<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: List[int]) -> int:

        patterns = defaultdict(lambda: set())
        equalPos = {}
        for i in range(len(arr)-1, -1, -1):
            num = arr[i]
            if num in equalPos:
                if i > 0 and i < len(arr)-1:
                    if arr[i-1] == arr[i] and arr[i+1] == arr[i]:
                        continue
                    if str(arr[i-1]) + " " + str(arr[i+1]) in patterns[num]:
                        continue
                    patterns[num].add(str(arr[i-1]) + " " + str(arr[i+1]))
                equalPos[num].append(i)
            else:
                equalPos[num] = [i]
            
        queue = [(0, 0)]
        visited = set()

        while queue:
            curIndex, curDepth = queue.pop(0)

            if curIndex in visited:
                continue
            visited.add(curIndex)

            if curIndex == len(arr)-1:
                return curDepth

            if curIndex + 1 not in visited:
                queue.append((curIndex + 1, curDepth+1))
                if curIndex + 1 == len(arr)-1:
                    return curDepth + 1
            
            if curIndex - 1 not in visited and curIndex > 0:
                queue.append((curIndex-1, curDepth+1))
            
            for paraIndex in equalPos[arr[curIndex]]:                
                
                if not paraIndex in visited:
                    queue.append((paraIndex, curDepth+1))
                if paraIndex == len(arr)-1:
                    return curDepth+1
        return -1
            
559