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.
import itertools
a = raw_input()
a = a.split()
r = int(a[0])
g = int(a[1])
b = int(a[2])

def f_one(*colors):
    ans = min(colors)
    if ans<0:
        ans = 0
    colors = [color - ans for color in colors]
    for color in colors:
        if color >= 3:
            ans = ans + (color/3)
    return ans
def f_three(colors,c):
    ans = 0
    for color in c:
        if colors[color]>= 3:
            #print colors[color],(colors[color] /3)
            ans = ans + (colors[color] /3)
            #print ans
    for i in c:
        colors[i] %=3
    return ans ,colors
colors = [r,g,b]

ans = []
for i in range(1,4):
     for j in itertools.combinations([0,1,2],i):
        f = [c for c in colors]
        a , f = f_three(f,j)
        #print a,f
        a += f_one(*f)
        #print a,j
        ans.append(a)
print max(ans)
