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"content": "<p>Alice and Bob take turns playing a game, with <strong>Alice starting first</strong>.</p>\n\n<p>There are <code>n</code> stones arranged in a row. On each player's turn, they can <strong>remove</strong> either the leftmost stone or the rightmost stone from the row and receive points equal to the <strong>sum</strong> of the remaining stones' values in the row. The winner is the one with the higher score when there are no stones left to remove.</p>\n\n<p>Bob found that he will always lose this game (poor Bob, he always loses), so he decided to <strong>minimize the score's difference</strong>. Alice's goal is to <strong>maximize the difference</strong> in the score.</p>\n\n<p>Given an array of integers <code>stones</code> where <code>stones[i]</code> represents the value of the <code>i<sup>th</sup></code> stone <strong>from the left</strong>, return <em>the <strong>difference</strong> in Alice and Bob's score if they both play <strong>optimally</strong>.</em></p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> stones = [5,3,1,4,2]\n<strong>Output:</strong> 6\n<strong>Explanation:</strong> \n- Alice removes 2 and gets 5 + 3 + 1 + 4 = 13 points. Alice = 13, Bob = 0, stones = [5,3,1,4].\n- Bob removes 5 and gets 3 + 1 + 4 = 8 points. Alice = 13, Bob = 8, stones = [3,1,4].\n- Alice removes 3 and gets 1 + 4 = 5 points. Alice = 18, Bob = 8, stones = [1,4].\n- Bob removes 1 and gets 4 points. Alice = 18, Bob = 12, stones = [4].\n- Alice removes 4 and gets 0 points. Alice = 18, Bob = 12, stones = [].\nThe score difference is 18 - 12 = 6.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> stones = [7,90,5,1,100,10,10,2]\n<strong>Output:</strong> 122</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == stones.length</code></li>\n\t<li><code>2 <= n <= 1000</code></li>\n\t<li><code>1 <= stones[i] <= 1000</code></li>\n</ul>\n",
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