<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:
    def minJumps(self, arr):
        n = len(arr)
        if n == 1:
            return 0
        
        min_count = {arr[n-1]:0}
        jumps = list(range(n))

        for idx, val in enumerate(arr[-2::-1]):
            if val in min_count:
                jumps[idx + 1] = min(jumps[idx] + 1, min_count[val] + 1)
                min_count[val] = min(min_count[val], jumps[idx + 1])
            else:
                jumps[idx + 1] = jumps[idx] + 1
                min_count[val] = jumps[idx + 1]

        previous = None

        while previous != jumps:
            previous = jumps.copy()
            for idx, val in enumerate(arr[-2:0:-1]):        
                jumps[idx + 1] = min(jumps[idx + 2] + 1, jumps[idx] + 1, min_count[val] + 1)
                min_count[val] = min(min_count[val], jumps[idx + 1])
            

        return min(min_count[arr[0]], jumps[n-2]) + 1
900