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() {
  int r, g, b, count = 0, exception = 0;
  cin >> r >> g >> b;
  if (r == 0 || g == 0 || b == 0) exception = 1;
  while (r > 2) {
    r = r - 3;
    count++;
  }
  while (g > 2) {
    g = g - 3;
    count++;
  }
  while (b > 2) {
    b = b - 3;
    count++;
  }
  while (r > 0 && g > 0 && b > 0) {
    r--;
    g--;
    b--;
    count++;
  }
  if (((r == 2 && g == 2) || (g == 2 && b == 2) || (r == 2 && b == 2)) &&
      (exception == 0))
    count++;
  cout << count << endl;
}
