#include <bits/stdc++.h>
using namespace std;
inline char gc() {
  static char buf[100000], *p1 = buf, *p2 = buf;
  return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 100000, stdin), p1 == p2)
             ? EOF
             : *p1++;
}
inline int read() {
  int x = 0;
  char ch = getchar();
  bool positive = 1;
  for (; !isdigit(ch); ch = getchar())
    if (ch == '-') positive = 0;
  for (; isdigit(ch); ch = getchar()) x = x * 10 + ch - '0';
  return positive ? x : -x;
}
inline void write(int a) {
  if (a < 0) {
    a = -a;
    putchar('-');
  }
  if (a >= 10) write(a / 10);
  putchar('0' + a % 10);
}
inline void writeln(int a) {
  if (a < 0) {
    a = -a;
    putchar('-');
  }
  write(a);
  puts("");
}
inline int rnd(int x) { return rand() % x; }
inline unsigned long long rnd() {
  return ((unsigned long long)rand() << 30 ^ rand()) << 4 | rand() % 4;
}
const int N = 2005;
int n, k, a, b, c, tot, que[N / 3], ycl[N][N];
char miu[N];
long long ans;
bitset<N> vis, heshu;
inline int qiu(int i, int j) {
  if (j == 0) return i;
  if (ycl[i][j]) return ycl[i][j];
  return qiu(j, i % j);
}
int main() {
  a = read();
  b = read();
  c = read();
  if (a > b) swap(a, b);
  if (a > c) swap(a, c);
  if (b > c) swap(b, c);
  n = c;
  miu[1] = 1;
  for (int i = 2; i <= n; i++) {
    if (!heshu[i]) {
      que[++tot] = i;
      miu[i] = -1;
    }
    for (int j = 1; j <= tot && que[j] * i <= n; j++) {
      int k = que[j] * i;
      heshu[k] = 1;
      if (i % que[j] == 0) {
        miu[k] = 0;
        break;
      }
      miu[k] = -miu[i];
    }
  }
  heshu[1] = 1;
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++) ycl[i][j] = qiu(i, j);
  for (int i = 1; i <= a; i++) {
    for (int j = 1; j <= b; j++) {
      int sum1 = 0, sum2 = 0;
      for (int k = j; k <= b; k += j)
        if (ycl[i][k] == 1) sum1 += b / k;
      for (int k = j; k <= c; k += j)
        if (ycl[i][k] == 1) sum2 += c / k;
      ans = (ans + miu[j] * sum1 * sum2 * (a / i));
    }
  }
  unsigned jb = ans;
  cout << jb % (1 << 30) << endl;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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:

<image>

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
inline char gc() {
  static char buf[100000], *p1 = buf, *p2 = buf;
  return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 100000, stdin), p1 == p2)
             ? EOF
             : *p1++;
}
inline int read() {
  int x = 0;
  char ch = getchar();
  bool positive = 1;
  for (; !isdigit(ch); ch = getchar())
    if (ch == '-') positive = 0;
  for (; isdigit(ch); ch = getchar()) x = x * 10 + ch - '0';
  return positive ? x : -x;
}
inline void write(int a) {
  if (a < 0) {
    a = -a;
    putchar('-');
  }
  if (a >= 10) write(a / 10);
  putchar('0' + a % 10);
}
inline void writeln(int a) {
  if (a < 0) {
    a = -a;
    putchar('-');
  }
  write(a);
  puts("");
}
inline int rnd(int x) { return rand() % x; }
inline unsigned long long rnd() {
  return ((unsigned long long)rand() << 30 ^ rand()) << 4 | rand() % 4;
}
const int N = 2005;
int n, k, a, b, c, tot, que[N / 3], ycl[N][N];
char miu[N];
long long ans;
bitset<N> vis, heshu;
inline int qiu(int i, int j) {
  if (j == 0) return i;
  if (ycl[i][j]) return ycl[i][j];
  return qiu(j, i % j);
}
int main() {
  a = read();
  b = read();
  c = read();
  if (a > b) swap(a, b);
  if (a > c) swap(a, c);
  if (b > c) swap(b, c);
  n = c;
  miu[1] = 1;
  for (int i = 2; i <= n; i++) {
    if (!heshu[i]) {
      que[++tot] = i;
      miu[i] = -1;
    }
    for (int j = 1; j <= tot && que[j] * i <= n; j++) {
      int k = que[j] * i;
      heshu[k] = 1;
      if (i % que[j] == 0) {
        miu[k] = 0;
        break;
      }
      miu[k] = -miu[i];
    }
  }
  heshu[1] = 1;
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++) ycl[i][j] = qiu(i, j);
  for (int i = 1; i <= a; i++) {
    for (int j = 1; j <= b; j++) {
      int sum1 = 0, sum2 = 0;
      for (int k = j; k <= b; k += j)
        if (ycl[i][k] == 1) sum1 += b / k;
      for (int k = j; k <= c; k += j)
        if (ycl[i][k] == 1) sum2 += c / k;
      ans = (ans + miu[j] * sum1 * sum2 * (a / i));
    }
  }
  unsigned jb = ans;
  cout << jb % (1 << 30) << endl;
}

```