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.
\n
Example 1:
\n\n\nInput: a = 2, b = 4, c = 6\nOutput: 6\nExplanation: The starting state is (2, 4, 6). One optimal set of moves is:\n- Take from 1st and 3rd piles, state is now (1, 4, 5)\n- Take from 1st and 3rd piles, state is now (0, 4, 4)\n- Take from 2nd and 3rd piles, state is now (0, 3, 3)\n- Take from 2nd and 3rd piles, state is now (0, 2, 2)\n- Take from 2nd and 3rd piles, state is now (0, 1, 1)\n- Take from 2nd and 3rd piles, state is now (0, 0, 0)\nThere are fewer than two non-empty piles, so the game ends. Total: 6 points.\n\n\n
Example 2:
\n\n\nInput: a = 4, b = 4, c = 6\nOutput: 7\nExplanation: The starting state is (4, 4, 6). One optimal set of moves is:\n- Take from 1st and 2nd piles, state is now (3, 3, 6)\n- Take from 1st and 3rd piles, state is now (2, 3, 5)\n- Take from 1st and 3rd piles, state is now (1, 3, 4)\n- Take from 1st and 3rd piles, state is now (0, 3, 3)\n- Take from 2nd and 3rd piles, state is now (0, 2, 2)\n- Take from 2nd and 3rd piles, state is now (0, 1, 1)\n- Take from 2nd and 3rd piles, state is now (0, 0, 0)\nThere are fewer than two non-empty piles, so the game ends. Total: 7 points.\n\n\n
Example 3:
\n\n\nInput: a = 1, b = 8, c = 8\nOutput: 8\nExplanation: One optimal set of moves is to take from the 2nd and 3rd piles for 8 turns until they are empty.\nAfter that, there are fewer than two non-empty piles, so the game ends.\n\n\n
\n
Constraints:
\n\n1 <= a, b, c <= 105你正在玩一个单人游戏，面前放置着大小分别为 a、b 和 c 的 三堆 石子。
每回合你都要从两个 不同的非空堆 中取出一颗石子，并在得分上加 1 分。当存在 两个或更多 的空堆时，游戏停止。
给你三个整数 a 、b 和 c ，返回可以得到的 最大分数 。
示例 1：
\n\n\n输入：a = 2, b = 4, c = 6\n输出：6\n解释：石子起始状态是 (2, 4, 6) ，最优的一组操作是：\n- 从第一和第三堆取，石子状态现在是 (1, 4, 5)\n- 从第一和第三堆取，石子状态现在是 (0, 4, 4)\n- 从第二和第三堆取，石子状态现在是 (0, 3, 3)\n- 从第二和第三堆取，石子状态现在是 (0, 2, 2)\n- 从第二和第三堆取，石子状态现在是 (0, 1, 1)\n- 从第二和第三堆取，石子状态现在是 (0, 0, 0)\n总分：6 分 。\n\n\n
示例 2：
\n\n\n输入：a = 4, b = 4, c = 6\n输出：7\n解释：石子起始状态是 (4, 4, 6) ，最优的一组操作是：\n- 从第一和第二堆取，石子状态现在是 (3, 3, 6)\n- 从第一和第三堆取，石子状态现在是 (2, 3, 5)\n- 从第一和第三堆取，石子状态现在是 (1, 3, 4)\n- 从第一和第三堆取，石子状态现在是 (0, 3, 3)\n- 从第二和第三堆取，石子状态现在是 (0, 2, 2)\n- 从第二和第三堆取，石子状态现在是 (0, 1, 1)\n- 从第二和第三堆取，石子状态现在是 (0, 0, 0)\n总分：7 分 。\n\n\n
示例 3：
\n\n\n输入：a = 1, b = 8, c = 8\n输出：8\n解释：最优的一组操作是连续从第二和第三堆取 8 回合，直到将它们取空。\n注意，由于第二和第三堆已经空了，游戏结束，不能继续从第一堆中取石子。\n\n\n
\n\n
提示：
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