range(1, a+1):
    for j in range(1, b+1):
        for k in range(1, c+1):
            rr = s(i*j*k)
            su += rr
            # print('asdfadf', i*j*k, rr)
            su %= 1073741824

print(su)
# print(s(int(input())))
