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
res = 0
a,b,c = map(int,input().split())
arr = [0]*1000001
for i in range(1,a+1):
    for j in range(1,b+1):
        for k in range(1,c+1):
            num = i*j*k
            count = 0
            if arr[num]:
                res += arr[num]
            else:
                for l in range(1,math.floor((num)**(1/2))+1):
                    if num % l == 0:
                        if num // l != l:
                            count += 2
                        else:
                            count += 1
                res += count
                arr[num] = count
print(res%(2**30))