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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <typename T>
T gcd(T a, T b) {
  return (b == 0) ? a : gcd(b, a % b);
}
template <typename T>
T lcm(T a, T b) {
  return a * (b / gcd(a, b));
}
long long modulo(long long a, long long b) {
  return a >= 0 ? a % b : (b - abs(a % b)) % b;
}
int divisor(int i) {
  int cnt = 0;
  for (int j = 1; j * j <= i; j++) {
    if (j * j == i)
      cnt++;
    else if (i % j == 0)
      cnt += 2;
  }
  return cnt;
}
void solve() {
  string st, stt;
  long long low = 0, high = 0;
  long long l, r;
  char ch;
  long long n, k, t, x, y, z, d = 0, cnt = 0, temp = 0, sum = 0, f = 0,
                              flag = 0;
  cin >> x >> y >> z;
  vector<long long> v, a;
  set<long long> s;
  map<long long, long long> m, mm;
  pair<long long, long long> p;
  temp = x * y * z;
  for (int i = 1; i <= x; i++) {
    for (int j = 1; j <= y; j++) {
      for (int q = 1; q <= z; q++) {
        d = i * j * q;
        if (m[d] == 0) m[d] = divisor(d);
        sum += m[d];
      }
    }
  }
  cout << sum % 1073741824 << endl;
}
int main() {
  int t;
  solve();
}