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 solve(a: int, b: int, c: int):
    maps = sorted(map(lambda x: (x % 3, x // 3), [a, b, c]))
    # print(maps)
    sum_of_quotients = sum(m[1] for m in maps)
    if maps[0][0] == 0 and maps[0][1] > 0 and maps[1][0] >= 2 and maps[2][0] >= 2:
        return sum_of_quotients + 1
    elif all(m[0] > 0 for m in maps):
        return sum_of_quotients + min(m[0] for m in maps)
    return sum_of_quotients


assert solve(3, 6, 9) == 6
assert solve(4, 4, 4) == 4
assert solve(0, 0, 0) == 0
a, b, c = map(int, input().split())
print(solve(a, b, c))
