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.
#!/usr/bin/python
from __future__ import division
from sys import stdin, stdout, maxint

R, G, B = map (int, stdin.readline ().split ())

lo, hi = 0, min (R, G, B) + 1
best = 0

while lo < hi:
	mid = (lo + hi) // 2
	
	# make *mid* mixing bouquets
	newR, newG, newB = R - mid, G - mid, B - mid
	tot = (newR // 3) + (newG // 3) + (newB // 3) + mid
	
	if tot >= best:
		best = tot
		lo = mid + 1
	else:
		hi = mid

print best