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.
a,b,c=map(int,input().split())
x,y,z=a,b,c
count=0
if c<b:
    b,c=c,b
if b<a:
    a,b=b,a
p,q,r=a,b,c
count=count+a
b=b-a
c=c-a
count=count+b//3+c//3
min=x//3+y//3+z//3
x=x%3
y=y%3
z=z%3
if z<y:
    y,z=z,y
if y<x:
    x,y=y,x
if min>count:
    count=min
elif min==count:
    if x==0 and y==2 and z==2 and p!=0:
        count=count+1
print(count)