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.
r, g, b = map(int, raw_input().split())
x = r % 3
y = g % 3
z = b % 3
d = x % 3 + y % 3 + z % 3
if r >= 1 and g >= 1 and b >= 1: d = min(d, (x + 2) % 3 + (y + 2) % 3 + (z + 2) % 3)
if r >= 2 and g >= 2 and b >= 2: d = min(d, (x + 1) % 3 + (y + 1) % 3 + (z + 1) % 3)
print (r + g + b - d) / 3
