<p>You are given a string <code>s</code> consisting of lowercase letters and an integer <code>k</code>. We call a string <code>t</code> <strong>ideal</strong> if the following conditions are satisfied:</p>

<ul>
	<li><code>t</code> is a <strong>subsequence</strong> of the string <code>s</code>.</li>
	<li>The absolute difference in the alphabet order of every two <strong>adjacent</strong> letters in <code>t</code> is less than or equal to <code>k</code>.</li>
</ul>

<p>Return <em>the length of the <strong>longest</strong> ideal string</em>.</p>

<p>A <strong>subsequence</strong> is a string that can be derived from another string by deleting some or no characters without changing the order of the remaining characters.</p>

<p><strong>Note</strong> that the alphabet order is not cyclic. For example, the absolute difference in the alphabet order of <code>&#39;a&#39;</code> and <code>&#39;z&#39;</code> is <code>25</code>, not <code>1</code>.</p>

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

<pre>
<strong>Input:</strong> s = &quot;acfgbd&quot;, k = 2
<strong>Output:</strong> 4
<strong>Explanation:</strong> The longest ideal string is &quot;acbd&quot;. The length of this string is 4, so 4 is returned.
Note that &quot;acfgbd&quot; is not ideal because &#39;c&#39; and &#39;f&#39; have a difference of 3 in alphabet order.</pre>

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

<pre>
<strong>Input:</strong> s = &quot;abcd&quot;, k = 3
<strong>Output:</strong> 4
<strong>Explanation:</strong> The longest ideal string is &quot;abcd&quot;. The length of this string is 4, so 4 is returned.
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= k &lt;= 25</code></li>
	<li><code>s</code> consists of lowercase English letters.</li>
</ul>

class Solution:
    def longestIdealString(self, s: str, k: int) -> int:
        # result = ""
        # print("char, ord(char)", 'a', ord('a'))
        # print("char, ord(char)", 'b', ord('b'))
        # print("char, ord(char)", 'c', ord('c'))

        charIdxes = defaultdict(list)

        for idx, char in enumerate(s):
            charIdxes[char].append(idx)
        
        dp = [1] * len(s)
        for idx in range(len(dp)):
            if idx == 0:
                continue
            
            maxlastLength = 0
            idxChar = s[idx]
            for charOrd in range(ord(idxChar) - k, ord(idxChar) + k + 1):
                visitingChar = chr(charOrd)
                if visitingChar in charIdxes.keys():
                    findIdx = bisect.bisect_left(charIdxes[visitingChar], idx - 0.5)
                    # print("visitingChar", visitingChar)
                    # print("idx - 0.5", idx - 0.5)
                    # print("charIdxes[visitingChar]", charIdxes[visitingChar])
                    # print("findIdx", findIdx)
                    if findIdx == 0:
                        continue

                    closestIdx = charIdxes[visitingChar][findIdx-1]
                    # print("closestIdx", closestIdx)
                
                    maxlastLength = max(maxlastLength, dp[closestIdx])
                    # print("maxlastLength", maxlastLength)
            
            
            dp[idx] += maxlastLength

        # print("dp",dp)
        return max(dp)
            
25500