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:
a,b,c=[int(x) for x in input().split(' ')]
mod=1073741824

def divisors(x):
	powers={}
	i=2
	while(x!=1):
		if x%i==0:
			if i in powers:
				powers[i]+=1
			else:
				powers[i]=1
			x//=i
		else:
			i+=1
	return powers

primeFactors={}

for x in range(1,101):
	primeFactors[x]=divisors(x)

def finalMapPrepare(finalMap,x):
	for k in primeFactors[x]:
		if k in finalMap:
			finalMap[k]+=primeFactors[x][k]
		else:
			finalMap[k]=primeFactors[x][k]
		
total=0
for i in range(1,a+1):
	for j in range(1,b+1):
		for k in range(1,c+1):
			finalMap={}
			finalMapPrepare(finalMap,i)
			finalMapPrepare(finalMap,j)
			finalMapPrepare(finalMap,k)
			ans=1
			for v in finalMap.values():
				ans*=(v+1)
			total+=(ans)%mod
print(total%mod)