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:
import math as m
a, b, c=map(int, input().split())
ans=0
def div(num):
    t=0
    for i in range(1, int(m.sqrt(num)) + 1):
        if num%i==0:
            t+=1
            if num//i!=i:
                t+=1
    return t
dic={}
for i in range(1, a+1):
    for j in range(1, b+1):
        for k in range(1, c+1):
            a=i*j*k
            if a in dic:
                ans=(ans+dic[a])%1073741824
            else:
                dic[a]=div(a)
                ans=(ans+dic[a])%1073741824
print(ans)