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 minJumps1(self, arr: List[int]) -> int:\n#         [100,-23,-23,404,100,23,23,23,3,404]\n        \n#         [0,   1,   2,  2,  1, 2, 3, 3, 4,  3]\n        \n        if not arr:\n            return 0\n        \n        dp = [float('inf')] * len(arr)\n        dp[0] = 0\n        minIdx = { arr[0]: (0, 0) }\n        for i in range(1, len(arr)):\n            x = arr[i]\n            stepRight = dp[i-1] + 1\n            jumpStep = minIdx[x][1] + 1 if x in minIdx else float('inf')\n            \n            dp[i] = min(stepRight, jumpStep)\n            \n            if x in minIdx:\n                if dp[i] < minIdx[x][1]:\n                    minIdx[x] = (i, dp[i])\n            else:\n                minIdx[x] = (i, dp[i])\n            \n            j = i - 1\n            while j >= 0 and dp[j] > dp[j + 1] + 1:\n                dp[j] = dp[j+1] + 1\n                y = arr[j]\n                if dp[j] < minIdx[y][1]:\n                    minIdx[y] = (j, dp[j])\n                j -= 1\n        \n        return dp[-1]\n            \n    def minJumps(self, arr: List[int]) -> int:\n        n = len(arr)\n        if n <= 1:\n            return 0\n\n        graph = {}\n        for i in range(n):\n            if arr[i] in graph:\n                graph[arr[i]].append(i)\n            else:\n                graph[arr[i]] = [i]\n\n        curs = [0]  # store current layers\n        visited = {0}\n        step = 0\n\n        # when current layer exists\n        while curs:\n            nex = []\n\n            # iterate the layer\n            for node in curs:\n                # check if reached end\n                if node == n-1:\n                    return step\n\n                # check same value\n                for child in graph[arr[node]]:\n                    if child not in visited:\n                        visited.add(child)\n                        nex.append(child)\n\n                # clear the list to prevent redundant search\n                graph[arr[node]].clear()\n\n                # check neighbors\n                for child in [node-1, node+1]:\n                    if 0 <= child < len(arr) and child not in visited:\n                        visited.add(child)\n                        nex.append(child)\n\n            curs = nex\n            step += 1\n\n        return -1"
_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: 7124