Suppose an array sorted in ascending order is rotated at some pivot unknown to you beforehand.

(i.e., [0,0,1,2,2,5,6] might become [2,5,6,0,0,1,2]).

You are given a target value to search. If found in the array return true, otherwise return false.

Example 1:


Input: nums = [2,5,6,0,0,1,2], target = 0
Output: true


Example 2:


Input: nums = [2,5,6,0,0,1,2], target = 3
Output: false

Follow up:


       This is a follow up problem to Search in Rotated Sorted Array, where nums may contain duplicates.
       Would this affect the run-time complexity? How and why?

```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 recursive(self, nums, left, right , target):\n         print((left, right))\n         if left > right:\n             return False\n         if left == right:\n             return nums[left] == target\n         if left + 1 == right:\n             return nums[left] == target or nums[right] == target\n         mid = (left + right) // 2\n         if nums[mid] == target:\n             return True\n         if nums[mid] == nums[left] and nums[mid] == nums[right]:\n             return self.recursive(nums, mid, right, target) or self.recursive(nums, left, mid, target)\n         else:\n             if nums[mid] < target:\n                 if nums[right] >= target or (nums[left] <= nums[mid] and nums[mid] >= nums[right]):\n                     return self.recursive(nums, mid, right, target)\n                 else:\n                     return self.recursive(nums, left, mid, target)\n             else:\n                 if nums[left] <=target or (nums[right] >= nums[mid] and nums[mid] <= nums[left]):\n                     return self.recursive(nums, left, mid, target)\n                 else:\n                     return self.recursive(nums, mid, right, target)\n             \n             \n         \n     def search(self, nums, target):\n         """\n         :type nums: List[int]\n         :type target: int\n         :rtype: bool\n         """\n         return self.recursive(nums, 0, len(nums) - 1, target)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'search'
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: 6627