Fox Ciel has some flowers: r red flowers, g green flowers and b blue flowers. She wants to use these flowers to make several bouquets. There are 4 types of bouquets:

  * To make a "red bouquet", it needs 3 red flowers. 
  * To make a "green bouquet", it needs 3 green flowers. 
  * To make a "blue bouquet", it needs 3 blue flowers. 
  * To make a "mixing bouquet", it needs 1 red, 1 green and 1 blue flower. 



Help Fox Ciel to find the maximal number of bouquets she can make.

Input

The first line contains three integers r, g and b (0 ≤ r, g, b ≤ 109) — the number of red, green and blue flowers.

Output

Print the maximal number of bouquets Fox Ciel can make.

Examples

Input

3 6 9


Output

6


Input

4 4 4


Output

4


Input

0 0 0


Output

0

Note

In test case 1, we can make 1 red bouquet, 2 green bouquets and 3 blue bouquets.

In test case 2, we can make 1 red, 1 green, 1 blue and 1 mixing bouquet.
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long z, t, r, b, i, j, m, c;
  long long a[3];
  cin >> z >> b >> t;
  a[0] = z;
  a[1] = b;
  a[2] = t;
  sort(a, a + 3);
  long long s1 = (a[1] / 3) + (a[2] / 3) + min(a[0], min(a[1] % 3, a[2] % 3)) +
                 ((a[0] - min(a[0], min(a[1] % 3, a[2] % 3))) / 3);
  a[1] = a[1] - a[0];
  a[2] = a[2] - a[0];
  long long s2 = a[0] + (a[1] / 3) + (a[2] / 3);
  cout << max(s1, s2);
  return 0;
}
