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

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'class Solution:\n    def minJumps(self, arr: List[int]) -> int:\n        # return self.bfs(arr)\n        return self.minJumpsBiBFS(arr)\n    def bfs(self, arr: List[int]):\n        arrLen = len(arr)\n        if arrLen <= 1:\n            return 0\n        adjList = defaultdict(set)\n        for i in range(len(arr)):\n            adjList[arr[i]].add(i)\n        queue = deque([0])\n        visited = set([0])\n        jump = 0\n        \n        while queue:\n            length = len(queue)\n            \n            for _ in range(length):\n                node = queue.popleft()\n                for nei in adjList[arr[node]]:\n                    if nei == arrLen-1:\n                        return jump+1\n                    if nei in visited:\n                        continue\n                    visited.add(nei)\n                    queue.append(nei)\n                adjList[arr[node]].clear()\n                    \n                if node + 1 < arrLen:\n                    if node + 1 == arrLen-1:\n                        return jump+1\n                    if node + 1 not in visited:\n                        visited.add(node + 1)\n                        queue.append(node + 1)\n                    \n                if node -1 >= 0:\n                    if node - 1 == arrLen-1:\n                        return jump+1\n                    if node - 1 not in visited:\n                        visited.add(node - 1)\n                        queue.append(node - 1)\n            jump += 1\n        return -1\n                \n            \n        \n    def minJumpsBiBFS(self, arr: List[int]) -> int:\n        arrLen = len(arr)\n        if arrLen <= 1:\n            return 0\n        adjList = defaultdict(set)\n        for i in range(len(arr)):\n            adjList[arr[i]].add(i)\n        frontQueue = deque([0])\n        rearQueue = deque([len(arr)-1])\n        visited = set([0])\n        jump = 0\n        \n        while frontQueue or rearQueue:\n            if len(frontQueue) > len(rearQueue):\n                frontQueue, rearQueue = rearQueue, frontQueue\n            length = len(frontQueue)\n            \n            for _ in range(length):\n                node = frontQueue.popleft()\n                for nei in adjList[arr[node]]:\n                    if nei in rearQueue:\n                        return jump+1\n                    if nei in visited:\n                        continue\n                    visited.add(nei)\n                    frontQueue.append(nei)\n                    \n                if node + 1 < arrLen:\n                    if node + 1 in rearQueue:\n                        return jump+1\n                    if node + 1 not in visited:\n                        visited.add(node + 1)\n                        frontQueue.append(node + 1)\n                    \n                if node -1 >= 0:\n                    if node - 1 in rearQueue:\n                        return jump+1\n                    if node - 1 not in visited:\n                        visited.add(node - 1)\n                        frontQueue.append(node - 1)\n            jump += 1\n        return -1\n                    \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'minJumps'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 9760