Given a non-empty array of integers, return the third maximum number in this array. If it does not exist, return the maximum number. The time complexity must be in O(n).

Example 1:

Input: [3, 2, 1]

Output: 1

Explanation: The third maximum is 1.



Example 2:

Input: [1, 2]

Output: 2

Explanation: The third maximum does not exist, so the maximum (2) is returned instead.



Example 3:

Input: [2, 2, 3, 1]

Output: 1

Explanation: Note that the third maximum here means the third maximum distinct number.
Both numbers with value 2 are both considered as second maximum.

```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 thirdMax(self, nums):\n         """\n         :type nums: List[int]\n         :rtype: int\n         """\n         \n         """\n         if len(nums) == 2 or len(nums) == 1:\n             return max(nums)\n         \n         maxes = [nums[0], nums[1], nums[2]]\n         maxes.sort() # ascending\n         \n         for i in range(3, len(nums)):\n             pos = self.findPos(nums[i], maxes)\n             if pos != None:\n                 maxes[pos] = nums[i]\n                 \n         if maxes[0] == maxes[1] or maxes[1] == maxes[2]:\n             return maxes[2]\n         else:\n             return maxes[0]\n                 \n     \n     def findPos(self, val, maxes):\n         maxPos = None\n         for ind, aMax in enumerate(maxes):\n             if val > aMax:\n                 maxPos = ind\n             \n         return maxPos\n         """\n         \n         maxes = []\n         \n         for i in nums:\n             if self.isNew(i, maxes):\n                 if len(maxes) < 3:\n                     maxes.append(i)\n                     maxes.sort() # ascending\n                 else:\n                     pos = self.findPos(i, maxes)\n                     if pos != None:\n                         maxes[pos] = i\n                         maxes.sort()\n         \n         if len(maxes) == 3:\n             return maxes[0]\n         else:\n             return maxes[-1]\n                 \n     \n     def isNew(self, val, maxes):\n         isNew = True\n         for i in maxes:\n             if val == i:\n                 isNew = False\n         return isNew\n     \n     def findPos(self, val, maxes):\n         for ind, aMax in enumerate(maxes):\n             if val > aMax:\n                 return ind\n             \n         return None'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'thirdMax'
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: 5656