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

def main():
    isPrime = [True] * 101
    primeList = []
    for i in xrange(2, 101):
        if isPrime[i] is True:
            primeList.append(i)
            for j in xrange(i + i, 101, i):
                isPrime[j] = False

    decomposition = [None] * 101
    decomposition[1] = {2:0} # special workaround
    for prime in primeList:
        decomposition[prime] = {prime : 1}
        for i in xrange(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())
#a, b, c = 78, 90, 100
    hashTable = [0] * (a * b * c + 1)
    ans = 0
    for ai in xrange(1, a+1):
        for bi in xrange(1, b+1):
            for ci in xrange(1, c+1):
                d = ai * bi * ci
                if hashTable[d] is not 0:
                    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

    print ans % 1073741824

if __name__ == "__main__":
    main()