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<p>You have an initial <strong>power</strong> of <code>power</code>, an initial <strong>score</strong> of <code>0</code>, and a bag of <code>tokens</code> where <code>tokens[i]</code> is the value of the <code>i<sup>th</sup></code> token (0-indexed).</p>
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<p>You start with an initial <strong>power</strong> of <code>power</code>, an initial <strong>score</strong> of <code>0</code>, and a bag of tokens given as an integer array <code>tokens</code>, where each <code>tokens[i]</code> denotes the value of token<em><sub>i</sub></em>.</p>
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<p>Your goal is to maximize your total <strong>score</strong> by potentially playing each token in one of two ways:</p>
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<p>Your goal is to <strong>maximize</strong> the total <strong>score</strong> by strategically playing these tokens. In one move, you can play an <strong>unplayed</strong> token in one of the two ways (but not both for the same token):</p>
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<ul>
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<li>If your current <strong>power</strong> is at least <code>tokens[i]</code>, you may play the <code>i<sup>th</sup></code> token face up, losing <code>tokens[i]</code> <strong>power</strong> and gaining <code>1</code> <strong>score</strong>.</li>
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<li>If your current <strong>score</strong> is at least <code>1</code>, you may play the <code>i<sup>th</sup></code> token face down, gaining <code>tokens[i]</code> <strong>power</strong> and losing <code>1</code> <strong>score</strong>.</li>
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<li><strong>Face-up</strong>: If your current power is <strong>at least</strong> <code>tokens[i]</code>, you may play token<em><sub>i</sub></em>, losing <code>tokens[i]</code> power and gaining <code>1</code> score.</li>
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<li><strong>Face-down</strong>: If your current score is <strong>at least</strong> <code>1</code>, you may play token<em><sub>i</sub></em>, gaining <code>tokens[i]</code> power and losing <code>1</code> score.</li>
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</ul>
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<p>Each token may be played <strong>at most</strong> once and <strong>in any order</strong>. You do <strong>not</strong> have to play all the tokens.</p>
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<p>Return <em>the largest possible <strong>score</strong> you can achieve after playing any number of tokens</em>.</p>
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<p>Return <em>the <strong>maximum</strong> possible score you can achieve after playing <strong>any</strong> number of tokens</em>.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> tokens = [100], power = 50
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<strong>Output:</strong> 0
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<strong>Explanation</strong><strong>:</strong> Playing the only token in the bag is impossible because you either have too little power or too little score.
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</pre>
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<div class="example-block" style="
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border-color: var(--border-tertiary);
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border-left-width: 2px;
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color: var(--text-secondary);
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font-size: .875rem;
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margin-bottom: 1rem;
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margin-top: 1rem;
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overflow: visible;
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padding-left: 1rem;
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">
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<p><strong>Input:</strong> <span class="example-io" style="
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font-family: Menlo,sans-serif;
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font-size: 0.85rem;
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">tokens = [100], power = 50</span></p>
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<p><strong>Output:</strong> <span class="example-io" style="
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font-family: Menlo,sans-serif;
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font-size: 0.85rem;
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">0</span></p>
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<p><strong>Explanation</strong><strong>:</strong> Since your score is <code>0</code> initially, you cannot play the token face-down. You also cannot play it face-up since your power (<code>50</code>) is less than <code>tokens[0]</code> (<code>100</code>).</p>
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</div>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> tokens = [100,200], power = 150
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<strong>Output:</strong> 1
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<strong>Explanation:</strong> Play the 0<sup>th</sup> token (100) face up, your power becomes 50 and score becomes 1.
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There is no need to play the 1<sup>st</sup> token since you cannot play it face up to add to your score.
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</pre>
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<div class="example-block" style="
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border-color: var(--border-tertiary);
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border-left-width: 2px;
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color: var(--text-secondary);
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font-size: .875rem;
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margin-bottom: 1rem;
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margin-top: 1rem;
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overflow: visible;
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padding-left: 1rem;
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">
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<p><strong>Input:</strong> <span class="example-io" style="
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font-family: Menlo,sans-serif;
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font-size: 0.85rem;
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">tokens = [200,100], power = 150</span></p>
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<p><strong>Output:</strong> <span class="example-io" style="
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font-family: Menlo,sans-serif;
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font-size: 0.85rem;
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">1</span></p>
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<p><strong>Explanation:</strong> Play token<em><sub>1</sub></em> (<code>100</code>) face-up, reducing your power to <code>50</code> and increasing your score to <code>1</code>.</p>
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<p>There is no need to play token<em><sub>0</sub></em>, since you cannot play it face-up to add to your score. The maximum score achievable is <code>1</code>.</p>
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</div>
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<p><strong class="example">Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> tokens = [100,200,300,400], power = 200
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<strong>Output:</strong> 2
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<strong>Explanation:</strong> Play the tokens in this order to get a score of 2:
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1. Play the 0<sup>th</sup> token (100) face up, your power becomes 100 and score becomes 1.
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2. Play the 3<sup>rd</sup> token (400) face down, your power becomes 500 and score becomes 0.
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3. Play the 1<sup>st</sup> token (200) face up, your power becomes 300 and score becomes 1.
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4. Play the 2<sup>nd </sup>token (300) face up, your power becomes 0 and score becomes 2.
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</pre>
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<div class="example-block" style="
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border-color: var(--border-tertiary);
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border-left-width: 2px;
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color: var(--text-secondary);
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font-size: .875rem;
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margin-bottom: 1rem;
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margin-top: 1rem;
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overflow: visible;
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padding-left: 1rem;
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">
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<p><strong>Input:</strong> <span class="example-io" style="
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font-family: Menlo,sans-serif;
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font-size: 0.85rem;
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">tokens = [100,200,300,400], power = 200</span></p>
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<p><strong>Output:</strong> <span class="example-io" style="
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font-family: Menlo,sans-serif;
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font-size: 0.85rem;
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">2</span></p>
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<p><strong>Explanation:</strong> Play the tokens in this order to get a score of <code>2</code>:</p>
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<ol>
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<li>Play token<em><sub>0</sub></em> (<code>100</code>) face-up, reducing power to <code>100</code> and increasing score to <code>1</code>.</li>
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<li>Play token<em><sub>3</sub></em> (<code>400</code>) face-down, increasing power to <code>500</code> and reducing score to <code>0</code>.</li>
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<li>Play token<em><sub>1</sub></em> (<code>200</code>) face-up, reducing power to <code>300</code> and increasing score to <code>1</code>.</li>
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<li>Play token<em><sub>2</sub></em> (<code>300</code>) face-up, reducing power to <code>0</code> and increasing score to <code>2</code>.</li>
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</ol>
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<p><span style="color: var(--text-secondary); font-size: 0.875rem;">The maximum score achievable is </span><code style="color: var(--text-secondary); font-size: 0.875rem;">2</code><span style="color: var(--text-secondary); font-size: 0.875rem;">.</span></p>
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</div>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>0 <= tokens.length <= 1000</code></li>
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<li><code>0 <= tokens[i], power < 10<sup>4</sup></code></li>
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<li><code>0 <= tokens[i], power < 10<sup>4</sup></code></li>
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</ul>
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