class Solution:
    def stoneGameIII(self, stoneValue: List[int]) -> str:

        from functools import lru_cache
        @lru_cache(maxsize=None)
        def getScore(i):
            if i == len(stoneValue):
                return 0
            best = float('-inf')
            score = 0
            for j in range(3):
                if i + j == len(stoneValue):
                    break
                x = stoneValue[i + j]
                score += x
                best = max(best, score - getScore(i + j + 1))
            return best


        total = sum(stoneValue)
        diff = getScore(0)
        if diff == 0:
            return "Tie"
        if diff > 0:
            return "Alice"
        return "Bob"