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 = 'import numpy as np\nimport heapq\nfrom collections import deque\n\nclass Solution:\n    def minJumps(self, arr: List[int]) -> int:\n        self.arr = arr\n\n        # Hashing indices by values\n        self.val2indx = {}\n        for i,v in enumerate(arr):\n            if not v in self.val2indx:  self.val2indx[v] = []\n            self.val2indx[v].append(i)\n        # print(\\"val hash: \\", self.val2indx)\n\n        # Solutions memoization table\n        self.solutions = [np.inf for i in range(len(arr))]\n        self.solutions[-1] = 0\n        self.visited = [False for i in range(len(arr))]\n        \n        node_q = deque()\n        node_q.append((0, len(arr)-1))\n        \n        while node_q:\n            # dist, indx = heapq.heappop(node_q)\n            dist, indx = node_q.popleft()\n            self.visited[indx] = True\n            if dist > self.solutions[indx]: continue\n                \n            # Extracting edges\n            next_indx, prev_indx = min(indx+1, len(self.arr)-1), max(indx-1, 0)\n            indices = [i for i in self.val2indx[self.arr[indx]] if i != indx and i != prev_indx and i != next_indx and not self.visited[i]]    \n            indices = [prev_indx, next_indx] + indices\n            if not self.visited[prev_indx]: indices.append(prev_indx)\n            if not self.visited[next_indx]: indices.append(next_indx)\n            # exclude already visited nodes\n            # indices = [i for i in indices if not self.visited[i]]\n            # print(\\"node:\\", indx, \\"edges\\", indices)\n                            \n            # Update neighbour distances\n            for j in indices:\n                newdist = dist + 1\n                if np.isinf(self.solutions[j]) or newdist < self.solutions[j] and not self.visited[j]:\n                    self.solutions[j] = newdist\n                    # heapq.heappush(node_q, (newdist, j))\n                    node_q.append((newdist,j))\n                    self.visited[j] = True\n                    if j == 0: return newdist\n        \n        # print(\\"solutions:\\", self.solutions)\n        return self.solutions[0]\n            \n            \n        \n        \n\n\n# class Solution:\n#     def getSolution(self, indx):\n#         self.visitations[indx] = True\n        \n#         # Checking presence in hash table for the solution\n#         if self.solutions[indx] is not None:\n#             return self.solutions[indx]\n#         else:\n#             # min(indx-1, indx+1, indicees of val2indx[arr[indx]])\n#             indices = [i for i in self.val2indx[self.arr[indx]] if i != indx]\n#             indices = [min(indx+1, len(self.arr)-1), max(indx-1, 0)] + indices\n#             indices = np.unique(indices)         \n#             # exclude already visited states\n#             indices = [i for i in indices if not self.visitations[i] or self.solutions[i] is not None]\n#             print(indx, indices, self.solutions)\n            \n#             solutions = []\n#             for i in indices:\n#                 solutions.append(self.getSolution(i))\n                \n#                 # Just a shortcut to avoid unnecessary search\n#                 if solutions[-1] == 1: \n#                     self.solutions[indx] = 2\n#                     return self.solutions[indx]\n            \n#             if len(solutions) == 0: return np.inf\n            \n#             print(\\"---\\", indx ,\\":\\", solutions, np.min(solutions), indices)\n#             self.solutions[indx] = 1 + np.min(solutions)\n#             return self.solutions[indx]\n    \n#     def minJumps(self, arr: List[int]) -> int:\n#         self.arr = arr\n\n#         # Solutions memoization table\n#         self.solutions = [None for i in range(len(arr))]\n#         self.solutions[-1] = 0\n#         self.solutions[-2] = 1\n#         # self.visitations = [False for i in range(len(arr))]\n#         # self.visitations[-2] = True\n        \n#         # Hashing indices by values\n#         self.val2indx = {}\n#         for i,v in enumerate(arr):\n#             if not v in self.val2indx:  self.val2indx[v] = []\n#             self.val2indx[v].append(i)\n        \n#         print(\\"arr:\\", arr)\n#         print(\\"val hash:\\", self.val2indx)\n#         # return 0\n        \n#         # Get solutions starting from the end\n#         for i in range(len(arr)-2, -1, -1):\n#             print(\\"indx:\\", i)\n#             self.visitations = [False for j in range(len(arr))]\n#             self.visitations[-2] = True\n#             self.getSolution(indx=i)\n        \n        \n#         print(\\"solutions: \\", self.solutions)\n#         return self.solutions[0]\n        \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: 8934