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;
void f(int& r, int& g, int& b) {
  if (r >= 3 && g % 3 == 2 && b % 3 == 2) {
    r += 4;
    g -= 2;
    b -= 2;
  }
}
int main(void) {
  int r, g, b;
  cin >> r >> g >> b;
  f(r, g, b);
  f(g, r, b);
  f(b, r, g);
  cout << r / 3 + g / 3 + b / 3 + min(r % 3, min(g % 3, b % 3)) << endl;
  return 0;
}
