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 ≤ 100).

Output

Print a single integer — the required sum modulo 1073741824 (230).

Examples

Input

2 2 2


Output

20


Input

5 6 7


Output

1520

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.
import sys, math, itertools, random, bisect
from collections import defaultdict
INF = sys.maxsize
def get_ints(): return map(int, sys.stdin.readline().strip().split())
def get_array(): return list(map(int, sys.stdin.readline().strip().split()))
def input(): return sys.stdin.readline().strip()
mod = 10**9 + 7

mp = {}

def d(x):
    global mp
    if x in mp: return mp[x]
    r = 1
    ans = 0
    while r*r <= x:
        if x%r==0:
            if x==r*r: ans += 1
            else: ans += 2
        r+=1
    mp[x] = ans
    return ans

for _ in range(1):
    a,b,c = get_ints()
    ans = 0
    for i in range(1,a+1):
        for j in range(1,b+1):
            for k in range(1,c+1):
                x = i*j*k
                ans += d(x)
    print(ans)


