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# 1345. Jump Game IV

Given an array of integers `arr`, you are initially positioned at the first index of the array.

In one step you can jump from index `i` to index:

• `i + 1` where: `i + 1 < arr.length`.
• `i - 1` where: `i - 1 >= 0`.
• `j` where: `arr[i] == arr[j]` and `i != j`.

Return the minimum number of steps to reach the last index of the array.

Notice that you can not jump outside of the array at any time.

Example 1:

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

Example 2:

```Input: arr = [7]
Output: 0
Explanation: Start index is the last index. You don't need to jump.
```

Example 3:

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

Example 4:

```Input: arr = [6,1,9]
Output: 2
```

Example 5:

```Input: arr = [11,22,7,7,7,7,7,7,7,22,13]
Output: 3
```

Constraints:

• `1 <= arr.length <= 5 * 10^4`
• `-10^8 <= arr[i] <= 10^8`

Hard

Normal