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 r, g, b;
  cin >> r >> g >> b;
  bool a = true;
  if (!r || !g || !b) a = false;
  long long ans = 0;
  ans = (r / 3) + (g / 3) + (b / 3);
  long long v[3] = {0};
  v[r % 3]++;
  v[g % 3]++;
  v[b % 3]++;
  ans += min((r % 3), min((g % 3), (b % 3)));
  if (v[2] == 2 && v[0] == 1 && a)
    cout << ans + 1;
  else
    cout << ans;
}
