<p>Given an array of&nbsp;integers <code>arr</code>, you are initially positioned at the first index of the array.</p>

<p>In one step you can jump from index <code>i</code> to index:</p>

<ul>
	<li><code>i + 1</code> where:&nbsp;<code>i + 1 &lt; arr.length</code>.</li>
	<li><code>i - 1</code> where:&nbsp;<code>i - 1 &gt;= 0</code>.</li>
	<li><code>j</code> where: <code>arr[i] == arr[j]</code> and <code>i != j</code>.</li>
</ul>

<p>Return <em>the minimum number of steps</em> to reach the <strong>last index</strong> of the array.</p>

<p>Notice that you can not jump outside of the array at any time.</p>

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

<pre>
<strong>Input:</strong> arr = [100,-23,-23,404,100,23,23,23,3,404]
<strong>Output:</strong> 3
<strong>Explanation:</strong> You need three jumps from index 0 --&gt; 4 --&gt; 3 --&gt; 9. Note that index 9 is the last index of the array.
</pre>

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

<pre>
<strong>Input:</strong> arr = [7]
<strong>Output:</strong> 0
<strong>Explanation:</strong> Start index is the last index. You do not need to jump.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> arr = [7,6,9,6,9,6,9,7]
<strong>Output:</strong> 1
<strong>Explanation:</strong> You can jump directly from index 0 to index 7 which is last index of the array.
</pre>

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

<ul>
	<li><code>1 &lt;= arr.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>-10<sup>8</sup> &lt;= arr[i] &lt;= 10<sup>8</sup></code></li>
</ul>

class Solution:
    from collections import defaultdict
    def minJumps(self, arr: List[int]) -> int:
        jump_num_to_indices = defaultdict(list)
        for i in range(len(arr)):
            jump_num = arr[i]
            jump_num_to_indices[jump_num].append(i)
        print(jump_num_to_indices)

        seen = set()
        seen_jump_nums = set()
        dist = 0
        indices_of_interest = [len(arr) - 1]
        while 0 not in indices_of_interest:
            new_indices_of_interest = list()
            for index in indices_of_interest:
                jump_num = arr[index]
                if jump_num in seen_jump_nums:
                    jump_num_indices = []
                else:
                    seen_jump_nums.add(jump_num)
                    jump_num_indices = jump_num_to_indices[jump_num]
                    
                for n_index in [index - 1, index + 1] + jump_num_indices:
                    if n_index < 0 or n_index >= len(arr) or n_index in seen:
                        continue
                    new_indices_of_interest.append(n_index)
                    seen.add(n_index)
            dist += 1
            indices_of_interest = new_indices_of_interest
        return dist
34026