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:

• <code>1 <= a, b, c <= 10⁵</code>