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 PYTHON):

Solution:
def mergeDict(a, b, c):
    ret = a.copy()
    for key, value in b.items():
        if ret.has_key(key):
            ret[key] += value
        else:
            ret[key] = value

    for key, value in c.items():
        if ret.has_key(key):
            ret[key] += value
        else:
            ret[key] = value
    return ret


isPrime = [True for i in range(101)]
for i in range(2, 101):
    if isPrime[i] is True:
        for j in range(i + i, 101, i):
            isPrime[j] = False
primeList = [i for i in range(2, 101) if isPrime[i] is True]

decomposition = [None] * 101
decomposition[1] = {2:0} # special workaround
for prime in primeList:
    decomposition[prime] = {prime : 1}
    for i in range(2, 101):
        if decomposition[i] is not None and i * prime < 101:
            decomposition[i * prime] = decomposition[i].copy()
            if prime not in decomposition[i * prime].keys():
                decomposition[i * prime][prime] = 1
            else:
                decomposition[i * prime][prime] += 1


a, b, c = map(int, raw_input().split())
hashTable = {}
ans = 0
for ai in range(1, a+1):
    for bi in range(1, b+1):
        for ci in range(1, c+1):
            d = ai * bi * ci
            if hashTable.has_key(d):
                ans += hashTable[d]
            else:
                merge = mergeDict(decomposition[ai], decomposition[bi], decomposition[ci])
                num = reduce(lambda x, y: x*y, map(lambda x: x+1, merge.values()))
                ans += num
                hashTable[d] = num
            ans %= 1073741824

print ans