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:
#NTFS: neharika_shah
from collections import defaultdict
mod = 1073741824
a,b,c = map(int,input().split())

def primeFactors(n):
	dic = defaultdict(int)
	factors = []
	while n % 2 == 0:
		dic[2] += 1
		n = n // 2
	
	i = 3
	while i * i <= n:
		while n % i == 0:
			dic[i] += 1
			n = n // i
		i += 2
	
	if n > 2:
		dic[n] += 1
	return dic


def calc(n):
	res = 1
	dic = primeFactors(n)
	for val in dic.values():
		res = (res*(val+1))%mod
	return res
# print(calc(8))
ans = 0
for i in range(1,a+1):
	for j in range(1,b+1):
		for k in range(1,c+1):
			# print(calc(i*j*k))
			ans = (ans+calc(i*j*k))%mod
print(ans)