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 $*b*$ ($0 ≤ *r*, *g*, *b* ≤ 10^{9}$) — the number of red, green and blue flowers.

Output

Print the maximal number of bouquets Fox Ciel can make.

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.