Given a string S, consider all duplicated substrings: (contiguous) substrings of S that occur 2 or more times.  (The occurrences may overlap.)
Return any duplicated substring that has the longest possible length.  (If S does not have a duplicated substring, the answer is "".)
 
Example 1:
Input: "banana"
Output: "ana"

Example 2:
Input: "abcd"
Output: ""

 
Note:

2 <= S.length <= 10^5
S consists of lowercase English letters.

```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 searchLongestStringOfKLen(self, S, total_len, compare_len):\n        search_len_hash = 0\n        for i in range(compare_len):\n            search_len_hash = (search_len_hash * self.uniq + self.nums[i]) %  self.mod\n\n        tmp_hash = {}\n        tmp_hash[search_len_hash] = True\n        \n        remove_old_power = pow(self.uniq,  compare_len, self.mod)\n        for i in range(1, total_len-compare_len+1):\n            search_len_hash = (search_len_hash * self.uniq - (remove_old_power * self.nums[i-1]) + self.nums[i+compare_len-1] )% self.mod\n            if search_len_hash in tmp_hash:\n                return i\n            tmp_hash[search_len_hash] = True\n            \n        return -1\n        \n    \n    def longestDupSubstring(self, S: str) -> str:\n        ls = len(S)\n        end = ls\n        start = 1 \n        mid = 0\n        self.nums = []\n        for i in range(ls):\n            self.nums.append(ord(S[i]) - ord('a'))\n\n        self.uniq = 26\n        self.mod = 2**32\n        while start <= end:\n            mid = start + (end-start)//2\n            if self.searchLongestStringOfKLen(S, ls, mid) != -1:\n                start = mid +  1\n            else :\n                end = mid - 1\n        \n        ds_sp = self.searchLongestStringOfKLen(S, ls, start -1)\n        return S[ds_sp:ds_sp+start-1]"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'longestDupSubstring'
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: 6464