You are playing a game with $3$ piles of stones containing a, b, and c stones respectively. In each move, you can choose $2$ distinct piles that are not empty, remove $1$ stone from each of the selected piles, and earn $1$ point. The game ends when there are fewer than $2$ piles with stones remaining.

Return the maximum score you can achieve.

Constraints:

• $1 \leq$ a, b, c $\leq 10^5$

Input: a = 1-int, b = 1-int, c = 1-int
Output: 1-int
Explanation: Two piles can be selected for one move, earning 1 point, after which only one pile remains nonempty.

Input: a = 1-int, b = 1-int, c = 100-int
Output: 2-int
Explanation: The two smaller piles can each be paired once with the large pile, resulting in 2 points.

Input: a = 5-int, b = 7-int, c = 9-int
Output: 10-int
Explanation: The total number of stones is 21, so at most 10 pairs can be formed. The piles are balanced enough to achieve this maximum.

Input: a = 100000-int, b = 99999-int, c = 50000-int
Output: 124999-int
Explanation: The total number of stones is 249999, so at most 124999 pairs can be formed, and the pile sizes allow this maximum to be achieved.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.