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.
def main():
    r, g, b = map(int, input().split())
    f = (r // 3) + (g // 3) + (b // 3) + min(r - (r // 3) * 3, g - (g // 3) * 3, b - (b // 3) * 3)
    t = min(r, g, b)
    s = t + (r - t) // 3 + (g - t) // 3 + (b - t) // 3
    ans = max(f, s)
    for t in range(0, min(2, r, g, b) + 1):
        ans = max(ans, t + (r - t) // 3 + (g - t) // 3 + (b - t) // 3)
    print(ans)


if __name__ == "__main__":
    main()
