<p>There are some prizes on the <strong>X-axis</strong>. You are given an integer array <code>prizePositions</code> that is <strong>sorted in non-decreasing order</strong>, where <code>prizePositions[i]</code> is the position of the <code>i<sup>th</sup></code> prize. There could be different prizes at the same position on the line. You are also given an integer <code>k</code>.</p>

<p>You are allowed to select two segments with integer endpoints. The length of each segment must be <code>k</code>. You will collect all prizes whose position falls within at least one of the two selected segments (including the endpoints of the segments). The two selected segments may intersect.</p>

<ul>
	<li>For example if <code>k = 2</code>, you can choose segments <code>[1, 3]</code> and <code>[2, 4]</code>, and you will win any prize <font face="monospace">i</font> that satisfies <code>1 &lt;= prizePositions[i] &lt;= 3</code> or <code>2 &lt;= prizePositions[i] &lt;= 4</code>.</li>
</ul>

<p>Return <em>the <strong>maximum</strong> number of prizes you can win if you choose the two segments optimally</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> prizePositions = [1,1,2,2,3,3,5], k = 2
<strong>Output:</strong> 7
<strong>Explanation:</strong> In this example, you can win all 7 prizes by selecting two segments [1, 3] and [3, 5].
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> prizePositions = [1,2,3,4], k = 0
<strong>Output:</strong> 2
<strong>Explanation:</strong> For this example, <strong>one choice</strong> for the segments is <code>[3, 3]</code> and <code>[4, 4],</code> and you will be able to get <code>2</code> prizes. 
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= prizePositions.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= prizePositions[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>0 &lt;= k &lt;= 10<sup>9</sup> </code></li>
	<li><code>prizePositions</code> is sorted in non-decreasing order.</li>
</ul>

<p>&nbsp;</p>
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class Solution:
    def maximizeWin(self, prizePositions: List[int], k: int) -> int:
        n = len(prizePositions)
        s, e = 0, 0
        dp = [0] * (n+1)
        ans = 0
        while s < n:
            target = prizePositions[s] + k
            while e < n and prizePositions[e] <= target:
                e += 1
                dp[e] = max(e-s,dp[e-1])
                ans = max(dp[s] + e - s, ans )      
            s += 1
        return min(ans,n)

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