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 PYTHON):

Solution:
d = {}

def gd(n):
    s, f, p, t = 2, {}, 1, n
    while n!=1:
        if n%s == 0:
            n = n/s
            f[s] = f.get(s,0)+1
            s = 2
        else:
            s+=1
    values = f.values()
    for x in values:
        p*=(x+1)
    d[t] = p
    return p


result = 0
x, y, z = map(int,raw_input().split())
import datetime
st = datetime.datetime.now()
for i in range(1,x+1):
    for j in range(1,y+1):
        for k in range(1,z+1):
            t = i*j*k
            r = d.get(t,None)
            if r is None:
                result+=gd(t)
            else:
                result+=r
print result%1073741824