<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:
        if arr is None or len(arr)==0:
            return -1
        
        n=len(arr)

        map={}
        for i in range(n):
            cur=arr[i]
            if cur not in map:
                map[cur]=[]

            map[cur].append(i)

        q1={0}
        q2={n-1}
        step=0
        seen={0}

        while len(q1)>0:
            size=len(q1)
            newq=set()
            for _ in range(size):
                cur_idx=q1.pop()
                if cur_idx in q2:
                    return step
                
                seen.add(cur_idx)
                
                if cur_idx-1>=0 and cur_idx-1 not in seen:
                    newq.add(cur_idx-1)
                
                if cur_idx+1<n and cur_idx+1 not in seen:
                    newq.add(cur_idx+1)
                
                if arr[cur_idx] in map:
                    for idx in map[arr[cur_idx]]:
                        if idx not in seen:
                            newq.add(idx)
                
                    map.pop(arr[cur_idx])
            
            q1=newq

            if len(q1)==0:
                return -1

            if len(q1)>len(q2):
                q1,q2=q2,q1

            step+=1

        return -1
                

        
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