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:
MOD = 1073741824

def findPrimeFact(n):
    fact = {}
    count = 0
    while(n%2 == 0):
        count += 1
        n //= 2
    if count:
        fact[2] = count
    for i in range(3, int(n**0.5)+1, 2):
        count = 0
        while n%i ==0:
            count += 1
            n //= i
        if count:
            fact[i] = count
    if n>2:
        fact[n] = 1
    return(fact)

a, b, c = map(int, input().split())
ans = 0
for i in range(1, a+1):
    for j in range(1, b+1):
        for k in range(1, c+1):
            fact = findPrimeFact(i*j*k)
            temp = 1
            for l in fact:
                temp *= (1+fact[l])
                temp %= MOD
            ans += temp
            ans %= MOD

print(ans%MOD)