public class Solution
extends Object
1753 - Maximum Score From Removing Stones\.
Medium
You are playing a solitaire game with **three piles** of stones of sizes `a`, `b`, and `c` respectively. Each turn you choose two **different non-empty** piles, take one stone from each, and add `1` point to your score. The game stops when there are **fewer than two non-empty** piles (meaning there are no more available moves).
Given three integers `a`, `b`, and `c`, return _the_ **_maximum_** _**score** you can get._
**Example 1:**
**Input:** a = 2, b = 4, c = 6
**Output:** 6
**Explanation:** The starting state is (2, 4, 6). One optimal set of moves is:
- Take from 1st and 3rd piles, state is now (1, 4, 5)
- Take from 1st and 3rd piles, state is now (0, 4, 4)
- Take from 2nd and 3rd piles, state is now (0, 3, 3)
- Take from 2nd and 3rd piles, state is now (0, 2, 2)
- Take from 2nd and 3rd piles, state is now (0, 1, 1)
- Take from 2nd and 3rd piles, state is now (0, 0, 0)
There are fewer than two non-empty piles, so the game ends. Total: 6 points.
**Example 2:**
**Input:** a = 4, b = 4, c = 6
**Output:** 7
**Explanation:** The starting state is (4, 4, 6). One optimal set of moves is:
- Take from 1st and 2nd piles, state is now (3, 3, 6)
- Take from 1st and 3rd piles, state is now (2, 3, 5)
- Take from 1st and 3rd piles, state is now (1, 3, 4)
- Take from 1st and 3rd piles, state is now (0, 3, 3)
- Take from 2nd and 3rd piles, state is now (0, 2, 2)
- Take from 2nd and 3rd piles, state is now (0, 1, 1)
- Take from 2nd and 3rd piles, state is now (0, 0, 0)
There are fewer than two non-empty piles, so the game ends. Total: 7 points.
**Example 3:**
**Input:** a = 1, b = 8, c = 8
**Output:** 8
**Explanation:** One optimal set of moves is to take from the 2nd and 3rd piles for 8 turns until they are empty. After that, there are fewer than two non-empty piles, so the game ends.
**Constraints:**
* 1 <= a, b, c <= 105