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 = 'from collections import defaultdict, deque\nclass Solution:\n    def minJumps(self, arr: List[int]) -> int:\n        node_h = defaultdict(list)\n        graph = defaultdict(set)\n        \n        # Constructring graph based on these rules\n        # i + 1 where: i + 1 < arr.length.\n        # i - 1 where: i - 1 >= 0.\n        # j where: arr[i] == arr[j] and i != j.\n        for idx, val in enumerate(arr):\n            # if idx - 1 >= 0:\n            #     graph[idx].add(idx-1)\n            # if idx + 1 < len(arr):\n            #     graph[idx].add(idx+1)\n            # for node_idx in node_h[val]:\n            #     # graph[idx].add(node_idx)\n            #     graph[val].add(idx)\n            #     # graph[node_idx].add(idx)\n            node_h[val].append(idx)\n\n        q = deque()\n        visited = set()\n        q.append((0, 0))\n        visited.add(0)\n        \n        while (q):\n            node, level = q.popleft()\n            if node == len(arr) - 1:\n                return level\n            nbrs = node_h[arr[node]]\n            nbrs.append(node - 1)\n            nbrs.append(node + 1)\n            # for nbr in graph[node]:\n            for nbr in nbrs:\n                if nbr == len(arr) - 1:\n                    return level + 1\n                if nbr >= 0 and nbr < len(arr) and nbr not in visited:\n                    q.append((nbr, level + 1))\n                    visited.add(nbr)\n            node_h[arr[node]] = [] # [BUG] Clearing this is crucial otherwise we might revisit the node again, causing TLE \n            \n        return 0\n        \n# [NOTE] First attempt failed with large input of same numbers with just the last number different :)\n# https://leetcode.com/submissions/detail/397710738/testcase/\n\n# Clearing up the processed node list helped with TLE better explanation here\n# https://leetcode.com/problems/jump-game-iv/discuss/502699/JavaC++-BFS-Solution-Clean-code-O(N)/445620\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: 8018