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:
primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
l = []
l.append(primes)
for i in range(100):
	ii = i+1
	a=[0]*25
	for j in range(25):
		if ii==1:
			break
		while ii%primes[j] == 0:
			a[j]+=1
			ii = ii/primes[j]
	l.append(a)
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):
			div = 1
			for d in range(25):
				div *= (1+l[i][d]+l[j][d]+l[k][d])
			ans += div
ans%=1073741824
print(ans)